Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,6,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(3.36806021607\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | 0.883883 | 0.441942 | − | 0.897044i | \(-0.354290\pi\) | ||||
0.441942 | + | 0.897044i | \(0.354290\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −7.00000 | −0.218750 | ||||||||
\(5\) | 94.0000 | 1.68152 | 0.840762 | − | 0.541406i | \(-0.182108\pi\) | ||||
0.840762 | + | 0.541406i | \(0.182108\pi\) | |||||||
\(6\) | 45.0000 | 0.510310 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | −195.000 | −1.07723 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 470.000 | 1.48627 | ||||||||
\(11\) | 52.0000 | 0.129575 | 0.0647876 | − | 0.997899i | \(-0.479363\pi\) | ||||
0.0647876 | + | 0.997899i | \(0.479363\pi\) | |||||||
\(12\) | −63.0000 | −0.126295 | ||||||||
\(13\) | −770.000 | −1.26367 | −0.631833 | − | 0.775104i | \(-0.717697\pi\) | ||||
−0.631833 | + | 0.775104i | \(0.717697\pi\) | |||||||
\(14\) | −245.000 | −0.334077 | ||||||||
\(15\) | 846.000 | 0.970828 | ||||||||
\(16\) | −751.000 | −0.733398 | ||||||||
\(17\) | −2022.00 | −1.69691 | −0.848455 | − | 0.529267i | \(-0.822467\pi\) | ||||
−0.848455 | + | 0.529267i | \(0.822467\pi\) | |||||||
\(18\) | 405.000 | 0.294628 | ||||||||
\(19\) | 1732.00 | 1.10069 | 0.550344 | − | 0.834938i | \(-0.314497\pi\) | ||||
0.550344 | + | 0.834938i | \(0.314497\pi\) | |||||||
\(20\) | −658.000 | −0.367833 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | 260.000 | 0.114529 | ||||||||
\(23\) | −576.000 | −0.227040 | −0.113520 | − | 0.993536i | \(-0.536213\pi\) | ||||
−0.113520 | + | 0.993536i | \(0.536213\pi\) | |||||||
\(24\) | −1755.00 | −0.621941 | ||||||||
\(25\) | 5711.00 | 1.82752 | ||||||||
\(26\) | −3850.00 | −1.11693 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 343.000 | 0.0826797 | ||||||||
\(29\) | 5518.00 | 1.21839 | 0.609196 | − | 0.793020i | \(-0.291492\pi\) | ||||
0.609196 | + | 0.793020i | \(0.291492\pi\) | |||||||
\(30\) | 4230.00 | 0.858099 | ||||||||
\(31\) | 6336.00 | 1.18416 | 0.592081 | − | 0.805879i | \(-0.298307\pi\) | ||||
0.592081 | + | 0.805879i | \(0.298307\pi\) | |||||||
\(32\) | 2485.00 | 0.428994 | ||||||||
\(33\) | 468.000 | 0.0748102 | ||||||||
\(34\) | −10110.0 | −1.49987 | ||||||||
\(35\) | −4606.00 | −0.635556 | ||||||||
\(36\) | −567.000 | −0.0729167 | ||||||||
\(37\) | −7338.00 | −0.881198 | −0.440599 | − | 0.897704i | \(-0.645234\pi\) | ||||
−0.440599 | + | 0.897704i | \(0.645234\pi\) | |||||||
\(38\) | 8660.00 | 0.972879 | ||||||||
\(39\) | −6930.00 | −0.729578 | ||||||||
\(40\) | −18330.0 | −1.81139 | ||||||||
\(41\) | −3262.00 | −0.303057 | −0.151528 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151528 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(42\) | −2205.00 | −0.192879 | ||||||||
\(43\) | 5420.00 | 0.447021 | 0.223511 | − | 0.974701i | \(-0.428248\pi\) | ||||
0.223511 | + | 0.974701i | \(0.428248\pi\) | |||||||
\(44\) | −364.000 | −0.0283446 | ||||||||
\(45\) | 7614.00 | 0.560508 | ||||||||
\(46\) | −2880.00 | −0.200677 | ||||||||
\(47\) | 864.000 | 0.0570518 | 0.0285259 | − | 0.999593i | \(-0.490919\pi\) | ||||
0.0285259 | + | 0.999593i | \(0.490919\pi\) | |||||||
\(48\) | −6759.00 | −0.423428 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 28555.0 | 1.61531 | ||||||||
\(51\) | −18198.0 | −0.979712 | ||||||||
\(52\) | 5390.00 | 0.276427 | ||||||||
\(53\) | 4182.00 | 0.204500 | 0.102250 | − | 0.994759i | \(-0.467396\pi\) | ||||
0.102250 | + | 0.994759i | \(0.467396\pi\) | |||||||
\(54\) | 3645.00 | 0.170103 | ||||||||
\(55\) | 4888.00 | 0.217884 | ||||||||
\(56\) | 9555.00 | 0.407156 | ||||||||
\(57\) | 15588.0 | 0.635482 | ||||||||
\(58\) | 27590.0 | 1.07692 | ||||||||
\(59\) | −11220.0 | −0.419626 | −0.209813 | − | 0.977741i | \(-0.567286\pi\) | ||||
−0.209813 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(60\) | −5922.00 | −0.212369 | ||||||||
\(61\) | −45602.0 | −1.56913 | −0.784566 | − | 0.620046i | \(-0.787114\pi\) | ||||
−0.784566 | + | 0.620046i | \(0.787114\pi\) | |||||||
\(62\) | 31680.0 | 1.04666 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 36457.0 | 1.11258 | ||||||||
\(65\) | −72380.0 | −2.12488 | ||||||||
\(66\) | 2340.00 | 0.0661235 | ||||||||
\(67\) | 1396.00 | 0.0379925 | 0.0189963 | − | 0.999820i | \(-0.493953\pi\) | ||||
0.0189963 | + | 0.999820i | \(0.493953\pi\) | |||||||
\(68\) | 14154.0 | 0.371199 | ||||||||
\(69\) | −5184.00 | −0.131082 | ||||||||
\(70\) | −23030.0 | −0.561757 | ||||||||
\(71\) | 18720.0 | 0.440717 | 0.220359 | − | 0.975419i | \(-0.429277\pi\) | ||||
0.220359 | + | 0.975419i | \(0.429277\pi\) | |||||||
\(72\) | −15795.0 | −0.359078 | ||||||||
\(73\) | 46362.0 | 1.01825 | 0.509126 | − | 0.860692i | \(-0.329969\pi\) | ||||
0.509126 | + | 0.860692i | \(0.329969\pi\) | |||||||
\(74\) | −36690.0 | −0.778876 | ||||||||
\(75\) | 51399.0 | 1.05512 | ||||||||
\(76\) | −12124.0 | −0.240775 | ||||||||
\(77\) | −2548.00 | −0.0489748 | ||||||||
\(78\) | −34650.0 | −0.644862 | ||||||||
\(79\) | 97424.0 | 1.75630 | 0.878149 | − | 0.478387i | \(-0.158778\pi\) | ||||
0.878149 | + | 0.478387i | \(0.158778\pi\) | |||||||
\(80\) | −70594.0 | −1.23323 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −16310.0 | −0.267867 | ||||||||
\(83\) | −81228.0 | −1.29423 | −0.647114 | − | 0.762394i | \(-0.724024\pi\) | ||||
−0.647114 | + | 0.762394i | \(0.724024\pi\) | |||||||
\(84\) | 3087.00 | 0.0477352 | ||||||||
\(85\) | −190068. | −2.85339 | ||||||||
\(86\) | 27100.0 | 0.395115 | ||||||||
\(87\) | 49662.0 | 0.703438 | ||||||||
\(88\) | −10140.0 | −0.139583 | ||||||||
\(89\) | −3182.00 | −0.0425819 | −0.0212910 | − | 0.999773i | \(-0.506778\pi\) | ||||
−0.0212910 | + | 0.999773i | \(0.506778\pi\) | |||||||
\(90\) | 38070.0 | 0.495424 | ||||||||
\(91\) | 37730.0 | 0.477621 | ||||||||
\(92\) | 4032.00 | 0.0496651 | ||||||||
\(93\) | 57024.0 | 0.683676 | ||||||||
\(94\) | 4320.00 | 0.0504271 | ||||||||
\(95\) | 162808. | 1.85083 | ||||||||
\(96\) | 22365.0 | 0.247680 | ||||||||
\(97\) | 4914.00 | 0.0530281 | 0.0265140 | − | 0.999648i | \(-0.491559\pi\) | ||||
0.0265140 | + | 0.999648i | \(0.491559\pi\) | |||||||
\(98\) | 12005.0 | 0.126269 | ||||||||
\(99\) | 4212.00 | 0.0431917 | ||||||||
\(100\) | −39977.0 | −0.399770 | ||||||||
\(101\) | −166354. | −1.62267 | −0.811334 | − | 0.584583i | \(-0.801258\pi\) | ||||
−0.811334 | + | 0.584583i | \(0.801258\pi\) | |||||||
\(102\) | −90990.0 | −0.865951 | ||||||||
\(103\) | 157160. | 1.45965 | 0.729825 | − | 0.683634i | \(-0.239601\pi\) | ||||
0.729825 | + | 0.683634i | \(0.239601\pi\) | |||||||
\(104\) | 150150. | 1.36126 | ||||||||
\(105\) | −41454.0 | −0.366938 | ||||||||
\(106\) | 20910.0 | 0.180755 | ||||||||
\(107\) | −6764.00 | −0.0571142 | −0.0285571 | − | 0.999592i | \(-0.509091\pi\) | ||||
−0.0285571 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(108\) | −5103.00 | −0.0420985 | ||||||||
\(109\) | 178398. | 1.43821 | 0.719107 | − | 0.694899i | \(-0.244551\pi\) | ||||
0.719107 | + | 0.694899i | \(0.244551\pi\) | |||||||
\(110\) | 24440.0 | 0.192584 | ||||||||
\(111\) | −66042.0 | −0.508760 | ||||||||
\(112\) | 36799.0 | 0.277199 | ||||||||
\(113\) | −45134.0 | −0.332512 | −0.166256 | − | 0.986083i | \(-0.553168\pi\) | ||||
−0.166256 | + | 0.986083i | \(0.553168\pi\) | |||||||
\(114\) | 77940.0 | 0.561692 | ||||||||
\(115\) | −54144.0 | −0.381773 | ||||||||
\(116\) | −38626.0 | −0.266523 | ||||||||
\(117\) | −62370.0 | −0.421222 | ||||||||
\(118\) | −56100.0 | −0.370901 | ||||||||
\(119\) | 99078.0 | 0.641372 | ||||||||
\(120\) | −164970. | −1.04581 | ||||||||
\(121\) | −158347. | −0.983210 | ||||||||
\(122\) | −228010. | −1.38693 | ||||||||
\(123\) | −29358.0 | −0.174970 | ||||||||
\(124\) | −44352.0 | −0.259035 | ||||||||
\(125\) | 243084. | 1.39149 | ||||||||
\(126\) | −19845.0 | −0.111359 | ||||||||
\(127\) | −205056. | −1.12814 | −0.564070 | − | 0.825727i | \(-0.690765\pi\) | ||||
−0.564070 | + | 0.825727i | \(0.690765\pi\) | |||||||
\(128\) | 102765. | 0.554396 | ||||||||
\(129\) | 48780.0 | 0.258088 | ||||||||
\(130\) | −361900. | −1.87815 | ||||||||
\(131\) | 72964.0 | 0.371476 | 0.185738 | − | 0.982599i | \(-0.440532\pi\) | ||||
0.185738 | + | 0.982599i | \(0.440532\pi\) | |||||||
\(132\) | −3276.00 | −0.0163647 | ||||||||
\(133\) | −84868.0 | −0.416021 | ||||||||
\(134\) | 6980.00 | 0.0335810 | ||||||||
\(135\) | 68526.0 | 0.323609 | ||||||||
\(136\) | 394290. | 1.82797 | ||||||||
\(137\) | −94182.0 | −0.428713 | −0.214356 | − | 0.976756i | \(-0.568765\pi\) | ||||
−0.214356 | + | 0.976756i | \(0.568765\pi\) | |||||||
\(138\) | −25920.0 | −0.115861 | ||||||||
\(139\) | −47796.0 | −0.209824 | −0.104912 | − | 0.994482i | \(-0.533456\pi\) | ||||
−0.104912 | + | 0.994482i | \(0.533456\pi\) | |||||||
\(140\) | 32242.0 | 0.139028 | ||||||||
\(141\) | 7776.00 | 0.0329389 | ||||||||
\(142\) | 93600.0 | 0.389543 | ||||||||
\(143\) | −40040.0 | −0.163740 | ||||||||
\(144\) | −60831.0 | −0.244466 | ||||||||
\(145\) | 518692. | 2.04875 | ||||||||
\(146\) | 231810. | 0.900016 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | 51366.0 | 0.192762 | ||||||||
\(149\) | −124266. | −0.458550 | −0.229275 | − | 0.973362i | \(-0.573636\pi\) | ||||
−0.229275 | + | 0.973362i | \(0.573636\pi\) | |||||||
\(150\) | 256995. | 0.932602 | ||||||||
\(151\) | −446296. | −1.59287 | −0.796436 | − | 0.604723i | \(-0.793284\pi\) | ||||
−0.796436 | + | 0.604723i | \(0.793284\pi\) | |||||||
\(152\) | −337740. | −1.18570 | ||||||||
\(153\) | −163782. | −0.565637 | ||||||||
\(154\) | −12740.0 | −0.0432880 | ||||||||
\(155\) | 595584. | 1.99119 | ||||||||
\(156\) | 48510.0 | 0.159595 | ||||||||
\(157\) | −159746. | −0.517227 | −0.258613 | − | 0.965981i | \(-0.583266\pi\) | ||||
−0.258613 | + | 0.965981i | \(0.583266\pi\) | |||||||
\(158\) | 487120. | 1.55236 | ||||||||
\(159\) | 37638.0 | 0.118068 | ||||||||
\(160\) | 233590. | 0.721364 | ||||||||
\(161\) | 28224.0 | 0.0858132 | ||||||||
\(162\) | 32805.0 | 0.0982093 | ||||||||
\(163\) | 247252. | 0.728905 | 0.364452 | − | 0.931222i | \(-0.381256\pi\) | ||||
0.364452 | + | 0.931222i | \(0.381256\pi\) | |||||||
\(164\) | 22834.0 | 0.0662937 | ||||||||
\(165\) | 43992.0 | 0.125795 | ||||||||
\(166\) | −406140. | −1.14395 | ||||||||
\(167\) | −684488. | −1.89922 | −0.949609 | − | 0.313438i | \(-0.898519\pi\) | ||||
−0.949609 | + | 0.313438i | \(0.898519\pi\) | |||||||
\(168\) | 85995.0 | 0.235072 | ||||||||
\(169\) | 221607. | 0.596852 | ||||||||
\(170\) | −950340. | −2.52207 | ||||||||
\(171\) | 140292. | 0.366896 | ||||||||
\(172\) | −37940.0 | −0.0977859 | ||||||||
\(173\) | −610474. | −1.55079 | −0.775393 | − | 0.631479i | \(-0.782448\pi\) | ||||
−0.775393 | + | 0.631479i | \(0.782448\pi\) | |||||||
\(174\) | 248310. | 0.621758 | ||||||||
\(175\) | −279839. | −0.690738 | ||||||||
\(176\) | −39052.0 | −0.0950302 | ||||||||
\(177\) | −100980. | −0.242271 | ||||||||
\(178\) | −15910.0 | −0.0376374 | ||||||||
\(179\) | 662252. | 1.54487 | 0.772433 | − | 0.635097i | \(-0.219040\pi\) | ||||
0.772433 | + | 0.635097i | \(0.219040\pi\) | |||||||
\(180\) | −53298.0 | −0.122611 | ||||||||
\(181\) | 154630. | 0.350830 | 0.175415 | − | 0.984495i | \(-0.443873\pi\) | ||||
0.175415 | + | 0.984495i | \(0.443873\pi\) | |||||||
\(182\) | 188650. | 0.422161 | ||||||||
\(183\) | −410418. | −0.905938 | ||||||||
\(184\) | 112320. | 0.244575 | ||||||||
\(185\) | −689772. | −1.48175 | ||||||||
\(186\) | 285120. | 0.604290 | ||||||||
\(187\) | −105144. | −0.219877 | ||||||||
\(188\) | −6048.00 | −0.0124801 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 814040. | 1.63592 | ||||||||
\(191\) | 486904. | 0.965739 | 0.482870 | − | 0.875692i | \(-0.339594\pi\) | ||||
0.482870 | + | 0.875692i | \(0.339594\pi\) | |||||||
\(192\) | 328113. | 0.642348 | ||||||||
\(193\) | 620546. | 1.19917 | 0.599585 | − | 0.800311i | \(-0.295332\pi\) | ||||
0.599585 | + | 0.800311i | \(0.295332\pi\) | |||||||
\(194\) | 24570.0 | 0.0468706 | ||||||||
\(195\) | −651420. | −1.22680 | ||||||||
\(196\) | −16807.0 | −0.0312500 | ||||||||
\(197\) | −236570. | −0.434304 | −0.217152 | − | 0.976138i | \(-0.569677\pi\) | ||||
−0.217152 | + | 0.976138i | \(0.569677\pi\) | |||||||
\(198\) | 21060.0 | 0.0381764 | ||||||||
\(199\) | 82104.0 | 0.146971 | 0.0734855 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734855 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(200\) | −1.11364e6 | −1.96866 | ||||||||
\(201\) | 12564.0 | 0.0219350 | ||||||||
\(202\) | −831770. | −1.43425 | ||||||||
\(203\) | −270382. | −0.460509 | ||||||||
\(204\) | 127386. | 0.214312 | ||||||||
\(205\) | −306628. | −0.509597 | ||||||||
\(206\) | 785800. | 1.29016 | ||||||||
\(207\) | −46656.0 | −0.0756801 | ||||||||
\(208\) | 578270. | 0.926771 | ||||||||
\(209\) | 90064.0 | 0.142622 | ||||||||
\(210\) | −207270. | −0.324331 | ||||||||
\(211\) | 99892.0 | 0.154463 | 0.0772315 | − | 0.997013i | \(-0.475392\pi\) | ||||
0.0772315 | + | 0.997013i | \(0.475392\pi\) | |||||||
\(212\) | −29274.0 | −0.0447345 | ||||||||
\(213\) | 168480. | 0.254448 | ||||||||
\(214\) | −33820.0 | −0.0504823 | ||||||||
\(215\) | 509480. | 0.751677 | ||||||||
\(216\) | −142155. | −0.207314 | ||||||||
\(217\) | −310464. | −0.447571 | ||||||||
\(218\) | 891990. | 1.27121 | ||||||||
\(219\) | 417258. | 0.587888 | ||||||||
\(220\) | −34216.0 | −0.0476620 | ||||||||
\(221\) | 1.55694e6 | 2.14433 | ||||||||
\(222\) | −330210. | −0.449684 | ||||||||
\(223\) | −186704. | −0.251415 | −0.125708 | − | 0.992067i | \(-0.540120\pi\) | ||||
−0.125708 | + | 0.992067i | \(0.540120\pi\) | |||||||
\(224\) | −121765. | −0.162145 | ||||||||
\(225\) | 462591. | 0.609173 | ||||||||
\(226\) | −225670. | −0.293902 | ||||||||
\(227\) | 336372. | 0.433267 | 0.216633 | − | 0.976253i | \(-0.430492\pi\) | ||||
0.216633 | + | 0.976253i | \(0.430492\pi\) | |||||||
\(228\) | −109116. | −0.139012 | ||||||||
\(229\) | −926314. | −1.16727 | −0.583633 | − | 0.812018i | \(-0.698369\pi\) | ||||
−0.583633 | + | 0.812018i | \(0.698369\pi\) | |||||||
\(230\) | −270720. | −0.337443 | ||||||||
\(231\) | −22932.0 | −0.0282756 | ||||||||
\(232\) | −1.07601e6 | −1.31249 | ||||||||
\(233\) | 1.25711e6 | 1.51700 | 0.758499 | − | 0.651675i | \(-0.225933\pi\) | ||||
0.758499 | + | 0.651675i | \(0.225933\pi\) | |||||||
\(234\) | −311850. | −0.372311 | ||||||||
\(235\) | 81216.0 | 0.0959339 | ||||||||
\(236\) | 78540.0 | 0.0917933 | ||||||||
\(237\) | 876816. | 1.01400 | ||||||||
\(238\) | 495390. | 0.566898 | ||||||||
\(239\) | −347016. | −0.392966 | −0.196483 | − | 0.980507i | \(-0.562952\pi\) | ||||
−0.196483 | + | 0.980507i | \(0.562952\pi\) | |||||||
\(240\) | −635346. | −0.712004 | ||||||||
\(241\) | 99170.0 | 0.109986 | 0.0549930 | − | 0.998487i | \(-0.482486\pi\) | ||||
0.0549930 | + | 0.998487i | \(0.482486\pi\) | |||||||
\(242\) | −791735. | −0.869043 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 319214. | 0.343247 | ||||||||
\(245\) | 225694. | 0.240218 | ||||||||
\(246\) | −146790. | −0.154653 | ||||||||
\(247\) | −1.33364e6 | −1.39090 | ||||||||
\(248\) | −1.23552e6 | −1.27562 | ||||||||
\(249\) | −731052. | −0.747222 | ||||||||
\(250\) | 1.21542e6 | 1.22992 | ||||||||
\(251\) | 344428. | 0.345076 | 0.172538 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172538 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(252\) | 27783.0 | 0.0275599 | ||||||||
\(253\) | −29952.0 | −0.0294188 | ||||||||
\(254\) | −1.02528e6 | −0.997145 | ||||||||
\(255\) | −1.71061e6 | −1.64741 | ||||||||
\(256\) | −652799. | −0.622558 | ||||||||
\(257\) | 295130. | 0.278728 | 0.139364 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139364 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(258\) | 243900. | 0.228120 | ||||||||
\(259\) | 359562. | 0.333061 | ||||||||
\(260\) | 506660. | 0.464818 | ||||||||
\(261\) | 446958. | 0.406130 | ||||||||
\(262\) | 364820. | 0.328341 | ||||||||
\(263\) | −1.27246e6 | −1.13437 | −0.567187 | − | 0.823589i | \(-0.691968\pi\) | ||||
−0.567187 | + | 0.823589i | \(0.691968\pi\) | |||||||
\(264\) | −91260.0 | −0.0805881 | ||||||||
\(265\) | 393108. | 0.343872 | ||||||||
\(266\) | −424340. | −0.367714 | ||||||||
\(267\) | −28638.0 | −0.0245847 | ||||||||
\(268\) | −9772.00 | −0.00831087 | ||||||||
\(269\) | 276774. | 0.233209 | 0.116604 | − | 0.993178i | \(-0.462799\pi\) | ||||
0.116604 | + | 0.993178i | \(0.462799\pi\) | |||||||
\(270\) | 342630. | 0.286033 | ||||||||
\(271\) | −1.28994e6 | −1.06695 | −0.533476 | − | 0.845815i | \(-0.679115\pi\) | ||||
−0.533476 | + | 0.845815i | \(0.679115\pi\) | |||||||
\(272\) | 1.51852e6 | 1.24451 | ||||||||
\(273\) | 339570. | 0.275755 | ||||||||
\(274\) | −470910. | −0.378932 | ||||||||
\(275\) | 296972. | 0.236801 | ||||||||
\(276\) | 36288.0 | 0.0286741 | ||||||||
\(277\) | 1.71655e6 | 1.34418 | 0.672089 | − | 0.740470i | \(-0.265397\pi\) | ||||
0.672089 | + | 0.740470i | \(0.265397\pi\) | |||||||
\(278\) | −238980. | −0.185460 | ||||||||
\(279\) | 513216. | 0.394720 | ||||||||
\(280\) | 898170. | 0.684642 | ||||||||
\(281\) | −1.47218e6 | −1.11223 | −0.556116 | − | 0.831104i | \(-0.687709\pi\) | ||||
−0.556116 | + | 0.831104i | \(0.687709\pi\) | |||||||
\(282\) | 38880.0 | 0.0291141 | ||||||||
\(283\) | 1.02881e6 | 0.763607 | 0.381804 | − | 0.924244i | \(-0.375303\pi\) | ||||
0.381804 | + | 0.924244i | \(0.375303\pi\) | |||||||
\(284\) | −131040. | −0.0964069 | ||||||||
\(285\) | 1.46527e6 | 1.06858 | ||||||||
\(286\) | −200200. | −0.144727 | ||||||||
\(287\) | 159838. | 0.114545 | ||||||||
\(288\) | 201285. | 0.142998 | ||||||||
\(289\) | 2.66863e6 | 1.87950 | ||||||||
\(290\) | 2.59346e6 | 1.81086 | ||||||||
\(291\) | 44226.0 | 0.0306158 | ||||||||
\(292\) | −324534. | −0.222742 | ||||||||
\(293\) | −1.18607e6 | −0.807123 | −0.403562 | − | 0.914952i | \(-0.632228\pi\) | ||||
−0.403562 | + | 0.914952i | \(0.632228\pi\) | |||||||
\(294\) | 108045. | 0.0729015 | ||||||||
\(295\) | −1.05468e6 | −0.705612 | ||||||||
\(296\) | 1.43091e6 | 0.949255 | ||||||||
\(297\) | 37908.0 | 0.0249367 | ||||||||
\(298\) | −621330. | −0.405305 | ||||||||
\(299\) | 443520. | 0.286903 | ||||||||
\(300\) | −359793. | −0.230807 | ||||||||
\(301\) | −265580. | −0.168958 | ||||||||
\(302\) | −2.23148e6 | −1.40791 | ||||||||
\(303\) | −1.49719e6 | −0.936848 | ||||||||
\(304\) | −1.30073e6 | −0.807242 | ||||||||
\(305\) | −4.28659e6 | −2.63853 | ||||||||
\(306\) | −818910. | −0.499957 | ||||||||
\(307\) | 1.51892e6 | 0.919788 | 0.459894 | − | 0.887974i | \(-0.347887\pi\) | ||||
0.459894 | + | 0.887974i | \(0.347887\pi\) | |||||||
\(308\) | 17836.0 | 0.0107132 | ||||||||
\(309\) | 1.41444e6 | 0.842730 | ||||||||
\(310\) | 2.97792e6 | 1.75998 | ||||||||
\(311\) | 212808. | 0.124763 | 0.0623817 | − | 0.998052i | \(-0.480130\pi\) | ||||
0.0623817 | + | 0.998052i | \(0.480130\pi\) | |||||||
\(312\) | 1.35135e6 | 0.785925 | ||||||||
\(313\) | −1894.00 | −0.00109275 | −0.000546373 | − | 1.00000i | \(-0.500174\pi\) | ||||
−0.000546373 | 1.00000i | \(0.500174\pi\) | ||||||||
\(314\) | −798730. | −0.457168 | ||||||||
\(315\) | −373086. | −0.211852 | ||||||||
\(316\) | −681968. | −0.384190 | ||||||||
\(317\) | −1.57898e6 | −0.882527 | −0.441263 | − | 0.897378i | \(-0.645470\pi\) | ||||
−0.441263 | + | 0.897378i | \(0.645470\pi\) | |||||||
\(318\) | 188190. | 0.104359 | ||||||||
\(319\) | 286936. | 0.157873 | ||||||||
\(320\) | 3.42696e6 | 1.87083 | ||||||||
\(321\) | −60876.0 | −0.0329749 | ||||||||
\(322\) | 141120. | 0.0758488 | ||||||||
\(323\) | −3.50210e6 | −1.86777 | ||||||||
\(324\) | −45927.0 | −0.0243056 | ||||||||
\(325\) | −4.39747e6 | −2.30938 | ||||||||
\(326\) | 1.23626e6 | 0.644267 | ||||||||
\(327\) | 1.60558e6 | 0.830354 | ||||||||
\(328\) | 636090. | 0.326463 | ||||||||
\(329\) | −42336.0 | −0.0215635 | ||||||||
\(330\) | 219960. | 0.111188 | ||||||||
\(331\) | −3.39471e6 | −1.70307 | −0.851535 | − | 0.524298i | \(-0.824328\pi\) | ||||
−0.851535 | + | 0.524298i | \(0.824328\pi\) | |||||||
\(332\) | 568596. | 0.283112 | ||||||||
\(333\) | −594378. | −0.293733 | ||||||||
\(334\) | −3.42244e6 | −1.67869 | ||||||||
\(335\) | 131224. | 0.0638853 | ||||||||
\(336\) | 331191. | 0.160041 | ||||||||
\(337\) | 2.02731e6 | 0.972403 | 0.486201 | − | 0.873847i | \(-0.338382\pi\) | ||||
0.486201 | + | 0.873847i | \(0.338382\pi\) | |||||||
\(338\) | 1.10804e6 | 0.527548 | ||||||||
\(339\) | −406206. | −0.191976 | ||||||||
\(340\) | 1.33048e6 | 0.624180 | ||||||||
\(341\) | 329472. | 0.153438 | ||||||||
\(342\) | 701460. | 0.324293 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −1.05690e6 | −0.481546 | ||||||||
\(345\) | −487296. | −0.220417 | ||||||||
\(346\) | −3.05237e6 | −1.37071 | ||||||||
\(347\) | 3.48885e6 | 1.55546 | 0.777730 | − | 0.628598i | \(-0.216371\pi\) | ||||
0.777730 | + | 0.628598i | \(0.216371\pi\) | |||||||
\(348\) | −347634. | −0.153877 | ||||||||
\(349\) | 965566. | 0.424344 | 0.212172 | − | 0.977232i | \(-0.431946\pi\) | ||||
0.212172 | + | 0.977232i | \(0.431946\pi\) | |||||||
\(350\) | −1.39919e6 | −0.610532 | ||||||||
\(351\) | −561330. | −0.243193 | ||||||||
\(352\) | 129220. | 0.0555870 | ||||||||
\(353\) | 1.15393e6 | 0.492882 | 0.246441 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246441 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(354\) | −504900. | −0.214140 | ||||||||
\(355\) | 1.75968e6 | 0.741076 | ||||||||
\(356\) | 22274.0 | 0.00931479 | ||||||||
\(357\) | 891702. | 0.370296 | ||||||||
\(358\) | 3.31126e6 | 1.36548 | ||||||||
\(359\) | 1.61110e6 | 0.659762 | 0.329881 | − | 0.944022i | \(-0.392991\pi\) | ||||
0.329881 | + | 0.944022i | \(0.392991\pi\) | |||||||
\(360\) | −1.48473e6 | −0.603797 | ||||||||
\(361\) | 523725. | 0.211512 | ||||||||
\(362\) | 773150. | 0.310093 | ||||||||
\(363\) | −1.42512e6 | −0.567657 | ||||||||
\(364\) | −264110. | −0.104480 | ||||||||
\(365\) | 4.35803e6 | 1.71221 | ||||||||
\(366\) | −2.05209e6 | −0.800744 | ||||||||
\(367\) | 3.67747e6 | 1.42523 | 0.712614 | − | 0.701557i | \(-0.247511\pi\) | ||||
0.712614 | + | 0.701557i | \(0.247511\pi\) | |||||||
\(368\) | 432576. | 0.166511 | ||||||||
\(369\) | −264222. | −0.101019 | ||||||||
\(370\) | −3.44886e6 | −1.30970 | ||||||||
\(371\) | −204918. | −0.0772939 | ||||||||
\(372\) | −399168. | −0.149554 | ||||||||
\(373\) | 649766. | 0.241816 | 0.120908 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120908 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(374\) | −525720. | −0.194346 | ||||||||
\(375\) | 2.18776e6 | 0.803379 | ||||||||
\(376\) | −168480. | −0.0614580 | ||||||||
\(377\) | −4.24886e6 | −1.53964 | ||||||||
\(378\) | −178605. | −0.0642931 | ||||||||
\(379\) | 320700. | 0.114683 | 0.0573417 | − | 0.998355i | \(-0.481738\pi\) | ||||
0.0573417 | + | 0.998355i | \(0.481738\pi\) | |||||||
\(380\) | −1.13966e6 | −0.404869 | ||||||||
\(381\) | −1.84550e6 | −0.651332 | ||||||||
\(382\) | 2.43452e6 | 0.853601 | ||||||||
\(383\) | −2.36189e6 | −0.822740 | −0.411370 | − | 0.911469i | \(-0.634950\pi\) | ||||
−0.411370 | + | 0.911469i | \(0.634950\pi\) | |||||||
\(384\) | 924885. | 0.320081 | ||||||||
\(385\) | −239512. | −0.0823522 | ||||||||
\(386\) | 3.10273e6 | 1.05993 | ||||||||
\(387\) | 439020. | 0.149007 | ||||||||
\(388\) | −34398.0 | −0.0115999 | ||||||||
\(389\) | −3.53390e6 | −1.18408 | −0.592039 | − | 0.805910i | \(-0.701677\pi\) | ||||
−0.592039 | + | 0.805910i | \(0.701677\pi\) | |||||||
\(390\) | −3.25710e6 | −1.08435 | ||||||||
\(391\) | 1.16467e6 | 0.385267 | ||||||||
\(392\) | −468195. | −0.153890 | ||||||||
\(393\) | 656676. | 0.214472 | ||||||||
\(394\) | −1.18285e6 | −0.383874 | ||||||||
\(395\) | 9.15786e6 | 2.95326 | ||||||||
\(396\) | −29484.0 | −0.00944819 | ||||||||
\(397\) | 4.04811e6 | 1.28907 | 0.644534 | − | 0.764575i | \(-0.277051\pi\) | ||||
0.644534 | + | 0.764575i | \(0.277051\pi\) | |||||||
\(398\) | 410520. | 0.129905 | ||||||||
\(399\) | −763812. | −0.240190 | ||||||||
\(400\) | −4.28896e6 | −1.34030 | ||||||||
\(401\) | 2.07645e6 | 0.644853 | 0.322426 | − | 0.946595i | \(-0.395502\pi\) | ||||
0.322426 | + | 0.946595i | \(0.395502\pi\) | |||||||
\(402\) | 62820.0 | 0.0193880 | ||||||||
\(403\) | −4.87872e6 | −1.49638 | ||||||||
\(404\) | 1.16448e6 | 0.354959 | ||||||||
\(405\) | 616734. | 0.186836 | ||||||||
\(406\) | −1.35191e6 | −0.407036 | ||||||||
\(407\) | −381576. | −0.114181 | ||||||||
\(408\) | 3.54861e6 | 1.05538 | ||||||||
\(409\) | 2.57431e6 | 0.760945 | 0.380472 | − | 0.924792i | \(-0.375761\pi\) | ||||
0.380472 | + | 0.924792i | \(0.375761\pi\) | |||||||
\(410\) | −1.53314e6 | −0.450425 | ||||||||
\(411\) | −847638. | −0.247517 | ||||||||
\(412\) | −1.10012e6 | −0.319299 | ||||||||
\(413\) | 549780. | 0.158604 | ||||||||
\(414\) | −233280. | −0.0668924 | ||||||||
\(415\) | −7.63543e6 | −2.17627 | ||||||||
\(416\) | −1.91345e6 | −0.542105 | ||||||||
\(417\) | −430164. | −0.121142 | ||||||||
\(418\) | 450320. | 0.126061 | ||||||||
\(419\) | 848148. | 0.236013 | 0.118007 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118007 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(420\) | 290178. | 0.0802678 | ||||||||
\(421\) | 1.43682e6 | 0.395092 | 0.197546 | − | 0.980294i | \(-0.436703\pi\) | ||||
0.197546 | + | 0.980294i | \(0.436703\pi\) | |||||||
\(422\) | 499460. | 0.136527 | ||||||||
\(423\) | 69984.0 | 0.0190173 | ||||||||
\(424\) | −815490. | −0.220295 | ||||||||
\(425\) | −1.15476e7 | −3.10114 | ||||||||
\(426\) | 842400. | 0.224903 | ||||||||
\(427\) | 2.23450e6 | 0.593076 | ||||||||
\(428\) | 47348.0 | 0.0124937 | ||||||||
\(429\) | −360360. | −0.0945352 | ||||||||
\(430\) | 2.54740e6 | 0.664394 | ||||||||
\(431\) | 2.35438e6 | 0.610496 | 0.305248 | − | 0.952273i | \(-0.401261\pi\) | ||||
0.305248 | + | 0.952273i | \(0.401261\pi\) | |||||||
\(432\) | −547479. | −0.141143 | ||||||||
\(433\) | −3.78808e6 | −0.970955 | −0.485478 | − | 0.874249i | \(-0.661354\pi\) | ||||
−0.485478 | + | 0.874249i | \(0.661354\pi\) | |||||||
\(434\) | −1.55232e6 | −0.395601 | ||||||||
\(435\) | 4.66823e6 | 1.18285 | ||||||||
\(436\) | −1.24879e6 | −0.314609 | ||||||||
\(437\) | −997632. | −0.249900 | ||||||||
\(438\) | 2.08629e6 | 0.519624 | ||||||||
\(439\) | −3.64322e6 | −0.902245 | −0.451123 | − | 0.892462i | \(-0.648976\pi\) | ||||
−0.451123 | + | 0.892462i | \(0.648976\pi\) | |||||||
\(440\) | −953160. | −0.234711 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 7.78470e6 | 1.89534 | ||||||||
\(443\) | 2.48389e6 | 0.601345 | 0.300672 | − | 0.953728i | \(-0.402789\pi\) | ||||
0.300672 | + | 0.953728i | \(0.402789\pi\) | |||||||
\(444\) | 462294. | 0.111291 | ||||||||
\(445\) | −299108. | −0.0716025 | ||||||||
\(446\) | −933520. | −0.222222 | ||||||||
\(447\) | −1.11839e6 | −0.264744 | ||||||||
\(448\) | −1.78639e6 | −0.420515 | ||||||||
\(449\) | −2.63177e6 | −0.616074 | −0.308037 | − | 0.951374i | \(-0.599672\pi\) | ||||
−0.308037 | + | 0.951374i | \(0.599672\pi\) | |||||||
\(450\) | 2.31295e6 | 0.538438 | ||||||||
\(451\) | −169624. | −0.0392686 | ||||||||
\(452\) | 315938. | 0.0727371 | ||||||||
\(453\) | −4.01666e6 | −0.919645 | ||||||||
\(454\) | 1.68186e6 | 0.382957 | ||||||||
\(455\) | 3.54662e6 | 0.803131 | ||||||||
\(456\) | −3.03966e6 | −0.684562 | ||||||||
\(457\) | −1.16130e6 | −0.260109 | −0.130054 | − | 0.991507i | \(-0.541515\pi\) | ||||
−0.130054 | + | 0.991507i | \(0.541515\pi\) | |||||||
\(458\) | −4.63157e6 | −1.03173 | ||||||||
\(459\) | −1.47404e6 | −0.326571 | ||||||||
\(460\) | 379008. | 0.0835129 | ||||||||
\(461\) | 2.81385e6 | 0.616663 | 0.308332 | − | 0.951279i | \(-0.400229\pi\) | ||||
0.308332 | + | 0.951279i | \(0.400229\pi\) | |||||||
\(462\) | −114660. | −0.0249923 | ||||||||
\(463\) | 6.84299e6 | 1.48352 | 0.741760 | − | 0.670665i | \(-0.233991\pi\) | ||||
0.741760 | + | 0.670665i | \(0.233991\pi\) | |||||||
\(464\) | −4.14402e6 | −0.893566 | ||||||||
\(465\) | 5.36026e6 | 1.14962 | ||||||||
\(466\) | 6.28557e6 | 1.34085 | ||||||||
\(467\) | 3.34314e6 | 0.709353 | 0.354676 | − | 0.934989i | \(-0.384591\pi\) | ||||
0.354676 | + | 0.934989i | \(0.384591\pi\) | |||||||
\(468\) | 436590. | 0.0921423 | ||||||||
\(469\) | −68404.0 | −0.0143598 | ||||||||
\(470\) | 406080. | 0.0847944 | ||||||||
\(471\) | −1.43771e6 | −0.298621 | ||||||||
\(472\) | 2.18790e6 | 0.452035 | ||||||||
\(473\) | 281840. | 0.0579228 | ||||||||
\(474\) | 4.38408e6 | 0.896257 | ||||||||
\(475\) | 9.89145e6 | 2.01153 | ||||||||
\(476\) | −693546. | −0.140300 | ||||||||
\(477\) | 338742. | 0.0681668 | ||||||||
\(478\) | −1.73508e6 | −0.347336 | ||||||||
\(479\) | −4.28248e6 | −0.852818 | −0.426409 | − | 0.904530i | \(-0.640222\pi\) | ||||
−0.426409 | + | 0.904530i | \(0.640222\pi\) | |||||||
\(480\) | 2.10231e6 | 0.416480 | ||||||||
\(481\) | 5.65026e6 | 1.11354 | ||||||||
\(482\) | 495850. | 0.0972149 | ||||||||
\(483\) | 254016. | 0.0495442 | ||||||||
\(484\) | 1.10843e6 | 0.215077 | ||||||||
\(485\) | 461916. | 0.0891679 | ||||||||
\(486\) | 295245. | 0.0567012 | ||||||||
\(487\) | −8.93175e6 | −1.70653 | −0.853266 | − | 0.521477i | \(-0.825381\pi\) | ||||
−0.853266 | + | 0.521477i | \(0.825381\pi\) | |||||||
\(488\) | 8.89239e6 | 1.69032 | ||||||||
\(489\) | 2.22527e6 | 0.420833 | ||||||||
\(490\) | 1.12847e6 | 0.212324 | ||||||||
\(491\) | 2.75306e6 | 0.515361 | 0.257681 | − | 0.966230i | \(-0.417042\pi\) | ||||
0.257681 | + | 0.966230i | \(0.417042\pi\) | |||||||
\(492\) | 205506. | 0.0382747 | ||||||||
\(493\) | −1.11574e7 | −2.06750 | ||||||||
\(494\) | −6.66820e6 | −1.22939 | ||||||||
\(495\) | 395928. | 0.0726279 | ||||||||
\(496\) | −4.75834e6 | −0.868462 | ||||||||
\(497\) | −917280. | −0.166575 | ||||||||
\(498\) | −3.65526e6 | −0.660458 | ||||||||
\(499\) | 4.80408e6 | 0.863693 | 0.431846 | − | 0.901947i | \(-0.357862\pi\) | ||||
0.431846 | + | 0.901947i | \(0.357862\pi\) | |||||||
\(500\) | −1.70159e6 | −0.304389 | ||||||||
\(501\) | −6.16039e6 | −1.09651 | ||||||||
\(502\) | 1.72214e6 | 0.305007 | ||||||||
\(503\) | −6.02465e6 | −1.06172 | −0.530862 | − | 0.847458i | \(-0.678132\pi\) | ||||
−0.530862 | + | 0.847458i | \(0.678132\pi\) | |||||||
\(504\) | 773955. | 0.135719 | ||||||||
\(505\) | −1.56373e7 | −2.72855 | ||||||||
\(506\) | −149760. | −0.0260028 | ||||||||
\(507\) | 1.99446e6 | 0.344593 | ||||||||
\(508\) | 1.43539e6 | 0.246781 | ||||||||
\(509\) | −8.42987e6 | −1.44220 | −0.721101 | − | 0.692830i | \(-0.756364\pi\) | ||||
−0.721101 | + | 0.692830i | \(0.756364\pi\) | |||||||
\(510\) | −8.55306e6 | −1.45612 | ||||||||
\(511\) | −2.27174e6 | −0.384863 | ||||||||
\(512\) | −6.55248e6 | −1.10466 | ||||||||
\(513\) | 1.26263e6 | 0.211827 | ||||||||
\(514\) | 1.47565e6 | 0.246363 | ||||||||
\(515\) | 1.47730e7 | 2.45444 | ||||||||
\(516\) | −341460. | −0.0564567 | ||||||||
\(517\) | 44928.0 | 0.00739249 | ||||||||
\(518\) | 1.79781e6 | 0.294388 | ||||||||
\(519\) | −5.49427e6 | −0.895347 | ||||||||
\(520\) | 1.41141e7 | 2.28899 | ||||||||
\(521\) | 9.25058e6 | 1.49305 | 0.746525 | − | 0.665357i | \(-0.231721\pi\) | ||||
0.746525 | + | 0.665357i | \(0.231721\pi\) | |||||||
\(522\) | 2.23479e6 | 0.358972 | ||||||||
\(523\) | 5.84494e6 | 0.934385 | 0.467192 | − | 0.884156i | \(-0.345266\pi\) | ||||
0.467192 | + | 0.884156i | \(0.345266\pi\) | |||||||
\(524\) | −510748. | −0.0812603 | ||||||||
\(525\) | −2.51855e6 | −0.398798 | ||||||||
\(526\) | −6.36232e6 | −1.00265 | ||||||||
\(527\) | −1.28114e7 | −2.00942 | ||||||||
\(528\) | −351468. | −0.0548657 | ||||||||
\(529\) | −6.10457e6 | −0.948453 | ||||||||
\(530\) | 1.96554e6 | 0.303943 | ||||||||
\(531\) | −908820. | −0.139875 | ||||||||
\(532\) | 594076. | 0.0910045 | ||||||||
\(533\) | 2.51174e6 | 0.382963 | ||||||||
\(534\) | −143190. | −0.0217300 | ||||||||
\(535\) | −635816. | −0.0960389 | ||||||||
\(536\) | −272220. | −0.0409268 | ||||||||
\(537\) | 5.96027e6 | 0.891929 | ||||||||
\(538\) | 1.38387e6 | 0.206129 | ||||||||
\(539\) | 124852. | 0.0185107 | ||||||||
\(540\) | −479682. | −0.0707895 | ||||||||
\(541\) | 9.22533e6 | 1.35515 | 0.677577 | − | 0.735452i | \(-0.263030\pi\) | ||||
0.677577 | + | 0.735452i | \(0.263030\pi\) | |||||||
\(542\) | −6.44968e6 | −0.943061 | ||||||||
\(543\) | 1.39167e6 | 0.202552 | ||||||||
\(544\) | −5.02467e6 | −0.727965 | ||||||||
\(545\) | 1.67694e7 | 2.41839 | ||||||||
\(546\) | 1.69785e6 | 0.243735 | ||||||||
\(547\) | −6.44337e6 | −0.920757 | −0.460378 | − | 0.887723i | \(-0.652286\pi\) | ||||
−0.460378 | + | 0.887723i | \(0.652286\pi\) | |||||||
\(548\) | 659274. | 0.0937809 | ||||||||
\(549\) | −3.69376e6 | −0.523044 | ||||||||
\(550\) | 1.48486e6 | 0.209305 | ||||||||
\(551\) | 9.55718e6 | 1.34107 | ||||||||
\(552\) | 1.01088e6 | 0.141206 | ||||||||
\(553\) | −4.77378e6 | −0.663818 | ||||||||
\(554\) | 8.58275e6 | 1.18810 | ||||||||
\(555\) | −6.20795e6 | −0.855491 | ||||||||
\(556\) | 334572. | 0.0458989 | ||||||||
\(557\) | 3.74213e6 | 0.511070 | 0.255535 | − | 0.966800i | \(-0.417748\pi\) | ||||
0.255535 | + | 0.966800i | \(0.417748\pi\) | |||||||
\(558\) | 2.56608e6 | 0.348887 | ||||||||
\(559\) | −4.17340e6 | −0.564886 | ||||||||
\(560\) | 3.45911e6 | 0.466116 | ||||||||
\(561\) | −946296. | −0.126946 | ||||||||
\(562\) | −7.36091e6 | −0.983084 | ||||||||
\(563\) | −1.46384e7 | −1.94635 | −0.973176 | − | 0.230060i | \(-0.926108\pi\) | ||||
−0.973176 | + | 0.230060i | \(0.926108\pi\) | |||||||
\(564\) | −54432.0 | −0.00720537 | ||||||||
\(565\) | −4.24260e6 | −0.559127 | ||||||||
\(566\) | 5.14406e6 | 0.674940 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | −3.65040e6 | −0.474755 | ||||||||
\(569\) | 1.41805e7 | 1.83616 | 0.918078 | − | 0.396400i | \(-0.129741\pi\) | ||||
0.918078 | + | 0.396400i | \(0.129741\pi\) | |||||||
\(570\) | 7.32636e6 | 0.944498 | ||||||||
\(571\) | −1.25160e6 | −0.160648 | −0.0803242 | − | 0.996769i | \(-0.525596\pi\) | ||||
−0.0803242 | + | 0.996769i | \(0.525596\pi\) | |||||||
\(572\) | 280280. | 0.0358181 | ||||||||
\(573\) | 4.38214e6 | 0.557570 | ||||||||
\(574\) | 799190. | 0.101244 | ||||||||
\(575\) | −3.28954e6 | −0.414921 | ||||||||
\(576\) | 2.95302e6 | 0.370860 | ||||||||
\(577\) | 5.94378e6 | 0.743230 | 0.371615 | − | 0.928387i | \(-0.378804\pi\) | ||||
0.371615 | + | 0.928387i | \(0.378804\pi\) | |||||||
\(578\) | 1.33431e7 | 1.66126 | ||||||||
\(579\) | 5.58491e6 | 0.692341 | ||||||||
\(580\) | −3.63084e6 | −0.448165 | ||||||||
\(581\) | 3.98017e6 | 0.489172 | ||||||||
\(582\) | 221130. | 0.0270608 | ||||||||
\(583\) | 217464. | 0.0264982 | ||||||||
\(584\) | −9.04059e6 | −1.09689 | ||||||||
\(585\) | −5.86278e6 | −0.708295 | ||||||||
\(586\) | −5.93033e6 | −0.713403 | ||||||||
\(587\) | −6.46192e6 | −0.774046 | −0.387023 | − | 0.922070i | \(-0.626497\pi\) | ||||
−0.387023 | + | 0.922070i | \(0.626497\pi\) | |||||||
\(588\) | −151263. | −0.0180422 | ||||||||
\(589\) | 1.09740e7 | 1.30339 | ||||||||
\(590\) | −5.27340e6 | −0.623678 | ||||||||
\(591\) | −2.12913e6 | −0.250746 | ||||||||
\(592\) | 5.51084e6 | 0.646269 | ||||||||
\(593\) | −2.34605e6 | −0.273969 | −0.136984 | − | 0.990573i | \(-0.543741\pi\) | ||||
−0.136984 | + | 0.990573i | \(0.543741\pi\) | |||||||
\(594\) | 189540. | 0.0220412 | ||||||||
\(595\) | 9.31333e6 | 1.07848 | ||||||||
\(596\) | 869862. | 0.100308 | ||||||||
\(597\) | 738936. | 0.0848537 | ||||||||
\(598\) | 2.21760e6 | 0.253589 | ||||||||
\(599\) | −1.34959e7 | −1.53686 | −0.768432 | − | 0.639931i | \(-0.778963\pi\) | ||||
−0.768432 | + | 0.639931i | \(0.778963\pi\) | |||||||
\(600\) | −1.00228e7 | −1.13661 | ||||||||
\(601\) | 3.87849e6 | 0.438002 | 0.219001 | − | 0.975725i | \(-0.429720\pi\) | ||||
0.219001 | + | 0.975725i | \(0.429720\pi\) | |||||||
\(602\) | −1.32790e6 | −0.149339 | ||||||||
\(603\) | 113076. | 0.0126642 | ||||||||
\(604\) | 3.12407e6 | 0.348441 | ||||||||
\(605\) | −1.48846e7 | −1.65329 | ||||||||
\(606\) | −7.48593e6 | −0.828065 | ||||||||
\(607\) | −533488. | −0.0587696 | −0.0293848 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293848 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(608\) | 4.30402e6 | 0.472188 | ||||||||
\(609\) | −2.43344e6 | −0.265875 | ||||||||
\(610\) | −2.14329e7 | −2.33215 | ||||||||
\(611\) | −665280. | −0.0720944 | ||||||||
\(612\) | 1.14647e6 | 0.123733 | ||||||||
\(613\) | 5.14610e6 | 0.553130 | 0.276565 | − | 0.960995i | \(-0.410804\pi\) | ||||
0.276565 | + | 0.960995i | \(0.410804\pi\) | |||||||
\(614\) | 7.59458e6 | 0.812986 | ||||||||
\(615\) | −2.75965e6 | −0.294216 | ||||||||
\(616\) | 496860. | 0.0527573 | ||||||||
\(617\) | −2.37860e6 | −0.251541 | −0.125770 | − | 0.992059i | \(-0.540140\pi\) | ||||
−0.125770 | + | 0.992059i | \(0.540140\pi\) | |||||||
\(618\) | 7.07220e6 | 0.744875 | ||||||||
\(619\) | 1.60023e7 | 1.67863 | 0.839317 | − | 0.543642i | \(-0.182955\pi\) | ||||
0.839317 | + | 0.543642i | \(0.182955\pi\) | |||||||
\(620\) | −4.16909e6 | −0.435574 | ||||||||
\(621\) | −419904. | −0.0436939 | ||||||||
\(622\) | 1.06404e6 | 0.110276 | ||||||||
\(623\) | 155918. | 0.0160944 | ||||||||
\(624\) | 5.20443e6 | 0.535071 | ||||||||
\(625\) | 5.00302e6 | 0.512309 | ||||||||
\(626\) | −9470.00 | −0.000965860 0 | ||||||||
\(627\) | 810576. | 0.0823427 | ||||||||
\(628\) | 1.11822e6 | 0.113143 | ||||||||
\(629\) | 1.48374e7 | 1.49531 | ||||||||
\(630\) | −1.86543e6 | −0.187252 | ||||||||
\(631\) | 1.23459e7 | 1.23439 | 0.617193 | − | 0.786812i | \(-0.288270\pi\) | ||||
0.617193 | + | 0.786812i | \(0.288270\pi\) | |||||||
\(632\) | −1.89977e7 | −1.89194 | ||||||||
\(633\) | 899028. | 0.0891793 | ||||||||
\(634\) | −7.89489e6 | −0.780051 | ||||||||
\(635\) | −1.92753e7 | −1.89699 | ||||||||
\(636\) | −263466. | −0.0258275 | ||||||||
\(637\) | −1.84877e6 | −0.180524 | ||||||||
\(638\) | 1.43468e6 | 0.139541 | ||||||||
\(639\) | 1.51632e6 | 0.146906 | ||||||||
\(640\) | 9.65991e6 | 0.932230 | ||||||||
\(641\) | −3.43755e6 | −0.330449 | −0.165224 | − | 0.986256i | \(-0.552835\pi\) | ||||
−0.165224 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(642\) | −304380. | −0.0291460 | ||||||||
\(643\) | −1.62191e7 | −1.54703 | −0.773515 | − | 0.633778i | \(-0.781503\pi\) | ||||
−0.773515 | + | 0.633778i | \(0.781503\pi\) | |||||||
\(644\) | −197568. | −0.0187716 | ||||||||
\(645\) | 4.58532e6 | 0.433981 | ||||||||
\(646\) | −1.75105e7 | −1.65089 | ||||||||
\(647\) | 1.19929e7 | 1.12632 | 0.563160 | − | 0.826348i | \(-0.309585\pi\) | ||||
0.563160 | + | 0.826348i | \(0.309585\pi\) | |||||||
\(648\) | −1.27940e6 | −0.119693 | ||||||||
\(649\) | −583440. | −0.0543731 | ||||||||
\(650\) | −2.19873e7 | −2.04122 | ||||||||
\(651\) | −2.79418e6 | −0.258405 | ||||||||
\(652\) | −1.73076e6 | −0.159448 | ||||||||
\(653\) | 1.58009e6 | 0.145011 | 0.0725053 | − | 0.997368i | \(-0.476901\pi\) | ||||
0.0725053 | + | 0.997368i | \(0.476901\pi\) | |||||||
\(654\) | 8.02791e6 | 0.733936 | ||||||||
\(655\) | 6.85862e6 | 0.624645 | ||||||||
\(656\) | 2.44976e6 | 0.222262 | ||||||||
\(657\) | 3.75532e6 | 0.339417 | ||||||||
\(658\) | −211680. | −0.0190597 | ||||||||
\(659\) | 6.98358e6 | 0.626419 | 0.313209 | − | 0.949684i | \(-0.398596\pi\) | ||||
0.313209 | + | 0.949684i | \(0.398596\pi\) | |||||||
\(660\) | −307944. | −0.0275177 | ||||||||
\(661\) | 3.69602e6 | 0.329027 | 0.164513 | − | 0.986375i | \(-0.447395\pi\) | ||||
0.164513 | + | 0.986375i | \(0.447395\pi\) | |||||||
\(662\) | −1.69735e7 | −1.50532 | ||||||||
\(663\) | 1.40125e7 | 1.23803 | ||||||||
\(664\) | 1.58395e7 | 1.39418 | ||||||||
\(665\) | −7.97759e6 | −0.699548 | ||||||||
\(666\) | −2.97189e6 | −0.259625 | ||||||||
\(667\) | −3.17837e6 | −0.276624 | ||||||||
\(668\) | 4.79142e6 | 0.415454 | ||||||||
\(669\) | −1.68034e6 | −0.145155 | ||||||||
\(670\) | 656120. | 0.0564672 | ||||||||
\(671\) | −2.37130e6 | −0.203320 | ||||||||
\(672\) | −1.09588e6 | −0.0936142 | ||||||||
\(673\) | 1.84688e6 | 0.157182 | 0.0785908 | − | 0.996907i | \(-0.474958\pi\) | ||||
0.0785908 | + | 0.996907i | \(0.474958\pi\) | |||||||
\(674\) | 1.01366e7 | 0.859491 | ||||||||
\(675\) | 4.16332e6 | 0.351706 | ||||||||
\(676\) | −1.55125e6 | −0.130561 | ||||||||
\(677\) | −7.68501e6 | −0.644426 | −0.322213 | − | 0.946667i | \(-0.604427\pi\) | ||||
−0.322213 | + | 0.946667i | \(0.604427\pi\) | |||||||
\(678\) | −2.03103e6 | −0.169684 | ||||||||
\(679\) | −240786. | −0.0200427 | ||||||||
\(680\) | 3.70633e7 | 3.07377 | ||||||||
\(681\) | 3.02735e6 | 0.250147 | ||||||||
\(682\) | 1.64736e6 | 0.135621 | ||||||||
\(683\) | 7.12180e6 | 0.584168 | 0.292084 | − | 0.956393i | \(-0.405651\pi\) | ||||
0.292084 | + | 0.956393i | \(0.405651\pi\) | |||||||
\(684\) | −982044. | −0.0802584 | ||||||||
\(685\) | −8.85311e6 | −0.720891 | ||||||||
\(686\) | −588245. | −0.0477252 | ||||||||
\(687\) | −8.33683e6 | −0.673921 | ||||||||
\(688\) | −4.07042e6 | −0.327845 | ||||||||
\(689\) | −3.22014e6 | −0.258420 | ||||||||
\(690\) | −2.43648e6 | −0.194823 | ||||||||
\(691\) | −3.23787e6 | −0.257967 | −0.128983 | − | 0.991647i | \(-0.541171\pi\) | ||||
−0.128983 | + | 0.991647i | \(0.541171\pi\) | |||||||
\(692\) | 4.27332e6 | 0.339234 | ||||||||
\(693\) | −206388. | −0.0163249 | ||||||||
\(694\) | 1.74443e7 | 1.37485 | ||||||||
\(695\) | −4.49282e6 | −0.352823 | ||||||||
\(696\) | −9.68409e6 | −0.757767 | ||||||||
\(697\) | 6.59576e6 | 0.514260 | ||||||||
\(698\) | 4.82783e6 | 0.375071 | ||||||||
\(699\) | 1.13140e7 | 0.875839 | ||||||||
\(700\) | 1.95887e6 | 0.151099 | ||||||||
\(701\) | −7.39163e6 | −0.568127 | −0.284063 | − | 0.958805i | \(-0.591683\pi\) | ||||
−0.284063 | + | 0.958805i | \(0.591683\pi\) | |||||||
\(702\) | −2.80665e6 | −0.214954 | ||||||||
\(703\) | −1.27094e7 | −0.969923 | ||||||||
\(704\) | 1.89576e6 | 0.144163 | ||||||||
\(705\) | 730944. | 0.0553874 | ||||||||
\(706\) | 5.76965e6 | 0.435650 | ||||||||
\(707\) | 8.15135e6 | 0.613311 | ||||||||
\(708\) | 706860. | 0.0529969 | ||||||||
\(709\) | −5.33361e6 | −0.398479 | −0.199240 | − | 0.979951i | \(-0.563847\pi\) | ||||
−0.199240 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(710\) | 8.79840e6 | 0.655025 | ||||||||
\(711\) | 7.89134e6 | 0.585433 | ||||||||
\(712\) | 620490. | 0.0458706 | ||||||||
\(713\) | −3.64954e6 | −0.268852 | ||||||||
\(714\) | 4.45851e6 | 0.327299 | ||||||||
\(715\) | −3.76376e6 | −0.275332 | ||||||||
\(716\) | −4.63576e6 | −0.337939 | ||||||||
\(717\) | −3.12314e6 | −0.226879 | ||||||||
\(718\) | 8.05552e6 | 0.583153 | ||||||||
\(719\) | −1.14564e7 | −0.826468 | −0.413234 | − | 0.910625i | \(-0.635601\pi\) | ||||
−0.413234 | + | 0.910625i | \(0.635601\pi\) | |||||||
\(720\) | −5.71811e6 | −0.411075 | ||||||||
\(721\) | −7.70084e6 | −0.551696 | ||||||||
\(722\) | 2.61862e6 | 0.186952 | ||||||||
\(723\) | 892530. | 0.0635005 | ||||||||
\(724\) | −1.08241e6 | −0.0767442 | ||||||||
\(725\) | 3.15133e7 | 2.22663 | ||||||||
\(726\) | −7.12562e6 | −0.501742 | ||||||||
\(727\) | −2.49540e7 | −1.75107 | −0.875536 | − | 0.483153i | \(-0.839492\pi\) | ||||
−0.875536 | + | 0.483153i | \(0.839492\pi\) | |||||||
\(728\) | −7.35735e6 | −0.514509 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.17901e7 | 1.51340 | ||||||||
\(731\) | −1.09592e7 | −0.758555 | ||||||||
\(732\) | 2.87293e6 | 0.198174 | ||||||||
\(733\) | −1.43398e7 | −0.985789 | −0.492894 | − | 0.870089i | \(-0.664061\pi\) | ||||
−0.492894 | + | 0.870089i | \(0.664061\pi\) | |||||||
\(734\) | 1.83874e7 | 1.25974 | ||||||||
\(735\) | 2.03125e6 | 0.138690 | ||||||||
\(736\) | −1.43136e6 | −0.0973990 | ||||||||
\(737\) | 72592.0 | 0.00492289 | ||||||||
\(738\) | −1.32111e6 | −0.0892890 | ||||||||
\(739\) | 922932. | 0.0621668 | 0.0310834 | − | 0.999517i | \(-0.490104\pi\) | ||||
0.0310834 | + | 0.999517i | \(0.490104\pi\) | |||||||
\(740\) | 4.82840e6 | 0.324134 | ||||||||
\(741\) | −1.20028e7 | −0.803037 | ||||||||
\(742\) | −1.02459e6 | −0.0683188 | ||||||||
\(743\) | −9.38995e6 | −0.624010 | −0.312005 | − | 0.950081i | \(-0.601001\pi\) | ||||
−0.312005 | + | 0.950081i | \(0.601001\pi\) | |||||||
\(744\) | −1.11197e7 | −0.736478 | ||||||||
\(745\) | −1.16810e7 | −0.771062 | ||||||||
\(746\) | 3.24883e6 | 0.213737 | ||||||||
\(747\) | −6.57947e6 | −0.431409 | ||||||||
\(748\) | 736008. | 0.0480982 | ||||||||
\(749\) | 331436. | 0.0215871 | ||||||||
\(750\) | 1.09388e7 | 0.710094 | ||||||||
\(751\) | −408032. | −0.0263994 | −0.0131997 | − | 0.999913i | \(-0.504202\pi\) | ||||
−0.0131997 | + | 0.999913i | \(0.504202\pi\) | |||||||
\(752\) | −648864. | −0.0418417 | ||||||||
\(753\) | 3.09985e6 | 0.199229 | ||||||||
\(754\) | −2.12443e7 | −1.36086 | ||||||||
\(755\) | −4.19518e7 | −2.67845 | ||||||||
\(756\) | 250047. | 0.0159117 | ||||||||
\(757\) | 2.59605e7 | 1.64654 | 0.823271 | − | 0.567649i | \(-0.192147\pi\) | ||||
0.823271 | + | 0.567649i | \(0.192147\pi\) | |||||||
\(758\) | 1.60350e6 | 0.101367 | ||||||||
\(759\) | −269568. | −0.0169849 | ||||||||
\(760\) | −3.17476e7 | −1.99378 | ||||||||
\(761\) | 1.83554e7 | 1.14895 | 0.574477 | − | 0.818521i | \(-0.305206\pi\) | ||||
0.574477 | + | 0.818521i | \(0.305206\pi\) | |||||||
\(762\) | −9.22752e6 | −0.575702 | ||||||||
\(763\) | −8.74150e6 | −0.543594 | ||||||||
\(764\) | −3.40833e6 | −0.211255 | ||||||||
\(765\) | −1.53955e7 | −0.951131 | ||||||||
\(766\) | −1.18094e7 | −0.727206 | ||||||||
\(767\) | 8.63940e6 | 0.530268 | ||||||||
\(768\) | −5.87519e6 | −0.359434 | ||||||||
\(769\) | −747166. | −0.0455618 | −0.0227809 | − | 0.999740i | \(-0.507252\pi\) | ||||
−0.0227809 | + | 0.999740i | \(0.507252\pi\) | |||||||
\(770\) | −1.19756e6 | −0.0727898 | ||||||||
\(771\) | 2.65617e6 | 0.160924 | ||||||||
\(772\) | −4.34382e6 | −0.262318 | ||||||||
\(773\) | 2.02692e7 | 1.22008 | 0.610038 | − | 0.792372i | \(-0.291154\pi\) | ||||
0.610038 | + | 0.792372i | \(0.291154\pi\) | |||||||
\(774\) | 2.19510e6 | 0.131705 | ||||||||
\(775\) | 3.61849e7 | 2.16408 | ||||||||
\(776\) | −958230. | −0.0571236 | ||||||||
\(777\) | 3.23606e6 | 0.192293 | ||||||||
\(778\) | −1.76695e7 | −1.04659 | ||||||||
\(779\) | −5.64978e6 | −0.333571 | ||||||||
\(780\) | 4.55994e6 | 0.268363 | ||||||||
\(781\) | 973440. | 0.0571060 | ||||||||
\(782\) | 5.82336e6 | 0.340531 | ||||||||
\(783\) | 4.02262e6 | 0.234479 | ||||||||
\(784\) | −1.80315e6 | −0.104771 | ||||||||
\(785\) | −1.50161e7 | −0.869729 | ||||||||
\(786\) | 3.28338e6 | 0.189568 | ||||||||
\(787\) | −4.69982e6 | −0.270486 | −0.135243 | − | 0.990812i | \(-0.543181\pi\) | ||||
−0.135243 | + | 0.990812i | \(0.543181\pi\) | |||||||
\(788\) | 1.65599e6 | 0.0950041 | ||||||||
\(789\) | −1.14522e7 | −0.654931 | ||||||||
\(790\) | 4.57893e7 | 2.61033 | ||||||||
\(791\) | 2.21157e6 | 0.125678 | ||||||||
\(792\) | −821340. | −0.0465275 | ||||||||
\(793\) | 3.51135e7 | 1.98286 | ||||||||
\(794\) | 2.02406e7 | 1.13939 | ||||||||
\(795\) | 3.53797e6 | 0.198535 | ||||||||
\(796\) | −574728. | −0.0321499 | ||||||||
\(797\) | 584710. | 0.0326058 | 0.0163029 | − | 0.999867i | \(-0.494810\pi\) | ||||
0.0163029 | + | 0.999867i | \(0.494810\pi\) | |||||||
\(798\) | −3.81906e6 | −0.212300 | ||||||||
\(799\) | −1.74701e6 | −0.0968117 | ||||||||
\(800\) | 1.41918e7 | 0.783996 | ||||||||
\(801\) | −257742. | −0.0141940 | ||||||||
\(802\) | 1.03822e7 | 0.569975 | ||||||||
\(803\) | 2.41082e6 | 0.131940 | ||||||||
\(804\) | −87948.0 | −0.00479828 | ||||||||
\(805\) | 2.65306e6 | 0.144297 | ||||||||
\(806\) | −2.43936e7 | −1.32263 | ||||||||
\(807\) | 2.49097e6 | 0.134643 | ||||||||
\(808\) | 3.24390e7 | 1.74799 | ||||||||
\(809\) | −1.64013e7 | −0.881061 | −0.440531 | − | 0.897738i | \(-0.645210\pi\) | ||||
−0.440531 | + | 0.897738i | \(0.645210\pi\) | |||||||
\(810\) | 3.08367e6 | 0.165141 | ||||||||
\(811\) | −304948. | −0.0162807 | −0.00814036 | − | 0.999967i | \(-0.502591\pi\) | ||||
−0.00814036 | + | 0.999967i | \(0.502591\pi\) | |||||||
\(812\) | 1.89267e6 | 0.100736 | ||||||||
\(813\) | −1.16094e7 | −0.616005 | ||||||||
\(814\) | −1.90788e6 | −0.100923 | ||||||||
\(815\) | 2.32417e7 | 1.22567 | ||||||||
\(816\) | 1.36667e7 | 0.718519 | ||||||||
\(817\) | 9.38744e6 | 0.492031 | ||||||||
\(818\) | 1.28716e7 | 0.672587 | ||||||||
\(819\) | 3.05613e6 | 0.159207 | ||||||||
\(820\) | 2.14640e6 | 0.111474 | ||||||||
\(821\) | 3.43428e7 | 1.77819 | 0.889095 | − | 0.457722i | \(-0.151335\pi\) | ||||
0.889095 | + | 0.457722i | \(0.151335\pi\) | |||||||
\(822\) | −4.23819e6 | −0.218777 | ||||||||
\(823\) | 1.56684e7 | 0.806351 | 0.403176 | − | 0.915123i | \(-0.367906\pi\) | ||||
0.403176 | + | 0.915123i | \(0.367906\pi\) | |||||||
\(824\) | −3.06462e7 | −1.57238 | ||||||||
\(825\) | 2.67275e6 | 0.136717 | ||||||||
\(826\) | 2.74890e6 | 0.140187 | ||||||||
\(827\) | −2.96886e7 | −1.50948 | −0.754738 | − | 0.656026i | \(-0.772236\pi\) | ||||
−0.754738 | + | 0.656026i | \(0.772236\pi\) | |||||||
\(828\) | 326592. | 0.0165550 | ||||||||
\(829\) | −2.30708e7 | −1.16594 | −0.582970 | − | 0.812494i | \(-0.698110\pi\) | ||||
−0.582970 | + | 0.812494i | \(0.698110\pi\) | |||||||
\(830\) | −3.81772e7 | −1.92357 | ||||||||
\(831\) | 1.54490e7 | 0.776062 | ||||||||
\(832\) | −2.80719e7 | −1.40593 | ||||||||
\(833\) | −4.85482e6 | −0.242416 | ||||||||
\(834\) | −2.15082e6 | −0.107075 | ||||||||
\(835\) | −6.43419e7 | −3.19358 | ||||||||
\(836\) | −630448. | −0.0311985 | ||||||||
\(837\) | 4.61894e6 | 0.227892 | ||||||||
\(838\) | 4.24074e6 | 0.208608 | ||||||||
\(839\) | 2.32642e7 | 1.14100 | 0.570498 | − | 0.821299i | \(-0.306750\pi\) | ||||
0.570498 | + | 0.821299i | \(0.306750\pi\) | |||||||
\(840\) | 8.08353e6 | 0.395278 | ||||||||
\(841\) | 9.93718e6 | 0.484477 | ||||||||
\(842\) | 7.18411e6 | 0.349215 | ||||||||
\(843\) | −1.32496e7 | −0.642148 | ||||||||
\(844\) | −699244. | −0.0337888 | ||||||||
\(845\) | 2.08311e7 | 1.00362 | ||||||||
\(846\) | 349920. | 0.0168090 | ||||||||
\(847\) | 7.75900e6 | 0.371619 | ||||||||
\(848\) | −3.14068e6 | −0.149980 | ||||||||
\(849\) | 9.25931e6 | 0.440869 | ||||||||
\(850\) | −5.77382e7 | −2.74104 | ||||||||
\(851\) | 4.22669e6 | 0.200067 | ||||||||
\(852\) | −1.17936e6 | −0.0556605 | ||||||||
\(853\) | 1.91515e7 | 0.901219 | 0.450610 | − | 0.892721i | \(-0.351207\pi\) | ||||
0.450610 | + | 0.892721i | \(0.351207\pi\) | |||||||
\(854\) | 1.11725e7 | 0.524210 | ||||||||
\(855\) | 1.31874e7 | 0.616944 | ||||||||
\(856\) | 1.31898e6 | 0.0615253 | ||||||||
\(857\) | −5.34683e6 | −0.248682 | −0.124341 | − | 0.992240i | \(-0.539682\pi\) | ||||
−0.124341 | + | 0.992240i | \(0.539682\pi\) | |||||||
\(858\) | −1.80180e6 | −0.0835581 | ||||||||
\(859\) | 3.95858e7 | 1.83045 | 0.915223 | − | 0.402948i | \(-0.132014\pi\) | ||||
0.915223 | + | 0.402948i | \(0.132014\pi\) | |||||||
\(860\) | −3.56636e6 | −0.164429 | ||||||||
\(861\) | 1.43854e6 | 0.0661325 | ||||||||
\(862\) | 1.17719e7 | 0.539607 | ||||||||
\(863\) | −2.50284e7 | −1.14395 | −0.571973 | − | 0.820272i | \(-0.693822\pi\) | ||||
−0.571973 | + | 0.820272i | \(0.693822\pi\) | |||||||
\(864\) | 1.81156e6 | 0.0825600 | ||||||||
\(865\) | −5.73846e7 | −2.60768 | ||||||||
\(866\) | −1.89404e7 | −0.858211 | ||||||||
\(867\) | 2.40176e7 | 1.08513 | ||||||||
\(868\) | 2.17325e6 | 0.0979062 | ||||||||
\(869\) | 5.06605e6 | 0.227573 | ||||||||
\(870\) | 2.33411e7 | 1.04550 | ||||||||
\(871\) | −1.07492e6 | −0.0480099 | ||||||||
\(872\) | −3.47876e7 | −1.54929 | ||||||||
\(873\) | 398034. | 0.0176760 | ||||||||
\(874\) | −4.98816e6 | −0.220883 | ||||||||
\(875\) | −1.19111e7 | −0.525935 | ||||||||
\(876\) | −2.92081e6 | −0.128600 | ||||||||
\(877\) | −5.02589e6 | −0.220655 | −0.110328 | − | 0.993895i | \(-0.535190\pi\) | ||||
−0.110328 | + | 0.993895i | \(0.535190\pi\) | |||||||
\(878\) | −1.82161e7 | −0.797480 | ||||||||
\(879\) | −1.06746e7 | −0.465993 | ||||||||
\(880\) | −3.67089e6 | −0.159795 | ||||||||
\(881\) | −2.60490e7 | −1.13071 | −0.565356 | − | 0.824847i | \(-0.691261\pi\) | ||||
−0.565356 | + | 0.824847i | \(0.691261\pi\) | |||||||
\(882\) | 972405. | 0.0420897 | ||||||||
\(883\) | −6.82462e6 | −0.294562 | −0.147281 | − | 0.989095i | \(-0.547052\pi\) | ||||
−0.147281 | + | 0.989095i | \(0.547052\pi\) | |||||||
\(884\) | −1.08986e7 | −0.469072 | ||||||||
\(885\) | −9.49212e6 | −0.407385 | ||||||||
\(886\) | 1.24195e7 | 0.531519 | ||||||||
\(887\) | 2.33835e7 | 0.997931 | 0.498965 | − | 0.866622i | \(-0.333713\pi\) | ||||
0.498965 | + | 0.866622i | \(0.333713\pi\) | |||||||
\(888\) | 1.28782e7 | 0.548053 | ||||||||
\(889\) | 1.00477e7 | 0.426397 | ||||||||
\(890\) | −1.49554e6 | −0.0632882 | ||||||||
\(891\) | 341172. | 0.0143972 | ||||||||
\(892\) | 1.30693e6 | 0.0549971 | ||||||||
\(893\) | 1.49645e6 | 0.0627961 | ||||||||
\(894\) | −5.59197e6 | −0.234003 | ||||||||
\(895\) | 6.22517e7 | 2.59773 | ||||||||
\(896\) | −5.03548e6 | −0.209542 | ||||||||
\(897\) | 3.99168e6 | 0.165644 | ||||||||
\(898\) | −1.31589e7 | −0.544537 | ||||||||
\(899\) | 3.49620e7 | 1.44277 | ||||||||
\(900\) | −3.23814e6 | −0.133257 | ||||||||
\(901\) | −8.45600e6 | −0.347019 | ||||||||
\(902\) | −848120. | −0.0347089 | ||||||||
\(903\) | −2.39022e6 | −0.0975480 | ||||||||
\(904\) | 8.80113e6 | 0.358193 | ||||||||
\(905\) | 1.45352e7 | 0.589930 | ||||||||
\(906\) | −2.00833e7 | −0.812859 | ||||||||
\(907\) | 3.95959e7 | 1.59820 | 0.799102 | − | 0.601196i | \(-0.205309\pi\) | ||||
0.799102 | + | 0.601196i | \(0.205309\pi\) | |||||||
\(908\) | −2.35460e6 | −0.0947771 | ||||||||
\(909\) | −1.34747e7 | −0.540890 | ||||||||
\(910\) | 1.77331e7 | 0.709874 | ||||||||
\(911\) | −4.67570e6 | −0.186660 | −0.0933300 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933300 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(912\) | −1.17066e7 | −0.466062 | ||||||||
\(913\) | −4.22386e6 | −0.167700 | ||||||||
\(914\) | −5.80651e6 | −0.229906 | ||||||||
\(915\) | −3.85793e7 | −1.52336 | ||||||||
\(916\) | 6.48420e6 | 0.255339 | ||||||||
\(917\) | −3.57524e6 | −0.140405 | ||||||||
\(918\) | −7.37019e6 | −0.288650 | ||||||||
\(919\) | −4.92594e6 | −0.192398 | −0.0961990 | − | 0.995362i | \(-0.530669\pi\) | ||||
−0.0961990 | + | 0.995362i | \(0.530669\pi\) | |||||||
\(920\) | 1.05581e7 | 0.411259 | ||||||||
\(921\) | 1.36702e7 | 0.531040 | ||||||||
\(922\) | 1.40692e7 | 0.545058 | ||||||||
\(923\) | −1.44144e7 | −0.556919 | ||||||||
\(924\) | 160524. | 0.00618529 | ||||||||
\(925\) | −4.19073e7 | −1.61041 | ||||||||
\(926\) | 3.42150e7 | 1.31126 | ||||||||
\(927\) | 1.27300e7 | 0.486550 | ||||||||
\(928\) | 1.37122e7 | 0.522683 | ||||||||
\(929\) | −3.23688e7 | −1.23052 | −0.615258 | − | 0.788326i | \(-0.710948\pi\) | ||||
−0.615258 | + | 0.788326i | \(0.710948\pi\) | |||||||
\(930\) | 2.68013e7 | 1.01613 | ||||||||
\(931\) | 4.15853e6 | 0.157241 | ||||||||
\(932\) | −8.79980e6 | −0.331843 | ||||||||
\(933\) | 1.91527e6 | 0.0720321 | ||||||||
\(934\) | 1.67157e7 | 0.626985 | ||||||||
\(935\) | −9.88354e6 | −0.369729 | ||||||||
\(936\) | 1.21622e7 | 0.453754 | ||||||||
\(937\) | −3.32337e7 | −1.23660 | −0.618301 | − | 0.785941i | \(-0.712179\pi\) | ||||
−0.618301 | + | 0.785941i | \(0.712179\pi\) | |||||||
\(938\) | −342020. | −0.0126924 | ||||||||
\(939\) | −17046.0 | −0.000630897 0 | ||||||||
\(940\) | −568512. | −0.0209855 | ||||||||
\(941\) | −2.66426e7 | −0.980852 | −0.490426 | − | 0.871483i | \(-0.663159\pi\) | ||||
−0.490426 | + | 0.871483i | \(0.663159\pi\) | |||||||
\(942\) | −7.18857e6 | −0.263946 | ||||||||
\(943\) | 1.87891e6 | 0.0688061 | ||||||||
\(944\) | 8.42622e6 | 0.307753 | ||||||||
\(945\) | −3.35777e6 | −0.122313 | ||||||||
\(946\) | 1.40920e6 | 0.0511970 | ||||||||
\(947\) | 3.14663e7 | 1.14017 | 0.570086 | − | 0.821585i | \(-0.306910\pi\) | ||||
0.570086 | + | 0.821585i | \(0.306910\pi\) | |||||||
\(948\) | −6.13771e6 | −0.221812 | ||||||||
\(949\) | −3.56987e7 | −1.28673 | ||||||||
\(950\) | 4.94573e7 | 1.77796 | ||||||||
\(951\) | −1.42108e7 | −0.509527 | ||||||||
\(952\) | −1.93202e7 | −0.690907 | ||||||||
\(953\) | −1.34516e7 | −0.479779 | −0.239890 | − | 0.970800i | \(-0.577111\pi\) | ||||
−0.239890 | + | 0.970800i | \(0.577111\pi\) | |||||||
\(954\) | 1.69371e6 | 0.0602515 | ||||||||
\(955\) | 4.57690e7 | 1.62391 | ||||||||
\(956\) | 2.42911e6 | 0.0859613 | ||||||||
\(957\) | 2.58242e6 | 0.0911481 | ||||||||
\(958\) | −2.14124e7 | −0.753792 | ||||||||
\(959\) | 4.61492e6 | 0.162038 | ||||||||
\(960\) | 3.08426e7 | 1.08012 | ||||||||
\(961\) | 1.15157e7 | 0.402238 | ||||||||
\(962\) | 2.82513e7 | 0.984239 | ||||||||
\(963\) | −547884. | −0.0190381 | ||||||||
\(964\) | −694190. | −0.0240595 | ||||||||
\(965\) | 5.83313e7 | 2.01643 | ||||||||
\(966\) | 1.27008e6 | 0.0437913 | ||||||||
\(967\) | −2.84963e7 | −0.979992 | −0.489996 | − | 0.871725i | \(-0.663002\pi\) | ||||
−0.489996 | + | 0.871725i | \(0.663002\pi\) | |||||||
\(968\) | 3.08777e7 | 1.05915 | ||||||||
\(969\) | −3.15189e7 | −1.07836 | ||||||||
\(970\) | 2.30958e6 | 0.0788141 | ||||||||
\(971\) | 1.81858e7 | 0.618990 | 0.309495 | − | 0.950901i | \(-0.399840\pi\) | ||||
0.309495 | + | 0.950901i | \(0.399840\pi\) | |||||||
\(972\) | −413343. | −0.0140328 | ||||||||
\(973\) | 2.34200e6 | 0.0793059 | ||||||||
\(974\) | −4.46588e7 | −1.50837 | ||||||||
\(975\) | −3.95772e7 | −1.33332 | ||||||||
\(976\) | 3.42471e7 | 1.15080 | ||||||||
\(977\) | 3.20941e7 | 1.07569 | 0.537847 | − | 0.843042i | \(-0.319238\pi\) | ||||
0.537847 | + | 0.843042i | \(0.319238\pi\) | |||||||
\(978\) | 1.11263e7 | 0.371968 | ||||||||
\(979\) | −165464. | −0.00551756 | ||||||||
\(980\) | −1.57986e6 | −0.0525476 | ||||||||
\(981\) | 1.44502e7 | 0.479405 | ||||||||
\(982\) | 1.37653e7 | 0.455519 | ||||||||
\(983\) | 1.56154e7 | 0.515429 | 0.257715 | − | 0.966221i | \(-0.417031\pi\) | ||||
0.257715 | + | 0.966221i | \(0.417031\pi\) | |||||||
\(984\) | 5.72481e6 | 0.188483 | ||||||||
\(985\) | −2.22376e7 | −0.730293 | ||||||||
\(986\) | −5.57870e7 | −1.82743 | ||||||||
\(987\) | −381024. | −0.0124497 | ||||||||
\(988\) | 9.33548e6 | 0.304260 | ||||||||
\(989\) | −3.12192e6 | −0.101492 | ||||||||
\(990\) | 1.97964e6 | 0.0641946 | ||||||||
\(991\) | 4.84499e7 | 1.56714 | 0.783572 | − | 0.621301i | \(-0.213395\pi\) | ||||
0.783572 | + | 0.621301i | \(0.213395\pi\) | |||||||
\(992\) | 1.57450e7 | 0.507998 | ||||||||
\(993\) | −3.05524e7 | −0.983268 | ||||||||
\(994\) | −4.58640e6 | −0.147233 | ||||||||
\(995\) | 7.71778e6 | 0.247135 | ||||||||
\(996\) | 5.11736e6 | 0.163455 | ||||||||
\(997\) | −4.54336e7 | −1.44757 | −0.723784 | − | 0.690027i | \(-0.757599\pi\) | ||||
−0.723784 | + | 0.690027i | \(0.757599\pi\) | |||||||
\(998\) | 2.40204e7 | 0.763404 | ||||||||
\(999\) | −5.34940e6 | −0.169587 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 21.6.a.c.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 63.6.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 336.6.a.i.1.1 | 1 | |||
5.2 | odd | 4 | 525.6.d.c.274.2 | 2 | |||
5.3 | odd | 4 | 525.6.d.c.274.1 | 2 | |||
5.4 | even | 2 | 525.6.a.b.1.1 | 1 | |||
7.2 | even | 3 | 147.6.e.c.67.1 | 2 | |||
7.3 | odd | 6 | 147.6.e.d.79.1 | 2 | |||
7.4 | even | 3 | 147.6.e.c.79.1 | 2 | |||
7.5 | odd | 6 | 147.6.e.d.67.1 | 2 | |||
7.6 | odd | 2 | 147.6.a.f.1.1 | 1 | |||
12.11 | even | 2 | 1008.6.a.a.1.1 | 1 | |||
21.20 | even | 2 | 441.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
63.6.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
147.6.a.f.1.1 | 1 | 7.6 | odd | 2 | |||
147.6.e.c.67.1 | 2 | 7.2 | even | 3 | |||
147.6.e.c.79.1 | 2 | 7.4 | even | 3 | |||
147.6.e.d.67.1 | 2 | 7.5 | odd | 6 | |||
147.6.e.d.79.1 | 2 | 7.3 | odd | 6 | |||
336.6.a.i.1.1 | 1 | 4.3 | odd | 2 | |||
441.6.a.c.1.1 | 1 | 21.20 | even | 2 | |||
525.6.a.b.1.1 | 1 | 5.4 | even | 2 | |||
525.6.d.c.274.1 | 2 | 5.3 | odd | 4 | |||
525.6.d.c.274.2 | 2 | 5.2 | odd | 4 | |||
1008.6.a.a.1.1 | 1 | 12.11 | even | 2 |