Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.7623 | −1.90253 | −0.951264 | − | 0.308376i | \(-0.900214\pi\) | ||||
−0.951264 | + | 0.308376i | \(0.900214\pi\) | |||||||
\(3\) | −11.3539 | −0.728351 | −0.364176 | − | 0.931330i | \(-0.618649\pi\) | ||||
−0.364176 | + | 0.931330i | \(0.618649\pi\) | |||||||
\(4\) | 83.8277 | 2.61962 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 122.194 | 1.38571 | ||||||||
\(7\) | −59.3342 | −0.457678 | −0.228839 | − | 0.973464i | \(-0.573493\pi\) | ||||
−0.228839 | + | 0.973464i | \(0.573493\pi\) | |||||||
\(8\) | −557.787 | −3.08137 | ||||||||
\(9\) | −114.090 | −0.469505 | ||||||||
\(10\) | −269.058 | −0.850837 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −951.769 | −1.90800 | ||||||||
\(13\) | 781.069 | 1.28183 | 0.640916 | − | 0.767611i | \(-0.278555\pi\) | ||||
0.640916 | + | 0.767611i | \(0.278555\pi\) | |||||||
\(14\) | 638.574 | 0.870745 | ||||||||
\(15\) | −283.847 | −0.325729 | ||||||||
\(16\) | 3320.60 | 3.24277 | ||||||||
\(17\) | 774.166 | 0.649699 | 0.324849 | − | 0.945766i | \(-0.394686\pi\) | ||||
0.324849 | + | 0.945766i | \(0.394686\pi\) | |||||||
\(18\) | 1227.87 | 0.893246 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | 2095.69 | 1.17153 | ||||||||
\(21\) | 673.673 | 0.333350 | ||||||||
\(22\) | −1302.24 | −0.573634 | ||||||||
\(23\) | 2900.65 | 1.14334 | 0.571671 | − | 0.820483i | \(-0.306295\pi\) | ||||
0.571671 | + | 0.820483i | \(0.306295\pi\) | |||||||
\(24\) | 6333.04 | 2.24432 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −8406.12 | −2.43872 | ||||||||
\(27\) | 4054.35 | 1.07032 | ||||||||
\(28\) | −4973.85 | −1.19894 | ||||||||
\(29\) | −2591.30 | −0.572167 | −0.286083 | − | 0.958205i | \(-0.592353\pi\) | ||||
−0.286083 | + | 0.958205i | \(0.592353\pi\) | |||||||
\(30\) | 3054.85 | 0.619708 | ||||||||
\(31\) | 2389.59 | 0.446600 | 0.223300 | − | 0.974750i | \(-0.428317\pi\) | ||||
0.223300 | + | 0.974750i | \(0.428317\pi\) | |||||||
\(32\) | −17888.2 | −3.08810 | ||||||||
\(33\) | −1373.82 | −0.219606 | ||||||||
\(34\) | −8331.83 | −1.23607 | ||||||||
\(35\) | −1483.35 | −0.204680 | ||||||||
\(36\) | −9563.87 | −1.22992 | ||||||||
\(37\) | 1235.84 | 0.148408 | 0.0742039 | − | 0.997243i | \(-0.476358\pi\) | ||||
0.0742039 | + | 0.997243i | \(0.476358\pi\) | |||||||
\(38\) | −3885.20 | −0.436470 | ||||||||
\(39\) | −8868.16 | −0.933624 | ||||||||
\(40\) | −13944.7 | −1.37803 | ||||||||
\(41\) | 8939.92 | 0.830566 | 0.415283 | − | 0.909692i | \(-0.363683\pi\) | ||||
0.415283 | + | 0.909692i | \(0.363683\pi\) | |||||||
\(42\) | −7250.29 | −0.634208 | ||||||||
\(43\) | −2987.40 | −0.246389 | −0.123195 | − | 0.992383i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992383i | \(0.539314\pi\) | |||||||
\(44\) | 10143.2 | 0.789844 | ||||||||
\(45\) | −2852.24 | −0.209969 | ||||||||
\(46\) | −31217.8 | −2.17524 | ||||||||
\(47\) | 23106.3 | 1.52576 | 0.762879 | − | 0.646542i | \(-0.223785\pi\) | ||||
0.762879 | + | 0.646542i | \(0.223785\pi\) | |||||||
\(48\) | −37701.7 | −2.36188 | ||||||||
\(49\) | −13286.5 | −0.790531 | ||||||||
\(50\) | −6726.46 | −0.380506 | ||||||||
\(51\) | −8789.79 | −0.473209 | ||||||||
\(52\) | 65475.2 | 3.35791 | ||||||||
\(53\) | 17689.3 | 0.865008 | 0.432504 | − | 0.901632i | \(-0.357630\pi\) | ||||
0.432504 | + | 0.901632i | \(0.357630\pi\) | |||||||
\(54\) | −43634.2 | −2.03631 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | 33095.8 | 1.41027 | ||||||||
\(57\) | −4098.75 | −0.167095 | ||||||||
\(58\) | 27888.4 | 1.08856 | ||||||||
\(59\) | −15720.2 | −0.587934 | −0.293967 | − | 0.955816i | \(-0.594976\pi\) | ||||
−0.293967 | + | 0.955816i | \(0.594976\pi\) | |||||||
\(60\) | −23794.2 | −0.853284 | ||||||||
\(61\) | 46680.1 | 1.60623 | 0.803115 | − | 0.595824i | \(-0.203175\pi\) | ||||
0.803115 | + | 0.595824i | \(0.203175\pi\) | |||||||
\(62\) | −25717.5 | −0.849670 | ||||||||
\(63\) | 6769.41 | 0.214882 | ||||||||
\(64\) | 86259.6 | 2.63243 | ||||||||
\(65\) | 19526.7 | 0.573253 | ||||||||
\(66\) | 14785.5 | 0.417807 | ||||||||
\(67\) | −24948.4 | −0.678978 | −0.339489 | − | 0.940610i | \(-0.610254\pi\) | ||||
−0.339489 | + | 0.940610i | \(0.610254\pi\) | |||||||
\(68\) | 64896.6 | 1.70196 | ||||||||
\(69\) | −32933.6 | −0.832754 | ||||||||
\(70\) | 15964.4 | 0.389409 | ||||||||
\(71\) | 6610.43 | 0.155627 | 0.0778133 | − | 0.996968i | \(-0.475206\pi\) | ||||
0.0778133 | + | 0.996968i | \(0.475206\pi\) | |||||||
\(72\) | 63637.7 | 1.44672 | ||||||||
\(73\) | 66614.6 | 1.46306 | 0.731530 | − | 0.681809i | \(-0.238806\pi\) | ||||
0.731530 | + | 0.681809i | \(0.238806\pi\) | |||||||
\(74\) | −13300.5 | −0.282350 | ||||||||
\(75\) | −7096.17 | −0.145670 | ||||||||
\(76\) | 30261.8 | 0.600981 | ||||||||
\(77\) | −7179.44 | −0.137995 | ||||||||
\(78\) | 95442.0 | 1.77625 | ||||||||
\(79\) | 54873.9 | 0.989232 | 0.494616 | − | 0.869112i | \(-0.335309\pi\) | ||||
0.494616 | + | 0.869112i | \(0.335309\pi\) | |||||||
\(80\) | 83015.0 | 1.45021 | ||||||||
\(81\) | −18308.8 | −0.310061 | ||||||||
\(82\) | −96214.4 | −1.58018 | ||||||||
\(83\) | 52528.5 | 0.836950 | 0.418475 | − | 0.908228i | \(-0.362565\pi\) | ||||
0.418475 | + | 0.908228i | \(0.362565\pi\) | |||||||
\(84\) | 56472.5 | 0.873250 | ||||||||
\(85\) | 19354.2 | 0.290554 | ||||||||
\(86\) | 32151.4 | 0.468763 | ||||||||
\(87\) | 29421.3 | 0.416738 | ||||||||
\(88\) | −67492.2 | −0.929067 | ||||||||
\(89\) | −27702.4 | −0.370716 | −0.185358 | − | 0.982671i | \(-0.559345\pi\) | ||||
−0.185358 | + | 0.982671i | \(0.559345\pi\) | |||||||
\(90\) | 30696.7 | 0.399472 | ||||||||
\(91\) | −46344.1 | −0.586666 | ||||||||
\(92\) | 243155. | 2.99512 | ||||||||
\(93\) | −27131.1 | −0.325282 | ||||||||
\(94\) | −248677. | −2.90280 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 203100. | 2.24922 | ||||||||
\(97\) | 19556.4 | 0.211038 | 0.105519 | − | 0.994417i | \(-0.466350\pi\) | ||||
0.105519 | + | 0.994417i | \(0.466350\pi\) | |||||||
\(98\) | 142993. | 1.50401 | ||||||||
\(99\) | −13804.8 | −0.141561 | ||||||||
\(100\) | 52392.3 | 0.523923 | ||||||||
\(101\) | −77117.1 | −0.752224 | −0.376112 | − | 0.926574i | \(-0.622739\pi\) | ||||
−0.376112 | + | 0.926574i | \(0.622739\pi\) | |||||||
\(102\) | 94598.6 | 0.900294 | ||||||||
\(103\) | −26847.9 | −0.249354 | −0.124677 | − | 0.992197i | \(-0.539790\pi\) | ||||
−0.124677 | + | 0.992197i | \(0.539790\pi\) | |||||||
\(104\) | −435670. | −3.94979 | ||||||||
\(105\) | 16841.8 | 0.149079 | ||||||||
\(106\) | −190378. | −1.64570 | ||||||||
\(107\) | 224022. | 1.89161 | 0.945806 | − | 0.324731i | \(-0.105274\pi\) | ||||
0.945806 | + | 0.324731i | \(0.105274\pi\) | |||||||
\(108\) | 339867. | 2.80382 | ||||||||
\(109\) | −41787.6 | −0.336884 | −0.168442 | − | 0.985712i | \(-0.553874\pi\) | ||||
−0.168442 | + | 0.985712i | \(0.553874\pi\) | |||||||
\(110\) | −32556.0 | −0.256537 | ||||||||
\(111\) | −14031.5 | −0.108093 | ||||||||
\(112\) | −197025. | −1.48415 | ||||||||
\(113\) | −35286.6 | −0.259964 | −0.129982 | − | 0.991516i | \(-0.541492\pi\) | ||||
−0.129982 | + | 0.991516i | \(0.541492\pi\) | |||||||
\(114\) | 44112.1 | 0.317904 | ||||||||
\(115\) | 72516.3 | 0.511318 | ||||||||
\(116\) | −217223. | −1.49886 | ||||||||
\(117\) | −89111.8 | −0.601826 | ||||||||
\(118\) | 169186. | 1.11856 | ||||||||
\(119\) | −45934.5 | −0.297353 | ||||||||
\(120\) | 158326. | 1.00369 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −502387. | −3.05590 | ||||||||
\(123\) | −101503. | −0.604944 | ||||||||
\(124\) | 200314. | 1.16992 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −72854.7 | −0.408819 | ||||||||
\(127\) | −177287. | −0.975367 | −0.487683 | − | 0.873021i | \(-0.662158\pi\) | ||||
−0.487683 | + | 0.873021i | \(0.662158\pi\) | |||||||
\(128\) | −355931. | −1.92018 | ||||||||
\(129\) | 33918.5 | 0.179458 | ||||||||
\(130\) | −210153. | −1.09063 | ||||||||
\(131\) | 103759. | 0.528260 | 0.264130 | − | 0.964487i | \(-0.414915\pi\) | ||||
0.264130 | + | 0.964487i | \(0.414915\pi\) | |||||||
\(132\) | −115164. | −0.575284 | ||||||||
\(133\) | −21419.6 | −0.104998 | ||||||||
\(134\) | 268503. | 1.29177 | ||||||||
\(135\) | 101359. | 0.478660 | ||||||||
\(136\) | −431820. | −2.00196 | ||||||||
\(137\) | −116243. | −0.529132 | −0.264566 | − | 0.964368i | \(-0.585229\pi\) | ||||
−0.264566 | + | 0.964368i | \(0.585229\pi\) | |||||||
\(138\) | 354443. | 1.58434 | ||||||||
\(139\) | −250320. | −1.09890 | −0.549451 | − | 0.835526i | \(-0.685163\pi\) | ||||
−0.549451 | + | 0.835526i | \(0.685163\pi\) | |||||||
\(140\) | −124346. | −0.536182 | ||||||||
\(141\) | −262346. | −1.11129 | ||||||||
\(142\) | −71143.6 | −0.296084 | ||||||||
\(143\) | 94509.3 | 0.386487 | ||||||||
\(144\) | −378846. | −1.52250 | ||||||||
\(145\) | −64782.5 | −0.255881 | ||||||||
\(146\) | −716928. | −2.78352 | ||||||||
\(147\) | 150853. | 0.575784 | ||||||||
\(148\) | 103597. | 0.388772 | ||||||||
\(149\) | −7538.50 | −0.0278176 | −0.0139088 | − | 0.999903i | \(-0.504427\pi\) | ||||
−0.0139088 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(150\) | 76371.3 | 0.277142 | ||||||||
\(151\) | −439881. | −1.56998 | −0.784988 | − | 0.619511i | \(-0.787331\pi\) | ||||
−0.784988 | + | 0.619511i | \(0.787331\pi\) | |||||||
\(152\) | −201361. | −0.706914 | ||||||||
\(153\) | −88324.3 | −0.305036 | ||||||||
\(154\) | 77267.5 | 0.262540 | ||||||||
\(155\) | 59739.7 | 0.199726 | ||||||||
\(156\) | −743397. | −2.44574 | ||||||||
\(157\) | 313502. | 1.01506 | 0.507529 | − | 0.861635i | \(-0.330559\pi\) | ||||
0.507529 | + | 0.861635i | \(0.330559\pi\) | |||||||
\(158\) | −590571. | −1.88204 | ||||||||
\(159\) | −200842. | −0.630030 | ||||||||
\(160\) | −447205. | −1.38104 | ||||||||
\(161\) | −172108. | −0.523282 | ||||||||
\(162\) | 197045. | 0.589900 | ||||||||
\(163\) | −134307. | −0.395941 | −0.197970 | − | 0.980208i | \(-0.563435\pi\) | ||||
−0.197970 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(164\) | 749413. | 2.17576 | ||||||||
\(165\) | −34345.5 | −0.0982109 | ||||||||
\(166\) | −565329. | −1.59232 | ||||||||
\(167\) | −235267. | −0.652785 | −0.326393 | − | 0.945234i | \(-0.605833\pi\) | ||||
−0.326393 | + | 0.945234i | \(0.605833\pi\) | |||||||
\(168\) | −375766. | −1.02717 | ||||||||
\(169\) | 238776. | 0.643093 | ||||||||
\(170\) | −208296. | −0.552788 | ||||||||
\(171\) | −41186.3 | −0.107712 | ||||||||
\(172\) | −250427. | −0.645446 | ||||||||
\(173\) | −267094. | −0.678499 | −0.339250 | − | 0.940696i | \(-0.610173\pi\) | ||||
−0.339250 | + | 0.940696i | \(0.610173\pi\) | |||||||
\(174\) | −316641. | −0.792857 | ||||||||
\(175\) | −37083.9 | −0.0915356 | ||||||||
\(176\) | 401793. | 0.977733 | ||||||||
\(177\) | 178485. | 0.428223 | ||||||||
\(178\) | 298142. | 0.705299 | ||||||||
\(179\) | −166988. | −0.389540 | −0.194770 | − | 0.980849i | \(-0.562396\pi\) | ||||
−0.194770 | + | 0.980849i | \(0.562396\pi\) | |||||||
\(180\) | −239097. | −0.550038 | ||||||||
\(181\) | −113407. | −0.257302 | −0.128651 | − | 0.991690i | \(-0.541065\pi\) | ||||
−0.128651 | + | 0.991690i | \(0.541065\pi\) | |||||||
\(182\) | 498770. | 1.11615 | ||||||||
\(183\) | −530000. | −1.16990 | ||||||||
\(184\) | −1.61795e6 | −3.52306 | ||||||||
\(185\) | 30895.9 | 0.0663700 | ||||||||
\(186\) | 291994. | 0.618858 | ||||||||
\(187\) | 93674.1 | 0.195892 | ||||||||
\(188\) | 1.93695e6 | 3.99690 | ||||||||
\(189\) | −240562. | −0.489860 | ||||||||
\(190\) | −97130.0 | −0.195195 | ||||||||
\(191\) | 915845. | 1.81651 | 0.908257 | − | 0.418414i | \(-0.137414\pi\) | ||||
0.908257 | + | 0.418414i | \(0.137414\pi\) | |||||||
\(192\) | −979381. | −1.91734 | ||||||||
\(193\) | −284642. | −0.550055 | −0.275027 | − | 0.961436i | \(-0.588687\pi\) | ||||
−0.275027 | + | 0.961436i | \(0.588687\pi\) | |||||||
\(194\) | −210473. | −0.401506 | ||||||||
\(195\) | −221704. | −0.417529 | ||||||||
\(196\) | −1.11377e6 | −2.07089 | ||||||||
\(197\) | 1.06139e6 | 1.94854 | 0.974269 | − | 0.225387i | \(-0.0723648\pi\) | ||||
0.974269 | + | 0.225387i | \(0.0723648\pi\) | |||||||
\(198\) | 148572. | 0.269324 | ||||||||
\(199\) | −316683. | −0.566881 | −0.283441 | − | 0.958990i | \(-0.591476\pi\) | ||||
−0.283441 | + | 0.958990i | \(0.591476\pi\) | |||||||
\(200\) | −348617. | −0.616273 | ||||||||
\(201\) | 283261. | 0.494534 | ||||||||
\(202\) | 829960. | 1.43113 | ||||||||
\(203\) | 153753. | 0.261868 | ||||||||
\(204\) | −736828. | −1.23963 | ||||||||
\(205\) | 223498. | 0.371440 | ||||||||
\(206\) | 288946. | 0.474404 | ||||||||
\(207\) | −330934. | −0.536804 | ||||||||
\(208\) | 2.59362e6 | 4.15669 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | −181257. | −0.283627 | ||||||||
\(211\) | −779443. | −1.20525 | −0.602626 | − | 0.798024i | \(-0.705879\pi\) | ||||
−0.602626 | + | 0.798024i | \(0.705879\pi\) | |||||||
\(212\) | 1.48285e6 | 2.26599 | ||||||||
\(213\) | −75054.0 | −0.113351 | ||||||||
\(214\) | −2.41100e6 | −3.59885 | ||||||||
\(215\) | −74684.9 | −0.110189 | ||||||||
\(216\) | −2.26146e6 | −3.29803 | ||||||||
\(217\) | −141784. | −0.204399 | ||||||||
\(218\) | 449731. | 0.640932 | ||||||||
\(219\) | −756334. | −1.06562 | ||||||||
\(220\) | 253579. | 0.353229 | ||||||||
\(221\) | 604677. | 0.832804 | ||||||||
\(222\) | 151012. | 0.205650 | ||||||||
\(223\) | −217590. | −0.293006 | −0.146503 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146503 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(224\) | 1.06138e6 | 1.41336 | ||||||||
\(225\) | −71306.0 | −0.0939009 | ||||||||
\(226\) | 379766. | 0.494590 | ||||||||
\(227\) | 1.11249e6 | 1.43295 | 0.716476 | − | 0.697611i | \(-0.245754\pi\) | ||||
0.716476 | + | 0.697611i | \(0.245754\pi\) | |||||||
\(228\) | −343589. | −0.437725 | ||||||||
\(229\) | −333227. | −0.419906 | −0.209953 | − | 0.977712i | \(-0.567331\pi\) | ||||
−0.209953 | + | 0.977712i | \(0.567331\pi\) | |||||||
\(230\) | −780444. | −0.972797 | ||||||||
\(231\) | 81514.4 | 0.100509 | ||||||||
\(232\) | 1.44539e6 | 1.76306 | ||||||||
\(233\) | −808064. | −0.975115 | −0.487558 | − | 0.873091i | \(-0.662112\pi\) | ||||
−0.487558 | + | 0.873091i | \(0.662112\pi\) | |||||||
\(234\) | 959051. | 1.14499 | ||||||||
\(235\) | 577657. | 0.682340 | ||||||||
\(236\) | −1.31779e6 | −1.54016 | ||||||||
\(237\) | −623031. | −0.720508 | ||||||||
\(238\) | 494363. | 0.565722 | ||||||||
\(239\) | −395232. | −0.447567 | −0.223783 | − | 0.974639i | \(-0.571841\pi\) | ||||
−0.223783 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(240\) | −942542. | −1.05626 | ||||||||
\(241\) | 899860. | 0.998004 | 0.499002 | − | 0.866601i | \(-0.333700\pi\) | ||||
0.499002 | + | 0.866601i | \(0.333700\pi\) | |||||||
\(242\) | −157571. | −0.172957 | ||||||||
\(243\) | −777331. | −0.844482 | ||||||||
\(244\) | 3.91309e6 | 4.20771 | ||||||||
\(245\) | −332161. | −0.353536 | ||||||||
\(246\) | 1.09241e6 | 1.15092 | ||||||||
\(247\) | 281966. | 0.294072 | ||||||||
\(248\) | −1.33288e6 | −1.37614 | ||||||||
\(249\) | −596402. | −0.609594 | ||||||||
\(250\) | −168161. | −0.170167 | ||||||||
\(251\) | −185739. | −0.186088 | −0.0930442 | − | 0.995662i | \(-0.529660\pi\) | ||||
−0.0930442 | + | 0.995662i | \(0.529660\pi\) | |||||||
\(252\) | 567465. | 0.562908 | ||||||||
\(253\) | 350979. | 0.344730 | ||||||||
\(254\) | 1.90802e6 | 1.85566 | ||||||||
\(255\) | −219745. | −0.211625 | ||||||||
\(256\) | 1.07034e6 | 1.02076 | ||||||||
\(257\) | −98722.1 | −0.0932356 | −0.0466178 | − | 0.998913i | \(-0.514844\pi\) | ||||
−0.0466178 | + | 0.998913i | \(0.514844\pi\) | |||||||
\(258\) | −365042. | −0.341424 | ||||||||
\(259\) | −73327.4 | −0.0679230 | ||||||||
\(260\) | 1.63688e6 | 1.50170 | ||||||||
\(261\) | 295640. | 0.268635 | ||||||||
\(262\) | −1.11669e6 | −1.00503 | ||||||||
\(263\) | 43322.8 | 0.0386213 | 0.0193107 | − | 0.999814i | \(-0.493853\pi\) | ||||
0.0193107 | + | 0.999814i | \(0.493853\pi\) | |||||||
\(264\) | 766298. | 0.676687 | ||||||||
\(265\) | 442232. | 0.386843 | ||||||||
\(266\) | 230525. | 0.199763 | ||||||||
\(267\) | 314529. | 0.270012 | ||||||||
\(268\) | −2.09137e6 | −1.77866 | ||||||||
\(269\) | 890980. | 0.750736 | 0.375368 | − | 0.926876i | \(-0.377516\pi\) | ||||
0.375368 | + | 0.926876i | \(0.377516\pi\) | |||||||
\(270\) | −1.09086e6 | −0.910664 | ||||||||
\(271\) | 960136. | 0.794163 | 0.397081 | − | 0.917783i | \(-0.370023\pi\) | ||||
0.397081 | + | 0.917783i | \(0.370023\pi\) | |||||||
\(272\) | 2.57070e6 | 2.10683 | ||||||||
\(273\) | 526185. | 0.427299 | ||||||||
\(274\) | 1.25104e6 | 1.00669 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | −2.76075e6 | −2.18150 | ||||||||
\(277\) | 931543. | 0.729463 | 0.364732 | − | 0.931113i | \(-0.381161\pi\) | ||||
0.364732 | + | 0.931113i | \(0.381161\pi\) | |||||||
\(278\) | 2.69403e6 | 2.09069 | ||||||||
\(279\) | −272627. | −0.209681 | ||||||||
\(280\) | 827396. | 0.630694 | ||||||||
\(281\) | −2.41833e6 | −1.82705 | −0.913524 | − | 0.406785i | \(-0.866650\pi\) | ||||
−0.913524 | + | 0.406785i | \(0.866650\pi\) | |||||||
\(282\) | 2.82345e6 | 2.11426 | ||||||||
\(283\) | 373999. | 0.277590 | 0.138795 | − | 0.990321i | \(-0.455677\pi\) | ||||
0.138795 | + | 0.990321i | \(0.455677\pi\) | |||||||
\(284\) | 554137. | 0.407682 | ||||||||
\(285\) | −102469. | −0.0747273 | ||||||||
\(286\) | −1.01714e6 | −0.735302 | ||||||||
\(287\) | −530443. | −0.380132 | ||||||||
\(288\) | 2.04086e6 | 1.44988 | ||||||||
\(289\) | −820523. | −0.577892 | ||||||||
\(290\) | 697210. | 0.486820 | ||||||||
\(291\) | −222041. | −0.153710 | ||||||||
\(292\) | 5.58415e6 | 3.83266 | ||||||||
\(293\) | −1.04044e6 | −0.708027 | −0.354013 | − | 0.935240i | \(-0.615183\pi\) | ||||
−0.354013 | + | 0.935240i | \(0.615183\pi\) | |||||||
\(294\) | −1.62353e6 | −1.09545 | ||||||||
\(295\) | −393006. | −0.262932 | ||||||||
\(296\) | −689334. | −0.457299 | ||||||||
\(297\) | 490576. | 0.322712 | ||||||||
\(298\) | 81131.9 | 0.0529238 | ||||||||
\(299\) | 2.26561e6 | 1.46557 | ||||||||
\(300\) | −594856. | −0.381600 | ||||||||
\(301\) | 177255. | 0.112767 | ||||||||
\(302\) | 4.73415e6 | 2.98693 | ||||||||
\(303\) | 875578. | 0.547883 | ||||||||
\(304\) | 1.19874e6 | 0.743943 | ||||||||
\(305\) | 1.16700e6 | 0.718328 | ||||||||
\(306\) | 950576. | 0.580341 | ||||||||
\(307\) | −1.38126e6 | −0.836430 | −0.418215 | − | 0.908348i | \(-0.637344\pi\) | ||||
−0.418215 | + | 0.908348i | \(0.637344\pi\) | |||||||
\(308\) | −601836. | −0.361494 | ||||||||
\(309\) | 304827. | 0.181618 | ||||||||
\(310\) | −642938. | −0.379984 | ||||||||
\(311\) | −1.83175e6 | −1.07390 | −0.536952 | − | 0.843613i | \(-0.680424\pi\) | ||||
−0.536952 | + | 0.843613i | \(0.680424\pi\) | |||||||
\(312\) | 4.94654e6 | 2.87684 | ||||||||
\(313\) | −1.95172e6 | −1.12605 | −0.563024 | − | 0.826440i | \(-0.690362\pi\) | ||||
−0.563024 | + | 0.826440i | \(0.690362\pi\) | |||||||
\(314\) | −3.37401e6 | −1.93118 | ||||||||
\(315\) | 169235. | 0.0960981 | ||||||||
\(316\) | 4.59996e6 | 2.59141 | ||||||||
\(317\) | −1.82443e6 | −1.01971 | −0.509857 | − | 0.860259i | \(-0.670302\pi\) | ||||
−0.509857 | + | 0.860259i | \(0.670302\pi\) | |||||||
\(318\) | 2.16152e6 | 1.19865 | ||||||||
\(319\) | −313547. | −0.172515 | ||||||||
\(320\) | 2.15649e6 | 1.17726 | ||||||||
\(321\) | −2.54352e6 | −1.37776 | ||||||||
\(322\) | 1.85228e6 | 0.995559 | ||||||||
\(323\) | 279474. | 0.149051 | ||||||||
\(324\) | −1.53478e6 | −0.812241 | ||||||||
\(325\) | 488168. | 0.256366 | ||||||||
\(326\) | 1.44546e6 | 0.753289 | ||||||||
\(327\) | 474451. | 0.245370 | ||||||||
\(328\) | −4.98657e6 | −2.55928 | ||||||||
\(329\) | −1.37099e6 | −0.698305 | ||||||||
\(330\) | 369637. | 0.186849 | ||||||||
\(331\) | 464579. | 0.233072 | 0.116536 | − | 0.993186i | \(-0.462821\pi\) | ||||
0.116536 | + | 0.993186i | \(0.462821\pi\) | |||||||
\(332\) | 4.40334e6 | 2.19249 | ||||||||
\(333\) | −140996. | −0.0696781 | ||||||||
\(334\) | 2.53202e6 | 1.24194 | ||||||||
\(335\) | −623710. | −0.303648 | ||||||||
\(336\) | 2.23700e6 | 1.08098 | ||||||||
\(337\) | 2.97214e6 | 1.42559 | 0.712795 | − | 0.701372i | \(-0.247429\pi\) | ||||
0.712795 | + | 0.701372i | \(0.247429\pi\) | |||||||
\(338\) | −2.56978e6 | −1.22350 | ||||||||
\(339\) | 400640. | 0.189345 | ||||||||
\(340\) | 1.62242e6 | 0.761140 | ||||||||
\(341\) | 289140. | 0.134655 | ||||||||
\(342\) | 443261. | 0.204925 | ||||||||
\(343\) | 1.78557e6 | 0.819486 | ||||||||
\(344\) | 1.66633e6 | 0.759216 | ||||||||
\(345\) | −823341. | −0.372419 | ||||||||
\(346\) | 2.87456e6 | 1.29086 | ||||||||
\(347\) | 343604. | 0.153191 | 0.0765957 | − | 0.997062i | \(-0.475595\pi\) | ||||
0.0765957 | + | 0.997062i | \(0.475595\pi\) | |||||||
\(348\) | 2.46632e6 | 1.09169 | ||||||||
\(349\) | 1.04465e6 | 0.459099 | 0.229549 | − | 0.973297i | \(-0.426275\pi\) | ||||
0.229549 | + | 0.973297i | \(0.426275\pi\) | |||||||
\(350\) | 399109. | 0.174149 | ||||||||
\(351\) | 3.16673e6 | 1.37196 | ||||||||
\(352\) | −2.16447e6 | −0.931099 | ||||||||
\(353\) | −2.06027e6 | −0.880009 | −0.440004 | − | 0.897996i | \(-0.645023\pi\) | ||||
−0.440004 | + | 0.897996i | \(0.645023\pi\) | |||||||
\(354\) | −1.92092e6 | −0.814706 | ||||||||
\(355\) | 165261. | 0.0695983 | ||||||||
\(356\) | −2.32223e6 | −0.971135 | ||||||||
\(357\) | 521535. | 0.216577 | ||||||||
\(358\) | 1.79718e6 | 0.741112 | ||||||||
\(359\) | 2.51980e6 | 1.03188 | 0.515941 | − | 0.856624i | \(-0.327442\pi\) | ||||
0.515941 | + | 0.856624i | \(0.327442\pi\) | |||||||
\(360\) | 1.59094e6 | 0.646991 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 1.22052e6 | 0.489525 | ||||||||
\(363\) | −166232. | −0.0662137 | ||||||||
\(364\) | −3.88492e6 | −1.53684 | ||||||||
\(365\) | 1.66537e6 | 0.654301 | ||||||||
\(366\) | 5.70404e6 | 2.22577 | ||||||||
\(367\) | −1.58811e6 | −0.615481 | −0.307740 | − | 0.951470i | \(-0.599573\pi\) | ||||
−0.307740 | + | 0.951470i | \(0.599573\pi\) | |||||||
\(368\) | 9.63191e6 | 3.70760 | ||||||||
\(369\) | −1.01995e6 | −0.389954 | ||||||||
\(370\) | −332512. | −0.126271 | ||||||||
\(371\) | −1.04958e6 | −0.395895 | ||||||||
\(372\) | −2.27434e6 | −0.852113 | ||||||||
\(373\) | −3.49518e6 | −1.30076 | −0.650380 | − | 0.759609i | \(-0.725390\pi\) | ||||
−0.650380 | + | 0.759609i | \(0.725390\pi\) | |||||||
\(374\) | −1.00815e6 | −0.372689 | ||||||||
\(375\) | −177404. | −0.0651457 | ||||||||
\(376\) | −1.28884e7 | −4.70142 | ||||||||
\(377\) | −2.02398e6 | −0.733421 | ||||||||
\(378\) | 2.58900e6 | 0.931972 | ||||||||
\(379\) | −4.78062e6 | −1.70957 | −0.854783 | − | 0.518985i | \(-0.826310\pi\) | ||||
−0.854783 | + | 0.518985i | \(0.826310\pi\) | |||||||
\(380\) | 756545. | 0.268767 | ||||||||
\(381\) | 2.01290e6 | 0.710410 | ||||||||
\(382\) | −9.85663e6 | −3.45597 | ||||||||
\(383\) | 2.32447e6 | 0.809705 | 0.404853 | − | 0.914382i | \(-0.367323\pi\) | ||||
0.404853 | + | 0.914382i | \(0.367323\pi\) | |||||||
\(384\) | 4.04120e6 | 1.39856 | ||||||||
\(385\) | −179486. | −0.0617133 | ||||||||
\(386\) | 3.06341e6 | 1.04650 | ||||||||
\(387\) | 340831. | 0.115681 | ||||||||
\(388\) | 1.63937e6 | 0.552839 | ||||||||
\(389\) | 1.27764e6 | 0.428089 | 0.214044 | − | 0.976824i | \(-0.431336\pi\) | ||||
0.214044 | + | 0.976824i | \(0.431336\pi\) | |||||||
\(390\) | 2.38605e6 | 0.794361 | ||||||||
\(391\) | 2.24559e6 | 0.742828 | ||||||||
\(392\) | 7.41101e6 | 2.43592 | ||||||||
\(393\) | −1.17807e6 | −0.384759 | ||||||||
\(394\) | −1.14230e7 | −3.70715 | ||||||||
\(395\) | 1.37185e6 | 0.442398 | ||||||||
\(396\) | −1.15723e6 | −0.370835 | ||||||||
\(397\) | −1.95724e6 | −0.623257 | −0.311629 | − | 0.950204i | \(-0.600874\pi\) | ||||
−0.311629 | + | 0.950204i | \(0.600874\pi\) | |||||||
\(398\) | 3.40825e6 | 1.07851 | ||||||||
\(399\) | 243196. | 0.0764758 | ||||||||
\(400\) | 2.07538e6 | 0.648555 | ||||||||
\(401\) | −4.33926e6 | −1.34758 | −0.673790 | − | 0.738923i | \(-0.735335\pi\) | ||||
−0.673790 | + | 0.738923i | \(0.735335\pi\) | |||||||
\(402\) | −3.04855e6 | −0.940866 | ||||||||
\(403\) | 1.86643e6 | 0.572466 | ||||||||
\(404\) | −6.46455e6 | −1.97054 | ||||||||
\(405\) | −457720. | −0.138663 | ||||||||
\(406\) | −1.65474e6 | −0.498211 | ||||||||
\(407\) | 149536. | 0.0447466 | ||||||||
\(408\) | 4.90283e6 | 1.45813 | ||||||||
\(409\) | 2.22731e6 | 0.658375 | 0.329187 | − | 0.944265i | \(-0.393225\pi\) | ||||
0.329187 | + | 0.944265i | \(0.393225\pi\) | |||||||
\(410\) | −2.40536e6 | −0.706676 | ||||||||
\(411\) | 1.31980e6 | 0.385394 | ||||||||
\(412\) | −2.25060e6 | −0.653213 | ||||||||
\(413\) | 932747. | 0.269084 | ||||||||
\(414\) | 3.56162e6 | 1.02129 | ||||||||
\(415\) | 1.31321e6 | 0.374295 | ||||||||
\(416\) | −1.39719e7 | −3.95843 | ||||||||
\(417\) | 2.84210e6 | 0.800386 | ||||||||
\(418\) | −470109. | −0.131601 | ||||||||
\(419\) | 5.15801e6 | 1.43531 | 0.717657 | − | 0.696396i | \(-0.245214\pi\) | ||||
0.717657 | + | 0.696396i | \(0.245214\pi\) | |||||||
\(420\) | 1.41181e6 | 0.390529 | ||||||||
\(421\) | 3.77198e6 | 1.03720 | 0.518602 | − | 0.855016i | \(-0.326453\pi\) | ||||
0.518602 | + | 0.855016i | \(0.326453\pi\) | |||||||
\(422\) | 8.38862e6 | 2.29303 | ||||||||
\(423\) | −2.63619e6 | −0.716350 | ||||||||
\(424\) | −9.86684e6 | −2.66541 | ||||||||
\(425\) | 483854. | 0.129940 | ||||||||
\(426\) | 807756. | 0.215653 | ||||||||
\(427\) | −2.76973e6 | −0.735136 | ||||||||
\(428\) | 1.87793e7 | 4.95530 | ||||||||
\(429\) | −1.07305e6 | −0.281498 | ||||||||
\(430\) | 803784. | 0.209637 | ||||||||
\(431\) | 5.46460e6 | 1.41699 | 0.708493 | − | 0.705718i | \(-0.249375\pi\) | ||||
0.708493 | + | 0.705718i | \(0.249375\pi\) | |||||||
\(432\) | 1.34629e7 | 3.47079 | ||||||||
\(433\) | −5.62184e6 | −1.44098 | −0.720491 | − | 0.693464i | \(-0.756083\pi\) | ||||
−0.720491 | + | 0.693464i | \(0.756083\pi\) | |||||||
\(434\) | 1.52593e6 | 0.388875 | ||||||||
\(435\) | 735532. | 0.186371 | ||||||||
\(436\) | −3.50296e6 | −0.882508 | ||||||||
\(437\) | 1.04714e6 | 0.262301 | ||||||||
\(438\) | 8.13991e6 | 2.02738 | ||||||||
\(439\) | −3.02707e6 | −0.749655 | −0.374827 | − | 0.927095i | \(-0.622298\pi\) | ||||
−0.374827 | + | 0.927095i | \(0.622298\pi\) | |||||||
\(440\) | −1.68731e6 | −0.415491 | ||||||||
\(441\) | 1.51585e6 | 0.371158 | ||||||||
\(442\) | −6.50774e6 | −1.58443 | ||||||||
\(443\) | 5.67545e6 | 1.37401 | 0.687007 | − | 0.726650i | \(-0.258924\pi\) | ||||
0.687007 | + | 0.726650i | \(0.258924\pi\) | |||||||
\(444\) | −1.17623e6 | −0.283162 | ||||||||
\(445\) | −692559. | −0.165789 | ||||||||
\(446\) | 2.34177e6 | 0.557452 | ||||||||
\(447\) | 85591.2 | 0.0202610 | ||||||||
\(448\) | −5.11814e6 | −1.20481 | ||||||||
\(449\) | −2.85299e6 | −0.667859 | −0.333930 | − | 0.942598i | \(-0.608375\pi\) | ||||
−0.333930 | + | 0.942598i | \(0.608375\pi\) | |||||||
\(450\) | 767419. | 0.178649 | ||||||||
\(451\) | 1.08173e6 | 0.250425 | ||||||||
\(452\) | −2.95800e6 | −0.681007 | ||||||||
\(453\) | 4.99436e6 | 1.14349 | ||||||||
\(454\) | −1.19730e7 | −2.72623 | ||||||||
\(455\) | −1.15860e6 | −0.262365 | ||||||||
\(456\) | 2.28623e6 | 0.514882 | ||||||||
\(457\) | 6.86476e6 | 1.53757 | 0.768785 | − | 0.639508i | \(-0.220862\pi\) | ||||
0.768785 | + | 0.639508i | \(0.220862\pi\) | |||||||
\(458\) | 3.58630e6 | 0.798883 | ||||||||
\(459\) | 3.13874e6 | 0.695383 | ||||||||
\(460\) | 6.07888e6 | 1.33946 | ||||||||
\(461\) | 4.26147e6 | 0.933914 | 0.466957 | − | 0.884280i | \(-0.345350\pi\) | ||||
0.466957 | + | 0.884280i | \(0.345350\pi\) | |||||||
\(462\) | −877285. | −0.191221 | ||||||||
\(463\) | 5.89172e6 | 1.27729 | 0.638645 | − | 0.769502i | \(-0.279495\pi\) | ||||
0.638645 | + | 0.769502i | \(0.279495\pi\) | |||||||
\(464\) | −8.60467e6 | −1.85541 | ||||||||
\(465\) | −678277. | −0.145470 | ||||||||
\(466\) | 8.69665e6 | 1.85518 | ||||||||
\(467\) | 184209. | 0.0390858 | 0.0195429 | − | 0.999809i | \(-0.493779\pi\) | ||||
0.0195429 | + | 0.999809i | \(0.493779\pi\) | |||||||
\(468\) | −7.47004e6 | −1.57655 | ||||||||
\(469\) | 1.48029e6 | 0.310753 | ||||||||
\(470\) | −6.21694e6 | −1.29817 | ||||||||
\(471\) | −3.55946e6 | −0.739318 | ||||||||
\(472\) | 8.76854e6 | 1.81164 | ||||||||
\(473\) | −361475. | −0.0742892 | ||||||||
\(474\) | 6.70527e6 | 1.37079 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | −3.85059e6 | −0.778950 | ||||||||
\(477\) | −2.01816e6 | −0.406125 | ||||||||
\(478\) | 4.25362e6 | 0.851509 | ||||||||
\(479\) | 6.60969e6 | 1.31626 | 0.658131 | − | 0.752903i | \(-0.271347\pi\) | ||||
0.658131 | + | 0.752903i | \(0.271347\pi\) | |||||||
\(480\) | 5.07751e6 | 1.00588 | ||||||||
\(481\) | 965274. | 0.190234 | ||||||||
\(482\) | −9.68459e6 | −1.89873 | ||||||||
\(483\) | 1.95409e6 | 0.381133 | ||||||||
\(484\) | 1.22732e6 | 0.238147 | ||||||||
\(485\) | 488911. | 0.0943791 | ||||||||
\(486\) | 8.36589e6 | 1.60665 | ||||||||
\(487\) | 6.87622e6 | 1.31379 | 0.656897 | − | 0.753980i | \(-0.271869\pi\) | ||||
0.656897 | + | 0.753980i | \(0.271869\pi\) | |||||||
\(488\) | −2.60376e7 | −4.94938 | ||||||||
\(489\) | 1.52491e6 | 0.288384 | ||||||||
\(490\) | 3.57483e6 | 0.672613 | ||||||||
\(491\) | 7.29840e6 | 1.36623 | 0.683116 | − | 0.730310i | \(-0.260624\pi\) | ||||
0.683116 | + | 0.730310i | \(0.260624\pi\) | |||||||
\(492\) | −8.50874e6 | −1.58472 | ||||||||
\(493\) | −2.00610e6 | −0.371736 | ||||||||
\(494\) | −3.03461e6 | −0.559481 | ||||||||
\(495\) | −345121. | −0.0633080 | ||||||||
\(496\) | 7.93487e6 | 1.44822 | ||||||||
\(497\) | −392225. | −0.0712269 | ||||||||
\(498\) | 6.41867e6 | 1.15977 | ||||||||
\(499\) | −1.01937e7 | −1.83265 | −0.916327 | − | 0.400431i | \(-0.868860\pi\) | ||||
−0.916327 | + | 0.400431i | \(0.868860\pi\) | |||||||
\(500\) | 1.30981e6 | 0.234306 | ||||||||
\(501\) | 2.67119e6 | 0.475457 | ||||||||
\(502\) | 1.99899e6 | 0.354039 | ||||||||
\(503\) | 6.25337e6 | 1.10203 | 0.551016 | − | 0.834495i | \(-0.314240\pi\) | ||||
0.551016 | + | 0.834495i | \(0.314240\pi\) | |||||||
\(504\) | −3.77589e6 | −0.662130 | ||||||||
\(505\) | −1.92793e6 | −0.336405 | ||||||||
\(506\) | −3.77735e6 | −0.655860 | ||||||||
\(507\) | −2.71103e6 | −0.468397 | ||||||||
\(508\) | −1.48616e7 | −2.55509 | ||||||||
\(509\) | 4.29252e6 | 0.734374 | 0.367187 | − | 0.930147i | \(-0.380321\pi\) | ||||
0.367187 | + | 0.930147i | \(0.380321\pi\) | |||||||
\(510\) | 2.36496e6 | 0.402624 | ||||||||
\(511\) | −3.95252e6 | −0.669611 | ||||||||
\(512\) | −129590. | −0.0218473 | ||||||||
\(513\) | 1.46362e6 | 0.245547 | ||||||||
\(514\) | 1.06248e6 | 0.177383 | ||||||||
\(515\) | −671197. | −0.111515 | ||||||||
\(516\) | 2.84331e6 | 0.470111 | ||||||||
\(517\) | 2.79586e6 | 0.460033 | ||||||||
\(518\) | 789173. | 0.129225 | ||||||||
\(519\) | 3.03255e6 | 0.494186 | ||||||||
\(520\) | −1.08918e7 | −1.76640 | ||||||||
\(521\) | 1.38612e6 | 0.223722 | 0.111861 | − | 0.993724i | \(-0.464319\pi\) | ||||
0.111861 | + | 0.993724i | \(0.464319\pi\) | |||||||
\(522\) | −3.18178e6 | −0.511085 | ||||||||
\(523\) | 3.93347e6 | 0.628814 | 0.314407 | − | 0.949288i | \(-0.398194\pi\) | ||||
0.314407 | + | 0.949288i | \(0.398194\pi\) | |||||||
\(524\) | 8.69789e6 | 1.38384 | ||||||||
\(525\) | 421045. | 0.0666700 | ||||||||
\(526\) | −466254. | −0.0734782 | ||||||||
\(527\) | 1.84994e6 | 0.290155 | ||||||||
\(528\) | −4.56190e6 | −0.712133 | ||||||||
\(529\) | 1.97744e6 | 0.307230 | ||||||||
\(530\) | −4.75944e6 | −0.735981 | ||||||||
\(531\) | 1.79351e6 | 0.276038 | ||||||||
\(532\) | −1.79556e6 | −0.275056 | ||||||||
\(533\) | 6.98270e6 | 1.06465 | ||||||||
\(534\) | −3.38507e6 | −0.513705 | ||||||||
\(535\) | 5.60056e6 | 0.845955 | ||||||||
\(536\) | 1.39159e7 | 2.09218 | ||||||||
\(537\) | 1.89596e6 | 0.283722 | ||||||||
\(538\) | −9.58902e6 | −1.42830 | ||||||||
\(539\) | −1.60766e6 | −0.238354 | ||||||||
\(540\) | 8.49667e6 | 1.25390 | ||||||||
\(541\) | 2.27386e6 | 0.334019 | 0.167010 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167010 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(542\) | −1.03333e7 | −1.51092 | ||||||||
\(543\) | 1.28761e6 | 0.187406 | ||||||||
\(544\) | −1.38485e7 | −2.00634 | ||||||||
\(545\) | −1.04469e6 | −0.150659 | ||||||||
\(546\) | −5.66297e6 | −0.812948 | ||||||||
\(547\) | −801558. | −0.114543 | −0.0572713 | − | 0.998359i | \(-0.518240\pi\) | ||||
−0.0572713 | + | 0.998359i | \(0.518240\pi\) | |||||||
\(548\) | −9.74435e6 | −1.38612 | ||||||||
\(549\) | −5.32572e6 | −0.754132 | ||||||||
\(550\) | −813901. | −0.114727 | ||||||||
\(551\) | −935459. | −0.131264 | ||||||||
\(552\) | 1.83700e7 | 2.56602 | ||||||||
\(553\) | −3.25590e6 | −0.452750 | ||||||||
\(554\) | −1.00256e7 | −1.38782 | ||||||||
\(555\) | −350788. | −0.0483407 | ||||||||
\(556\) | −2.09838e7 | −2.87870 | ||||||||
\(557\) | −3.90669e6 | −0.533545 | −0.266772 | − | 0.963760i | \(-0.585957\pi\) | ||||
−0.266772 | + | 0.963760i | \(0.585957\pi\) | |||||||
\(558\) | 2.93410e6 | 0.398924 | ||||||||
\(559\) | −2.33336e6 | −0.315830 | ||||||||
\(560\) | −4.92563e6 | −0.663730 | ||||||||
\(561\) | −1.06356e6 | −0.142678 | ||||||||
\(562\) | 2.60269e7 | 3.47601 | ||||||||
\(563\) | −1.35944e7 | −1.80755 | −0.903774 | − | 0.428010i | \(-0.859215\pi\) | ||||
−0.903774 | + | 0.428010i | \(0.859215\pi\) | |||||||
\(564\) | −2.19919e7 | −2.91115 | ||||||||
\(565\) | −882165. | −0.116260 | ||||||||
\(566\) | −4.02510e6 | −0.528123 | ||||||||
\(567\) | 1.08634e6 | 0.141908 | ||||||||
\(568\) | −3.68721e6 | −0.479543 | ||||||||
\(569\) | −4.90008e6 | −0.634487 | −0.317244 | − | 0.948344i | \(-0.602757\pi\) | ||||
−0.317244 | + | 0.948344i | \(0.602757\pi\) | |||||||
\(570\) | 1.10280e6 | 0.142171 | ||||||||
\(571\) | 8.27029e6 | 1.06153 | 0.530763 | − | 0.847520i | \(-0.321906\pi\) | ||||
0.530763 | + | 0.847520i | \(0.321906\pi\) | |||||||
\(572\) | 7.92250e6 | 1.01245 | ||||||||
\(573\) | −1.03984e7 | −1.32306 | ||||||||
\(574\) | 5.70880e6 | 0.723211 | ||||||||
\(575\) | 1.81291e6 | 0.228668 | ||||||||
\(576\) | −9.84132e6 | −1.23594 | ||||||||
\(577\) | 7.05888e6 | 0.882666 | 0.441333 | − | 0.897343i | \(-0.354506\pi\) | ||||
0.441333 | + | 0.897343i | \(0.354506\pi\) | |||||||
\(578\) | 8.83074e6 | 1.09946 | ||||||||
\(579\) | 3.23179e6 | 0.400633 | ||||||||
\(580\) | −5.43057e6 | −0.670309 | ||||||||
\(581\) | −3.11673e6 | −0.383053 | ||||||||
\(582\) | 2.38968e6 | 0.292437 | ||||||||
\(583\) | 2.14040e6 | 0.260810 | ||||||||
\(584\) | −3.71568e7 | −4.50823 | ||||||||
\(585\) | −2.22780e6 | −0.269145 | ||||||||
\(586\) | 1.11976e7 | 1.34704 | ||||||||
\(587\) | 2.47297e6 | 0.296226 | 0.148113 | − | 0.988970i | \(-0.452680\pi\) | ||||
0.148113 | + | 0.988970i | \(0.452680\pi\) | |||||||
\(588\) | 1.26456e7 | 1.50833 | ||||||||
\(589\) | 862641. | 0.102457 | ||||||||
\(590\) | 4.22966e6 | 0.500236 | ||||||||
\(591\) | −1.20509e7 | −1.41922 | ||||||||
\(592\) | 4.10372e6 | 0.481253 | ||||||||
\(593\) | 64423.8 | 0.00752332 | 0.00376166 | − | 0.999993i | \(-0.498803\pi\) | ||||
0.00376166 | + | 0.999993i | \(0.498803\pi\) | |||||||
\(594\) | −5.27974e6 | −0.613969 | ||||||||
\(595\) | −1.14836e6 | −0.132980 | ||||||||
\(596\) | −631936. | −0.0728714 | ||||||||
\(597\) | 3.59558e6 | 0.412889 | ||||||||
\(598\) | −2.43832e7 | −2.78829 | ||||||||
\(599\) | 1.57792e6 | 0.179688 | 0.0898440 | − | 0.995956i | \(-0.471363\pi\) | ||||
0.0898440 | + | 0.995956i | \(0.471363\pi\) | |||||||
\(600\) | 3.95815e6 | 0.448864 | ||||||||
\(601\) | −821710. | −0.0927967 | −0.0463984 | − | 0.998923i | \(-0.514774\pi\) | ||||
−0.0463984 | + | 0.998923i | \(0.514774\pi\) | |||||||
\(602\) | −1.90767e6 | −0.214542 | ||||||||
\(603\) | 2.84635e6 | 0.318783 | ||||||||
\(604\) | −3.68743e7 | −4.11274 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | −9.42326e6 | −1.04236 | ||||||||
\(607\) | −798319. | −0.0879437 | −0.0439719 | − | 0.999033i | \(-0.514001\pi\) | ||||
−0.0439719 | + | 0.999033i | \(0.514001\pi\) | |||||||
\(608\) | −6.45764e6 | −0.708460 | ||||||||
\(609\) | −1.74569e6 | −0.190732 | ||||||||
\(610\) | −1.25597e7 | −1.36664 | ||||||||
\(611\) | 1.80476e7 | 1.95576 | ||||||||
\(612\) | −7.40403e6 | −0.799079 | ||||||||
\(613\) | −1.54064e7 | −1.65597 | −0.827983 | − | 0.560754i | \(-0.810511\pi\) | ||||
−0.827983 | + | 0.560754i | \(0.810511\pi\) | |||||||
\(614\) | 1.48656e7 | 1.59133 | ||||||||
\(615\) | −2.53757e6 | −0.270539 | ||||||||
\(616\) | 4.00460e6 | 0.425213 | ||||||||
\(617\) | −1.90156e6 | −0.201094 | −0.100547 | − | 0.994932i | \(-0.532059\pi\) | ||||
−0.100547 | + | 0.994932i | \(0.532059\pi\) | |||||||
\(618\) | −3.28065e6 | −0.345533 | ||||||||
\(619\) | −8.77685e6 | −0.920687 | −0.460344 | − | 0.887741i | \(-0.652274\pi\) | ||||
−0.460344 | + | 0.887741i | \(0.652274\pi\) | |||||||
\(620\) | 5.00784e6 | 0.523205 | ||||||||
\(621\) | 1.17603e7 | 1.22374 | ||||||||
\(622\) | 1.97139e7 | 2.04313 | ||||||||
\(623\) | 1.64370e6 | 0.169669 | ||||||||
\(624\) | −2.94476e7 | −3.02753 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.10051e7 | 2.14234 | ||||||||
\(627\) | −495948. | −0.0503811 | ||||||||
\(628\) | 2.62801e7 | 2.65906 | ||||||||
\(629\) | 956743. | 0.0964204 | ||||||||
\(630\) | −1.82137e6 | −0.182829 | ||||||||
\(631\) | 2.07418e6 | 0.207383 | 0.103692 | − | 0.994609i | \(-0.466934\pi\) | ||||
0.103692 | + | 0.994609i | \(0.466934\pi\) | |||||||
\(632\) | −3.06080e7 | −3.04819 | ||||||||
\(633\) | 8.84969e6 | 0.877847 | ||||||||
\(634\) | 1.96351e7 | 1.94003 | ||||||||
\(635\) | −4.43218e6 | −0.436197 | ||||||||
\(636\) | −1.68361e7 | −1.65044 | ||||||||
\(637\) | −1.03776e7 | −1.01333 | ||||||||
\(638\) | 3.37450e6 | 0.328214 | ||||||||
\(639\) | −754181. | −0.0730674 | ||||||||
\(640\) | −8.89829e6 | −0.858730 | ||||||||
\(641\) | 1.58592e7 | 1.52453 | 0.762267 | − | 0.647263i | \(-0.224086\pi\) | ||||
0.762267 | + | 0.647263i | \(0.224086\pi\) | |||||||
\(642\) | 2.73742e7 | 2.62123 | ||||||||
\(643\) | −8.24222e6 | −0.786171 | −0.393085 | − | 0.919502i | \(-0.628592\pi\) | ||||
−0.393085 | + | 0.919502i | \(0.628592\pi\) | |||||||
\(644\) | −1.44274e7 | −1.37080 | ||||||||
\(645\) | 847963. | 0.0802560 | ||||||||
\(646\) | −3.00779e6 | −0.283574 | ||||||||
\(647\) | 3.71842e6 | 0.349219 | 0.174609 | − | 0.984638i | \(-0.444134\pi\) | ||||
0.174609 | + | 0.984638i | \(0.444134\pi\) | |||||||
\(648\) | 1.02124e7 | 0.955412 | ||||||||
\(649\) | −1.90215e6 | −0.177269 | ||||||||
\(650\) | −5.25383e6 | −0.487744 | ||||||||
\(651\) | 1.60980e6 | 0.148874 | ||||||||
\(652\) | −1.12587e7 | −1.03721 | ||||||||
\(653\) | 264259. | 0.0242519 | 0.0121260 | − | 0.999926i | \(-0.496140\pi\) | ||||
0.0121260 | + | 0.999926i | \(0.496140\pi\) | |||||||
\(654\) | −5.10619e6 | −0.466824 | ||||||||
\(655\) | 2.59398e6 | 0.236245 | ||||||||
\(656\) | 2.96859e7 | 2.69334 | ||||||||
\(657\) | −7.60004e6 | −0.686914 | ||||||||
\(658\) | 1.47551e7 | 1.32855 | ||||||||
\(659\) | 1.85292e7 | 1.66205 | 0.831023 | − | 0.556237i | \(-0.187755\pi\) | ||||
0.831023 | + | 0.556237i | \(0.187755\pi\) | |||||||
\(660\) | −2.87910e6 | −0.257275 | ||||||||
\(661\) | −6.74709e6 | −0.600638 | −0.300319 | − | 0.953839i | \(-0.597093\pi\) | ||||
−0.300319 | + | 0.953839i | \(0.597093\pi\) | |||||||
\(662\) | −4.99996e6 | −0.443426 | ||||||||
\(663\) | −6.86543e6 | −0.606574 | ||||||||
\(664\) | −2.92997e7 | −2.57895 | ||||||||
\(665\) | −535491. | −0.0469568 | ||||||||
\(666\) | 1.51745e6 | 0.132565 | ||||||||
\(667\) | −7.51646e6 | −0.654182 | ||||||||
\(668\) | −1.97219e7 | −1.71005 | ||||||||
\(669\) | 2.47048e6 | 0.213411 | ||||||||
\(670\) | 6.71257e6 | 0.577699 | ||||||||
\(671\) | 5.64830e6 | 0.484296 | ||||||||
\(672\) | −1.20508e7 | −1.02942 | ||||||||
\(673\) | 1.54373e6 | 0.131382 | 0.0656908 | − | 0.997840i | \(-0.479075\pi\) | ||||
0.0656908 | + | 0.997840i | \(0.479075\pi\) | |||||||
\(674\) | −3.19872e7 | −2.71223 | ||||||||
\(675\) | 2.53397e6 | 0.214063 | ||||||||
\(676\) | 2.00160e7 | 1.68466 | ||||||||
\(677\) | −1.23313e7 | −1.03404 | −0.517020 | − | 0.855973i | \(-0.672959\pi\) | ||||
−0.517020 | + | 0.855973i | \(0.672959\pi\) | |||||||
\(678\) | −4.31181e6 | −0.360235 | ||||||||
\(679\) | −1.16037e6 | −0.0965874 | ||||||||
\(680\) | −1.07955e7 | −0.895304 | ||||||||
\(681\) | −1.26311e7 | −1.04369 | ||||||||
\(682\) | −3.11182e6 | −0.256185 | ||||||||
\(683\) | 1.65020e7 | 1.35359 | 0.676793 | − | 0.736174i | \(-0.263369\pi\) | ||||
0.676793 | + | 0.736174i | \(0.263369\pi\) | |||||||
\(684\) | −3.45256e6 | −0.282163 | ||||||||
\(685\) | −2.90606e6 | −0.236635 | ||||||||
\(686\) | −1.92169e7 | −1.55910 | ||||||||
\(687\) | 3.78342e6 | 0.305839 | ||||||||
\(688\) | −9.91996e6 | −0.798985 | ||||||||
\(689\) | 1.38165e7 | 1.10879 | ||||||||
\(690\) | 8.86106e6 | 0.708538 | ||||||||
\(691\) | −1.82638e7 | −1.45511 | −0.727557 | − | 0.686047i | \(-0.759344\pi\) | ||||
−0.727557 | + | 0.686047i | \(0.759344\pi\) | |||||||
\(692\) | −2.23899e7 | −1.77741 | ||||||||
\(693\) | 819099. | 0.0647893 | ||||||||
\(694\) | −3.69798e6 | −0.291451 | ||||||||
\(695\) | −6.25800e6 | −0.491444 | ||||||||
\(696\) | −1.64108e7 | −1.28412 | ||||||||
\(697\) | 6.92099e6 | 0.539618 | ||||||||
\(698\) | −1.12428e7 | −0.873448 | ||||||||
\(699\) | 9.17465e6 | 0.710226 | ||||||||
\(700\) | −3.10866e6 | −0.239788 | ||||||||
\(701\) | 1.06232e7 | 0.816508 | 0.408254 | − | 0.912868i | \(-0.366138\pi\) | ||||
0.408254 | + | 0.912868i | \(0.366138\pi\) | |||||||
\(702\) | −3.40814e7 | −2.61020 | ||||||||
\(703\) | 446137. | 0.0340471 | ||||||||
\(704\) | 1.04374e7 | 0.793709 | ||||||||
\(705\) | −6.55865e6 | −0.496983 | ||||||||
\(706\) | 2.21733e7 | 1.67424 | ||||||||
\(707\) | 4.57568e6 | 0.344276 | ||||||||
\(708\) | 1.49620e7 | 1.12178 | ||||||||
\(709\) | 5.50436e6 | 0.411236 | 0.205618 | − | 0.978632i | \(-0.434080\pi\) | ||||
0.205618 | + | 0.978632i | \(0.434080\pi\) | |||||||
\(710\) | −1.77859e6 | −0.132413 | ||||||||
\(711\) | −6.26054e6 | −0.464449 | ||||||||
\(712\) | 1.54520e7 | 1.14231 | ||||||||
\(713\) | 6.93136e6 | 0.510616 | ||||||||
\(714\) | −5.61293e6 | −0.412044 | ||||||||
\(715\) | 2.36273e6 | 0.172842 | ||||||||
\(716\) | −1.39982e7 | −1.02045 | ||||||||
\(717\) | 4.48742e6 | 0.325986 | ||||||||
\(718\) | −2.71189e7 | −1.96319 | ||||||||
\(719\) | 7.09249e6 | 0.511654 | 0.255827 | − | 0.966723i | \(-0.417652\pi\) | ||||
0.255827 | + | 0.966723i | \(0.417652\pi\) | |||||||
\(720\) | −9.47115e6 | −0.680881 | ||||||||
\(721\) | 1.59300e6 | 0.114124 | ||||||||
\(722\) | −1.40256e6 | −0.100133 | ||||||||
\(723\) | −1.02169e7 | −0.726898 | ||||||||
\(724\) | −9.50665e6 | −0.674033 | ||||||||
\(725\) | −1.61956e6 | −0.114433 | ||||||||
\(726\) | 1.78904e6 | 0.125974 | ||||||||
\(727\) | 2.70960e7 | 1.90138 | 0.950692 | − | 0.310137i | \(-0.100375\pi\) | ||||
0.950692 | + | 0.310137i | \(0.100375\pi\) | |||||||
\(728\) | 2.58501e7 | 1.80773 | ||||||||
\(729\) | 1.32748e7 | 0.925141 | ||||||||
\(730\) | −1.79232e7 | −1.24483 | ||||||||
\(731\) | −2.31274e6 | −0.160079 | ||||||||
\(732\) | −4.44287e7 | −3.06469 | ||||||||
\(733\) | 2.83368e7 | 1.94801 | 0.974004 | − | 0.226531i | \(-0.0727385\pi\) | ||||
0.974004 | + | 0.226531i | \(0.0727385\pi\) | |||||||
\(734\) | 1.70917e7 | 1.17097 | ||||||||
\(735\) | 3.77132e6 | 0.257499 | ||||||||
\(736\) | −5.18875e7 | −3.53076 | ||||||||
\(737\) | −3.01875e6 | −0.204719 | ||||||||
\(738\) | 1.09771e7 | 0.741900 | ||||||||
\(739\) | 3.55006e6 | 0.239125 | 0.119563 | − | 0.992827i | \(-0.461851\pi\) | ||||
0.119563 | + | 0.992827i | \(0.461851\pi\) | |||||||
\(740\) | 2.58993e6 | 0.173864 | ||||||||
\(741\) | −3.20140e6 | −0.214188 | ||||||||
\(742\) | 1.12959e7 | 0.753202 | ||||||||
\(743\) | 634499. | 0.0421656 | 0.0210828 | − | 0.999778i | \(-0.493289\pi\) | ||||
0.0210828 | + | 0.999778i | \(0.493289\pi\) | |||||||
\(744\) | 1.51334e7 | 1.00231 | ||||||||
\(745\) | −188463. | −0.0124404 | ||||||||
\(746\) | 3.76163e7 | 2.47473 | ||||||||
\(747\) | −5.99295e6 | −0.392952 | ||||||||
\(748\) | 7.85249e6 | 0.513161 | ||||||||
\(749\) | −1.32922e7 | −0.865749 | ||||||||
\(750\) | 1.90928e6 | 0.123942 | ||||||||
\(751\) | 1.57078e7 | 1.01628 | 0.508141 | − | 0.861274i | \(-0.330333\pi\) | ||||
0.508141 | + | 0.861274i | \(0.330333\pi\) | |||||||
\(752\) | 7.67268e7 | 4.94769 | ||||||||
\(753\) | 2.10886e6 | 0.135538 | ||||||||
\(754\) | 2.17828e7 | 1.39536 | ||||||||
\(755\) | −1.09970e7 | −0.702115 | ||||||||
\(756\) | −2.01657e7 | −1.28324 | ||||||||
\(757\) | −1.38932e7 | −0.881176 | −0.440588 | − | 0.897709i | \(-0.645230\pi\) | ||||
−0.440588 | + | 0.897709i | \(0.645230\pi\) | |||||||
\(758\) | 5.14506e7 | 3.25250 | ||||||||
\(759\) | −3.98497e6 | −0.251085 | ||||||||
\(760\) | −5.03403e6 | −0.316142 | ||||||||
\(761\) | 1.18702e7 | 0.743014 | 0.371507 | − | 0.928430i | \(-0.378841\pi\) | ||||
0.371507 | + | 0.928430i | \(0.378841\pi\) | |||||||
\(762\) | −2.16634e7 | −1.35158 | ||||||||
\(763\) | 2.47943e6 | 0.154184 | ||||||||
\(764\) | 7.67732e7 | 4.75857 | ||||||||
\(765\) | −2.20811e6 | −0.136416 | ||||||||
\(766\) | −2.50167e7 | −1.54049 | ||||||||
\(767\) | −1.22786e7 | −0.753633 | ||||||||
\(768\) | −1.21526e7 | −0.743472 | ||||||||
\(769\) | 2.38420e6 | 0.145387 | 0.0726936 | − | 0.997354i | \(-0.476840\pi\) | ||||
0.0726936 | + | 0.997354i | \(0.476840\pi\) | |||||||
\(770\) | 1.93169e6 | 0.117411 | ||||||||
\(771\) | 1.12088e6 | 0.0679083 | ||||||||
\(772\) | −2.38609e7 | −1.44093 | ||||||||
\(773\) | −2.25242e7 | −1.35582 | −0.677909 | − | 0.735146i | \(-0.737114\pi\) | ||||
−0.677909 | + | 0.735146i | \(0.737114\pi\) | |||||||
\(774\) | −3.66814e6 | −0.220086 | ||||||||
\(775\) | 1.49349e6 | 0.0893200 | ||||||||
\(776\) | −1.09083e7 | −0.650286 | ||||||||
\(777\) | 832549. | 0.0494718 | ||||||||
\(778\) | −1.37504e7 | −0.814451 | ||||||||
\(779\) | 3.22731e6 | 0.190545 | ||||||||
\(780\) | −1.85849e7 | −1.09377 | ||||||||
\(781\) | 799862. | 0.0469232 | ||||||||
\(782\) | −2.41677e7 | −1.41325 | ||||||||
\(783\) | −1.05060e7 | −0.612399 | ||||||||
\(784\) | −4.41190e7 | −2.56351 | ||||||||
\(785\) | 7.83754e6 | 0.453947 | ||||||||
\(786\) | 1.26788e7 | 0.732015 | ||||||||
\(787\) | 1.10526e7 | 0.636105 | 0.318052 | − | 0.948073i | \(-0.396971\pi\) | ||||
0.318052 | + | 0.948073i | \(0.396971\pi\) | |||||||
\(788\) | 8.89738e7 | 5.10442 | ||||||||
\(789\) | −491882. | −0.0281299 | ||||||||
\(790\) | −1.47643e7 | −0.841675 | ||||||||
\(791\) | 2.09370e6 | 0.118980 | ||||||||
\(792\) | 7.70016e6 | 0.436201 | ||||||||
\(793\) | 3.64604e7 | 2.05892 | ||||||||
\(794\) | 2.10644e7 | 1.18576 | ||||||||
\(795\) | −5.02104e6 | −0.281758 | ||||||||
\(796\) | −2.65468e7 | −1.48501 | ||||||||
\(797\) | 1.18016e7 | 0.658107 | 0.329053 | − | 0.944311i | \(-0.393270\pi\) | ||||
0.329053 | + | 0.944311i | \(0.393270\pi\) | |||||||
\(798\) | −2.61735e6 | −0.145497 | ||||||||
\(799\) | 1.78881e7 | 0.991283 | ||||||||
\(800\) | −1.11801e7 | −0.617621 | ||||||||
\(801\) | 3.16055e6 | 0.174053 | ||||||||
\(802\) | 4.67005e7 | 2.56381 | ||||||||
\(803\) | 8.06037e6 | 0.441129 | ||||||||
\(804\) | 2.37451e7 | 1.29549 | ||||||||
\(805\) | −4.30270e6 | −0.234019 | ||||||||
\(806\) | −2.00872e7 | −1.08913 | ||||||||
\(807\) | −1.01161e7 | −0.546800 | ||||||||
\(808\) | 4.30149e7 | 2.31788 | ||||||||
\(809\) | 3.28789e7 | 1.76622 | 0.883112 | − | 0.469162i | \(-0.155444\pi\) | ||||
0.883112 | + | 0.469162i | \(0.155444\pi\) | |||||||
\(810\) | 4.92613e6 | 0.263811 | ||||||||
\(811\) | 3.21795e7 | 1.71802 | 0.859008 | − | 0.511963i | \(-0.171081\pi\) | ||||
0.859008 | + | 0.511963i | \(0.171081\pi\) | |||||||
\(812\) | 1.28887e7 | 0.685994 | ||||||||
\(813\) | −1.09013e7 | −0.578430 | ||||||||
\(814\) | −1.60936e6 | −0.0851318 | ||||||||
\(815\) | −3.35768e6 | −0.177070 | ||||||||
\(816\) | −2.91874e7 | −1.53451 | ||||||||
\(817\) | −1.07845e6 | −0.0565256 | ||||||||
\(818\) | −2.39711e7 | −1.25258 | ||||||||
\(819\) | 5.28738e6 | 0.275442 | ||||||||
\(820\) | 1.87353e7 | 0.973031 | ||||||||
\(821\) | 1.16127e7 | 0.601278 | 0.300639 | − | 0.953738i | \(-0.402800\pi\) | ||||
0.300639 | + | 0.953738i | \(0.402800\pi\) | |||||||
\(822\) | −1.42042e7 | −0.733223 | ||||||||
\(823\) | 8.87616e6 | 0.456799 | 0.228400 | − | 0.973567i | \(-0.426651\pi\) | ||||
0.228400 | + | 0.973567i | \(0.426651\pi\) | |||||||
\(824\) | 1.49754e7 | 0.768353 | ||||||||
\(825\) | −858637. | −0.0439212 | ||||||||
\(826\) | −1.00385e7 | −0.511941 | ||||||||
\(827\) | −7.58442e6 | −0.385619 | −0.192810 | − | 0.981236i | \(-0.561760\pi\) | ||||
−0.192810 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(828\) | −2.77415e7 | −1.40622 | ||||||||
\(829\) | −1.00226e7 | −0.506519 | −0.253260 | − | 0.967398i | \(-0.581503\pi\) | ||||
−0.253260 | + | 0.967398i | \(0.581503\pi\) | |||||||
\(830\) | −1.41332e7 | −0.712108 | ||||||||
\(831\) | −1.05766e7 | −0.531305 | ||||||||
\(832\) | 6.73747e7 | 3.37434 | ||||||||
\(833\) | −1.02859e7 | −0.513607 | ||||||||
\(834\) | −3.05876e7 | −1.52276 | ||||||||
\(835\) | −5.88168e6 | −0.291934 | ||||||||
\(836\) | 3.66168e6 | 0.181203 | ||||||||
\(837\) | 9.68822e6 | 0.478003 | ||||||||
\(838\) | −5.55122e7 | −2.73073 | ||||||||
\(839\) | −2.77359e7 | −1.36031 | −0.680153 | − | 0.733070i | \(-0.738087\pi\) | ||||
−0.680153 | + | 0.733070i | \(0.738087\pi\) | |||||||
\(840\) | −9.39415e6 | −0.459366 | ||||||||
\(841\) | −1.37963e7 | −0.672625 | ||||||||
\(842\) | −4.05953e7 | −1.97331 | ||||||||
\(843\) | 2.74574e7 | 1.33073 | ||||||||
\(844\) | −6.53389e7 | −3.15730 | ||||||||
\(845\) | 5.96939e6 | 0.287600 | ||||||||
\(846\) | 2.83715e7 | 1.36288 | ||||||||
\(847\) | −868712. | −0.0416071 | ||||||||
\(848\) | 5.87390e7 | 2.80503 | ||||||||
\(849\) | −4.24633e6 | −0.202183 | ||||||||
\(850\) | −5.20740e6 | −0.247214 | ||||||||
\(851\) | 3.58473e6 | 0.169681 | ||||||||
\(852\) | −6.29160e6 | −0.296936 | ||||||||
\(853\) | −2.03117e7 | −0.955814 | −0.477907 | − | 0.878410i | \(-0.658604\pi\) | ||||
−0.477907 | + | 0.878410i | \(0.658604\pi\) | |||||||
\(854\) | 2.98087e7 | 1.39862 | ||||||||
\(855\) | −1.02966e6 | −0.0481701 | ||||||||
\(856\) | −1.24957e8 | −5.82875 | ||||||||
\(857\) | 2.27983e7 | 1.06035 | 0.530176 | − | 0.847888i | \(-0.322126\pi\) | ||||
0.530176 | + | 0.847888i | \(0.322126\pi\) | |||||||
\(858\) | 1.15485e7 | 0.535558 | ||||||||
\(859\) | −2.14205e7 | −0.990484 | −0.495242 | − | 0.868755i | \(-0.664921\pi\) | ||||
−0.495242 | + | 0.868755i | \(0.664921\pi\) | |||||||
\(860\) | −6.26067e6 | −0.288652 | ||||||||
\(861\) | 6.02258e6 | 0.276869 | ||||||||
\(862\) | −5.88119e7 | −2.69586 | ||||||||
\(863\) | −9.24837e6 | −0.422706 | −0.211353 | − | 0.977410i | \(-0.567787\pi\) | ||||
−0.211353 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(864\) | −7.25251e7 | −3.30525 | ||||||||
\(865\) | −6.67736e6 | −0.303434 | ||||||||
\(866\) | 6.05041e7 | 2.74151 | ||||||||
\(867\) | 9.31612e6 | 0.420908 | ||||||||
\(868\) | −1.18855e7 | −0.535447 | ||||||||
\(869\) | 6.63974e6 | 0.298265 | ||||||||
\(870\) | −7.91604e6 | −0.354576 | ||||||||
\(871\) | −1.94864e7 | −0.870335 | ||||||||
\(872\) | 2.33086e7 | 1.03806 | ||||||||
\(873\) | −2.23119e6 | −0.0990833 | ||||||||
\(874\) | −1.12696e7 | −0.499034 | ||||||||
\(875\) | −927097. | −0.0409360 | ||||||||
\(876\) | −6.34018e7 | −2.79152 | ||||||||
\(877\) | 3.63817e7 | 1.59729 | 0.798646 | − | 0.601802i | \(-0.205550\pi\) | ||||
0.798646 | + | 0.601802i | \(0.205550\pi\) | |||||||
\(878\) | 3.25783e7 | 1.42624 | ||||||||
\(879\) | 1.18131e7 | 0.515692 | ||||||||
\(880\) | 1.00448e7 | 0.437256 | ||||||||
\(881\) | −2.16771e7 | −0.940937 | −0.470469 | − | 0.882417i | \(-0.655915\pi\) | ||||
−0.470469 | + | 0.882417i | \(0.655915\pi\) | |||||||
\(882\) | −1.63140e7 | −0.706139 | ||||||||
\(883\) | 9.31432e6 | 0.402021 | 0.201011 | − | 0.979589i | \(-0.435577\pi\) | ||||
0.201011 | + | 0.979589i | \(0.435577\pi\) | |||||||
\(884\) | 5.06887e7 | 2.18163 | ||||||||
\(885\) | 4.46213e6 | 0.191507 | ||||||||
\(886\) | −6.10811e7 | −2.61410 | ||||||||
\(887\) | 3.26365e7 | 1.39282 | 0.696410 | − | 0.717644i | \(-0.254780\pi\) | ||||
0.696410 | + | 0.717644i | \(0.254780\pi\) | |||||||
\(888\) | 7.82661e6 | 0.333074 | ||||||||
\(889\) | 1.05192e7 | 0.446404 | ||||||||
\(890\) | 7.45355e6 | 0.315419 | ||||||||
\(891\) | −2.21536e6 | −0.0934869 | ||||||||
\(892\) | −1.82400e7 | −0.767562 | ||||||||
\(893\) | 8.34137e6 | 0.350033 | ||||||||
\(894\) | −921161. | −0.0385471 | ||||||||
\(895\) | −4.17470e6 | −0.174208 | ||||||||
\(896\) | 2.11189e7 | 0.878823 | ||||||||
\(897\) | −2.57234e7 | −1.06745 | ||||||||
\(898\) | 3.07049e7 | 1.27062 | ||||||||
\(899\) | −6.19214e6 | −0.255530 | ||||||||
\(900\) | −5.97742e6 | −0.245984 | ||||||||
\(901\) | 1.36944e7 | 0.561995 | ||||||||
\(902\) | −1.16419e7 | −0.476441 | ||||||||
\(903\) | −2.01253e6 | −0.0821339 | ||||||||
\(904\) | 1.96824e7 | 0.801046 | ||||||||
\(905\) | −2.83517e6 | −0.115069 | ||||||||
\(906\) | −5.37509e7 | −2.17553 | ||||||||
\(907\) | 7.02589e6 | 0.283585 | 0.141792 | − | 0.989896i | \(-0.454713\pi\) | ||||
0.141792 | + | 0.989896i | \(0.454713\pi\) | |||||||
\(908\) | 9.32576e7 | 3.75379 | ||||||||
\(909\) | 8.79826e6 | 0.353173 | ||||||||
\(910\) | 1.24693e7 | 0.499157 | ||||||||
\(911\) | −461521. | −0.0184245 | −0.00921225 | − | 0.999958i | \(-0.502932\pi\) | ||||
−0.00921225 | + | 0.999958i | \(0.502932\pi\) | |||||||
\(912\) | −1.36103e7 | −0.541852 | ||||||||
\(913\) | 6.35594e6 | 0.252350 | ||||||||
\(914\) | −7.38808e7 | −2.92527 | ||||||||
\(915\) | −1.32500e7 | −0.523195 | ||||||||
\(916\) | −2.79337e7 | −1.09999 | ||||||||
\(917\) | −6.15646e6 | −0.241773 | ||||||||
\(918\) | −3.37802e7 | −1.32299 | ||||||||
\(919\) | −2.34434e7 | −0.915655 | −0.457827 | − | 0.889041i | \(-0.651372\pi\) | ||||
−0.457827 | + | 0.889041i | \(0.651372\pi\) | |||||||
\(920\) | −4.04487e7 | −1.57556 | ||||||||
\(921\) | 1.56827e7 | 0.609215 | ||||||||
\(922\) | −4.58633e7 | −1.77680 | ||||||||
\(923\) | 5.16320e6 | 0.199487 | ||||||||
\(924\) | 6.83317e6 | 0.263295 | ||||||||
\(925\) | 772398. | 0.0296816 | ||||||||
\(926\) | −6.34086e7 | −2.43008 | ||||||||
\(927\) | 3.06306e6 | 0.117073 | ||||||||
\(928\) | 4.63537e7 | 1.76691 | ||||||||
\(929\) | 4.22693e7 | 1.60689 | 0.803444 | − | 0.595380i | \(-0.202998\pi\) | ||||
0.803444 | + | 0.595380i | \(0.202998\pi\) | |||||||
\(930\) | 7.29984e6 | 0.276762 | ||||||||
\(931\) | −4.79641e6 | −0.181360 | ||||||||
\(932\) | −6.77382e7 | −2.55443 | ||||||||
\(933\) | 2.07974e7 | 0.782179 | ||||||||
\(934\) | −1.98252e6 | −0.0743619 | ||||||||
\(935\) | 2.34185e6 | 0.0876054 | ||||||||
\(936\) | 4.97054e7 | 1.85445 | ||||||||
\(937\) | −1.99938e7 | −0.743954 | −0.371977 | − | 0.928242i | \(-0.621320\pi\) | ||||
−0.371977 | + | 0.928242i | \(0.621320\pi\) | |||||||
\(938\) | −1.59314e7 | −0.591217 | ||||||||
\(939\) | 2.21596e7 | 0.820159 | ||||||||
\(940\) | 4.84237e7 | 1.78747 | ||||||||
\(941\) | −2.22235e6 | −0.0818161 | −0.0409081 | − | 0.999163i | \(-0.513025\pi\) | ||||
−0.0409081 | + | 0.999163i | \(0.513025\pi\) | |||||||
\(942\) | 3.83080e7 | 1.40657 | ||||||||
\(943\) | 2.59316e7 | 0.949621 | ||||||||
\(944\) | −5.22006e7 | −1.90654 | ||||||||
\(945\) | −6.01404e6 | −0.219072 | ||||||||
\(946\) | 3.89031e6 | 0.141337 | ||||||||
\(947\) | −3.46033e7 | −1.25384 | −0.626921 | − | 0.779083i | \(-0.715685\pi\) | ||||
−0.626921 | + | 0.779083i | \(0.715685\pi\) | |||||||
\(948\) | −5.22273e7 | −1.88746 | ||||||||
\(949\) | 5.20306e7 | 1.87540 | ||||||||
\(950\) | −2.42825e6 | −0.0872940 | ||||||||
\(951\) | 2.07143e7 | 0.742709 | ||||||||
\(952\) | 2.56217e7 | 0.916253 | ||||||||
\(953\) | 3.96218e7 | 1.41320 | 0.706598 | − | 0.707615i | \(-0.250229\pi\) | ||||
0.706598 | + | 0.707615i | \(0.250229\pi\) | |||||||
\(954\) | 2.17201e7 | 0.772665 | ||||||||
\(955\) | 2.28961e7 | 0.812369 | ||||||||
\(956\) | −3.31314e7 | −1.17245 | ||||||||
\(957\) | 3.55997e6 | 0.125651 | ||||||||
\(958\) | −7.11357e7 | −2.50423 | ||||||||
\(959\) | 6.89716e6 | 0.242172 | ||||||||
\(960\) | −2.44845e7 | −0.857459 | ||||||||
\(961\) | −2.29190e7 | −0.800548 | ||||||||
\(962\) | −1.03886e7 | −0.361925 | ||||||||
\(963\) | −2.55586e7 | −0.888121 | ||||||||
\(964\) | 7.54332e7 | 2.61439 | ||||||||
\(965\) | −7.11605e6 | −0.245992 | ||||||||
\(966\) | −2.10306e7 | −0.725117 | ||||||||
\(967\) | −4.44968e7 | −1.53025 | −0.765126 | − | 0.643881i | \(-0.777323\pi\) | ||||
−0.765126 | + | 0.643881i | \(0.777323\pi\) | |||||||
\(968\) | −8.16656e6 | −0.280124 | ||||||||
\(969\) | −3.17311e6 | −0.108562 | ||||||||
\(970\) | −5.26182e6 | −0.179559 | ||||||||
\(971\) | −2.71793e7 | −0.925104 | −0.462552 | − | 0.886592i | \(-0.653066\pi\) | ||||
−0.462552 | + | 0.886592i | \(0.653066\pi\) | |||||||
\(972\) | −6.51619e7 | −2.21222 | ||||||||
\(973\) | 1.48525e7 | 0.502943 | ||||||||
\(974\) | −7.40041e7 | −2.49953 | ||||||||
\(975\) | −5.54260e6 | −0.186725 | ||||||||
\(976\) | 1.55006e8 | 5.20864 | ||||||||
\(977\) | −1.83806e7 | −0.616060 | −0.308030 | − | 0.951377i | \(-0.599670\pi\) | ||||
−0.308030 | + | 0.951377i | \(0.599670\pi\) | |||||||
\(978\) | −1.64115e7 | −0.548659 | ||||||||
\(979\) | −3.35199e6 | −0.111775 | ||||||||
\(980\) | −2.78443e7 | −0.926129 | ||||||||
\(981\) | 4.76753e6 | 0.158169 | ||||||||
\(982\) | −7.85478e7 | −2.59929 | ||||||||
\(983\) | 3.36412e7 | 1.11042 | 0.555211 | − | 0.831709i | \(-0.312637\pi\) | ||||
0.555211 | + | 0.831709i | \(0.312637\pi\) | |||||||
\(984\) | 5.66169e7 | 1.86405 | ||||||||
\(985\) | 2.65347e7 | 0.871413 | ||||||||
\(986\) | 2.15903e7 | 0.707238 | ||||||||
\(987\) | 1.55661e7 | 0.508612 | ||||||||
\(988\) | 2.36366e7 | 0.770357 | ||||||||
\(989\) | −8.66540e6 | −0.281707 | ||||||||
\(990\) | 3.71431e6 | 0.120445 | ||||||||
\(991\) | −4.62718e7 | −1.49669 | −0.748346 | − | 0.663308i | \(-0.769152\pi\) | ||||
−0.748346 | + | 0.663308i | \(0.769152\pi\) | |||||||
\(992\) | −4.27455e7 | −1.37915 | ||||||||
\(993\) | −5.27477e6 | −0.169758 | ||||||||
\(994\) | 4.22125e6 | 0.135511 | ||||||||
\(995\) | −7.91707e6 | −0.253517 | ||||||||
\(996\) | −4.99950e7 | −1.59690 | ||||||||
\(997\) | −2.98971e7 | −0.952556 | −0.476278 | − | 0.879295i | \(-0.658014\pi\) | ||||
−0.476278 | + | 0.879295i | \(0.658014\pi\) | |||||||
\(998\) | 1.09708e8 | 3.48668 | ||||||||
\(999\) | 5.01051e6 | 0.158843 |
(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 | 1045.6.a.h.1.1 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.h.1.1 | ✓ | 40 | 1.1 | even | 1 | trivial |