Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,6,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, 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("21.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(3.36806021607\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.0000 | 1.76777 | 0.883883 | − | 0.467707i | \(-0.154920\pi\) | ||||
0.883883 | + | 0.467707i | \(0.154920\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 68.0000 | 2.12500 | ||||||||
\(5\) | −106.000 | −1.89619 | −0.948093 | − | 0.317994i | \(-0.896991\pi\) | ||||
−0.948093 | + | 0.317994i | \(0.896991\pi\) | |||||||
\(6\) | 90.0000 | 1.02062 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 360.000 | 1.98874 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −1060.00 | −3.35201 | ||||||||
\(11\) | 92.0000 | 0.229248 | 0.114624 | − | 0.993409i | \(-0.463434\pi\) | ||||
0.114624 | + | 0.993409i | \(0.463434\pi\) | |||||||
\(12\) | 612.000 | 1.22687 | ||||||||
\(13\) | 670.000 | 1.09955 | 0.549777 | − | 0.835312i | \(-0.314713\pi\) | ||||
0.549777 | + | 0.835312i | \(0.314713\pi\) | |||||||
\(14\) | −490.000 | −0.668153 | ||||||||
\(15\) | −954.000 | −1.09476 | ||||||||
\(16\) | 1424.00 | 1.39062 | ||||||||
\(17\) | −222.000 | −0.186308 | −0.0931538 | − | 0.995652i | \(-0.529695\pi\) | ||||
−0.0931538 | + | 0.995652i | \(0.529695\pi\) | |||||||
\(18\) | 810.000 | 0.589256 | ||||||||
\(19\) | −908.000 | −0.577035 | −0.288517 | − | 0.957475i | \(-0.593162\pi\) | ||||
−0.288517 | + | 0.957475i | \(0.593162\pi\) | |||||||
\(20\) | −7208.00 | −4.02939 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | 920.000 | 0.405258 | ||||||||
\(23\) | −1176.00 | −0.463541 | −0.231770 | − | 0.972771i | \(-0.574452\pi\) | ||||
−0.231770 | + | 0.972771i | \(0.574452\pi\) | |||||||
\(24\) | 3240.00 | 1.14820 | ||||||||
\(25\) | 8111.00 | 2.59552 | ||||||||
\(26\) | 6700.00 | 1.94375 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −3332.00 | −0.803175 | ||||||||
\(29\) | 1118.00 | 0.246858 | 0.123429 | − | 0.992353i | \(-0.460611\pi\) | ||||
0.123429 | + | 0.992353i | \(0.460611\pi\) | |||||||
\(30\) | −9540.00 | −1.93529 | ||||||||
\(31\) | 3696.00 | 0.690761 | 0.345380 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345380 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(32\) | 2720.00 | 0.469563 | ||||||||
\(33\) | 828.000 | 0.132357 | ||||||||
\(34\) | −2220.00 | −0.329348 | ||||||||
\(35\) | 5194.00 | 0.716691 | ||||||||
\(36\) | 5508.00 | 0.708333 | ||||||||
\(37\) | 4182.00 | 0.502203 | 0.251102 | − | 0.967961i | \(-0.419207\pi\) | ||||
0.251102 | + | 0.967961i | \(0.419207\pi\) | |||||||
\(38\) | −9080.00 | −1.02006 | ||||||||
\(39\) | 6030.00 | 0.634828 | ||||||||
\(40\) | −38160.0 | −3.77102 | ||||||||
\(41\) | −6662.00 | −0.618935 | −0.309467 | − | 0.950910i | \(-0.600151\pi\) | ||||
−0.309467 | + | 0.950910i | \(0.600151\pi\) | |||||||
\(42\) | −4410.00 | −0.385758 | ||||||||
\(43\) | −3700.00 | −0.305162 | −0.152581 | − | 0.988291i | \(-0.548759\pi\) | ||||
−0.152581 | + | 0.988291i | \(0.548759\pi\) | |||||||
\(44\) | 6256.00 | 0.487153 | ||||||||
\(45\) | −8586.00 | −0.632062 | ||||||||
\(46\) | −11760.0 | −0.819432 | ||||||||
\(47\) | −7056.00 | −0.465923 | −0.232961 | − | 0.972486i | \(-0.574842\pi\) | ||||
−0.232961 | + | 0.972486i | \(0.574842\pi\) | |||||||
\(48\) | 12816.0 | 0.802878 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 81110.0 | 4.58827 | ||||||||
\(51\) | −1998.00 | −0.107565 | ||||||||
\(52\) | 45560.0 | 2.33655 | ||||||||
\(53\) | −37578.0 | −1.83757 | −0.918785 | − | 0.394758i | \(-0.870828\pi\) | ||||
−0.918785 | + | 0.394758i | \(0.870828\pi\) | |||||||
\(54\) | 7290.00 | 0.340207 | ||||||||
\(55\) | −9752.00 | −0.434697 | ||||||||
\(56\) | −17640.0 | −0.751672 | ||||||||
\(57\) | −8172.00 | −0.333151 | ||||||||
\(58\) | 11180.0 | 0.436387 | ||||||||
\(59\) | 32700.0 | 1.22298 | 0.611488 | − | 0.791254i | \(-0.290571\pi\) | ||||
0.611488 | + | 0.791254i | \(0.290571\pi\) | |||||||
\(60\) | −64872.0 | −2.32637 | ||||||||
\(61\) | −10802.0 | −0.371689 | −0.185844 | − | 0.982579i | \(-0.559502\pi\) | ||||
−0.185844 | + | 0.982579i | \(0.559502\pi\) | |||||||
\(62\) | 36960.0 | 1.22110 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | −18368.0 | −0.560547 | ||||||||
\(65\) | −71020.0 | −2.08496 | ||||||||
\(66\) | 8280.00 | 0.233976 | ||||||||
\(67\) | 64996.0 | 1.76889 | 0.884443 | − | 0.466649i | \(-0.154539\pi\) | ||||
0.884443 | + | 0.466649i | \(0.154539\pi\) | |||||||
\(68\) | −15096.0 | −0.395904 | ||||||||
\(69\) | −10584.0 | −0.267625 | ||||||||
\(70\) | 51940.0 | 1.26694 | ||||||||
\(71\) | −61320.0 | −1.44363 | −0.721816 | − | 0.692085i | \(-0.756692\pi\) | ||||
−0.721816 | + | 0.692085i | \(0.756692\pi\) | |||||||
\(72\) | 29160.0 | 0.662913 | ||||||||
\(73\) | 38922.0 | 0.854846 | 0.427423 | − | 0.904052i | \(-0.359421\pi\) | ||||
0.427423 | + | 0.904052i | \(0.359421\pi\) | |||||||
\(74\) | 41820.0 | 0.887779 | ||||||||
\(75\) | 72999.0 | 1.49852 | ||||||||
\(76\) | −61744.0 | −1.22620 | ||||||||
\(77\) | −4508.00 | −0.0866477 | ||||||||
\(78\) | 60300.0 | 1.12223 | ||||||||
\(79\) | −88096.0 | −1.58814 | −0.794069 | − | 0.607827i | \(-0.792041\pi\) | ||||
−0.794069 | + | 0.607827i | \(0.792041\pi\) | |||||||
\(80\) | −150944. | −2.63688 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −66620.0 | −1.09413 | ||||||||
\(83\) | 71892.0 | 1.14547 | 0.572737 | − | 0.819739i | \(-0.305882\pi\) | ||||
0.572737 | + | 0.819739i | \(0.305882\pi\) | |||||||
\(84\) | −29988.0 | −0.463713 | ||||||||
\(85\) | 23532.0 | 0.353274 | ||||||||
\(86\) | −37000.0 | −0.539455 | ||||||||
\(87\) | 10062.0 | 0.142523 | ||||||||
\(88\) | 33120.0 | 0.455915 | ||||||||
\(89\) | 111818. | 1.49636 | 0.748181 | − | 0.663495i | \(-0.230927\pi\) | ||||
0.748181 | + | 0.663495i | \(0.230927\pi\) | |||||||
\(90\) | −85860.0 | −1.11734 | ||||||||
\(91\) | −32830.0 | −0.415592 | ||||||||
\(92\) | −79968.0 | −0.985024 | ||||||||
\(93\) | 33264.0 | 0.398811 | ||||||||
\(94\) | −70560.0 | −0.823643 | ||||||||
\(95\) | 96248.0 | 1.09416 | ||||||||
\(96\) | 24480.0 | 0.271102 | ||||||||
\(97\) | −150846. | −1.62781 | −0.813906 | − | 0.580996i | \(-0.802663\pi\) | ||||
−0.813906 | + | 0.580996i | \(0.802663\pi\) | |||||||
\(98\) | 24010.0 | 0.252538 | ||||||||
\(99\) | 7452.00 | 0.0764161 | ||||||||
\(100\) | 551548. | 5.51548 | ||||||||
\(101\) | −137354. | −1.33979 | −0.669897 | − | 0.742454i | \(-0.733662\pi\) | ||||
−0.669897 | + | 0.742454i | \(0.733662\pi\) | |||||||
\(102\) | −19980.0 | −0.190149 | ||||||||
\(103\) | 28760.0 | 0.267113 | 0.133557 | − | 0.991041i | \(-0.457360\pi\) | ||||
0.133557 | + | 0.991041i | \(0.457360\pi\) | |||||||
\(104\) | 241200. | 2.18672 | ||||||||
\(105\) | 46746.0 | 0.413782 | ||||||||
\(106\) | −375780. | −3.24840 | ||||||||
\(107\) | 22556.0 | 0.190460 | 0.0952298 | − | 0.995455i | \(-0.469641\pi\) | ||||
0.0952298 | + | 0.995455i | \(0.469641\pi\) | |||||||
\(108\) | 49572.0 | 0.408956 | ||||||||
\(109\) | 19998.0 | 0.161221 | 0.0806103 | − | 0.996746i | \(-0.474313\pi\) | ||||
0.0806103 | + | 0.996746i | \(0.474313\pi\) | |||||||
\(110\) | −97520.0 | −0.768444 | ||||||||
\(111\) | 37638.0 | 0.289947 | ||||||||
\(112\) | −69776.0 | −0.525607 | ||||||||
\(113\) | 17906.0 | 0.131918 | 0.0659588 | − | 0.997822i | \(-0.478989\pi\) | ||||
0.0659588 | + | 0.997822i | \(0.478989\pi\) | |||||||
\(114\) | −81720.0 | −0.588933 | ||||||||
\(115\) | 124656. | 0.878959 | ||||||||
\(116\) | 76024.0 | 0.524573 | ||||||||
\(117\) | 54270.0 | 0.366518 | ||||||||
\(118\) | 327000. | 2.16194 | ||||||||
\(119\) | 10878.0 | 0.0704177 | ||||||||
\(120\) | −343440. | −2.17720 | ||||||||
\(121\) | −152587. | −0.947445 | ||||||||
\(122\) | −108020. | −0.657059 | ||||||||
\(123\) | −59958.0 | −0.357342 | ||||||||
\(124\) | 251328. | 1.46787 | ||||||||
\(125\) | −528516. | −3.02540 | ||||||||
\(126\) | −39690.0 | −0.222718 | ||||||||
\(127\) | 66864.0 | 0.367860 | 0.183930 | − | 0.982939i | \(-0.441118\pi\) | ||||
0.183930 | + | 0.982939i | \(0.441118\pi\) | |||||||
\(128\) | −270720. | −1.46048 | ||||||||
\(129\) | −33300.0 | −0.176185 | ||||||||
\(130\) | −710200. | −3.68572 | ||||||||
\(131\) | 153764. | 0.782846 | 0.391423 | − | 0.920211i | \(-0.371983\pi\) | ||||
0.391423 | + | 0.920211i | \(0.371983\pi\) | |||||||
\(132\) | 56304.0 | 0.281258 | ||||||||
\(133\) | 44492.0 | 0.218099 | ||||||||
\(134\) | 649960. | 3.12698 | ||||||||
\(135\) | −77274.0 | −0.364921 | ||||||||
\(136\) | −79920.0 | −0.370517 | ||||||||
\(137\) | 255978. | 1.16520 | 0.582601 | − | 0.812758i | \(-0.302035\pi\) | ||||
0.582601 | + | 0.812758i | \(0.302035\pi\) | |||||||
\(138\) | −105840. | −0.473099 | ||||||||
\(139\) | 282924. | 1.24203 | 0.621016 | − | 0.783798i | \(-0.286720\pi\) | ||||
0.621016 | + | 0.783798i | \(0.286720\pi\) | |||||||
\(140\) | 353192. | 1.52297 | ||||||||
\(141\) | −63504.0 | −0.269001 | ||||||||
\(142\) | −613200. | −2.55200 | ||||||||
\(143\) | 61640.0 | 0.252071 | ||||||||
\(144\) | 115344. | 0.463542 | ||||||||
\(145\) | −118508. | −0.468088 | ||||||||
\(146\) | 389220. | 1.51117 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | 284376. | 1.06718 | ||||||||
\(149\) | 408054. | 1.50575 | 0.752873 | − | 0.658165i | \(-0.228667\pi\) | ||||
0.752873 | + | 0.658165i | \(0.228667\pi\) | |||||||
\(150\) | 729990. | 2.64904 | ||||||||
\(151\) | 362504. | 1.29381 | 0.646905 | − | 0.762571i | \(-0.276063\pi\) | ||||
0.646905 | + | 0.762571i | \(0.276063\pi\) | |||||||
\(152\) | −326880. | −1.14757 | ||||||||
\(153\) | −17982.0 | −0.0621025 | ||||||||
\(154\) | −45080.0 | −0.153173 | ||||||||
\(155\) | −391776. | −1.30981 | ||||||||
\(156\) | 410040. | 1.34901 | ||||||||
\(157\) | −152786. | −0.494691 | −0.247346 | − | 0.968927i | \(-0.579558\pi\) | ||||
−0.247346 | + | 0.968927i | \(0.579558\pi\) | |||||||
\(158\) | −880960. | −2.80746 | ||||||||
\(159\) | −338202. | −1.06092 | ||||||||
\(160\) | −288320. | −0.890379 | ||||||||
\(161\) | 57624.0 | 0.175202 | ||||||||
\(162\) | 65610.0 | 0.196419 | ||||||||
\(163\) | −150428. | −0.443465 | −0.221733 | − | 0.975107i | \(-0.571171\pi\) | ||||
−0.221733 | + | 0.975107i | \(0.571171\pi\) | |||||||
\(164\) | −453016. | −1.31524 | ||||||||
\(165\) | −87768.0 | −0.250973 | ||||||||
\(166\) | 718920. | 2.02493 | ||||||||
\(167\) | −7288.00 | −0.0202217 | −0.0101108 | − | 0.999949i | \(-0.503218\pi\) | ||||
−0.0101108 | + | 0.999949i | \(0.503218\pi\) | |||||||
\(168\) | −158760. | −0.433978 | ||||||||
\(169\) | 77607.0 | 0.209018 | ||||||||
\(170\) | 235320. | 0.624506 | ||||||||
\(171\) | −73548.0 | −0.192345 | ||||||||
\(172\) | −251600. | −0.648469 | ||||||||
\(173\) | −289154. | −0.734537 | −0.367269 | − | 0.930115i | \(-0.619707\pi\) | ||||
−0.367269 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(174\) | 100620. | 0.251948 | ||||||||
\(175\) | −397439. | −0.981014 | ||||||||
\(176\) | 131008. | 0.318798 | ||||||||
\(177\) | 294300. | 0.706085 | ||||||||
\(178\) | 1.11818e6 | 2.64522 | ||||||||
\(179\) | 199492. | 0.465364 | 0.232682 | − | 0.972553i | \(-0.425250\pi\) | ||||
0.232682 | + | 0.972553i | \(0.425250\pi\) | |||||||
\(180\) | −583848. | −1.34313 | ||||||||
\(181\) | 240550. | 0.545769 | 0.272885 | − | 0.962047i | \(-0.412022\pi\) | ||||
0.272885 | + | 0.962047i | \(0.412022\pi\) | |||||||
\(182\) | −328300. | −0.734670 | ||||||||
\(183\) | −97218.0 | −0.214595 | ||||||||
\(184\) | −423360. | −0.921861 | ||||||||
\(185\) | −443292. | −0.952271 | ||||||||
\(186\) | 332640. | 0.705005 | ||||||||
\(187\) | −20424.0 | −0.0427107 | ||||||||
\(188\) | −479808. | −0.990086 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 962480. | 1.93423 | ||||||||
\(191\) | 290384. | 0.575956 | 0.287978 | − | 0.957637i | \(-0.407017\pi\) | ||||
0.287978 | + | 0.957637i | \(0.407017\pi\) | |||||||
\(192\) | −165312. | −0.323632 | ||||||||
\(193\) | −171454. | −0.331325 | −0.165663 | − | 0.986182i | \(-0.552976\pi\) | ||||
−0.165663 | + | 0.986182i | \(0.552976\pi\) | |||||||
\(194\) | −1.50846e6 | −2.87759 | ||||||||
\(195\) | −639180. | −1.20375 | ||||||||
\(196\) | 163268. | 0.303571 | ||||||||
\(197\) | 401990. | 0.737989 | 0.368994 | − | 0.929432i | \(-0.379702\pi\) | ||||
0.368994 | + | 0.929432i | \(0.379702\pi\) | |||||||
\(198\) | 74520.0 | 0.135086 | ||||||||
\(199\) | −259176. | −0.463940 | −0.231970 | − | 0.972723i | \(-0.574517\pi\) | ||||
−0.231970 | + | 0.972723i | \(0.574517\pi\) | |||||||
\(200\) | 2.91996e6 | 5.16181 | ||||||||
\(201\) | 584964. | 1.02127 | ||||||||
\(202\) | −1.37354e6 | −2.36844 | ||||||||
\(203\) | −54782.0 | −0.0933035 | ||||||||
\(204\) | −135864. | −0.228575 | ||||||||
\(205\) | 706172. | 1.17362 | ||||||||
\(206\) | 287600. | 0.472194 | ||||||||
\(207\) | −95256.0 | −0.154514 | ||||||||
\(208\) | 954080. | 1.52907 | ||||||||
\(209\) | −83536.0 | −0.132284 | ||||||||
\(210\) | 467460. | 0.731469 | ||||||||
\(211\) | −1.19179e6 | −1.84286 | −0.921431 | − | 0.388542i | \(-0.872979\pi\) | ||||
−0.921431 | + | 0.388542i | \(0.872979\pi\) | |||||||
\(212\) | −2.55530e6 | −3.90484 | ||||||||
\(213\) | −551880. | −0.833481 | ||||||||
\(214\) | 225560. | 0.336688 | ||||||||
\(215\) | 392200. | 0.578644 | ||||||||
\(216\) | 262440. | 0.382733 | ||||||||
\(217\) | −181104. | −0.261083 | ||||||||
\(218\) | 199980. | 0.285000 | ||||||||
\(219\) | 350298. | 0.493546 | ||||||||
\(220\) | −663136. | −0.923732 | ||||||||
\(221\) | −148740. | −0.204855 | ||||||||
\(222\) | 376380. | 0.512559 | ||||||||
\(223\) | −218384. | −0.294075 | −0.147038 | − | 0.989131i | \(-0.546974\pi\) | ||||
−0.147038 | + | 0.989131i | \(0.546974\pi\) | |||||||
\(224\) | −133280. | −0.177478 | ||||||||
\(225\) | 656991. | 0.865173 | ||||||||
\(226\) | 179060. | 0.233199 | ||||||||
\(227\) | 582852. | 0.750747 | 0.375374 | − | 0.926874i | \(-0.377514\pi\) | ||||
0.375374 | + | 0.926874i | \(0.377514\pi\) | |||||||
\(228\) | −555696. | −0.707946 | ||||||||
\(229\) | 961046. | 1.21103 | 0.605516 | − | 0.795833i | \(-0.292967\pi\) | ||||
0.605516 | + | 0.795833i | \(0.292967\pi\) | |||||||
\(230\) | 1.24656e6 | 1.55379 | ||||||||
\(231\) | −40572.0 | −0.0500261 | ||||||||
\(232\) | 402480. | 0.490935 | ||||||||
\(233\) | 605994. | 0.731271 | 0.365636 | − | 0.930758i | \(-0.380852\pi\) | ||||
0.365636 | + | 0.930758i | \(0.380852\pi\) | |||||||
\(234\) | 542700. | 0.647918 | ||||||||
\(235\) | 747936. | 0.883476 | ||||||||
\(236\) | 2.22360e6 | 2.59882 | ||||||||
\(237\) | −792864. | −0.916912 | ||||||||
\(238\) | 108780. | 0.124482 | ||||||||
\(239\) | 1.17014e6 | 1.32509 | 0.662544 | − | 0.749023i | \(-0.269477\pi\) | ||||
0.662544 | + | 0.749023i | \(0.269477\pi\) | |||||||
\(240\) | −1.35850e6 | −1.52241 | ||||||||
\(241\) | −1.23691e6 | −1.37181 | −0.685907 | − | 0.727689i | \(-0.740595\pi\) | ||||
−0.685907 | + | 0.727689i | \(0.740595\pi\) | |||||||
\(242\) | −1.52587e6 | −1.67486 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −734536. | −0.789839 | ||||||||
\(245\) | −254506. | −0.270884 | ||||||||
\(246\) | −599580. | −0.631698 | ||||||||
\(247\) | −608360. | −0.634480 | ||||||||
\(248\) | 1.33056e6 | 1.37374 | ||||||||
\(249\) | 647028. | 0.661340 | ||||||||
\(250\) | −5.28516e6 | −5.34821 | ||||||||
\(251\) | 959708. | 0.961512 | 0.480756 | − | 0.876854i | \(-0.340362\pi\) | ||||
0.480756 | + | 0.876854i | \(0.340362\pi\) | |||||||
\(252\) | −269892. | −0.267725 | ||||||||
\(253\) | −108192. | −0.106266 | ||||||||
\(254\) | 668640. | 0.650291 | ||||||||
\(255\) | 211788. | 0.203963 | ||||||||
\(256\) | −2.11942e6 | −2.02124 | ||||||||
\(257\) | −1.21259e6 | −1.14520 | −0.572600 | − | 0.819835i | \(-0.694065\pi\) | ||||
−0.572600 | + | 0.819835i | \(0.694065\pi\) | |||||||
\(258\) | −333000. | −0.311455 | ||||||||
\(259\) | −204918. | −0.189815 | ||||||||
\(260\) | −4.82936e6 | −4.43054 | ||||||||
\(261\) | 90558.0 | 0.0822859 | ||||||||
\(262\) | 1.53764e6 | 1.38389 | ||||||||
\(263\) | −1.25274e6 | −1.11679 | −0.558397 | − | 0.829574i | \(-0.688583\pi\) | ||||
−0.558397 | + | 0.829574i | \(0.688583\pi\) | |||||||
\(264\) | 298080. | 0.263223 | ||||||||
\(265\) | 3.98327e6 | 3.48437 | ||||||||
\(266\) | 444920. | 0.385547 | ||||||||
\(267\) | 1.00636e6 | 0.863925 | ||||||||
\(268\) | 4.41973e6 | 3.75888 | ||||||||
\(269\) | −136866. | −0.115323 | −0.0576614 | − | 0.998336i | \(-0.518364\pi\) | ||||
−0.0576614 | + | 0.998336i | \(0.518364\pi\) | |||||||
\(270\) | −772740. | −0.645095 | ||||||||
\(271\) | −960896. | −0.794791 | −0.397396 | − | 0.917647i | \(-0.630086\pi\) | ||||
−0.397396 | + | 0.917647i | \(0.630086\pi\) | |||||||
\(272\) | −316128. | −0.259084 | ||||||||
\(273\) | −295470. | −0.239942 | ||||||||
\(274\) | 2.55978e6 | 2.05981 | ||||||||
\(275\) | 746212. | 0.595019 | ||||||||
\(276\) | −719712. | −0.568704 | ||||||||
\(277\) | 905830. | 0.709328 | 0.354664 | − | 0.934994i | \(-0.384595\pi\) | ||||
0.354664 | + | 0.934994i | \(0.384595\pi\) | |||||||
\(278\) | 2.82924e6 | 2.19562 | ||||||||
\(279\) | 299376. | 0.230254 | ||||||||
\(280\) | 1.86984e6 | 1.42531 | ||||||||
\(281\) | −33062.0 | −0.0249783 | −0.0124892 | − | 0.999922i | \(-0.503976\pi\) | ||||
−0.0124892 | + | 0.999922i | \(0.503976\pi\) | |||||||
\(282\) | −635040. | −0.475530 | ||||||||
\(283\) | −863588. | −0.640974 | −0.320487 | − | 0.947253i | \(-0.603847\pi\) | ||||
−0.320487 | + | 0.947253i | \(0.603847\pi\) | |||||||
\(284\) | −4.16976e6 | −3.06772 | ||||||||
\(285\) | 866232. | 0.631716 | ||||||||
\(286\) | 616400. | 0.445602 | ||||||||
\(287\) | 326438. | 0.233935 | ||||||||
\(288\) | 220320. | 0.156521 | ||||||||
\(289\) | −1.37057e6 | −0.965289 | ||||||||
\(290\) | −1.18508e6 | −0.827471 | ||||||||
\(291\) | −1.35761e6 | −0.939818 | ||||||||
\(292\) | 2.64670e6 | 1.81655 | ||||||||
\(293\) | −1.33755e6 | −0.910206 | −0.455103 | − | 0.890439i | \(-0.650398\pi\) | ||||
−0.455103 | + | 0.890439i | \(0.650398\pi\) | |||||||
\(294\) | 216090. | 0.145803 | ||||||||
\(295\) | −3.46620e6 | −2.31899 | ||||||||
\(296\) | 1.50552e6 | 0.998751 | ||||||||
\(297\) | 67068.0 | 0.0441189 | ||||||||
\(298\) | 4.08054e6 | 2.66181 | ||||||||
\(299\) | −787920. | −0.509688 | ||||||||
\(300\) | 4.96393e6 | 3.18436 | ||||||||
\(301\) | 181300. | 0.115340 | ||||||||
\(302\) | 3.62504e6 | 2.28715 | ||||||||
\(303\) | −1.23619e6 | −0.773530 | ||||||||
\(304\) | −1.29299e6 | −0.802439 | ||||||||
\(305\) | 1.14501e6 | 0.704791 | ||||||||
\(306\) | −179820. | −0.109783 | ||||||||
\(307\) | −1.32820e6 | −0.804301 | −0.402151 | − | 0.915573i | \(-0.631737\pi\) | ||||
−0.402151 | + | 0.915573i | \(0.631737\pi\) | |||||||
\(308\) | −306544. | −0.184126 | ||||||||
\(309\) | 258840. | 0.154218 | ||||||||
\(310\) | −3.91776e6 | −2.31544 | ||||||||
\(311\) | −665832. | −0.390359 | −0.195179 | − | 0.980768i | \(-0.562529\pi\) | ||||
−0.195179 | + | 0.980768i | \(0.562529\pi\) | |||||||
\(312\) | 2.17080e6 | 1.26251 | ||||||||
\(313\) | −3.09021e6 | −1.78290 | −0.891451 | − | 0.453116i | \(-0.850312\pi\) | ||||
−0.891451 | + | 0.453116i | \(0.850312\pi\) | |||||||
\(314\) | −1.52786e6 | −0.874499 | ||||||||
\(315\) | 420714. | 0.238897 | ||||||||
\(316\) | −5.99053e6 | −3.37479 | ||||||||
\(317\) | −974178. | −0.544490 | −0.272245 | − | 0.962228i | \(-0.587766\pi\) | ||||
−0.272245 | + | 0.962228i | \(0.587766\pi\) | |||||||
\(318\) | −3.38202e6 | −1.87546 | ||||||||
\(319\) | 102856. | 0.0565917 | ||||||||
\(320\) | 1.94701e6 | 1.06290 | ||||||||
\(321\) | 203004. | 0.109962 | ||||||||
\(322\) | 576240. | 0.309716 | ||||||||
\(323\) | 201576. | 0.107506 | ||||||||
\(324\) | 446148. | 0.236111 | ||||||||
\(325\) | 5.43437e6 | 2.85391 | ||||||||
\(326\) | −1.50428e6 | −0.783943 | ||||||||
\(327\) | 179982. | 0.0930807 | ||||||||
\(328\) | −2.39832e6 | −1.23090 | ||||||||
\(329\) | 345744. | 0.176102 | ||||||||
\(330\) | −877680. | −0.443661 | ||||||||
\(331\) | 781772. | 0.392202 | 0.196101 | − | 0.980584i | \(-0.437172\pi\) | ||||
0.196101 | + | 0.980584i | \(0.437172\pi\) | |||||||
\(332\) | 4.88866e6 | 2.43413 | ||||||||
\(333\) | 338742. | 0.167401 | ||||||||
\(334\) | −72880.0 | −0.0357472 | ||||||||
\(335\) | −6.88958e6 | −3.35413 | ||||||||
\(336\) | −627984. | −0.303459 | ||||||||
\(337\) | 348754. | 0.167280 | 0.0836401 | − | 0.996496i | \(-0.473345\pi\) | ||||
0.0836401 | + | 0.996496i | \(0.473345\pi\) | |||||||
\(338\) | 776070. | 0.369495 | ||||||||
\(339\) | 161154. | 0.0761626 | ||||||||
\(340\) | 1.60018e6 | 0.750707 | ||||||||
\(341\) | 340032. | 0.158356 | ||||||||
\(342\) | −735480. | −0.340021 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −1.33200e6 | −0.606887 | ||||||||
\(345\) | 1.12190e6 | 0.507467 | ||||||||
\(346\) | −2.89154e6 | −1.29849 | ||||||||
\(347\) | 2.50625e6 | 1.11738 | 0.558690 | − | 0.829376i | \(-0.311304\pi\) | ||||
0.558690 | + | 0.829376i | \(0.311304\pi\) | |||||||
\(348\) | 684216. | 0.302862 | ||||||||
\(349\) | 3.05861e6 | 1.34419 | 0.672094 | − | 0.740466i | \(-0.265395\pi\) | ||||
0.672094 | + | 0.740466i | \(0.265395\pi\) | |||||||
\(350\) | −3.97439e6 | −1.73420 | ||||||||
\(351\) | 488430. | 0.211609 | ||||||||
\(352\) | 250240. | 0.107647 | ||||||||
\(353\) | −3.49291e6 | −1.49194 | −0.745969 | − | 0.665981i | \(-0.768013\pi\) | ||||
−0.745969 | + | 0.665981i | \(0.768013\pi\) | |||||||
\(354\) | 2.94300e6 | 1.24819 | ||||||||
\(355\) | 6.49992e6 | 2.73739 | ||||||||
\(356\) | 7.60362e6 | 3.17977 | ||||||||
\(357\) | 97902.0 | 0.0406557 | ||||||||
\(358\) | 1.99492e6 | 0.822655 | ||||||||
\(359\) | 2.12034e6 | 0.868301 | 0.434150 | − | 0.900840i | \(-0.357049\pi\) | ||||
0.434150 | + | 0.900840i | \(0.357049\pi\) | |||||||
\(360\) | −3.09096e6 | −1.25701 | ||||||||
\(361\) | −1.65163e6 | −0.667031 | ||||||||
\(362\) | 2.40550e6 | 0.964793 | ||||||||
\(363\) | −1.37328e6 | −0.547008 | ||||||||
\(364\) | −2.23244e6 | −0.883133 | ||||||||
\(365\) | −4.12573e6 | −1.62095 | ||||||||
\(366\) | −972180. | −0.379353 | ||||||||
\(367\) | 746592. | 0.289346 | 0.144673 | − | 0.989479i | \(-0.453787\pi\) | ||||
0.144673 | + | 0.989479i | \(0.453787\pi\) | |||||||
\(368\) | −1.67462e6 | −0.644611 | ||||||||
\(369\) | −539622. | −0.206312 | ||||||||
\(370\) | −4.43292e6 | −1.68339 | ||||||||
\(371\) | 1.84132e6 | 0.694536 | ||||||||
\(372\) | 2.26195e6 | 0.847473 | ||||||||
\(373\) | −939034. | −0.349469 | −0.174735 | − | 0.984616i | \(-0.555907\pi\) | ||||
−0.174735 | + | 0.984616i | \(0.555907\pi\) | |||||||
\(374\) | −204240. | −0.0755026 | ||||||||
\(375\) | −4.75664e6 | −1.74672 | ||||||||
\(376\) | −2.54016e6 | −0.926598 | ||||||||
\(377\) | 749060. | 0.271433 | ||||||||
\(378\) | −357210. | −0.128586 | ||||||||
\(379\) | 5.16534e6 | 1.84714 | 0.923572 | − | 0.383424i | \(-0.125255\pi\) | ||||
0.923572 | + | 0.383424i | \(0.125255\pi\) | |||||||
\(380\) | 6.54486e6 | 2.32510 | ||||||||
\(381\) | 601776. | 0.212384 | ||||||||
\(382\) | 2.90384e6 | 1.01816 | ||||||||
\(383\) | 400512. | 0.139514 | 0.0697571 | − | 0.997564i | \(-0.477778\pi\) | ||||
0.0697571 | + | 0.997564i | \(0.477778\pi\) | |||||||
\(384\) | −2.43648e6 | −0.843208 | ||||||||
\(385\) | 477848. | 0.164300 | ||||||||
\(386\) | −1.71454e6 | −0.585706 | ||||||||
\(387\) | −299700. | −0.101721 | ||||||||
\(388\) | −1.02575e7 | −3.45910 | ||||||||
\(389\) | 306822. | 0.102805 | 0.0514023 | − | 0.998678i | \(-0.483631\pi\) | ||||
0.0514023 | + | 0.998678i | \(0.483631\pi\) | |||||||
\(390\) | −6.39180e6 | −2.12795 | ||||||||
\(391\) | 261072. | 0.0863611 | ||||||||
\(392\) | 864360. | 0.284105 | ||||||||
\(393\) | 1.38388e6 | 0.451976 | ||||||||
\(394\) | 4.01990e6 | 1.30459 | ||||||||
\(395\) | 9.33818e6 | 3.01141 | ||||||||
\(396\) | 506736. | 0.162384 | ||||||||
\(397\) | −3.83421e6 | −1.22095 | −0.610477 | − | 0.792034i | \(-0.709022\pi\) | ||||
−0.610477 | + | 0.792034i | \(0.709022\pi\) | |||||||
\(398\) | −2.59176e6 | −0.820138 | ||||||||
\(399\) | 400428. | 0.125919 | ||||||||
\(400\) | 1.15501e7 | 3.60940 | ||||||||
\(401\) | −3.29355e6 | −1.02283 | −0.511415 | − | 0.859334i | \(-0.670878\pi\) | ||||
−0.511415 | + | 0.859334i | \(0.670878\pi\) | |||||||
\(402\) | 5.84964e6 | 1.80536 | ||||||||
\(403\) | 2.47632e6 | 0.759529 | ||||||||
\(404\) | −9.34007e6 | −2.84706 | ||||||||
\(405\) | −695466. | −0.210687 | ||||||||
\(406\) | −547820. | −0.164939 | ||||||||
\(407\) | 384744. | 0.115129 | ||||||||
\(408\) | −719280. | −0.213918 | ||||||||
\(409\) | −1.35473e6 | −0.400445 | −0.200223 | − | 0.979750i | \(-0.564167\pi\) | ||||
−0.200223 | + | 0.979750i | \(0.564167\pi\) | |||||||
\(410\) | 7.06172e6 | 2.07468 | ||||||||
\(411\) | 2.30380e6 | 0.672730 | ||||||||
\(412\) | 1.95568e6 | 0.567616 | ||||||||
\(413\) | −1.60230e6 | −0.462241 | ||||||||
\(414\) | −952560. | −0.273144 | ||||||||
\(415\) | −7.62055e6 | −2.17203 | ||||||||
\(416\) | 1.82240e6 | 0.516310 | ||||||||
\(417\) | 2.54632e6 | 0.717088 | ||||||||
\(418\) | −835360. | −0.233848 | ||||||||
\(419\) | 5.08199e6 | 1.41416 | 0.707080 | − | 0.707134i | \(-0.250012\pi\) | ||||
0.707080 | + | 0.707134i | \(0.250012\pi\) | |||||||
\(420\) | 3.17873e6 | 0.879286 | ||||||||
\(421\) | 628022. | 0.172691 | 0.0863455 | − | 0.996265i | \(-0.472481\pi\) | ||||
0.0863455 | + | 0.996265i | \(0.472481\pi\) | |||||||
\(422\) | −1.19179e7 | −3.25775 | ||||||||
\(423\) | −571536. | −0.155308 | ||||||||
\(424\) | −1.35281e7 | −3.65445 | ||||||||
\(425\) | −1.80064e6 | −0.483565 | ||||||||
\(426\) | −5.51880e6 | −1.47340 | ||||||||
\(427\) | 529298. | 0.140485 | ||||||||
\(428\) | 1.53381e6 | 0.404726 | ||||||||
\(429\) | 554760. | 0.145533 | ||||||||
\(430\) | 3.92200e6 | 1.02291 | ||||||||
\(431\) | −3.00086e6 | −0.778132 | −0.389066 | − | 0.921210i | \(-0.627202\pi\) | ||||
−0.389066 | + | 0.921210i | \(0.627202\pi\) | |||||||
\(432\) | 1.03810e6 | 0.267626 | ||||||||
\(433\) | 1.21496e6 | 0.311417 | 0.155709 | − | 0.987803i | \(-0.450234\pi\) | ||||
0.155709 | + | 0.987803i | \(0.450234\pi\) | |||||||
\(434\) | −1.81104e6 | −0.461534 | ||||||||
\(435\) | −1.06657e6 | −0.270251 | ||||||||
\(436\) | 1.35986e6 | 0.342594 | ||||||||
\(437\) | 1.06781e6 | 0.267479 | ||||||||
\(438\) | 3.50298e6 | 0.872474 | ||||||||
\(439\) | 4.00654e6 | 0.992219 | 0.496110 | − | 0.868260i | \(-0.334761\pi\) | ||||
0.496110 | + | 0.868260i | \(0.334761\pi\) | |||||||
\(440\) | −3.51072e6 | −0.864499 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | −1.48740e6 | −0.362136 | ||||||||
\(443\) | −5.44751e6 | −1.31883 | −0.659415 | − | 0.751779i | \(-0.729196\pi\) | ||||
−0.659415 | + | 0.751779i | \(0.729196\pi\) | |||||||
\(444\) | 2.55938e6 | 0.616138 | ||||||||
\(445\) | −1.18527e7 | −2.83738 | ||||||||
\(446\) | −2.18384e6 | −0.519857 | ||||||||
\(447\) | 3.67249e6 | 0.869343 | ||||||||
\(448\) | 900032. | 0.211867 | ||||||||
\(449\) | −1.81577e6 | −0.425056 | −0.212528 | − | 0.977155i | \(-0.568170\pi\) | ||||
−0.212528 | + | 0.977155i | \(0.568170\pi\) | |||||||
\(450\) | 6.56991e6 | 1.52942 | ||||||||
\(451\) | −612904. | −0.141890 | ||||||||
\(452\) | 1.21761e6 | 0.280325 | ||||||||
\(453\) | 3.26254e6 | 0.746981 | ||||||||
\(454\) | 5.82852e6 | 1.32715 | ||||||||
\(455\) | 3.47998e6 | 0.788040 | ||||||||
\(456\) | −2.94192e6 | −0.662550 | ||||||||
\(457\) | −5.30082e6 | −1.18728 | −0.593639 | − | 0.804731i | \(-0.702309\pi\) | ||||
−0.593639 | + | 0.804731i | \(0.702309\pi\) | |||||||
\(458\) | 9.61046e6 | 2.14082 | ||||||||
\(459\) | −161838. | −0.0358549 | ||||||||
\(460\) | 8.47661e6 | 1.86779 | ||||||||
\(461\) | 3.20381e6 | 0.702124 | 0.351062 | − | 0.936352i | \(-0.385821\pi\) | ||||
0.351062 | + | 0.936352i | \(0.385821\pi\) | |||||||
\(462\) | −405720. | −0.0884344 | ||||||||
\(463\) | −1.11853e6 | −0.242490 | −0.121245 | − | 0.992623i | \(-0.538689\pi\) | ||||
−0.121245 | + | 0.992623i | \(0.538689\pi\) | |||||||
\(464\) | 1.59203e6 | 0.343287 | ||||||||
\(465\) | −3.52598e6 | −0.756220 | ||||||||
\(466\) | 6.05994e6 | 1.29272 | ||||||||
\(467\) | −3.85134e6 | −0.817184 | −0.408592 | − | 0.912717i | \(-0.633980\pi\) | ||||
−0.408592 | + | 0.912717i | \(0.633980\pi\) | |||||||
\(468\) | 3.69036e6 | 0.778850 | ||||||||
\(469\) | −3.18480e6 | −0.668576 | ||||||||
\(470\) | 7.47936e6 | 1.56178 | ||||||||
\(471\) | −1.37507e6 | −0.285610 | ||||||||
\(472\) | 1.17720e7 | 2.43218 | ||||||||
\(473\) | −340400. | −0.0699579 | ||||||||
\(474\) | −7.92864e6 | −1.62089 | ||||||||
\(475\) | −7.36479e6 | −1.49770 | ||||||||
\(476\) | 739704. | 0.149638 | ||||||||
\(477\) | −3.04382e6 | −0.612523 | ||||||||
\(478\) | 1.17014e7 | 2.34245 | ||||||||
\(479\) | 1.43536e6 | 0.285839 | 0.142920 | − | 0.989734i | \(-0.454351\pi\) | ||||
0.142920 | + | 0.989734i | \(0.454351\pi\) | |||||||
\(480\) | −2.59488e6 | −0.514060 | ||||||||
\(481\) | 2.80194e6 | 0.552200 | ||||||||
\(482\) | −1.23691e7 | −2.42505 | ||||||||
\(483\) | 518616. | 0.101153 | ||||||||
\(484\) | −1.03759e7 | −2.01332 | ||||||||
\(485\) | 1.59897e7 | 3.08664 | ||||||||
\(486\) | 590490. | 0.113402 | ||||||||
\(487\) | 4.61097e6 | 0.880987 | 0.440494 | − | 0.897756i | \(-0.354803\pi\) | ||||
0.440494 | + | 0.897756i | \(0.354803\pi\) | |||||||
\(488\) | −3.88872e6 | −0.739192 | ||||||||
\(489\) | −1.35385e6 | −0.256035 | ||||||||
\(490\) | −2.54506e6 | −0.478859 | ||||||||
\(491\) | 7.40518e6 | 1.38622 | 0.693110 | − | 0.720832i | \(-0.256240\pi\) | ||||
0.693110 | + | 0.720832i | \(0.256240\pi\) | |||||||
\(492\) | −4.07714e6 | −0.759352 | ||||||||
\(493\) | −248196. | −0.0459915 | ||||||||
\(494\) | −6.08360e6 | −1.12161 | ||||||||
\(495\) | −789912. | −0.144899 | ||||||||
\(496\) | 5.26310e6 | 0.960589 | ||||||||
\(497\) | 3.00468e6 | 0.545641 | ||||||||
\(498\) | 6.47028e6 | 1.16909 | ||||||||
\(499\) | 3.93432e6 | 0.707325 | 0.353662 | − | 0.935373i | \(-0.384936\pi\) | ||||
0.353662 | + | 0.935373i | \(0.384936\pi\) | |||||||
\(500\) | −3.59391e7 | −6.42898 | ||||||||
\(501\) | −65592.0 | −0.0116750 | ||||||||
\(502\) | 9.59708e6 | 1.69973 | ||||||||
\(503\) | 3.40975e6 | 0.600901 | 0.300450 | − | 0.953797i | \(-0.402863\pi\) | ||||
0.300450 | + | 0.953797i | \(0.402863\pi\) | |||||||
\(504\) | −1.42884e6 | −0.250557 | ||||||||
\(505\) | 1.45595e7 | 2.54050 | ||||||||
\(506\) | −1.08192e6 | −0.187853 | ||||||||
\(507\) | 698463. | 0.120677 | ||||||||
\(508\) | 4.54675e6 | 0.781703 | ||||||||
\(509\) | −7.72383e6 | −1.32141 | −0.660706 | − | 0.750645i | \(-0.729743\pi\) | ||||
−0.660706 | + | 0.750645i | \(0.729743\pi\) | |||||||
\(510\) | 2.11788e6 | 0.360559 | ||||||||
\(511\) | −1.90718e6 | −0.323102 | ||||||||
\(512\) | −1.25312e7 | −2.11260 | ||||||||
\(513\) | −661932. | −0.111050 | ||||||||
\(514\) | −1.21259e7 | −2.02445 | ||||||||
\(515\) | −3.04856e6 | −0.506497 | ||||||||
\(516\) | −2.26440e6 | −0.374394 | ||||||||
\(517\) | −649152. | −0.106812 | ||||||||
\(518\) | −2.04918e6 | −0.335549 | ||||||||
\(519\) | −2.60239e6 | −0.424085 | ||||||||
\(520\) | −2.55672e7 | −4.14643 | ||||||||
\(521\) | −4.77658e6 | −0.770944 | −0.385472 | − | 0.922719i | \(-0.625961\pi\) | ||||
−0.385472 | + | 0.922719i | \(0.625961\pi\) | |||||||
\(522\) | 905580. | 0.145462 | ||||||||
\(523\) | −9.28754e6 | −1.48473 | −0.742363 | − | 0.669998i | \(-0.766295\pi\) | ||||
−0.742363 | + | 0.669998i | \(0.766295\pi\) | |||||||
\(524\) | 1.04560e7 | 1.66355 | ||||||||
\(525\) | −3.57695e6 | −0.566389 | ||||||||
\(526\) | −1.25274e7 | −1.97423 | ||||||||
\(527\) | −820512. | −0.128694 | ||||||||
\(528\) | 1.17907e6 | 0.184058 | ||||||||
\(529\) | −5.05337e6 | −0.785130 | ||||||||
\(530\) | 3.98327e7 | 6.15956 | ||||||||
\(531\) | 2.64870e6 | 0.407658 | ||||||||
\(532\) | 3.02546e6 | 0.463459 | ||||||||
\(533\) | −4.46354e6 | −0.680552 | ||||||||
\(534\) | 1.00636e7 | 1.52722 | ||||||||
\(535\) | −2.39094e6 | −0.361147 | ||||||||
\(536\) | 2.33986e7 | 3.51785 | ||||||||
\(537\) | 1.79543e6 | 0.268678 | ||||||||
\(538\) | −1.36866e6 | −0.203864 | ||||||||
\(539\) | 220892. | 0.0327498 | ||||||||
\(540\) | −5.25463e6 | −0.775457 | ||||||||
\(541\) | 7.72917e6 | 1.13538 | 0.567688 | − | 0.823244i | \(-0.307838\pi\) | ||||
0.567688 | + | 0.823244i | \(0.307838\pi\) | |||||||
\(542\) | −9.60896e6 | −1.40501 | ||||||||
\(543\) | 2.16495e6 | 0.315100 | ||||||||
\(544\) | −603840. | −0.0874832 | ||||||||
\(545\) | −2.11979e6 | −0.305704 | ||||||||
\(546\) | −2.95470e6 | −0.424162 | ||||||||
\(547\) | −8.60361e6 | −1.22945 | −0.614727 | − | 0.788740i | \(-0.710734\pi\) | ||||
−0.614727 | + | 0.788740i | \(0.710734\pi\) | |||||||
\(548\) | 1.74065e7 | 2.47605 | ||||||||
\(549\) | −874962. | −0.123896 | ||||||||
\(550\) | 7.46212e6 | 1.05185 | ||||||||
\(551\) | −1.01514e6 | −0.142445 | ||||||||
\(552\) | −3.81024e6 | −0.532236 | ||||||||
\(553\) | 4.31670e6 | 0.600260 | ||||||||
\(554\) | 9.05830e6 | 1.25393 | ||||||||
\(555\) | −3.98963e6 | −0.549794 | ||||||||
\(556\) | 1.92388e7 | 2.63932 | ||||||||
\(557\) | −1.77723e6 | −0.242721 | −0.121360 | − | 0.992609i | \(-0.538726\pi\) | ||||
−0.121360 | + | 0.992609i | \(0.538726\pi\) | |||||||
\(558\) | 2.99376e6 | 0.407035 | ||||||||
\(559\) | −2.47900e6 | −0.335542 | ||||||||
\(560\) | 7.39626e6 | 0.996648 | ||||||||
\(561\) | −183816. | −0.0246590 | ||||||||
\(562\) | −330620. | −0.0441559 | ||||||||
\(563\) | 2.68860e6 | 0.357482 | 0.178741 | − | 0.983896i | \(-0.442798\pi\) | ||||
0.178741 | + | 0.983896i | \(0.442798\pi\) | |||||||
\(564\) | −4.31827e6 | −0.571626 | ||||||||
\(565\) | −1.89804e6 | −0.250140 | ||||||||
\(566\) | −8.63588e6 | −1.13309 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | −2.20752e7 | −2.87100 | ||||||||
\(569\) | 5.32630e6 | 0.689675 | 0.344838 | − | 0.938662i | \(-0.387934\pi\) | ||||
0.344838 | + | 0.938662i | \(0.387934\pi\) | |||||||
\(570\) | 8.66232e6 | 1.11673 | ||||||||
\(571\) | 1.33992e7 | 1.71984 | 0.859921 | − | 0.510427i | \(-0.170513\pi\) | ||||
0.859921 | + | 0.510427i | \(0.170513\pi\) | |||||||
\(572\) | 4.19152e6 | 0.535650 | ||||||||
\(573\) | 2.61346e6 | 0.332528 | ||||||||
\(574\) | 3.26438e6 | 0.413543 | ||||||||
\(575\) | −9.53854e6 | −1.20313 | ||||||||
\(576\) | −1.48781e6 | −0.186849 | ||||||||
\(577\) | −1.10502e6 | −0.138176 | −0.0690878 | − | 0.997611i | \(-0.522009\pi\) | ||||
−0.0690878 | + | 0.997611i | \(0.522009\pi\) | |||||||
\(578\) | −1.37057e7 | −1.70641 | ||||||||
\(579\) | −1.54309e6 | −0.191291 | ||||||||
\(580\) | −8.05854e6 | −0.994687 | ||||||||
\(581\) | −3.52271e6 | −0.432949 | ||||||||
\(582\) | −1.35761e7 | −1.66138 | ||||||||
\(583\) | −3.45718e6 | −0.421260 | ||||||||
\(584\) | 1.40119e7 | 1.70007 | ||||||||
\(585\) | −5.75262e6 | −0.694986 | ||||||||
\(586\) | −1.33755e7 | −1.60903 | ||||||||
\(587\) | 5.97288e6 | 0.715465 | 0.357732 | − | 0.933824i | \(-0.383550\pi\) | ||||
0.357732 | + | 0.933824i | \(0.383550\pi\) | |||||||
\(588\) | 1.46941e6 | 0.175267 | ||||||||
\(589\) | −3.35597e6 | −0.398593 | ||||||||
\(590\) | −3.46620e7 | −4.09943 | ||||||||
\(591\) | 3.61791e6 | 0.426078 | ||||||||
\(592\) | 5.95517e6 | 0.698377 | ||||||||
\(593\) | −1.11945e7 | −1.30728 | −0.653639 | − | 0.756807i | \(-0.726758\pi\) | ||||
−0.653639 | + | 0.756807i | \(0.726758\pi\) | |||||||
\(594\) | 670680. | 0.0779919 | ||||||||
\(595\) | −1.15307e6 | −0.133525 | ||||||||
\(596\) | 2.77477e7 | 3.19971 | ||||||||
\(597\) | −2.33258e6 | −0.267856 | ||||||||
\(598\) | −7.87920e6 | −0.901009 | ||||||||
\(599\) | 1.09055e7 | 1.24187 | 0.620937 | − | 0.783860i | \(-0.286752\pi\) | ||||
0.620937 | + | 0.783860i | \(0.286752\pi\) | |||||||
\(600\) | 2.62796e7 | 2.98017 | ||||||||
\(601\) | 7.39737e6 | 0.835394 | 0.417697 | − | 0.908586i | \(-0.362837\pi\) | ||||
0.417697 | + | 0.908586i | \(0.362837\pi\) | |||||||
\(602\) | 1.81300e6 | 0.203895 | ||||||||
\(603\) | 5.26468e6 | 0.589628 | ||||||||
\(604\) | 2.46503e7 | 2.74935 | ||||||||
\(605\) | 1.61742e7 | 1.79653 | ||||||||
\(606\) | −1.23619e7 | −1.36742 | ||||||||
\(607\) | 7.13355e6 | 0.785840 | 0.392920 | − | 0.919573i | \(-0.371465\pi\) | ||||
0.392920 | + | 0.919573i | \(0.371465\pi\) | |||||||
\(608\) | −2.46976e6 | −0.270954 | ||||||||
\(609\) | −493038. | −0.0538688 | ||||||||
\(610\) | 1.14501e7 | 1.24591 | ||||||||
\(611\) | −4.72752e6 | −0.512307 | ||||||||
\(612\) | −1.22278e6 | −0.131968 | ||||||||
\(613\) | −1.71264e7 | −1.84083 | −0.920416 | − | 0.390939i | \(-0.872150\pi\) | ||||
−0.920416 | + | 0.390939i | \(0.872150\pi\) | |||||||
\(614\) | −1.32820e7 | −1.42182 | ||||||||
\(615\) | 6.35555e6 | 0.677587 | ||||||||
\(616\) | −1.62288e6 | −0.172320 | ||||||||
\(617\) | 2.29924e6 | 0.243149 | 0.121574 | − | 0.992582i | \(-0.461206\pi\) | ||||
0.121574 | + | 0.992582i | \(0.461206\pi\) | |||||||
\(618\) | 2.58840e6 | 0.272622 | ||||||||
\(619\) | −1.85176e6 | −0.194249 | −0.0971245 | − | 0.995272i | \(-0.530965\pi\) | ||||
−0.0971245 | + | 0.995272i | \(0.530965\pi\) | |||||||
\(620\) | −2.66408e7 | −2.78335 | ||||||||
\(621\) | −857304. | −0.0892084 | ||||||||
\(622\) | −6.65832e6 | −0.690063 | ||||||||
\(623\) | −5.47908e6 | −0.565572 | ||||||||
\(624\) | 8.58672e6 | 0.882807 | ||||||||
\(625\) | 3.06758e7 | 3.14120 | ||||||||
\(626\) | −3.09021e7 | −3.15176 | ||||||||
\(627\) | −751824. | −0.0763743 | ||||||||
\(628\) | −1.03894e7 | −1.05122 | ||||||||
\(629\) | −928404. | −0.0935643 | ||||||||
\(630\) | 4.20714e6 | 0.422314 | ||||||||
\(631\) | 9.25978e6 | 0.925822 | 0.462911 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462911 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(632\) | −3.17146e7 | −3.15839 | ||||||||
\(633\) | −1.07261e7 | −1.06398 | ||||||||
\(634\) | −9.74178e6 | −0.962532 | ||||||||
\(635\) | −7.08758e6 | −0.697532 | ||||||||
\(636\) | −2.29977e7 | −2.25446 | ||||||||
\(637\) | 1.60867e6 | 0.157079 | ||||||||
\(638\) | 1.02856e6 | 0.100041 | ||||||||
\(639\) | −4.96692e6 | −0.481210 | ||||||||
\(640\) | 2.86963e7 | 2.76934 | ||||||||
\(641\) | 1.79419e7 | 1.72474 | 0.862369 | − | 0.506280i | \(-0.168980\pi\) | ||||
0.862369 | + | 0.506280i | \(0.168980\pi\) | |||||||
\(642\) | 2.03004e6 | 0.194387 | ||||||||
\(643\) | 6.70020e6 | 0.639087 | 0.319544 | − | 0.947572i | \(-0.396470\pi\) | ||||
0.319544 | + | 0.947572i | \(0.396470\pi\) | |||||||
\(644\) | 3.91843e6 | 0.372304 | ||||||||
\(645\) | 3.52980e6 | 0.334080 | ||||||||
\(646\) | 2.01576e6 | 0.190045 | ||||||||
\(647\) | −1.12549e7 | −1.05701 | −0.528507 | − | 0.848929i | \(-0.677248\pi\) | ||||
−0.528507 | + | 0.848929i | \(0.677248\pi\) | |||||||
\(648\) | 2.36196e6 | 0.220971 | ||||||||
\(649\) | 3.00840e6 | 0.280365 | ||||||||
\(650\) | 5.43437e7 | 5.04505 | ||||||||
\(651\) | −1.62994e6 | −0.150736 | ||||||||
\(652\) | −1.02291e7 | −0.942364 | ||||||||
\(653\) | 1.31704e7 | 1.20869 | 0.604347 | − | 0.796721i | \(-0.293434\pi\) | ||||
0.604347 | + | 0.796721i | \(0.293434\pi\) | |||||||
\(654\) | 1.79982e6 | 0.164545 | ||||||||
\(655\) | −1.62990e7 | −1.48442 | ||||||||
\(656\) | −9.48669e6 | −0.860706 | ||||||||
\(657\) | 3.15268e6 | 0.284949 | ||||||||
\(658\) | 3.45744e6 | 0.311308 | ||||||||
\(659\) | −1.43453e7 | −1.28676 | −0.643380 | − | 0.765547i | \(-0.722468\pi\) | ||||
−0.643380 | + | 0.765547i | \(0.722468\pi\) | |||||||
\(660\) | −5.96822e6 | −0.533317 | ||||||||
\(661\) | −14138.0 | −0.00125859 | −0.000629295 | − | 1.00000i | \(-0.500200\pi\) | ||||
−0.000629295 | 1.00000i | \(0.500200\pi\) | ||||||||
\(662\) | 7.81772e6 | 0.693322 | ||||||||
\(663\) | −1.33866e6 | −0.118273 | ||||||||
\(664\) | 2.58811e7 | 2.27805 | ||||||||
\(665\) | −4.71615e6 | −0.413555 | ||||||||
\(666\) | 3.38742e6 | 0.295926 | ||||||||
\(667\) | −1.31477e6 | −0.114429 | ||||||||
\(668\) | −495584. | −0.0429711 | ||||||||
\(669\) | −1.96546e6 | −0.169784 | ||||||||
\(670\) | −6.88958e7 | −5.92933 | ||||||||
\(671\) | −993784. | −0.0852090 | ||||||||
\(672\) | −1.19952e6 | −0.102467 | ||||||||
\(673\) | 1.37787e7 | 1.17266 | 0.586329 | − | 0.810073i | \(-0.300573\pi\) | ||||
0.586329 | + | 0.810073i | \(0.300573\pi\) | |||||||
\(674\) | 3.48754e6 | 0.295712 | ||||||||
\(675\) | 5.91292e6 | 0.499508 | ||||||||
\(676\) | 5.27728e6 | 0.444164 | ||||||||
\(677\) | 1.26155e7 | 1.05787 | 0.528936 | − | 0.848662i | \(-0.322591\pi\) | ||||
0.528936 | + | 0.848662i | \(0.322591\pi\) | |||||||
\(678\) | 1.61154e6 | 0.134638 | ||||||||
\(679\) | 7.39145e6 | 0.615255 | ||||||||
\(680\) | 8.47152e6 | 0.702569 | ||||||||
\(681\) | 5.24567e6 | 0.433444 | ||||||||
\(682\) | 3.40032e6 | 0.279936 | ||||||||
\(683\) | −1.08656e6 | −0.0891258 | −0.0445629 | − | 0.999007i | \(-0.514190\pi\) | ||||
−0.0445629 | + | 0.999007i | \(0.514190\pi\) | |||||||
\(684\) | −5.00126e6 | −0.408733 | ||||||||
\(685\) | −2.71337e7 | −2.20944 | ||||||||
\(686\) | −1.17649e6 | −0.0954504 | ||||||||
\(687\) | 8.64941e6 | 0.699189 | ||||||||
\(688\) | −5.26880e6 | −0.424366 | ||||||||
\(689\) | −2.51773e7 | −2.02051 | ||||||||
\(690\) | 1.12190e7 | 0.897084 | ||||||||
\(691\) | 1.91229e7 | 1.52356 | 0.761780 | − | 0.647836i | \(-0.224326\pi\) | ||||
0.761780 | + | 0.647836i | \(0.224326\pi\) | |||||||
\(692\) | −1.96625e7 | −1.56089 | ||||||||
\(693\) | −365148. | −0.0288826 | ||||||||
\(694\) | 2.50625e7 | 1.97527 | ||||||||
\(695\) | −2.99899e7 | −2.35512 | ||||||||
\(696\) | 3.62232e6 | 0.283442 | ||||||||
\(697\) | 1.47896e6 | 0.115312 | ||||||||
\(698\) | 3.05861e7 | 2.37621 | ||||||||
\(699\) | 5.45395e6 | 0.422200 | ||||||||
\(700\) | −2.70259e7 | −2.08466 | ||||||||
\(701\) | 1.15000e7 | 0.883897 | 0.441948 | − | 0.897040i | \(-0.354287\pi\) | ||||
0.441948 | + | 0.897040i | \(0.354287\pi\) | |||||||
\(702\) | 4.88430e6 | 0.374076 | ||||||||
\(703\) | −3.79726e6 | −0.289789 | ||||||||
\(704\) | −1.68986e6 | −0.128504 | ||||||||
\(705\) | 6.73142e6 | 0.510075 | ||||||||
\(706\) | −3.49291e7 | −2.63740 | ||||||||
\(707\) | 6.73035e6 | 0.506394 | ||||||||
\(708\) | 2.00124e7 | 1.50043 | ||||||||
\(709\) | 6.97551e6 | 0.521147 | 0.260574 | − | 0.965454i | \(-0.416088\pi\) | ||||
0.260574 | + | 0.965454i | \(0.416088\pi\) | |||||||
\(710\) | 6.49992e7 | 4.83907 | ||||||||
\(711\) | −7.13578e6 | −0.529380 | ||||||||
\(712\) | 4.02545e7 | 2.97587 | ||||||||
\(713\) | −4.34650e6 | −0.320196 | ||||||||
\(714\) | 979020. | 0.0718697 | ||||||||
\(715\) | −6.53384e6 | −0.477973 | ||||||||
\(716\) | 1.35655e7 | 0.988899 | ||||||||
\(717\) | 1.05313e7 | 0.765040 | ||||||||
\(718\) | 2.12034e7 | 1.53495 | ||||||||
\(719\) | −1.44264e6 | −0.104072 | −0.0520362 | − | 0.998645i | \(-0.516571\pi\) | ||||
−0.0520362 | + | 0.998645i | \(0.516571\pi\) | |||||||
\(720\) | −1.22265e7 | −0.878961 | ||||||||
\(721\) | −1.40924e6 | −0.100959 | ||||||||
\(722\) | −1.65164e7 | −1.17916 | ||||||||
\(723\) | −1.11322e7 | −0.792018 | ||||||||
\(724\) | 1.63574e7 | 1.15976 | ||||||||
\(725\) | 9.06810e6 | 0.640724 | ||||||||
\(726\) | −1.37328e7 | −0.966982 | ||||||||
\(727\) | −1.90334e7 | −1.33561 | −0.667807 | − | 0.744334i | \(-0.732767\pi\) | ||||
−0.667807 | + | 0.744334i | \(0.732767\pi\) | |||||||
\(728\) | −1.18188e7 | −0.826504 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −4.12573e7 | −2.86546 | ||||||||
\(731\) | 821400. | 0.0568540 | ||||||||
\(732\) | −6.61082e6 | −0.456014 | ||||||||
\(733\) | 5.45585e6 | 0.375062 | 0.187531 | − | 0.982259i | \(-0.439952\pi\) | ||||
0.187531 | + | 0.982259i | \(0.439952\pi\) | |||||||
\(734\) | 7.46592e6 | 0.511497 | ||||||||
\(735\) | −2.29055e6 | −0.156395 | ||||||||
\(736\) | −3.19872e6 | −0.217662 | ||||||||
\(737\) | 5.97963e6 | 0.405514 | ||||||||
\(738\) | −5.39622e6 | −0.364711 | ||||||||
\(739\) | 7.85197e6 | 0.528893 | 0.264446 | − | 0.964400i | \(-0.414811\pi\) | ||||
0.264446 | + | 0.964400i | \(0.414811\pi\) | |||||||
\(740\) | −3.01439e7 | −2.02358 | ||||||||
\(741\) | −5.47524e6 | −0.366317 | ||||||||
\(742\) | 1.84132e7 | 1.22778 | ||||||||
\(743\) | −1.48695e7 | −0.988154 | −0.494077 | − | 0.869418i | \(-0.664494\pi\) | ||||
−0.494077 | + | 0.869418i | \(0.664494\pi\) | |||||||
\(744\) | 1.19750e7 | 0.793130 | ||||||||
\(745\) | −4.32537e7 | −2.85518 | ||||||||
\(746\) | −9.39034e6 | −0.617781 | ||||||||
\(747\) | 5.82325e6 | 0.381825 | ||||||||
\(748\) | −1.38883e6 | −0.0907603 | ||||||||
\(749\) | −1.10524e6 | −0.0719869 | ||||||||
\(750\) | −4.75664e7 | −3.08779 | ||||||||
\(751\) | −2.51309e7 | −1.62595 | −0.812977 | − | 0.582295i | \(-0.802155\pi\) | ||||
−0.812977 | + | 0.582295i | \(0.802155\pi\) | |||||||
\(752\) | −1.00477e7 | −0.647924 | ||||||||
\(753\) | 8.63737e6 | 0.555129 | ||||||||
\(754\) | 7.49060e6 | 0.479831 | ||||||||
\(755\) | −3.84254e7 | −2.45330 | ||||||||
\(756\) | −2.42903e6 | −0.154571 | ||||||||
\(757\) | −1.97874e7 | −1.25501 | −0.627507 | − | 0.778611i | \(-0.715925\pi\) | ||||
−0.627507 | + | 0.778611i | \(0.715925\pi\) | |||||||
\(758\) | 5.16534e7 | 3.26532 | ||||||||
\(759\) | −973728. | −0.0613526 | ||||||||
\(760\) | 3.46493e7 | 2.17601 | ||||||||
\(761\) | −1.49642e7 | −0.936678 | −0.468339 | − | 0.883549i | \(-0.655147\pi\) | ||||
−0.468339 | + | 0.883549i | \(0.655147\pi\) | |||||||
\(762\) | 6.01776e6 | 0.375446 | ||||||||
\(763\) | −979902. | −0.0609356 | ||||||||
\(764\) | 1.97461e7 | 1.22391 | ||||||||
\(765\) | 1.90609e6 | 0.117758 | ||||||||
\(766\) | 4.00512e6 | 0.246629 | ||||||||
\(767\) | 2.19090e7 | 1.34473 | ||||||||
\(768\) | −1.90748e7 | −1.16696 | ||||||||
\(769\) | 5.06419e6 | 0.308812 | 0.154406 | − | 0.988007i | \(-0.450654\pi\) | ||||
0.154406 | + | 0.988007i | \(0.450654\pi\) | |||||||
\(770\) | 4.77848e6 | 0.290444 | ||||||||
\(771\) | −1.09133e7 | −0.661181 | ||||||||
\(772\) | −1.16589e7 | −0.704066 | ||||||||
\(773\) | 2.63025e7 | 1.58324 | 0.791622 | − | 0.611011i | \(-0.209237\pi\) | ||||
0.791622 | + | 0.611011i | \(0.209237\pi\) | |||||||
\(774\) | −2.99700e6 | −0.179818 | ||||||||
\(775\) | 2.99783e7 | 1.79288 | ||||||||
\(776\) | −5.43046e7 | −3.23729 | ||||||||
\(777\) | −1.84426e6 | −0.109590 | ||||||||
\(778\) | 3.06822e6 | 0.181735 | ||||||||
\(779\) | 6.04910e6 | 0.357147 | ||||||||
\(780\) | −4.34642e7 | −2.55797 | ||||||||
\(781\) | −5.64144e6 | −0.330950 | ||||||||
\(782\) | 2.61072e6 | 0.152666 | ||||||||
\(783\) | 815022. | 0.0475078 | ||||||||
\(784\) | 3.41902e6 | 0.198661 | ||||||||
\(785\) | 1.61953e7 | 0.938027 | ||||||||
\(786\) | 1.38388e7 | 0.798989 | ||||||||
\(787\) | 1.00525e7 | 0.578545 | 0.289273 | − | 0.957247i | \(-0.406587\pi\) | ||||
0.289273 | + | 0.957247i | \(0.406587\pi\) | |||||||
\(788\) | 2.73353e7 | 1.56823 | ||||||||
\(789\) | −1.12747e7 | −0.644781 | ||||||||
\(790\) | 9.33818e7 | 5.32346 | ||||||||
\(791\) | −877394. | −0.0498601 | ||||||||
\(792\) | 2.68272e6 | 0.151972 | ||||||||
\(793\) | −7.23734e6 | −0.408692 | ||||||||
\(794\) | −3.83421e7 | −2.15836 | ||||||||
\(795\) | 3.58494e7 | 2.01170 | ||||||||
\(796\) | −1.76240e7 | −0.985873 | ||||||||
\(797\) | 2.78516e7 | 1.55312 | 0.776560 | − | 0.630044i | \(-0.216963\pi\) | ||||
0.776560 | + | 0.630044i | \(0.216963\pi\) | |||||||
\(798\) | 4.00428e6 | 0.222596 | ||||||||
\(799\) | 1.56643e6 | 0.0868050 | ||||||||
\(800\) | 2.20619e7 | 1.21876 | ||||||||
\(801\) | 9.05726e6 | 0.498787 | ||||||||
\(802\) | −3.29355e7 | −1.80812 | ||||||||
\(803\) | 3.58082e6 | 0.195972 | ||||||||
\(804\) | 3.97776e7 | 2.17019 | ||||||||
\(805\) | −6.10814e6 | −0.332215 | ||||||||
\(806\) | 2.47632e7 | 1.34267 | ||||||||
\(807\) | −1.23179e6 | −0.0665816 | ||||||||
\(808\) | −4.94474e7 | −2.66450 | ||||||||
\(809\) | −1.96936e7 | −1.05792 | −0.528961 | − | 0.848646i | \(-0.677418\pi\) | ||||
−0.528961 | + | 0.848646i | \(0.677418\pi\) | |||||||
\(810\) | −6.95466e6 | −0.372446 | ||||||||
\(811\) | 5.05617e6 | 0.269942 | 0.134971 | − | 0.990850i | \(-0.456906\pi\) | ||||
0.134971 | + | 0.990850i | \(0.456906\pi\) | |||||||
\(812\) | −3.72518e6 | −0.198270 | ||||||||
\(813\) | −8.64806e6 | −0.458873 | ||||||||
\(814\) | 3.84744e6 | 0.203522 | ||||||||
\(815\) | 1.59454e7 | 0.840893 | ||||||||
\(816\) | −2.84515e6 | −0.149582 | ||||||||
\(817\) | 3.35960e6 | 0.176089 | ||||||||
\(818\) | −1.35473e7 | −0.707894 | ||||||||
\(819\) | −2.65923e6 | −0.138531 | ||||||||
\(820\) | 4.80197e7 | 2.49393 | ||||||||
\(821\) | −2.82324e6 | −0.146181 | −0.0730904 | − | 0.997325i | \(-0.523286\pi\) | ||||
−0.0730904 | + | 0.997325i | \(0.523286\pi\) | |||||||
\(822\) | 2.30380e7 | 1.18923 | ||||||||
\(823\) | 2.54741e7 | 1.31099 | 0.655494 | − | 0.755201i | \(-0.272461\pi\) | ||||
0.655494 | + | 0.755201i | \(0.272461\pi\) | |||||||
\(824\) | 1.03536e7 | 0.531219 | ||||||||
\(825\) | 6.71591e6 | 0.343534 | ||||||||
\(826\) | −1.60230e7 | −0.817135 | ||||||||
\(827\) | −1.75616e7 | −0.892893 | −0.446446 | − | 0.894810i | \(-0.647311\pi\) | ||||
−0.446446 | + | 0.894810i | \(0.647311\pi\) | |||||||
\(828\) | −6.47741e6 | −0.328341 | ||||||||
\(829\) | 9.14728e6 | 0.462280 | 0.231140 | − | 0.972920i | \(-0.425754\pi\) | ||||
0.231140 | + | 0.972920i | \(0.425754\pi\) | |||||||
\(830\) | −7.62055e7 | −3.83965 | ||||||||
\(831\) | 8.15247e6 | 0.409531 | ||||||||
\(832\) | −1.23066e7 | −0.616351 | ||||||||
\(833\) | −533022. | −0.0266154 | ||||||||
\(834\) | 2.54632e7 | 1.26764 | ||||||||
\(835\) | 772528. | 0.0383441 | ||||||||
\(836\) | −5.68045e6 | −0.281104 | ||||||||
\(837\) | 2.69438e6 | 0.132937 | ||||||||
\(838\) | 5.08199e7 | 2.49991 | ||||||||
\(839\) | −1.09891e7 | −0.538961 | −0.269481 | − | 0.963006i | \(-0.586852\pi\) | ||||
−0.269481 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(840\) | 1.68286e7 | 0.822903 | ||||||||
\(841\) | −1.92612e7 | −0.939061 | ||||||||
\(842\) | 6.28022e6 | 0.305277 | ||||||||
\(843\) | −297558. | −0.0144212 | ||||||||
\(844\) | −8.10416e7 | −3.91608 | ||||||||
\(845\) | −8.22634e6 | −0.396337 | ||||||||
\(846\) | −5.71536e6 | −0.274548 | ||||||||
\(847\) | 7.47676e6 | 0.358101 | ||||||||
\(848\) | −5.35111e7 | −2.55537 | ||||||||
\(849\) | −7.77229e6 | −0.370067 | ||||||||
\(850\) | −1.80064e7 | −0.854831 | ||||||||
\(851\) | −4.91803e6 | −0.232792 | ||||||||
\(852\) | −3.75278e7 | −1.77115 | ||||||||
\(853\) | −1.34854e7 | −0.634586 | −0.317293 | − | 0.948328i | \(-0.602774\pi\) | ||||
−0.317293 | + | 0.948328i | \(0.602774\pi\) | |||||||
\(854\) | 5.29298e6 | 0.248345 | ||||||||
\(855\) | 7.79609e6 | 0.364722 | ||||||||
\(856\) | 8.12016e6 | 0.378774 | ||||||||
\(857\) | 1.07032e7 | 0.497808 | 0.248904 | − | 0.968528i | \(-0.419930\pi\) | ||||
0.248904 | + | 0.968528i | \(0.419930\pi\) | |||||||
\(858\) | 5.54760e6 | 0.257269 | ||||||||
\(859\) | −1.33747e7 | −0.618446 | −0.309223 | − | 0.950990i | \(-0.600069\pi\) | ||||
−0.309223 | + | 0.950990i | \(0.600069\pi\) | |||||||
\(860\) | 2.66696e7 | 1.22962 | ||||||||
\(861\) | 2.93794e6 | 0.135063 | ||||||||
\(862\) | −3.00086e7 | −1.37556 | ||||||||
\(863\) | 1.99768e7 | 0.913058 | 0.456529 | − | 0.889708i | \(-0.349092\pi\) | ||||
0.456529 | + | 0.889708i | \(0.349092\pi\) | |||||||
\(864\) | 1.98288e6 | 0.0903675 | ||||||||
\(865\) | 3.06503e7 | 1.39282 | ||||||||
\(866\) | 1.21496e7 | 0.550513 | ||||||||
\(867\) | −1.23352e7 | −0.557310 | ||||||||
\(868\) | −1.23151e7 | −0.554802 | ||||||||
\(869\) | −8.10483e6 | −0.364078 | ||||||||
\(870\) | −1.06657e7 | −0.477740 | ||||||||
\(871\) | 4.35473e7 | 1.94498 | ||||||||
\(872\) | 7.19928e6 | 0.320625 | ||||||||
\(873\) | −1.22185e7 | −0.542604 | ||||||||
\(874\) | 1.06781e7 | 0.472840 | ||||||||
\(875\) | 2.58973e7 | 1.14349 | ||||||||
\(876\) | 2.38203e7 | 1.04878 | ||||||||
\(877\) | 8.81107e6 | 0.386838 | 0.193419 | − | 0.981116i | \(-0.438042\pi\) | ||||
0.193419 | + | 0.981116i | \(0.438042\pi\) | |||||||
\(878\) | 4.00654e7 | 1.75401 | ||||||||
\(879\) | −1.20379e7 | −0.525508 | ||||||||
\(880\) | −1.38868e7 | −0.604501 | ||||||||
\(881\) | 4.01078e7 | 1.74096 | 0.870481 | − | 0.492202i | \(-0.163808\pi\) | ||||
0.870481 | + | 0.492202i | \(0.163808\pi\) | |||||||
\(882\) | 1.94481e6 | 0.0841794 | ||||||||
\(883\) | 1.49664e7 | 0.645976 | 0.322988 | − | 0.946403i | \(-0.395313\pi\) | ||||
0.322988 | + | 0.946403i | \(0.395313\pi\) | |||||||
\(884\) | −1.01143e7 | −0.435317 | ||||||||
\(885\) | −3.11958e7 | −1.33887 | ||||||||
\(886\) | −5.44751e7 | −2.33138 | ||||||||
\(887\) | −575144. | −0.0245453 | −0.0122726 | − | 0.999925i | \(-0.503907\pi\) | ||||
−0.0122726 | + | 0.999925i | \(0.503907\pi\) | |||||||
\(888\) | 1.35497e7 | 0.576629 | ||||||||
\(889\) | −3.27634e6 | −0.139038 | ||||||||
\(890\) | −1.18527e8 | −5.01583 | ||||||||
\(891\) | 603612. | 0.0254720 | ||||||||
\(892\) | −1.48501e7 | −0.624910 | ||||||||
\(893\) | 6.40685e6 | 0.268854 | ||||||||
\(894\) | 3.67249e7 | 1.53680 | ||||||||
\(895\) | −2.11462e7 | −0.882417 | ||||||||
\(896\) | 1.32653e7 | 0.552009 | ||||||||
\(897\) | −7.09128e6 | −0.294268 | ||||||||
\(898\) | −1.81577e7 | −0.751400 | ||||||||
\(899\) | 4.13213e6 | 0.170520 | ||||||||
\(900\) | 4.46754e7 | 1.83849 | ||||||||
\(901\) | 8.34232e6 | 0.342353 | ||||||||
\(902\) | −6.12904e6 | −0.250828 | ||||||||
\(903\) | 1.63170e6 | 0.0665918 | ||||||||
\(904\) | 6.44616e6 | 0.262349 | ||||||||
\(905\) | −2.54983e7 | −1.03488 | ||||||||
\(906\) | 3.26254e7 | 1.32049 | ||||||||
\(907\) | −3.33367e7 | −1.34557 | −0.672783 | − | 0.739840i | \(-0.734901\pi\) | ||||
−0.672783 | + | 0.739840i | \(0.734901\pi\) | |||||||
\(908\) | 3.96339e7 | 1.59534 | ||||||||
\(909\) | −1.11257e7 | −0.446598 | ||||||||
\(910\) | 3.47998e7 | 1.39307 | ||||||||
\(911\) | 2.17451e7 | 0.868090 | 0.434045 | − | 0.900891i | \(-0.357086\pi\) | ||||
0.434045 | + | 0.900891i | \(0.357086\pi\) | |||||||
\(912\) | −1.16369e7 | −0.463288 | ||||||||
\(913\) | 6.61406e6 | 0.262598 | ||||||||
\(914\) | −5.30082e7 | −2.09883 | ||||||||
\(915\) | 1.03051e7 | 0.406911 | ||||||||
\(916\) | 6.53511e7 | 2.57344 | ||||||||
\(917\) | −7.53444e6 | −0.295888 | ||||||||
\(918\) | −1.61838e6 | −0.0633831 | ||||||||
\(919\) | −4.03986e6 | −0.157789 | −0.0788947 | − | 0.996883i | \(-0.525139\pi\) | ||||
−0.0788947 | + | 0.996883i | \(0.525139\pi\) | |||||||
\(920\) | 4.48762e7 | 1.74802 | ||||||||
\(921\) | −1.19538e7 | −0.464364 | ||||||||
\(922\) | 3.20381e7 | 1.24119 | ||||||||
\(923\) | −4.10844e7 | −1.58735 | ||||||||
\(924\) | −2.75890e6 | −0.106305 | ||||||||
\(925\) | 3.39202e7 | 1.30348 | ||||||||
\(926\) | −1.11853e7 | −0.428666 | ||||||||
\(927\) | 2.32956e6 | 0.0890378 | ||||||||
\(928\) | 3.04096e6 | 0.115915 | ||||||||
\(929\) | 7.69679e6 | 0.292597 | 0.146299 | − | 0.989240i | \(-0.453264\pi\) | ||||
0.146299 | + | 0.989240i | \(0.453264\pi\) | |||||||
\(930\) | −3.52598e7 | −1.33682 | ||||||||
\(931\) | −2.18011e6 | −0.0824335 | ||||||||
\(932\) | 4.12076e7 | 1.55395 | ||||||||
\(933\) | −5.99249e6 | −0.225374 | ||||||||
\(934\) | −3.85134e7 | −1.44459 | ||||||||
\(935\) | 2.16494e6 | 0.0809874 | ||||||||
\(936\) | 1.95372e7 | 0.728908 | ||||||||
\(937\) | −453558. | −0.0168766 | −0.00843828 | − | 0.999964i | \(-0.502686\pi\) | ||||
−0.00843828 | + | 0.999964i | \(0.502686\pi\) | |||||||
\(938\) | −3.18480e7 | −1.18189 | ||||||||
\(939\) | −2.78119e7 | −1.02936 | ||||||||
\(940\) | 5.08596e7 | 1.87739 | ||||||||
\(941\) | −2.43852e7 | −0.897745 | −0.448873 | − | 0.893596i | \(-0.648174\pi\) | ||||
−0.448873 | + | 0.893596i | \(0.648174\pi\) | |||||||
\(942\) | −1.37507e7 | −0.504892 | ||||||||
\(943\) | 7.83451e6 | 0.286901 | ||||||||
\(944\) | 4.65648e7 | 1.70070 | ||||||||
\(945\) | 3.78643e6 | 0.137927 | ||||||||
\(946\) | −3.40400e6 | −0.123669 | ||||||||
\(947\) | −2.18745e7 | −0.792615 | −0.396308 | − | 0.918118i | \(-0.629709\pi\) | ||||
−0.396308 | + | 0.918118i | \(0.629709\pi\) | |||||||
\(948\) | −5.39148e7 | −1.94844 | ||||||||
\(949\) | 2.60777e7 | 0.939949 | ||||||||
\(950\) | −7.36479e7 | −2.64759 | ||||||||
\(951\) | −8.76760e6 | −0.314362 | ||||||||
\(952\) | 3.91608e6 | 0.140042 | ||||||||
\(953\) | −3.93319e7 | −1.40286 | −0.701428 | − | 0.712741i | \(-0.747454\pi\) | ||||
−0.701428 | + | 0.712741i | \(0.747454\pi\) | |||||||
\(954\) | −3.04382e7 | −1.08280 | ||||||||
\(955\) | −3.07807e7 | −1.09212 | ||||||||
\(956\) | 7.95698e7 | 2.81581 | ||||||||
\(957\) | 925704. | 0.0326732 | ||||||||
\(958\) | 1.43536e7 | 0.505297 | ||||||||
\(959\) | −1.25429e7 | −0.440405 | ||||||||
\(960\) | 1.75231e7 | 0.613666 | ||||||||
\(961\) | −1.49687e7 | −0.522849 | ||||||||
\(962\) | 2.80194e7 | 0.976160 | ||||||||
\(963\) | 1.82704e6 | 0.0634865 | ||||||||
\(964\) | −8.41099e7 | −2.91511 | ||||||||
\(965\) | 1.81741e7 | 0.628254 | ||||||||
\(966\) | 5.18616e6 | 0.178815 | ||||||||
\(967\) | 3.85234e7 | 1.32483 | 0.662413 | − | 0.749139i | \(-0.269532\pi\) | ||||
0.662413 | + | 0.749139i | \(0.269532\pi\) | |||||||
\(968\) | −5.49313e7 | −1.88422 | ||||||||
\(969\) | 1.81418e6 | 0.0620686 | ||||||||
\(970\) | 1.59897e8 | 5.45645 | ||||||||
\(971\) | 2.43543e7 | 0.828947 | 0.414473 | − | 0.910061i | \(-0.363966\pi\) | ||||
0.414473 | + | 0.910061i | \(0.363966\pi\) | |||||||
\(972\) | 4.01533e6 | 0.136319 | ||||||||
\(973\) | −1.38633e7 | −0.469444 | ||||||||
\(974\) | 4.61097e7 | 1.55738 | ||||||||
\(975\) | 4.89093e7 | 1.64771 | ||||||||
\(976\) | −1.53820e7 | −0.516880 | ||||||||
\(977\) | 1.62534e7 | 0.544763 | 0.272382 | − | 0.962189i | \(-0.412189\pi\) | ||||
0.272382 | + | 0.962189i | \(0.412189\pi\) | |||||||
\(978\) | −1.35385e7 | −0.452610 | ||||||||
\(979\) | 1.02873e7 | 0.343038 | ||||||||
\(980\) | −1.73064e7 | −0.575628 | ||||||||
\(981\) | 1.61984e6 | 0.0537402 | ||||||||
\(982\) | 7.40518e7 | 2.45051 | ||||||||
\(983\) | −252456. | −0.00833301 | −0.00416650 | − | 0.999991i | \(-0.501326\pi\) | ||||
−0.00416650 | + | 0.999991i | \(0.501326\pi\) | |||||||
\(984\) | −2.15849e7 | −0.710660 | ||||||||
\(985\) | −4.26109e7 | −1.39936 | ||||||||
\(986\) | −2.48196e6 | −0.0813022 | ||||||||
\(987\) | 3.11170e6 | 0.101673 | ||||||||
\(988\) | −4.13685e7 | −1.34827 | ||||||||
\(989\) | 4.35120e6 | 0.141455 | ||||||||
\(990\) | −7.89912e6 | −0.256148 | ||||||||
\(991\) | −2.49728e7 | −0.807761 | −0.403880 | − | 0.914812i | \(-0.632339\pi\) | ||||
−0.403880 | + | 0.914812i | \(0.632339\pi\) | |||||||
\(992\) | 1.00531e7 | 0.324356 | ||||||||
\(993\) | 7.03595e6 | 0.226438 | ||||||||
\(994\) | 3.00468e7 | 0.964567 | ||||||||
\(995\) | 2.74727e7 | 0.879717 | ||||||||
\(996\) | 4.39979e7 | 1.40535 | ||||||||
\(997\) | −3.60983e7 | −1.15013 | −0.575067 | − | 0.818106i | \(-0.695024\pi\) | ||||
−0.575067 | + | 0.818106i | \(0.695024\pi\) | |||||||
\(998\) | 3.93432e7 | 1.25039 | ||||||||
\(999\) | 3.04868e6 | 0.0966491 |
(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 | 21.6.a.d.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 63.6.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 336.6.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 525.6.d.a.274.2 | 2 | |||
5.3 | odd | 4 | 525.6.d.a.274.1 | 2 | |||
5.4 | even | 2 | 525.6.a.a.1.1 | 1 | |||
7.2 | even | 3 | 147.6.e.a.67.1 | 2 | |||
7.3 | odd | 6 | 147.6.e.b.79.1 | 2 | |||
7.4 | even | 3 | 147.6.e.a.79.1 | 2 | |||
7.5 | odd | 6 | 147.6.e.b.67.1 | 2 | |||
7.6 | odd | 2 | 147.6.a.g.1.1 | 1 | |||
12.11 | even | 2 | 1008.6.a.bc.1.1 | 1 | |||
21.20 | even | 2 | 441.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.d.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
63.6.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
147.6.a.g.1.1 | 1 | 7.6 | odd | 2 | |||
147.6.e.a.67.1 | 2 | 7.2 | even | 3 | |||
147.6.e.a.79.1 | 2 | 7.4 | even | 3 | |||
147.6.e.b.67.1 | 2 | 7.5 | odd | 6 | |||
147.6.e.b.79.1 | 2 | 7.3 | odd | 6 | |||
336.6.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
441.6.a.b.1.1 | 1 | 21.20 | even | 2 | |||
525.6.a.a.1.1 | 1 | 5.4 | even | 2 | |||
525.6.d.a.274.1 | 2 | 5.3 | odd | 4 | |||
525.6.d.a.274.2 | 2 | 5.2 | odd | 4 | |||
1008.6.a.bc.1.1 | 1 | 12.11 | even | 2 |