Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(91.4187772934\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2696x^{2} + 13833x + 894635 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(23.8661\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 241.678 | 1.86419 | 0.932097 | − | 0.362208i | \(-0.117977\pi\) | ||||
0.932097 | + | 0.362208i | \(0.117977\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | 48.9152 | 0.121888 | 0.0609441 | − | 0.998141i | \(-0.480589\pi\) | ||||
0.0609441 | + | 0.998141i | \(0.480589\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −273.990 | −0.449652 | −0.224826 | − | 0.974399i | \(-0.572181\pi\) | ||||
−0.224826 | + | 0.974399i | \(0.572181\pi\) | |||||||
\(14\) | −966.710 | −1.31818 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 601.513 | 0.504804 | 0.252402 | − | 0.967623i | \(-0.418780\pi\) | ||||
0.252402 | + | 0.967623i | \(0.418780\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | −2175.10 | −1.07629 | ||||||||
\(22\) | −195.661 | −0.0861880 | ||||||||
\(23\) | −4654.90 | −1.83481 | −0.917405 | − | 0.397955i | \(-0.869720\pi\) | ||||
−0.917405 | + | 0.397955i | \(0.869720\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1095.96 | 0.317952 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 3866.84 | 0.932097 | ||||||||
\(29\) | 1701.83 | 0.375770 | 0.187885 | − | 0.982191i | \(-0.439837\pi\) | ||||
0.187885 | + | 0.982191i | \(0.439837\pi\) | |||||||
\(30\) | −900.000 | −0.182574 | ||||||||
\(31\) | −4349.54 | −0.812904 | −0.406452 | − | 0.913672i | \(-0.633234\pi\) | ||||
−0.406452 | + | 0.913672i | \(0.633234\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −440.237 | −0.0703722 | ||||||||
\(34\) | −2406.05 | −0.356950 | ||||||||
\(35\) | −6041.94 | −0.833693 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −4042.97 | −0.485508 | −0.242754 | − | 0.970088i | \(-0.578051\pi\) | ||||
−0.242754 | + | 0.970088i | \(0.578051\pi\) | |||||||
\(38\) | 1444.00 | 0.162221 | ||||||||
\(39\) | 2465.91 | 0.259607 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | −7242.68 | −0.672883 | −0.336442 | − | 0.941704i | \(-0.609223\pi\) | ||||
−0.336442 | + | 0.941704i | \(0.609223\pi\) | |||||||
\(42\) | 8700.39 | 0.761054 | ||||||||
\(43\) | 9462.67 | 0.780445 | 0.390223 | − | 0.920720i | \(-0.372398\pi\) | ||||
0.390223 | + | 0.920720i | \(0.372398\pi\) | |||||||
\(44\) | 782.643 | 0.0609441 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | 18619.6 | 1.29741 | ||||||||
\(47\) | 3596.39 | 0.237477 | 0.118739 | − | 0.992926i | \(-0.462115\pi\) | ||||
0.118739 | + | 0.992926i | \(0.462115\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 41601.1 | 2.47522 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −5413.61 | −0.291449 | ||||||||
\(52\) | −4383.85 | −0.224826 | ||||||||
\(53\) | −12980.4 | −0.634743 | −0.317371 | − | 0.948301i | \(-0.602800\pi\) | ||||
−0.317371 | + | 0.948301i | \(0.602800\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | −1222.88 | −0.0545101 | ||||||||
\(56\) | −15467.4 | −0.659092 | ||||||||
\(57\) | 3249.00 | 0.132453 | ||||||||
\(58\) | −6807.33 | −0.265710 | ||||||||
\(59\) | 2882.74 | 0.107814 | 0.0539071 | − | 0.998546i | \(-0.482833\pi\) | ||||
0.0539071 | + | 0.998546i | \(0.482833\pi\) | |||||||
\(60\) | 3600.00 | 0.129099 | ||||||||
\(61\) | −17026.9 | −0.585883 | −0.292942 | − | 0.956130i | \(-0.594634\pi\) | ||||
−0.292942 | + | 0.956130i | \(0.594634\pi\) | |||||||
\(62\) | 17398.2 | 0.574810 | ||||||||
\(63\) | 19575.9 | 0.621398 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 6849.76 | 0.201091 | ||||||||
\(66\) | 1760.95 | 0.0497607 | ||||||||
\(67\) | 18191.1 | 0.495075 | 0.247538 | − | 0.968878i | \(-0.420379\pi\) | ||||
0.247538 | + | 0.968878i | \(0.420379\pi\) | |||||||
\(68\) | 9624.20 | 0.252402 | ||||||||
\(69\) | 41894.1 | 1.05933 | ||||||||
\(70\) | 24167.8 | 0.589510 | ||||||||
\(71\) | 2789.02 | 0.0656608 | 0.0328304 | − | 0.999461i | \(-0.489548\pi\) | ||||
0.0328304 | + | 0.999461i | \(0.489548\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 47602.4 | 1.04549 | 0.522747 | − | 0.852488i | \(-0.324907\pi\) | ||||
0.522747 | + | 0.852488i | \(0.324907\pi\) | |||||||
\(74\) | 16171.9 | 0.343306 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | −5776.00 | −0.114708 | ||||||||
\(77\) | 11821.7 | 0.227223 | ||||||||
\(78\) | −9863.65 | −0.183570 | ||||||||
\(79\) | 58422.6 | 1.05320 | 0.526602 | − | 0.850112i | \(-0.323466\pi\) | ||||
0.526602 | + | 0.850112i | \(0.323466\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 28970.7 | 0.475800 | ||||||||
\(83\) | −50749.5 | −0.808605 | −0.404302 | − | 0.914625i | \(-0.632486\pi\) | ||||
−0.404302 | + | 0.914625i | \(0.632486\pi\) | |||||||
\(84\) | −34801.6 | −0.538147 | ||||||||
\(85\) | −15037.8 | −0.225755 | ||||||||
\(86\) | −37850.7 | −0.551858 | ||||||||
\(87\) | −15316.5 | −0.216951 | ||||||||
\(88\) | −3130.57 | −0.0430940 | ||||||||
\(89\) | −55007.9 | −0.736123 | −0.368061 | − | 0.929802i | \(-0.619978\pi\) | ||||
−0.368061 | + | 0.929802i | \(0.619978\pi\) | |||||||
\(90\) | 8100.00 | 0.105409 | ||||||||
\(91\) | −66217.3 | −0.838239 | ||||||||
\(92\) | −74478.4 | −0.917405 | ||||||||
\(93\) | 39145.9 | 0.469330 | ||||||||
\(94\) | −14385.6 | −0.167922 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −85108.9 | −0.918429 | −0.459215 | − | 0.888325i | \(-0.651869\pi\) | ||||
−0.459215 | + | 0.888325i | \(0.651869\pi\) | |||||||
\(98\) | −166404. | −1.75025 | ||||||||
\(99\) | 3962.13 | 0.0406294 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −112004. | −1.09253 | −0.546263 | − | 0.837614i | \(-0.683950\pi\) | ||||
−0.546263 | + | 0.837614i | \(0.683950\pi\) | |||||||
\(102\) | 21654.5 | 0.206085 | ||||||||
\(103\) | 121864. | 1.13183 | 0.565915 | − | 0.824463i | \(-0.308523\pi\) | ||||
0.565915 | + | 0.824463i | \(0.308523\pi\) | |||||||
\(104\) | 17535.4 | 0.158976 | ||||||||
\(105\) | 54377.5 | 0.481333 | ||||||||
\(106\) | 51921.5 | 0.448831 | ||||||||
\(107\) | −151510. | −1.27933 | −0.639664 | − | 0.768655i | \(-0.720926\pi\) | ||||
−0.639664 | + | 0.768655i | \(0.720926\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 26225.9 | 0.211429 | 0.105714 | − | 0.994397i | \(-0.466287\pi\) | ||||
0.105714 | + | 0.994397i | \(0.466287\pi\) | |||||||
\(110\) | 4891.52 | 0.0385445 | ||||||||
\(111\) | 36386.7 | 0.280308 | ||||||||
\(112\) | 61869.5 | 0.466049 | ||||||||
\(113\) | −157470. | −1.16012 | −0.580058 | − | 0.814575i | \(-0.696970\pi\) | ||||
−0.580058 | + | 0.814575i | \(0.696970\pi\) | |||||||
\(114\) | −12996.0 | −0.0936586 | ||||||||
\(115\) | 116373. | 0.820552 | ||||||||
\(116\) | 27229.3 | 0.187885 | ||||||||
\(117\) | −22193.2 | −0.149884 | ||||||||
\(118\) | −11531.0 | −0.0762362 | ||||||||
\(119\) | 145372. | 0.941052 | ||||||||
\(120\) | −14400.0 | −0.0912871 | ||||||||
\(121\) | −158658. | −0.985143 | ||||||||
\(122\) | 68107.6 | 0.414282 | ||||||||
\(123\) | 65184.1 | 0.388489 | ||||||||
\(124\) | −69592.7 | −0.406452 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −78303.5 | −0.439395 | ||||||||
\(127\) | 170009. | 0.935325 | 0.467663 | − | 0.883907i | \(-0.345096\pi\) | ||||
0.467663 | + | 0.883907i | \(0.345096\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −85164.0 | −0.450590 | ||||||||
\(130\) | −27399.0 | −0.142193 | ||||||||
\(131\) | 254959. | 1.29805 | 0.649026 | − | 0.760766i | \(-0.275176\pi\) | ||||
0.649026 | + | 0.760766i | \(0.275176\pi\) | |||||||
\(132\) | −7043.79 | −0.0351861 | ||||||||
\(133\) | −87245.6 | −0.427676 | ||||||||
\(134\) | −72764.3 | −0.350071 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | −38496.8 | −0.178475 | ||||||||
\(137\) | 301598. | 1.37286 | 0.686431 | − | 0.727195i | \(-0.259176\pi\) | ||||
0.686431 | + | 0.727195i | \(0.259176\pi\) | |||||||
\(138\) | −167577. | −0.749058 | ||||||||
\(139\) | −90083.8 | −0.395466 | −0.197733 | − | 0.980256i | \(-0.563358\pi\) | ||||
−0.197733 | + | 0.980256i | \(0.563358\pi\) | |||||||
\(140\) | −96671.0 | −0.416847 | ||||||||
\(141\) | −32367.5 | −0.137108 | ||||||||
\(142\) | −11156.1 | −0.0464292 | ||||||||
\(143\) | −13402.3 | −0.0548073 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −42545.8 | −0.168049 | ||||||||
\(146\) | −190410. | −0.739277 | ||||||||
\(147\) | −374410. | −1.42907 | ||||||||
\(148\) | −64687.5 | −0.242754 | ||||||||
\(149\) | −37471.4 | −0.138272 | −0.0691361 | − | 0.997607i | \(-0.522024\pi\) | ||||
−0.0691361 | + | 0.997607i | \(0.522024\pi\) | |||||||
\(150\) | 22500.0 | 0.0816497 | ||||||||
\(151\) | −343904. | −1.22743 | −0.613713 | − | 0.789529i | \(-0.710325\pi\) | ||||
−0.613713 | + | 0.789529i | \(0.710325\pi\) | |||||||
\(152\) | 23104.0 | 0.0811107 | ||||||||
\(153\) | 48722.5 | 0.168268 | ||||||||
\(154\) | −47286.8 | −0.160671 | ||||||||
\(155\) | 108739. | 0.363542 | ||||||||
\(156\) | 39454.6 | 0.129803 | ||||||||
\(157\) | 211593. | 0.685096 | 0.342548 | − | 0.939500i | \(-0.388710\pi\) | ||||
0.342548 | + | 0.939500i | \(0.388710\pi\) | |||||||
\(158\) | −233690. | −0.744728 | ||||||||
\(159\) | 116823. | 0.366469 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | −1.12499e6 | −3.42044 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −460898. | −1.35874 | −0.679369 | − | 0.733797i | \(-0.737746\pi\) | ||||
−0.679369 | + | 0.733797i | \(0.737746\pi\) | |||||||
\(164\) | −115883. | −0.336442 | ||||||||
\(165\) | 11005.9 | 0.0314714 | ||||||||
\(166\) | 202998. | 0.571770 | ||||||||
\(167\) | 298005. | 0.826860 | 0.413430 | − | 0.910536i | \(-0.364331\pi\) | ||||
0.413430 | + | 0.910536i | \(0.364331\pi\) | |||||||
\(168\) | 139206. | 0.380527 | ||||||||
\(169\) | −296222. | −0.797813 | ||||||||
\(170\) | 60151.3 | 0.159633 | ||||||||
\(171\) | −29241.0 | −0.0764719 | ||||||||
\(172\) | 151403. | 0.390223 | ||||||||
\(173\) | −422602. | −1.07354 | −0.536768 | − | 0.843730i | \(-0.680355\pi\) | ||||
−0.536768 | + | 0.843730i | \(0.680355\pi\) | |||||||
\(174\) | 61266.0 | 0.153407 | ||||||||
\(175\) | 151048. | 0.372839 | ||||||||
\(176\) | 12522.3 | 0.0304721 | ||||||||
\(177\) | −25944.7 | −0.0622466 | ||||||||
\(178\) | 220032. | 0.520517 | ||||||||
\(179\) | −43456.8 | −0.101374 | −0.0506869 | − | 0.998715i | \(-0.516141\pi\) | ||||
−0.0506869 | + | 0.998715i | \(0.516141\pi\) | |||||||
\(180\) | −32400.0 | −0.0745356 | ||||||||
\(181\) | −192237. | −0.436155 | −0.218077 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218077 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(182\) | 264869. | 0.592725 | ||||||||
\(183\) | 153242. | 0.338260 | ||||||||
\(184\) | 297914. | 0.648703 | ||||||||
\(185\) | 101074. | 0.217126 | ||||||||
\(186\) | −156584. | −0.331867 | ||||||||
\(187\) | 29423.1 | 0.0615296 | ||||||||
\(188\) | 57542.2 | 0.118739 | ||||||||
\(189\) | −176183. | −0.358764 | ||||||||
\(190\) | −36100.0 | −0.0725476 | ||||||||
\(191\) | 51099.9 | 0.101353 | 0.0506766 | − | 0.998715i | \(-0.483862\pi\) | ||||
0.0506766 | + | 0.998715i | \(0.483862\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −515621. | −0.996409 | −0.498205 | − | 0.867060i | \(-0.666007\pi\) | ||||
−0.498205 | + | 0.867060i | \(0.666007\pi\) | |||||||
\(194\) | 340436. | 0.649427 | ||||||||
\(195\) | −61647.8 | −0.116100 | ||||||||
\(196\) | 665617. | 1.23761 | ||||||||
\(197\) | −559885. | −1.02786 | −0.513929 | − | 0.857833i | \(-0.671810\pi\) | ||||
−0.513929 | + | 0.857833i | \(0.671810\pi\) | |||||||
\(198\) | −15848.5 | −0.0287293 | ||||||||
\(199\) | −905154. | −1.62028 | −0.810140 | − | 0.586237i | \(-0.800609\pi\) | ||||
−0.810140 | + | 0.586237i | \(0.800609\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −163720. | −0.285832 | ||||||||
\(202\) | 448018. | 0.772532 | ||||||||
\(203\) | 411295. | 0.700508 | ||||||||
\(204\) | −86617.8 | −0.145724 | ||||||||
\(205\) | 181067. | 0.300922 | ||||||||
\(206\) | −487455. | −0.800325 | ||||||||
\(207\) | −377047. | −0.611603 | ||||||||
\(208\) | −70141.5 | −0.112413 | ||||||||
\(209\) | −17658.4 | −0.0279631 | ||||||||
\(210\) | −217510. | −0.340354 | ||||||||
\(211\) | −722060. | −1.11652 | −0.558261 | − | 0.829666i | \(-0.688531\pi\) | ||||
−0.558261 | + | 0.829666i | \(0.688531\pi\) | |||||||
\(212\) | −207686. | −0.317371 | ||||||||
\(213\) | −25101.2 | −0.0379093 | ||||||||
\(214\) | 606040. | 0.904621 | ||||||||
\(215\) | −236567. | −0.349026 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −1.05119e6 | −1.51541 | ||||||||
\(218\) | −104904. | −0.149503 | ||||||||
\(219\) | −428422. | −0.603617 | ||||||||
\(220\) | −19566.1 | −0.0272550 | ||||||||
\(221\) | −164809. | −0.226986 | ||||||||
\(222\) | −145547. | −0.198208 | ||||||||
\(223\) | −408801. | −0.550490 | −0.275245 | − | 0.961374i | \(-0.588759\pi\) | ||||
−0.275245 | + | 0.961374i | \(0.588759\pi\) | |||||||
\(224\) | −247478. | −0.329546 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 629880. | 0.820326 | ||||||||
\(227\) | −612099. | −0.788419 | −0.394210 | − | 0.919021i | \(-0.628982\pi\) | ||||
−0.394210 | + | 0.919021i | \(0.628982\pi\) | |||||||
\(228\) | 51984.0 | 0.0662266 | ||||||||
\(229\) | 274614. | 0.346046 | 0.173023 | − | 0.984918i | \(-0.444647\pi\) | ||||
0.173023 | + | 0.984918i | \(0.444647\pi\) | |||||||
\(230\) | −465490. | −0.580218 | ||||||||
\(231\) | −106395. | −0.131188 | ||||||||
\(232\) | −108917. | −0.132855 | ||||||||
\(233\) | 327043. | 0.394653 | 0.197326 | − | 0.980338i | \(-0.436774\pi\) | ||||
0.197326 | + | 0.980338i | \(0.436774\pi\) | |||||||
\(234\) | 88772.9 | 0.105984 | ||||||||
\(235\) | −89909.8 | −0.106203 | ||||||||
\(236\) | 46123.9 | 0.0539071 | ||||||||
\(237\) | −525803. | −0.608068 | ||||||||
\(238\) | −581489. | −0.665424 | ||||||||
\(239\) | −539189. | −0.610585 | −0.305293 | − | 0.952259i | \(-0.598754\pi\) | ||||
−0.305293 | + | 0.952259i | \(0.598754\pi\) | |||||||
\(240\) | 57600.0 | 0.0645497 | ||||||||
\(241\) | −102491. | −0.113669 | −0.0568346 | − | 0.998384i | \(-0.518101\pi\) | ||||
−0.0568346 | + | 0.998384i | \(0.518101\pi\) | |||||||
\(242\) | 634633. | 0.696601 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −272431. | −0.292942 | ||||||||
\(245\) | −1.04003e6 | −1.10695 | ||||||||
\(246\) | −260736. | −0.274703 | ||||||||
\(247\) | 98910.5 | 0.103157 | ||||||||
\(248\) | 278371. | 0.287405 | ||||||||
\(249\) | 456745. | 0.466848 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | −931446. | −0.933197 | −0.466599 | − | 0.884469i | \(-0.654521\pi\) | ||||
−0.466599 | + | 0.884469i | \(0.654521\pi\) | |||||||
\(252\) | 313214. | 0.310699 | ||||||||
\(253\) | −227695. | −0.223642 | ||||||||
\(254\) | −680036. | −0.661375 | ||||||||
\(255\) | 135340. | 0.130340 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −29506.6 | −0.0278668 | −0.0139334 | − | 0.999903i | \(-0.504435\pi\) | ||||
−0.0139334 | + | 0.999903i | \(0.504435\pi\) | |||||||
\(258\) | 340656. | 0.318616 | ||||||||
\(259\) | −977095. | −0.905081 | ||||||||
\(260\) | 109596. | 0.100545 | ||||||||
\(261\) | 137849. | 0.125257 | ||||||||
\(262\) | −1.01984e6 | −0.917862 | ||||||||
\(263\) | 1.26941e6 | 1.13165 | 0.565826 | − | 0.824525i | \(-0.308558\pi\) | ||||
0.565826 | + | 0.824525i | \(0.308558\pi\) | |||||||
\(264\) | 28175.1 | 0.0248803 | ||||||||
\(265\) | 324509. | 0.283865 | ||||||||
\(266\) | 348982. | 0.302412 | ||||||||
\(267\) | 495071. | 0.425001 | ||||||||
\(268\) | 291057. | 0.247538 | ||||||||
\(269\) | −1.96862e6 | −1.65875 | −0.829375 | − | 0.558692i | \(-0.811303\pi\) | ||||
−0.829375 | + | 0.558692i | \(0.811303\pi\) | |||||||
\(270\) | −72900.0 | −0.0608581 | ||||||||
\(271\) | 548933. | 0.454042 | 0.227021 | − | 0.973890i | \(-0.427101\pi\) | ||||
0.227021 | + | 0.973890i | \(0.427101\pi\) | |||||||
\(272\) | 153987. | 0.126201 | ||||||||
\(273\) | 595956. | 0.483958 | ||||||||
\(274\) | −1.20639e6 | −0.970760 | ||||||||
\(275\) | 30572.0 | 0.0243777 | ||||||||
\(276\) | 670306. | 0.529664 | ||||||||
\(277\) | 1.85299e6 | 1.45102 | 0.725512 | − | 0.688210i | \(-0.241603\pi\) | ||||
0.725512 | + | 0.688210i | \(0.241603\pi\) | |||||||
\(278\) | 360335. | 0.279637 | ||||||||
\(279\) | −352313. | −0.270968 | ||||||||
\(280\) | 386684. | 0.294755 | ||||||||
\(281\) | −2.25804e6 | −1.70595 | −0.852975 | − | 0.521952i | \(-0.825204\pi\) | ||||
−0.852975 | + | 0.521952i | \(0.825204\pi\) | |||||||
\(282\) | 129470. | 0.0969497 | ||||||||
\(283\) | 1.90922e6 | 1.41706 | 0.708532 | − | 0.705679i | \(-0.249358\pi\) | ||||
0.708532 | + | 0.705679i | \(0.249358\pi\) | |||||||
\(284\) | 44624.3 | 0.0328304 | ||||||||
\(285\) | −81225.0 | −0.0592349 | ||||||||
\(286\) | 53609.1 | 0.0387546 | ||||||||
\(287\) | −1.75039e6 | −1.25439 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −1.05804e6 | −0.745173 | ||||||||
\(290\) | 170183. | 0.118829 | ||||||||
\(291\) | 765980. | 0.530255 | ||||||||
\(292\) | 761639. | 0.522747 | ||||||||
\(293\) | 2.33353e6 | 1.58798 | 0.793989 | − | 0.607932i | \(-0.208001\pi\) | ||||
0.793989 | + | 0.607932i | \(0.208001\pi\) | |||||||
\(294\) | 1.49764e6 | 1.01051 | ||||||||
\(295\) | −72068.6 | −0.0482160 | ||||||||
\(296\) | 258750. | 0.171653 | ||||||||
\(297\) | −35659.2 | −0.0234574 | ||||||||
\(298\) | 149886. | 0.0977732 | ||||||||
\(299\) | 1.27540e6 | 0.825026 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | 2.28692e6 | 1.45490 | ||||||||
\(302\) | 1.37562e6 | 0.867921 | ||||||||
\(303\) | 1.00804e6 | 0.630770 | ||||||||
\(304\) | −92416.0 | −0.0573539 | ||||||||
\(305\) | 425673. | 0.262015 | ||||||||
\(306\) | −194890. | −0.118983 | ||||||||
\(307\) | 878028. | 0.531695 | 0.265847 | − | 0.964015i | \(-0.414348\pi\) | ||||
0.265847 | + | 0.964015i | \(0.414348\pi\) | |||||||
\(308\) | 189147. | 0.113612 | ||||||||
\(309\) | −1.09677e6 | −0.653463 | ||||||||
\(310\) | −434954. | −0.257063 | ||||||||
\(311\) | −469932. | −0.275508 | −0.137754 | − | 0.990466i | \(-0.543988\pi\) | ||||
−0.137754 | + | 0.990466i | \(0.543988\pi\) | |||||||
\(312\) | −157818. | −0.0917849 | ||||||||
\(313\) | 1.34014e6 | 0.773194 | 0.386597 | − | 0.922249i | \(-0.373650\pi\) | ||||
0.386597 | + | 0.922249i | \(0.373650\pi\) | |||||||
\(314\) | −846371. | −0.484436 | ||||||||
\(315\) | −489397. | −0.277898 | ||||||||
\(316\) | 934761. | 0.526602 | ||||||||
\(317\) | −2.61609e6 | −1.46219 | −0.731096 | − | 0.682274i | \(-0.760991\pi\) | ||||
−0.731096 | + | 0.682274i | \(0.760991\pi\) | |||||||
\(318\) | −467294. | −0.259133 | ||||||||
\(319\) | 83245.5 | 0.0458020 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | 1.36359e6 | 0.738620 | ||||||||
\(322\) | 4.49994e6 | 2.41862 | ||||||||
\(323\) | −217146. | −0.115810 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −171244. | −0.0899305 | ||||||||
\(326\) | 1.84359e6 | 0.960772 | ||||||||
\(327\) | −236033. | −0.122068 | ||||||||
\(328\) | 463531. | 0.237900 | ||||||||
\(329\) | 869167. | 0.442704 | ||||||||
\(330\) | −44023.7 | −0.0222537 | ||||||||
\(331\) | −2.14809e6 | −1.07766 | −0.538831 | − | 0.842414i | \(-0.681134\pi\) | ||||
−0.538831 | + | 0.842414i | \(0.681134\pi\) | |||||||
\(332\) | −811991. | −0.404302 | ||||||||
\(333\) | −327480. | −0.161836 | ||||||||
\(334\) | −1.19202e6 | −0.584678 | ||||||||
\(335\) | −454777. | −0.221404 | ||||||||
\(336\) | −556825. | −0.269073 | ||||||||
\(337\) | 3.34596e6 | 1.60489 | 0.802447 | − | 0.596723i | \(-0.203531\pi\) | ||||
0.802447 | + | 0.596723i | \(0.203531\pi\) | |||||||
\(338\) | 1.18489e6 | 0.564139 | ||||||||
\(339\) | 1.41723e6 | 0.669794 | ||||||||
\(340\) | −240605. | −0.112878 | ||||||||
\(341\) | −212759. | −0.0990835 | ||||||||
\(342\) | 116964. | 0.0540738 | ||||||||
\(343\) | 5.99217e6 | 2.75010 | ||||||||
\(344\) | −605611. | −0.275929 | ||||||||
\(345\) | −1.04735e6 | −0.473746 | ||||||||
\(346\) | 1.69041e6 | 0.759104 | ||||||||
\(347\) | −495113. | −0.220740 | −0.110370 | − | 0.993891i | \(-0.535204\pi\) | ||||
−0.110370 | + | 0.993891i | \(0.535204\pi\) | |||||||
\(348\) | −245064. | −0.108475 | ||||||||
\(349\) | 388990. | 0.170952 | 0.0854762 | − | 0.996340i | \(-0.472759\pi\) | ||||
0.0854762 | + | 0.996340i | \(0.472759\pi\) | |||||||
\(350\) | −604194. | −0.263637 | ||||||||
\(351\) | 199739. | 0.0865356 | ||||||||
\(352\) | −50089.1 | −0.0215470 | ||||||||
\(353\) | −1.91329e6 | −0.817227 | −0.408614 | − | 0.912707i | \(-0.633988\pi\) | ||||
−0.408614 | + | 0.912707i | \(0.633988\pi\) | |||||||
\(354\) | 103779. | 0.0440150 | ||||||||
\(355\) | −69725.5 | −0.0293644 | ||||||||
\(356\) | −880127. | −0.368061 | ||||||||
\(357\) | −1.30835e6 | −0.543317 | ||||||||
\(358\) | 173827. | 0.0716820 | ||||||||
\(359\) | −1.12700e6 | −0.461515 | −0.230758 | − | 0.973011i | \(-0.574120\pi\) | ||||
−0.230758 | + | 0.973011i | \(0.574120\pi\) | |||||||
\(360\) | 129600. | 0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 768948. | 0.308408 | ||||||||
\(363\) | 1.42792e6 | 0.568773 | ||||||||
\(364\) | −1.05948e6 | −0.419120 | ||||||||
\(365\) | −1.19006e6 | −0.467560 | ||||||||
\(366\) | −612969. | −0.239186 | ||||||||
\(367\) | 4.69344e6 | 1.81897 | 0.909486 | − | 0.415735i | \(-0.136475\pi\) | ||||
0.909486 | + | 0.415735i | \(0.136475\pi\) | |||||||
\(368\) | −1.19166e6 | −0.458702 | ||||||||
\(369\) | −586657. | −0.224294 | ||||||||
\(370\) | −404297. | −0.153531 | ||||||||
\(371\) | −3.13707e6 | −1.18328 | ||||||||
\(372\) | 626334. | 0.234665 | ||||||||
\(373\) | −325600. | −0.121175 | −0.0605874 | − | 0.998163i | \(-0.519297\pi\) | ||||
−0.0605874 | + | 0.998163i | \(0.519297\pi\) | |||||||
\(374\) | −117692. | −0.0435080 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | −230169. | −0.0839609 | ||||||||
\(377\) | −466286. | −0.168966 | ||||||||
\(378\) | 704732. | 0.253685 | ||||||||
\(379\) | −4.29635e6 | −1.53639 | −0.768195 | − | 0.640216i | \(-0.778845\pi\) | ||||
−0.768195 | + | 0.640216i | \(0.778845\pi\) | |||||||
\(380\) | 144400. | 0.0512989 | ||||||||
\(381\) | −1.53008e6 | −0.540010 | ||||||||
\(382\) | −204400. | −0.0716675 | ||||||||
\(383\) | −778069. | −0.271032 | −0.135516 | − | 0.990775i | \(-0.543269\pi\) | ||||
−0.135516 | + | 0.990775i | \(0.543269\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −295543. | −0.101617 | ||||||||
\(386\) | 2.06249e6 | 0.704568 | ||||||||
\(387\) | 766476. | 0.260148 | ||||||||
\(388\) | −1.36174e6 | −0.459215 | ||||||||
\(389\) | 1.40575e6 | 0.471015 | 0.235508 | − | 0.971873i | \(-0.424325\pi\) | ||||
0.235508 | + | 0.971873i | \(0.424325\pi\) | |||||||
\(390\) | 246591. | 0.0820949 | ||||||||
\(391\) | −2.79998e6 | −0.926219 | ||||||||
\(392\) | −2.66247e6 | −0.875123 | ||||||||
\(393\) | −2.29463e6 | −0.749431 | ||||||||
\(394\) | 2.23954e6 | 0.726805 | ||||||||
\(395\) | −1.46056e6 | −0.471008 | ||||||||
\(396\) | 63394.1 | 0.0203147 | ||||||||
\(397\) | 4.27508e6 | 1.36134 | 0.680672 | − | 0.732589i | \(-0.261688\pi\) | ||||
0.680672 | + | 0.732589i | \(0.261688\pi\) | |||||||
\(398\) | 3.62062e6 | 1.14571 | ||||||||
\(399\) | 785210. | 0.246919 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 5.58537e6 | 1.73457 | 0.867283 | − | 0.497816i | \(-0.165865\pi\) | ||||
0.867283 | + | 0.497816i | \(0.165865\pi\) | |||||||
\(402\) | 654878. | 0.202114 | ||||||||
\(403\) | 1.19173e6 | 0.365524 | ||||||||
\(404\) | −1.79207e6 | −0.546263 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −1.64518e6 | −0.495334 | ||||||||
\(407\) | −197763. | −0.0591777 | ||||||||
\(408\) | 346471. | 0.103043 | ||||||||
\(409\) | −5.31519e6 | −1.57112 | −0.785562 | − | 0.618783i | \(-0.787626\pi\) | ||||
−0.785562 | + | 0.618783i | \(0.787626\pi\) | |||||||
\(410\) | −724268. | −0.212784 | ||||||||
\(411\) | −2.71438e6 | −0.792622 | ||||||||
\(412\) | 1.94982e6 | 0.565915 | ||||||||
\(413\) | 696695. | 0.200987 | ||||||||
\(414\) | 1.50819e6 | 0.432469 | ||||||||
\(415\) | 1.26874e6 | 0.361619 | ||||||||
\(416\) | 280566. | 0.0794880 | ||||||||
\(417\) | 810754. | 0.228323 | ||||||||
\(418\) | 70633.5 | 0.0197729 | ||||||||
\(419\) | −6.55749e6 | −1.82475 | −0.912373 | − | 0.409361i | \(-0.865752\pi\) | ||||
−0.912373 | + | 0.409361i | \(0.865752\pi\) | |||||||
\(420\) | 870039. | 0.240667 | ||||||||
\(421\) | 1.95134e6 | 0.536570 | 0.268285 | − | 0.963340i | \(-0.413543\pi\) | ||||
0.268285 | + | 0.963340i | \(0.413543\pi\) | |||||||
\(422\) | 2.88824e6 | 0.789500 | ||||||||
\(423\) | 291308. | 0.0791591 | ||||||||
\(424\) | 830744. | 0.224415 | ||||||||
\(425\) | 375945. | 0.100961 | ||||||||
\(426\) | 100405. | 0.0268059 | ||||||||
\(427\) | −4.11502e6 | −1.09220 | ||||||||
\(428\) | −2.42416e6 | −0.639664 | ||||||||
\(429\) | 120621. | 0.0316430 | ||||||||
\(430\) | 946267. | 0.246799 | ||||||||
\(431\) | 1.28413e6 | 0.332979 | 0.166490 | − | 0.986043i | \(-0.446757\pi\) | ||||
0.166490 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 3.19273e6 | 0.818356 | 0.409178 | − | 0.912455i | \(-0.365815\pi\) | ||||
0.409178 | + | 0.912455i | \(0.365815\pi\) | |||||||
\(434\) | 4.20475e6 | 1.07156 | ||||||||
\(435\) | 382913. | 0.0970234 | ||||||||
\(436\) | 419614. | 0.105714 | ||||||||
\(437\) | 1.68042e6 | 0.420934 | ||||||||
\(438\) | 1.71369e6 | 0.426822 | ||||||||
\(439\) | −6.27887e6 | −1.55496 | −0.777482 | − | 0.628905i | \(-0.783503\pi\) | ||||
−0.777482 | + | 0.628905i | \(0.783503\pi\) | |||||||
\(440\) | 78264.3 | 0.0192722 | ||||||||
\(441\) | 3.36969e6 | 0.825074 | ||||||||
\(442\) | 659235. | 0.160503 | ||||||||
\(443\) | −1.54141e6 | −0.373172 | −0.186586 | − | 0.982439i | \(-0.559742\pi\) | ||||
−0.186586 | + | 0.982439i | \(0.559742\pi\) | |||||||
\(444\) | 582187. | 0.140154 | ||||||||
\(445\) | 1.37520e6 | 0.329204 | ||||||||
\(446\) | 1.63520e6 | 0.389255 | ||||||||
\(447\) | 337243. | 0.0798315 | ||||||||
\(448\) | 989911. | 0.233024 | ||||||||
\(449\) | 6.96040e6 | 1.62937 | 0.814683 | − | 0.579907i | \(-0.196911\pi\) | ||||
0.814683 | + | 0.579907i | \(0.196911\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | −354277. | −0.0820166 | ||||||||
\(452\) | −2.51952e6 | −0.580058 | ||||||||
\(453\) | 3.09514e6 | 0.708655 | ||||||||
\(454\) | 2.44840e6 | 0.557497 | ||||||||
\(455\) | 1.65543e6 | 0.374872 | ||||||||
\(456\) | −207936. | −0.0468293 | ||||||||
\(457\) | −529337. | −0.118561 | −0.0592805 | − | 0.998241i | \(-0.518881\pi\) | ||||
−0.0592805 | + | 0.998241i | \(0.518881\pi\) | |||||||
\(458\) | −1.09845e6 | −0.244691 | ||||||||
\(459\) | −438503. | −0.0971495 | ||||||||
\(460\) | 1.86196e6 | 0.410276 | ||||||||
\(461\) | −7.40968e6 | −1.62385 | −0.811927 | − | 0.583759i | \(-0.801581\pi\) | ||||
−0.811927 | + | 0.583759i | \(0.801581\pi\) | |||||||
\(462\) | 425581. | 0.0927636 | ||||||||
\(463\) | −2.51847e6 | −0.545989 | −0.272995 | − | 0.962016i | \(-0.588014\pi\) | ||||
−0.272995 | + | 0.962016i | \(0.588014\pi\) | |||||||
\(464\) | 435669. | 0.0939425 | ||||||||
\(465\) | −978647. | −0.209891 | ||||||||
\(466\) | −1.30817e6 | −0.279061 | ||||||||
\(467\) | −6.81787e6 | −1.44663 | −0.723313 | − | 0.690520i | \(-0.757382\pi\) | ||||
−0.723313 | + | 0.690520i | \(0.757382\pi\) | |||||||
\(468\) | −355091. | −0.0749421 | ||||||||
\(469\) | 4.39637e6 | 0.922917 | ||||||||
\(470\) | 359639. | 0.0750969 | ||||||||
\(471\) | −1.90433e6 | −0.395541 | ||||||||
\(472\) | −184496. | −0.0381181 | ||||||||
\(473\) | 462868. | 0.0951272 | ||||||||
\(474\) | 2.10321e6 | 0.429969 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | 2.32595e6 | 0.470526 | ||||||||
\(477\) | −1.05141e6 | −0.211581 | ||||||||
\(478\) | 2.15676e6 | 0.431749 | ||||||||
\(479\) | 9.82434e6 | 1.95643 | 0.978215 | − | 0.207593i | \(-0.0665628\pi\) | ||||
0.978215 | + | 0.207593i | \(0.0665628\pi\) | |||||||
\(480\) | −230400. | −0.0456435 | ||||||||
\(481\) | 1.10773e6 | 0.218310 | ||||||||
\(482\) | 409964. | 0.0803763 | ||||||||
\(483\) | 1.01249e7 | 1.97479 | ||||||||
\(484\) | −2.53853e6 | −0.492572 | ||||||||
\(485\) | 2.12772e6 | 0.410734 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −7.71482e6 | −1.47402 | −0.737010 | − | 0.675882i | \(-0.763763\pi\) | ||||
−0.737010 | + | 0.675882i | \(0.763763\pi\) | |||||||
\(488\) | 1.08972e6 | 0.207141 | ||||||||
\(489\) | 4.14808e6 | 0.784467 | ||||||||
\(490\) | 4.16011e6 | 0.782734 | ||||||||
\(491\) | 3.43591e6 | 0.643189 | 0.321595 | − | 0.946877i | \(-0.395781\pi\) | ||||
0.321595 | + | 0.946877i | \(0.395781\pi\) | |||||||
\(492\) | 1.04295e6 | 0.194245 | ||||||||
\(493\) | 1.02367e6 | 0.189690 | ||||||||
\(494\) | −395642. | −0.0729432 | ||||||||
\(495\) | −99053.2 | −0.0181700 | ||||||||
\(496\) | −1.11348e6 | −0.203226 | ||||||||
\(497\) | 674044. | 0.122404 | ||||||||
\(498\) | −1.82698e6 | −0.330111 | ||||||||
\(499\) | −485954. | −0.0873663 | −0.0436832 | − | 0.999045i | \(-0.513909\pi\) | ||||
−0.0436832 | + | 0.999045i | \(0.513909\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | −2.68204e6 | −0.477388 | ||||||||
\(502\) | 3.72579e6 | 0.659870 | ||||||||
\(503\) | −4.76630e6 | −0.839966 | −0.419983 | − | 0.907532i | \(-0.637964\pi\) | ||||
−0.419983 | + | 0.907532i | \(0.637964\pi\) | |||||||
\(504\) | −1.25286e6 | −0.219697 | ||||||||
\(505\) | 2.80011e6 | 0.488592 | ||||||||
\(506\) | 910782. | 0.158139 | ||||||||
\(507\) | 2.66600e6 | 0.460617 | ||||||||
\(508\) | 2.72014e6 | 0.467663 | ||||||||
\(509\) | −9.08039e6 | −1.55350 | −0.776748 | − | 0.629812i | \(-0.783132\pi\) | ||||
−0.776748 | + | 0.629812i | \(0.783132\pi\) | |||||||
\(510\) | −541361. | −0.0921641 | ||||||||
\(511\) | 1.15044e7 | 1.94901 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 263169. | 0.0441511 | ||||||||
\(514\) | 118027. | 0.0197048 | ||||||||
\(515\) | −3.04659e6 | −0.506170 | ||||||||
\(516\) | −1.36262e6 | −0.225295 | ||||||||
\(517\) | 175918. | 0.0289457 | ||||||||
\(518\) | 3.90838e6 | 0.639989 | ||||||||
\(519\) | 3.80342e6 | 0.619806 | ||||||||
\(520\) | −438385. | −0.0710963 | ||||||||
\(521\) | 4.07561e6 | 0.657807 | 0.328904 | − | 0.944363i | \(-0.393321\pi\) | ||||
0.328904 | + | 0.944363i | \(0.393321\pi\) | |||||||
\(522\) | −551394. | −0.0885698 | ||||||||
\(523\) | −7.54955e6 | −1.20689 | −0.603444 | − | 0.797405i | \(-0.706205\pi\) | ||||
−0.603444 | + | 0.797405i | \(0.706205\pi\) | |||||||
\(524\) | 4.07935e6 | 0.649026 | ||||||||
\(525\) | −1.35944e6 | −0.215259 | ||||||||
\(526\) | −5.07764e6 | −0.800198 | ||||||||
\(527\) | −2.61630e6 | −0.410357 | ||||||||
\(528\) | −112701. | −0.0175931 | ||||||||
\(529\) | 1.52318e7 | 2.36653 | ||||||||
\(530\) | −1.29804e6 | −0.200723 | ||||||||
\(531\) | 233502. | 0.0359381 | ||||||||
\(532\) | −1.39593e6 | −0.213838 | ||||||||
\(533\) | 1.98442e6 | 0.302563 | ||||||||
\(534\) | −1.98029e6 | −0.300521 | ||||||||
\(535\) | 3.78775e6 | 0.572133 | ||||||||
\(536\) | −1.16423e6 | −0.175036 | ||||||||
\(537\) | 391111. | 0.0585281 | ||||||||
\(538\) | 7.87448e6 | 1.17291 | ||||||||
\(539\) | 2.03492e6 | 0.301701 | ||||||||
\(540\) | 291600. | 0.0430331 | ||||||||
\(541\) | −6.84906e6 | −1.00609 | −0.503046 | − | 0.864260i | \(-0.667787\pi\) | ||||
−0.503046 | + | 0.864260i | \(0.667787\pi\) | |||||||
\(542\) | −2.19573e6 | −0.321056 | ||||||||
\(543\) | 1.73013e6 | 0.251814 | ||||||||
\(544\) | −615949. | −0.0892375 | ||||||||
\(545\) | −655647. | −0.0945537 | ||||||||
\(546\) | −2.38382e6 | −0.342210 | ||||||||
\(547\) | −4.68823e6 | −0.669948 | −0.334974 | − | 0.942227i | \(-0.608727\pi\) | ||||
−0.334974 | + | 0.942227i | \(0.608727\pi\) | |||||||
\(548\) | 4.82557e6 | 0.686431 | ||||||||
\(549\) | −1.37918e6 | −0.195294 | ||||||||
\(550\) | −122288. | −0.0172376 | ||||||||
\(551\) | −614362. | −0.0862075 | ||||||||
\(552\) | −2.68122e6 | −0.374529 | ||||||||
\(553\) | 1.41194e7 | 1.96338 | ||||||||
\(554\) | −7.41197e6 | −1.02603 | ||||||||
\(555\) | −909668. | −0.125358 | ||||||||
\(556\) | −1.44134e6 | −0.197733 | ||||||||
\(557\) | −3.10332e6 | −0.423827 | −0.211913 | − | 0.977288i | \(-0.567969\pi\) | ||||
−0.211913 | + | 0.977288i | \(0.567969\pi\) | |||||||
\(558\) | 1.40925e6 | 0.191603 | ||||||||
\(559\) | −2.59268e6 | −0.350929 | ||||||||
\(560\) | −1.54674e6 | −0.208423 | ||||||||
\(561\) | −264808. | −0.0355242 | ||||||||
\(562\) | 9.03217e6 | 1.20629 | ||||||||
\(563\) | 3.39399e6 | 0.451274 | 0.225637 | − | 0.974211i | \(-0.427554\pi\) | ||||
0.225637 | + | 0.974211i | \(0.427554\pi\) | |||||||
\(564\) | −517880. | −0.0685538 | ||||||||
\(565\) | 3.93675e6 | 0.518820 | ||||||||
\(566\) | −7.63687e6 | −1.00202 | ||||||||
\(567\) | 1.58565e6 | 0.207133 | ||||||||
\(568\) | −178497. | −0.0232146 | ||||||||
\(569\) | 5.18383e6 | 0.671228 | 0.335614 | − | 0.942000i | \(-0.391056\pi\) | ||||
0.335614 | + | 0.942000i | \(0.391056\pi\) | |||||||
\(570\) | 324900. | 0.0418854 | ||||||||
\(571\) | −2.15935e6 | −0.277161 | −0.138581 | − | 0.990351i | \(-0.544254\pi\) | ||||
−0.138581 | + | 0.990351i | \(0.544254\pi\) | |||||||
\(572\) | −214437. | −0.0274037 | ||||||||
\(573\) | −459900. | −0.0585162 | ||||||||
\(574\) | 7.00157e6 | 0.886984 | ||||||||
\(575\) | −2.90931e6 | −0.366962 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 1.52795e6 | 0.191060 | 0.0955299 | − | 0.995427i | \(-0.469545\pi\) | ||||
0.0955299 | + | 0.995427i | \(0.469545\pi\) | |||||||
\(578\) | 4.23216e6 | 0.526917 | ||||||||
\(579\) | 4.64059e6 | 0.575277 | ||||||||
\(580\) | −680733. | −0.0840247 | ||||||||
\(581\) | −1.22650e7 | −1.50740 | ||||||||
\(582\) | −3.06392e6 | −0.374947 | ||||||||
\(583\) | −634937. | −0.0773677 | ||||||||
\(584\) | −3.04656e6 | −0.369638 | ||||||||
\(585\) | 554830. | 0.0670302 | ||||||||
\(586\) | −9.33413e6 | −1.12287 | ||||||||
\(587\) | −8.44316e6 | −1.01137 | −0.505684 | − | 0.862719i | \(-0.668760\pi\) | ||||
−0.505684 | + | 0.862719i | \(0.668760\pi\) | |||||||
\(588\) | −5.99055e6 | −0.714535 | ||||||||
\(589\) | 1.57018e6 | 0.186493 | ||||||||
\(590\) | 288274. | 0.0340939 | ||||||||
\(591\) | 5.03896e6 | 0.593434 | ||||||||
\(592\) | −1.03500e6 | −0.121377 | ||||||||
\(593\) | 4.70109e6 | 0.548987 | 0.274494 | − | 0.961589i | \(-0.411490\pi\) | ||||
0.274494 | + | 0.961589i | \(0.411490\pi\) | |||||||
\(594\) | 142637. | 0.0165869 | ||||||||
\(595\) | −3.63430e6 | −0.420851 | ||||||||
\(596\) | −599543. | −0.0691361 | ||||||||
\(597\) | 8.14639e6 | 0.935469 | ||||||||
\(598\) | −5.10159e6 | −0.583382 | ||||||||
\(599\) | −3.34478e6 | −0.380891 | −0.190445 | − | 0.981698i | \(-0.560993\pi\) | ||||
−0.190445 | + | 0.981698i | \(0.560993\pi\) | |||||||
\(600\) | 360000. | 0.0408248 | ||||||||
\(601\) | −2.61862e6 | −0.295723 | −0.147862 | − | 0.989008i | \(-0.547239\pi\) | ||||
−0.147862 | + | 0.989008i | \(0.547239\pi\) | |||||||
\(602\) | −9.14766e6 | −1.02877 | ||||||||
\(603\) | 1.47348e6 | 0.165025 | ||||||||
\(604\) | −5.50247e6 | −0.613713 | ||||||||
\(605\) | 3.96646e6 | 0.440569 | ||||||||
\(606\) | −4.03216e6 | −0.446022 | ||||||||
\(607\) | −7.66986e6 | −0.844920 | −0.422460 | − | 0.906382i | \(-0.638833\pi\) | ||||
−0.422460 | + | 0.906382i | \(0.638833\pi\) | |||||||
\(608\) | 369664. | 0.0405554 | ||||||||
\(609\) | −3.70166e6 | −0.404439 | ||||||||
\(610\) | −1.70269e6 | −0.185273 | ||||||||
\(611\) | −985376. | −0.106782 | ||||||||
\(612\) | 779560. | 0.0841339 | ||||||||
\(613\) | −6.36378e6 | −0.684012 | −0.342006 | − | 0.939698i | \(-0.611106\pi\) | ||||
−0.342006 | + | 0.939698i | \(0.611106\pi\) | |||||||
\(614\) | −3.51211e6 | −0.375965 | ||||||||
\(615\) | −1.62960e6 | −0.173738 | ||||||||
\(616\) | −756589. | −0.0803356 | ||||||||
\(617\) | −3.24409e6 | −0.343068 | −0.171534 | − | 0.985178i | \(-0.554872\pi\) | ||||
−0.171534 | + | 0.985178i | \(0.554872\pi\) | |||||||
\(618\) | 4.38709e6 | 0.462068 | ||||||||
\(619\) | −5.90973e6 | −0.619928 | −0.309964 | − | 0.950748i | \(-0.600317\pi\) | ||||
−0.309964 | + | 0.950748i | \(0.600317\pi\) | |||||||
\(620\) | 1.73982e6 | 0.181771 | ||||||||
\(621\) | 3.39342e6 | 0.353109 | ||||||||
\(622\) | 1.87973e6 | 0.194813 | ||||||||
\(623\) | −1.32942e7 | −1.37228 | ||||||||
\(624\) | 631274. | 0.0649017 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −5.36055e6 | −0.546731 | ||||||||
\(627\) | 158925. | 0.0161445 | ||||||||
\(628\) | 3.38548e6 | 0.342548 | ||||||||
\(629\) | −2.43190e6 | −0.245086 | ||||||||
\(630\) | 1.95759e6 | 0.196503 | ||||||||
\(631\) | −9.48728e6 | −0.948568 | −0.474284 | − | 0.880372i | \(-0.657293\pi\) | ||||
−0.474284 | + | 0.880372i | \(0.657293\pi\) | |||||||
\(632\) | −3.73904e6 | −0.372364 | ||||||||
\(633\) | 6.49854e6 | 0.644624 | ||||||||
\(634\) | 1.04644e7 | 1.03393 | ||||||||
\(635\) | −4.25023e6 | −0.418290 | ||||||||
\(636\) | 1.86917e6 | 0.183234 | ||||||||
\(637\) | −1.13983e7 | −1.11299 | ||||||||
\(638\) | −332982. | −0.0323869 | ||||||||
\(639\) | 225911. | 0.0218869 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | −1.30834e7 | −1.25770 | −0.628849 | − | 0.777528i | \(-0.716473\pi\) | ||||
−0.628849 | + | 0.777528i | \(0.716473\pi\) | |||||||
\(642\) | −5.45436e6 | −0.522283 | ||||||||
\(643\) | −1.53137e6 | −0.146067 | −0.0730337 | − | 0.997329i | \(-0.523268\pi\) | ||||
−0.0730337 | + | 0.997329i | \(0.523268\pi\) | |||||||
\(644\) | −1.79998e7 | −1.71022 | ||||||||
\(645\) | 2.12910e6 | 0.201510 | ||||||||
\(646\) | 868584. | 0.0818900 | ||||||||
\(647\) | −1.02797e7 | −0.965428 | −0.482714 | − | 0.875778i | \(-0.660349\pi\) | ||||
−0.482714 | + | 0.875778i | \(0.660349\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 141010. | 0.0131413 | ||||||||
\(650\) | 684976. | 0.0635904 | ||||||||
\(651\) | 9.46068e6 | 0.874923 | ||||||||
\(652\) | −7.37436e6 | −0.679369 | ||||||||
\(653\) | 8.17907e6 | 0.750621 | 0.375311 | − | 0.926899i | \(-0.377536\pi\) | ||||
0.375311 | + | 0.926899i | \(0.377536\pi\) | |||||||
\(654\) | 944132. | 0.0863154 | ||||||||
\(655\) | −6.37398e6 | −0.580507 | ||||||||
\(656\) | −1.85413e6 | −0.168221 | ||||||||
\(657\) | 3.85580e6 | 0.348498 | ||||||||
\(658\) | −3.47667e6 | −0.313039 | ||||||||
\(659\) | 9.70084e6 | 0.870153 | 0.435076 | − | 0.900394i | \(-0.356721\pi\) | ||||
0.435076 | + | 0.900394i | \(0.356721\pi\) | |||||||
\(660\) | 176095. | 0.0157357 | ||||||||
\(661\) | 4.46335e6 | 0.397336 | 0.198668 | − | 0.980067i | \(-0.436339\pi\) | ||||
0.198668 | + | 0.980067i | \(0.436339\pi\) | |||||||
\(662\) | 8.59236e6 | 0.762022 | ||||||||
\(663\) | 1.48328e6 | 0.131050 | ||||||||
\(664\) | 3.24797e6 | 0.285885 | ||||||||
\(665\) | 2.18114e6 | 0.191262 | ||||||||
\(666\) | 1.30992e6 | 0.114435 | ||||||||
\(667\) | −7.92187e6 | −0.689466 | ||||||||
\(668\) | 4.76808e6 | 0.413430 | ||||||||
\(669\) | 3.67921e6 | 0.317826 | ||||||||
\(670\) | 1.81911e6 | 0.156557 | ||||||||
\(671\) | −832874. | −0.0714123 | ||||||||
\(672\) | 2.22730e6 | 0.190264 | ||||||||
\(673\) | 3.74229e6 | 0.318493 | 0.159246 | − | 0.987239i | \(-0.449094\pi\) | ||||
0.159246 | + | 0.987239i | \(0.449094\pi\) | |||||||
\(674\) | −1.33839e7 | −1.13483 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | −4.73956e6 | −0.398906 | ||||||||
\(677\) | 4.60520e6 | 0.386168 | 0.193084 | − | 0.981182i | \(-0.438151\pi\) | ||||
0.193084 | + | 0.981182i | \(0.438151\pi\) | |||||||
\(678\) | −5.66892e6 | −0.473616 | ||||||||
\(679\) | −2.05689e7 | −1.71213 | ||||||||
\(680\) | 962420. | 0.0798165 | ||||||||
\(681\) | 5.50889e6 | 0.455194 | ||||||||
\(682\) | 851034. | 0.0700626 | ||||||||
\(683\) | −1.04539e7 | −0.857484 | −0.428742 | − | 0.903427i | \(-0.641043\pi\) | ||||
−0.428742 | + | 0.903427i | \(0.641043\pi\) | |||||||
\(684\) | −467856. | −0.0382360 | ||||||||
\(685\) | −7.53995e6 | −0.613963 | ||||||||
\(686\) | −2.39687e7 | −1.94462 | ||||||||
\(687\) | −2.47152e6 | −0.199789 | ||||||||
\(688\) | 2.42244e6 | 0.195111 | ||||||||
\(689\) | 3.55650e6 | 0.285413 | ||||||||
\(690\) | 4.18941e6 | 0.334989 | ||||||||
\(691\) | 1.22485e7 | 0.975863 | 0.487931 | − | 0.872882i | \(-0.337752\pi\) | ||||
0.487931 | + | 0.872882i | \(0.337752\pi\) | |||||||
\(692\) | −6.76163e6 | −0.536768 | ||||||||
\(693\) | 957558. | 0.0757412 | ||||||||
\(694\) | 1.98045e6 | 0.156087 | ||||||||
\(695\) | 2.25209e6 | 0.176858 | ||||||||
\(696\) | 980256. | 0.0767037 | ||||||||
\(697\) | −4.35656e6 | −0.339674 | ||||||||
\(698\) | −1.55596e6 | −0.120882 | ||||||||
\(699\) | −2.94339e6 | −0.227853 | ||||||||
\(700\) | 2.41678e6 | 0.186419 | ||||||||
\(701\) | 1.70224e7 | 1.30835 | 0.654177 | − | 0.756342i | \(-0.273015\pi\) | ||||
0.654177 | + | 0.756342i | \(0.273015\pi\) | |||||||
\(702\) | −798956. | −0.0611899 | ||||||||
\(703\) | 1.45951e6 | 0.111383 | ||||||||
\(704\) | 200357. | 0.0152360 | ||||||||
\(705\) | 809188. | 0.0613164 | ||||||||
\(706\) | 7.65314e6 | 0.577867 | ||||||||
\(707\) | −2.70690e7 | −2.03668 | ||||||||
\(708\) | −415115. | −0.0311233 | ||||||||
\(709\) | −1.32934e7 | −0.993160 | −0.496580 | − | 0.867991i | \(-0.665411\pi\) | ||||
−0.496580 | + | 0.867991i | \(0.665411\pi\) | |||||||
\(710\) | 278902. | 0.0207638 | ||||||||
\(711\) | 4.73223e6 | 0.351068 | ||||||||
\(712\) | 3.52051e6 | 0.260259 | ||||||||
\(713\) | 2.02467e7 | 1.49152 | ||||||||
\(714\) | 5.23340e6 | 0.384183 | ||||||||
\(715\) | 335057. | 0.0245106 | ||||||||
\(716\) | −695309. | −0.0506869 | ||||||||
\(717\) | 4.85270e6 | 0.352522 | ||||||||
\(718\) | 4.50798e6 | 0.326341 | ||||||||
\(719\) | 1.73058e7 | 1.24845 | 0.624224 | − | 0.781246i | \(-0.285415\pi\) | ||||
0.624224 | + | 0.781246i | \(0.285415\pi\) | |||||||
\(720\) | −518400. | −0.0372678 | ||||||||
\(721\) | 2.94517e7 | 2.10995 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | 922418. | 0.0656270 | ||||||||
\(724\) | −3.07579e6 | −0.218077 | ||||||||
\(725\) | 1.06365e6 | 0.0751540 | ||||||||
\(726\) | −5.71170e6 | −0.402183 | ||||||||
\(727\) | −1.60509e7 | −1.12632 | −0.563161 | − | 0.826347i | \(-0.690415\pi\) | ||||
−0.563161 | + | 0.826347i | \(0.690415\pi\) | |||||||
\(728\) | 4.23791e6 | 0.296362 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 4.76024e6 | 0.330615 | ||||||||
\(731\) | 5.69192e6 | 0.393972 | ||||||||
\(732\) | 2.45188e6 | 0.169130 | ||||||||
\(733\) | −1.83712e7 | −1.26292 | −0.631461 | − | 0.775408i | \(-0.717544\pi\) | ||||
−0.631461 | + | 0.775408i | \(0.717544\pi\) | |||||||
\(734\) | −1.87738e7 | −1.28621 | ||||||||
\(735\) | 9.36024e6 | 0.639100 | ||||||||
\(736\) | 4.76662e6 | 0.324352 | ||||||||
\(737\) | 889819. | 0.0603439 | ||||||||
\(738\) | 2.34663e6 | 0.158600 | ||||||||
\(739\) | −1.07251e7 | −0.722420 | −0.361210 | − | 0.932484i | \(-0.617636\pi\) | ||||
−0.361210 | + | 0.932484i | \(0.617636\pi\) | |||||||
\(740\) | 1.61719e6 | 0.108563 | ||||||||
\(741\) | −890195. | −0.0595579 | ||||||||
\(742\) | 1.25483e7 | 0.836708 | ||||||||
\(743\) | 2.08108e7 | 1.38299 | 0.691493 | − | 0.722384i | \(-0.256953\pi\) | ||||
0.691493 | + | 0.722384i | \(0.256953\pi\) | |||||||
\(744\) | −2.50534e6 | −0.165933 | ||||||||
\(745\) | 936786. | 0.0618372 | ||||||||
\(746\) | 1.30240e6 | 0.0856836 | ||||||||
\(747\) | −4.11071e6 | −0.269535 | ||||||||
\(748\) | 470770. | 0.0307648 | ||||||||
\(749\) | −3.66166e7 | −2.38492 | ||||||||
\(750\) | −562500. | −0.0365148 | ||||||||
\(751\) | −1.73564e7 | −1.12295 | −0.561475 | − | 0.827494i | \(-0.689766\pi\) | ||||
−0.561475 | + | 0.827494i | \(0.689766\pi\) | |||||||
\(752\) | 920676. | 0.0593693 | ||||||||
\(753\) | 8.38302e6 | 0.538782 | ||||||||
\(754\) | 1.86514e6 | 0.119477 | ||||||||
\(755\) | 8.59761e6 | 0.548922 | ||||||||
\(756\) | −2.81893e6 | −0.179382 | ||||||||
\(757\) | −1.81699e7 | −1.15243 | −0.576214 | − | 0.817299i | \(-0.695470\pi\) | ||||
−0.576214 | + | 0.817299i | \(0.695470\pi\) | |||||||
\(758\) | 1.71854e7 | 1.08639 | ||||||||
\(759\) | 2.04926e6 | 0.129120 | ||||||||
\(760\) | −577600. | −0.0362738 | ||||||||
\(761\) | −1.77814e7 | −1.11303 | −0.556513 | − | 0.830839i | \(-0.687861\pi\) | ||||
−0.556513 | + | 0.830839i | \(0.687861\pi\) | |||||||
\(762\) | 6.12032e6 | 0.381845 | ||||||||
\(763\) | 6.33821e6 | 0.394144 | ||||||||
\(764\) | 817599. | 0.0506766 | ||||||||
\(765\) | −1.21806e6 | −0.0752517 | ||||||||
\(766\) | 3.11228e6 | 0.191649 | ||||||||
\(767\) | −789844. | −0.0484789 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −2.28095e7 | −1.39091 | −0.695457 | − | 0.718568i | \(-0.744798\pi\) | ||||
−0.695457 | + | 0.718568i | \(0.744798\pi\) | |||||||
\(770\) | 1.18217e6 | 0.0718544 | ||||||||
\(771\) | 265560. | 0.0160889 | ||||||||
\(772\) | −8.24994e6 | −0.498205 | ||||||||
\(773\) | −1.00065e7 | −0.602326 | −0.301163 | − | 0.953573i | \(-0.597375\pi\) | ||||
−0.301163 | + | 0.953573i | \(0.597375\pi\) | |||||||
\(774\) | −3.06591e6 | −0.183953 | ||||||||
\(775\) | −2.71846e6 | −0.162581 | ||||||||
\(776\) | 5.44697e6 | 0.324714 | ||||||||
\(777\) | 8.79385e6 | 0.522549 | ||||||||
\(778\) | −5.62301e6 | −0.333058 | ||||||||
\(779\) | 2.61461e6 | 0.154370 | ||||||||
\(780\) | −986365. | −0.0580499 | ||||||||
\(781\) | 136425. | 0.00800328 | ||||||||
\(782\) | 1.11999e7 | 0.654935 | ||||||||
\(783\) | −1.24064e6 | −0.0723170 | ||||||||
\(784\) | 1.06499e7 | 0.618806 | ||||||||
\(785\) | −5.28982e6 | −0.306384 | ||||||||
\(786\) | 9.17853e6 | 0.529928 | ||||||||
\(787\) | 1.54717e7 | 0.890434 | 0.445217 | − | 0.895423i | \(-0.353127\pi\) | ||||
0.445217 | + | 0.895423i | \(0.353127\pi\) | |||||||
\(788\) | −8.95815e6 | −0.513929 | ||||||||
\(789\) | −1.14247e7 | −0.653359 | ||||||||
\(790\) | 5.84226e6 | 0.333053 | ||||||||
\(791\) | −3.80570e7 | −2.16268 | ||||||||
\(792\) | −253576. | −0.0143647 | ||||||||
\(793\) | 4.66521e6 | 0.263444 | ||||||||
\(794\) | −1.71003e7 | −0.962615 | ||||||||
\(795\) | −2.92058e6 | −0.163890 | ||||||||
\(796\) | −1.44825e7 | −0.810140 | ||||||||
\(797\) | 1.03258e6 | 0.0575806 | 0.0287903 | − | 0.999585i | \(-0.490834\pi\) | ||||
0.0287903 | + | 0.999585i | \(0.490834\pi\) | |||||||
\(798\) | −3.14084e6 | −0.174598 | ||||||||
\(799\) | 2.16327e6 | 0.119879 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −4.45564e6 | −0.245374 | ||||||||
\(802\) | −2.23415e7 | −1.22652 | ||||||||
\(803\) | 2.32848e6 | 0.127434 | ||||||||
\(804\) | −2.61951e6 | −0.142916 | ||||||||
\(805\) | 2.81246e7 | 1.52967 | ||||||||
\(806\) | −4.76693e6 | −0.258465 | ||||||||
\(807\) | 1.77176e7 | 0.957680 | ||||||||
\(808\) | 7.16828e6 | 0.386266 | ||||||||
\(809\) | 5.97165e6 | 0.320792 | 0.160396 | − | 0.987053i | \(-0.448723\pi\) | ||||
0.160396 | + | 0.987053i | \(0.448723\pi\) | |||||||
\(810\) | 656100. | 0.0351364 | ||||||||
\(811\) | 1.63253e7 | 0.871586 | 0.435793 | − | 0.900047i | \(-0.356468\pi\) | ||||
0.435793 | + | 0.900047i | \(0.356468\pi\) | |||||||
\(812\) | 6.58072e6 | 0.350254 | ||||||||
\(813\) | −4.94040e6 | −0.262141 | ||||||||
\(814\) | 791050. | 0.0418449 | ||||||||
\(815\) | 1.15224e7 | 0.607646 | ||||||||
\(816\) | −1.38589e6 | −0.0728621 | ||||||||
\(817\) | −3.41602e6 | −0.179046 | ||||||||
\(818\) | 2.12607e7 | 1.11095 | ||||||||
\(819\) | −5.36360e6 | −0.279413 | ||||||||
\(820\) | 2.89707e6 | 0.150461 | ||||||||
\(821\) | −1.91047e7 | −0.989199 | −0.494599 | − | 0.869121i | \(-0.664685\pi\) | ||||
−0.494599 | + | 0.869121i | \(0.664685\pi\) | |||||||
\(822\) | 1.08575e7 | 0.560469 | ||||||||
\(823\) | 1.42437e7 | 0.733031 | 0.366516 | − | 0.930412i | \(-0.380551\pi\) | ||||
0.366516 | + | 0.930412i | \(0.380551\pi\) | |||||||
\(824\) | −7.79928e6 | −0.400163 | ||||||||
\(825\) | −275148. | −0.0140744 | ||||||||
\(826\) | −2.78678e6 | −0.142119 | ||||||||
\(827\) | −5.77314e6 | −0.293527 | −0.146764 | − | 0.989172i | \(-0.546886\pi\) | ||||
−0.146764 | + | 0.989172i | \(0.546886\pi\) | |||||||
\(828\) | −6.03275e6 | −0.305802 | ||||||||
\(829\) | −2.71339e7 | −1.37128 | −0.685640 | − | 0.727941i | \(-0.740478\pi\) | ||||
−0.685640 | + | 0.727941i | \(0.740478\pi\) | |||||||
\(830\) | −5.07495e6 | −0.255703 | ||||||||
\(831\) | −1.66769e7 | −0.837749 | ||||||||
\(832\) | −1.12226e6 | −0.0562065 | ||||||||
\(833\) | 2.50236e7 | 1.24950 | ||||||||
\(834\) | −3.24302e6 | −0.161448 | ||||||||
\(835\) | −7.45012e6 | −0.369783 | ||||||||
\(836\) | −282534. | −0.0139815 | ||||||||
\(837\) | 3.17082e6 | 0.156443 | ||||||||
\(838\) | 2.62299e7 | 1.29029 | ||||||||
\(839\) | 2.28209e7 | 1.11925 | 0.559627 | − | 0.828745i | \(-0.310944\pi\) | ||||
0.559627 | + | 0.828745i | \(0.310944\pi\) | |||||||
\(840\) | −3.48016e6 | −0.170177 | ||||||||
\(841\) | −1.76149e7 | −0.858797 | ||||||||
\(842\) | −7.80534e6 | −0.379413 | ||||||||
\(843\) | 2.03224e7 | 0.984931 | ||||||||
\(844\) | −1.15530e7 | −0.558261 | ||||||||
\(845\) | 7.40556e6 | 0.356793 | ||||||||
\(846\) | −1.16523e6 | −0.0559739 | ||||||||
\(847\) | −3.83442e7 | −1.83650 | ||||||||
\(848\) | −3.32298e6 | −0.158686 | ||||||||
\(849\) | −1.71830e7 | −0.818142 | ||||||||
\(850\) | −1.50378e6 | −0.0713900 | ||||||||
\(851\) | 1.88196e7 | 0.890814 | ||||||||
\(852\) | −401619. | −0.0189546 | ||||||||
\(853\) | 3.22282e7 | 1.51657 | 0.758287 | − | 0.651921i | \(-0.226037\pi\) | ||||
0.758287 | + | 0.651921i | \(0.226037\pi\) | |||||||
\(854\) | 1.64601e7 | 0.772303 | ||||||||
\(855\) | 731025. | 0.0341993 | ||||||||
\(856\) | 9.69664e6 | 0.452310 | ||||||||
\(857\) | 1.78756e7 | 0.831396 | 0.415698 | − | 0.909503i | \(-0.363537\pi\) | ||||
0.415698 | + | 0.909503i | \(0.363537\pi\) | |||||||
\(858\) | −482482. | −0.0223750 | ||||||||
\(859\) | 1.66307e7 | 0.769005 | 0.384502 | − | 0.923124i | \(-0.374373\pi\) | ||||
0.384502 | + | 0.923124i | \(0.374373\pi\) | |||||||
\(860\) | −3.78507e6 | −0.174513 | ||||||||
\(861\) | 1.57535e7 | 0.724220 | ||||||||
\(862\) | −5.13653e6 | −0.235452 | ||||||||
\(863\) | −6.66946e6 | −0.304834 | −0.152417 | − | 0.988316i | \(-0.548706\pi\) | ||||
−0.152417 | + | 0.988316i | \(0.548706\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 1.05651e7 | 0.480100 | ||||||||
\(866\) | −1.27709e7 | −0.578665 | ||||||||
\(867\) | 9.52236e6 | 0.430226 | ||||||||
\(868\) | −1.68190e7 | −0.757706 | ||||||||
\(869\) | 2.85775e6 | 0.128373 | ||||||||
\(870\) | −1.53165e6 | −0.0686059 | ||||||||
\(871\) | −4.98418e6 | −0.222612 | ||||||||
\(872\) | −1.67846e6 | −0.0747513 | ||||||||
\(873\) | −6.89382e6 | −0.306143 | ||||||||
\(874\) | −6.72168e6 | −0.297645 | ||||||||
\(875\) | −3.77621e6 | −0.166739 | ||||||||
\(876\) | −6.85475e6 | −0.301808 | ||||||||
\(877\) | −2.26346e7 | −0.993744 | −0.496872 | − | 0.867824i | \(-0.665518\pi\) | ||||
−0.496872 | + | 0.867824i | \(0.665518\pi\) | |||||||
\(878\) | 2.51155e7 | 1.09953 | ||||||||
\(879\) | −2.10018e7 | −0.916820 | ||||||||
\(880\) | −313057. | −0.0136275 | ||||||||
\(881\) | −1.51706e7 | −0.658512 | −0.329256 | − | 0.944241i | \(-0.606798\pi\) | ||||
−0.329256 | + | 0.944241i | \(0.606798\pi\) | |||||||
\(882\) | −1.34787e7 | −0.583415 | ||||||||
\(883\) | 1.10451e7 | 0.476724 | 0.238362 | − | 0.971176i | \(-0.423390\pi\) | ||||
0.238362 | + | 0.971176i | \(0.423390\pi\) | |||||||
\(884\) | −2.63694e6 | −0.113493 | ||||||||
\(885\) | 648617. | 0.0278375 | ||||||||
\(886\) | 6.16565e6 | 0.263873 | ||||||||
\(887\) | 5.03118e6 | 0.214714 | 0.107357 | − | 0.994221i | \(-0.465761\pi\) | ||||
0.107357 | + | 0.994221i | \(0.465761\pi\) | |||||||
\(888\) | −2.32875e6 | −0.0991038 | ||||||||
\(889\) | 4.10874e7 | 1.74363 | ||||||||
\(890\) | −5.50079e6 | −0.232782 | ||||||||
\(891\) | 320932. | 0.0135431 | ||||||||
\(892\) | −6.54081e6 | −0.275245 | ||||||||
\(893\) | −1.29830e6 | −0.0544810 | ||||||||
\(894\) | −1.34897e6 | −0.0564494 | ||||||||
\(895\) | 1.08642e6 | 0.0453357 | ||||||||
\(896\) | −3.95965e6 | −0.164773 | ||||||||
\(897\) | −1.14786e7 | −0.476329 | ||||||||
\(898\) | −2.78416e7 | −1.15214 | ||||||||
\(899\) | −7.40220e6 | −0.305465 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | −7.80786e6 | −0.320420 | ||||||||
\(902\) | 1.41711e6 | 0.0579945 | ||||||||
\(903\) | −2.05822e7 | −0.839988 | ||||||||
\(904\) | 1.00781e7 | 0.410163 | ||||||||
\(905\) | 4.80593e6 | 0.195054 | ||||||||
\(906\) | −1.23806e7 | −0.501095 | ||||||||
\(907\) | −1.33481e7 | −0.538768 | −0.269384 | − | 0.963033i | \(-0.586820\pi\) | ||||
−0.269384 | + | 0.963033i | \(0.586820\pi\) | |||||||
\(908\) | −9.79359e6 | −0.394210 | ||||||||
\(909\) | −9.07236e6 | −0.364175 | ||||||||
\(910\) | −6.62173e6 | −0.265075 | ||||||||
\(911\) | 1.03425e7 | 0.412884 | 0.206442 | − | 0.978459i | \(-0.433812\pi\) | ||||
0.206442 | + | 0.978459i | \(0.433812\pi\) | |||||||
\(912\) | 831744. | 0.0331133 | ||||||||
\(913\) | −2.48242e6 | −0.0985594 | ||||||||
\(914\) | 2.11735e6 | 0.0838353 | ||||||||
\(915\) | −3.83105e6 | −0.151274 | ||||||||
\(916\) | 4.39382e6 | 0.173023 | ||||||||
\(917\) | 6.16179e7 | 2.41982 | ||||||||
\(918\) | 1.75401e6 | 0.0686951 | ||||||||
\(919\) | 3.74100e7 | 1.46116 | 0.730582 | − | 0.682825i | \(-0.239249\pi\) | ||||
0.730582 | + | 0.682825i | \(0.239249\pi\) | |||||||
\(920\) | −7.44784e6 | −0.290109 | ||||||||
\(921\) | −7.90225e6 | −0.306974 | ||||||||
\(922\) | 2.96387e7 | 1.14824 | ||||||||
\(923\) | −764165. | −0.0295245 | ||||||||
\(924\) | −1.70233e6 | −0.0655938 | ||||||||
\(925\) | −2.52686e6 | −0.0971015 | ||||||||
\(926\) | 1.00739e7 | 0.386073 | ||||||||
\(927\) | 9.87096e6 | 0.377277 | ||||||||
\(928\) | −1.74268e6 | −0.0664274 | ||||||||
\(929\) | 1.06945e7 | 0.406556 | 0.203278 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203278 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(930\) | 3.91459e6 | 0.148415 | ||||||||
\(931\) | −1.50180e7 | −0.567855 | ||||||||
\(932\) | 5.23269e6 | 0.197326 | ||||||||
\(933\) | 4.22939e6 | 0.159065 | ||||||||
\(934\) | 2.72715e7 | 1.02292 | ||||||||
\(935\) | −735577. | −0.0275169 | ||||||||
\(936\) | 1.42037e6 | 0.0529920 | ||||||||
\(937\) | 3.74036e7 | 1.39176 | 0.695881 | − | 0.718157i | \(-0.255014\pi\) | ||||
0.695881 | + | 0.718157i | \(0.255014\pi\) | |||||||
\(938\) | −1.75855e7 | −0.652601 | ||||||||
\(939\) | −1.20612e7 | −0.446404 | ||||||||
\(940\) | −1.43856e6 | −0.0531016 | ||||||||
\(941\) | 3.60949e7 | 1.32884 | 0.664419 | − | 0.747360i | \(-0.268679\pi\) | ||||
0.664419 | + | 0.747360i | \(0.268679\pi\) | |||||||
\(942\) | 7.61734e6 | 0.279689 | ||||||||
\(943\) | 3.37140e7 | 1.23461 | ||||||||
\(944\) | 737982. | 0.0269536 | ||||||||
\(945\) | 4.40457e6 | 0.160444 | ||||||||
\(946\) | −1.85147e6 | −0.0672651 | ||||||||
\(947\) | −2.01552e7 | −0.730320 | −0.365160 | − | 0.930945i | \(-0.618986\pi\) | ||||
−0.365160 | + | 0.930945i | \(0.618986\pi\) | |||||||
\(948\) | −8.41285e6 | −0.304034 | ||||||||
\(949\) | −1.30426e7 | −0.470109 | ||||||||
\(950\) | 902500. | 0.0324443 | ||||||||
\(951\) | 2.35448e7 | 0.844197 | ||||||||
\(952\) | −9.30382e6 | −0.332712 | ||||||||
\(953\) | 3.16559e7 | 1.12907 | 0.564537 | − | 0.825408i | \(-0.309055\pi\) | ||||
0.564537 | + | 0.825408i | \(0.309055\pi\) | |||||||
\(954\) | 4.20564e6 | 0.149610 | ||||||||
\(955\) | −1.27750e6 | −0.0453265 | ||||||||
\(956\) | −8.62702e6 | −0.305293 | ||||||||
\(957\) | −749209. | −0.0264438 | ||||||||
\(958\) | −3.92973e7 | −1.38341 | ||||||||
\(959\) | 7.28895e7 | 2.55928 | ||||||||
\(960\) | 921600. | 0.0322749 | ||||||||
\(961\) | −9.71064e6 | −0.339187 | ||||||||
\(962\) | −4.43094e6 | −0.154368 | ||||||||
\(963\) | −1.22723e7 | −0.426442 | ||||||||
\(964\) | −1.63986e6 | −0.0568346 | ||||||||
\(965\) | 1.28905e7 | 0.445608 | ||||||||
\(966\) | −4.04995e7 | −1.39639 | ||||||||
\(967\) | 7.36938e6 | 0.253434 | 0.126717 | − | 0.991939i | \(-0.459556\pi\) | ||||
0.126717 | + | 0.991939i | \(0.459556\pi\) | |||||||
\(968\) | 1.01541e7 | 0.348301 | ||||||||
\(969\) | 1.95431e6 | 0.0668629 | ||||||||
\(970\) | −8.51089e6 | −0.290433 | ||||||||
\(971\) | −2.15114e7 | −0.732183 | −0.366092 | − | 0.930579i | \(-0.619304\pi\) | ||||
−0.366092 | + | 0.930579i | \(0.619304\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −2.17712e7 | −0.737226 | ||||||||
\(974\) | 3.08593e7 | 1.04229 | ||||||||
\(975\) | 1.54120e6 | 0.0519214 | ||||||||
\(976\) | −4.35889e6 | −0.146471 | ||||||||
\(977\) | −8.15455e6 | −0.273315 | −0.136657 | − | 0.990618i | \(-0.543636\pi\) | ||||
−0.136657 | + | 0.990618i | \(0.543636\pi\) | |||||||
\(978\) | −1.65923e7 | −0.554702 | ||||||||
\(979\) | −2.69072e6 | −0.0897247 | ||||||||
\(980\) | −1.66404e7 | −0.553476 | ||||||||
\(981\) | 2.12430e6 | 0.0704762 | ||||||||
\(982\) | −1.37437e7 | −0.454803 | ||||||||
\(983\) | 4.52106e7 | 1.49230 | 0.746150 | − | 0.665778i | \(-0.231900\pi\) | ||||
0.746150 | + | 0.665778i | \(0.231900\pi\) | |||||||
\(984\) | −4.17178e6 | −0.137352 | ||||||||
\(985\) | 1.39971e7 | 0.459672 | ||||||||
\(986\) | −4.09470e6 | −0.134131 | ||||||||
\(987\) | −7.82250e6 | −0.255595 | ||||||||
\(988\) | 1.58257e6 | 0.0515787 | ||||||||
\(989\) | −4.40478e7 | −1.43197 | ||||||||
\(990\) | 396213. | 0.0128482 | ||||||||
\(991\) | −1.96001e7 | −0.633979 | −0.316989 | − | 0.948429i | \(-0.602672\pi\) | ||||
−0.316989 | + | 0.948429i | \(0.602672\pi\) | |||||||
\(992\) | 4.45393e6 | 0.143702 | ||||||||
\(993\) | 1.93328e7 | 0.622189 | ||||||||
\(994\) | −2.69618e6 | −0.0865530 | ||||||||
\(995\) | 2.26289e7 | 0.724611 | ||||||||
\(996\) | 7.30792e6 | 0.233424 | ||||||||
\(997\) | 5.61167e7 | 1.78794 | 0.893972 | − | 0.448122i | \(-0.147907\pi\) | ||||
0.893972 | + | 0.448122i | \(0.147907\pi\) | |||||||
\(998\) | 1.94382e6 | 0.0617773 | ||||||||
\(999\) | 2.94732e6 | 0.0934360 |
(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 | 570.6.a.i.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.i.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |