Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.788.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.476452\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.64018 | 0.997052 | 0.498526 | − | 0.866875i | \(-0.333875\pi\) | ||||
0.498526 | + | 0.866875i | \(0.333875\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −0.188384 | −0.00588699 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 50.7616 | 0.575648 | ||||||||
\(7\) | −145.021 | −1.11863 | −0.559315 | − | 0.828955i | \(-0.688936\pi\) | ||||
−0.559315 | + | 0.828955i | \(0.688936\pi\) | |||||||
\(8\) | −181.548 | −1.00292 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −1.69545 | −0.00339886 | ||||||||
\(13\) | 69.9067 | 0.114726 | 0.0573628 | − | 0.998353i | \(-0.481731\pi\) | ||||
0.0573628 | + | 0.998353i | \(0.481731\pi\) | |||||||
\(14\) | −817.946 | −1.11533 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1017.94 | −0.994078 | ||||||||
\(17\) | 500.495 | 0.420027 | 0.210014 | − | 0.977698i | \(-0.432649\pi\) | ||||
0.210014 | + | 0.977698i | \(0.432649\pi\) | |||||||
\(18\) | 456.854 | 0.332351 | ||||||||
\(19\) | −670.685 | −0.426221 | −0.213110 | − | 0.977028i | \(-0.568359\pi\) | ||||
−0.213110 | + | 0.977028i | \(0.568359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1305.19 | −0.645842 | ||||||||
\(22\) | −682.462 | −0.300623 | ||||||||
\(23\) | −791.025 | −0.311796 | −0.155898 | − | 0.987773i | \(-0.549827\pi\) | ||||
−0.155898 | + | 0.987773i | \(0.549827\pi\) | |||||||
\(24\) | −1633.93 | −0.579037 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 394.287 | 0.114388 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 27.3196 | 0.00658537 | ||||||||
\(29\) | 1545.91 | 0.341342 | 0.170671 | − | 0.985328i | \(-0.445406\pi\) | ||||
0.170671 | + | 0.985328i | \(0.445406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2703.09 | 0.505191 | 0.252596 | − | 0.967572i | \(-0.418716\pi\) | ||||
0.252596 | + | 0.967572i | \(0.418716\pi\) | |||||||
\(32\) | 68.2013 | 0.0117738 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 2822.88 | 0.418789 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15.2591 | −0.00196233 | ||||||||
\(37\) | 2667.13 | 0.320287 | 0.160144 | − | 0.987094i | \(-0.448804\pi\) | ||||
0.160144 | + | 0.987094i | \(0.448804\pi\) | |||||||
\(38\) | −3782.78 | −0.424964 | ||||||||
\(39\) | 629.161 | 0.0662369 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9622.09 | 0.893942 | 0.446971 | − | 0.894548i | \(-0.352503\pi\) | ||||
0.446971 | + | 0.894548i | \(0.352503\pi\) | |||||||
\(42\) | −7361.51 | −0.643938 | ||||||||
\(43\) | 6681.57 | 0.551070 | 0.275535 | − | 0.961291i | \(-0.411145\pi\) | ||||
0.275535 | + | 0.961291i | \(0.411145\pi\) | |||||||
\(44\) | 22.7944 | 0.00177499 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4461.52 | −0.310877 | ||||||||
\(47\) | 1167.06 | 0.0770632 | 0.0385316 | − | 0.999257i | \(-0.487732\pi\) | ||||
0.0385316 | + | 0.999257i | \(0.487732\pi\) | |||||||
\(48\) | −9161.43 | −0.573931 | ||||||||
\(49\) | 4224.17 | 0.251334 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4504.46 | 0.242503 | ||||||||
\(52\) | −13.1693 | −0.000675389 0 | ||||||||
\(53\) | −28872.9 | −1.41189 | −0.705944 | − | 0.708268i | \(-0.749477\pi\) | ||||
−0.705944 | + | 0.708268i | \(0.749477\pi\) | |||||||
\(54\) | 4111.69 | 0.191883 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 26328.4 | 1.12190 | ||||||||
\(57\) | −6036.16 | −0.246079 | ||||||||
\(58\) | 8719.22 | 0.340336 | ||||||||
\(59\) | 23599.3 | 0.882610 | 0.441305 | − | 0.897357i | \(-0.354516\pi\) | ||||
0.441305 | + | 0.897357i | \(0.354516\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17601.3 | 0.605648 | 0.302824 | − | 0.953046i | \(-0.402070\pi\) | ||||
0.302824 | + | 0.953046i | \(0.402070\pi\) | |||||||
\(62\) | 15245.9 | 0.503702 | ||||||||
\(63\) | −11746.7 | −0.372877 | ||||||||
\(64\) | 32958.6 | 1.00582 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6142.15 | −0.173565 | ||||||||
\(67\) | −16501.5 | −0.449092 | −0.224546 | − | 0.974463i | \(-0.572090\pi\) | ||||
−0.224546 | + | 0.974463i | \(0.572090\pi\) | |||||||
\(68\) | −94.2851 | −0.00247270 | ||||||||
\(69\) | −7119.22 | −0.180016 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 72059.4 | 1.69646 | 0.848232 | − | 0.529625i | \(-0.177667\pi\) | ||||
0.848232 | + | 0.529625i | \(0.177667\pi\) | |||||||
\(72\) | −14705.4 | −0.334307 | ||||||||
\(73\) | 45480.8 | 0.998898 | 0.499449 | − | 0.866343i | \(-0.333536\pi\) | ||||
0.499449 | + | 0.866343i | \(0.333536\pi\) | |||||||
\(74\) | 15043.1 | 0.319343 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 126.346 | 0.00250916 | ||||||||
\(77\) | 17547.6 | 0.337280 | ||||||||
\(78\) | 3548.58 | 0.0660417 | ||||||||
\(79\) | −21688.7 | −0.390990 | −0.195495 | − | 0.980705i | \(-0.562631\pi\) | ||||
−0.195495 | + | 0.980705i | \(0.562631\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 54270.3 | 0.891307 | ||||||||
\(83\) | −6934.34 | −0.110487 | −0.0552434 | − | 0.998473i | \(-0.517593\pi\) | ||||
−0.0552434 | + | 0.998473i | \(0.517593\pi\) | |||||||
\(84\) | 245.877 | 0.00380206 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 37685.2 | 0.549446 | ||||||||
\(87\) | 13913.2 | 0.197074 | ||||||||
\(88\) | 21967.3 | 0.302392 | ||||||||
\(89\) | 42779.8 | 0.572484 | 0.286242 | − | 0.958157i | \(-0.407594\pi\) | ||||
0.286242 | + | 0.958157i | \(0.407594\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10138.0 | −0.128336 | ||||||||
\(92\) | 149.016 | 0.00183554 | ||||||||
\(93\) | 24327.8 | 0.291672 | ||||||||
\(94\) | 6582.41 | 0.0768361 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 613.812 | 0.00679762 | ||||||||
\(97\) | 20992.6 | 0.226535 | 0.113268 | − | 0.993565i | \(-0.463868\pi\) | ||||
0.113268 | + | 0.993565i | \(0.463868\pi\) | |||||||
\(98\) | 23825.1 | 0.250593 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 189654. | 1.84995 | 0.924973 | − | 0.380033i | \(-0.124087\pi\) | ||||
0.924973 | + | 0.380033i | \(0.124087\pi\) | |||||||
\(102\) | 25405.9 | 0.241788 | ||||||||
\(103\) | 160899. | 1.49438 | 0.747190 | − | 0.664611i | \(-0.231403\pi\) | ||||
0.747190 | + | 0.664611i | \(0.231403\pi\) | |||||||
\(104\) | −12691.4 | −0.115061 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −162848. | −1.40773 | ||||||||
\(107\) | −113244. | −0.956216 | −0.478108 | − | 0.878301i | \(-0.658677\pi\) | ||||
−0.478108 | + | 0.878301i | \(0.658677\pi\) | |||||||
\(108\) | −137.332 | −0.00113295 | ||||||||
\(109\) | −1768.32 | −0.0142559 | −0.00712797 | − | 0.999975i | \(-0.502269\pi\) | ||||
−0.00712797 | + | 0.999975i | \(0.502269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24004.1 | 0.184918 | ||||||||
\(112\) | 147622. | 1.11201 | ||||||||
\(113\) | 77273.2 | 0.569289 | 0.284645 | − | 0.958633i | \(-0.408124\pi\) | ||||
0.284645 | + | 0.958633i | \(0.408124\pi\) | |||||||
\(114\) | −34045.0 | −0.245353 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −291.224 | −0.00200948 | ||||||||
\(117\) | 5662.45 | 0.0382419 | ||||||||
\(118\) | 133104. | 0.880008 | ||||||||
\(119\) | −72582.5 | −0.469855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 99274.6 | 0.603863 | ||||||||
\(123\) | 86598.8 | 0.516118 | ||||||||
\(124\) | −509.218 | −0.00297406 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −66253.6 | −0.371778 | ||||||||
\(127\) | −104707. | −0.576058 | −0.288029 | − | 0.957622i | \(-0.593000\pi\) | ||||
−0.288029 | + | 0.957622i | \(0.593000\pi\) | |||||||
\(128\) | 183710. | 0.991079 | ||||||||
\(129\) | 60134.1 | 0.318161 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 101248. | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(132\) | 205.150 | 0.00102479 | ||||||||
\(133\) | 97263.6 | 0.476783 | ||||||||
\(134\) | −93071.2 | −0.447768 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −90864.0 | −0.421255 | ||||||||
\(137\) | −128311. | −0.584068 | −0.292034 | − | 0.956408i | \(-0.594332\pi\) | ||||
−0.292034 | + | 0.956408i | \(0.594332\pi\) | |||||||
\(138\) | −40153.7 | −0.179485 | ||||||||
\(139\) | 161754. | 0.710100 | 0.355050 | − | 0.934847i | \(-0.384464\pi\) | ||||
0.355050 | + | 0.934847i | \(0.384464\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10503.5 | 0.0444925 | ||||||||
\(142\) | 406428. | 1.69146 | ||||||||
\(143\) | −8458.72 | −0.0345911 | ||||||||
\(144\) | −82452.8 | −0.331359 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 256520. | 0.995954 | ||||||||
\(147\) | 38017.5 | 0.145108 | ||||||||
\(148\) | −502.443 | −0.00188553 | ||||||||
\(149\) | −404421. | −1.49234 | −0.746170 | − | 0.665755i | \(-0.768110\pi\) | ||||
−0.746170 | + | 0.665755i | \(0.768110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 416180. | 1.48538 | 0.742692 | − | 0.669633i | \(-0.233549\pi\) | ||||
0.742692 | + | 0.669633i | \(0.233549\pi\) | |||||||
\(152\) | 121762. | 0.427466 | ||||||||
\(153\) | 40540.1 | 0.140009 | ||||||||
\(154\) | 98971.5 | 0.336286 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −118.524 | −0.000389936 0 | ||||||||
\(157\) | −332834. | −1.07765 | −0.538827 | − | 0.842417i | \(-0.681132\pi\) | ||||
−0.538827 | + | 0.842417i | \(0.681132\pi\) | |||||||
\(158\) | −122328. | −0.389837 | ||||||||
\(159\) | −259856. | −0.815154 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114715. | 0.348785 | ||||||||
\(162\) | 37005.2 | 0.110784 | ||||||||
\(163\) | 14764.9 | 0.0435272 | 0.0217636 | − | 0.999763i | \(-0.493072\pi\) | ||||
0.0217636 | + | 0.999763i | \(0.493072\pi\) | |||||||
\(164\) | −1812.64 | −0.00526263 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −39110.9 | −0.110161 | ||||||||
\(167\) | −169960. | −0.471579 | −0.235790 | − | 0.971804i | \(-0.575768\pi\) | ||||
−0.235790 | + | 0.971804i | \(0.575768\pi\) | |||||||
\(168\) | 236955. | 0.647729 | ||||||||
\(169\) | −366406. | −0.986838 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −54325.5 | −0.142074 | ||||||||
\(172\) | −1258.70 | −0.00324415 | ||||||||
\(173\) | −725869. | −1.84392 | −0.921962 | − | 0.387281i | \(-0.873414\pi\) | ||||
−0.921962 | + | 0.387281i | \(0.873414\pi\) | |||||||
\(174\) | 78472.9 | 0.196493 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 123170. | 0.299726 | ||||||||
\(177\) | 212394. | 0.509575 | ||||||||
\(178\) | 241286. | 0.570797 | ||||||||
\(179\) | 69311.4 | 0.161686 | 0.0808429 | − | 0.996727i | \(-0.474239\pi\) | ||||
0.0808429 | + | 0.996727i | \(0.474239\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 790396. | 1.79328 | 0.896640 | − | 0.442761i | \(-0.146001\pi\) | ||||
0.896640 | + | 0.442761i | \(0.146001\pi\) | |||||||
\(182\) | −57179.9 | −0.127957 | ||||||||
\(183\) | 158412. | 0.349671 | ||||||||
\(184\) | 143609. | 0.312707 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 137213. | 0.290813 | ||||||||
\(187\) | −60559.9 | −0.126643 | ||||||||
\(188\) | −219.854 | −0.000453670 0 | ||||||||
\(189\) | −105721. | −0.215281 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 418979. | 0.831015 | 0.415507 | − | 0.909590i | \(-0.363604\pi\) | ||||
0.415507 | + | 0.909590i | \(0.363604\pi\) | |||||||
\(192\) | 296628. | 0.580709 | ||||||||
\(193\) | −265524. | −0.513110 | −0.256555 | − | 0.966530i | \(-0.582587\pi\) | ||||
−0.256555 | + | 0.966530i | \(0.582587\pi\) | |||||||
\(194\) | 118402. | 0.225868 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −795.765 | −0.00147960 | ||||||||
\(197\) | 87754.1 | 0.161102 | 0.0805512 | − | 0.996750i | \(-0.474332\pi\) | ||||
0.0805512 | + | 0.996750i | \(0.474332\pi\) | |||||||
\(198\) | −55279.4 | −0.100208 | ||||||||
\(199\) | 380988. | 0.681992 | 0.340996 | − | 0.940065i | \(-0.389236\pi\) | ||||
0.340996 | + | 0.940065i | \(0.389236\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −148513. | −0.259284 | ||||||||
\(202\) | 1.06968e6 | 1.84449 | ||||||||
\(203\) | −224190. | −0.381835 | ||||||||
\(204\) | −848.566 | −0.00142761 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 907501. | 1.48997 | ||||||||
\(207\) | −64073.0 | −0.103932 | ||||||||
\(208\) | −71160.6 | −0.114046 | ||||||||
\(209\) | 81152.9 | 0.128510 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 624404. | 0.965516 | 0.482758 | − | 0.875754i | \(-0.339635\pi\) | ||||
0.482758 | + | 0.875754i | \(0.339635\pi\) | |||||||
\(212\) | 5439.18 | 0.00831177 | ||||||||
\(213\) | 648534. | 0.979454 | ||||||||
\(214\) | −638717. | −0.953398 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −132349. | −0.193012 | ||||||||
\(217\) | −392005. | −0.565123 | ||||||||
\(218\) | −9973.67 | −0.0142139 | ||||||||
\(219\) | 409328. | 0.576714 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34988.0 | 0.0481879 | ||||||||
\(222\) | 135388. | 0.184373 | ||||||||
\(223\) | 658298. | 0.886462 | 0.443231 | − | 0.896407i | \(-0.353832\pi\) | ||||
0.443231 | + | 0.896407i | \(0.353832\pi\) | |||||||
\(224\) | −9890.64 | −0.0131706 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 435835. | 0.567611 | ||||||||
\(227\) | −219954. | −0.283313 | −0.141657 | − | 0.989916i | \(-0.545243\pi\) | ||||
−0.141657 | + | 0.989916i | \(0.545243\pi\) | |||||||
\(228\) | 1137.11 | 0.00144866 | ||||||||
\(229\) | −313324. | −0.394825 | −0.197412 | − | 0.980321i | \(-0.563254\pi\) | ||||
−0.197412 | + | 0.980321i | \(0.563254\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 157928. | 0.194729 | ||||||||
\(232\) | −280657. | −0.342339 | ||||||||
\(233\) | 1.01608e6 | 1.22614 | 0.613069 | − | 0.790030i | \(-0.289935\pi\) | ||||
0.613069 | + | 0.790030i | \(0.289935\pi\) | |||||||
\(234\) | 31937.2 | 0.0381292 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4445.72 | −0.00519592 | ||||||||
\(237\) | −195198. | −0.225738 | ||||||||
\(238\) | −409378. | −0.468470 | ||||||||
\(239\) | 762420. | 0.863375 | 0.431688 | − | 0.902023i | \(-0.357918\pi\) | ||||
0.431688 | + | 0.902023i | \(0.357918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22909.2 | −0.0254078 | −0.0127039 | − | 0.999919i | \(-0.504044\pi\) | ||||
−0.0127039 | + | 0.999919i | \(0.504044\pi\) | |||||||
\(242\) | 82577.9 | 0.0906411 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −3315.80 | −0.00356545 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 488433. | 0.514596 | ||||||||
\(247\) | −46885.4 | −0.0488985 | ||||||||
\(248\) | −490741. | −0.506668 | ||||||||
\(249\) | −62409.1 | −0.0637895 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −691159. | −0.692458 | −0.346229 | − | 0.938150i | \(-0.612538\pi\) | ||||
−0.346229 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(252\) | 2212.89 | 0.00219512 | ||||||||
\(253\) | 95714.0 | 0.0940100 | ||||||||
\(254\) | −590566. | −0.574360 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −18518.2 | −0.0176604 | ||||||||
\(257\) | 1.34845e6 | 1.27351 | 0.636753 | − | 0.771068i | \(-0.280277\pi\) | ||||
0.636753 | + | 0.771068i | \(0.280277\pi\) | |||||||
\(258\) | 339167. | 0.317223 | ||||||||
\(259\) | −386790. | −0.358283 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 125219. | 0.113781 | ||||||||
\(262\) | 571057. | 0.513957 | ||||||||
\(263\) | −1.34541e6 | −1.19940 | −0.599700 | − | 0.800225i | \(-0.704713\pi\) | ||||
−0.599700 | + | 0.800225i | \(0.704713\pi\) | |||||||
\(264\) | 197706. | 0.174586 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 548584. | 0.475378 | ||||||||
\(267\) | 385018. | 0.330524 | ||||||||
\(268\) | 3108.61 | 0.00264380 | ||||||||
\(269\) | −2.03803e6 | −1.71724 | −0.858620 | − | 0.512613i | \(-0.828678\pi\) | ||||
−0.858620 | + | 0.512613i | \(0.828678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −218053. | −0.180360 | −0.0901799 | − | 0.995925i | \(-0.528744\pi\) | ||||
−0.0901799 | + | 0.995925i | \(0.528744\pi\) | |||||||
\(272\) | −509472. | −0.417540 | ||||||||
\(273\) | −91241.7 | −0.0740946 | ||||||||
\(274\) | −723698. | −0.582346 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1341.15 | 0.00105975 | ||||||||
\(277\) | 410179. | 0.321199 | 0.160599 | − | 0.987020i | \(-0.448657\pi\) | ||||
0.160599 | + | 0.987020i | \(0.448657\pi\) | |||||||
\(278\) | 912324. | 0.708006 | ||||||||
\(279\) | 218950. | 0.168397 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −406589. | −0.307178 | −0.153589 | − | 0.988135i | \(-0.549083\pi\) | ||||
−0.153589 | + | 0.988135i | \(0.549083\pi\) | |||||||
\(282\) | 59241.7 | 0.0443613 | ||||||||
\(283\) | −1.26416e6 | −0.938291 | −0.469146 | − | 0.883121i | \(-0.655438\pi\) | ||||
−0.469146 | + | 0.883121i | \(0.655438\pi\) | |||||||
\(284\) | −13574.8 | −0.00998707 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −47708.7 | −0.0344891 | ||||||||
\(287\) | −1.39541e6 | −0.999991 | ||||||||
\(288\) | 5524.30 | 0.00392461 | ||||||||
\(289\) | −1.16936e6 | −0.823577 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 188933. | 0.130790 | ||||||||
\(292\) | −8567.85 | −0.00588050 | ||||||||
\(293\) | −351099. | −0.238924 | −0.119462 | − | 0.992839i | \(-0.538117\pi\) | ||||
−0.119462 | + | 0.992839i | \(0.538117\pi\) | |||||||
\(294\) | 214426. | 0.144680 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −484212. | −0.321223 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −2.28101e6 | −1.48794 | ||||||||
\(299\) | −55298.0 | −0.0357710 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −968969. | −0.616444 | ||||||||
\(302\) | 2.34733e6 | 1.48101 | ||||||||
\(303\) | 1.70689e6 | 1.06807 | ||||||||
\(304\) | 682714. | 0.423697 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 228654. | 0.139596 | ||||||||
\(307\) | 1.46228e6 | 0.885493 | 0.442747 | − | 0.896647i | \(-0.354004\pi\) | ||||
0.442747 | + | 0.896647i | \(0.354004\pi\) | |||||||
\(308\) | −3305.68 | −0.00198556 | ||||||||
\(309\) | 1.44809e6 | 0.862781 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.20292e6 | 1.29151 | 0.645755 | − | 0.763545i | \(-0.276543\pi\) | ||||
0.645755 | + | 0.763545i | \(0.276543\pi\) | |||||||
\(312\) | −114223. | −0.0664304 | ||||||||
\(313\) | −647848. | −0.373777 | −0.186888 | − | 0.982381i | \(-0.559840\pi\) | ||||
−0.186888 | + | 0.982381i | \(0.559840\pi\) | |||||||
\(314\) | −1.87725e6 | −1.07448 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4085.80 | 0.00230175 | ||||||||
\(317\) | 1.62933e6 | 0.910670 | 0.455335 | − | 0.890320i | \(-0.349519\pi\) | ||||
0.455335 | + | 0.890320i | \(0.349519\pi\) | |||||||
\(318\) | −1.46563e6 | −0.812751 | ||||||||
\(319\) | −187055. | −0.102918 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.01920e6 | −0.552072 | ||||||||
\(322\) | 647016. | 0.347756 | ||||||||
\(323\) | −335675. | −0.179024 | ||||||||
\(324\) | −1235.99 | −0.000654110 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 83276.6 | 0.0433989 | ||||||||
\(327\) | −15914.9 | −0.00823067 | ||||||||
\(328\) | −1.74687e6 | −0.896554 | ||||||||
\(329\) | −169248. | −0.0862053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 799339. | 0.401016 | 0.200508 | − | 0.979692i | \(-0.435741\pi\) | ||||
0.200508 | + | 0.979692i | \(0.435741\pi\) | |||||||
\(332\) | 1306.32 | 0.000650434 0 | ||||||||
\(333\) | 216037. | 0.106762 | ||||||||
\(334\) | −958603. | −0.470189 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.32860e6 | 0.642017 | ||||||||
\(337\) | 3.76736e6 | 1.80702 | 0.903508 | − | 0.428570i | \(-0.140983\pi\) | ||||
0.903508 | + | 0.428570i | \(0.140983\pi\) | |||||||
\(338\) | −2.06660e6 | −0.983929 | ||||||||
\(339\) | 695459. | 0.328679 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −327074. | −0.152321 | ||||||||
\(342\) | −306405. | −0.141655 | ||||||||
\(343\) | 1.82478e6 | 0.837481 | ||||||||
\(344\) | −1.21303e6 | −0.552681 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.09403e6 | −1.83849 | ||||||||
\(347\) | −923519. | −0.411739 | −0.205869 | − | 0.978579i | \(-0.566002\pi\) | ||||
−0.205869 | + | 0.978579i | \(0.566002\pi\) | |||||||
\(348\) | −2621.02 | −0.00116017 | ||||||||
\(349\) | 2.61022e6 | 1.14713 | 0.573567 | − | 0.819159i | \(-0.305559\pi\) | ||||
0.573567 | + | 0.819159i | \(0.305559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 50962.0 | 0.0220790 | ||||||||
\(352\) | −8252.36 | −0.00354994 | ||||||||
\(353\) | −1.25644e6 | −0.536669 | −0.268335 | − | 0.963326i | \(-0.586473\pi\) | ||||
−0.268335 | + | 0.963326i | \(0.586473\pi\) | |||||||
\(354\) | 1.19794e6 | 0.508073 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8059.01 | −0.00337021 | ||||||||
\(357\) | −653242. | −0.271271 | ||||||||
\(358\) | 390928. | 0.161209 | ||||||||
\(359\) | −2.38200e6 | −0.975451 | −0.487726 | − | 0.872997i | \(-0.662173\pi\) | ||||
−0.487726 | + | 0.872997i | \(0.662173\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.02628e6 | −0.818336 | ||||||||
\(362\) | 4.45797e6 | 1.78799 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 1909.83 | 0.000755511 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 893471. | 0.348641 | ||||||||
\(367\) | 3.46320e6 | 1.34219 | 0.671093 | − | 0.741373i | \(-0.265825\pi\) | ||||
0.671093 | + | 0.741373i | \(0.265825\pi\) | |||||||
\(368\) | 805213. | 0.309950 | ||||||||
\(369\) | 779389. | 0.297981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.18718e6 | 1.57938 | ||||||||
\(372\) | −4582.96 | −0.00171707 | ||||||||
\(373\) | −811517. | −0.302013 | −0.151006 | − | 0.988533i | \(-0.548251\pi\) | ||||
−0.151006 | + | 0.988533i | \(0.548251\pi\) | |||||||
\(374\) | −341569. | −0.126270 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −211877. | −0.0772884 | ||||||||
\(377\) | 108070. | 0.0391607 | ||||||||
\(378\) | −596283. | −0.214646 | ||||||||
\(379\) | −522481. | −0.186841 | −0.0934206 | − | 0.995627i | \(-0.529780\pi\) | ||||
−0.0934206 | + | 0.995627i | \(0.529780\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −942362. | −0.332587 | ||||||||
\(382\) | 2.36312e6 | 0.828565 | ||||||||
\(383\) | 2.24960e6 | 0.783625 | 0.391813 | − | 0.920045i | \(-0.371848\pi\) | ||||
0.391813 | + | 0.920045i | \(0.371848\pi\) | |||||||
\(384\) | 1.65339e6 | 0.572200 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.49760e6 | −0.511598 | ||||||||
\(387\) | 541207. | 0.183690 | ||||||||
\(388\) | −3954.65 | −0.00133361 | ||||||||
\(389\) | −2.42055e6 | −0.811035 | −0.405518 | − | 0.914087i | \(-0.632909\pi\) | ||||
−0.405518 | + | 0.914087i | \(0.632909\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −395904. | −0.130963 | ||||||||
\(392\) | −766891. | −0.252068 | ||||||||
\(393\) | 911233. | 0.297610 | ||||||||
\(394\) | 494949. | 0.160627 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1846.35 | 0.000591665 0 | ||||||||
\(397\) | −1.96075e6 | −0.624375 | −0.312187 | − | 0.950021i | \(-0.601062\pi\) | ||||
−0.312187 | + | 0.950021i | \(0.601062\pi\) | |||||||
\(398\) | 2.14884e6 | 0.679981 | ||||||||
\(399\) | 875372. | 0.275271 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.86313e6 | −1.19972 | −0.599858 | − | 0.800107i | \(-0.704776\pi\) | ||||
−0.599858 | + | 0.800107i | \(0.704776\pi\) | |||||||
\(402\) | −837641. | −0.258519 | ||||||||
\(403\) | 188964. | 0.0579584 | ||||||||
\(404\) | −35727.8 | −0.0108906 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.26447e6 | −0.380710 | ||||||||
\(407\) | −322722. | −0.0965702 | ||||||||
\(408\) | −817776. | −0.243212 | ||||||||
\(409\) | 1.75292e6 | 0.518149 | 0.259075 | − | 0.965857i | \(-0.416582\pi\) | ||||
0.259075 | + | 0.965857i | \(0.416582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.15480e6 | −0.337212 | ||||||||
\(412\) | −30310.8 | −0.00879740 | ||||||||
\(413\) | −3.42240e6 | −0.987314 | ||||||||
\(414\) | −361383. | −0.103626 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4767.73 | 0.00135076 | ||||||||
\(417\) | 1.45579e6 | 0.409976 | ||||||||
\(418\) | 457717. | 0.128132 | ||||||||
\(419\) | −4.28414e6 | −1.19214 | −0.596071 | − | 0.802932i | \(-0.703272\pi\) | ||||
−0.596071 | + | 0.802932i | \(0.703272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.74050e6 | 1.57850 | 0.789250 | − | 0.614072i | \(-0.210470\pi\) | ||||
0.789250 | + | 0.614072i | \(0.210470\pi\) | |||||||
\(422\) | 3.52175e6 | 0.962670 | ||||||||
\(423\) | 94531.6 | 0.0256877 | ||||||||
\(424\) | 5.24182e6 | 1.41601 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.65785e6 | 0.976567 | ||||||||
\(427\) | −2.55257e6 | −0.677497 | ||||||||
\(428\) | 21333.3 | 0.00562924 | ||||||||
\(429\) | −76128.4 | −0.0199712 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.29228e6 | 1.37230 | 0.686150 | − | 0.727460i | \(-0.259299\pi\) | ||||
0.686150 | + | 0.727460i | \(0.259299\pi\) | |||||||
\(432\) | −742076. | −0.191310 | ||||||||
\(433\) | 2.37840e6 | 0.609628 | 0.304814 | − | 0.952412i | \(-0.401406\pi\) | ||||
0.304814 | + | 0.952412i | \(0.401406\pi\) | |||||||
\(434\) | −2.21098e6 | −0.563457 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 333.123 | 8.39245e−5 0 | ||||||||
\(437\) | 530528. | 0.132894 | ||||||||
\(438\) | 2.30868e6 | 0.575014 | ||||||||
\(439\) | 6.44393e6 | 1.59584 | 0.797921 | − | 0.602762i | \(-0.205933\pi\) | ||||
0.797921 | + | 0.602762i | \(0.205933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 342158. | 0.0837780 | ||||||||
\(442\) | 197339. | 0.0480459 | ||||||||
\(443\) | −2501.14 | −0.000605520 0 | −0.000302760 | − | 1.00000i | \(-0.500096\pi\) | ||||
−0.000302760 | 1.00000i | \(0.500096\pi\) | ||||||||
\(444\) | −4521.99 | −0.00108861 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.71292e6 | 0.883849 | ||||||||
\(447\) | −3.63979e6 | −0.861603 | ||||||||
\(448\) | −4.77970e6 | −1.12514 | ||||||||
\(449\) | −5.04731e6 | −1.18153 | −0.590764 | − | 0.806844i | \(-0.701174\pi\) | ||||
−0.590764 | + | 0.806844i | \(0.701174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.16427e6 | −0.269534 | ||||||||
\(452\) | −14557.0 | −0.00335140 | ||||||||
\(453\) | 3.74562e6 | 0.857587 | ||||||||
\(454\) | −1.24058e6 | −0.282478 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.09585e6 | 0.246798 | ||||||||
\(457\) | −4.62692e6 | −1.03634 | −0.518169 | − | 0.855278i | \(-0.673386\pi\) | ||||
−0.518169 | + | 0.855278i | \(0.673386\pi\) | |||||||
\(458\) | −1.76720e6 | −0.393661 | ||||||||
\(459\) | 364861. | 0.0808343 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.43209e6 | 0.313846 | 0.156923 | − | 0.987611i | \(-0.449842\pi\) | ||||
0.156923 | + | 0.987611i | \(0.449842\pi\) | |||||||
\(462\) | 890743. | 0.194155 | ||||||||
\(463\) | −1.58115e6 | −0.342785 | −0.171393 | − | 0.985203i | \(-0.554827\pi\) | ||||
−0.171393 | + | 0.985203i | \(0.554827\pi\) | |||||||
\(464\) | −1.57364e6 | −0.339321 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.73089e6 | 1.22252 | ||||||||
\(467\) | −8724.92 | −0.00185127 | −0.000925634 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000925634 | 1.00000i | \(0.500295\pi\) | ||||||||
\(468\) | −1066.71 | −0.000225130 0 | ||||||||
\(469\) | 2.39306e6 | 0.502368 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.99551e6 | −0.622183 | ||||||||
\(472\) | −4.28441e6 | −0.885189 | ||||||||
\(473\) | −808470. | −0.166154 | ||||||||
\(474\) | −1.10095e6 | −0.225073 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13673.4 | 0.00276603 | ||||||||
\(477\) | −2.33870e6 | −0.470629 | ||||||||
\(478\) | 4.30018e6 | 0.860830 | ||||||||
\(479\) | 8.15482e6 | 1.62396 | 0.811981 | − | 0.583684i | \(-0.198389\pi\) | ||||
0.811981 | + | 0.583684i | \(0.198389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 186450. | 0.0367452 | ||||||||
\(482\) | −129212. | −0.0253329 | ||||||||
\(483\) | 1.03244e6 | 0.201371 | ||||||||
\(484\) | −2758.13 | −0.000535181 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 333047. | 0.0639609 | ||||||||
\(487\) | −9.00123e6 | −1.71981 | −0.859903 | − | 0.510457i | \(-0.829476\pi\) | ||||
−0.859903 | + | 0.510457i | \(0.829476\pi\) | |||||||
\(488\) | −3.19549e6 | −0.607418 | ||||||||
\(489\) | 132884. | 0.0251305 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.03644e6 | 1.13000 | 0.564999 | − | 0.825092i | \(-0.308877\pi\) | ||||
0.564999 | + | 0.825092i | \(0.308877\pi\) | |||||||
\(492\) | −16313.8 | −0.00303838 | ||||||||
\(493\) | 773721. | 0.143373 | ||||||||
\(494\) | −264442. | −0.0487543 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.75157e6 | −0.502200 | ||||||||
\(497\) | −1.04501e7 | −1.89772 | ||||||||
\(498\) | −351998. | −0.0636015 | ||||||||
\(499\) | 233452. | 0.0419707 | 0.0209853 | − | 0.999780i | \(-0.493320\pi\) | ||||
0.0209853 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.52964e6 | −0.272267 | ||||||||
\(502\) | −3.89826e6 | −0.690417 | ||||||||
\(503\) | 7.79728e6 | 1.37412 | 0.687058 | − | 0.726603i | \(-0.258902\pi\) | ||||
0.687058 | + | 0.726603i | \(0.258902\pi\) | |||||||
\(504\) | 2.13260e6 | 0.373966 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 539844. | 0.0937329 | ||||||||
\(507\) | −3.29765e6 | −0.569751 | ||||||||
\(508\) | 19725.1 | 0.00339125 | ||||||||
\(509\) | 5.32415e6 | 0.910869 | 0.455434 | − | 0.890269i | \(-0.349484\pi\) | ||||
0.455434 | + | 0.890269i | \(0.349484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.59569e6 | −1.11740 | ||||||||
\(512\) | −5.98317e6 | −1.00869 | ||||||||
\(513\) | −488929. | −0.0820262 | ||||||||
\(514\) | 7.60548e6 | 1.26975 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11328.3 | −0.00187301 | ||||||||
\(517\) | −141214. | −0.0232354 | ||||||||
\(518\) | −2.18157e6 | −0.357227 | ||||||||
\(519\) | −6.53282e6 | −1.06459 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.42076e6 | −1.35912 | −0.679559 | − | 0.733621i | \(-0.737829\pi\) | ||||
−0.679559 | + | 0.733621i | \(0.737829\pi\) | |||||||
\(522\) | 706257. | 0.113445 | ||||||||
\(523\) | 6.81759e6 | 1.08988 | 0.544938 | − | 0.838476i | \(-0.316553\pi\) | ||||
0.544938 | + | 0.838476i | \(0.316553\pi\) | |||||||
\(524\) | −19073.5 | −0.00303460 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.58833e6 | −1.19586 | ||||||||
\(527\) | 1.35288e6 | 0.212194 | ||||||||
\(528\) | 1.10853e6 | 0.173047 | ||||||||
\(529\) | −5.81062e6 | −0.902783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.91154e6 | 0.294203 | ||||||||
\(532\) | −18322.9 | −0.00280682 | ||||||||
\(533\) | 672649. | 0.102558 | ||||||||
\(534\) | 2.17157e6 | 0.329550 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.99581e6 | 0.450404 | ||||||||
\(537\) | 623802. | 0.0933493 | ||||||||
\(538\) | −1.14949e7 | −1.71218 | ||||||||
\(539\) | −511125. | −0.0757801 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00313e7 | −1.47354 | −0.736770 | − | 0.676143i | \(-0.763650\pi\) | ||||
−0.736770 | + | 0.676143i | \(0.763650\pi\) | |||||||
\(542\) | −1.22986e6 | −0.179828 | ||||||||
\(543\) | 7.11356e6 | 1.03535 | ||||||||
\(544\) | 34134.4 | 0.00494533 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −514619. | −0.0738762 | ||||||||
\(547\) | −341056. | −0.0487368 | −0.0243684 | − | 0.999703i | \(-0.507757\pi\) | ||||
−0.0243684 | + | 0.999703i | \(0.507757\pi\) | |||||||
\(548\) | 24171.7 | 0.00343840 | ||||||||
\(549\) | 1.42571e6 | 0.201883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.03682e6 | −0.145487 | ||||||||
\(552\) | 1.29248e6 | 0.180541 | ||||||||
\(553\) | 3.14532e6 | 0.437373 | ||||||||
\(554\) | 2.31348e6 | 0.320252 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30471.9 | −0.00418035 | ||||||||
\(557\) | −8.70989e6 | −1.18953 | −0.594764 | − | 0.803901i | \(-0.702754\pi\) | ||||
−0.594764 | + | 0.803901i | \(0.702754\pi\) | |||||||
\(558\) | 1.23492e6 | 0.167901 | ||||||||
\(559\) | 467087. | 0.0632219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −545039. | −0.0731174 | ||||||||
\(562\) | −2.29324e6 | −0.306272 | ||||||||
\(563\) | 1.05570e7 | 1.40369 | 0.701845 | − | 0.712330i | \(-0.252360\pi\) | ||||
0.701845 | + | 0.712330i | \(0.252360\pi\) | |||||||
\(564\) | −1978.69 | −0.000261927 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.13011e6 | −0.935525 | ||||||||
\(567\) | −951485. | −0.124292 | ||||||||
\(568\) | −1.30823e7 | −1.70142 | ||||||||
\(569\) | −2.88092e6 | −0.373035 | −0.186518 | − | 0.982452i | \(-0.559720\pi\) | ||||
−0.186518 | + | 0.982452i | \(0.559720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00484e6 | −1.02745 | −0.513727 | − | 0.857954i | \(-0.671735\pi\) | ||||
−0.513727 | + | 0.857954i | \(0.671735\pi\) | |||||||
\(572\) | 1593.48 | 0.000203637 0 | ||||||||
\(573\) | 3.77081e6 | 0.479786 | ||||||||
\(574\) | −7.87035e6 | −0.997043 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.66965e6 | 0.335272 | ||||||||
\(577\) | 1.42967e7 | 1.78770 | 0.893852 | − | 0.448361i | \(-0.147992\pi\) | ||||
0.893852 | + | 0.448361i | \(0.147992\pi\) | |||||||
\(578\) | −6.59541e6 | −0.821149 | ||||||||
\(579\) | −2.38972e6 | −0.296244 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00563e6 | 0.123594 | ||||||||
\(582\) | 1.06562e6 | 0.130405 | ||||||||
\(583\) | 3.49362e6 | 0.425700 | ||||||||
\(584\) | −8.25697e6 | −1.00182 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.98026e6 | −0.238220 | ||||||||
\(587\) | −9.83619e6 | −1.17823 | −0.589117 | − | 0.808047i | \(-0.700524\pi\) | ||||
−0.589117 | + | 0.808047i | \(0.700524\pi\) | |||||||
\(588\) | −7161.88 | −0.000854248 0 | ||||||||
\(589\) | −1.81292e6 | −0.215323 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 789787. | 0.0930125 | ||||||||
\(592\) | −2.71497e6 | −0.318390 | ||||||||
\(593\) | 9.84429e6 | 1.14960 | 0.574801 | − | 0.818293i | \(-0.305079\pi\) | ||||
0.574801 | + | 0.818293i | \(0.305079\pi\) | |||||||
\(594\) | −497515. | −0.0578548 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 76186.3 | 0.00878540 | ||||||||
\(597\) | 3.42890e6 | 0.393748 | ||||||||
\(598\) | −311890. | −0.0356656 | ||||||||
\(599\) | −3.94699e6 | −0.449468 | −0.224734 | − | 0.974420i | \(-0.572151\pi\) | ||||
−0.224734 | + | 0.974420i | \(0.572151\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.63150e6 | −0.861834 | −0.430917 | − | 0.902392i | \(-0.641810\pi\) | ||||
−0.430917 | + | 0.902392i | \(0.641810\pi\) | |||||||
\(602\) | −5.46516e6 | −0.614627 | ||||||||
\(603\) | −1.33662e6 | −0.149697 | ||||||||
\(604\) | −78401.5 | −0.00874444 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.62715e6 | 1.06492 | ||||||||
\(607\) | 1.12292e7 | 1.23703 | 0.618513 | − | 0.785775i | \(-0.287736\pi\) | ||||
0.618513 | + | 0.785775i | \(0.287736\pi\) | |||||||
\(608\) | −45741.6 | −0.00501825 | ||||||||
\(609\) | −2.01771e6 | −0.220453 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 81585.1 | 0.00884113 | ||||||||
\(612\) | −7637.10 | −0.000824232 0 | ||||||||
\(613\) | −2.62390e6 | −0.282031 | −0.141016 | − | 0.990007i | \(-0.545037\pi\) | ||||
−0.141016 | + | 0.990007i | \(0.545037\pi\) | |||||||
\(614\) | 8.24753e6 | 0.882883 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.18573e6 | −0.338265 | ||||||||
\(617\) | 3.59228e6 | 0.379889 | 0.189945 | − | 0.981795i | \(-0.439169\pi\) | ||||
0.189945 | + | 0.981795i | \(0.439169\pi\) | |||||||
\(618\) | 8.16750e6 | 0.860237 | ||||||||
\(619\) | −1.19777e7 | −1.25646 | −0.628228 | − | 0.778029i | \(-0.716219\pi\) | ||||
−0.628228 | + | 0.778029i | \(0.716219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −576657. | −0.0600052 | ||||||||
\(622\) | 1.24249e7 | 1.28770 | ||||||||
\(623\) | −6.20398e6 | −0.640398 | ||||||||
\(624\) | −640445. | −0.0658447 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.65398e6 | −0.372675 | ||||||||
\(627\) | 730376. | 0.0741955 | ||||||||
\(628\) | 62700.6 | 0.00634413 | ||||||||
\(629\) | 1.33488e6 | 0.134529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.50844e6 | 0.250801 | 0.125401 | − | 0.992106i | \(-0.459978\pi\) | ||||
0.125401 | + | 0.992106i | \(0.459978\pi\) | |||||||
\(632\) | 3.93754e6 | 0.392132 | ||||||||
\(633\) | 5.61963e6 | 0.557441 | ||||||||
\(634\) | 9.18972e6 | 0.907986 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 48952.6 | 0.00479880 | ||||||||
\(637\) | 295298. | 0.0288345 | ||||||||
\(638\) | −1.05503e6 | −0.102615 | ||||||||
\(639\) | 5.83681e6 | 0.565488 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12431e7 | 1.08079 | 0.540395 | − | 0.841411i | \(-0.318275\pi\) | ||||
0.540395 | + | 0.841411i | \(0.318275\pi\) | |||||||
\(642\) | −5.74845e6 | −0.550444 | ||||||||
\(643\) | −5.61271e6 | −0.535360 | −0.267680 | − | 0.963508i | \(-0.586257\pi\) | ||||
−0.267680 | + | 0.963508i | \(0.586257\pi\) | |||||||
\(644\) | −21610.5 | −0.00205329 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.89326e6 | −0.178497 | ||||||||
\(647\) | −1.10739e7 | −1.04002 | −0.520008 | − | 0.854162i | \(-0.674071\pi\) | ||||
−0.520008 | + | 0.854162i | \(0.674071\pi\) | |||||||
\(648\) | −1.19114e6 | −0.111436 | ||||||||
\(649\) | −2.85551e6 | −0.266117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.52805e6 | −0.326274 | ||||||||
\(652\) | −2781.46 | −0.000256244 0 | ||||||||
\(653\) | 7.83486e6 | 0.719032 | 0.359516 | − | 0.933139i | \(-0.382942\pi\) | ||||
0.359516 | + | 0.933139i | \(0.382942\pi\) | |||||||
\(654\) | −89763.0 | −0.00820640 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.79467e6 | −0.888649 | ||||||||
\(657\) | 3.68395e6 | 0.332966 | ||||||||
\(658\) | −954589. | −0.0859511 | ||||||||
\(659\) | 1.02774e7 | 0.921868 | 0.460934 | − | 0.887434i | \(-0.347514\pi\) | ||||
0.460934 | + | 0.887434i | \(0.347514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.42467e7 | −1.26827 | −0.634134 | − | 0.773223i | \(-0.718643\pi\) | ||||
−0.634134 | + | 0.773223i | \(0.718643\pi\) | |||||||
\(662\) | 4.50842e6 | 0.399833 | ||||||||
\(663\) | 314892. | 0.0278213 | ||||||||
\(664\) | 1.25892e6 | 0.110810 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.21849e6 | 0.106448 | ||||||||
\(667\) | −1.22285e6 | −0.106429 | ||||||||
\(668\) | 32017.6 | 0.00277618 | ||||||||
\(669\) | 5.92468e6 | 0.511799 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.12976e6 | −0.182610 | ||||||||
\(672\) | −89015.7 | −0.00760403 | ||||||||
\(673\) | 3.85183e6 | 0.327815 | 0.163908 | − | 0.986476i | \(-0.447590\pi\) | ||||
0.163908 | + | 0.986476i | \(0.447590\pi\) | |||||||
\(674\) | 2.12486e7 | 1.80169 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 69024.9 | 0.00580951 | ||||||||
\(677\) | −1.39430e7 | −1.16919 | −0.584594 | − | 0.811326i | \(-0.698746\pi\) | ||||
−0.584594 | + | 0.811326i | \(0.698746\pi\) | |||||||
\(678\) | 3.92251e6 | 0.327710 | ||||||||
\(679\) | −3.04437e6 | −0.253409 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.97959e6 | −0.163571 | ||||||||
\(682\) | −1.84475e6 | −0.151872 | ||||||||
\(683\) | 1.24329e7 | 1.01981 | 0.509905 | − | 0.860231i | \(-0.329681\pi\) | ||||
0.509905 | + | 0.860231i | \(0.329681\pi\) | |||||||
\(684\) | 10234.0 | 0.000836386 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.02921e7 | 0.835012 | ||||||||
\(687\) | −2.81991e6 | −0.227952 | ||||||||
\(688\) | −6.80141e6 | −0.547807 | ||||||||
\(689\) | −2.01841e6 | −0.161980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.46905e7 | 1.17042 | 0.585208 | − | 0.810883i | \(-0.301013\pi\) | ||||
0.585208 | + | 0.810883i | \(0.301013\pi\) | |||||||
\(692\) | 136742. | 0.0108552 | ||||||||
\(693\) | 1.42135e6 | 0.112427 | ||||||||
\(694\) | −5.20881e6 | −0.410525 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.52592e6 | −0.197650 | ||||||||
\(697\) | 4.81581e6 | 0.375480 | ||||||||
\(698\) | 1.47221e7 | 1.14375 | ||||||||
\(699\) | 9.14474e6 | 0.707911 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.55096e6 | −0.272930 | −0.136465 | − | 0.990645i | \(-0.543574\pi\) | ||||
−0.136465 | + | 0.990645i | \(0.543574\pi\) | |||||||
\(702\) | 287435. | 0.0220139 | ||||||||
\(703\) | −1.78880e6 | −0.136513 | ||||||||
\(704\) | −3.98799e6 | −0.303265 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.08657e6 | −0.535087 | ||||||||
\(707\) | −2.75039e7 | −2.06941 | ||||||||
\(708\) | −40011.5 | −0.00299986 | ||||||||
\(709\) | −8.56408e6 | −0.639831 | −0.319915 | − | 0.947446i | \(-0.603654\pi\) | ||||
−0.319915 | + | 0.947446i | \(0.603654\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75678e6 | −0.130330 | ||||||||
\(712\) | −7.76659e6 | −0.574157 | ||||||||
\(713\) | −2.13821e6 | −0.157517 | ||||||||
\(714\) | −3.68440e6 | −0.270472 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13057.1 | −0.000951843 0 | ||||||||
\(717\) | 6.86178e6 | 0.498470 | ||||||||
\(718\) | −1.34349e7 | −0.972576 | ||||||||
\(719\) | 1.07318e7 | 0.774195 | 0.387097 | − | 0.922039i | \(-0.373478\pi\) | ||||
0.387097 | + | 0.922039i | \(0.373478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.33338e7 | −1.67166 | ||||||||
\(722\) | −1.14286e7 | −0.815924 | ||||||||
\(723\) | −206182. | −0.0146692 | ||||||||
\(724\) | −148898. | −0.0105570 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 743201. | 0.0523317 | ||||||||
\(727\) | −1.49237e7 | −1.04722 | −0.523611 | − | 0.851957i | \(-0.675416\pi\) | ||||
−0.523611 | + | 0.851957i | \(0.675416\pi\) | |||||||
\(728\) | 1.84053e6 | 0.128711 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.34409e6 | 0.231465 | ||||||||
\(732\) | −29842.2 | −0.00205851 | ||||||||
\(733\) | −1.21777e7 | −0.837155 | −0.418577 | − | 0.908181i | \(-0.637471\pi\) | ||||
−0.418577 | + | 0.908181i | \(0.637471\pi\) | |||||||
\(734\) | 1.95331e7 | 1.33823 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53948.9 | −0.00367103 | ||||||||
\(737\) | 1.99668e6 | 0.135406 | ||||||||
\(738\) | 4.39589e6 | 0.297102 | ||||||||
\(739\) | 4.10708e6 | 0.276644 | 0.138322 | − | 0.990387i | \(-0.455829\pi\) | ||||
0.138322 | + | 0.990387i | \(0.455829\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −421969. | −0.0282315 | ||||||||
\(742\) | 2.36164e7 | 1.57472 | ||||||||
\(743\) | −2.73077e7 | −1.81474 | −0.907368 | − | 0.420337i | \(-0.861912\pi\) | ||||
−0.907368 | + | 0.420337i | \(0.861912\pi\) | |||||||
\(744\) | −4.41667e6 | −0.292525 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.57710e6 | −0.301123 | ||||||||
\(747\) | −561682. | −0.0368289 | ||||||||
\(748\) | 11408.5 | 0.000745546 0 | ||||||||
\(749\) | 1.64228e7 | 1.06965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.54004e7 | −0.996398 | −0.498199 | − | 0.867063i | \(-0.666005\pi\) | ||||
−0.498199 | + | 0.867063i | \(0.666005\pi\) | |||||||
\(752\) | −1.18799e6 | −0.0766069 | ||||||||
\(753\) | −6.22043e6 | −0.399791 | ||||||||
\(754\) | 609532. | 0.0390452 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19916.0 | 0.00126735 | ||||||||
\(757\) | −8.23327e6 | −0.522195 | −0.261097 | − | 0.965312i | \(-0.584084\pi\) | ||||
−0.261097 | + | 0.965312i | \(0.584084\pi\) | |||||||
\(758\) | −2.94689e6 | −0.186290 | ||||||||
\(759\) | 861426. | 0.0542767 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.69020e7 | 1.05798 | 0.528989 | − | 0.848629i | \(-0.322571\pi\) | ||||
0.528989 | + | 0.848629i | \(0.322571\pi\) | |||||||
\(762\) | −5.31509e6 | −0.331607 | ||||||||
\(763\) | 256445. | 0.0159471 | ||||||||
\(764\) | −78928.8 | −0.00489217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.26881e7 | 0.781315 | ||||||||
\(767\) | 1.64975e6 | 0.101258 | ||||||||
\(768\) | −166664. | −0.0101962 | ||||||||
\(769\) | −1.72204e7 | −1.05009 | −0.525045 | − | 0.851075i | \(-0.675951\pi\) | ||||
−0.525045 | + | 0.851075i | \(0.675951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.21360e7 | 0.735259 | ||||||||
\(772\) | 50020.4 | 0.00302067 | ||||||||
\(773\) | −1.86902e7 | −1.12503 | −0.562517 | − | 0.826786i | \(-0.690167\pi\) | ||||
−0.562517 | + | 0.826786i | \(0.690167\pi\) | |||||||
\(774\) | 3.05250e6 | 0.183149 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.81116e6 | −0.227197 | ||||||||
\(777\) | −3.48111e6 | −0.206855 | ||||||||
\(778\) | −1.36523e7 | −0.808644 | ||||||||
\(779\) | −6.45339e6 | −0.381017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.71919e6 | −0.511503 | ||||||||
\(782\) | −2.23297e6 | −0.130577 | ||||||||
\(783\) | 1.12697e6 | 0.0656913 | ||||||||
\(784\) | −4.29994e6 | −0.249846 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.13952e6 | 0.296733 | ||||||||
\(787\) | 8.17563e6 | 0.470527 | 0.235264 | − | 0.971932i | \(-0.424405\pi\) | ||||
0.235264 | + | 0.971932i | \(0.424405\pi\) | |||||||
\(788\) | −16531.4 | −0.000948408 0 | ||||||||
\(789\) | −1.21087e7 | −0.692474 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.12063e7 | −0.636824 | ||||||||
\(792\) | 1.77935e6 | 0.100797 | ||||||||
\(793\) | 1.23045e6 | 0.0694834 | ||||||||
\(794\) | −1.10590e7 | −0.622534 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −71772.0 | −0.00401488 | ||||||||
\(797\) | 3.39844e7 | 1.89511 | 0.947554 | − | 0.319595i | \(-0.103547\pi\) | ||||
0.947554 | + | 0.319595i | \(0.103547\pi\) | |||||||
\(798\) | 4.93726e6 | 0.274460 | ||||||||
\(799\) | 584106. | 0.0323687 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.46516e6 | 0.190828 | ||||||||
\(802\) | −2.17887e7 | −1.19618 | ||||||||
\(803\) | −5.50318e6 | −0.301179 | ||||||||
\(804\) | 27977.5 | 0.00152640 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.06579e6 | 0.0577876 | ||||||||
\(807\) | −1.83423e7 | −0.991449 | ||||||||
\(808\) | −3.44314e7 | −1.85535 | ||||||||
\(809\) | 2.50619e7 | 1.34630 | 0.673151 | − | 0.739505i | \(-0.264940\pi\) | ||||
0.673151 | + | 0.739505i | \(0.264940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.73791e7 | −0.927844 | −0.463922 | − | 0.885876i | \(-0.653558\pi\) | ||||
−0.463922 | + | 0.885876i | \(0.653558\pi\) | |||||||
\(812\) | 42233.7 | 0.00224786 | ||||||||
\(813\) | −1.96248e6 | −0.104131 | ||||||||
\(814\) | −1.82021e6 | −0.0962855 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.58525e6 | −0.241067 | ||||||||
\(817\) | −4.48123e6 | −0.234878 | ||||||||
\(818\) | 9.88681e6 | 0.516622 | ||||||||
\(819\) | −821175. | −0.0427786 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.21448e7 | −0.628827 | −0.314413 | − | 0.949286i | \(-0.601808\pi\) | ||||
−0.314413 | + | 0.949286i | \(0.601808\pi\) | |||||||
\(822\) | −6.51329e6 | −0.336218 | ||||||||
\(823\) | −9.33503e6 | −0.480415 | −0.240207 | − | 0.970722i | \(-0.577215\pi\) | ||||
−0.240207 | + | 0.970722i | \(0.577215\pi\) | |||||||
\(824\) | −2.92110e7 | −1.49875 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.93029e7 | −0.984404 | ||||||||
\(827\) | 1.15378e7 | 0.586622 | 0.293311 | − | 0.956017i | \(-0.405243\pi\) | ||||
0.293311 | + | 0.956017i | \(0.405243\pi\) | |||||||
\(828\) | 12070.3 | 0.000611847 0 | ||||||||
\(829\) | −1.25927e7 | −0.636404 | −0.318202 | − | 0.948023i | \(-0.603079\pi\) | ||||
−0.318202 | + | 0.948023i | \(0.603079\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.69161e6 | 0.185444 | ||||||||
\(832\) | 2.30403e6 | 0.115393 | ||||||||
\(833\) | 2.11418e6 | 0.105567 | ||||||||
\(834\) | 8.21092e6 | 0.408768 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15287.9 | −0.000756539 0 | ||||||||
\(837\) | 1.97055e6 | 0.0972241 | ||||||||
\(838\) | −2.41633e7 | −1.18863 | ||||||||
\(839\) | 3.69853e7 | 1.81395 | 0.906973 | − | 0.421189i | \(-0.138387\pi\) | ||||
0.906973 | + | 0.421189i | \(0.138387\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.81213e7 | −0.883486 | ||||||||
\(842\) | 3.23775e7 | 1.57385 | ||||||||
\(843\) | −3.65930e6 | −0.177349 | ||||||||
\(844\) | −117627. | −0.00568398 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 533175. | 0.0256120 | ||||||||
\(847\) | −2.12326e6 | −0.101694 | ||||||||
\(848\) | 2.93907e7 | 1.40353 | ||||||||
\(849\) | −1.13775e7 | −0.541723 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.10976e6 | −0.0998642 | ||||||||
\(852\) | −122173. | −0.00576604 | ||||||||
\(853\) | −3.49513e7 | −1.64471 | −0.822357 | − | 0.568972i | \(-0.807341\pi\) | ||||
−0.822357 | + | 0.568972i | \(0.807341\pi\) | |||||||
\(854\) | −1.43969e7 | −0.675500 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.05593e7 | 0.959010 | ||||||||
\(857\) | 2.24410e7 | 1.04373 | 0.521867 | − | 0.853027i | \(-0.325236\pi\) | ||||
0.521867 | + | 0.853027i | \(0.325236\pi\) | |||||||
\(858\) | −429378. | −0.0199123 | ||||||||
\(859\) | 3.30887e7 | 1.53002 | 0.765010 | − | 0.644019i | \(-0.222734\pi\) | ||||
0.765010 | + | 0.644019i | \(0.222734\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.25587e7 | −0.577345 | ||||||||
\(862\) | 2.98494e7 | 1.36826 | ||||||||
\(863\) | −1.58950e6 | −0.0726495 | −0.0363248 | − | 0.999340i | \(-0.511565\pi\) | ||||
−0.0363248 | + | 0.999340i | \(0.511565\pi\) | |||||||
\(864\) | 49718.7 | 0.00226587 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.34146e7 | 0.607830 | ||||||||
\(867\) | −1.05243e7 | −0.475492 | ||||||||
\(868\) | 73847.4 | 0.00332687 | ||||||||
\(869\) | 2.62433e6 | 0.117888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.15356e6 | −0.0515224 | ||||||||
\(872\) | 321036. | 0.0142976 | ||||||||
\(873\) | 1.70040e6 | 0.0755118 | ||||||||
\(874\) | 2.99228e6 | 0.132502 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −77110.6 | −0.00339511 | ||||||||
\(877\) | 1.78401e7 | 0.783246 | 0.391623 | − | 0.920126i | \(-0.371914\pi\) | ||||
0.391623 | + | 0.920126i | \(0.371914\pi\) | |||||||
\(878\) | 3.63449e7 | 1.59114 | ||||||||
\(879\) | −3.15989e6 | −0.137943 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.53213e7 | −0.665054 | −0.332527 | − | 0.943094i | \(-0.607901\pi\) | ||||
−0.332527 | + | 0.943094i | \(0.607901\pi\) | |||||||
\(882\) | 1.92983e6 | 0.0835310 | ||||||||
\(883\) | −1.92226e7 | −0.829680 | −0.414840 | − | 0.909894i | \(-0.636162\pi\) | ||||
−0.414840 | + | 0.909894i | \(0.636162\pi\) | |||||||
\(884\) | −6591.17 | −0.000283682 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14106.9 | −0.000603735 0 | ||||||||
\(887\) | 1.78729e7 | 0.762756 | 0.381378 | − | 0.924419i | \(-0.375450\pi\) | ||||
0.381378 | + | 0.924419i | \(0.375450\pi\) | |||||||
\(888\) | −4.35791e6 | −0.185458 | ||||||||
\(889\) | 1.51847e7 | 0.644396 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −124013. | −0.00521860 | ||||||||
\(893\) | −782727. | −0.0328459 | ||||||||
\(894\) | −2.05291e7 | −0.859063 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.66419e7 | −1.10865 | ||||||||
\(897\) | −497682. | −0.0206524 | ||||||||
\(898\) | −2.84677e7 | −1.17804 | ||||||||
\(899\) | 4.17874e6 | 0.172443 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.44507e7 | −0.593032 | ||||||||
\(902\) | −6.56670e6 | −0.268739 | ||||||||
\(903\) | −8.72072e6 | −0.355904 | ||||||||
\(904\) | −1.40288e7 | −0.570953 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.11260e7 | 0.855059 | ||||||||
\(907\) | −2.36602e7 | −0.954993 | −0.477497 | − | 0.878634i | \(-0.658456\pi\) | ||||
−0.477497 | + | 0.878634i | \(0.658456\pi\) | |||||||
\(908\) | 41435.7 | 0.00166786 | ||||||||
\(909\) | 1.53620e7 | 0.616649 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.62399e7 | 1.04753 | 0.523766 | − | 0.851862i | \(-0.324527\pi\) | ||||
0.523766 | + | 0.851862i | \(0.324527\pi\) | |||||||
\(912\) | 6.14443e6 | 0.244621 | ||||||||
\(913\) | 839056. | 0.0333130 | ||||||||
\(914\) | −2.60966e7 | −1.03328 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 59025.0 | 0.00232433 | ||||||||
\(917\) | −1.46831e7 | −0.576627 | ||||||||
\(918\) | 2.05788e6 | 0.0805960 | ||||||||
\(919\) | 1.05336e7 | 0.411422 | 0.205711 | − | 0.978613i | \(-0.434049\pi\) | ||||
0.205711 | + | 0.978613i | \(0.434049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.31605e7 | 0.511240 | ||||||||
\(922\) | 8.07723e6 | 0.312921 | ||||||||
\(923\) | 5.03744e6 | 0.194628 | ||||||||
\(924\) | −29751.1 | −0.00114637 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.91800e6 | −0.341775 | ||||||||
\(927\) | 1.30328e7 | 0.498127 | ||||||||
\(928\) | 105433. | 0.00401890 | ||||||||
\(929\) | 4.93218e7 | 1.87499 | 0.937497 | − | 0.347993i | \(-0.113137\pi\) | ||||
0.937497 | + | 0.347993i | \(0.113137\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.83309e6 | −0.107124 | ||||||||
\(932\) | −191413. | −0.00721826 | ||||||||
\(933\) | 1.98263e7 | 0.745653 | ||||||||
\(934\) | −49210.1 | −0.00184581 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.02801e6 | −0.0383536 | ||||||||
\(937\) | −3.96100e6 | −0.147386 | −0.0736929 | − | 0.997281i | \(-0.523478\pi\) | ||||
−0.0736929 | + | 0.997281i | \(0.523478\pi\) | |||||||
\(938\) | 1.34973e7 | 0.500887 | ||||||||
\(939\) | −5.83063e6 | −0.215800 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.82868e7 | 1.40953 | 0.704766 | − | 0.709440i | \(-0.251052\pi\) | ||||
0.704766 | + | 0.709440i | \(0.251052\pi\) | |||||||
\(942\) | −1.68952e7 | −0.620349 | ||||||||
\(943\) | −7.61131e6 | −0.278728 | ||||||||
\(944\) | −2.40226e7 | −0.877383 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.55991e6 | −0.165664 | ||||||||
\(947\) | 1.34832e7 | 0.488562 | 0.244281 | − | 0.969705i | \(-0.421448\pi\) | ||||
0.244281 | + | 0.969705i | \(0.421448\pi\) | |||||||
\(948\) | 36772.2 | 0.00132892 | ||||||||
\(949\) | 3.17942e6 | 0.114599 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.46640e7 | 0.525776 | ||||||||
\(952\) | 1.31772e7 | 0.471228 | ||||||||
\(953\) | 9.20696e6 | 0.328385 | 0.164193 | − | 0.986428i | \(-0.447498\pi\) | ||||
0.164193 | + | 0.986428i | \(0.447498\pi\) | |||||||
\(954\) | −1.31907e7 | −0.469242 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −143627. | −0.00508268 | ||||||||
\(957\) | −1.68350e6 | −0.0594200 | ||||||||
\(958\) | 4.59947e7 | 1.61917 | ||||||||
\(959\) | 1.86079e7 | 0.653356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.13225e7 | −0.744782 | ||||||||
\(962\) | 1.05161e6 | 0.0366368 | ||||||||
\(963\) | −9.17277e6 | −0.318739 | ||||||||
\(964\) | 4315.71 | 0.000149575 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.82314e6 | 0.200777 | ||||||||
\(967\) | −2.95285e6 | −0.101549 | −0.0507745 | − | 0.998710i | \(-0.516169\pi\) | ||||
−0.0507745 | + | 0.998710i | \(0.516169\pi\) | |||||||
\(968\) | −2.65805e6 | −0.0911747 | ||||||||
\(969\) | −3.02107e6 | −0.103360 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.09624e7 | −1.05387 | −0.526935 | − | 0.849906i | \(-0.676659\pi\) | ||||
−0.526935 | + | 0.849906i | \(0.676659\pi\) | |||||||
\(972\) | −11123.9 | −0.000377651 0 | ||||||||
\(973\) | −2.34578e7 | −0.794339 | ||||||||
\(974\) | −5.07686e7 | −1.71474 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.79170e7 | −0.602062 | ||||||||
\(977\) | 2.85400e7 | 0.956573 | 0.478287 | − | 0.878204i | \(-0.341258\pi\) | ||||
0.478287 | + | 0.878204i | \(0.341258\pi\) | |||||||
\(978\) | 749489. | 0.0250564 | ||||||||
\(979\) | −5.17635e6 | −0.172610 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −143234. | −0.00475198 | ||||||||
\(982\) | 3.40466e7 | 1.12667 | ||||||||
\(983\) | 4.46869e7 | 1.47501 | 0.737507 | − | 0.675340i | \(-0.236003\pi\) | ||||
0.737507 | + | 0.675340i | \(0.236003\pi\) | |||||||
\(984\) | −1.57219e7 | −0.517626 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.36393e6 | 0.142950 | ||||||||
\(987\) | −1.52323e6 | −0.0497706 | ||||||||
\(988\) | 8832.44 | 0.000287865 0 | ||||||||
\(989\) | −5.28529e6 | −0.171822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.85115e7 | 1.89259 | 0.946296 | − | 0.323302i | \(-0.104793\pi\) | ||||
0.946296 | + | 0.323302i | \(0.104793\pi\) | |||||||
\(992\) | 184354. | 0.00594804 | ||||||||
\(993\) | 7.19405e6 | 0.231526 | ||||||||
\(994\) | −5.89407e7 | −1.89212 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 11756.9 | 0.000375528 0 | ||||||||
\(997\) | 4.32684e7 | 1.37858 | 0.689292 | − | 0.724483i | \(-0.257922\pi\) | ||||
0.689292 | + | 0.724483i | \(0.257922\pi\) | |||||||
\(998\) | 1.31671e6 | 0.0418469 | ||||||||
\(999\) | 1.94434e6 | 0.0616393 |
(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 | 825.6.a.h.1.3 | 3 | ||
5.4 | even | 2 | 165.6.a.d.1.1 | ✓ | 3 | ||
15.14 | odd | 2 | 495.6.a.c.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.d.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
495.6.a.c.1.3 | 3 | 15.14 | odd | 2 | |||
825.6.a.h.1.3 | 3 | 1.1 | even | 1 | trivial |