Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [130,6,Mod(1,130)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(130, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("130.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.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: | \(20.8498965757\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 13.8114 | 0.886001 | 0.443000 | − | 0.896521i | \(-0.353914\pi\) | ||||
0.443000 | + | 0.896521i | \(0.353914\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −55.2456 | −0.626497 | ||||||||
\(7\) | 213.246 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −52.2456 | −0.215002 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 587.285 | 1.46341 | 0.731707 | − | 0.681620i | \(-0.238724\pi\) | ||||
0.731707 | + | 0.681620i | \(0.238724\pi\) | |||||||
\(12\) | 220.982 | 0.443000 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | −852.982 | −1.16311 | ||||||||
\(15\) | 345.285 | 0.396232 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 162.605 | 0.136462 | 0.0682310 | − | 0.997670i | \(-0.478265\pi\) | ||||
0.0682310 | + | 0.997670i | \(0.478265\pi\) | |||||||
\(18\) | 208.982 | 0.152030 | ||||||||
\(19\) | −81.3914 | −0.0517243 | −0.0258622 | − | 0.999666i | \(-0.508233\pi\) | ||||
−0.0258622 | + | 0.999666i | \(0.508233\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 2945.22 | 1.45737 | ||||||||
\(22\) | −2349.14 | −1.03479 | ||||||||
\(23\) | −2948.84 | −1.16234 | −0.581169 | − | 0.813783i | \(-0.697404\pi\) | ||||
−0.581169 | + | 0.813783i | \(0.697404\pi\) | |||||||
\(24\) | −883.929 | −0.313249 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 676.000 | 0.196116 | ||||||||
\(27\) | −4077.75 | −1.07649 | ||||||||
\(28\) | 3411.93 | 0.822441 | ||||||||
\(29\) | 6254.43 | 1.38100 | 0.690499 | − | 0.723333i | \(-0.257391\pi\) | ||||
0.690499 | + | 0.723333i | \(0.257391\pi\) | |||||||
\(30\) | −1381.14 | −0.280178 | ||||||||
\(31\) | −4034.62 | −0.754048 | −0.377024 | − | 0.926204i | \(-0.623052\pi\) | ||||
−0.377024 | + | 0.926204i | \(0.623052\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 8111.22 | 1.29659 | ||||||||
\(34\) | −650.420 | −0.0964932 | ||||||||
\(35\) | 5331.14 | 0.735614 | ||||||||
\(36\) | −835.929 | −0.107501 | ||||||||
\(37\) | 7617.22 | 0.914728 | 0.457364 | − | 0.889280i | \(-0.348794\pi\) | ||||
0.457364 | + | 0.889280i | \(0.348794\pi\) | |||||||
\(38\) | 325.566 | 0.0365746 | ||||||||
\(39\) | −2334.12 | −0.245732 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | 958.121 | 0.0890145 | 0.0445072 | − | 0.999009i | \(-0.485828\pi\) | ||||
0.0445072 | + | 0.999009i | \(0.485828\pi\) | |||||||
\(42\) | −11780.9 | −1.03051 | ||||||||
\(43\) | 169.655 | 0.0139925 | 0.00699624 | − | 0.999976i | \(-0.497773\pi\) | ||||
0.00699624 | + | 0.999976i | \(0.497773\pi\) | |||||||
\(44\) | 9396.56 | 0.731707 | ||||||||
\(45\) | −1306.14 | −0.0961519 | ||||||||
\(46\) | 11795.4 | 0.821897 | ||||||||
\(47\) | 21612.6 | 1.42712 | 0.713562 | − | 0.700592i | \(-0.247081\pi\) | ||||
0.713562 | + | 0.700592i | \(0.247081\pi\) | |||||||
\(48\) | 3535.72 | 0.221500 | ||||||||
\(49\) | 28666.7 | 1.70564 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 2245.80 | 0.120905 | ||||||||
\(52\) | −2704.00 | −0.138675 | ||||||||
\(53\) | 24789.1 | 1.21219 | 0.606096 | − | 0.795392i | \(-0.292735\pi\) | ||||
0.606096 | + | 0.795392i | \(0.292735\pi\) | |||||||
\(54\) | 16311.0 | 0.761196 | ||||||||
\(55\) | 14682.1 | 0.654458 | ||||||||
\(56\) | −13647.7 | −0.581554 | ||||||||
\(57\) | −1124.13 | −0.0458278 | ||||||||
\(58\) | −25017.7 | −0.976513 | ||||||||
\(59\) | 40109.2 | 1.50008 | 0.750040 | − | 0.661392i | \(-0.230034\pi\) | ||||
0.750040 | + | 0.661392i | \(0.230034\pi\) | |||||||
\(60\) | 5524.56 | 0.198116 | ||||||||
\(61\) | −16343.0 | −0.562351 | −0.281176 | − | 0.959656i | \(-0.590724\pi\) | ||||
−0.281176 | + | 0.959656i | \(0.590724\pi\) | |||||||
\(62\) | 16138.5 | 0.533192 | ||||||||
\(63\) | −11141.1 | −0.353653 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −4225.00 | −0.124035 | ||||||||
\(66\) | −32444.9 | −0.916824 | ||||||||
\(67\) | 18362.1 | 0.499731 | 0.249866 | − | 0.968281i | \(-0.419614\pi\) | ||||
0.249866 | + | 0.968281i | \(0.419614\pi\) | |||||||
\(68\) | 2601.68 | 0.0682310 | ||||||||
\(69\) | −40727.6 | −1.02983 | ||||||||
\(70\) | −21324.6 | −0.520158 | ||||||||
\(71\) | −77846.0 | −1.83270 | −0.916348 | − | 0.400382i | \(-0.868877\pi\) | ||||
−0.916348 | + | 0.400382i | \(0.868877\pi\) | |||||||
\(72\) | 3343.72 | 0.0760148 | ||||||||
\(73\) | −62130.2 | −1.36457 | −0.682285 | − | 0.731087i | \(-0.739014\pi\) | ||||
−0.682285 | + | 0.731087i | \(0.739014\pi\) | |||||||
\(74\) | −30468.9 | −0.646810 | ||||||||
\(75\) | 8632.12 | 0.177200 | ||||||||
\(76\) | −1302.26 | −0.0258622 | ||||||||
\(77\) | 125236. | 2.40714 | ||||||||
\(78\) | 9336.50 | 0.173759 | ||||||||
\(79\) | −60599.1 | −1.09244 | −0.546221 | − | 0.837641i | \(-0.683934\pi\) | ||||
−0.546221 | + | 0.837641i | \(0.683934\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | −43623.7 | −0.738772 | ||||||||
\(82\) | −3832.48 | −0.0629427 | ||||||||
\(83\) | −2654.46 | −0.0422941 | −0.0211471 | − | 0.999776i | \(-0.506732\pi\) | ||||
−0.0211471 | + | 0.999776i | \(0.506732\pi\) | |||||||
\(84\) | 47123.5 | 0.728684 | ||||||||
\(85\) | 4065.12 | 0.0610276 | ||||||||
\(86\) | −678.619 | −0.00989418 | ||||||||
\(87\) | 86382.4 | 1.22357 | ||||||||
\(88\) | −37586.2 | −0.517395 | ||||||||
\(89\) | 8229.77 | 0.110132 | 0.0550659 | − | 0.998483i | \(-0.482463\pi\) | ||||
0.0550659 | + | 0.998483i | \(0.482463\pi\) | |||||||
\(90\) | 5224.56 | 0.0679897 | ||||||||
\(91\) | −36038.5 | −0.456208 | ||||||||
\(92\) | −47181.5 | −0.581169 | ||||||||
\(93\) | −55723.7 | −0.668087 | ||||||||
\(94\) | −86450.3 | −1.00913 | ||||||||
\(95\) | −2034.79 | −0.0231318 | ||||||||
\(96\) | −14142.9 | −0.156624 | ||||||||
\(97\) | −53844.0 | −0.581042 | −0.290521 | − | 0.956869i | \(-0.593829\pi\) | ||||
−0.290521 | + | 0.956869i | \(0.593829\pi\) | |||||||
\(98\) | −114667. | −1.20607 | ||||||||
\(99\) | −30683.0 | −0.314637 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −167556. | −1.63439 | −0.817196 | − | 0.576360i | \(-0.804473\pi\) | ||||
−0.817196 | + | 0.576360i | \(0.804473\pi\) | |||||||
\(102\) | −8983.20 | −0.0854930 | ||||||||
\(103\) | 30973.8 | 0.287675 | 0.143837 | − | 0.989601i | \(-0.454056\pi\) | ||||
0.143837 | + | 0.989601i | \(0.454056\pi\) | |||||||
\(104\) | 10816.0 | 0.0980581 | ||||||||
\(105\) | 73630.4 | 0.651755 | ||||||||
\(106\) | −99156.4 | −0.857149 | ||||||||
\(107\) | −97343.8 | −0.821956 | −0.410978 | − | 0.911645i | \(-0.634813\pi\) | ||||
−0.410978 | + | 0.911645i | \(0.634813\pi\) | |||||||
\(108\) | −65244.0 | −0.538247 | ||||||||
\(109\) | 16696.8 | 0.134607 | 0.0673035 | − | 0.997733i | \(-0.478560\pi\) | ||||
0.0673035 | + | 0.997733i | \(0.478560\pi\) | |||||||
\(110\) | −58728.5 | −0.462772 | ||||||||
\(111\) | 105204. | 0.810450 | ||||||||
\(112\) | 54590.9 | 0.411221 | ||||||||
\(113\) | 219357. | 1.61605 | 0.808027 | − | 0.589145i | \(-0.200535\pi\) | ||||
0.808027 | + | 0.589145i | \(0.200535\pi\) | |||||||
\(114\) | 4496.51 | 0.0324051 | ||||||||
\(115\) | −73721.1 | −0.519813 | ||||||||
\(116\) | 100071. | 0.690499 | ||||||||
\(117\) | 8829.50 | 0.0596309 | ||||||||
\(118\) | −160437. | −1.06072 | ||||||||
\(119\) | 34674.8 | 0.224464 | ||||||||
\(120\) | −22098.2 | −0.140089 | ||||||||
\(121\) | 183852. | 1.14158 | ||||||||
\(122\) | 65372.1 | 0.397642 | ||||||||
\(123\) | 13233.0 | 0.0788669 | ||||||||
\(124\) | −64554.0 | −0.377024 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 44564.5 | 0.250071 | ||||||||
\(127\) | 158753. | 0.873399 | 0.436700 | − | 0.899607i | \(-0.356147\pi\) | ||||
0.436700 | + | 0.899607i | \(0.356147\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 2343.17 | 0.0123974 | ||||||||
\(130\) | 16900.0 | 0.0877058 | ||||||||
\(131\) | 160566. | 0.817477 | 0.408739 | − | 0.912651i | \(-0.365969\pi\) | ||||
0.408739 | + | 0.912651i | \(0.365969\pi\) | |||||||
\(132\) | 129779. | 0.648293 | ||||||||
\(133\) | −17356.4 | −0.0850804 | ||||||||
\(134\) | −73448.6 | −0.353363 | ||||||||
\(135\) | −101944. | −0.481422 | ||||||||
\(136\) | −10406.7 | −0.0482466 | ||||||||
\(137\) | −295668. | −1.34587 | −0.672934 | − | 0.739702i | \(-0.734966\pi\) | ||||
−0.672934 | + | 0.739702i | \(0.734966\pi\) | |||||||
\(138\) | 162910. | 0.728201 | ||||||||
\(139\) | 6197.57 | 0.0272072 | 0.0136036 | − | 0.999907i | \(-0.495670\pi\) | ||||
0.0136036 | + | 0.999907i | \(0.495670\pi\) | |||||||
\(140\) | 85298.2 | 0.367807 | ||||||||
\(141\) | 298500. | 1.26443 | ||||||||
\(142\) | 311384. | 1.29591 | ||||||||
\(143\) | −99251.1 | −0.405878 | ||||||||
\(144\) | −13374.9 | −0.0537506 | ||||||||
\(145\) | 156361. | 0.617601 | ||||||||
\(146\) | 248521. | 0.964896 | ||||||||
\(147\) | 395926. | 1.51120 | ||||||||
\(148\) | 121875. | 0.457364 | ||||||||
\(149\) | −371033. | −1.36914 | −0.684569 | − | 0.728948i | \(-0.740010\pi\) | ||||
−0.684569 | + | 0.728948i | \(0.740010\pi\) | |||||||
\(150\) | −34528.5 | −0.125299 | ||||||||
\(151\) | −508361. | −1.81439 | −0.907193 | − | 0.420714i | \(-0.861780\pi\) | ||||
−0.907193 | + | 0.420714i | \(0.861780\pi\) | |||||||
\(152\) | 5209.05 | 0.0182873 | ||||||||
\(153\) | −8495.39 | −0.0293396 | ||||||||
\(154\) | −500943. | −1.70211 | ||||||||
\(155\) | −100866. | −0.337220 | ||||||||
\(156\) | −37346.0 | −0.122866 | ||||||||
\(157\) | 60014.9 | 0.194317 | 0.0971583 | − | 0.995269i | \(-0.469025\pi\) | ||||
0.0971583 | + | 0.995269i | \(0.469025\pi\) | |||||||
\(158\) | 242397. | 0.772474 | ||||||||
\(159\) | 342372. | 1.07400 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −628828. | −1.91191 | ||||||||
\(162\) | 174495. | 0.522391 | ||||||||
\(163\) | −365913. | −1.07872 | −0.539360 | − | 0.842075i | \(-0.681334\pi\) | ||||
−0.539360 | + | 0.842075i | \(0.681334\pi\) | |||||||
\(164\) | 15329.9 | 0.0445072 | ||||||||
\(165\) | 202780. | 0.579851 | ||||||||
\(166\) | 10617.8 | 0.0299065 | ||||||||
\(167\) | 67392.0 | 0.186990 | 0.0934948 | − | 0.995620i | \(-0.470196\pi\) | ||||
0.0934948 | + | 0.995620i | \(0.470196\pi\) | |||||||
\(168\) | −188494. | −0.515257 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | −16260.5 | −0.0431531 | ||||||||
\(171\) | 4252.34 | 0.0111208 | ||||||||
\(172\) | 2714.48 | 0.00699624 | ||||||||
\(173\) | 518921. | 1.31821 | 0.659107 | − | 0.752049i | \(-0.270934\pi\) | ||||
0.659107 | + | 0.752049i | \(0.270934\pi\) | |||||||
\(174\) | −345530. | −0.865191 | ||||||||
\(175\) | 133278. | 0.328977 | ||||||||
\(176\) | 150345. | 0.365853 | ||||||||
\(177\) | 553964. | 1.32907 | ||||||||
\(178\) | −32919.1 | −0.0778750 | ||||||||
\(179\) | −89728.6 | −0.209314 | −0.104657 | − | 0.994508i | \(-0.533374\pi\) | ||||
−0.104657 | + | 0.994508i | \(0.533374\pi\) | |||||||
\(180\) | −20898.2 | −0.0480760 | ||||||||
\(181\) | −376272. | −0.853700 | −0.426850 | − | 0.904322i | \(-0.640377\pi\) | ||||
−0.426850 | + | 0.904322i | \(0.640377\pi\) | |||||||
\(182\) | 144154. | 0.322588 | ||||||||
\(183\) | −225720. | −0.498244 | ||||||||
\(184\) | 188726. | 0.410948 | ||||||||
\(185\) | 190430. | 0.409079 | ||||||||
\(186\) | 222895. | 0.472409 | ||||||||
\(187\) | 95495.4 | 0.199700 | ||||||||
\(188\) | 345801. | 0.713562 | ||||||||
\(189\) | −869562. | −1.77070 | ||||||||
\(190\) | 8139.14 | 0.0163567 | ||||||||
\(191\) | 206748. | 0.410070 | 0.205035 | − | 0.978755i | \(-0.434269\pi\) | ||||
0.205035 | + | 0.978755i | \(0.434269\pi\) | |||||||
\(192\) | 56571.4 | 0.110750 | ||||||||
\(193\) | −413088. | −0.798269 | −0.399135 | − | 0.916892i | \(-0.630689\pi\) | ||||
−0.399135 | + | 0.916892i | \(0.630689\pi\) | |||||||
\(194\) | 215376. | 0.410859 | ||||||||
\(195\) | −58353.1 | −0.109895 | ||||||||
\(196\) | 458667. | 0.852819 | ||||||||
\(197\) | 538825. | 0.989196 | 0.494598 | − | 0.869122i | \(-0.335315\pi\) | ||||
0.494598 | + | 0.869122i | \(0.335315\pi\) | |||||||
\(198\) | 122732. | 0.222482 | ||||||||
\(199\) | −147336. | −0.263740 | −0.131870 | − | 0.991267i | \(-0.542098\pi\) | ||||
−0.131870 | + | 0.991267i | \(0.542098\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 253607. | 0.442762 | ||||||||
\(202\) | 670223. | 1.15569 | ||||||||
\(203\) | 1.33373e6 | 2.27158 | ||||||||
\(204\) | 35932.8 | 0.0604527 | ||||||||
\(205\) | 23953.0 | 0.0398085 | ||||||||
\(206\) | −123895. | −0.203417 | ||||||||
\(207\) | 154064. | 0.249905 | ||||||||
\(208\) | −43264.0 | −0.0693375 | ||||||||
\(209\) | −47799.9 | −0.0756940 | ||||||||
\(210\) | −294522. | −0.460860 | ||||||||
\(211\) | −1.14921e6 | −1.77703 | −0.888515 | − | 0.458847i | \(-0.848262\pi\) | ||||
−0.888515 | + | 0.458847i | \(0.848262\pi\) | |||||||
\(212\) | 396626. | 0.606096 | ||||||||
\(213\) | −1.07516e6 | −1.62377 | ||||||||
\(214\) | 389375. | 0.581211 | ||||||||
\(215\) | 4241.37 | 0.00625763 | ||||||||
\(216\) | 260976. | 0.380598 | ||||||||
\(217\) | −860365. | −1.24032 | ||||||||
\(218\) | −66787.3 | −0.0951815 | ||||||||
\(219\) | −858104. | −1.20901 | ||||||||
\(220\) | 234914. | 0.327229 | ||||||||
\(221\) | −27480.2 | −0.0378477 | ||||||||
\(222\) | −420817. | −0.573075 | ||||||||
\(223\) | −1.39430e6 | −1.87756 | −0.938782 | − | 0.344513i | \(-0.888044\pi\) | ||||
−0.938782 | + | 0.344513i | \(0.888044\pi\) | |||||||
\(224\) | −218363. | −0.290777 | ||||||||
\(225\) | −32653.5 | −0.0430005 | ||||||||
\(226\) | −877429. | −1.14272 | ||||||||
\(227\) | 1.40291e6 | 1.80703 | 0.903515 | − | 0.428556i | \(-0.140977\pi\) | ||||
0.903515 | + | 0.428556i | \(0.140977\pi\) | |||||||
\(228\) | −17986.1 | −0.0229139 | ||||||||
\(229\) | −796626. | −1.00384 | −0.501922 | − | 0.864913i | \(-0.667373\pi\) | ||||
−0.501922 | + | 0.864913i | \(0.667373\pi\) | |||||||
\(230\) | 294884. | 0.367563 | ||||||||
\(231\) | 1.72968e6 | 2.13273 | ||||||||
\(232\) | −400284. | −0.488257 | ||||||||
\(233\) | 1.15975e6 | 1.39951 | 0.699753 | − | 0.714385i | \(-0.253293\pi\) | ||||
0.699753 | + | 0.714385i | \(0.253293\pi\) | |||||||
\(234\) | −35318.0 | −0.0421654 | ||||||||
\(235\) | 540314. | 0.638230 | ||||||||
\(236\) | 641748. | 0.750040 | ||||||||
\(237\) | −836958. | −0.967905 | ||||||||
\(238\) | −138699. | −0.158720 | ||||||||
\(239\) | −687529. | −0.778568 | −0.389284 | − | 0.921118i | \(-0.627278\pi\) | ||||
−0.389284 | + | 0.921118i | \(0.627278\pi\) | |||||||
\(240\) | 88392.9 | 0.0990579 | ||||||||
\(241\) | −391345. | −0.434028 | −0.217014 | − | 0.976169i | \(-0.569632\pi\) | ||||
−0.217014 | + | 0.976169i | \(0.569632\pi\) | |||||||
\(242\) | −735409. | −0.807218 | ||||||||
\(243\) | 388389. | 0.421941 | ||||||||
\(244\) | −261488. | −0.281176 | ||||||||
\(245\) | 716667. | 0.762785 | ||||||||
\(246\) | −52931.9 | −0.0557673 | ||||||||
\(247\) | 13755.2 | 0.0143457 | ||||||||
\(248\) | 258216. | 0.266596 | ||||||||
\(249\) | −36661.7 | −0.0374727 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | 944723. | 0.946499 | 0.473249 | − | 0.880928i | \(-0.343081\pi\) | ||||
0.473249 | + | 0.880928i | \(0.343081\pi\) | |||||||
\(252\) | −178258. | −0.176827 | ||||||||
\(253\) | −1.73181e6 | −1.70098 | ||||||||
\(254\) | −635012. | −0.617587 | ||||||||
\(255\) | 56145.0 | 0.0540705 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 297219. | 0.280701 | 0.140351 | − | 0.990102i | \(-0.455177\pi\) | ||||
0.140351 | + | 0.990102i | \(0.455177\pi\) | |||||||
\(258\) | −9372.67 | −0.00876626 | ||||||||
\(259\) | 1.62434e6 | 1.50462 | ||||||||
\(260\) | −67600.0 | −0.0620174 | ||||||||
\(261\) | −326766. | −0.296918 | ||||||||
\(262\) | −642264. | −0.578044 | ||||||||
\(263\) | −1.53097e6 | −1.36483 | −0.682414 | − | 0.730966i | \(-0.739070\pi\) | ||||
−0.682414 | + | 0.730966i | \(0.739070\pi\) | |||||||
\(264\) | −519118. | −0.458412 | ||||||||
\(265\) | 619728. | 0.542109 | ||||||||
\(266\) | 69425.4 | 0.0601609 | ||||||||
\(267\) | 113665. | 0.0975769 | ||||||||
\(268\) | 293794. | 0.249866 | ||||||||
\(269\) | −1.00878e6 | −0.849994 | −0.424997 | − | 0.905195i | \(-0.639725\pi\) | ||||
−0.424997 | + | 0.905195i | \(0.639725\pi\) | |||||||
\(270\) | 407775. | 0.340417 | ||||||||
\(271\) | 2.19122e6 | 1.81244 | 0.906220 | − | 0.422806i | \(-0.138955\pi\) | ||||
0.906220 | + | 0.422806i | \(0.138955\pi\) | |||||||
\(272\) | 41626.9 | 0.0341155 | ||||||||
\(273\) | −497742. | −0.404201 | ||||||||
\(274\) | 1.18267e6 | 0.951673 | ||||||||
\(275\) | 367053. | 0.292683 | ||||||||
\(276\) | −651642. | −0.514916 | ||||||||
\(277\) | −17924.0 | −0.0140357 | −0.00701786 | − | 0.999975i | \(-0.502234\pi\) | ||||
−0.00701786 | + | 0.999975i | \(0.502234\pi\) | |||||||
\(278\) | −24790.3 | −0.0192384 | ||||||||
\(279\) | 210791. | 0.162122 | ||||||||
\(280\) | −341193. | −0.260079 | ||||||||
\(281\) | −2.40663e6 | −1.81821 | −0.909106 | − | 0.416566i | \(-0.863234\pi\) | ||||
−0.909106 | + | 0.416566i | \(0.863234\pi\) | |||||||
\(282\) | −1.19400e6 | −0.894090 | ||||||||
\(283\) | −1.36921e6 | −1.01626 | −0.508128 | − | 0.861281i | \(-0.669662\pi\) | ||||
−0.508128 | + | 0.861281i | \(0.669662\pi\) | |||||||
\(284\) | −1.24554e6 | −0.916348 | ||||||||
\(285\) | −28103.2 | −0.0204948 | ||||||||
\(286\) | 397004. | 0.286999 | ||||||||
\(287\) | 204315. | 0.146418 | ||||||||
\(288\) | 53499.4 | 0.0380074 | ||||||||
\(289\) | −1.39342e6 | −0.981378 | ||||||||
\(290\) | −625443. | −0.436710 | ||||||||
\(291\) | −743660. | −0.514804 | ||||||||
\(292\) | −994083. | −0.682285 | ||||||||
\(293\) | −390649. | −0.265838 | −0.132919 | − | 0.991127i | \(-0.542435\pi\) | ||||
−0.132919 | + | 0.991127i | \(0.542435\pi\) | |||||||
\(294\) | −1.58371e6 | −1.06858 | ||||||||
\(295\) | 1.00273e6 | 0.670856 | ||||||||
\(296\) | −487502. | −0.323405 | ||||||||
\(297\) | −2.39480e6 | −1.57535 | ||||||||
\(298\) | 1.48413e6 | 0.968127 | ||||||||
\(299\) | 498355. | 0.322374 | ||||||||
\(300\) | 138114. | 0.0886001 | ||||||||
\(301\) | 36178.1 | 0.0230160 | ||||||||
\(302\) | 2.03344e6 | 1.28297 | ||||||||
\(303\) | −2.31418e6 | −1.44807 | ||||||||
\(304\) | −20836.2 | −0.0129311 | ||||||||
\(305\) | −408575. | −0.251491 | ||||||||
\(306\) | 33981.6 | 0.0207463 | ||||||||
\(307\) | 566546. | 0.343075 | 0.171537 | − | 0.985178i | \(-0.445127\pi\) | ||||
0.171537 | + | 0.985178i | \(0.445127\pi\) | |||||||
\(308\) | 2.00377e6 | 1.20357 | ||||||||
\(309\) | 427791. | 0.254880 | ||||||||
\(310\) | 403462. | 0.238451 | ||||||||
\(311\) | 881239. | 0.516646 | 0.258323 | − | 0.966059i | \(-0.416830\pi\) | ||||
0.258323 | + | 0.966059i | \(0.416830\pi\) | |||||||
\(312\) | 149384. | 0.0868795 | ||||||||
\(313\) | −916421. | −0.528731 | −0.264365 | − | 0.964423i | \(-0.585162\pi\) | ||||
−0.264365 | + | 0.964423i | \(0.585162\pi\) | |||||||
\(314\) | −240060. | −0.137403 | ||||||||
\(315\) | −278528. | −0.158159 | ||||||||
\(316\) | −969586. | −0.546221 | ||||||||
\(317\) | 2.01084e6 | 1.12390 | 0.561951 | − | 0.827170i | \(-0.310051\pi\) | ||||
0.561951 | + | 0.827170i | \(0.310051\pi\) | |||||||
\(318\) | −1.36949e6 | −0.759435 | ||||||||
\(319\) | 3.67313e6 | 2.02097 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | −1.34445e6 | −0.728254 | ||||||||
\(322\) | 2.51531e6 | 1.35192 | ||||||||
\(323\) | −13234.7 | −0.00705840 | ||||||||
\(324\) | −697980. | −0.369386 | ||||||||
\(325\) | −105625. | −0.0554700 | ||||||||
\(326\) | 1.46365e6 | 0.762770 | ||||||||
\(327\) | 230606. | 0.119262 | ||||||||
\(328\) | −61319.7 | −0.0314714 | ||||||||
\(329\) | 4.60879e6 | 2.34745 | ||||||||
\(330\) | −811122. | −0.410016 | ||||||||
\(331\) | 2.47715e6 | 1.24275 | 0.621373 | − | 0.783515i | \(-0.286575\pi\) | ||||
0.621373 | + | 0.783515i | \(0.286575\pi\) | |||||||
\(332\) | −42471.3 | −0.0211471 | ||||||||
\(333\) | −397966. | −0.196669 | ||||||||
\(334\) | −269568. | −0.132222 | ||||||||
\(335\) | 459054. | 0.223487 | ||||||||
\(336\) | 753976. | 0.364342 | ||||||||
\(337\) | 2.55550e6 | 1.22575 | 0.612873 | − | 0.790181i | \(-0.290014\pi\) | ||||
0.612873 | + | 0.790181i | \(0.290014\pi\) | |||||||
\(338\) | −114244. | −0.0543928 | ||||||||
\(339\) | 3.02963e6 | 1.43183 | ||||||||
\(340\) | 65042.0 | 0.0305138 | ||||||||
\(341\) | −2.36947e6 | −1.10348 | ||||||||
\(342\) | −17009.4 | −0.00786362 | ||||||||
\(343\) | 2.52902e6 | 1.16069 | ||||||||
\(344\) | −10857.9 | −0.00494709 | ||||||||
\(345\) | −1.01819e6 | −0.460555 | ||||||||
\(346\) | −2.07568e6 | −0.932118 | ||||||||
\(347\) | −475000. | −0.211773 | −0.105886 | − | 0.994378i | \(-0.533768\pi\) | ||||
−0.105886 | + | 0.994378i | \(0.533768\pi\) | |||||||
\(348\) | 1.38212e6 | 0.611783 | ||||||||
\(349\) | 615277. | 0.270400 | 0.135200 | − | 0.990818i | \(-0.456832\pi\) | ||||
0.135200 | + | 0.990818i | \(0.456832\pi\) | |||||||
\(350\) | −533114. | −0.232622 | ||||||||
\(351\) | 689140. | 0.298565 | ||||||||
\(352\) | −601380. | −0.258697 | ||||||||
\(353\) | −4.37400e6 | −1.86828 | −0.934140 | − | 0.356908i | \(-0.883831\pi\) | ||||
−0.934140 | + | 0.356908i | \(0.883831\pi\) | |||||||
\(354\) | −2.21586e6 | −0.939796 | ||||||||
\(355\) | −1.94615e6 | −0.819607 | ||||||||
\(356\) | 131676. | 0.0550659 | ||||||||
\(357\) | 478907. | 0.198875 | ||||||||
\(358\) | 358914. | 0.148007 | ||||||||
\(359\) | 4.59562e6 | 1.88195 | 0.940975 | − | 0.338476i | \(-0.109911\pi\) | ||||
0.940975 | + | 0.338476i | \(0.109911\pi\) | |||||||
\(360\) | 83592.9 | 0.0339948 | ||||||||
\(361\) | −2.46947e6 | −0.997325 | ||||||||
\(362\) | 1.50509e6 | 0.603657 | ||||||||
\(363\) | 2.53926e6 | 1.01144 | ||||||||
\(364\) | −576616. | −0.228104 | ||||||||
\(365\) | −1.55326e6 | −0.610254 | ||||||||
\(366\) | 902879. | 0.352312 | ||||||||
\(367\) | −4.59362e6 | −1.78029 | −0.890143 | − | 0.455681i | \(-0.849396\pi\) | ||||
−0.890143 | + | 0.455681i | \(0.849396\pi\) | |||||||
\(368\) | −754904. | −0.290584 | ||||||||
\(369\) | −50057.6 | −0.0191383 | ||||||||
\(370\) | −761722. | −0.289262 | ||||||||
\(371\) | 5.28617e6 | 1.99391 | ||||||||
\(372\) | −891580. | −0.334043 | ||||||||
\(373\) | 1.74314e6 | 0.648724 | 0.324362 | − | 0.945933i | \(-0.394850\pi\) | ||||
0.324362 | + | 0.945933i | \(0.394850\pi\) | |||||||
\(374\) | −381982. | −0.141209 | ||||||||
\(375\) | 215803. | 0.0792463 | ||||||||
\(376\) | −1.38320e6 | −0.504565 | ||||||||
\(377\) | −1.05700e6 | −0.383020 | ||||||||
\(378\) | 3.47825e6 | 1.25208 | ||||||||
\(379\) | −4.42529e6 | −1.58250 | −0.791250 | − | 0.611493i | \(-0.790569\pi\) | ||||
−0.791250 | + | 0.611493i | \(0.790569\pi\) | |||||||
\(380\) | −32556.6 | −0.0115659 | ||||||||
\(381\) | 2.19260e6 | 0.773833 | ||||||||
\(382\) | −826992. | −0.289963 | ||||||||
\(383\) | 1.39773e6 | 0.486884 | 0.243442 | − | 0.969915i | \(-0.421723\pi\) | ||||
0.243442 | + | 0.969915i | \(0.421723\pi\) | |||||||
\(384\) | −226286. | −0.0783122 | ||||||||
\(385\) | 3.13090e6 | 1.07651 | ||||||||
\(386\) | 1.65235e6 | 0.564462 | ||||||||
\(387\) | −8863.71 | −0.00300842 | ||||||||
\(388\) | −861504. | −0.290521 | ||||||||
\(389\) | 1.63535e6 | 0.547946 | 0.273973 | − | 0.961737i | \(-0.411662\pi\) | ||||
0.273973 | + | 0.961737i | \(0.411662\pi\) | |||||||
\(390\) | 233412. | 0.0777074 | ||||||||
\(391\) | −479497. | −0.158615 | ||||||||
\(392\) | −1.83467e6 | −0.603034 | ||||||||
\(393\) | 2.21764e6 | 0.724286 | ||||||||
\(394\) | −2.15530e6 | −0.699468 | ||||||||
\(395\) | −1.51498e6 | −0.488555 | ||||||||
\(396\) | −490928. | −0.157319 | ||||||||
\(397\) | 4.90653e6 | 1.56242 | 0.781210 | − | 0.624268i | \(-0.214603\pi\) | ||||
0.781210 | + | 0.624268i | \(0.214603\pi\) | |||||||
\(398\) | 589344. | 0.186493 | ||||||||
\(399\) | −239715. | −0.0753813 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −951184. | −0.295395 | −0.147698 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147698 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(402\) | −1.01443e6 | −0.313080 | ||||||||
\(403\) | 681851. | 0.209135 | ||||||||
\(404\) | −2.68089e6 | −0.817196 | ||||||||
\(405\) | −1.09059e6 | −0.330389 | ||||||||
\(406\) | −5.33492e6 | −1.60625 | ||||||||
\(407\) | 4.47348e6 | 1.33863 | ||||||||
\(408\) | −143731. | −0.0427465 | ||||||||
\(409\) | 4.49464e6 | 1.32858 | 0.664289 | − | 0.747476i | \(-0.268735\pi\) | ||||
0.664289 | + | 0.747476i | \(0.268735\pi\) | |||||||
\(410\) | −95812.1 | −0.0281488 | ||||||||
\(411\) | −4.08358e6 | −1.19244 | ||||||||
\(412\) | 495581. | 0.143837 | ||||||||
\(413\) | 8.55312e6 | 2.46746 | ||||||||
\(414\) | −616256. | −0.176710 | ||||||||
\(415\) | −66361.4 | −0.0189145 | ||||||||
\(416\) | 173056. | 0.0490290 | ||||||||
\(417\) | 85597.0 | 0.0241056 | ||||||||
\(418\) | 191200. | 0.0535238 | ||||||||
\(419\) | −828906. | −0.230659 | −0.115329 | − | 0.993327i | \(-0.536792\pi\) | ||||
−0.115329 | + | 0.993327i | \(0.536792\pi\) | |||||||
\(420\) | 1.17809e6 | 0.325877 | ||||||||
\(421\) | 744813. | 0.204806 | 0.102403 | − | 0.994743i | \(-0.467347\pi\) | ||||
0.102403 | + | 0.994743i | \(0.467347\pi\) | |||||||
\(422\) | 4.59686e6 | 1.25655 | ||||||||
\(423\) | −1.12916e6 | −0.306835 | ||||||||
\(424\) | −1.58650e6 | −0.428574 | ||||||||
\(425\) | 101628. | 0.0272924 | ||||||||
\(426\) | 4.30065e6 | 1.14818 | ||||||||
\(427\) | −3.48508e6 | −0.925002 | ||||||||
\(428\) | −1.55750e6 | −0.410978 | ||||||||
\(429\) | −1.37080e6 | −0.359608 | ||||||||
\(430\) | −16965.5 | −0.00442481 | ||||||||
\(431\) | −3.89529e6 | −1.01006 | −0.505030 | − | 0.863102i | \(-0.668519\pi\) | ||||
−0.505030 | + | 0.863102i | \(0.668519\pi\) | |||||||
\(432\) | −1.04390e6 | −0.269123 | ||||||||
\(433\) | −5.88297e6 | −1.50792 | −0.753958 | − | 0.656923i | \(-0.771858\pi\) | ||||
−0.753958 | + | 0.656923i | \(0.771858\pi\) | |||||||
\(434\) | 3.44146e6 | 0.877038 | ||||||||
\(435\) | 2.15956e6 | 0.547195 | ||||||||
\(436\) | 267149. | 0.0673035 | ||||||||
\(437\) | 240011. | 0.0601211 | ||||||||
\(438\) | 3.43242e6 | 0.854899 | ||||||||
\(439\) | 1.73024e6 | 0.428495 | 0.214248 | − | 0.976779i | \(-0.431270\pi\) | ||||
0.214248 | + | 0.976779i | \(0.431270\pi\) | |||||||
\(440\) | −939656. | −0.231386 | ||||||||
\(441\) | −1.49771e6 | −0.366716 | ||||||||
\(442\) | 109921. | 0.0267624 | ||||||||
\(443\) | −106432. | −0.0257670 | −0.0128835 | − | 0.999917i | \(-0.504101\pi\) | ||||
−0.0128835 | + | 0.999917i | \(0.504101\pi\) | |||||||
\(444\) | 1.68327e6 | 0.405225 | ||||||||
\(445\) | 205744. | 0.0492524 | ||||||||
\(446\) | 5.57721e6 | 1.32764 | ||||||||
\(447\) | −5.12449e6 | −1.21306 | ||||||||
\(448\) | 873454. | 0.205610 | ||||||||
\(449\) | −4.89220e6 | −1.14522 | −0.572609 | − | 0.819828i | \(-0.694069\pi\) | ||||
−0.572609 | + | 0.819828i | \(0.694069\pi\) | |||||||
\(450\) | 130614. | 0.0304059 | ||||||||
\(451\) | 562690. | 0.130265 | ||||||||
\(452\) | 3.50972e6 | 0.808027 | ||||||||
\(453\) | −7.02117e6 | −1.60755 | ||||||||
\(454\) | −5.61165e6 | −1.27776 | ||||||||
\(455\) | −900962. | −0.204023 | ||||||||
\(456\) | 71944.2 | 0.0162026 | ||||||||
\(457\) | 177252. | 0.0397008 | 0.0198504 | − | 0.999803i | \(-0.493681\pi\) | ||||
0.0198504 | + | 0.999803i | \(0.493681\pi\) | |||||||
\(458\) | 3.18651e6 | 0.709824 | ||||||||
\(459\) | −663063. | −0.146900 | ||||||||
\(460\) | −1.17954e6 | −0.259906 | ||||||||
\(461\) | 7.15676e6 | 1.56843 | 0.784213 | − | 0.620491i | \(-0.213067\pi\) | ||||
0.784213 | + | 0.620491i | \(0.213067\pi\) | |||||||
\(462\) | −6.91872e6 | −1.50807 | ||||||||
\(463\) | 3.44228e6 | 0.746267 | 0.373133 | − | 0.927778i | \(-0.378283\pi\) | ||||
0.373133 | + | 0.927778i | \(0.378283\pi\) | |||||||
\(464\) | 1.60114e6 | 0.345249 | ||||||||
\(465\) | −1.39309e6 | −0.298778 | ||||||||
\(466\) | −4.63900e6 | −0.989600 | ||||||||
\(467\) | −9.22486e6 | −1.95735 | −0.978673 | − | 0.205423i | \(-0.934143\pi\) | ||||
−0.978673 | + | 0.205423i | \(0.934143\pi\) | |||||||
\(468\) | 141272. | 0.0298155 | ||||||||
\(469\) | 3.91565e6 | 0.821999 | ||||||||
\(470\) | −2.16126e6 | −0.451296 | ||||||||
\(471\) | 828889. | 0.172165 | ||||||||
\(472\) | −2.56699e6 | −0.530358 | ||||||||
\(473\) | 99635.7 | 0.0204768 | ||||||||
\(474\) | 3.34783e6 | 0.684412 | ||||||||
\(475\) | −50869.6 | −0.0103449 | ||||||||
\(476\) | 554797. | 0.112232 | ||||||||
\(477\) | −1.29512e6 | −0.260624 | ||||||||
\(478\) | 2.75012e6 | 0.550531 | ||||||||
\(479\) | 1.23331e6 | 0.245602 | 0.122801 | − | 0.992431i | \(-0.460812\pi\) | ||||
0.122801 | + | 0.992431i | \(0.460812\pi\) | |||||||
\(480\) | −353572. | −0.0700445 | ||||||||
\(481\) | −1.28731e6 | −0.253700 | ||||||||
\(482\) | 1.56538e6 | 0.306904 | ||||||||
\(483\) | −8.68498e6 | −1.69395 | ||||||||
\(484\) | 2.94164e6 | 0.570789 | ||||||||
\(485\) | −1.34610e6 | −0.259850 | ||||||||
\(486\) | −1.55356e6 | −0.298357 | ||||||||
\(487\) | −6.21276e6 | −1.18703 | −0.593516 | − | 0.804823i | \(-0.702260\pi\) | ||||
−0.593516 | + | 0.804823i | \(0.702260\pi\) | |||||||
\(488\) | 1.04595e6 | 0.198821 | ||||||||
\(489\) | −5.05376e6 | −0.955747 | ||||||||
\(490\) | −2.86667e6 | −0.539370 | ||||||||
\(491\) | −7.05221e6 | −1.32014 | −0.660072 | − | 0.751202i | \(-0.729474\pi\) | ||||
−0.660072 | + | 0.751202i | \(0.729474\pi\) | |||||||
\(492\) | 211728. | 0.0394335 | ||||||||
\(493\) | 1.01700e6 | 0.188454 | ||||||||
\(494\) | −55020.6 | −0.0101440 | ||||||||
\(495\) | −767075. | −0.140710 | ||||||||
\(496\) | −1.03286e6 | −0.188512 | ||||||||
\(497\) | −1.66003e7 | −3.01457 | ||||||||
\(498\) | 146647. | 0.0264972 | ||||||||
\(499\) | 5.63009e6 | 1.01220 | 0.506098 | − | 0.862476i | \(-0.331088\pi\) | ||||
0.506098 | + | 0.862476i | \(0.331088\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 930778. | 0.165673 | ||||||||
\(502\) | −3.77889e6 | −0.669276 | ||||||||
\(503\) | 9.65803e6 | 1.70204 | 0.851018 | − | 0.525137i | \(-0.175986\pi\) | ||||
0.851018 | + | 0.525137i | \(0.175986\pi\) | |||||||
\(504\) | 713032. | 0.125035 | ||||||||
\(505\) | −4.18890e6 | −0.730922 | ||||||||
\(506\) | 6.92724e6 | 1.20277 | ||||||||
\(507\) | 394467. | 0.0681539 | ||||||||
\(508\) | 2.54005e6 | 0.436700 | ||||||||
\(509\) | −4.39209e6 | −0.751409 | −0.375705 | − | 0.926739i | \(-0.622599\pi\) | ||||
−0.375705 | + | 0.926739i | \(0.622599\pi\) | |||||||
\(510\) | −224580. | −0.0382337 | ||||||||
\(511\) | −1.32490e7 | −2.24456 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 331894. | 0.0556809 | ||||||||
\(514\) | −1.18888e6 | −0.198486 | ||||||||
\(515\) | 774345. | 0.128652 | ||||||||
\(516\) | 37490.7 | 0.00619868 | ||||||||
\(517\) | 1.26927e7 | 2.08847 | ||||||||
\(518\) | −6.49735e6 | −1.06393 | ||||||||
\(519\) | 7.16702e6 | 1.16794 | ||||||||
\(520\) | 270400. | 0.0438529 | ||||||||
\(521\) | −8.38443e6 | −1.35325 | −0.676627 | − | 0.736326i | \(-0.736559\pi\) | ||||
−0.676627 | + | 0.736326i | \(0.736559\pi\) | |||||||
\(522\) | 1.30707e6 | 0.209953 | ||||||||
\(523\) | 2.54489e6 | 0.406831 | 0.203416 | − | 0.979092i | \(-0.434796\pi\) | ||||
0.203416 | + | 0.979092i | \(0.434796\pi\) | |||||||
\(524\) | 2.56906e6 | 0.408739 | ||||||||
\(525\) | 1.84076e6 | 0.291474 | ||||||||
\(526\) | 6.12389e6 | 0.965080 | ||||||||
\(527\) | −656050. | −0.102899 | ||||||||
\(528\) | 2.07647e6 | 0.324146 | ||||||||
\(529\) | 2.25933e6 | 0.351028 | ||||||||
\(530\) | −2.47891e6 | −0.383329 | ||||||||
\(531\) | −2.09553e6 | −0.322521 | ||||||||
\(532\) | −277702. | −0.0425402 | ||||||||
\(533\) | −161922. | −0.0246882 | ||||||||
\(534\) | −454658. | −0.0689973 | ||||||||
\(535\) | −2.43359e6 | −0.367590 | ||||||||
\(536\) | −1.17518e6 | −0.176682 | ||||||||
\(537\) | −1.23928e6 | −0.185452 | ||||||||
\(538\) | 4.03512e6 | 0.601036 | ||||||||
\(539\) | 1.68355e7 | 2.49605 | ||||||||
\(540\) | −1.63110e6 | −0.240711 | ||||||||
\(541\) | −3.83465e6 | −0.563290 | −0.281645 | − | 0.959519i | \(-0.590880\pi\) | ||||
−0.281645 | + | 0.959519i | \(0.590880\pi\) | |||||||
\(542\) | −8.76490e6 | −1.28159 | ||||||||
\(543\) | −5.19684e6 | −0.756379 | ||||||||
\(544\) | −166508. | −0.0241233 | ||||||||
\(545\) | 417421. | 0.0601981 | ||||||||
\(546\) | 1.99097e6 | 0.285813 | ||||||||
\(547\) | −2.61787e6 | −0.374093 | −0.187047 | − | 0.982351i | \(-0.559892\pi\) | ||||
−0.187047 | + | 0.982351i | \(0.559892\pi\) | |||||||
\(548\) | −4.73068e6 | −0.672934 | ||||||||
\(549\) | 853850. | 0.120907 | ||||||||
\(550\) | −1.46821e6 | −0.206958 | ||||||||
\(551\) | −509057. | −0.0714312 | ||||||||
\(552\) | 2.60657e6 | 0.364101 | ||||||||
\(553\) | −1.29225e7 | −1.79694 | ||||||||
\(554\) | 71695.9 | 0.00992476 | ||||||||
\(555\) | 2.63011e6 | 0.362444 | ||||||||
\(556\) | 99161.1 | 0.0136036 | ||||||||
\(557\) | 5.40419e6 | 0.738061 | 0.369031 | − | 0.929417i | \(-0.379690\pi\) | ||||
0.369031 | + | 0.929417i | \(0.379690\pi\) | |||||||
\(558\) | −843164. | −0.114638 | ||||||||
\(559\) | −28671.7 | −0.00388082 | ||||||||
\(560\) | 1.36477e6 | 0.183903 | ||||||||
\(561\) | 1.31892e6 | 0.176935 | ||||||||
\(562\) | 9.62654e6 | 1.28567 | ||||||||
\(563\) | 904604. | 0.120278 | 0.0601392 | − | 0.998190i | \(-0.480846\pi\) | ||||
0.0601392 | + | 0.998190i | \(0.480846\pi\) | |||||||
\(564\) | 4.77599e6 | 0.632217 | ||||||||
\(565\) | 5.48393e6 | 0.722722 | ||||||||
\(566\) | 5.47683e6 | 0.718602 | ||||||||
\(567\) | −9.30257e6 | −1.21519 | ||||||||
\(568\) | 4.98215e6 | 0.647956 | ||||||||
\(569\) | −6.69355e6 | −0.866714 | −0.433357 | − | 0.901222i | \(-0.642671\pi\) | ||||
−0.433357 | + | 0.901222i | \(0.642671\pi\) | |||||||
\(570\) | 112413. | 0.0144920 | ||||||||
\(571\) | 8.22981e6 | 1.05633 | 0.528165 | − | 0.849142i | \(-0.322880\pi\) | ||||
0.528165 | + | 0.849142i | \(0.322880\pi\) | |||||||
\(572\) | −1.58802e6 | −0.202939 | ||||||||
\(573\) | 2.85548e6 | 0.363322 | ||||||||
\(574\) | −817260. | −0.103533 | ||||||||
\(575\) | −1.84303e6 | −0.232467 | ||||||||
\(576\) | −213998. | −0.0268753 | ||||||||
\(577\) | 3.07720e6 | 0.384783 | 0.192391 | − | 0.981318i | \(-0.438376\pi\) | ||||
0.192391 | + | 0.981318i | \(0.438376\pi\) | |||||||
\(578\) | 5.57367e6 | 0.693939 | ||||||||
\(579\) | −5.70532e6 | −0.707267 | ||||||||
\(580\) | 2.50177e6 | 0.308801 | ||||||||
\(581\) | −566051. | −0.0695689 | ||||||||
\(582\) | 2.97464e6 | 0.364021 | ||||||||
\(583\) | 1.45583e7 | 1.77394 | ||||||||
\(584\) | 3.97633e6 | 0.482448 | ||||||||
\(585\) | 220737. | 0.0266678 | ||||||||
\(586\) | 1.56260e6 | 0.187976 | ||||||||
\(587\) | 2.64175e6 | 0.316443 | 0.158222 | − | 0.987404i | \(-0.449424\pi\) | ||||
0.158222 | + | 0.987404i | \(0.449424\pi\) | |||||||
\(588\) | 6.33482e6 | 0.755599 | ||||||||
\(589\) | 328384. | 0.0390026 | ||||||||
\(590\) | −4.01092e6 | −0.474367 | ||||||||
\(591\) | 7.44193e6 | 0.876429 | ||||||||
\(592\) | 1.95001e6 | 0.228682 | ||||||||
\(593\) | −5.06641e6 | −0.591649 | −0.295824 | − | 0.955242i | \(-0.595594\pi\) | ||||
−0.295824 | + | 0.955242i | \(0.595594\pi\) | |||||||
\(594\) | 9.57920e6 | 1.11394 | ||||||||
\(595\) | 866870. | 0.100383 | ||||||||
\(596\) | −5.93654e6 | −0.684569 | ||||||||
\(597\) | −2.03492e6 | −0.233674 | ||||||||
\(598\) | −1.99342e6 | −0.227953 | ||||||||
\(599\) | 1.31136e7 | 1.49332 | 0.746662 | − | 0.665204i | \(-0.231655\pi\) | ||||
0.746662 | + | 0.665204i | \(0.231655\pi\) | |||||||
\(600\) | −552456. | −0.0626497 | ||||||||
\(601\) | 7.53425e6 | 0.850852 | 0.425426 | − | 0.904993i | \(-0.360124\pi\) | ||||
0.425426 | + | 0.904993i | \(0.360124\pi\) | |||||||
\(602\) | −144713. | −0.0162748 | ||||||||
\(603\) | −959341. | −0.107443 | ||||||||
\(604\) | −8.13378e6 | −0.907193 | ||||||||
\(605\) | 4.59631e6 | 0.510529 | ||||||||
\(606\) | 9.25672e6 | 1.02394 | ||||||||
\(607\) | 8.76101e6 | 0.965123 | 0.482561 | − | 0.875862i | \(-0.339707\pi\) | ||||
0.482561 | + | 0.875862i | \(0.339707\pi\) | |||||||
\(608\) | 83344.8 | 0.00914365 | ||||||||
\(609\) | 1.84207e7 | 2.01262 | ||||||||
\(610\) | 1.63430e6 | 0.177831 | ||||||||
\(611\) | −3.65253e6 | −0.395813 | ||||||||
\(612\) | −135926. | −0.0146698 | ||||||||
\(613\) | −469316. | −0.0504445 | −0.0252223 | − | 0.999682i | \(-0.508029\pi\) | ||||
−0.0252223 | + | 0.999682i | \(0.508029\pi\) | |||||||
\(614\) | −2.26618e6 | −0.242591 | ||||||||
\(615\) | 330824. | 0.0352704 | ||||||||
\(616\) | −8.01509e6 | −0.851054 | ||||||||
\(617\) | −4.14114e6 | −0.437933 | −0.218966 | − | 0.975732i | \(-0.570268\pi\) | ||||
−0.218966 | + | 0.975732i | \(0.570268\pi\) | |||||||
\(618\) | −1.71116e6 | −0.180227 | ||||||||
\(619\) | −1.31422e7 | −1.37861 | −0.689304 | − | 0.724472i | \(-0.742084\pi\) | ||||
−0.689304 | + | 0.724472i | \(0.742084\pi\) | |||||||
\(620\) | −1.61385e6 | −0.168610 | ||||||||
\(621\) | 1.20246e7 | 1.25125 | ||||||||
\(622\) | −3.52496e6 | −0.365324 | ||||||||
\(623\) | 1.75496e6 | 0.181154 | ||||||||
\(624\) | −597536. | −0.0614331 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 3.66569e6 | 0.373869 | ||||||||
\(627\) | −660184. | −0.0670650 | ||||||||
\(628\) | 960239. | 0.0971583 | ||||||||
\(629\) | 1.23860e6 | 0.124826 | ||||||||
\(630\) | 1.11411e6 | 0.111835 | ||||||||
\(631\) | 9.79229e6 | 0.979063 | 0.489532 | − | 0.871986i | \(-0.337168\pi\) | ||||
0.489532 | + | 0.871986i | \(0.337168\pi\) | |||||||
\(632\) | 3.87834e6 | 0.386237 | ||||||||
\(633\) | −1.58722e7 | −1.57445 | ||||||||
\(634\) | −8.04335e6 | −0.794719 | ||||||||
\(635\) | 3.96883e6 | 0.390596 | ||||||||
\(636\) | 5.47795e6 | 0.537001 | ||||||||
\(637\) | −4.84467e6 | −0.473059 | ||||||||
\(638\) | −1.46925e7 | −1.42904 | ||||||||
\(639\) | 4.06711e6 | 0.394034 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | 3.38154e6 | 0.325064 | 0.162532 | − | 0.986703i | \(-0.448034\pi\) | ||||
0.162532 | + | 0.986703i | \(0.448034\pi\) | |||||||
\(642\) | 5.37781e6 | 0.514953 | ||||||||
\(643\) | −3.04366e6 | −0.290314 | −0.145157 | − | 0.989409i | \(-0.546369\pi\) | ||||
−0.145157 | + | 0.989409i | \(0.546369\pi\) | |||||||
\(644\) | −1.00612e7 | −0.955954 | ||||||||
\(645\) | 58579.2 | 0.00554427 | ||||||||
\(646\) | 52938.6 | 0.00499104 | ||||||||
\(647\) | 8.51735e6 | 0.799915 | 0.399957 | − | 0.916534i | \(-0.369025\pi\) | ||||
0.399957 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(648\) | 2.79192e6 | 0.261195 | ||||||||
\(649\) | 2.35555e7 | 2.19524 | ||||||||
\(650\) | 422500. | 0.0392232 | ||||||||
\(651\) | −1.18828e7 | −1.09892 | ||||||||
\(652\) | −5.85461e6 | −0.539360 | ||||||||
\(653\) | −8.83998e6 | −0.811275 | −0.405638 | − | 0.914034i | \(-0.632950\pi\) | ||||
−0.405638 | + | 0.914034i | \(0.632950\pi\) | |||||||
\(654\) | −922425. | −0.0843309 | ||||||||
\(655\) | 4.01415e6 | 0.365587 | ||||||||
\(656\) | 245279. | 0.0222536 | ||||||||
\(657\) | 3.24603e6 | 0.293386 | ||||||||
\(658\) | −1.84351e7 | −1.65990 | ||||||||
\(659\) | −2.97807e6 | −0.267129 | −0.133564 | − | 0.991040i | \(-0.542642\pi\) | ||||
−0.133564 | + | 0.991040i | \(0.542642\pi\) | |||||||
\(660\) | 3.24449e6 | 0.289925 | ||||||||
\(661\) | −7.90309e6 | −0.703548 | −0.351774 | − | 0.936085i | \(-0.614421\pi\) | ||||
−0.351774 | + | 0.936085i | \(0.614421\pi\) | |||||||
\(662\) | −9.90860e6 | −0.878754 | ||||||||
\(663\) | −379540. | −0.0335331 | ||||||||
\(664\) | 169885. | 0.0149532 | ||||||||
\(665\) | −433909. | −0.0380491 | ||||||||
\(666\) | 1.59186e6 | 0.139066 | ||||||||
\(667\) | −1.84433e7 | −1.60519 | ||||||||
\(668\) | 1.07827e6 | 0.0934948 | ||||||||
\(669\) | −1.92572e7 | −1.66352 | ||||||||
\(670\) | −1.83621e6 | −0.158029 | ||||||||
\(671\) | −9.59800e6 | −0.822952 | ||||||||
\(672\) | −3.01590e6 | −0.257629 | ||||||||
\(673\) | 1.82522e7 | 1.55338 | 0.776688 | − | 0.629885i | \(-0.216898\pi\) | ||||
0.776688 | + | 0.629885i | \(0.216898\pi\) | |||||||
\(674\) | −1.02220e7 | −0.866734 | ||||||||
\(675\) | −2.54859e6 | −0.215299 | ||||||||
\(676\) | 456976. | 0.0384615 | ||||||||
\(677\) | 5.39380e6 | 0.452296 | 0.226148 | − | 0.974093i | \(-0.427387\pi\) | ||||
0.226148 | + | 0.974093i | \(0.427387\pi\) | |||||||
\(678\) | −1.21185e7 | −1.01245 | ||||||||
\(679\) | −1.14820e7 | −0.955746 | ||||||||
\(680\) | −260168. | −0.0215765 | ||||||||
\(681\) | 1.93762e7 | 1.60103 | ||||||||
\(682\) | 9.47789e6 | 0.780280 | ||||||||
\(683\) | 2.30171e7 | 1.88799 | 0.943994 | − | 0.329963i | \(-0.107036\pi\) | ||||
0.943994 | + | 0.329963i | \(0.107036\pi\) | |||||||
\(684\) | 68037.4 | 0.00556042 | ||||||||
\(685\) | −7.39169e6 | −0.601891 | ||||||||
\(686\) | −1.01161e7 | −0.820733 | ||||||||
\(687\) | −1.10025e7 | −0.889406 | ||||||||
\(688\) | 43431.6 | 0.00349812 | ||||||||
\(689\) | −4.18936e6 | −0.336201 | ||||||||
\(690\) | 4.07276e6 | 0.325661 | ||||||||
\(691\) | 4.87910e6 | 0.388727 | 0.194364 | − | 0.980930i | \(-0.437736\pi\) | ||||
0.194364 | + | 0.980930i | \(0.437736\pi\) | |||||||
\(692\) | 8.30274e6 | 0.659107 | ||||||||
\(693\) | −6.54302e6 | −0.517541 | ||||||||
\(694\) | 1.90000e6 | 0.149746 | ||||||||
\(695\) | 154939. | 0.0121674 | ||||||||
\(696\) | −5.52847e6 | −0.432596 | ||||||||
\(697\) | 155795. | 0.0121471 | ||||||||
\(698\) | −2.46111e6 | −0.191202 | ||||||||
\(699\) | 1.60178e7 | 1.23996 | ||||||||
\(700\) | 2.13246e6 | 0.164488 | ||||||||
\(701\) | 1.47820e7 | 1.13615 | 0.568077 | − | 0.822976i | \(-0.307688\pi\) | ||||
0.568077 | + | 0.822976i | \(0.307688\pi\) | |||||||
\(702\) | −2.75656e6 | −0.211118 | ||||||||
\(703\) | −619976. | −0.0473137 | ||||||||
\(704\) | 2.40552e6 | 0.182927 | ||||||||
\(705\) | 7.46249e6 | 0.565472 | ||||||||
\(706\) | 1.74960e7 | 1.32107 | ||||||||
\(707\) | −3.57305e7 | −2.68838 | ||||||||
\(708\) | 8.86343e6 | 0.664536 | ||||||||
\(709\) | −2.75364e6 | −0.205727 | −0.102863 | − | 0.994695i | \(-0.532800\pi\) | ||||
−0.102863 | + | 0.994695i | \(0.532800\pi\) | |||||||
\(710\) | 7.78460e6 | 0.579550 | ||||||||
\(711\) | 3.16603e6 | 0.234878 | ||||||||
\(712\) | −526705. | −0.0389375 | ||||||||
\(713\) | 1.18975e7 | 0.876457 | ||||||||
\(714\) | −1.91563e6 | −0.140626 | ||||||||
\(715\) | −2.48128e6 | −0.181514 | ||||||||
\(716\) | −1.43566e6 | −0.104657 | ||||||||
\(717\) | −9.49574e6 | −0.689812 | ||||||||
\(718\) | −1.83825e7 | −1.33074 | ||||||||
\(719\) | −2.10250e7 | −1.51675 | −0.758373 | − | 0.651820i | \(-0.774006\pi\) | ||||
−0.758373 | + | 0.651820i | \(0.774006\pi\) | |||||||
\(720\) | −334372. | −0.0240380 | ||||||||
\(721\) | 6.60502e6 | 0.473191 | ||||||||
\(722\) | 9.87790e6 | 0.705215 | ||||||||
\(723\) | −5.40502e6 | −0.384549 | ||||||||
\(724\) | −6.02035e6 | −0.426850 | ||||||||
\(725\) | 3.90902e6 | 0.276200 | ||||||||
\(726\) | −1.01570e7 | −0.715196 | ||||||||
\(727\) | 2.21381e7 | 1.55347 | 0.776737 | − | 0.629825i | \(-0.216873\pi\) | ||||
0.776737 | + | 0.629825i | \(0.216873\pi\) | |||||||
\(728\) | 2.30646e6 | 0.161294 | ||||||||
\(729\) | 1.59648e7 | 1.11261 | ||||||||
\(730\) | 6.21302e6 | 0.431515 | ||||||||
\(731\) | 27586.7 | 0.00190944 | ||||||||
\(732\) | −3.61152e6 | −0.249122 | ||||||||
\(733\) | 1.23177e7 | 0.846775 | 0.423388 | − | 0.905949i | \(-0.360841\pi\) | ||||
0.423388 | + | 0.905949i | \(0.360841\pi\) | |||||||
\(734\) | 1.83745e7 | 1.25885 | ||||||||
\(735\) | 9.89816e6 | 0.675828 | ||||||||
\(736\) | 3.01962e6 | 0.205474 | ||||||||
\(737\) | 1.07838e7 | 0.731313 | ||||||||
\(738\) | 200230. | 0.0135328 | ||||||||
\(739\) | −1.79039e7 | −1.20597 | −0.602986 | − | 0.797752i | \(-0.706023\pi\) | ||||
−0.602986 | + | 0.797752i | \(0.706023\pi\) | |||||||
\(740\) | 3.04689e6 | 0.204539 | ||||||||
\(741\) | 189978. | 0.0127103 | ||||||||
\(742\) | −2.11447e7 | −1.40991 | ||||||||
\(743\) | −9.82085e6 | −0.652645 | −0.326323 | − | 0.945258i | \(-0.605810\pi\) | ||||
−0.326323 | + | 0.945258i | \(0.605810\pi\) | |||||||
\(744\) | 3.56632e6 | 0.236204 | ||||||||
\(745\) | −9.27584e6 | −0.612297 | ||||||||
\(746\) | −6.97256e6 | −0.458717 | ||||||||
\(747\) | 138684. | 0.00909334 | ||||||||
\(748\) | 1.52793e6 | 0.0998501 | ||||||||
\(749\) | −2.07581e7 | −1.35202 | ||||||||
\(750\) | −863212. | −0.0560356 | ||||||||
\(751\) | 1.04747e7 | 0.677705 | 0.338852 | − | 0.940840i | \(-0.389961\pi\) | ||||
0.338852 | + | 0.940840i | \(0.389961\pi\) | |||||||
\(752\) | 5.53282e6 | 0.356781 | ||||||||
\(753\) | 1.30479e7 | 0.838599 | ||||||||
\(754\) | 4.22800e6 | 0.270836 | ||||||||
\(755\) | −1.27090e7 | −0.811418 | ||||||||
\(756\) | −1.39130e7 | −0.885352 | ||||||||
\(757\) | 2.20487e7 | 1.39844 | 0.699219 | − | 0.714908i | \(-0.253531\pi\) | ||||
0.699219 | + | 0.714908i | \(0.253531\pi\) | |||||||
\(758\) | 1.77012e7 | 1.11900 | ||||||||
\(759\) | −2.39187e7 | −1.50707 | ||||||||
\(760\) | 130226. | 0.00817833 | ||||||||
\(761\) | −2.75293e7 | −1.72319 | −0.861596 | − | 0.507594i | \(-0.830535\pi\) | ||||
−0.861596 | + | 0.507594i | \(0.830535\pi\) | |||||||
\(762\) | −8.77040e6 | −0.547182 | ||||||||
\(763\) | 3.56052e6 | 0.221413 | ||||||||
\(764\) | 3.30797e6 | 0.205035 | ||||||||
\(765\) | −212385. | −0.0131211 | ||||||||
\(766\) | −5.59091e6 | −0.344279 | ||||||||
\(767\) | −6.77846e6 | −0.416047 | ||||||||
\(768\) | 905143. | 0.0553751 | ||||||||
\(769\) | 1.50464e7 | 0.917525 | 0.458763 | − | 0.888559i | \(-0.348293\pi\) | ||||
0.458763 | + | 0.888559i | \(0.348293\pi\) | |||||||
\(770\) | −1.25236e7 | −0.761205 | ||||||||
\(771\) | 4.10501e6 | 0.248701 | ||||||||
\(772\) | −6.60941e6 | −0.399135 | ||||||||
\(773\) | 2.28606e6 | 0.137606 | 0.0688031 | − | 0.997630i | \(-0.478082\pi\) | ||||
0.0688031 | + | 0.997630i | \(0.478082\pi\) | |||||||
\(774\) | 35454.8 | 0.00212727 | ||||||||
\(775\) | −2.52164e6 | −0.150810 | ||||||||
\(776\) | 3.44601e6 | 0.205430 | ||||||||
\(777\) | 2.24344e7 | 1.33310 | ||||||||
\(778\) | −6.54142e6 | −0.387456 | ||||||||
\(779\) | −77982.8 | −0.00460421 | ||||||||
\(780\) | −933650. | −0.0549474 | ||||||||
\(781\) | −4.57178e7 | −2.68199 | ||||||||
\(782\) | 1.91799e6 | 0.112158 | ||||||||
\(783\) | −2.55040e7 | −1.48663 | ||||||||
\(784\) | 7.33867e6 | 0.426410 | ||||||||
\(785\) | 1.50037e6 | 0.0869011 | ||||||||
\(786\) | −8.87056e6 | −0.512147 | ||||||||
\(787\) | 9.89052e6 | 0.569223 | 0.284611 | − | 0.958643i | \(-0.408135\pi\) | ||||
0.284611 | + | 0.958643i | \(0.408135\pi\) | |||||||
\(788\) | 8.62121e6 | 0.494598 | ||||||||
\(789\) | −2.11449e7 | −1.20924 | ||||||||
\(790\) | 6.05991e6 | 0.345461 | ||||||||
\(791\) | 4.67770e7 | 2.65822 | ||||||||
\(792\) | 1.96371e6 | 0.111241 | ||||||||
\(793\) | 2.76197e6 | 0.155968 | ||||||||
\(794\) | −1.96261e7 | −1.10480 | ||||||||
\(795\) | 8.55930e6 | 0.480309 | ||||||||
\(796\) | −2.35738e6 | −0.131870 | ||||||||
\(797\) | 2.93049e7 | 1.63416 | 0.817080 | − | 0.576525i | \(-0.195592\pi\) | ||||
0.817080 | + | 0.576525i | \(0.195592\pi\) | |||||||
\(798\) | 958862. | 0.0533026 | ||||||||
\(799\) | 3.51431e6 | 0.194748 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −429969. | −0.0236786 | ||||||||
\(802\) | 3.80474e6 | 0.208876 | ||||||||
\(803\) | −3.64881e7 | −1.99693 | ||||||||
\(804\) | 4.05771e6 | 0.221381 | ||||||||
\(805\) | −1.57207e7 | −0.855031 | ||||||||
\(806\) | −2.72741e6 | −0.147881 | ||||||||
\(807\) | −1.39327e7 | −0.753095 | ||||||||
\(808\) | 1.07236e7 | 0.577845 | ||||||||
\(809\) | 1.02027e7 | 0.548078 | 0.274039 | − | 0.961719i | \(-0.411640\pi\) | ||||
0.274039 | + | 0.961719i | \(0.411640\pi\) | |||||||
\(810\) | 4.36237e6 | 0.233620 | ||||||||
\(811\) | −1.26432e7 | −0.675001 | −0.337501 | − | 0.941325i | \(-0.609582\pi\) | ||||
−0.337501 | + | 0.941325i | \(0.609582\pi\) | |||||||
\(812\) | 2.13397e7 | 1.13579 | ||||||||
\(813\) | 3.02639e7 | 1.60582 | ||||||||
\(814\) | −1.78939e7 | −0.946551 | ||||||||
\(815\) | −9.14782e6 | −0.482418 | ||||||||
\(816\) | 574925. | 0.0302264 | ||||||||
\(817\) | −13808.4 | −0.000723752 0 | ||||||||
\(818\) | −1.79786e7 | −0.939446 | ||||||||
\(819\) | 1.88285e6 | 0.0980858 | ||||||||
\(820\) | 383248. | 0.0199042 | ||||||||
\(821\) | −1.56881e7 | −0.812294 | −0.406147 | − | 0.913808i | \(-0.633128\pi\) | ||||
−0.406147 | + | 0.913808i | \(0.633128\pi\) | |||||||
\(822\) | 1.63343e7 | 0.843183 | ||||||||
\(823\) | 2.45799e7 | 1.26497 | 0.632487 | − | 0.774571i | \(-0.282034\pi\) | ||||
0.632487 | + | 0.774571i | \(0.282034\pi\) | |||||||
\(824\) | −1.98232e6 | −0.101708 | ||||||||
\(825\) | 5.06951e6 | 0.259317 | ||||||||
\(826\) | −3.42125e7 | −1.74475 | ||||||||
\(827\) | 3.62365e7 | 1.84239 | 0.921197 | − | 0.389098i | \(-0.127213\pi\) | ||||
0.921197 | + | 0.389098i | \(0.127213\pi\) | |||||||
\(828\) | 2.46502e6 | 0.124953 | ||||||||
\(829\) | −2.81815e7 | −1.42422 | −0.712110 | − | 0.702068i | \(-0.752260\pi\) | ||||
−0.712110 | + | 0.702068i | \(0.752260\pi\) | |||||||
\(830\) | 265446. | 0.0133746 | ||||||||
\(831\) | −247555. | −0.0124357 | ||||||||
\(832\) | −692224. | −0.0346688 | ||||||||
\(833\) | 4.66134e6 | 0.232755 | ||||||||
\(834\) | −342388. | −0.0170453 | ||||||||
\(835\) | 1.68480e6 | 0.0836243 | ||||||||
\(836\) | −764799. | −0.0378470 | ||||||||
\(837\) | 1.64522e7 | 0.811727 | ||||||||
\(838\) | 3.31562e6 | 0.163100 | ||||||||
\(839\) | −8.42806e6 | −0.413354 | −0.206677 | − | 0.978409i | \(-0.566265\pi\) | ||||
−0.206677 | + | 0.978409i | \(0.566265\pi\) | |||||||
\(840\) | −4.71235e6 | −0.230430 | ||||||||
\(841\) | 1.86068e7 | 0.907155 | ||||||||
\(842\) | −2.97925e6 | −0.144820 | ||||||||
\(843\) | −3.32390e7 | −1.61094 | ||||||||
\(844\) | −1.83874e7 | −0.888515 | ||||||||
\(845\) | 714025. | 0.0344010 | ||||||||
\(846\) | 4.51664e6 | 0.216965 | ||||||||
\(847\) | 3.92057e7 | 1.87776 | ||||||||
\(848\) | 6.34601e6 | 0.303048 | ||||||||
\(849\) | −1.89107e7 | −0.900404 | ||||||||
\(850\) | −406512. | −0.0192986 | ||||||||
\(851\) | −2.24620e7 | −1.06322 | ||||||||
\(852\) | −1.72026e7 | −0.811886 | ||||||||
\(853\) | −3.10763e7 | −1.46237 | −0.731184 | − | 0.682180i | \(-0.761032\pi\) | ||||
−0.731184 | + | 0.682180i | \(0.761032\pi\) | |||||||
\(854\) | 1.39403e7 | 0.654075 | ||||||||
\(855\) | 106309. | 0.00497339 | ||||||||
\(856\) | 6.23000e6 | 0.290605 | ||||||||
\(857\) | −5.72064e6 | −0.266068 | −0.133034 | − | 0.991111i | \(-0.542472\pi\) | ||||
−0.133034 | + | 0.991111i | \(0.542472\pi\) | |||||||
\(858\) | 5.48318e6 | 0.254281 | ||||||||
\(859\) | −6.04140e6 | −0.279354 | −0.139677 | − | 0.990197i | \(-0.544606\pi\) | ||||
−0.139677 | + | 0.990197i | \(0.544606\pi\) | |||||||
\(860\) | 67861.9 | 0.00312882 | ||||||||
\(861\) | 2.82187e6 | 0.129727 | ||||||||
\(862\) | 1.55812e7 | 0.714220 | ||||||||
\(863\) | 2.09227e7 | 0.956292 | 0.478146 | − | 0.878280i | \(-0.341309\pi\) | ||||
0.478146 | + | 0.878280i | \(0.341309\pi\) | |||||||
\(864\) | 4.17562e6 | 0.190299 | ||||||||
\(865\) | 1.29730e7 | 0.589523 | ||||||||
\(866\) | 2.35319e7 | 1.06626 | ||||||||
\(867\) | −1.92450e7 | −0.869502 | ||||||||
\(868\) | −1.37658e7 | −0.620160 | ||||||||
\(869\) | −3.55889e7 | −1.59869 | ||||||||
\(870\) | −8.63824e6 | −0.386925 | ||||||||
\(871\) | −3.10320e6 | −0.138601 | ||||||||
\(872\) | −1.06860e6 | −0.0475908 | ||||||||
\(873\) | 2.81311e6 | 0.124925 | ||||||||
\(874\) | −960042. | −0.0425120 | ||||||||
\(875\) | 3.33196e6 | 0.147123 | ||||||||
\(876\) | −1.37297e7 | −0.604505 | ||||||||
\(877\) | −5.01539e6 | −0.220194 | −0.110097 | − | 0.993921i | \(-0.535116\pi\) | ||||
−0.110097 | + | 0.993921i | \(0.535116\pi\) | |||||||
\(878\) | −6.92097e6 | −0.302992 | ||||||||
\(879\) | −5.39541e6 | −0.235533 | ||||||||
\(880\) | 3.75862e6 | 0.163615 | ||||||||
\(881\) | −2.14791e7 | −0.932346 | −0.466173 | − | 0.884694i | \(-0.654368\pi\) | ||||
−0.466173 | + | 0.884694i | \(0.654368\pi\) | |||||||
\(882\) | 5.99082e6 | 0.259307 | ||||||||
\(883\) | 996549. | 0.0430127 | 0.0215064 | − | 0.999769i | \(-0.493154\pi\) | ||||
0.0215064 | + | 0.999769i | \(0.493154\pi\) | |||||||
\(884\) | −439684. | −0.0189239 | ||||||||
\(885\) | 1.38491e7 | 0.594379 | ||||||||
\(886\) | 425728. | 0.0182200 | ||||||||
\(887\) | 4.67336e6 | 0.199444 | 0.0997219 | − | 0.995015i | \(-0.468205\pi\) | ||||
0.0997219 | + | 0.995015i | \(0.468205\pi\) | |||||||
\(888\) | −6.73308e6 | −0.286537 | ||||||||
\(889\) | 3.38534e7 | 1.43664 | ||||||||
\(890\) | −822977. | −0.0348267 | ||||||||
\(891\) | −2.56196e7 | −1.08113 | ||||||||
\(892\) | −2.23088e7 | −0.938782 | ||||||||
\(893\) | −1.75908e6 | −0.0738170 | ||||||||
\(894\) | 2.04980e7 | 0.857762 | ||||||||
\(895\) | −2.24321e6 | −0.0936080 | ||||||||
\(896\) | −3.49382e6 | −0.145388 | ||||||||
\(897\) | 6.88297e6 | 0.285624 | ||||||||
\(898\) | 1.95688e7 | 0.809792 | ||||||||
\(899\) | −2.52343e7 | −1.04134 | ||||||||
\(900\) | −522456. | −0.0215002 | ||||||||
\(901\) | 4.03083e6 | 0.165418 | ||||||||
\(902\) | −2.25076e6 | −0.0921112 | ||||||||
\(903\) | 499670. | 0.0203922 | ||||||||
\(904\) | −1.40389e7 | −0.571362 | ||||||||
\(905\) | −9.40680e6 | −0.381786 | ||||||||
\(906\) | 2.80847e7 | 1.13671 | ||||||||
\(907\) | 1.18130e7 | 0.476807 | 0.238403 | − | 0.971166i | \(-0.423376\pi\) | ||||
0.238403 | + | 0.971166i | \(0.423376\pi\) | |||||||
\(908\) | 2.24466e7 | 0.903515 | ||||||||
\(909\) | 8.75405e6 | 0.351398 | ||||||||
\(910\) | 3.60385e6 | 0.144266 | ||||||||
\(911\) | 3.55560e7 | 1.41944 | 0.709721 | − | 0.704483i | \(-0.248821\pi\) | ||||
0.709721 | + | 0.704483i | \(0.248821\pi\) | |||||||
\(912\) | −287777. | −0.0114569 | ||||||||
\(913\) | −1.55892e6 | −0.0618938 | ||||||||
\(914\) | −709006. | −0.0280727 | ||||||||
\(915\) | −5.64299e6 | −0.222821 | ||||||||
\(916\) | −1.27460e7 | −0.501922 | ||||||||
\(917\) | 3.42400e7 | 1.34465 | ||||||||
\(918\) | 2.65225e6 | 0.103874 | ||||||||
\(919\) | 2.66902e7 | 1.04247 | 0.521235 | − | 0.853413i | \(-0.325472\pi\) | ||||
0.521235 | + | 0.853413i | \(0.325472\pi\) | |||||||
\(920\) | 4.71815e6 | 0.183782 | ||||||||
\(921\) | 7.82478e6 | 0.303965 | ||||||||
\(922\) | −2.86270e7 | −1.10905 | ||||||||
\(923\) | 1.31560e7 | 0.508299 | ||||||||
\(924\) | 2.76749e7 | 1.06637 | ||||||||
\(925\) | 4.76076e6 | 0.182946 | ||||||||
\(926\) | −1.37691e7 | −0.527690 | ||||||||
\(927\) | −1.61824e6 | −0.0618507 | ||||||||
\(928\) | −6.40454e6 | −0.244128 | ||||||||
\(929\) | −3.08229e7 | −1.17175 | −0.585874 | − | 0.810402i | \(-0.699249\pi\) | ||||
−0.585874 | + | 0.810402i | \(0.699249\pi\) | |||||||
\(930\) | 5.57237e6 | 0.211268 | ||||||||
\(931\) | −2.33322e6 | −0.0882230 | ||||||||
\(932\) | 1.85560e7 | 0.699753 | ||||||||
\(933\) | 1.21711e7 | 0.457749 | ||||||||
\(934\) | 3.68994e7 | 1.38405 | ||||||||
\(935\) | 2.38739e6 | 0.0893087 | ||||||||
\(936\) | −565088. | −0.0210827 | ||||||||
\(937\) | 2.78462e7 | 1.03613 | 0.518067 | − | 0.855340i | \(-0.326652\pi\) | ||||
0.518067 | + | 0.855340i | \(0.326652\pi\) | |||||||
\(938\) | −1.56626e7 | −0.581241 | ||||||||
\(939\) | −1.26571e7 | −0.468456 | ||||||||
\(940\) | 8.64503e6 | 0.319115 | ||||||||
\(941\) | 2.80836e7 | 1.03390 | 0.516950 | − | 0.856016i | \(-0.327067\pi\) | ||||
0.516950 | + | 0.856016i | \(0.327067\pi\) | |||||||
\(942\) | −3.31556e6 | −0.121739 | ||||||||
\(943\) | −2.82535e6 | −0.103465 | ||||||||
\(944\) | 1.02680e7 | 0.375020 | ||||||||
\(945\) | −2.17391e7 | −0.791883 | ||||||||
\(946\) | −398543. | −0.0144793 | ||||||||
\(947\) | −4.49006e7 | −1.62696 | −0.813481 | − | 0.581592i | \(-0.802430\pi\) | ||||
−0.813481 | + | 0.581592i | \(0.802430\pi\) | |||||||
\(948\) | −1.33913e7 | −0.483953 | ||||||||
\(949\) | 1.05000e7 | 0.378463 | ||||||||
\(950\) | 203479. | 0.00731492 | ||||||||
\(951\) | 2.77724e7 | 0.995779 | ||||||||
\(952\) | −2.21919e6 | −0.0793600 | ||||||||
\(953\) | −1.13992e7 | −0.406577 | −0.203289 | − | 0.979119i | \(-0.565163\pi\) | ||||
−0.203289 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(954\) | 5.18048e6 | 0.184289 | ||||||||
\(955\) | 5.16870e6 | 0.183389 | ||||||||
\(956\) | −1.10005e7 | −0.389284 | ||||||||
\(957\) | 5.07311e7 | 1.79058 | ||||||||
\(958\) | −4.93322e6 | −0.173667 | ||||||||
\(959\) | −6.30498e7 | −2.21380 | ||||||||
\(960\) | 1.41429e6 | 0.0495290 | ||||||||
\(961\) | −1.23510e7 | −0.431412 | ||||||||
\(962\) | 5.14924e6 | 0.179393 | ||||||||
\(963\) | 5.08578e6 | 0.176722 | ||||||||
\(964\) | −6.26152e6 | −0.217014 | ||||||||
\(965\) | −1.03272e7 | −0.356997 | ||||||||
\(966\) | 3.47399e7 | 1.19781 | ||||||||
\(967\) | −5.54751e7 | −1.90780 | −0.953898 | − | 0.300130i | \(-0.902970\pi\) | ||||
−0.953898 | + | 0.300130i | \(0.902970\pi\) | |||||||
\(968\) | −1.17665e7 | −0.403609 | ||||||||
\(969\) | −182789. | −0.00625375 | ||||||||
\(970\) | 5.38440e6 | 0.183742 | ||||||||
\(971\) | −2.45562e6 | −0.0835819 | −0.0417910 | − | 0.999126i | \(-0.513306\pi\) | ||||
−0.0417910 | + | 0.999126i | \(0.513306\pi\) | |||||||
\(972\) | 6.21423e6 | 0.210970 | ||||||||
\(973\) | 1.32160e6 | 0.0447527 | ||||||||
\(974\) | 2.48510e7 | 0.839358 | ||||||||
\(975\) | −1.45883e6 | −0.0491465 | ||||||||
\(976\) | −4.18381e6 | −0.140588 | ||||||||
\(977\) | 3.31344e7 | 1.11056 | 0.555280 | − | 0.831663i | \(-0.312611\pi\) | ||||
0.555280 | + | 0.831663i | \(0.312611\pi\) | |||||||
\(978\) | 2.02151e7 | 0.675815 | ||||||||
\(979\) | 4.83322e6 | 0.161168 | ||||||||
\(980\) | 1.14667e7 | 0.381392 | ||||||||
\(981\) | −872335. | −0.0289408 | ||||||||
\(982\) | 2.82088e7 | 0.933483 | ||||||||
\(983\) | −4.46461e7 | −1.47367 | −0.736834 | − | 0.676073i | \(-0.763680\pi\) | ||||
−0.736834 | + | 0.676073i | \(0.763680\pi\) | |||||||
\(984\) | −846911. | −0.0278837 | ||||||||
\(985\) | 1.34706e7 | 0.442382 | ||||||||
\(986\) | −4.06801e6 | −0.133257 | ||||||||
\(987\) | 6.36537e7 | 2.07985 | ||||||||
\(988\) | 220082. | 0.00717287 | ||||||||
\(989\) | −500285. | −0.0162640 | ||||||||
\(990\) | 3.06830e6 | 0.0994970 | ||||||||
\(991\) | 4.99797e7 | 1.61662 | 0.808312 | − | 0.588754i | \(-0.200381\pi\) | ||||
0.808312 | + | 0.588754i | \(0.200381\pi\) | |||||||
\(992\) | 4.13145e6 | 0.133298 | ||||||||
\(993\) | 3.42129e7 | 1.10107 | ||||||||
\(994\) | 6.64013e7 | 2.13162 | ||||||||
\(995\) | −3.68340e6 | −0.117948 | ||||||||
\(996\) | −586588. | −0.0187363 | ||||||||
\(997\) | −1.25647e7 | −0.400326 | −0.200163 | − | 0.979763i | \(-0.564147\pi\) | ||||
−0.200163 | + | 0.979763i | \(0.564147\pi\) | |||||||
\(998\) | −2.25204e7 | −0.715730 | ||||||||
\(999\) | −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 | 130.6.a.a.1.2 | ✓ | 2 | |
4.3 | odd | 2 | 1040.6.a.e.1.1 | 2 | |||
5.2 | odd | 4 | 650.6.b.g.599.1 | 4 | |||
5.3 | odd | 4 | 650.6.b.g.599.4 | 4 | |||
5.4 | even | 2 | 650.6.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.6.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
650.6.a.h.1.1 | 2 | 5.4 | even | 2 | |||
650.6.b.g.599.1 | 4 | 5.2 | odd | 4 | |||
650.6.b.g.599.4 | 4 | 5.3 | odd | 4 | |||
1040.6.a.e.1.1 | 2 | 4.3 | odd | 2 |