Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(91.4187772934\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 1748x^{2} - 8028x + 111960 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-38.2281\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | −34.1064 | −0.263082 | −0.131541 | − | 0.991311i | \(-0.541992\pi\) | ||||
−0.131541 | + | 0.991311i | \(0.541992\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 31.8722 | 0.0794201 | 0.0397100 | − | 0.999211i | \(-0.487357\pi\) | ||||
0.0397100 | + | 0.999211i | \(0.487357\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | 149.931 | 0.246055 | 0.123028 | − | 0.992403i | \(-0.460740\pi\) | ||||
0.123028 | + | 0.992403i | \(0.460740\pi\) | |||||||
\(14\) | 136.426 | 0.186027 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −915.453 | −0.768270 | −0.384135 | − | 0.923277i | \(-0.625500\pi\) | ||||
−0.384135 | + | 0.923277i | \(0.625500\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −306.957 | −0.151890 | ||||||||
\(22\) | −127.489 | −0.0561585 | ||||||||
\(23\) | −2354.30 | −0.927986 | −0.463993 | − | 0.885839i | \(-0.653584\pi\) | ||||
−0.463993 | + | 0.885839i | \(0.653584\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −599.724 | −0.173987 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −545.702 | −0.131541 | ||||||||
\(29\) | 7726.26 | 1.70598 | 0.852990 | − | 0.521926i | \(-0.174786\pi\) | ||||
0.852990 | + | 0.521926i | \(0.174786\pi\) | |||||||
\(30\) | −900.000 | −0.182574 | ||||||||
\(31\) | −2288.97 | −0.427795 | −0.213898 | − | 0.976856i | \(-0.568616\pi\) | ||||
−0.213898 | + | 0.976856i | \(0.568616\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 286.850 | 0.0458532 | ||||||||
\(34\) | 3661.81 | 0.543249 | ||||||||
\(35\) | −852.660 | −0.117654 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −12623.5 | −1.51592 | −0.757959 | − | 0.652302i | \(-0.773803\pi\) | ||||
−0.757959 | + | 0.652302i | \(0.773803\pi\) | |||||||
\(38\) | 1444.00 | 0.162221 | ||||||||
\(39\) | 1349.38 | 0.142060 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | 4219.60 | 0.392023 | 0.196012 | − | 0.980602i | \(-0.437201\pi\) | ||||
0.196012 | + | 0.980602i | \(0.437201\pi\) | |||||||
\(42\) | 1227.83 | 0.107403 | ||||||||
\(43\) | 2698.26 | 0.222542 | 0.111271 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111271 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(44\) | 509.955 | 0.0397100 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | 9417.19 | 0.656185 | ||||||||
\(47\) | −23938.1 | −1.58068 | −0.790340 | − | 0.612668i | \(-0.790096\pi\) | ||||
−0.790340 | + | 0.612668i | \(0.790096\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | −15643.8 | −0.930788 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −8239.08 | −0.443561 | ||||||||
\(52\) | 2398.89 | 0.123028 | ||||||||
\(53\) | 11944.5 | 0.584087 | 0.292043 | − | 0.956405i | \(-0.405665\pi\) | ||||
0.292043 | + | 0.956405i | \(0.405665\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 796.805 | 0.0355177 | ||||||||
\(56\) | 2182.81 | 0.0930134 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | −30905.0 | −1.20631 | ||||||||
\(59\) | −52867.6 | −1.97724 | −0.988620 | − | 0.150437i | \(-0.951932\pi\) | ||||
−0.988620 | + | 0.150437i | \(0.951932\pi\) | |||||||
\(60\) | 3600.00 | 0.129099 | ||||||||
\(61\) | −20386.5 | −0.701486 | −0.350743 | − | 0.936472i | \(-0.614071\pi\) | ||||
−0.350743 | + | 0.936472i | \(0.614071\pi\) | |||||||
\(62\) | 9155.88 | 0.302497 | ||||||||
\(63\) | −2762.62 | −0.0876939 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 3748.27 | 0.110039 | ||||||||
\(66\) | −1147.40 | −0.0324231 | ||||||||
\(67\) | 60223.7 | 1.63901 | 0.819503 | − | 0.573075i | \(-0.194249\pi\) | ||||
0.819503 | + | 0.573075i | \(0.194249\pi\) | |||||||
\(68\) | −14647.2 | −0.384135 | ||||||||
\(69\) | −21188.7 | −0.535773 | ||||||||
\(70\) | 3410.64 | 0.0831937 | ||||||||
\(71\) | −2912.51 | −0.0685681 | −0.0342840 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342840 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 27640.1 | 0.607061 | 0.303531 | − | 0.952822i | \(-0.401835\pi\) | ||||
0.303531 | + | 0.952822i | \(0.401835\pi\) | |||||||
\(74\) | 50494.0 | 1.07192 | ||||||||
\(75\) | 5625.00 | 0.115470 | ||||||||
\(76\) | −5776.00 | −0.114708 | ||||||||
\(77\) | −1087.05 | −0.0208940 | ||||||||
\(78\) | −5397.51 | −0.100452 | ||||||||
\(79\) | 26610.9 | 0.479725 | 0.239862 | − | 0.970807i | \(-0.422898\pi\) | ||||
0.239862 | + | 0.970807i | \(0.422898\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −16878.4 | −0.277202 | ||||||||
\(83\) | −67400.5 | −1.07391 | −0.536955 | − | 0.843611i | \(-0.680425\pi\) | ||||
−0.536955 | + | 0.843611i | \(0.680425\pi\) | |||||||
\(84\) | −4911.32 | −0.0759451 | ||||||||
\(85\) | −22886.3 | −0.343581 | ||||||||
\(86\) | −10793.0 | −0.157361 | ||||||||
\(87\) | 69536.3 | 0.984949 | ||||||||
\(88\) | −2039.82 | −0.0280792 | ||||||||
\(89\) | 90174.9 | 1.20673 | 0.603366 | − | 0.797465i | \(-0.293826\pi\) | ||||
0.603366 | + | 0.797465i | \(0.293826\pi\) | |||||||
\(90\) | −8100.00 | −0.105409 | ||||||||
\(91\) | −5113.60 | −0.0647326 | ||||||||
\(92\) | −37668.7 | −0.463993 | ||||||||
\(93\) | −20600.7 | −0.246988 | ||||||||
\(94\) | 95752.2 | 1.11771 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −142174. | −1.53423 | −0.767114 | − | 0.641511i | \(-0.778308\pi\) | ||||
−0.767114 | + | 0.641511i | \(0.778308\pi\) | |||||||
\(98\) | 62575.0 | 0.658167 | ||||||||
\(99\) | 2581.65 | 0.0264734 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 90923.0 | 0.886891 | 0.443446 | − | 0.896301i | \(-0.353756\pi\) | ||||
0.443446 | + | 0.896301i | \(0.353756\pi\) | |||||||
\(102\) | 32956.3 | 0.313645 | ||||||||
\(103\) | 27767.1 | 0.257892 | 0.128946 | − | 0.991652i | \(-0.458841\pi\) | ||||
0.128946 | + | 0.991652i | \(0.458841\pi\) | |||||||
\(104\) | −9595.58 | −0.0869937 | ||||||||
\(105\) | −7673.94 | −0.0679274 | ||||||||
\(106\) | −47777.9 | −0.413012 | ||||||||
\(107\) | −25276.8 | −0.213433 | −0.106717 | − | 0.994289i | \(-0.534034\pi\) | ||||
−0.106717 | + | 0.994289i | \(0.534034\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | 18627.6 | 0.150172 | 0.0750861 | − | 0.997177i | \(-0.476077\pi\) | ||||
0.0750861 | + | 0.997177i | \(0.476077\pi\) | |||||||
\(110\) | −3187.22 | −0.0251148 | ||||||||
\(111\) | −113612. | −0.875216 | ||||||||
\(112\) | −8731.23 | −0.0657704 | ||||||||
\(113\) | 26316.7 | 0.193881 | 0.0969404 | − | 0.995290i | \(-0.469094\pi\) | ||||
0.0969404 | + | 0.995290i | \(0.469094\pi\) | |||||||
\(114\) | 12996.0 | 0.0936586 | ||||||||
\(115\) | −58857.4 | −0.415008 | ||||||||
\(116\) | 123620. | 0.852990 | ||||||||
\(117\) | 12144.4 | 0.0820184 | ||||||||
\(118\) | 211470. | 1.39812 | ||||||||
\(119\) | 31222.8 | 0.202118 | ||||||||
\(120\) | −14400.0 | −0.0912871 | ||||||||
\(121\) | −160035. | −0.993692 | ||||||||
\(122\) | 81546.2 | 0.496025 | ||||||||
\(123\) | 37976.4 | 0.226335 | ||||||||
\(124\) | −36623.5 | −0.213898 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 11050.5 | 0.0620089 | ||||||||
\(127\) | −146357. | −0.805202 | −0.402601 | − | 0.915376i | \(-0.631894\pi\) | ||||
−0.402601 | + | 0.915376i | \(0.631894\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 24284.3 | 0.128485 | ||||||||
\(130\) | −14993.1 | −0.0778095 | ||||||||
\(131\) | 190779. | 0.971299 | 0.485650 | − | 0.874154i | \(-0.338583\pi\) | ||||
0.485650 | + | 0.874154i | \(0.338583\pi\) | |||||||
\(132\) | 4589.60 | 0.0229266 | ||||||||
\(133\) | 12312.4 | 0.0603551 | ||||||||
\(134\) | −240895. | −1.15895 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | 58589.0 | 0.271624 | ||||||||
\(137\) | −347454. | −1.58160 | −0.790799 | − | 0.612076i | \(-0.790335\pi\) | ||||
−0.790799 | + | 0.612076i | \(0.790335\pi\) | |||||||
\(138\) | 84754.7 | 0.378849 | ||||||||
\(139\) | −108960. | −0.478334 | −0.239167 | − | 0.970978i | \(-0.576874\pi\) | ||||
−0.239167 | + | 0.970978i | \(0.576874\pi\) | |||||||
\(140\) | −13642.6 | −0.0588268 | ||||||||
\(141\) | −215442. | −0.912607 | ||||||||
\(142\) | 11650.1 | 0.0484850 | ||||||||
\(143\) | 4778.63 | 0.0195417 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 193156. | 0.762938 | ||||||||
\(146\) | −110560. | −0.429257 | ||||||||
\(147\) | −140794. | −0.537391 | ||||||||
\(148\) | −201976. | −0.757959 | ||||||||
\(149\) | 137095. | 0.505890 | 0.252945 | − | 0.967481i | \(-0.418601\pi\) | ||||
0.252945 | + | 0.967481i | \(0.418601\pi\) | |||||||
\(150\) | −22500.0 | −0.0816497 | ||||||||
\(151\) | −288866. | −1.03099 | −0.515495 | − | 0.856893i | \(-0.672392\pi\) | ||||
−0.515495 | + | 0.856893i | \(0.672392\pi\) | |||||||
\(152\) | 23104.0 | 0.0811107 | ||||||||
\(153\) | −74151.7 | −0.256090 | ||||||||
\(154\) | 4348.18 | 0.0147743 | ||||||||
\(155\) | −57224.3 | −0.191316 | ||||||||
\(156\) | 21590.1 | 0.0710301 | ||||||||
\(157\) | 30764.1 | 0.0996081 | 0.0498041 | − | 0.998759i | \(-0.484140\pi\) | ||||
0.0498041 | + | 0.998759i | \(0.484140\pi\) | |||||||
\(158\) | −106444. | −0.339217 | ||||||||
\(159\) | 107500. | 0.337223 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | 80296.5 | 0.244136 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −124833. | −0.368009 | −0.184005 | − | 0.982925i | \(-0.558906\pi\) | ||||
−0.184005 | + | 0.982925i | \(0.558906\pi\) | |||||||
\(164\) | 67513.6 | 0.196012 | ||||||||
\(165\) | 7171.24 | 0.0205062 | ||||||||
\(166\) | 269602. | 0.759369 | ||||||||
\(167\) | 101944. | 0.282859 | 0.141429 | − | 0.989948i | \(-0.454830\pi\) | ||||
0.141429 | + | 0.989948i | \(0.454830\pi\) | |||||||
\(168\) | 19645.3 | 0.0537013 | ||||||||
\(169\) | −348814. | −0.939457 | ||||||||
\(170\) | 91545.3 | 0.242948 | ||||||||
\(171\) | −29241.0 | −0.0764719 | ||||||||
\(172\) | 43172.1 | 0.111271 | ||||||||
\(173\) | 187595. | 0.476548 | 0.238274 | − | 0.971198i | \(-0.423418\pi\) | ||||
0.238274 | + | 0.971198i | \(0.423418\pi\) | |||||||
\(174\) | −278145. | −0.696464 | ||||||||
\(175\) | −21316.5 | −0.0526163 | ||||||||
\(176\) | 8159.28 | 0.0198550 | ||||||||
\(177\) | −475808. | −1.14156 | ||||||||
\(178\) | −360700. | −0.853288 | ||||||||
\(179\) | 177581. | 0.414252 | 0.207126 | − | 0.978314i | \(-0.433589\pi\) | ||||
0.207126 | + | 0.978314i | \(0.433589\pi\) | |||||||
\(180\) | 32400.0 | 0.0745356 | ||||||||
\(181\) | −673638. | −1.52838 | −0.764188 | − | 0.644994i | \(-0.776860\pi\) | ||||
−0.764188 | + | 0.644994i | \(0.776860\pi\) | |||||||
\(182\) | 20454.4 | 0.0457729 | ||||||||
\(183\) | −183479. | −0.405003 | ||||||||
\(184\) | 150675. | 0.328093 | ||||||||
\(185\) | −315588. | −0.677939 | ||||||||
\(186\) | 82403.0 | 0.174647 | ||||||||
\(187\) | −29177.5 | −0.0610160 | ||||||||
\(188\) | −383009. | −0.790340 | ||||||||
\(189\) | −24863.6 | −0.0506301 | ||||||||
\(190\) | 36100.0 | 0.0725476 | ||||||||
\(191\) | −959796. | −1.90369 | −0.951843 | − | 0.306585i | \(-0.900814\pi\) | ||||
−0.951843 | + | 0.306585i | \(0.900814\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | −447537. | −0.864840 | −0.432420 | − | 0.901672i | \(-0.642340\pi\) | ||||
−0.432420 | + | 0.901672i | \(0.642340\pi\) | |||||||
\(194\) | 568695. | 1.08486 | ||||||||
\(195\) | 33734.5 | 0.0635312 | ||||||||
\(196\) | −250300. | −0.465394 | ||||||||
\(197\) | 70806.9 | 0.129990 | 0.0649951 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649951 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(198\) | −10326.6 | −0.0187195 | ||||||||
\(199\) | −864193. | −1.54696 | −0.773478 | − | 0.633823i | \(-0.781485\pi\) | ||||
−0.773478 | + | 0.633823i | \(0.781485\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 542014. | 0.946281 | ||||||||
\(202\) | −363692. | −0.627127 | ||||||||
\(203\) | −263515. | −0.448812 | ||||||||
\(204\) | −131825. | −0.221780 | ||||||||
\(205\) | 105490. | 0.175318 | ||||||||
\(206\) | −111069. | −0.182357 | ||||||||
\(207\) | −190698. | −0.309329 | ||||||||
\(208\) | 38382.3 | 0.0615138 | ||||||||
\(209\) | −11505.9 | −0.0182202 | ||||||||
\(210\) | 30695.7 | 0.0480319 | ||||||||
\(211\) | −418770. | −0.647545 | −0.323772 | − | 0.946135i | \(-0.604951\pi\) | ||||
−0.323772 | + | 0.946135i | \(0.604951\pi\) | |||||||
\(212\) | 191112. | 0.292043 | ||||||||
\(213\) | −26212.6 | −0.0395878 | ||||||||
\(214\) | 101107. | 0.150920 | ||||||||
\(215\) | 67456.5 | 0.0995239 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 78068.5 | 0.112545 | ||||||||
\(218\) | −74510.2 | −0.106188 | ||||||||
\(219\) | 248761. | 0.350487 | ||||||||
\(220\) | 12748.9 | 0.0177589 | ||||||||
\(221\) | −137255. | −0.189037 | ||||||||
\(222\) | 454446. | 0.618871 | ||||||||
\(223\) | −1.02581e6 | −1.38135 | −0.690675 | − | 0.723165i | \(-0.742686\pi\) | ||||
−0.690675 | + | 0.723165i | \(0.742686\pi\) | |||||||
\(224\) | 34924.9 | 0.0465067 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −105267. | −0.137094 | ||||||||
\(227\) | −782919. | −1.00844 | −0.504222 | − | 0.863574i | \(-0.668221\pi\) | ||||
−0.504222 | + | 0.863574i | \(0.668221\pi\) | |||||||
\(228\) | −51984.0 | −0.0662266 | ||||||||
\(229\) | 879635. | 1.10844 | 0.554222 | − | 0.832369i | \(-0.313016\pi\) | ||||
0.554222 | + | 0.832369i | \(0.313016\pi\) | |||||||
\(230\) | 235430. | 0.293455 | ||||||||
\(231\) | −9783.41 | −0.0120631 | ||||||||
\(232\) | −494480. | −0.603155 | ||||||||
\(233\) | 112744. | 0.136051 | 0.0680257 | − | 0.997684i | \(-0.478330\pi\) | ||||
0.0680257 | + | 0.997684i | \(0.478330\pi\) | |||||||
\(234\) | −48577.6 | −0.0579958 | ||||||||
\(235\) | −598451. | −0.706902 | ||||||||
\(236\) | −845881. | −0.988620 | ||||||||
\(237\) | 239498. | 0.276969 | ||||||||
\(238\) | −124891. | −0.142919 | ||||||||
\(239\) | 99236.2 | 0.112376 | 0.0561882 | − | 0.998420i | \(-0.482105\pi\) | ||||
0.0561882 | + | 0.998420i | \(0.482105\pi\) | |||||||
\(240\) | 57600.0 | 0.0645497 | ||||||||
\(241\) | −107560. | −0.119291 | −0.0596456 | − | 0.998220i | \(-0.518997\pi\) | ||||
−0.0596456 | + | 0.998220i | \(0.518997\pi\) | |||||||
\(242\) | 640141. | 0.702647 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −326185. | −0.350743 | ||||||||
\(245\) | −391094. | −0.416261 | ||||||||
\(246\) | −151906. | −0.160043 | ||||||||
\(247\) | −54125.1 | −0.0564490 | ||||||||
\(248\) | 146494. | 0.151248 | ||||||||
\(249\) | −606604. | −0.620022 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | 310433. | 0.311016 | 0.155508 | − | 0.987835i | \(-0.450299\pi\) | ||||
0.155508 | + | 0.987835i | \(0.450299\pi\) | |||||||
\(252\) | −44201.9 | −0.0438469 | ||||||||
\(253\) | −75036.6 | −0.0737007 | ||||||||
\(254\) | 585429. | 0.569364 | ||||||||
\(255\) | −205977. | −0.198366 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 285738. | 0.269858 | 0.134929 | − | 0.990855i | \(-0.456919\pi\) | ||||
0.134929 | + | 0.990855i | \(0.456919\pi\) | |||||||
\(258\) | −97137.3 | −0.0908525 | ||||||||
\(259\) | 430542. | 0.398810 | ||||||||
\(260\) | 59972.4 | 0.0550196 | ||||||||
\(261\) | 625827. | 0.568660 | ||||||||
\(262\) | −763117. | −0.686812 | ||||||||
\(263\) | 1.18199e6 | 1.05372 | 0.526860 | − | 0.849952i | \(-0.323369\pi\) | ||||
0.526860 | + | 0.849952i | \(0.323369\pi\) | |||||||
\(264\) | −18358.4 | −0.0162116 | ||||||||
\(265\) | 298612. | 0.261211 | ||||||||
\(266\) | −49249.6 | −0.0426775 | ||||||||
\(267\) | 811574. | 0.696707 | ||||||||
\(268\) | 963580. | 0.819503 | ||||||||
\(269\) | 1.21848e6 | 1.02669 | 0.513344 | − | 0.858183i | \(-0.328406\pi\) | ||||
0.513344 | + | 0.858183i | \(0.328406\pi\) | |||||||
\(270\) | −72900.0 | −0.0608581 | ||||||||
\(271\) | −2.03262e6 | −1.68126 | −0.840628 | − | 0.541613i | \(-0.817814\pi\) | ||||
−0.840628 | + | 0.541613i | \(0.817814\pi\) | |||||||
\(272\) | −234356. | −0.192067 | ||||||||
\(273\) | −46022.4 | −0.0373734 | ||||||||
\(274\) | 1.38982e6 | 1.11836 | ||||||||
\(275\) | 19920.1 | 0.0158840 | ||||||||
\(276\) | −339019. | −0.267887 | ||||||||
\(277\) | −2.02586e6 | −1.58639 | −0.793196 | − | 0.608967i | \(-0.791584\pi\) | ||||
−0.793196 | + | 0.608967i | \(0.791584\pi\) | |||||||
\(278\) | 435841. | 0.338233 | ||||||||
\(279\) | −185407. | −0.142598 | ||||||||
\(280\) | 54570.2 | 0.0415969 | ||||||||
\(281\) | −703127. | −0.531212 | −0.265606 | − | 0.964082i | \(-0.585572\pi\) | ||||
−0.265606 | + | 0.964082i | \(0.585572\pi\) | |||||||
\(282\) | 861770. | 0.645310 | ||||||||
\(283\) | −2.47935e6 | −1.84023 | −0.920115 | − | 0.391649i | \(-0.871905\pi\) | ||||
−0.920115 | + | 0.391649i | \(0.871905\pi\) | |||||||
\(284\) | −46600.2 | −0.0342840 | ||||||||
\(285\) | −81225.0 | −0.0592349 | ||||||||
\(286\) | −19114.5 | −0.0138181 | ||||||||
\(287\) | −143915. | −0.103134 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −581803. | −0.409762 | ||||||||
\(290\) | −772626. | −0.539479 | ||||||||
\(291\) | −1.27956e6 | −0.885787 | ||||||||
\(292\) | 442242. | 0.303531 | ||||||||
\(293\) | −2.81648e6 | −1.91663 | −0.958314 | − | 0.285718i | \(-0.907768\pi\) | ||||
−0.958314 | + | 0.285718i | \(0.907768\pi\) | |||||||
\(294\) | 563175. | 0.379993 | ||||||||
\(295\) | −1.32169e6 | −0.884248 | ||||||||
\(296\) | 807904. | 0.535958 | ||||||||
\(297\) | 23234.8 | 0.0152844 | ||||||||
\(298\) | −548381. | −0.357718 | ||||||||
\(299\) | −352982. | −0.228336 | ||||||||
\(300\) | 90000.0 | 0.0577350 | ||||||||
\(301\) | −92027.8 | −0.0585468 | ||||||||
\(302\) | 1.15546e6 | 0.729019 | ||||||||
\(303\) | 818307. | 0.512047 | ||||||||
\(304\) | −92416.0 | −0.0573539 | ||||||||
\(305\) | −509664. | −0.313714 | ||||||||
\(306\) | 296607. | 0.181083 | ||||||||
\(307\) | 2.31303e6 | 1.40067 | 0.700333 | − | 0.713816i | \(-0.253035\pi\) | ||||
0.700333 | + | 0.713816i | \(0.253035\pi\) | |||||||
\(308\) | −17392.7 | −0.0104470 | ||||||||
\(309\) | 249904. | 0.148894 | ||||||||
\(310\) | 228897. | 0.135281 | ||||||||
\(311\) | 2.61499e6 | 1.53310 | 0.766549 | − | 0.642186i | \(-0.221972\pi\) | ||||
0.766549 | + | 0.642186i | \(0.221972\pi\) | |||||||
\(312\) | −86360.2 | −0.0502258 | ||||||||
\(313\) | 3.35313e6 | 1.93459 | 0.967296 | − | 0.253649i | \(-0.0816308\pi\) | ||||
0.967296 | + | 0.253649i | \(0.0816308\pi\) | |||||||
\(314\) | −123056. | −0.0704336 | ||||||||
\(315\) | −69065.4 | −0.0392179 | ||||||||
\(316\) | 425775. | 0.239862 | ||||||||
\(317\) | 1.20646e6 | 0.674320 | 0.337160 | − | 0.941447i | \(-0.390534\pi\) | ||||
0.337160 | + | 0.941447i | \(0.390534\pi\) | |||||||
\(318\) | −430001. | −0.238452 | ||||||||
\(319\) | 246253. | 0.135489 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | −227491. | −0.123226 | ||||||||
\(322\) | −321186. | −0.172630 | ||||||||
\(323\) | 330478. | 0.176253 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 93706.8 | 0.0492111 | ||||||||
\(326\) | 499330. | 0.260222 | ||||||||
\(327\) | 167648. | 0.0867020 | ||||||||
\(328\) | −270054. | −0.138601 | ||||||||
\(329\) | 816440. | 0.415848 | ||||||||
\(330\) | −28685.0 | −0.0145001 | ||||||||
\(331\) | 1.34627e6 | 0.675403 | 0.337701 | − | 0.941253i | \(-0.390351\pi\) | ||||
0.337701 | + | 0.941253i | \(0.390351\pi\) | |||||||
\(332\) | −1.07841e6 | −0.536955 | ||||||||
\(333\) | −1.02250e6 | −0.505306 | ||||||||
\(334\) | −407775. | −0.200011 | ||||||||
\(335\) | 1.50559e6 | 0.732986 | ||||||||
\(336\) | −78581.1 | −0.0379726 | ||||||||
\(337\) | −4.11904e6 | −1.97570 | −0.987850 | − | 0.155409i | \(-0.950331\pi\) | ||||
−0.987850 | + | 0.155409i | \(0.950331\pi\) | |||||||
\(338\) | 1.39525e6 | 0.664296 | ||||||||
\(339\) | 236850. | 0.111937 | ||||||||
\(340\) | −366181. | −0.171790 | ||||||||
\(341\) | −72954.5 | −0.0339755 | ||||||||
\(342\) | 116964. | 0.0540738 | ||||||||
\(343\) | 1.10678e6 | 0.507955 | ||||||||
\(344\) | −172689. | −0.0786806 | ||||||||
\(345\) | −529717. | −0.239605 | ||||||||
\(346\) | −750381. | −0.336970 | ||||||||
\(347\) | 4.06552e6 | 1.81256 | 0.906281 | − | 0.422676i | \(-0.138909\pi\) | ||||
0.906281 | + | 0.422676i | \(0.138909\pi\) | |||||||
\(348\) | 1.11258e6 | 0.492474 | ||||||||
\(349\) | −1.68169e6 | −0.739065 | −0.369532 | − | 0.929218i | \(-0.620482\pi\) | ||||
−0.369532 | + | 0.929218i | \(0.620482\pi\) | |||||||
\(350\) | 85266.0 | 0.0372054 | ||||||||
\(351\) | 109300. | 0.0473534 | ||||||||
\(352\) | −32637.1 | −0.0140396 | ||||||||
\(353\) | −483067. | −0.206334 | −0.103167 | − | 0.994664i | \(-0.532898\pi\) | ||||
−0.103167 | + | 0.994664i | \(0.532898\pi\) | |||||||
\(354\) | 1.90323e6 | 0.807205 | ||||||||
\(355\) | −72812.8 | −0.0306646 | ||||||||
\(356\) | 1.44280e6 | 0.603366 | ||||||||
\(357\) | 281005. | 0.116693 | ||||||||
\(358\) | −710325. | −0.292920 | ||||||||
\(359\) | 65764.0 | 0.0269310 | 0.0134655 | − | 0.999909i | \(-0.495714\pi\) | ||||
0.0134655 | + | 0.999909i | \(0.495714\pi\) | |||||||
\(360\) | −129600. | −0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 2.69455e6 | 1.08072 | ||||||||
\(363\) | −1.44032e6 | −0.573709 | ||||||||
\(364\) | −81817.6 | −0.0323663 | ||||||||
\(365\) | 691002. | 0.271486 | ||||||||
\(366\) | 733916. | 0.286380 | ||||||||
\(367\) | 1.90927e6 | 0.739948 | 0.369974 | − | 0.929042i | \(-0.379367\pi\) | ||||
0.369974 | + | 0.929042i | \(0.379367\pi\) | |||||||
\(368\) | −602700. | −0.231997 | ||||||||
\(369\) | 341788. | 0.130674 | ||||||||
\(370\) | 1.26235e6 | 0.479375 | ||||||||
\(371\) | −407383. | −0.153662 | ||||||||
\(372\) | −329612. | −0.123494 | ||||||||
\(373\) | −2.86806e6 | −1.06737 | −0.533687 | − | 0.845682i | \(-0.679194\pi\) | ||||
−0.533687 | + | 0.845682i | \(0.679194\pi\) | |||||||
\(374\) | 116710. | 0.0431448 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | 1.53204e6 | 0.558855 | ||||||||
\(377\) | 1.15840e6 | 0.419766 | ||||||||
\(378\) | 99454.2 | 0.0358009 | ||||||||
\(379\) | 919638. | 0.328866 | 0.164433 | − | 0.986388i | \(-0.447421\pi\) | ||||
0.164433 | + | 0.986388i | \(0.447421\pi\) | |||||||
\(380\) | −144400. | −0.0512989 | ||||||||
\(381\) | −1.31721e6 | −0.464883 | ||||||||
\(382\) | 3.83918e6 | 1.34611 | ||||||||
\(383\) | −4.50769e6 | −1.57021 | −0.785104 | − | 0.619364i | \(-0.787391\pi\) | ||||
−0.785104 | + | 0.619364i | \(0.787391\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −27176.1 | −0.00934406 | ||||||||
\(386\) | 1.79015e6 | 0.611535 | ||||||||
\(387\) | 218559. | 0.0741807 | ||||||||
\(388\) | −2.27478e6 | −0.767114 | ||||||||
\(389\) | 5.57054e6 | 1.86648 | 0.933240 | − | 0.359254i | \(-0.116969\pi\) | ||||
0.933240 | + | 0.359254i | \(0.116969\pi\) | |||||||
\(390\) | −134938. | −0.0449234 | ||||||||
\(391\) | 2.15525e6 | 0.712944 | ||||||||
\(392\) | 1.00120e6 | 0.329083 | ||||||||
\(393\) | 1.71701e6 | 0.560780 | ||||||||
\(394\) | −283228. | −0.0919169 | ||||||||
\(395\) | 665273. | 0.214539 | ||||||||
\(396\) | 41306.4 | 0.0132367 | ||||||||
\(397\) | −1.16290e6 | −0.370312 | −0.185156 | − | 0.982709i | \(-0.559279\pi\) | ||||
−0.185156 | + | 0.982709i | \(0.559279\pi\) | |||||||
\(398\) | 3.45677e6 | 1.09386 | ||||||||
\(399\) | 110812. | 0.0348460 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −2.35244e6 | −0.730563 | −0.365281 | − | 0.930897i | \(-0.619027\pi\) | ||||
−0.365281 | + | 0.930897i | \(0.619027\pi\) | |||||||
\(402\) | −2.16805e6 | −0.669122 | ||||||||
\(403\) | −343187. | −0.105261 | ||||||||
\(404\) | 1.45477e6 | 0.443446 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | 1.05406e6 | 0.317358 | ||||||||
\(407\) | −402339. | −0.120394 | ||||||||
\(408\) | 527301. | 0.156822 | ||||||||
\(409\) | 5.44543e6 | 1.60962 | 0.804811 | − | 0.593531i | \(-0.202266\pi\) | ||||
0.804811 | + | 0.593531i | \(0.202266\pi\) | |||||||
\(410\) | −421960. | −0.123969 | ||||||||
\(411\) | −3.12709e6 | −0.913136 | ||||||||
\(412\) | 444274. | 0.128946 | ||||||||
\(413\) | 1.80312e6 | 0.520175 | ||||||||
\(414\) | 762792. | 0.218728 | ||||||||
\(415\) | −1.68501e6 | −0.480267 | ||||||||
\(416\) | −153529. | −0.0434968 | ||||||||
\(417\) | −980642. | −0.276166 | ||||||||
\(418\) | 46023.4 | 0.0128836 | ||||||||
\(419\) | 4.12834e6 | 1.14879 | 0.574395 | − | 0.818578i | \(-0.305237\pi\) | ||||
0.574395 | + | 0.818578i | \(0.305237\pi\) | |||||||
\(420\) | −122783. | −0.0339637 | ||||||||
\(421\) | 5.15670e6 | 1.41797 | 0.708984 | − | 0.705224i | \(-0.249154\pi\) | ||||
0.708984 | + | 0.705224i | \(0.249154\pi\) | |||||||
\(422\) | 1.67508e6 | 0.457883 | ||||||||
\(423\) | −1.93898e6 | −0.526894 | ||||||||
\(424\) | −764446. | −0.206506 | ||||||||
\(425\) | −572158. | −0.153654 | ||||||||
\(426\) | 104850. | 0.0279928 | ||||||||
\(427\) | 695311. | 0.184548 | ||||||||
\(428\) | −404428. | −0.106717 | ||||||||
\(429\) | 43007.6 | 0.0112824 | ||||||||
\(430\) | −269826. | −0.0703740 | ||||||||
\(431\) | −1.43854e6 | −0.373017 | −0.186509 | − | 0.982453i | \(-0.559717\pi\) | ||||
−0.186509 | + | 0.982453i | \(0.559717\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | 4.26997e6 | 1.09447 | 0.547237 | − | 0.836978i | \(-0.315680\pi\) | ||||
0.547237 | + | 0.836978i | \(0.315680\pi\) | |||||||
\(434\) | −312274. | −0.0795814 | ||||||||
\(435\) | 1.73841e6 | 0.440482 | ||||||||
\(436\) | 298041. | 0.0750861 | ||||||||
\(437\) | 849901. | 0.212895 | ||||||||
\(438\) | −995043. | −0.247832 | ||||||||
\(439\) | 5.38398e6 | 1.33334 | 0.666672 | − | 0.745351i | \(-0.267718\pi\) | ||||
0.666672 | + | 0.745351i | \(0.267718\pi\) | |||||||
\(440\) | −50995.5 | −0.0125574 | ||||||||
\(441\) | −1.26714e6 | −0.310263 | ||||||||
\(442\) | 549019. | 0.133669 | ||||||||
\(443\) | 1.83295e6 | 0.443752 | 0.221876 | − | 0.975075i | \(-0.428782\pi\) | ||||
0.221876 | + | 0.975075i | \(0.428782\pi\) | |||||||
\(444\) | −1.81779e6 | −0.437608 | ||||||||
\(445\) | 2.25437e6 | 0.539667 | ||||||||
\(446\) | 4.10323e6 | 0.976762 | ||||||||
\(447\) | 1.23386e6 | 0.292076 | ||||||||
\(448\) | −139700. | −0.0328852 | ||||||||
\(449\) | −5.33052e6 | −1.24783 | −0.623913 | − | 0.781494i | \(-0.714458\pi\) | ||||
−0.623913 | + | 0.781494i | \(0.714458\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | 134488. | 0.0311345 | ||||||||
\(452\) | 421067. | 0.0969404 | ||||||||
\(453\) | −2.59979e6 | −0.595242 | ||||||||
\(454\) | 3.13168e6 | 0.713078 | ||||||||
\(455\) | −127840. | −0.0289493 | ||||||||
\(456\) | 207936. | 0.0468293 | ||||||||
\(457\) | 560697. | 0.125585 | 0.0627925 | − | 0.998027i | \(-0.479999\pi\) | ||||
0.0627925 | + | 0.998027i | \(0.479999\pi\) | |||||||
\(458\) | −3.51854e6 | −0.783788 | ||||||||
\(459\) | −667365. | −0.147854 | ||||||||
\(460\) | −941719. | −0.207504 | ||||||||
\(461\) | 3.92602e6 | 0.860399 | 0.430200 | − | 0.902734i | \(-0.358443\pi\) | ||||
0.430200 | + | 0.902734i | \(0.358443\pi\) | |||||||
\(462\) | 39133.6 | 0.00852992 | ||||||||
\(463\) | −6.79474e6 | −1.47306 | −0.736529 | − | 0.676406i | \(-0.763537\pi\) | ||||
−0.736529 | + | 0.676406i | \(0.763537\pi\) | |||||||
\(464\) | 1.97792e6 | 0.426495 | ||||||||
\(465\) | −515018. | −0.110456 | ||||||||
\(466\) | −450975. | −0.0962028 | ||||||||
\(467\) | −1.43475e6 | −0.304427 | −0.152213 | − | 0.988348i | \(-0.548640\pi\) | ||||
−0.152213 | + | 0.988348i | \(0.548640\pi\) | |||||||
\(468\) | 194310. | 0.0410092 | ||||||||
\(469\) | −2.05401e6 | −0.431193 | ||||||||
\(470\) | 2.39381e6 | 0.499855 | ||||||||
\(471\) | 276877. | 0.0575088 | ||||||||
\(472\) | 3.38352e6 | 0.699060 | ||||||||
\(473\) | 85999.4 | 0.0176743 | ||||||||
\(474\) | −957993. | −0.195847 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | 499565. | 0.101059 | ||||||||
\(477\) | 967502. | 0.194696 | ||||||||
\(478\) | −396945. | −0.0794622 | ||||||||
\(479\) | 7.30911e6 | 1.45555 | 0.727773 | − | 0.685818i | \(-0.240556\pi\) | ||||
0.727773 | + | 0.685818i | \(0.240556\pi\) | |||||||
\(480\) | −230400. | −0.0456435 | ||||||||
\(481\) | −1.89265e6 | −0.373000 | ||||||||
\(482\) | 430240. | 0.0843516 | ||||||||
\(483\) | 722669. | 0.140952 | ||||||||
\(484\) | −2.56056e6 | −0.496846 | ||||||||
\(485\) | −3.55434e6 | −0.686128 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −3.60156e6 | −0.688126 | −0.344063 | − | 0.938947i | \(-0.611803\pi\) | ||||
−0.344063 | + | 0.938947i | \(0.611803\pi\) | |||||||
\(488\) | 1.30474e6 | 0.248013 | ||||||||
\(489\) | −1.12349e6 | −0.212470 | ||||||||
\(490\) | 1.56438e6 | 0.294341 | ||||||||
\(491\) | 7.80138e6 | 1.46039 | 0.730193 | − | 0.683241i | \(-0.239430\pi\) | ||||
0.730193 | + | 0.683241i | \(0.239430\pi\) | |||||||
\(492\) | 607623. | 0.113167 | ||||||||
\(493\) | −7.07302e6 | −1.31065 | ||||||||
\(494\) | 216500. | 0.0399154 | ||||||||
\(495\) | 64541.2 | 0.0118392 | ||||||||
\(496\) | −585977. | −0.106949 | ||||||||
\(497\) | 99335.3 | 0.0180390 | ||||||||
\(498\) | 2.42642e6 | 0.438422 | ||||||||
\(499\) | 946880. | 0.170233 | 0.0851165 | − | 0.996371i | \(-0.472874\pi\) | ||||
0.0851165 | + | 0.996371i | \(0.472874\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 917494. | 0.163309 | ||||||||
\(502\) | −1.24173e6 | −0.219922 | ||||||||
\(503\) | −5.54090e6 | −0.976474 | −0.488237 | − | 0.872711i | \(-0.662360\pi\) | ||||
−0.488237 | + | 0.872711i | \(0.662360\pi\) | |||||||
\(504\) | 176807. | 0.0310045 | ||||||||
\(505\) | 2.27308e6 | 0.396630 | ||||||||
\(506\) | 300146. | 0.0521143 | ||||||||
\(507\) | −3.13932e6 | −0.542396 | ||||||||
\(508\) | −2.34171e6 | −0.402601 | ||||||||
\(509\) | 4.56492e6 | 0.780977 | 0.390489 | − | 0.920608i | \(-0.372306\pi\) | ||||
0.390489 | + | 0.920608i | \(0.372306\pi\) | |||||||
\(510\) | 823908. | 0.140266 | ||||||||
\(511\) | −942704. | −0.159707 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | −1.14295e6 | −0.190818 | ||||||||
\(515\) | 694178. | 0.115333 | ||||||||
\(516\) | 388549. | 0.0642424 | ||||||||
\(517\) | −762958. | −0.125538 | ||||||||
\(518\) | −1.72217e6 | −0.282001 | ||||||||
\(519\) | 1.68836e6 | 0.275135 | ||||||||
\(520\) | −239889. | −0.0389048 | ||||||||
\(521\) | 5.99857e6 | 0.968174 | 0.484087 | − | 0.875020i | \(-0.339152\pi\) | ||||
0.484087 | + | 0.875020i | \(0.339152\pi\) | |||||||
\(522\) | −2.50331e6 | −0.402104 | ||||||||
\(523\) | −5273.94 | −0.000843103 0 | −0.000421552 | − | 1.00000i | \(-0.500134\pi\) | ||||
−0.000421552 | 1.00000i | \(0.500134\pi\) | ||||||||
\(524\) | 3.05247e6 | 0.485650 | ||||||||
\(525\) | −191848. | −0.0303781 | ||||||||
\(526\) | −4.72797e6 | −0.745092 | ||||||||
\(527\) | 2.09544e6 | 0.328662 | ||||||||
\(528\) | 73433.5 | 0.0114633 | ||||||||
\(529\) | −893629. | −0.138841 | ||||||||
\(530\) | −1.19445e6 | −0.184704 | ||||||||
\(531\) | −4.28227e6 | −0.659080 | ||||||||
\(532\) | 196998. | 0.0301775 | ||||||||
\(533\) | 632649. | 0.0964594 | ||||||||
\(534\) | −3.24630e6 | −0.492646 | ||||||||
\(535\) | −631919. | −0.0954503 | ||||||||
\(536\) | −3.85432e6 | −0.579476 | ||||||||
\(537\) | 1.59823e6 | 0.239168 | ||||||||
\(538\) | −4.87393e6 | −0.725979 | ||||||||
\(539\) | −498601. | −0.0739232 | ||||||||
\(540\) | 291600. | 0.0430331 | ||||||||
\(541\) | −7.25642e6 | −1.06593 | −0.532966 | − | 0.846137i | \(-0.678923\pi\) | ||||
−0.532966 | + | 0.846137i | \(0.678923\pi\) | |||||||
\(542\) | 8.13050e6 | 1.18883 | ||||||||
\(543\) | −6.06274e6 | −0.882408 | ||||||||
\(544\) | 937424. | 0.135812 | ||||||||
\(545\) | 465689. | 0.0671591 | ||||||||
\(546\) | 184090. | 0.0264270 | ||||||||
\(547\) | −4.30048e6 | −0.614537 | −0.307269 | − | 0.951623i | \(-0.599415\pi\) | ||||
−0.307269 | + | 0.951623i | \(0.599415\pi\) | |||||||
\(548\) | −5.55927e6 | −0.790799 | ||||||||
\(549\) | −1.65131e6 | −0.233829 | ||||||||
\(550\) | −79680.5 | −0.0112317 | ||||||||
\(551\) | −2.78918e6 | −0.391379 | ||||||||
\(552\) | 1.35607e6 | 0.189424 | ||||||||
\(553\) | −907602. | −0.126207 | ||||||||
\(554\) | 8.10345e6 | 1.12175 | ||||||||
\(555\) | −2.84029e6 | −0.391408 | ||||||||
\(556\) | −1.74336e6 | −0.239167 | ||||||||
\(557\) | 687162. | 0.0938471 | 0.0469235 | − | 0.998898i | \(-0.485058\pi\) | ||||
0.0469235 | + | 0.998898i | \(0.485058\pi\) | |||||||
\(558\) | 741627. | 0.100832 | ||||||||
\(559\) | 404552. | 0.0547577 | ||||||||
\(560\) | −218281. | −0.0294134 | ||||||||
\(561\) | −262597. | −0.0352276 | ||||||||
\(562\) | 2.81251e6 | 0.375623 | ||||||||
\(563\) | 5.51555e6 | 0.733361 | 0.366681 | − | 0.930347i | \(-0.380494\pi\) | ||||
0.366681 | + | 0.930347i | \(0.380494\pi\) | |||||||
\(564\) | −3.44708e6 | −0.456303 | ||||||||
\(565\) | 657917. | 0.0867061 | ||||||||
\(566\) | 9.91741e6 | 1.30124 | ||||||||
\(567\) | −223772. | −0.0292313 | ||||||||
\(568\) | 186401. | 0.0242425 | ||||||||
\(569\) | −5.32410e6 | −0.689391 | −0.344695 | − | 0.938715i | \(-0.612018\pi\) | ||||
−0.344695 | + | 0.938715i | \(0.612018\pi\) | |||||||
\(570\) | 324900. | 0.0418854 | ||||||||
\(571\) | 4.94172e6 | 0.634290 | 0.317145 | − | 0.948377i | \(-0.397276\pi\) | ||||
0.317145 | + | 0.948377i | \(0.397276\pi\) | |||||||
\(572\) | 76458.0 | 0.00977086 | ||||||||
\(573\) | −8.63816e6 | −1.09909 | ||||||||
\(574\) | 575661. | 0.0729268 | ||||||||
\(575\) | −1.47144e6 | −0.185597 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 3.57994e6 | 0.447647 | 0.223824 | − | 0.974630i | \(-0.428146\pi\) | ||||
0.223824 | + | 0.974630i | \(0.428146\pi\) | |||||||
\(578\) | 2.32721e6 | 0.289745 | ||||||||
\(579\) | −4.02784e6 | −0.499316 | ||||||||
\(580\) | 3.09050e6 | 0.381469 | ||||||||
\(581\) | 2.29879e6 | 0.282526 | ||||||||
\(582\) | 5.11825e6 | 0.626346 | ||||||||
\(583\) | 380696. | 0.0463882 | ||||||||
\(584\) | −1.76897e6 | −0.214629 | ||||||||
\(585\) | 303610. | 0.0366798 | ||||||||
\(586\) | 1.12659e7 | 1.35526 | ||||||||
\(587\) | −1.04531e7 | −1.25214 | −0.626069 | − | 0.779768i | \(-0.715337\pi\) | ||||
−0.626069 | + | 0.779768i | \(0.715337\pi\) | |||||||
\(588\) | −2.25270e6 | −0.268695 | ||||||||
\(589\) | 826319. | 0.0981430 | ||||||||
\(590\) | 5.28676e6 | 0.625258 | ||||||||
\(591\) | 637262. | 0.0750498 | ||||||||
\(592\) | −3.23162e6 | −0.378980 | ||||||||
\(593\) | −8.82696e6 | −1.03080 | −0.515400 | − | 0.856950i | \(-0.672357\pi\) | ||||
−0.515400 | + | 0.856950i | \(0.672357\pi\) | |||||||
\(594\) | −92939.3 | −0.0108077 | ||||||||
\(595\) | 780570. | 0.0903898 | ||||||||
\(596\) | 2.19352e6 | 0.252945 | ||||||||
\(597\) | −7.77774e6 | −0.893136 | ||||||||
\(598\) | 1.41193e6 | 0.161458 | ||||||||
\(599\) | −301924. | −0.0343819 | −0.0171910 | − | 0.999852i | \(-0.505472\pi\) | ||||
−0.0171910 | + | 0.999852i | \(0.505472\pi\) | |||||||
\(600\) | −360000. | −0.0408248 | ||||||||
\(601\) | −929593. | −0.104980 | −0.0524900 | − | 0.998621i | \(-0.516716\pi\) | ||||
−0.0524900 | + | 0.998621i | \(0.516716\pi\) | |||||||
\(602\) | 368111. | 0.0413988 | ||||||||
\(603\) | 4.87812e6 | 0.546335 | ||||||||
\(604\) | −4.62186e6 | −0.515495 | ||||||||
\(605\) | −4.00088e6 | −0.444393 | ||||||||
\(606\) | −3.27323e6 | −0.362072 | ||||||||
\(607\) | 1.38633e7 | 1.52720 | 0.763598 | − | 0.645692i | \(-0.223431\pi\) | ||||
0.763598 | + | 0.645692i | \(0.223431\pi\) | |||||||
\(608\) | 369664. | 0.0405554 | ||||||||
\(609\) | −2.37163e6 | −0.259122 | ||||||||
\(610\) | 2.03865e6 | 0.221829 | ||||||||
\(611\) | −3.58905e6 | −0.388935 | ||||||||
\(612\) | −1.18643e6 | −0.128045 | ||||||||
\(613\) | −5.89166e6 | −0.633266 | −0.316633 | − | 0.948548i | \(-0.602552\pi\) | ||||
−0.316633 | + | 0.948548i | \(0.602552\pi\) | |||||||
\(614\) | −9.25210e6 | −0.990420 | ||||||||
\(615\) | 949410. | 0.101220 | ||||||||
\(616\) | 69570.9 | 0.00738713 | ||||||||
\(617\) | 1.30582e7 | 1.38093 | 0.690464 | − | 0.723367i | \(-0.257406\pi\) | ||||
0.690464 | + | 0.723367i | \(0.257406\pi\) | |||||||
\(618\) | −999617. | −0.105284 | ||||||||
\(619\) | −6.38767e6 | −0.670063 | −0.335032 | − | 0.942207i | \(-0.608747\pi\) | ||||
−0.335032 | + | 0.942207i | \(0.608747\pi\) | |||||||
\(620\) | −915588. | −0.0956579 | ||||||||
\(621\) | −1.71628e6 | −0.178591 | ||||||||
\(622\) | −1.04600e7 | −1.08406 | ||||||||
\(623\) | −3.07554e6 | −0.317469 | ||||||||
\(624\) | 345441. | 0.0355150 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.34125e7 | −1.36796 | ||||||||
\(627\) | −103553. | −0.0105194 | ||||||||
\(628\) | 492225. | 0.0498041 | ||||||||
\(629\) | 1.15562e7 | 1.16463 | ||||||||
\(630\) | 276262. | 0.0277312 | ||||||||
\(631\) | 8.42759e6 | 0.842616 | 0.421308 | − | 0.906918i | \(-0.361571\pi\) | ||||
0.421308 | + | 0.906918i | \(0.361571\pi\) | |||||||
\(632\) | −1.70310e6 | −0.169608 | ||||||||
\(633\) | −3.76893e6 | −0.373860 | ||||||||
\(634\) | −4.82585e6 | −0.476816 | ||||||||
\(635\) | −3.65893e6 | −0.360097 | ||||||||
\(636\) | 1.72000e6 | 0.168611 | ||||||||
\(637\) | −2.34548e6 | −0.229025 | ||||||||
\(638\) | −985011. | −0.0958053 | ||||||||
\(639\) | −235914. | −0.0228560 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −9.99104e6 | −0.960430 | −0.480215 | − | 0.877151i | \(-0.659441\pi\) | ||||
−0.480215 | + | 0.877151i | \(0.659441\pi\) | |||||||
\(642\) | 909964. | 0.0871338 | ||||||||
\(643\) | −2.00027e7 | −1.90793 | −0.953964 | − | 0.299920i | \(-0.903040\pi\) | ||||
−0.953964 | + | 0.299920i | \(0.903040\pi\) | |||||||
\(644\) | 1.28474e6 | 0.122068 | ||||||||
\(645\) | 607108. | 0.0574602 | ||||||||
\(646\) | −1.32191e6 | −0.124630 | ||||||||
\(647\) | 874950. | 0.0821718 | 0.0410859 | − | 0.999156i | \(-0.486918\pi\) | ||||
0.0410859 | + | 0.999156i | \(0.486918\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | −1.68500e6 | −0.157032 | ||||||||
\(650\) | −374827. | −0.0347975 | ||||||||
\(651\) | 702617. | 0.0649779 | ||||||||
\(652\) | −1.99732e6 | −0.184005 | ||||||||
\(653\) | −4.14665e6 | −0.380552 | −0.190276 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190276 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(654\) | −670592. | −0.0613075 | ||||||||
\(655\) | 4.76948e6 | 0.434378 | ||||||||
\(656\) | 1.08022e6 | 0.0980058 | ||||||||
\(657\) | 2.23885e6 | 0.202354 | ||||||||
\(658\) | −3.26576e6 | −0.294049 | ||||||||
\(659\) | −8.70090e6 | −0.780460 | −0.390230 | − | 0.920717i | \(-0.627604\pi\) | ||||
−0.390230 | + | 0.920717i | \(0.627604\pi\) | |||||||
\(660\) | 114740. | 0.0102531 | ||||||||
\(661\) | 1.49078e7 | 1.32712 | 0.663559 | − | 0.748124i | \(-0.269045\pi\) | ||||
0.663559 | + | 0.748124i | \(0.269045\pi\) | |||||||
\(662\) | −5.38509e6 | −0.477582 | ||||||||
\(663\) | −1.23529e6 | −0.109140 | ||||||||
\(664\) | 4.31363e6 | 0.379684 | ||||||||
\(665\) | 307810. | 0.0269916 | ||||||||
\(666\) | 4.09002e6 | 0.357305 | ||||||||
\(667\) | −1.81899e7 | −1.58313 | ||||||||
\(668\) | 1.63110e6 | 0.141429 | ||||||||
\(669\) | −9.23227e6 | −0.797523 | ||||||||
\(670\) | −6.02237e6 | −0.518299 | ||||||||
\(671\) | −649764. | −0.0557121 | ||||||||
\(672\) | 314324. | 0.0268507 | ||||||||
\(673\) | −9.57636e6 | −0.815010 | −0.407505 | − | 0.913203i | \(-0.633601\pi\) | ||||
−0.407505 | + | 0.913203i | \(0.633601\pi\) | |||||||
\(674\) | 1.64762e7 | 1.39703 | ||||||||
\(675\) | 455625. | 0.0384900 | ||||||||
\(676\) | −5.58102e6 | −0.469728 | ||||||||
\(677\) | 1.49767e7 | 1.25587 | 0.627936 | − | 0.778265i | \(-0.283900\pi\) | ||||
0.627936 | + | 0.778265i | \(0.283900\pi\) | |||||||
\(678\) | −947400. | −0.0791515 | ||||||||
\(679\) | 4.84903e6 | 0.403627 | ||||||||
\(680\) | 1.46472e6 | 0.121474 | ||||||||
\(681\) | −7.04627e6 | −0.582226 | ||||||||
\(682\) | 291818. | 0.0240243 | ||||||||
\(683\) | 2.04298e7 | 1.67576 | 0.837881 | − | 0.545853i | \(-0.183794\pi\) | ||||
0.837881 | + | 0.545853i | \(0.183794\pi\) | |||||||
\(684\) | −467856. | −0.0382360 | ||||||||
\(685\) | −8.68635e6 | −0.707312 | ||||||||
\(686\) | −4.42711e6 | −0.359178 | ||||||||
\(687\) | 7.91671e6 | 0.639960 | ||||||||
\(688\) | 690754. | 0.0556356 | ||||||||
\(689\) | 1.79085e6 | 0.143718 | ||||||||
\(690\) | 2.11887e6 | 0.169426 | ||||||||
\(691\) | 2.21732e7 | 1.76658 | 0.883290 | − | 0.468826i | \(-0.155323\pi\) | ||||
0.883290 | + | 0.468826i | \(0.155323\pi\) | |||||||
\(692\) | 3.00152e6 | 0.238274 | ||||||||
\(693\) | −88050.7 | −0.00696465 | ||||||||
\(694\) | −1.62621e7 | −1.28167 | ||||||||
\(695\) | −2.72401e6 | −0.213917 | ||||||||
\(696\) | −4.45032e6 | −0.348232 | ||||||||
\(697\) | −3.86285e6 | −0.301180 | ||||||||
\(698\) | 6.72676e6 | 0.522598 | ||||||||
\(699\) | 1.01469e6 | 0.0785493 | ||||||||
\(700\) | −341064. | −0.0263082 | ||||||||
\(701\) | 1.33739e7 | 1.02793 | 0.513965 | − | 0.857811i | \(-0.328176\pi\) | ||||
0.513965 | + | 0.857811i | \(0.328176\pi\) | |||||||
\(702\) | −437199. | −0.0334839 | ||||||||
\(703\) | 4.55709e6 | 0.347775 | ||||||||
\(704\) | 130548. | 0.00992751 | ||||||||
\(705\) | −5.38606e6 | −0.408130 | ||||||||
\(706\) | 1.93227e6 | 0.145900 | ||||||||
\(707\) | −3.10106e6 | −0.233325 | ||||||||
\(708\) | −7.61293e6 | −0.570780 | ||||||||
\(709\) | 1.55456e7 | 1.16143 | 0.580713 | − | 0.814108i | \(-0.302774\pi\) | ||||
0.580713 | + | 0.814108i | \(0.302774\pi\) | |||||||
\(710\) | 291251. | 0.0216831 | ||||||||
\(711\) | 2.15548e6 | 0.159908 | ||||||||
\(712\) | −5.77119e6 | −0.426644 | ||||||||
\(713\) | 5.38892e6 | 0.396988 | ||||||||
\(714\) | −1.12402e6 | −0.0825142 | ||||||||
\(715\) | 119466. | 0.00873933 | ||||||||
\(716\) | 2.84130e6 | 0.207126 | ||||||||
\(717\) | 893126. | 0.0648806 | ||||||||
\(718\) | −263056. | −0.0190431 | ||||||||
\(719\) | 5.40570e6 | 0.389968 | 0.194984 | − | 0.980806i | \(-0.437534\pi\) | ||||
0.194984 | + | 0.980806i | \(0.437534\pi\) | |||||||
\(720\) | 518400. | 0.0372678 | ||||||||
\(721\) | −947036. | −0.0678467 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | −968040. | −0.0688728 | ||||||||
\(724\) | −1.07782e7 | −0.764188 | ||||||||
\(725\) | 4.82891e6 | 0.341196 | ||||||||
\(726\) | 5.76127e6 | 0.405673 | ||||||||
\(727\) | 2.98586e6 | 0.209524 | 0.104762 | − | 0.994497i | \(-0.466592\pi\) | ||||
0.104762 | + | 0.994497i | \(0.466592\pi\) | |||||||
\(728\) | 327270. | 0.0228864 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.76401e6 | −0.191970 | ||||||||
\(731\) | −2.47013e6 | −0.170972 | ||||||||
\(732\) | −2.93566e6 | −0.202502 | ||||||||
\(733\) | 4.85325e6 | 0.333636 | 0.166818 | − | 0.985988i | \(-0.446651\pi\) | ||||
0.166818 | + | 0.985988i | \(0.446651\pi\) | |||||||
\(734\) | −7.63706e6 | −0.523222 | ||||||||
\(735\) | −3.51984e6 | −0.240328 | ||||||||
\(736\) | 2.41080e6 | 0.164046 | ||||||||
\(737\) | 1.91946e6 | 0.130170 | ||||||||
\(738\) | −1.36715e6 | −0.0924008 | ||||||||
\(739\) | −5.27708e6 | −0.355453 | −0.177727 | − | 0.984080i | \(-0.556874\pi\) | ||||
−0.177727 | + | 0.984080i | \(0.556874\pi\) | |||||||
\(740\) | −5.04940e6 | −0.338970 | ||||||||
\(741\) | −487126. | −0.0325908 | ||||||||
\(742\) | 1.62953e6 | 0.108656 | ||||||||
\(743\) | −2.36362e7 | −1.57074 | −0.785372 | − | 0.619024i | \(-0.787528\pi\) | ||||
−0.785372 | + | 0.619024i | \(0.787528\pi\) | |||||||
\(744\) | 1.31845e6 | 0.0873234 | ||||||||
\(745\) | 3.42738e6 | 0.226241 | ||||||||
\(746\) | 1.14723e7 | 0.754748 | ||||||||
\(747\) | −5.45944e6 | −0.357970 | ||||||||
\(748\) | −466840. | −0.0305080 | ||||||||
\(749\) | 862099. | 0.0561504 | ||||||||
\(750\) | −562500. | −0.0365148 | ||||||||
\(751\) | −1.38581e7 | −0.896613 | −0.448306 | − | 0.893880i | \(-0.647973\pi\) | ||||
−0.448306 | + | 0.893880i | \(0.647973\pi\) | |||||||
\(752\) | −6.12814e6 | −0.395170 | ||||||||
\(753\) | 2.79389e6 | 0.179565 | ||||||||
\(754\) | −4.63362e6 | −0.296819 | ||||||||
\(755\) | −7.22165e6 | −0.461072 | ||||||||
\(756\) | −397817. | −0.0253150 | ||||||||
\(757\) | 1.88210e7 | 1.19372 | 0.596860 | − | 0.802345i | \(-0.296415\pi\) | ||||
0.596860 | + | 0.802345i | \(0.296415\pi\) | |||||||
\(758\) | −3.67855e6 | −0.232543 | ||||||||
\(759\) | −675329. | −0.0425511 | ||||||||
\(760\) | 577600. | 0.0362738 | ||||||||
\(761\) | 3.69012e6 | 0.230983 | 0.115491 | − | 0.993308i | \(-0.463156\pi\) | ||||
0.115491 | + | 0.993308i | \(0.463156\pi\) | |||||||
\(762\) | 5.26886e6 | 0.328722 | ||||||||
\(763\) | −635318. | −0.0395076 | ||||||||
\(764\) | −1.53567e7 | −0.951843 | ||||||||
\(765\) | −1.85379e6 | −0.114527 | ||||||||
\(766\) | 1.80308e7 | 1.11031 | ||||||||
\(767\) | −7.92648e6 | −0.486510 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 3.15204e6 | 0.192210 | 0.0961051 | − | 0.995371i | \(-0.469362\pi\) | ||||
0.0961051 | + | 0.995371i | \(0.469362\pi\) | |||||||
\(770\) | 108705. | 0.00660725 | ||||||||
\(771\) | 2.57164e6 | 0.155802 | ||||||||
\(772\) | −7.16060e6 | −0.432420 | ||||||||
\(773\) | −158167. | −0.00952066 | −0.00476033 | − | 0.999989i | \(-0.501515\pi\) | ||||
−0.00476033 | + | 0.999989i | \(0.501515\pi\) | |||||||
\(774\) | −874236. | −0.0524537 | ||||||||
\(775\) | −1.43061e6 | −0.0855591 | ||||||||
\(776\) | 9.09912e6 | 0.542432 | ||||||||
\(777\) | 3.87488e6 | 0.230253 | ||||||||
\(778\) | −2.22822e7 | −1.31980 | ||||||||
\(779\) | −1.52328e6 | −0.0899363 | ||||||||
\(780\) | 539751. | 0.0317656 | ||||||||
\(781\) | −92828.2 | −0.00544568 | ||||||||
\(782\) | −8.62099e6 | −0.504127 | ||||||||
\(783\) | 5.63244e6 | 0.328316 | ||||||||
\(784\) | −4.00480e6 | −0.232697 | ||||||||
\(785\) | 769102. | 0.0445461 | ||||||||
\(786\) | −6.86806e6 | −0.396531 | ||||||||
\(787\) | 2.12157e7 | 1.22101 | 0.610507 | − | 0.792011i | \(-0.290966\pi\) | ||||
0.610507 | + | 0.792011i | \(0.290966\pi\) | |||||||
\(788\) | 1.13291e6 | 0.0649951 | ||||||||
\(789\) | 1.06379e7 | 0.608365 | ||||||||
\(790\) | −2.66109e6 | −0.151702 | ||||||||
\(791\) | −897566. | −0.0510065 | ||||||||
\(792\) | −165225. | −0.00935974 | ||||||||
\(793\) | −3.05657e6 | −0.172604 | ||||||||
\(794\) | 4.65162e6 | 0.261850 | ||||||||
\(795\) | 2.68751e6 | 0.150811 | ||||||||
\(796\) | −1.38271e7 | −0.773478 | ||||||||
\(797\) | −1.41948e7 | −0.791560 | −0.395780 | − | 0.918345i | \(-0.629526\pi\) | ||||
−0.395780 | + | 0.918345i | \(0.629526\pi\) | |||||||
\(798\) | −443247. | −0.0246399 | ||||||||
\(799\) | 2.19142e7 | 1.21439 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 7.30417e6 | 0.402244 | ||||||||
\(802\) | 9.40976e6 | 0.516586 | ||||||||
\(803\) | 880950. | 0.0482128 | ||||||||
\(804\) | 8.67222e6 | 0.473140 | ||||||||
\(805\) | 2.00741e6 | 0.109181 | ||||||||
\(806\) | 1.37275e6 | 0.0744310 | ||||||||
\(807\) | 1.09663e7 | 0.592759 | ||||||||
\(808\) | −5.81907e6 | −0.313563 | ||||||||
\(809\) | −519774. | −0.0279218 | −0.0139609 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139609 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(810\) | −656100. | −0.0351364 | ||||||||
\(811\) | 4.77302e6 | 0.254825 | 0.127412 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127412 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(812\) | −4.21624e6 | −0.224406 | ||||||||
\(813\) | −1.82936e7 | −0.970674 | ||||||||
\(814\) | 1.60936e6 | 0.0851316 | ||||||||
\(815\) | −3.12081e6 | −0.164579 | ||||||||
\(816\) | −2.10920e6 | −0.110890 | ||||||||
\(817\) | −974071. | −0.0510547 | ||||||||
\(818\) | −2.17817e7 | −1.13818 | ||||||||
\(819\) | −414202. | −0.0215775 | ||||||||
\(820\) | 1.68784e6 | 0.0876591 | ||||||||
\(821\) | 1.77632e7 | 0.919738 | 0.459869 | − | 0.887987i | \(-0.347896\pi\) | ||||
0.459869 | + | 0.887987i | \(0.347896\pi\) | |||||||
\(822\) | 1.25083e7 | 0.645685 | ||||||||
\(823\) | −2.20845e7 | −1.13655 | −0.568275 | − | 0.822839i | \(-0.692389\pi\) | ||||
−0.568275 | + | 0.822839i | \(0.692389\pi\) | |||||||
\(824\) | −1.77710e6 | −0.0911786 | ||||||||
\(825\) | 179281. | 0.00917064 | ||||||||
\(826\) | −7.21248e6 | −0.367820 | ||||||||
\(827\) | −1.49320e7 | −0.759195 | −0.379598 | − | 0.925152i | \(-0.623938\pi\) | ||||
−0.379598 | + | 0.925152i | \(0.623938\pi\) | |||||||
\(828\) | −3.05117e6 | −0.154664 | ||||||||
\(829\) | 1.86878e7 | 0.944433 | 0.472217 | − | 0.881483i | \(-0.343454\pi\) | ||||
0.472217 | + | 0.881483i | \(0.343454\pi\) | |||||||
\(830\) | 6.74005e6 | 0.339600 | ||||||||
\(831\) | −1.82328e7 | −0.915904 | ||||||||
\(832\) | 614117. | 0.0307569 | ||||||||
\(833\) | 1.43211e7 | 0.715096 | ||||||||
\(834\) | 3.92257e6 | 0.195279 | ||||||||
\(835\) | 2.54859e6 | 0.126498 | ||||||||
\(836\) | −184094. | −0.00911011 | ||||||||
\(837\) | −1.66866e6 | −0.0823293 | ||||||||
\(838\) | −1.65134e7 | −0.812317 | ||||||||
\(839\) | 2.52104e7 | 1.23645 | 0.618224 | − | 0.786002i | \(-0.287853\pi\) | ||||
0.618224 | + | 0.786002i | \(0.287853\pi\) | |||||||
\(840\) | 491132. | 0.0240160 | ||||||||
\(841\) | 3.91839e7 | 1.91037 | ||||||||
\(842\) | −2.06268e7 | −1.00266 | ||||||||
\(843\) | −6.32814e6 | −0.306695 | ||||||||
\(844\) | −6.70033e6 | −0.323772 | ||||||||
\(845\) | −8.72034e6 | −0.420138 | ||||||||
\(846\) | 7.75593e6 | 0.372570 | ||||||||
\(847\) | 5.45822e6 | 0.261422 | ||||||||
\(848\) | 3.05778e6 | 0.146022 | ||||||||
\(849\) | −2.23142e7 | −1.06246 | ||||||||
\(850\) | 2.28863e6 | 0.108650 | ||||||||
\(851\) | 2.97195e7 | 1.40675 | ||||||||
\(852\) | −419402. | −0.0197939 | ||||||||
\(853\) | −2.75534e7 | −1.29659 | −0.648295 | − | 0.761389i | \(-0.724518\pi\) | ||||
−0.648295 | + | 0.761389i | \(0.724518\pi\) | |||||||
\(854\) | −2.78124e6 | −0.130495 | ||||||||
\(855\) | −731025. | −0.0341993 | ||||||||
\(856\) | 1.61771e6 | 0.0754601 | ||||||||
\(857\) | −1.95715e7 | −0.910272 | −0.455136 | − | 0.890422i | \(-0.650409\pi\) | ||||
−0.455136 | + | 0.890422i | \(0.650409\pi\) | |||||||
\(858\) | −172031. | −0.00797788 | ||||||||
\(859\) | −2.99519e7 | −1.38497 | −0.692486 | − | 0.721432i | \(-0.743484\pi\) | ||||
−0.692486 | + | 0.721432i | \(0.743484\pi\) | |||||||
\(860\) | 1.07930e6 | 0.0497620 | ||||||||
\(861\) | −1.29524e6 | −0.0595445 | ||||||||
\(862\) | 5.75416e6 | 0.263763 | ||||||||
\(863\) | −6.02134e6 | −0.275211 | −0.137606 | − | 0.990487i | \(-0.543941\pi\) | ||||
−0.137606 | + | 0.990487i | \(0.543941\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 4.68988e6 | 0.213119 | ||||||||
\(866\) | −1.70799e7 | −0.773909 | ||||||||
\(867\) | −5.23623e6 | −0.236576 | ||||||||
\(868\) | 1.24910e6 | 0.0562726 | ||||||||
\(869\) | 848148. | 0.0380998 | ||||||||
\(870\) | −6.95363e6 | −0.311468 | ||||||||
\(871\) | 9.02940e6 | 0.403286 | ||||||||
\(872\) | −1.19216e6 | −0.0530939 | ||||||||
\(873\) | −1.15161e7 | −0.511409 | ||||||||
\(874\) | −3.39960e6 | −0.150539 | ||||||||
\(875\) | −532912. | −0.0235307 | ||||||||
\(876\) | 3.98017e6 | 0.175243 | ||||||||
\(877\) | 2.29639e7 | 1.00820 | 0.504101 | − | 0.863645i | \(-0.331824\pi\) | ||||
0.504101 | + | 0.863645i | \(0.331824\pi\) | |||||||
\(878\) | −2.15359e7 | −0.942816 | ||||||||
\(879\) | −2.53483e7 | −1.10657 | ||||||||
\(880\) | 203982. | 0.00887943 | ||||||||
\(881\) | 1.92625e6 | 0.0836130 | 0.0418065 | − | 0.999126i | \(-0.486689\pi\) | ||||
0.0418065 | + | 0.999126i | \(0.486689\pi\) | |||||||
\(882\) | 5.06858e6 | 0.219389 | ||||||||
\(883\) | 2.69881e7 | 1.16485 | 0.582427 | − | 0.812883i | \(-0.302103\pi\) | ||||
0.582427 | + | 0.812883i | \(0.302103\pi\) | |||||||
\(884\) | −2.19607e6 | −0.0945184 | ||||||||
\(885\) | −1.18952e7 | −0.510521 | ||||||||
\(886\) | −7.33179e6 | −0.313780 | ||||||||
\(887\) | −2.30796e7 | −0.984962 | −0.492481 | − | 0.870323i | \(-0.663910\pi\) | ||||
−0.492481 | + | 0.870323i | \(0.663910\pi\) | |||||||
\(888\) | 7.27114e6 | 0.309435 | ||||||||
\(889\) | 4.99171e6 | 0.211834 | ||||||||
\(890\) | −9.01749e6 | −0.381602 | ||||||||
\(891\) | 209113. | 0.00882445 | ||||||||
\(892\) | −1.64129e7 | −0.690675 | ||||||||
\(893\) | 8.64164e6 | 0.362633 | ||||||||
\(894\) | −4.93542e6 | −0.206529 | ||||||||
\(895\) | 4.43953e6 | 0.185259 | ||||||||
\(896\) | 558799. | 0.0232534 | ||||||||
\(897\) | −3.17684e6 | −0.131830 | ||||||||
\(898\) | 2.13221e7 | 0.882346 | ||||||||
\(899\) | −1.76852e7 | −0.729811 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | −1.09346e7 | −0.448736 | ||||||||
\(902\) | −537952. | −0.0220154 | ||||||||
\(903\) | −828251. | −0.0338020 | ||||||||
\(904\) | −1.68427e6 | −0.0685472 | ||||||||
\(905\) | −1.68409e7 | −0.683510 | ||||||||
\(906\) | 1.03992e7 | 0.420900 | ||||||||
\(907\) | 1.56301e7 | 0.630876 | 0.315438 | − | 0.948946i | \(-0.397849\pi\) | ||||
0.315438 | + | 0.948946i | \(0.397849\pi\) | |||||||
\(908\) | −1.25267e7 | −0.504222 | ||||||||
\(909\) | 7.36476e6 | 0.295630 | ||||||||
\(910\) | 511360. | 0.0204703 | ||||||||
\(911\) | 1.76849e7 | 0.706003 | 0.353001 | − | 0.935623i | \(-0.385161\pi\) | ||||
0.353001 | + | 0.935623i | \(0.385161\pi\) | |||||||
\(912\) | −831744. | −0.0331133 | ||||||||
\(913\) | −2.14820e6 | −0.0852899 | ||||||||
\(914\) | −2.24279e6 | −0.0888021 | ||||||||
\(915\) | −4.58697e6 | −0.181123 | ||||||||
\(916\) | 1.40742e7 | 0.554222 | ||||||||
\(917\) | −6.50679e6 | −0.255531 | ||||||||
\(918\) | 2.66946e6 | 0.104548 | ||||||||
\(919\) | −1.45332e7 | −0.567640 | −0.283820 | − | 0.958878i | \(-0.591602\pi\) | ||||
−0.283820 | + | 0.958878i | \(0.591602\pi\) | |||||||
\(920\) | 3.76687e6 | 0.146728 | ||||||||
\(921\) | 2.08172e7 | 0.808675 | ||||||||
\(922\) | −1.57041e7 | −0.608394 | ||||||||
\(923\) | −436676. | −0.0168715 | ||||||||
\(924\) | −156534. | −0.00603157 | ||||||||
\(925\) | −7.88969e6 | −0.303184 | ||||||||
\(926\) | 2.71789e7 | 1.04161 | ||||||||
\(927\) | 2.24914e6 | 0.0859640 | ||||||||
\(928\) | −7.91169e6 | −0.301578 | ||||||||
\(929\) | −5.41583e6 | −0.205886 | −0.102943 | − | 0.994687i | \(-0.532826\pi\) | ||||
−0.102943 | + | 0.994687i | \(0.532826\pi\) | |||||||
\(930\) | 2.06007e6 | 0.0781044 | ||||||||
\(931\) | 5.64740e6 | 0.213537 | ||||||||
\(932\) | 1.80390e6 | 0.0680257 | ||||||||
\(933\) | 2.35350e7 | 0.885134 | ||||||||
\(934\) | 5.73898e6 | 0.215262 | ||||||||
\(935\) | −729437. | −0.0272872 | ||||||||
\(936\) | −777242. | −0.0289979 | ||||||||
\(937\) | 3.60577e7 | 1.34168 | 0.670841 | − | 0.741601i | \(-0.265933\pi\) | ||||
0.670841 | + | 0.741601i | \(0.265933\pi\) | |||||||
\(938\) | 8.21605e6 | 0.304899 | ||||||||
\(939\) | 3.01782e7 | 1.11694 | ||||||||
\(940\) | −9.57522e6 | −0.353451 | ||||||||
\(941\) | 4.81040e7 | 1.77095 | 0.885477 | − | 0.464683i | \(-0.153832\pi\) | ||||
0.885477 | + | 0.464683i | \(0.153832\pi\) | |||||||
\(942\) | −1.10751e6 | −0.0406648 | ||||||||
\(943\) | −9.93419e6 | −0.363792 | ||||||||
\(944\) | −1.35341e7 | −0.494310 | ||||||||
\(945\) | −621589. | −0.0226425 | ||||||||
\(946\) | −343998. | −0.0124976 | ||||||||
\(947\) | 4.75198e7 | 1.72187 | 0.860934 | − | 0.508716i | \(-0.169880\pi\) | ||||
0.860934 | + | 0.508716i | \(0.169880\pi\) | |||||||
\(948\) | 3.83197e6 | 0.138485 | ||||||||
\(949\) | 4.14410e6 | 0.149371 | ||||||||
\(950\) | 902500. | 0.0324443 | ||||||||
\(951\) | 1.08582e7 | 0.389319 | ||||||||
\(952\) | −1.99826e6 | −0.0714594 | ||||||||
\(953\) | 2.35327e6 | 0.0839341 | 0.0419671 | − | 0.999119i | \(-0.486638\pi\) | ||||
0.0419671 | + | 0.999119i | \(0.486638\pi\) | |||||||
\(954\) | −3.87001e6 | −0.137671 | ||||||||
\(955\) | −2.39949e7 | −0.851354 | ||||||||
\(956\) | 1.58778e6 | 0.0561882 | ||||||||
\(957\) | 2.21627e6 | 0.0782247 | ||||||||
\(958\) | −2.92364e7 | −1.02923 | ||||||||
\(959\) | 1.18504e7 | 0.416089 | ||||||||
\(960\) | 921600. | 0.0322749 | ||||||||
\(961\) | −2.33898e7 | −0.816991 | ||||||||
\(962\) | 7.57062e6 | 0.263751 | ||||||||
\(963\) | −2.04742e6 | −0.0711444 | ||||||||
\(964\) | −1.72096e6 | −0.0596456 | ||||||||
\(965\) | −1.11884e7 | −0.386768 | ||||||||
\(966\) | −2.89068e6 | −0.0996682 | ||||||||
\(967\) | −4.51703e7 | −1.55341 | −0.776706 | − | 0.629864i | \(-0.783111\pi\) | ||||
−0.776706 | + | 0.629864i | \(0.783111\pi\) | |||||||
\(968\) | 1.02423e7 | 0.351323 | ||||||||
\(969\) | 2.97431e6 | 0.101760 | ||||||||
\(970\) | 1.42174e7 | 0.485165 | ||||||||
\(971\) | −3.92928e7 | −1.33741 | −0.668706 | − | 0.743527i | \(-0.733152\pi\) | ||||
−0.668706 | + | 0.743527i | \(0.733152\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 3.71624e6 | 0.125841 | ||||||||
\(974\) | 1.44062e7 | 0.486579 | ||||||||
\(975\) | 843361. | 0.0284120 | ||||||||
\(976\) | −5.21895e6 | −0.175371 | ||||||||
\(977\) | −2.43011e7 | −0.814496 | −0.407248 | − | 0.913318i | \(-0.633512\pi\) | ||||
−0.407248 | + | 0.913318i | \(0.633512\pi\) | |||||||
\(978\) | 4.49397e6 | 0.150239 | ||||||||
\(979\) | 2.87407e6 | 0.0958387 | ||||||||
\(980\) | −6.25750e6 | −0.208131 | ||||||||
\(981\) | 1.50883e6 | 0.0500574 | ||||||||
\(982\) | −3.12055e7 | −1.03265 | ||||||||
\(983\) | −3.32344e7 | −1.09699 | −0.548496 | − | 0.836153i | \(-0.684799\pi\) | ||||
−0.548496 | + | 0.836153i | \(0.684799\pi\) | |||||||
\(984\) | −2.43049e6 | −0.0800214 | ||||||||
\(985\) | 1.77017e6 | 0.0581333 | ||||||||
\(986\) | 2.82921e7 | 0.926772 | ||||||||
\(987\) | 7.34796e6 | 0.240090 | ||||||||
\(988\) | −866001. | −0.0282245 | ||||||||
\(989\) | −6.35250e6 | −0.206516 | ||||||||
\(990\) | −258165. | −0.00837161 | ||||||||
\(991\) | 2.71928e7 | 0.879570 | 0.439785 | − | 0.898103i | \(-0.355055\pi\) | ||||
0.439785 | + | 0.898103i | \(0.355055\pi\) | |||||||
\(992\) | 2.34391e6 | 0.0756242 | ||||||||
\(993\) | 1.21164e7 | 0.389944 | ||||||||
\(994\) | −397341. | −0.0127555 | ||||||||
\(995\) | −2.16048e7 | −0.691820 | ||||||||
\(996\) | −9.70567e6 | −0.310011 | ||||||||
\(997\) | 5.03197e6 | 0.160325 | 0.0801623 | − | 0.996782i | \(-0.474456\pi\) | ||||
0.0801623 | + | 0.996782i | \(0.474456\pi\) | |||||||
\(998\) | −3.78752e6 | −0.120373 | ||||||||
\(999\) | −9.20254e6 | −0.291739 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 570.6.a.l.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.l.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |