Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [650,6,Mod(599,650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(650, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("650.599");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(104.249482878\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.1 | ||
Root | \(-1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 650.599 |
Dual form | 650.6.b.g.599.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | − 13.8114i | − 0.886001i | −0.896521 | − | 0.443000i | \(-0.853914\pi\) | ||||
0.896521 | − | 0.443000i | \(-0.146086\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −55.2456 | −0.626497 | ||||||||
\(7\) | 213.246i | 1.64488i | 0.568850 | + | 0.822441i | \(0.307388\pi\) | ||||
−0.568850 | + | 0.822441i | \(0.692612\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 52.2456 | 0.215002 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 587.285 | 1.46341 | 0.731707 | − | 0.681620i | \(-0.238724\pi\) | ||||
0.731707 | + | 0.681620i | \(0.238724\pi\) | |||||||
\(12\) | 220.982i | 0.443000i | ||||||||
\(13\) | 169.000i | 0.277350i | ||||||||
\(14\) | 852.982 | 1.16311 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 162.605i | 0.136462i | 0.997670 | + | 0.0682310i | \(0.0217355\pi\) | ||||
−0.997670 | + | 0.0682310i | \(0.978265\pi\) | |||||||
\(18\) | − 208.982i | − 0.152030i | ||||||||
\(19\) | 81.3914 | 0.0517243 | 0.0258622 | − | 0.999666i | \(-0.491767\pi\) | ||||
0.0258622 | + | 0.999666i | \(0.491767\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2945.22 | 1.45737 | ||||||||
\(22\) | − 2349.14i | − 1.03479i | ||||||||
\(23\) | 2948.84i | 1.16234i | 0.813783 | + | 0.581169i | \(0.197404\pi\) | ||||
−0.813783 | + | 0.581169i | \(0.802596\pi\) | |||||||
\(24\) | 883.929 | 0.313249 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 676.000 | 0.196116 | ||||||||
\(27\) | − 4077.75i | − 1.07649i | ||||||||
\(28\) | − 3411.93i | − 0.822441i | ||||||||
\(29\) | −6254.43 | −1.38100 | −0.690499 | − | 0.723333i | \(-0.742609\pi\) | ||||
−0.690499 | + | 0.723333i | \(0.742609\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4034.62 | −0.754048 | −0.377024 | − | 0.926204i | \(-0.623052\pi\) | ||||
−0.377024 | + | 0.926204i | \(0.623052\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | − 8111.22i | − 1.29659i | ||||||||
\(34\) | 650.420 | 0.0964932 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −835.929 | −0.107501 | ||||||||
\(37\) | 7617.22i | 0.914728i | 0.889280 | + | 0.457364i | \(0.151206\pi\) | ||||
−0.889280 | + | 0.457364i | \(0.848794\pi\) | |||||||
\(38\) | − 325.566i | − 0.0365746i | ||||||||
\(39\) | 2334.12 | 0.245732 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 958.121 | 0.0890145 | 0.0445072 | − | 0.999009i | \(-0.485828\pi\) | ||||
0.0445072 | + | 0.999009i | \(0.485828\pi\) | |||||||
\(42\) | − 11780.9i | − 1.03051i | ||||||||
\(43\) | − 169.655i | − 0.0139925i | −0.999976 | − | 0.00699624i | \(-0.997773\pi\) | ||||
0.999976 | − | 0.00699624i | \(-0.00222699\pi\) | |||||||
\(44\) | −9396.56 | −0.731707 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11795.4 | 0.821897 | ||||||||
\(47\) | 21612.6i | 1.42712i | 0.700592 | + | 0.713562i | \(0.252919\pi\) | ||||
−0.700592 | + | 0.713562i | \(0.747081\pi\) | |||||||
\(48\) | − 3535.72i | − 0.221500i | ||||||||
\(49\) | −28666.7 | −1.70564 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2245.80 | 0.120905 | ||||||||
\(52\) | − 2704.00i | − 0.138675i | ||||||||
\(53\) | − 24789.1i | − 1.21219i | −0.795392 | − | 0.606096i | \(-0.792735\pi\) | ||||
0.795392 | − | 0.606096i | \(-0.207265\pi\) | |||||||
\(54\) | −16311.0 | −0.761196 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13647.7 | −0.581554 | ||||||||
\(57\) | − 1124.13i | − 0.0458278i | ||||||||
\(58\) | 25017.7i | 0.976513i | ||||||||
\(59\) | −40109.2 | −1.50008 | −0.750040 | − | 0.661392i | \(-0.769966\pi\) | ||||
−0.750040 | + | 0.661392i | \(0.769966\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16343.0 | −0.562351 | −0.281176 | − | 0.959656i | \(-0.590724\pi\) | ||||
−0.281176 | + | 0.959656i | \(0.590724\pi\) | |||||||
\(62\) | 16138.5i | 0.533192i | ||||||||
\(63\) | 11141.1i | 0.353653i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −32444.9 | −0.916824 | ||||||||
\(67\) | 18362.1i | 0.499731i | 0.968281 | + | 0.249866i | \(0.0803864\pi\) | ||||
−0.968281 | + | 0.249866i | \(0.919614\pi\) | |||||||
\(68\) | − 2601.68i | − 0.0682310i | ||||||||
\(69\) | 40727.6 | 1.02983 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −77846.0 | −1.83270 | −0.916348 | − | 0.400382i | \(-0.868877\pi\) | ||||
−0.916348 | + | 0.400382i | \(0.868877\pi\) | |||||||
\(72\) | 3343.72i | 0.0760148i | ||||||||
\(73\) | 62130.2i | 1.36457i | 0.731087 | + | 0.682285i | \(0.239014\pi\) | ||||
−0.731087 | + | 0.682285i | \(0.760986\pi\) | |||||||
\(74\) | 30468.9 | 0.646810 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1302.26 | −0.0258622 | ||||||||
\(77\) | 125236.i | 2.40714i | ||||||||
\(78\) | − 9336.50i | − 0.173759i | ||||||||
\(79\) | 60599.1 | 1.09244 | 0.546221 | − | 0.837641i | \(-0.316066\pi\) | ||||
0.546221 | + | 0.837641i | \(0.316066\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −43623.7 | −0.738772 | ||||||||
\(82\) | − 3832.48i | − 0.0629427i | ||||||||
\(83\) | 2654.46i | 0.0422941i | 0.999776 | + | 0.0211471i | \(0.00673182\pi\) | ||||
−0.999776 | + | 0.0211471i | \(0.993268\pi\) | |||||||
\(84\) | −47123.5 | −0.728684 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −678.619 | −0.00989418 | ||||||||
\(87\) | 86382.4i | 1.22357i | ||||||||
\(88\) | 37586.2i | 0.517395i | ||||||||
\(89\) | −8229.77 | −0.110132 | −0.0550659 | − | 0.998483i | \(-0.517537\pi\) | ||||
−0.0550659 | + | 0.998483i | \(0.517537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −36038.5 | −0.456208 | ||||||||
\(92\) | − 47181.5i | − 0.581169i | ||||||||
\(93\) | 55723.7i | 0.668087i | ||||||||
\(94\) | 86450.3 | 1.00913 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14142.9 | −0.156624 | ||||||||
\(97\) | − 53844.0i | − 0.581042i | −0.956869 | − | 0.290521i | \(-0.906171\pi\) | ||||
0.956869 | − | 0.290521i | \(-0.0938287\pi\) | |||||||
\(98\) | 114667.i | 1.20607i | ||||||||
\(99\) | 30683.0 | 0.314637 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −167556. | −1.63439 | −0.817196 | − | 0.576360i | \(-0.804473\pi\) | ||||
−0.817196 | + | 0.576360i | \(0.804473\pi\) | |||||||
\(102\) | − 8983.20i | − 0.0854930i | ||||||||
\(103\) | − 30973.8i | − 0.287675i | −0.989601 | − | 0.143837i | \(-0.954056\pi\) | ||||
0.989601 | − | 0.143837i | \(-0.0459442\pi\) | |||||||
\(104\) | −10816.0 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −99156.4 | −0.857149 | ||||||||
\(107\) | − 97343.8i | − 0.821956i | −0.911645 | − | 0.410978i | \(-0.865187\pi\) | ||||
0.911645 | − | 0.410978i | \(-0.134813\pi\) | |||||||
\(108\) | 65244.0i | 0.538247i | ||||||||
\(109\) | −16696.8 | −0.134607 | −0.0673035 | − | 0.997733i | \(-0.521440\pi\) | ||||
−0.0673035 | + | 0.997733i | \(0.521440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 105204. | 0.810450 | ||||||||
\(112\) | 54590.9i | 0.411221i | ||||||||
\(113\) | − 219357.i | − 1.61605i | −0.589145 | − | 0.808027i | \(-0.700535\pi\) | ||||
0.589145 | − | 0.808027i | \(-0.299465\pi\) | |||||||
\(114\) | −4496.51 | −0.0324051 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 100071. | 0.690499 | ||||||||
\(117\) | 8829.50i | 0.0596309i | ||||||||
\(118\) | 160437.i | 1.06072i | ||||||||
\(119\) | −34674.8 | −0.224464 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 183852. | 1.14158 | ||||||||
\(122\) | 65372.1i | 0.397642i | ||||||||
\(123\) | − 13233.0i | − 0.0788669i | ||||||||
\(124\) | 64554.0 | 0.377024 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 44564.5 | 0.250071 | ||||||||
\(127\) | 158753.i | 0.873399i | 0.899607 | + | 0.436700i | \(0.143853\pi\) | ||||
−0.899607 | + | 0.436700i | \(0.856147\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | −2343.17 | −0.0123974 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 160566. | 0.817477 | 0.408739 | − | 0.912651i | \(-0.365969\pi\) | ||||
0.408739 | + | 0.912651i | \(0.365969\pi\) | |||||||
\(132\) | 129779.i | 0.648293i | ||||||||
\(133\) | 17356.4i | 0.0850804i | ||||||||
\(134\) | 73448.6 | 0.353363 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10406.7 | −0.0482466 | ||||||||
\(137\) | − 295668.i | − 1.34587i | −0.739702 | − | 0.672934i | \(-0.765034\pi\) | ||||
0.739702 | − | 0.672934i | \(-0.234966\pi\) | |||||||
\(138\) | − 162910.i | − 0.728201i | ||||||||
\(139\) | −6197.57 | −0.0272072 | −0.0136036 | − | 0.999907i | \(-0.504330\pi\) | ||||
−0.0136036 | + | 0.999907i | \(0.504330\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 298500. | 1.26443 | ||||||||
\(142\) | 311384.i | 1.29591i | ||||||||
\(143\) | 99251.1i | 0.405878i | ||||||||
\(144\) | 13374.9 | 0.0537506 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 248521. | 0.964896 | ||||||||
\(147\) | 395926.i | 1.51120i | ||||||||
\(148\) | − 121875.i | − 0.457364i | ||||||||
\(149\) | 371033. | 1.36914 | 0.684569 | − | 0.728948i | \(-0.259990\pi\) | ||||
0.684569 | + | 0.728948i | \(0.259990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −508361. | −1.81439 | −0.907193 | − | 0.420714i | \(-0.861780\pi\) | ||||
−0.907193 | + | 0.420714i | \(0.861780\pi\) | |||||||
\(152\) | 5209.05i | 0.0182873i | ||||||||
\(153\) | 8495.39i | 0.0293396i | ||||||||
\(154\) | 500943. | 1.70211 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −37346.0 | −0.122866 | ||||||||
\(157\) | 60014.9i | 0.194317i | 0.995269 | + | 0.0971583i | \(0.0309753\pi\) | ||||
−0.995269 | + | 0.0971583i | \(0.969025\pi\) | |||||||
\(158\) | − 242397.i | − 0.772474i | ||||||||
\(159\) | −342372. | −1.07400 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −628828. | −1.91191 | ||||||||
\(162\) | 174495.i | 0.522391i | ||||||||
\(163\) | 365913.i | 1.07872i | 0.842075 | + | 0.539360i | \(0.181334\pi\) | ||||
−0.842075 | + | 0.539360i | \(0.818666\pi\) | |||||||
\(164\) | −15329.9 | −0.0445072 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10617.8 | 0.0299065 | ||||||||
\(167\) | 67392.0i | 0.186990i | 0.995620 | + | 0.0934948i | \(0.0298038\pi\) | ||||
−0.995620 | + | 0.0934948i | \(0.970196\pi\) | |||||||
\(168\) | 188494.i | 0.515257i | ||||||||
\(169\) | −28561.0 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4252.34 | 0.0111208 | ||||||||
\(172\) | 2714.48i | 0.00699624i | ||||||||
\(173\) | − 518921.i | − 1.31821i | −0.752049 | − | 0.659107i | \(-0.770934\pi\) | ||||
0.752049 | − | 0.659107i | \(-0.229066\pi\) | |||||||
\(174\) | 345530. | 0.865191 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 150345. | 0.365853 | ||||||||
\(177\) | 553964.i | 1.32907i | ||||||||
\(178\) | 32919.1i | 0.0778750i | ||||||||
\(179\) | 89728.6 | 0.209314 | 0.104657 | − | 0.994508i | \(-0.466626\pi\) | ||||
0.104657 | + | 0.994508i | \(0.466626\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −376272. | −0.853700 | −0.426850 | − | 0.904322i | \(-0.640377\pi\) | ||||
−0.426850 | + | 0.904322i | \(0.640377\pi\) | |||||||
\(182\) | 144154.i | 0.322588i | ||||||||
\(183\) | 225720.i | 0.498244i | ||||||||
\(184\) | −188726. | −0.410948 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 222895. | 0.472409 | ||||||||
\(187\) | 95495.4i | 0.199700i | ||||||||
\(188\) | − 345801.i | − 0.713562i | ||||||||
\(189\) | 869562. | 1.77070 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 206748. | 0.410070 | 0.205035 | − | 0.978755i | \(-0.434269\pi\) | ||||
0.205035 | + | 0.978755i | \(0.434269\pi\) | |||||||
\(192\) | 56571.4i | 0.110750i | ||||||||
\(193\) | 413088.i | 0.798269i | 0.916892 | + | 0.399135i | \(0.130689\pi\) | ||||
−0.916892 | + | 0.399135i | \(0.869311\pi\) | |||||||
\(194\) | −215376. | −0.410859 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 458667. | 0.852819 | ||||||||
\(197\) | 538825.i | 0.989196i | 0.869122 | + | 0.494598i | \(0.164685\pi\) | ||||
−0.869122 | + | 0.494598i | \(0.835315\pi\) | |||||||
\(198\) | − 122732.i | − 0.222482i | ||||||||
\(199\) | 147336. | 0.263740 | 0.131870 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131870 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 253607. | 0.442762 | ||||||||
\(202\) | 670223.i | 1.15569i | ||||||||
\(203\) | − 1.33373e6i | − 2.27158i | ||||||||
\(204\) | −35932.8 | −0.0604527 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −123895. | −0.203417 | ||||||||
\(207\) | 154064.i | 0.249905i | ||||||||
\(208\) | 43264.0i | 0.0693375i | ||||||||
\(209\) | 47799.9 | 0.0756940 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.14921e6 | −1.77703 | −0.888515 | − | 0.458847i | \(-0.848262\pi\) | ||||
−0.888515 | + | 0.458847i | \(0.848262\pi\) | |||||||
\(212\) | 396626.i | 0.606096i | ||||||||
\(213\) | 1.07516e6i | 1.62377i | ||||||||
\(214\) | −389375. | −0.581211 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 260976. | 0.380598 | ||||||||
\(217\) | − 860365.i | − 1.24032i | ||||||||
\(218\) | 66787.3i | 0.0951815i | ||||||||
\(219\) | 858104. | 1.20901 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27480.2 | −0.0378477 | ||||||||
\(222\) | − 420817.i | − 0.573075i | ||||||||
\(223\) | 1.39430e6i | 1.87756i | 0.344513 | + | 0.938782i | \(0.388044\pi\) | ||||
−0.344513 | + | 0.938782i | \(0.611956\pi\) | |||||||
\(224\) | 218363. | 0.290777 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −877429. | −1.14272 | ||||||||
\(227\) | 1.40291e6i | 1.80703i | 0.428556 | + | 0.903515i | \(0.359023\pi\) | ||||
−0.428556 | + | 0.903515i | \(0.640977\pi\) | |||||||
\(228\) | 17986.1i | 0.0229139i | ||||||||
\(229\) | 796626. | 1.00384 | 0.501922 | − | 0.864913i | \(-0.332627\pi\) | ||||
0.501922 | + | 0.864913i | \(0.332627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.72968e6 | 2.13273 | ||||||||
\(232\) | − 400284.i | − 0.488257i | ||||||||
\(233\) | − 1.15975e6i | − 1.39951i | −0.714385 | − | 0.699753i | \(-0.753293\pi\) | ||||
0.714385 | − | 0.699753i | \(-0.246707\pi\) | |||||||
\(234\) | 35318.0 | 0.0421654 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 641748. | 0.750040 | ||||||||
\(237\) | − 836958.i | − 0.967905i | ||||||||
\(238\) | 138699.i | 0.158720i | ||||||||
\(239\) | 687529. | 0.778568 | 0.389284 | − | 0.921118i | \(-0.372722\pi\) | ||||
0.389284 | + | 0.921118i | \(0.372722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −391345. | −0.434028 | −0.217014 | − | 0.976169i | \(-0.569632\pi\) | ||||
−0.217014 | + | 0.976169i | \(0.569632\pi\) | |||||||
\(242\) | − 735409.i | − 0.807218i | ||||||||
\(243\) | − 388389.i | − 0.421941i | ||||||||
\(244\) | 261488. | 0.281176 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −52931.9 | −0.0557673 | ||||||||
\(247\) | 13755.2i | 0.0143457i | ||||||||
\(248\) | − 258216.i | − 0.266596i | ||||||||
\(249\) | 36661.7 | 0.0374727 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 944723. | 0.946499 | 0.473249 | − | 0.880928i | \(-0.343081\pi\) | ||||
0.473249 | + | 0.880928i | \(0.343081\pi\) | |||||||
\(252\) | − 178258.i | − 0.176827i | ||||||||
\(253\) | 1.73181e6i | 1.70098i | ||||||||
\(254\) | 635012. | 0.617587 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 297219.i | 0.280701i | 0.990102 | + | 0.140351i | \(0.0448230\pi\) | ||||
−0.990102 | + | 0.140351i | \(0.955177\pi\) | |||||||
\(258\) | 9372.67i | 0.00876626i | ||||||||
\(259\) | −1.62434e6 | −1.50462 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −326766. | −0.296918 | ||||||||
\(262\) | − 642264.i | − 0.578044i | ||||||||
\(263\) | 1.53097e6i | 1.36483i | 0.730966 | + | 0.682414i | \(0.239070\pi\) | ||||
−0.730966 | + | 0.682414i | \(0.760930\pi\) | |||||||
\(264\) | 519118. | 0.458412 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 69425.4 | 0.0601609 | ||||||||
\(267\) | 113665.i | 0.0975769i | ||||||||
\(268\) | − 293794.i | − 0.249866i | ||||||||
\(269\) | 1.00878e6 | 0.849994 | 0.424997 | − | 0.905195i | \(-0.360275\pi\) | ||||
0.424997 | + | 0.905195i | \(0.360275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.19122e6 | 1.81244 | 0.906220 | − | 0.422806i | \(-0.138955\pi\) | ||||
0.906220 | + | 0.422806i | \(0.138955\pi\) | |||||||
\(272\) | 41626.9i | 0.0341155i | ||||||||
\(273\) | 497742.i | 0.404201i | ||||||||
\(274\) | −1.18267e6 | −0.951673 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −651642. | −0.514916 | ||||||||
\(277\) | − 17924.0i | − 0.0140357i | −0.999975 | − | 0.00701786i | \(-0.997766\pi\) | ||||
0.999975 | − | 0.00701786i | \(-0.00223387\pi\) | |||||||
\(278\) | 24790.3i | 0.0192384i | ||||||||
\(279\) | −210791. | −0.162122 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.40663e6 | −1.81821 | −0.909106 | − | 0.416566i | \(-0.863234\pi\) | ||||
−0.909106 | + | 0.416566i | \(0.863234\pi\) | |||||||
\(282\) | − 1.19400e6i | − 0.894090i | ||||||||
\(283\) | 1.36921e6i | 1.01626i | 0.861281 | + | 0.508128i | \(0.169662\pi\) | ||||
−0.861281 | + | 0.508128i | \(0.830338\pi\) | |||||||
\(284\) | 1.24554e6 | 0.916348 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 397004. | 0.286999 | ||||||||
\(287\) | 204315.i | 0.146418i | ||||||||
\(288\) | − 53499.4i | − 0.0380074i | ||||||||
\(289\) | 1.39342e6 | 0.981378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −743660. | −0.514804 | ||||||||
\(292\) | − 994083.i | − 0.682285i | ||||||||
\(293\) | 390649.i | 0.265838i | 0.991127 | + | 0.132919i | \(0.0424351\pi\) | ||||
−0.991127 | + | 0.132919i | \(0.957565\pi\) | |||||||
\(294\) | 1.58371e6 | 1.06858 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −487502. | −0.323405 | ||||||||
\(297\) | − 2.39480e6i | − 1.57535i | ||||||||
\(298\) | − 1.48413e6i | − 0.968127i | ||||||||
\(299\) | −498355. | −0.322374 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36178.1 | 0.0230160 | ||||||||
\(302\) | 2.03344e6i | 1.28297i | ||||||||
\(303\) | 2.31418e6i | 1.44807i | ||||||||
\(304\) | 20836.2 | 0.0129311 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 33981.6 | 0.0207463 | ||||||||
\(307\) | 566546.i | 0.343075i | 0.985178 | + | 0.171537i | \(0.0548735\pi\) | ||||
−0.985178 | + | 0.171537i | \(0.945127\pi\) | |||||||
\(308\) | − 2.00377e6i | − 1.20357i | ||||||||
\(309\) | −427791. | −0.254880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 881239. | 0.516646 | 0.258323 | − | 0.966059i | \(-0.416830\pi\) | ||||
0.258323 | + | 0.966059i | \(0.416830\pi\) | |||||||
\(312\) | 149384.i | 0.0868795i | ||||||||
\(313\) | 916421.i | 0.528731i | 0.964423 | + | 0.264365i | \(0.0851624\pi\) | ||||
−0.964423 | + | 0.264365i | \(0.914838\pi\) | |||||||
\(314\) | 240060. | 0.137403 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −969586. | −0.546221 | ||||||||
\(317\) | 2.01084e6i | 1.12390i | 0.827170 | + | 0.561951i | \(0.189949\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(318\) | 1.36949e6i | 0.759435i | ||||||||
\(319\) | −3.67313e6 | −2.02097 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.34445e6 | −0.728254 | ||||||||
\(322\) | 2.51531e6i | 1.35192i | ||||||||
\(323\) | 13234.7i | 0.00705840i | ||||||||
\(324\) | 697980. | 0.369386 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.46365e6 | 0.762770 | ||||||||
\(327\) | 230606.i | 0.119262i | ||||||||
\(328\) | 61319.7i | 0.0314714i | ||||||||
\(329\) | −4.60879e6 | −2.34745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.47715e6 | 1.24275 | 0.621373 | − | 0.783515i | \(-0.286575\pi\) | ||||
0.621373 | + | 0.783515i | \(0.286575\pi\) | |||||||
\(332\) | − 42471.3i | − 0.0211471i | ||||||||
\(333\) | 397966.i | 0.196669i | ||||||||
\(334\) | 269568. | 0.132222 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 753976. | 0.364342 | ||||||||
\(337\) | 2.55550e6i | 1.22575i | 0.790181 | + | 0.612873i | \(0.209986\pi\) | ||||
−0.790181 | + | 0.612873i | \(0.790014\pi\) | |||||||
\(338\) | 114244.i | 0.0543928i | ||||||||
\(339\) | −3.02963e6 | −1.43183 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.36947e6 | −1.10348 | ||||||||
\(342\) | − 17009.4i | − 0.00786362i | ||||||||
\(343\) | − 2.52902e6i | − 1.16069i | ||||||||
\(344\) | 10857.9 | 0.00494709 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.07568e6 | −0.932118 | ||||||||
\(347\) | − 475000.i | − 0.211773i | −0.994378 | − | 0.105886i | \(-0.966232\pi\) | ||||
0.994378 | − | 0.105886i | \(-0.0337680\pi\) | |||||||
\(348\) | − 1.38212e6i | − 0.611783i | ||||||||
\(349\) | −615277. | −0.270400 | −0.135200 | − | 0.990818i | \(-0.543168\pi\) | ||||
−0.135200 | + | 0.990818i | \(0.543168\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 689140. | 0.298565 | ||||||||
\(352\) | − 601380.i | − 0.258697i | ||||||||
\(353\) | 4.37400e6i | 1.86828i | 0.356908 | + | 0.934140i | \(0.383831\pi\) | ||||
−0.356908 | + | 0.934140i | \(0.616169\pi\) | |||||||
\(354\) | 2.21586e6 | 0.939796 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 131676. | 0.0550659 | ||||||||
\(357\) | 478907.i | 0.198875i | ||||||||
\(358\) | − 358914.i | − 0.148007i | ||||||||
\(359\) | −4.59562e6 | −1.88195 | −0.940975 | − | 0.338476i | \(-0.890089\pi\) | ||||
−0.940975 | + | 0.338476i | \(0.890089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.46947e6 | −0.997325 | ||||||||
\(362\) | 1.50509e6i | 0.603657i | ||||||||
\(363\) | − 2.53926e6i | − 1.01144i | ||||||||
\(364\) | 576616. | 0.228104 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 902879. | 0.352312 | ||||||||
\(367\) | − 4.59362e6i | − 1.78029i | −0.455681 | − | 0.890143i | \(-0.650604\pi\) | ||||
0.455681 | − | 0.890143i | \(-0.349396\pi\) | |||||||
\(368\) | 754904.i | 0.290584i | ||||||||
\(369\) | 50057.6 | 0.0191383 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.28617e6 | 1.99391 | ||||||||
\(372\) | − 891580.i | − 0.334043i | ||||||||
\(373\) | − 1.74314e6i | − 0.648724i | −0.945933 | − | 0.324362i | \(-0.894850\pi\) | ||||
0.945933 | − | 0.324362i | \(-0.105150\pi\) | |||||||
\(374\) | 381982. | 0.141209 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.38320e6 | −0.504565 | ||||||||
\(377\) | − 1.05700e6i | − 0.383020i | ||||||||
\(378\) | − 3.47825e6i | − 1.25208i | ||||||||
\(379\) | 4.42529e6 | 1.58250 | 0.791250 | − | 0.611493i | \(-0.209431\pi\) | ||||
0.791250 | + | 0.611493i | \(0.209431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.19260e6 | 0.773833 | ||||||||
\(382\) | − 826992.i | − 0.289963i | ||||||||
\(383\) | − 1.39773e6i | − 0.486884i | −0.969915 | − | 0.243442i | \(-0.921723\pi\) | ||||
0.969915 | − | 0.243442i | \(-0.0782766\pi\) | |||||||
\(384\) | 226286. | 0.0783122 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.65235e6 | 0.564462 | ||||||||
\(387\) | − 8863.71i | − 0.00300842i | ||||||||
\(388\) | 861504.i | 0.290521i | ||||||||
\(389\) | −1.63535e6 | −0.547946 | −0.273973 | − | 0.961737i | \(-0.588338\pi\) | ||||
−0.273973 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −479497. | −0.158615 | ||||||||
\(392\) | − 1.83467e6i | − 0.603034i | ||||||||
\(393\) | − 2.21764e6i | − 0.724286i | ||||||||
\(394\) | 2.15530e6 | 0.699468 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −490928. | −0.157319 | ||||||||
\(397\) | 4.90653e6i | 1.56242i | 0.624268 | + | 0.781210i | \(0.285397\pi\) | ||||
−0.624268 | + | 0.781210i | \(0.714603\pi\) | |||||||
\(398\) | − 589344.i | − 0.186493i | ||||||||
\(399\) | 239715. | 0.0753813 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −951184. | −0.295395 | −0.147698 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147698 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(402\) | − 1.01443e6i | − 0.313080i | ||||||||
\(403\) | − 681851.i | − 0.209135i | ||||||||
\(404\) | 2.68089e6 | 0.817196 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.33492e6 | −1.60625 | ||||||||
\(407\) | 4.47348e6i | 1.33863i | ||||||||
\(408\) | 143731.i | 0.0427465i | ||||||||
\(409\) | −4.49464e6 | −1.32858 | −0.664289 | − | 0.747476i | \(-0.731265\pi\) | ||||
−0.664289 | + | 0.747476i | \(0.731265\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.08358e6 | −1.19244 | ||||||||
\(412\) | 495581.i | 0.143837i | ||||||||
\(413\) | − 8.55312e6i | − 2.46746i | ||||||||
\(414\) | 616256. | 0.176710 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 173056. | 0.0490290 | ||||||||
\(417\) | 85597.0i | 0.0241056i | ||||||||
\(418\) | − 191200.i | − 0.0535238i | ||||||||
\(419\) | 828906. | 0.230659 | 0.115329 | − | 0.993327i | \(-0.463208\pi\) | ||||
0.115329 | + | 0.993327i | \(0.463208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 744813. | 0.204806 | 0.102403 | − | 0.994743i | \(-0.467347\pi\) | ||||
0.102403 | + | 0.994743i | \(0.467347\pi\) | |||||||
\(422\) | 4.59686e6i | 1.25655i | ||||||||
\(423\) | 1.12916e6i | 0.306835i | ||||||||
\(424\) | 1.58650e6 | 0.428574 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.30065e6 | 1.14818 | ||||||||
\(427\) | − 3.48508e6i | − 0.925002i | ||||||||
\(428\) | 1.55750e6i | 0.410978i | ||||||||
\(429\) | 1.37080e6 | 0.359608 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.89529e6 | −1.01006 | −0.505030 | − | 0.863102i | \(-0.668519\pi\) | ||||
−0.505030 | + | 0.863102i | \(0.668519\pi\) | |||||||
\(432\) | − 1.04390e6i | − 0.269123i | ||||||||
\(433\) | 5.88297e6i | 1.50792i | 0.656923 | + | 0.753958i | \(0.271858\pi\) | ||||
−0.656923 | + | 0.753958i | \(0.728142\pi\) | |||||||
\(434\) | −3.44146e6 | −0.877038 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 267149. | 0.0673035 | ||||||||
\(437\) | 240011.i | 0.0601211i | ||||||||
\(438\) | − 3.43242e6i | − 0.854899i | ||||||||
\(439\) | −1.73024e6 | −0.428495 | −0.214248 | − | 0.976779i | \(-0.568730\pi\) | ||||
−0.214248 | + | 0.976779i | \(0.568730\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.49771e6 | −0.366716 | ||||||||
\(442\) | 109921.i | 0.0267624i | ||||||||
\(443\) | 106432.i | 0.0257670i | 0.999917 | + | 0.0128835i | \(0.00410105\pi\) | ||||
−0.999917 | + | 0.0128835i | \(0.995899\pi\) | |||||||
\(444\) | −1.68327e6 | −0.405225 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.57721e6 | 1.32764 | ||||||||
\(447\) | − 5.12449e6i | − 1.21306i | ||||||||
\(448\) | − 873454.i | − 0.205610i | ||||||||
\(449\) | 4.89220e6 | 1.14522 | 0.572609 | − | 0.819828i | \(-0.305931\pi\) | ||||
0.572609 | + | 0.819828i | \(0.305931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 562690. | 0.130265 | ||||||||
\(452\) | 3.50972e6i | 0.808027i | ||||||||
\(453\) | 7.02117e6i | 1.60755i | ||||||||
\(454\) | 5.61165e6 | 1.27776 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 71944.2 | 0.0162026 | ||||||||
\(457\) | 177252.i | 0.0397008i | 0.999803 | + | 0.0198504i | \(0.00631900\pi\) | ||||
−0.999803 | + | 0.0198504i | \(0.993681\pi\) | |||||||
\(458\) | − 3.18651e6i | − 0.709824i | ||||||||
\(459\) | 663063. | 0.146900 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.15676e6 | 1.56843 | 0.784213 | − | 0.620491i | \(-0.213067\pi\) | ||||
0.784213 | + | 0.620491i | \(0.213067\pi\) | |||||||
\(462\) | − 6.91872e6i | − 1.50807i | ||||||||
\(463\) | − 3.44228e6i | − 0.746267i | −0.927778 | − | 0.373133i | \(-0.878283\pi\) | ||||
0.927778 | − | 0.373133i | \(-0.121717\pi\) | |||||||
\(464\) | −1.60114e6 | −0.345249 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.63900e6 | −0.989600 | ||||||||
\(467\) | − 9.22486e6i | − 1.95735i | −0.205423 | − | 0.978673i | \(-0.565857\pi\) | ||||
0.205423 | − | 0.978673i | \(-0.434143\pi\) | |||||||
\(468\) | − 141272.i | − 0.0298155i | ||||||||
\(469\) | −3.91565e6 | −0.821999 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 828889. | 0.172165 | ||||||||
\(472\) | − 2.56699e6i | − 0.530358i | ||||||||
\(473\) | − 99635.7i | − 0.0204768i | ||||||||
\(474\) | −3.34783e6 | −0.684412 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 554797. | 0.112232 | ||||||||
\(477\) | − 1.29512e6i | − 0.260624i | ||||||||
\(478\) | − 2.75012e6i | − 0.550531i | ||||||||
\(479\) | −1.23331e6 | −0.245602 | −0.122801 | − | 0.992431i | \(-0.539188\pi\) | ||||
−0.122801 | + | 0.992431i | \(0.539188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.28731e6 | −0.253700 | ||||||||
\(482\) | 1.56538e6i | 0.306904i | ||||||||
\(483\) | 8.68498e6i | 1.69395i | ||||||||
\(484\) | −2.94164e6 | −0.570789 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.55356e6 | −0.298357 | ||||||||
\(487\) | − 6.21276e6i | − 1.18703i | −0.804823 | − | 0.593516i | \(-0.797740\pi\) | ||||
0.804823 | − | 0.593516i | \(-0.202260\pi\) | |||||||
\(488\) | − 1.04595e6i | − 0.198821i | ||||||||
\(489\) | 5.05376e6 | 0.955747 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.05221e6 | −1.32014 | −0.660072 | − | 0.751202i | \(-0.729474\pi\) | ||||
−0.660072 | + | 0.751202i | \(0.729474\pi\) | |||||||
\(492\) | 211728.i | 0.0394335i | ||||||||
\(493\) | − 1.01700e6i | − 0.188454i | ||||||||
\(494\) | 55020.6 | 0.0101440 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.03286e6 | −0.188512 | ||||||||
\(497\) | − 1.66003e7i | − 3.01457i | ||||||||
\(498\) | − 146647.i | − 0.0264972i | ||||||||
\(499\) | −5.63009e6 | −1.01220 | −0.506098 | − | 0.862476i | \(-0.668912\pi\) | ||||
−0.506098 | + | 0.862476i | \(0.668912\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 930778. | 0.165673 | ||||||||
\(502\) | − 3.77889e6i | − 0.669276i | ||||||||
\(503\) | − 9.65803e6i | − 1.70204i | −0.525137 | − | 0.851018i | \(-0.675986\pi\) | ||||
0.525137 | − | 0.851018i | \(-0.324014\pi\) | |||||||
\(504\) | −713032. | −0.125035 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.92724e6 | 1.20277 | ||||||||
\(507\) | 394467.i | 0.0681539i | ||||||||
\(508\) | − 2.54005e6i | − 0.436700i | ||||||||
\(509\) | 4.39209e6 | 0.751409 | 0.375705 | − | 0.926739i | \(-0.377401\pi\) | ||||
0.375705 | + | 0.926739i | \(0.377401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.32490e7 | −2.24456 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | − 331894.i | − 0.0556809i | ||||||||
\(514\) | 1.18888e6 | 0.198486 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 37490.7 | 0.00619868 | ||||||||
\(517\) | 1.26927e7i | 2.08847i | ||||||||
\(518\) | 6.49735e6i | 1.06393i | ||||||||
\(519\) | −7.16702e6 | −1.16794 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.38443e6 | −1.35325 | −0.676627 | − | 0.736326i | \(-0.736559\pi\) | ||||
−0.676627 | + | 0.736326i | \(0.736559\pi\) | |||||||
\(522\) | 1.30707e6i | 0.209953i | ||||||||
\(523\) | − 2.54489e6i | − 0.406831i | −0.979092 | − | 0.203416i | \(-0.934796\pi\) | ||||
0.979092 | − | 0.203416i | \(-0.0652042\pi\) | |||||||
\(524\) | −2.56906e6 | −0.408739 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.12389e6 | 0.965080 | ||||||||
\(527\) | − 656050.i | − 0.102899i | ||||||||
\(528\) | − 2.07647e6i | − 0.324146i | ||||||||
\(529\) | −2.25933e6 | −0.351028 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.09553e6 | −0.322521 | ||||||||
\(532\) | − 277702.i | − 0.0425402i | ||||||||
\(533\) | 161922.i | 0.0246882i | ||||||||
\(534\) | 454658. | 0.0689973 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.17518e6 | −0.176682 | ||||||||
\(537\) | − 1.23928e6i | − 0.185452i | ||||||||
\(538\) | − 4.03512e6i | − 0.601036i | ||||||||
\(539\) | −1.68355e7 | −2.49605 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.83465e6 | −0.563290 | −0.281645 | − | 0.959519i | \(-0.590880\pi\) | ||||
−0.281645 | + | 0.959519i | \(0.590880\pi\) | |||||||
\(542\) | − 8.76490e6i | − 1.28159i | ||||||||
\(543\) | 5.19684e6i | 0.756379i | ||||||||
\(544\) | 166508. | 0.0241233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.99097e6 | 0.285813 | ||||||||
\(547\) | − 2.61787e6i | − 0.374093i | −0.982351 | − | 0.187047i | \(-0.940108\pi\) | ||||
0.982351 | − | 0.187047i | \(-0.0598916\pi\) | |||||||
\(548\) | 4.73068e6i | 0.672934i | ||||||||
\(549\) | −853850. | −0.120907 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −509057. | −0.0714312 | ||||||||
\(552\) | 2.60657e6i | 0.364101i | ||||||||
\(553\) | 1.29225e7i | 1.79694i | ||||||||
\(554\) | −71695.9 | −0.00992476 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 99161.1 | 0.0136036 | ||||||||
\(557\) | 5.40419e6i | 0.738061i | 0.929417 | + | 0.369031i | \(0.120310\pi\) | ||||
−0.929417 | + | 0.369031i | \(0.879690\pi\) | |||||||
\(558\) | 843164.i | 0.114638i | ||||||||
\(559\) | 28671.7 | 0.00388082 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.31892e6 | 0.176935 | ||||||||
\(562\) | 9.62654e6i | 1.28567i | ||||||||
\(563\) | − 904604.i | − 0.120278i | −0.998190 | − | 0.0601392i | \(-0.980846\pi\) | ||||
0.998190 | − | 0.0601392i | \(-0.0191545\pi\) | |||||||
\(564\) | −4.77599e6 | −0.632217 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.47683e6 | 0.718602 | ||||||||
\(567\) | − 9.30257e6i | − 1.21519i | ||||||||
\(568\) | − 4.98215e6i | − 0.647956i | ||||||||
\(569\) | 6.69355e6 | 0.866714 | 0.433357 | − | 0.901222i | \(-0.357329\pi\) | ||||
0.433357 | + | 0.901222i | \(0.357329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.22981e6 | 1.05633 | 0.528165 | − | 0.849142i | \(-0.322880\pi\) | ||||
0.528165 | + | 0.849142i | \(0.322880\pi\) | |||||||
\(572\) | − 1.58802e6i | − 0.202939i | ||||||||
\(573\) | − 2.85548e6i | − 0.363322i | ||||||||
\(574\) | 817260. | 0.103533 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −213998. | −0.0268753 | ||||||||
\(577\) | 3.07720e6i | 0.384783i | 0.981318 | + | 0.192391i | \(0.0616243\pi\) | ||||
−0.981318 | + | 0.192391i | \(0.938376\pi\) | |||||||
\(578\) | − 5.57367e6i | − 0.693939i | ||||||||
\(579\) | 5.70532e6 | 0.707267 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −566051. | −0.0695689 | ||||||||
\(582\) | 2.97464e6i | 0.364021i | ||||||||
\(583\) | − 1.45583e7i | − 1.77394i | ||||||||
\(584\) | −3.97633e6 | −0.482448 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.56260e6 | 0.187976 | ||||||||
\(587\) | 2.64175e6i | 0.316443i | 0.987404 | + | 0.158222i | \(0.0505761\pi\) | ||||
−0.987404 | + | 0.158222i | \(0.949424\pi\) | |||||||
\(588\) | − 6.33482e6i | − 0.755599i | ||||||||
\(589\) | −328384. | −0.0390026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.44193e6 | 0.876429 | ||||||||
\(592\) | 1.95001e6i | 0.228682i | ||||||||
\(593\) | 5.06641e6i | 0.591649i | 0.955242 | + | 0.295824i | \(0.0955943\pi\) | ||||
−0.955242 | + | 0.295824i | \(0.904406\pi\) | |||||||
\(594\) | −9.57920e6 | −1.11394 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.93654e6 | −0.684569 | ||||||||
\(597\) | − 2.03492e6i | − 0.233674i | ||||||||
\(598\) | 1.99342e6i | 0.227953i | ||||||||
\(599\) | −1.31136e7 | −1.49332 | −0.746662 | − | 0.665204i | \(-0.768345\pi\) | ||||
−0.746662 | + | 0.665204i | \(0.768345\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.53425e6 | 0.850852 | 0.425426 | − | 0.904993i | \(-0.360124\pi\) | ||||
0.425426 | + | 0.904993i | \(0.360124\pi\) | |||||||
\(602\) | − 144713.i | − 0.0162748i | ||||||||
\(603\) | 959341.i | 0.107443i | ||||||||
\(604\) | 8.13378e6 | 0.907193 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.25672e6 | 1.02394 | ||||||||
\(607\) | 8.76101e6i | 0.965123i | 0.875862 | + | 0.482561i | \(0.160293\pi\) | ||||
−0.875862 | + | 0.482561i | \(0.839707\pi\) | |||||||
\(608\) | − 83344.8i | − 0.00914365i | ||||||||
\(609\) | −1.84207e7 | −2.01262 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.65253e6 | −0.395813 | ||||||||
\(612\) | − 135926.i | − 0.0146698i | ||||||||
\(613\) | 469316.i | 0.0504445i | 0.999682 | + | 0.0252223i | \(0.00802935\pi\) | ||||
−0.999682 | + | 0.0252223i | \(0.991971\pi\) | |||||||
\(614\) | 2.26618e6 | 0.242591 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.01509e6 | −0.851054 | ||||||||
\(617\) | − 4.14114e6i | − 0.437933i | −0.975732 | − | 0.218966i | \(-0.929732\pi\) | ||||
0.975732 | − | 0.218966i | \(-0.0702685\pi\) | |||||||
\(618\) | 1.71116e6i | 0.180227i | ||||||||
\(619\) | 1.31422e7 | 1.37861 | 0.689304 | − | 0.724472i | \(-0.257916\pi\) | ||||
0.689304 | + | 0.724472i | \(0.257916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.20246e7 | 1.25125 | ||||||||
\(622\) | − 3.52496e6i | − 0.365324i | ||||||||
\(623\) | − 1.75496e6i | − 0.181154i | ||||||||
\(624\) | 597536. | 0.0614331 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.66569e6 | 0.373869 | ||||||||
\(627\) | − 660184.i | − 0.0670650i | ||||||||
\(628\) | − 960239.i | − 0.0971583i | ||||||||
\(629\) | −1.23860e6 | −0.124826 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.79229e6 | 0.979063 | 0.489532 | − | 0.871986i | \(-0.337168\pi\) | ||||
0.489532 | + | 0.871986i | \(0.337168\pi\) | |||||||
\(632\) | 3.87834e6i | 0.386237i | ||||||||
\(633\) | 1.58722e7i | 1.57445i | ||||||||
\(634\) | 8.04335e6 | 0.794719 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.47795e6 | 0.537001 | ||||||||
\(637\) | − 4.84467e6i | − 0.473059i | ||||||||
\(638\) | 1.46925e7i | 1.42904i | ||||||||
\(639\) | −4.06711e6 | −0.394034 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.38154e6 | 0.325064 | 0.162532 | − | 0.986703i | \(-0.448034\pi\) | ||||
0.162532 | + | 0.986703i | \(0.448034\pi\) | |||||||
\(642\) | 5.37781e6i | 0.514953i | ||||||||
\(643\) | 3.04366e6i | 0.290314i | 0.989409 | + | 0.145157i | \(0.0463687\pi\) | ||||
−0.989409 | + | 0.145157i | \(0.953631\pi\) | |||||||
\(644\) | 1.00612e7 | 0.955954 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 52938.6 | 0.00499104 | ||||||||
\(647\) | 8.51735e6i | 0.799915i | 0.916534 | + | 0.399957i | \(0.130975\pi\) | ||||
−0.916534 | + | 0.399957i | \(0.869025\pi\) | |||||||
\(648\) | − 2.79192e6i | − 0.261195i | ||||||||
\(649\) | −2.35555e7 | −2.19524 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.18828e7 | −1.09892 | ||||||||
\(652\) | − 5.85461e6i | − 0.539360i | ||||||||
\(653\) | 8.83998e6i | 0.811275i | 0.914034 | + | 0.405638i | \(0.132950\pi\) | ||||
−0.914034 | + | 0.405638i | \(0.867050\pi\) | |||||||
\(654\) | 922425. | 0.0843309 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 245279. | 0.0222536 | ||||||||
\(657\) | 3.24603e6i | 0.293386i | ||||||||
\(658\) | 1.84351e7i | 1.65990i | ||||||||
\(659\) | 2.97807e6 | 0.267129 | 0.133564 | − | 0.991040i | \(-0.457358\pi\) | ||||
0.133564 | + | 0.991040i | \(0.457358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.90309e6 | −0.703548 | −0.351774 | − | 0.936085i | \(-0.614421\pi\) | ||||
−0.351774 | + | 0.936085i | \(0.614421\pi\) | |||||||
\(662\) | − 9.90860e6i | − 0.878754i | ||||||||
\(663\) | 379540.i | 0.0335331i | ||||||||
\(664\) | −169885. | −0.0149532 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.59186e6 | 0.139066 | ||||||||
\(667\) | − 1.84433e7i | − 1.60519i | ||||||||
\(668\) | − 1.07827e6i | − 0.0934948i | ||||||||
\(669\) | 1.92572e7 | 1.66352 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.59800e6 | −0.822952 | ||||||||
\(672\) | − 3.01590e6i | − 0.257629i | ||||||||
\(673\) | − 1.82522e7i | − 1.55338i | −0.629885 | − | 0.776688i | \(-0.716898\pi\) | ||||
0.629885 | − | 0.776688i | \(-0.283102\pi\) | |||||||
\(674\) | 1.02220e7 | 0.866734 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 456976. | 0.0384615 | ||||||||
\(677\) | 5.39380e6i | 0.452296i | 0.974093 | + | 0.226148i | \(0.0726134\pi\) | ||||
−0.974093 | + | 0.226148i | \(0.927387\pi\) | |||||||
\(678\) | 1.21185e7i | 1.01245i | ||||||||
\(679\) | 1.14820e7 | 0.955746 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.93762e7 | 1.60103 | ||||||||
\(682\) | 9.47789e6i | 0.780280i | ||||||||
\(683\) | − 2.30171e7i | − 1.88799i | −0.329963 | − | 0.943994i | \(-0.607036\pi\) | ||||
0.329963 | − | 0.943994i | \(-0.392964\pi\) | |||||||
\(684\) | −68037.4 | −0.00556042 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.01161e7 | −0.820733 | ||||||||
\(687\) | − 1.10025e7i | − 0.889406i | ||||||||
\(688\) | − 43431.6i | − 0.00349812i | ||||||||
\(689\) | 4.18936e6 | 0.336201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.87910e6 | 0.388727 | 0.194364 | − | 0.980930i | \(-0.437736\pi\) | ||||
0.194364 | + | 0.980930i | \(0.437736\pi\) | |||||||
\(692\) | 8.30274e6i | 0.659107i | ||||||||
\(693\) | 6.54302e6i | 0.517541i | ||||||||
\(694\) | −1.90000e6 | −0.149746 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.52847e6 | −0.432596 | ||||||||
\(697\) | 155795.i | 0.0121471i | ||||||||
\(698\) | 2.46111e6i | 0.191202i | ||||||||
\(699\) | −1.60178e7 | −1.23996 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.47820e7 | 1.13615 | 0.568077 | − | 0.822976i | \(-0.307688\pi\) | ||||
0.568077 | + | 0.822976i | \(0.307688\pi\) | |||||||
\(702\) | − 2.75656e6i | − 0.211118i | ||||||||
\(703\) | 619976.i | 0.0473137i | ||||||||
\(704\) | −2.40552e6 | −0.182927 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.74960e7 | 1.32107 | ||||||||
\(707\) | − 3.57305e7i | − 2.68838i | ||||||||
\(708\) | − 8.86343e6i | − 0.664536i | ||||||||
\(709\) | 2.75364e6 | 0.205727 | 0.102863 | − | 0.994695i | \(-0.467200\pi\) | ||||
0.102863 | + | 0.994695i | \(0.467200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.16603e6 | 0.234878 | ||||||||
\(712\) | − 526705.i | − 0.0389375i | ||||||||
\(713\) | − 1.18975e7i | − 0.876457i | ||||||||
\(714\) | 1.91563e6 | 0.140626 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.43566e6 | −0.104657 | ||||||||
\(717\) | − 9.49574e6i | − 0.689812i | ||||||||
\(718\) | 1.83825e7i | 1.33074i | ||||||||
\(719\) | 2.10250e7 | 1.51675 | 0.758373 | − | 0.651820i | \(-0.225994\pi\) | ||||
0.758373 | + | 0.651820i | \(0.225994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.60502e6 | 0.473191 | ||||||||
\(722\) | 9.87790e6i | 0.705215i | ||||||||
\(723\) | 5.40502e6i | 0.384549i | ||||||||
\(724\) | 6.02035e6 | 0.426850 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.01570e7 | −0.715196 | ||||||||
\(727\) | 2.21381e7i | 1.55347i | 0.629825 | + | 0.776737i | \(0.283127\pi\) | ||||
−0.629825 | + | 0.776737i | \(0.716873\pi\) | |||||||
\(728\) | − 2.30646e6i | − 0.161294i | ||||||||
\(729\) | −1.59648e7 | −1.11261 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27586.7 | 0.00190944 | ||||||||
\(732\) | − 3.61152e6i | − 0.249122i | ||||||||
\(733\) | − 1.23177e7i | − 0.846775i | −0.905949 | − | 0.423388i | \(-0.860841\pi\) | ||||
0.905949 | − | 0.423388i | \(-0.139159\pi\) | |||||||
\(734\) | −1.83745e7 | −1.25885 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.01962e6 | 0.205474 | ||||||||
\(737\) | 1.07838e7i | 0.731313i | ||||||||
\(738\) | − 200230.i | − 0.0135328i | ||||||||
\(739\) | 1.79039e7 | 1.20597 | 0.602986 | − | 0.797752i | \(-0.293977\pi\) | ||||
0.602986 | + | 0.797752i | \(0.293977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 189978. | 0.0127103 | ||||||||
\(742\) | − 2.11447e7i | − 1.40991i | ||||||||
\(743\) | 9.82085e6i | 0.652645i | 0.945258 | + | 0.326323i | \(0.105810\pi\) | ||||
−0.945258 | + | 0.326323i | \(0.894190\pi\) | |||||||
\(744\) | −3.56632e6 | −0.236204 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.97256e6 | −0.458717 | ||||||||
\(747\) | 138684.i | 0.00909334i | ||||||||
\(748\) | − 1.52793e6i | − 0.0998501i | ||||||||
\(749\) | 2.07581e7 | 1.35202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.04747e7 | 0.677705 | 0.338852 | − | 0.940840i | \(-0.389961\pi\) | ||||
0.338852 | + | 0.940840i | \(0.389961\pi\) | |||||||
\(752\) | 5.53282e6i | 0.356781i | ||||||||
\(753\) | − 1.30479e7i | − 0.838599i | ||||||||
\(754\) | −4.22800e6 | −0.270836 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.39130e7 | −0.885352 | ||||||||
\(757\) | 2.20487e7i | 1.39844i | 0.714908 | + | 0.699219i | \(0.246469\pi\) | ||||
−0.714908 | + | 0.699219i | \(0.753531\pi\) | |||||||
\(758\) | − 1.77012e7i | − 1.11900i | ||||||||
\(759\) | 2.39187e7 | 1.50707 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.75293e7 | −1.72319 | −0.861596 | − | 0.507594i | \(-0.830535\pi\) | ||||
−0.861596 | + | 0.507594i | \(0.830535\pi\) | |||||||
\(762\) | − 8.77040e6i | − 0.547182i | ||||||||
\(763\) | − 3.56052e6i | − 0.221413i | ||||||||
\(764\) | −3.30797e6 | −0.205035 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.59091e6 | −0.344279 | ||||||||
\(767\) | − 6.77846e6i | − 0.416047i | ||||||||
\(768\) | − 905143.i | − 0.0553751i | ||||||||
\(769\) | −1.50464e7 | −0.917525 | −0.458763 | − | 0.888559i | \(-0.651707\pi\) | ||||
−0.458763 | + | 0.888559i | \(0.651707\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.10501e6 | 0.248701 | ||||||||
\(772\) | − 6.60941e6i | − 0.399135i | ||||||||
\(773\) | − 2.28606e6i | − 0.137606i | −0.997630 | − | 0.0688031i | \(-0.978082\pi\) | ||||
0.997630 | − | 0.0688031i | \(-0.0219180\pi\) | |||||||
\(774\) | −35454.8 | −0.00212727 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.44601e6 | 0.205430 | ||||||||
\(777\) | 2.24344e7i | 1.33310i | ||||||||
\(778\) | 6.54142e6i | 0.387456i | ||||||||
\(779\) | 77982.8 | 0.00460421 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.57178e7 | −2.68199 | ||||||||
\(782\) | 1.91799e6i | 0.112158i | ||||||||
\(783\) | 2.55040e7i | 1.48663i | ||||||||
\(784\) | −7.33867e6 | −0.426410 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.87056e6 | −0.512147 | ||||||||
\(787\) | 9.89052e6i | 0.569223i | 0.958643 | + | 0.284611i | \(0.0918646\pi\) | ||||
−0.958643 | + | 0.284611i | \(0.908135\pi\) | |||||||
\(788\) | − 8.62121e6i | − 0.494598i | ||||||||
\(789\) | 2.11449e7 | 1.20924 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.67770e7 | 2.65822 | ||||||||
\(792\) | 1.96371e6i | 0.111241i | ||||||||
\(793\) | − 2.76197e6i | − 0.155968i | ||||||||
\(794\) | 1.96261e7 | 1.10480 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.35738e6 | −0.131870 | ||||||||
\(797\) | 2.93049e7i | 1.63416i | 0.576525 | + | 0.817080i | \(0.304408\pi\) | ||||
−0.576525 | + | 0.817080i | \(0.695592\pi\) | |||||||
\(798\) | − 958862.i | − 0.0533026i | ||||||||
\(799\) | −3.51431e6 | −0.194748 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −429969. | −0.0236786 | ||||||||
\(802\) | 3.80474e6i | 0.208876i | ||||||||
\(803\) | 3.64881e7i | 1.99693i | ||||||||
\(804\) | −4.05771e6 | −0.221381 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.72741e6 | −0.147881 | ||||||||
\(807\) | − 1.39327e7i | − 0.753095i | ||||||||
\(808\) | − 1.07236e7i | − 0.577845i | ||||||||
\(809\) | −1.02027e7 | −0.548078 | −0.274039 | − | 0.961719i | \(-0.588360\pi\) | ||||
−0.274039 | + | 0.961719i | \(0.588360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.26432e7 | −0.675001 | −0.337501 | − | 0.941325i | \(-0.609582\pi\) | ||||
−0.337501 | + | 0.941325i | \(0.609582\pi\) | |||||||
\(812\) | 2.13397e7i | 1.13579i | ||||||||
\(813\) | − 3.02639e7i | − 1.60582i | ||||||||
\(814\) | 1.78939e7 | 0.946551 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 574925. | 0.0302264 | ||||||||
\(817\) | − 13808.4i | 0 0.000723752i | ||||||||
\(818\) | 1.79786e7i | 0.939446i | ||||||||
\(819\) | −1.88285e6 | −0.0980858 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.56881e7 | −0.812294 | −0.406147 | − | 0.913808i | \(-0.633128\pi\) | ||||
−0.406147 | + | 0.913808i | \(0.633128\pi\) | |||||||
\(822\) | 1.63343e7i | 0.843183i | ||||||||
\(823\) | − 2.45799e7i | − 1.26497i | −0.774571 | − | 0.632487i | \(-0.782034\pi\) | ||||
0.774571 | − | 0.632487i | \(-0.217966\pi\) | |||||||
\(824\) | 1.98232e6 | 0.101708 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.42125e7 | −1.74475 | ||||||||
\(827\) | 3.62365e7i | 1.84239i | 0.389098 | + | 0.921197i | \(0.372787\pi\) | ||||
−0.389098 | + | 0.921197i | \(0.627213\pi\) | |||||||
\(828\) | − 2.46502e6i | − 0.124953i | ||||||||
\(829\) | 2.81815e7 | 1.42422 | 0.712110 | − | 0.702068i | \(-0.247740\pi\) | ||||
0.712110 | + | 0.702068i | \(0.247740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −247555. | −0.0124357 | ||||||||
\(832\) | − 692224.i | − 0.0346688i | ||||||||
\(833\) | − 4.66134e6i | − 0.232755i | ||||||||
\(834\) | 342388. | 0.0170453 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −764799. | −0.0378470 | ||||||||
\(837\) | 1.64522e7i | 0.811727i | ||||||||
\(838\) | − 3.31562e6i | − 0.163100i | ||||||||
\(839\) | 8.42806e6 | 0.413354 | 0.206677 | − | 0.978409i | \(-0.433735\pi\) | ||||
0.206677 | + | 0.978409i | \(0.433735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.86068e7 | 0.907155 | ||||||||
\(842\) | − 2.97925e6i | − 0.144820i | ||||||||
\(843\) | 3.32390e7i | 1.61094i | ||||||||
\(844\) | 1.83874e7 | 0.888515 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.51664e6 | 0.216965 | ||||||||
\(847\) | 3.92057e7i | 1.87776i | ||||||||
\(848\) | − 6.34601e6i | − 0.303048i | ||||||||
\(849\) | 1.89107e7 | 0.900404 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.24620e7 | −1.06322 | ||||||||
\(852\) | − 1.72026e7i | − 0.811886i | ||||||||
\(853\) | 3.10763e7i | 1.46237i | 0.682180 | + | 0.731184i | \(0.261032\pi\) | ||||
−0.682180 | + | 0.731184i | \(0.738968\pi\) | |||||||
\(854\) | −1.39403e7 | −0.654075 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.23000e6 | 0.290605 | ||||||||
\(857\) | − 5.72064e6i | − 0.266068i | −0.991111 | − | 0.133034i | \(-0.957528\pi\) | ||||
0.991111 | − | 0.133034i | \(-0.0424720\pi\) | |||||||
\(858\) | − 5.48318e6i | − 0.254281i | ||||||||
\(859\) | 6.04140e6 | 0.279354 | 0.139677 | − | 0.990197i | \(-0.455394\pi\) | ||||
0.139677 | + | 0.990197i | \(0.455394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.82187e6 | 0.129727 | ||||||||
\(862\) | 1.55812e7i | 0.714220i | ||||||||
\(863\) | − 2.09227e7i | − 0.956292i | −0.878280 | − | 0.478146i | \(-0.841309\pi\) | ||||
0.878280 | − | 0.478146i | \(-0.158691\pi\) | |||||||
\(864\) | −4.17562e6 | −0.190299 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.35319e7 | 1.06626 | ||||||||
\(867\) | − 1.92450e7i | − 0.869502i | ||||||||
\(868\) | 1.37658e7i | 0.620160i | ||||||||
\(869\) | 3.55889e7 | 1.59869 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.10320e6 | −0.138601 | ||||||||
\(872\) | − 1.06860e6i | − 0.0475908i | ||||||||
\(873\) | − 2.81311e6i | − 0.124925i | ||||||||
\(874\) | 960042. | 0.0425120 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.37297e7 | −0.604505 | ||||||||
\(877\) | − 5.01539e6i | − 0.220194i | −0.993921 | − | 0.110097i | \(-0.964884\pi\) | ||||
0.993921 | − | 0.110097i | \(-0.0351162\pi\) | |||||||
\(878\) | 6.92097e6i | 0.302992i | ||||||||
\(879\) | 5.39541e6 | 0.235533 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.14791e7 | −0.932346 | −0.466173 | − | 0.884694i | \(-0.654368\pi\) | ||||
−0.466173 | + | 0.884694i | \(0.654368\pi\) | |||||||
\(882\) | 5.99082e6i | 0.259307i | ||||||||
\(883\) | − 996549.i | − 0.0430127i | −0.999769 | − | 0.0215064i | \(-0.993154\pi\) | ||||
0.999769 | − | 0.0215064i | \(-0.00684621\pi\) | |||||||
\(884\) | 439684. | 0.0189239 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 425728. | 0.0182200 | ||||||||
\(887\) | 4.67336e6i | 0.199444i | 0.995015 | + | 0.0997219i | \(0.0317953\pi\) | ||||
−0.995015 | + | 0.0997219i | \(0.968205\pi\) | |||||||
\(888\) | 6.73308e6i | 0.286537i | ||||||||
\(889\) | −3.38534e7 | −1.43664 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.56196e7 | −1.08113 | ||||||||
\(892\) | − 2.23088e7i | − 0.938782i | ||||||||
\(893\) | 1.75908e6i | 0.0738170i | ||||||||
\(894\) | −2.04980e7 | −0.857762 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.49382e6 | −0.145388 | ||||||||
\(897\) | 6.88297e6i | 0.285624i | ||||||||
\(898\) | − 1.95688e7i | − 0.809792i | ||||||||
\(899\) | 2.52343e7 | 1.04134 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.03083e6 | 0.165418 | ||||||||
\(902\) | − 2.25076e6i | − 0.0921112i | ||||||||
\(903\) | − 499670.i | − 0.0203922i | ||||||||
\(904\) | 1.40389e7 | 0.571362 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.80847e7 | 1.13671 | ||||||||
\(907\) | 1.18130e7i | 0.476807i | 0.971166 | + | 0.238403i | \(0.0766240\pi\) | ||||
−0.971166 | + | 0.238403i | \(0.923376\pi\) | |||||||
\(908\) | − 2.24466e7i | − 0.903515i | ||||||||
\(909\) | −8.75405e6 | −0.351398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.55560e7 | 1.41944 | 0.709721 | − | 0.704483i | \(-0.248821\pi\) | ||||
0.709721 | + | 0.704483i | \(0.248821\pi\) | |||||||
\(912\) | − 287777.i | − 0.0114569i | ||||||||
\(913\) | 1.55892e6i | 0.0618938i | ||||||||
\(914\) | 709006. | 0.0280727 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.27460e7 | −0.501922 | ||||||||
\(917\) | 3.42400e7i | 1.34465i | ||||||||
\(918\) | − 2.65225e6i | − 0.103874i | ||||||||
\(919\) | −2.66902e7 | −1.04247 | −0.521235 | − | 0.853413i | \(-0.674528\pi\) | ||||
−0.521235 | + | 0.853413i | \(0.674528\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.82478e6 | 0.303965 | ||||||||
\(922\) | − 2.86270e7i | − 1.10905i | ||||||||
\(923\) | − 1.31560e7i | − 0.508299i | ||||||||
\(924\) | −2.76749e7 | −1.06637 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.37691e7 | −0.527690 | ||||||||
\(927\) | − 1.61824e6i | − 0.0618507i | ||||||||
\(928\) | 6.40454e6i | 0.244128i | ||||||||
\(929\) | 3.08229e7 | 1.17175 | 0.585874 | − | 0.810402i | \(-0.300751\pi\) | ||||
0.585874 | + | 0.810402i | \(0.300751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.33322e6 | −0.0882230 | ||||||||
\(932\) | 1.85560e7i | 0.699753i | ||||||||
\(933\) | − 1.21711e7i | − 0.457749i | ||||||||
\(934\) | −3.68994e7 | −1.38405 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −565088. | −0.0210827 | ||||||||
\(937\) | 2.78462e7i | 1.03613i | 0.855340 | + | 0.518067i | \(0.173348\pi\) | ||||
−0.855340 | + | 0.518067i | \(0.826652\pi\) | |||||||
\(938\) | 1.56626e7i | 0.581241i | ||||||||
\(939\) | 1.26571e7 | 0.468456 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.80836e7 | 1.03390 | 0.516950 | − | 0.856016i | \(-0.327067\pi\) | ||||
0.516950 | + | 0.856016i | \(0.327067\pi\) | |||||||
\(942\) | − 3.31556e6i | − 0.121739i | ||||||||
\(943\) | 2.82535e6i | 0.103465i | ||||||||
\(944\) | −1.02680e7 | −0.375020 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −398543. | −0.0144793 | ||||||||
\(947\) | − 4.49006e7i | − 1.62696i | −0.581592 | − | 0.813481i | \(-0.697570\pi\) | ||||
0.581592 | − | 0.813481i | \(-0.302430\pi\) | |||||||
\(948\) | 1.33913e7i | 0.483953i | ||||||||
\(949\) | −1.05000e7 | −0.378463 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.77724e7 | 0.995779 | ||||||||
\(952\) | − 2.21919e6i | − 0.0793600i | ||||||||
\(953\) | 1.13992e7i | 0.406577i | 0.979119 | + | 0.203289i | \(0.0651630\pi\) | ||||
−0.979119 | + | 0.203289i | \(0.934837\pi\) | |||||||
\(954\) | −5.18048e6 | −0.184289 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.10005e7 | −0.389284 | ||||||||
\(957\) | 5.07311e7i | 1.79058i | ||||||||
\(958\) | 4.93322e6i | 0.173667i | ||||||||
\(959\) | 6.30498e7 | 2.21380 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.23510e7 | −0.431412 | ||||||||
\(962\) | 5.14924e6i | 0.179393i | ||||||||
\(963\) | − 5.08578e6i | − 0.176722i | ||||||||
\(964\) | 6.26152e6 | 0.217014 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.47399e7 | 1.19781 | ||||||||
\(967\) | − 5.54751e7i | − 1.90780i | −0.300130 | − | 0.953898i | \(-0.597030\pi\) | ||||
0.300130 | − | 0.953898i | \(-0.402970\pi\) | |||||||
\(968\) | 1.17665e7i | 0.403609i | ||||||||
\(969\) | 182789. | 0.00625375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.45562e6 | −0.0835819 | −0.0417910 | − | 0.999126i | \(-0.513306\pi\) | ||||
−0.0417910 | + | 0.999126i | \(0.513306\pi\) | |||||||
\(972\) | 6.21423e6i | 0.210970i | ||||||||
\(973\) | − 1.32160e6i | − 0.0447527i | ||||||||
\(974\) | −2.48510e7 | −0.839358 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.18381e6 | −0.140588 | ||||||||
\(977\) | 3.31344e7i | 1.11056i | 0.831663 | + | 0.555280i | \(0.187389\pi\) | ||||
−0.831663 | + | 0.555280i | \(0.812611\pi\) | |||||||
\(978\) | − 2.02151e7i | − 0.675815i | ||||||||
\(979\) | −4.83322e6 | −0.161168 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −872335. | −0.0289408 | ||||||||
\(982\) | 2.82088e7i | 0.933483i | ||||||||
\(983\) | 4.46461e7i | 1.47367i | 0.676073 | + | 0.736834i | \(0.263680\pi\) | ||||
−0.676073 | + | 0.736834i | \(0.736320\pi\) | |||||||
\(984\) | 846911. | 0.0278837 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.06801e6 | −0.133257 | ||||||||
\(987\) | 6.36537e7i | 2.07985i | ||||||||
\(988\) | − 220082.i | − 0.00717287i | ||||||||
\(989\) | 500285. | 0.0162640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.99797e7 | 1.61662 | 0.808312 | − | 0.588754i | \(-0.200381\pi\) | ||||
0.808312 | + | 0.588754i | \(0.200381\pi\) | |||||||
\(992\) | 4.13145e6i | 0.133298i | ||||||||
\(993\) | − 3.42129e7i | − 1.10107i | ||||||||
\(994\) | −6.64013e7 | −2.13162 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −586588. | −0.0187363 | ||||||||
\(997\) | − 1.25647e7i | − 0.400326i | −0.979763 | − | 0.200163i | \(-0.935853\pi\) | ||||
0.979763 | − | 0.200163i | \(-0.0641472\pi\) | |||||||
\(998\) | 2.25204e7i | 0.715730i | ||||||||
\(999\) | 3.10611e7 | 0.984699 |
(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 | 650.6.b.g.599.1 | 4 | ||
5.2 | odd | 4 | 650.6.a.h.1.1 | 2 | |||
5.3 | odd | 4 | 130.6.a.a.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 650.6.b.g.599.4 | 4 | ||
20.3 | even | 4 | 1040.6.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.6.a.a.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
650.6.a.h.1.1 | 2 | 5.2 | odd | 4 | |||
650.6.b.g.599.1 | 4 | 1.1 | even | 1 | trivial | ||
650.6.b.g.599.4 | 4 | 5.4 | even | 2 | inner | ||
1040.6.a.e.1.1 | 2 | 20.3 | even | 4 |