Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,6,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, 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("966.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(154.930769939\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 966.1 |
$q$-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 | ||||||||
\(5\) | −54.0000 | −0.965981 | −0.482991 | − | 0.875625i | \(-0.660450\pi\) | ||||
−0.482991 | + | 0.875625i | \(0.660450\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 216.000 | 0.683052 | ||||||||
\(11\) | 564.000 | 1.40539 | 0.702696 | − | 0.711490i | \(-0.251979\pi\) | ||||
0.702696 | + | 0.711490i | \(0.251979\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 476.000 | 0.781175 | 0.390588 | − | 0.920566i | \(-0.372272\pi\) | ||||
0.390588 | + | 0.920566i | \(0.372272\pi\) | |||||||
\(14\) | −196.000 | −0.267261 | ||||||||
\(15\) | 486.000 | 0.557710 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1308.00 | −1.09770 | −0.548852 | − | 0.835919i | \(-0.684935\pi\) | ||||
−0.548852 | + | 0.835919i | \(0.684935\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 14.0000 | 0.00889701 | 0.00444850 | − | 0.999990i | \(-0.498584\pi\) | ||||
0.00444850 | + | 0.999990i | \(0.498584\pi\) | |||||||
\(20\) | −864.000 | −0.482991 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | −2256.00 | −0.993762 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | −209.000 | −0.0668800 | ||||||||
\(26\) | −1904.00 | −0.552374 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 784.000 | 0.188982 | ||||||||
\(29\) | −6702.00 | −1.47982 | −0.739911 | − | 0.672705i | \(-0.765132\pi\) | ||||
−0.739911 | + | 0.672705i | \(0.765132\pi\) | |||||||
\(30\) | −1944.00 | −0.394360 | ||||||||
\(31\) | −10258.0 | −1.91716 | −0.958580 | − | 0.284823i | \(-0.908065\pi\) | ||||
−0.958580 | + | 0.284823i | \(0.908065\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −5076.00 | −0.811403 | ||||||||
\(34\) | 5232.00 | 0.776194 | ||||||||
\(35\) | −2646.00 | −0.365107 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 14078.0 | 1.69058 | 0.845292 | − | 0.534305i | \(-0.179427\pi\) | ||||
0.845292 | + | 0.534305i | \(0.179427\pi\) | |||||||
\(38\) | −56.0000 | −0.00629114 | ||||||||
\(39\) | −4284.00 | −0.451012 | ||||||||
\(40\) | 3456.00 | 0.341526 | ||||||||
\(41\) | −2826.00 | −0.262550 | −0.131275 | − | 0.991346i | \(-0.541907\pi\) | ||||
−0.131275 | + | 0.991346i | \(0.541907\pi\) | |||||||
\(42\) | 1764.00 | 0.154303 | ||||||||
\(43\) | 14216.0 | 1.17248 | 0.586241 | − | 0.810137i | \(-0.300607\pi\) | ||||
0.586241 | + | 0.810137i | \(0.300607\pi\) | |||||||
\(44\) | 9024.00 | 0.702696 | ||||||||
\(45\) | −4374.00 | −0.321994 | ||||||||
\(46\) | −2116.00 | −0.147442 | ||||||||
\(47\) | −9990.00 | −0.659661 | −0.329831 | − | 0.944040i | \(-0.606992\pi\) | ||||
−0.329831 | + | 0.944040i | \(0.606992\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 836.000 | 0.0472913 | ||||||||
\(51\) | 11772.0 | 0.633760 | ||||||||
\(52\) | 7616.00 | 0.390588 | ||||||||
\(53\) | 16698.0 | 0.816535 | 0.408267 | − | 0.912862i | \(-0.366133\pi\) | ||||
0.408267 | + | 0.912862i | \(0.366133\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | −30456.0 | −1.35758 | ||||||||
\(56\) | −3136.00 | −0.133631 | ||||||||
\(57\) | −126.000 | −0.00513669 | ||||||||
\(58\) | 26808.0 | 1.04639 | ||||||||
\(59\) | 19044.0 | 0.712243 | 0.356121 | − | 0.934440i | \(-0.384099\pi\) | ||||
0.356121 | + | 0.934440i | \(0.384099\pi\) | |||||||
\(60\) | 7776.00 | 0.278855 | ||||||||
\(61\) | 5678.00 | 0.195376 | 0.0976879 | − | 0.995217i | \(-0.468855\pi\) | ||||
0.0976879 | + | 0.995217i | \(0.468855\pi\) | |||||||
\(62\) | 41032.0 | 1.35564 | ||||||||
\(63\) | 3969.00 | 0.125988 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −25704.0 | −0.754601 | ||||||||
\(66\) | 20304.0 | 0.573749 | ||||||||
\(67\) | −39736.0 | −1.08143 | −0.540713 | − | 0.841207i | \(-0.681846\pi\) | ||||
−0.540713 | + | 0.841207i | \(0.681846\pi\) | |||||||
\(68\) | −20928.0 | −0.548852 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | 10584.0 | 0.258169 | ||||||||
\(71\) | 60108.0 | 1.41510 | 0.707549 | − | 0.706664i | \(-0.249801\pi\) | ||||
0.707549 | + | 0.706664i | \(0.249801\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | −7714.00 | −0.169423 | −0.0847115 | − | 0.996406i | \(-0.526997\pi\) | ||||
−0.0847115 | + | 0.996406i | \(0.526997\pi\) | |||||||
\(74\) | −56312.0 | −1.19542 | ||||||||
\(75\) | 1881.00 | 0.0386132 | ||||||||
\(76\) | 224.000 | 0.00444850 | ||||||||
\(77\) | 27636.0 | 0.531188 | ||||||||
\(78\) | 17136.0 | 0.318914 | ||||||||
\(79\) | 106472. | 1.91941 | 0.959705 | − | 0.281010i | \(-0.0906694\pi\) | ||||
0.959705 | + | 0.281010i | \(0.0906694\pi\) | |||||||
\(80\) | −13824.0 | −0.241495 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 11304.0 | 0.185651 | ||||||||
\(83\) | −7662.00 | −0.122081 | −0.0610403 | − | 0.998135i | \(-0.519442\pi\) | ||||
−0.0610403 | + | 0.998135i | \(0.519442\pi\) | |||||||
\(84\) | −7056.00 | −0.109109 | ||||||||
\(85\) | 70632.0 | 1.06036 | ||||||||
\(86\) | −56864.0 | −0.829070 | ||||||||
\(87\) | 60318.0 | 0.854376 | ||||||||
\(88\) | −36096.0 | −0.496881 | ||||||||
\(89\) | −76536.0 | −1.02421 | −0.512107 | − | 0.858922i | \(-0.671135\pi\) | ||||
−0.512107 | + | 0.858922i | \(0.671135\pi\) | |||||||
\(90\) | 17496.0 | 0.227684 | ||||||||
\(91\) | 23324.0 | 0.295257 | ||||||||
\(92\) | 8464.00 | 0.104257 | ||||||||
\(93\) | 92322.0 | 1.10687 | ||||||||
\(94\) | 39960.0 | 0.466451 | ||||||||
\(95\) | −756.000 | −0.00859434 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −19048.0 | −0.205551 | −0.102776 | − | 0.994705i | \(-0.532772\pi\) | ||||
−0.102776 | + | 0.994705i | \(0.532772\pi\) | |||||||
\(98\) | −9604.00 | −0.101015 | ||||||||
\(99\) | 45684.0 | 0.468464 | ||||||||
\(100\) | −3344.00 | −0.0334400 | ||||||||
\(101\) | 67176.0 | 0.655256 | 0.327628 | − | 0.944807i | \(-0.393751\pi\) | ||||
0.327628 | + | 0.944807i | \(0.393751\pi\) | |||||||
\(102\) | −47088.0 | −0.448136 | ||||||||
\(103\) | −6052.00 | −0.0562090 | −0.0281045 | − | 0.999605i | \(-0.508947\pi\) | ||||
−0.0281045 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(104\) | −30464.0 | −0.276187 | ||||||||
\(105\) | 23814.0 | 0.210794 | ||||||||
\(106\) | −66792.0 | −0.577377 | ||||||||
\(107\) | −182748. | −1.54310 | −0.771548 | − | 0.636171i | \(-0.780517\pi\) | ||||
−0.771548 | + | 0.636171i | \(0.780517\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 136274. | 1.09862 | 0.549309 | − | 0.835619i | \(-0.314891\pi\) | ||||
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(110\) | 121824. | 0.959956 | ||||||||
\(111\) | −126702. | −0.976059 | ||||||||
\(112\) | 12544.0 | 0.0944911 | ||||||||
\(113\) | −233886. | −1.72309 | −0.861545 | − | 0.507681i | \(-0.830503\pi\) | ||||
−0.861545 | + | 0.507681i | \(0.830503\pi\) | |||||||
\(114\) | 504.000 | 0.00363219 | ||||||||
\(115\) | −28566.0 | −0.201421 | ||||||||
\(116\) | −107232. | −0.739911 | ||||||||
\(117\) | 38556.0 | 0.260392 | ||||||||
\(118\) | −76176.0 | −0.503632 | ||||||||
\(119\) | −64092.0 | −0.414893 | ||||||||
\(120\) | −31104.0 | −0.197180 | ||||||||
\(121\) | 157045. | 0.975126 | ||||||||
\(122\) | −22712.0 | −0.138152 | ||||||||
\(123\) | 25434.0 | 0.151583 | ||||||||
\(124\) | −164128. | −0.958580 | ||||||||
\(125\) | 180036. | 1.03059 | ||||||||
\(126\) | −15876.0 | −0.0890871 | ||||||||
\(127\) | −183124. | −1.00748 | −0.503739 | − | 0.863856i | \(-0.668043\pi\) | ||||
−0.503739 | + | 0.863856i | \(0.668043\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −127944. | −0.676933 | ||||||||
\(130\) | 102816. | 0.533583 | ||||||||
\(131\) | −227148. | −1.15646 | −0.578230 | − | 0.815874i | \(-0.696256\pi\) | ||||
−0.578230 | + | 0.815874i | \(0.696256\pi\) | |||||||
\(132\) | −81216.0 | −0.405702 | ||||||||
\(133\) | 686.000 | 0.00336275 | ||||||||
\(134\) | 158944. | 0.764684 | ||||||||
\(135\) | 39366.0 | 0.185903 | ||||||||
\(136\) | 83712.0 | 0.388097 | ||||||||
\(137\) | 319902. | 1.45618 | 0.728091 | − | 0.685481i | \(-0.240408\pi\) | ||||
0.728091 | + | 0.685481i | \(0.240408\pi\) | |||||||
\(138\) | 19044.0 | 0.0851257 | ||||||||
\(139\) | 126944. | 0.557282 | 0.278641 | − | 0.960395i | \(-0.410116\pi\) | ||||
0.278641 | + | 0.960395i | \(0.410116\pi\) | |||||||
\(140\) | −42336.0 | −0.182553 | ||||||||
\(141\) | 89910.0 | 0.380855 | ||||||||
\(142\) | −240432. | −1.00063 | ||||||||
\(143\) | 268464. | 1.09786 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 361908. | 1.42948 | ||||||||
\(146\) | 30856.0 | 0.119800 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | 225248. | 0.845292 | ||||||||
\(149\) | 129990. | 0.479672 | 0.239836 | − | 0.970813i | \(-0.422906\pi\) | ||||
0.239836 | + | 0.970813i | \(0.422906\pi\) | |||||||
\(150\) | −7524.00 | −0.0273036 | ||||||||
\(151\) | −326932. | −1.16685 | −0.583425 | − | 0.812167i | \(-0.698288\pi\) | ||||
−0.583425 | + | 0.812167i | \(0.698288\pi\) | |||||||
\(152\) | −896.000 | −0.00314557 | ||||||||
\(153\) | −105948. | −0.365901 | ||||||||
\(154\) | −110544. | −0.375607 | ||||||||
\(155\) | 553932. | 1.85194 | ||||||||
\(156\) | −68544.0 | −0.225506 | ||||||||
\(157\) | 469394. | 1.51981 | 0.759903 | − | 0.650036i | \(-0.225246\pi\) | ||||
0.759903 | + | 0.650036i | \(0.225246\pi\) | |||||||
\(158\) | −425888. | −1.35723 | ||||||||
\(159\) | −150282. | −0.471427 | ||||||||
\(160\) | 55296.0 | 0.170763 | ||||||||
\(161\) | 25921.0 | 0.0788110 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | 113348. | 0.334153 | 0.167076 | − | 0.985944i | \(-0.446567\pi\) | ||||
0.167076 | + | 0.985944i | \(0.446567\pi\) | |||||||
\(164\) | −45216.0 | −0.131275 | ||||||||
\(165\) | 274104. | 0.783800 | ||||||||
\(166\) | 30648.0 | 0.0863241 | ||||||||
\(167\) | −220386. | −0.611495 | −0.305747 | − | 0.952113i | \(-0.598906\pi\) | ||||
−0.305747 | + | 0.952113i | \(0.598906\pi\) | |||||||
\(168\) | 28224.0 | 0.0771517 | ||||||||
\(169\) | −144717. | −0.389765 | ||||||||
\(170\) | −282528. | −0.749789 | ||||||||
\(171\) | 1134.00 | 0.00296567 | ||||||||
\(172\) | 227456. | 0.586241 | ||||||||
\(173\) | −647784. | −1.64556 | −0.822782 | − | 0.568357i | \(-0.807579\pi\) | ||||
−0.822782 | + | 0.568357i | \(0.807579\pi\) | |||||||
\(174\) | −241272. | −0.604135 | ||||||||
\(175\) | −10241.0 | −0.0252783 | ||||||||
\(176\) | 144384. | 0.351348 | ||||||||
\(177\) | −171396. | −0.411214 | ||||||||
\(178\) | 306144. | 0.724229 | ||||||||
\(179\) | 402348. | 0.938576 | 0.469288 | − | 0.883045i | \(-0.344511\pi\) | ||||
0.469288 | + | 0.883045i | \(0.344511\pi\) | |||||||
\(180\) | −69984.0 | −0.160997 | ||||||||
\(181\) | 338150. | 0.767208 | 0.383604 | − | 0.923498i | \(-0.374683\pi\) | ||||
0.383604 | + | 0.923498i | \(0.374683\pi\) | |||||||
\(182\) | −93296.0 | −0.208778 | ||||||||
\(183\) | −51102.0 | −0.112800 | ||||||||
\(184\) | −33856.0 | −0.0737210 | ||||||||
\(185\) | −760212. | −1.63307 | ||||||||
\(186\) | −369288. | −0.782677 | ||||||||
\(187\) | −737712. | −1.54270 | ||||||||
\(188\) | −159840. | −0.329831 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 3024.00 | 0.00607712 | ||||||||
\(191\) | 34992.0 | 0.0694041 | 0.0347021 | − | 0.999398i | \(-0.488952\pi\) | ||||
0.0347021 | + | 0.999398i | \(0.488952\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 733766. | 1.41796 | 0.708981 | − | 0.705228i | \(-0.249155\pi\) | ||||
0.708981 | + | 0.705228i | \(0.249155\pi\) | |||||||
\(194\) | 76192.0 | 0.145347 | ||||||||
\(195\) | 231336. | 0.435669 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −191970. | −0.352426 | −0.176213 | − | 0.984352i | \(-0.556385\pi\) | ||||
−0.176213 | + | 0.984352i | \(0.556385\pi\) | |||||||
\(198\) | −182736. | −0.331254 | ||||||||
\(199\) | 295412. | 0.528805 | 0.264402 | − | 0.964412i | \(-0.414825\pi\) | ||||
0.264402 | + | 0.964412i | \(0.414825\pi\) | |||||||
\(200\) | 13376.0 | 0.0236457 | ||||||||
\(201\) | 357624. | 0.624362 | ||||||||
\(202\) | −268704. | −0.463336 | ||||||||
\(203\) | −328398. | −0.559320 | ||||||||
\(204\) | 188352. | 0.316880 | ||||||||
\(205\) | 152604. | 0.253619 | ||||||||
\(206\) | 24208.0 | 0.0397458 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | 121856. | 0.195294 | ||||||||
\(209\) | 7896.00 | 0.0125038 | ||||||||
\(210\) | −95256.0 | −0.149054 | ||||||||
\(211\) | −605956. | −0.936990 | −0.468495 | − | 0.883466i | \(-0.655204\pi\) | ||||
−0.468495 | + | 0.883466i | \(0.655204\pi\) | |||||||
\(212\) | 267168. | 0.408267 | ||||||||
\(213\) | −540972. | −0.817007 | ||||||||
\(214\) | 730992. | 1.09113 | ||||||||
\(215\) | −767664. | −1.13260 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −502642. | −0.724619 | ||||||||
\(218\) | −545096. | −0.776840 | ||||||||
\(219\) | 69426.0 | 0.0978164 | ||||||||
\(220\) | −487296. | −0.678791 | ||||||||
\(221\) | −622608. | −0.857500 | ||||||||
\(222\) | 506808. | 0.690178 | ||||||||
\(223\) | −702694. | −0.946246 | −0.473123 | − | 0.880996i | \(-0.656873\pi\) | ||||
−0.473123 | + | 0.880996i | \(0.656873\pi\) | |||||||
\(224\) | −50176.0 | −0.0668153 | ||||||||
\(225\) | −16929.0 | −0.0222933 | ||||||||
\(226\) | 935544. | 1.21841 | ||||||||
\(227\) | 268398. | 0.345712 | 0.172856 | − | 0.984947i | \(-0.444700\pi\) | ||||
0.172856 | + | 0.984947i | \(0.444700\pi\) | |||||||
\(228\) | −2016.00 | −0.00256835 | ||||||||
\(229\) | 275966. | 0.347750 | 0.173875 | − | 0.984768i | \(-0.444371\pi\) | ||||
0.173875 | + | 0.984768i | \(0.444371\pi\) | |||||||
\(230\) | 114264. | 0.142426 | ||||||||
\(231\) | −248724. | −0.306682 | ||||||||
\(232\) | 428928. | 0.523196 | ||||||||
\(233\) | 492054. | 0.593776 | 0.296888 | − | 0.954912i | \(-0.404051\pi\) | ||||
0.296888 | + | 0.954912i | \(0.404051\pi\) | |||||||
\(234\) | −154224. | −0.184125 | ||||||||
\(235\) | 539460. | 0.637220 | ||||||||
\(236\) | 304704. | 0.356121 | ||||||||
\(237\) | −958248. | −1.10817 | ||||||||
\(238\) | 256368. | 0.293374 | ||||||||
\(239\) | −476556. | −0.539659 | −0.269829 | − | 0.962908i | \(-0.586967\pi\) | ||||
−0.269829 | + | 0.962908i | \(0.586967\pi\) | |||||||
\(240\) | 124416. | 0.139427 | ||||||||
\(241\) | 910508. | 1.00981 | 0.504907 | − | 0.863174i | \(-0.331527\pi\) | ||||
0.504907 | + | 0.863174i | \(0.331527\pi\) | |||||||
\(242\) | −628180. | −0.689518 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 90848.0 | 0.0976879 | ||||||||
\(245\) | −129654. | −0.137997 | ||||||||
\(246\) | −101736. | −0.107186 | ||||||||
\(247\) | 6664.00 | 0.00695012 | ||||||||
\(248\) | 656512. | 0.677819 | ||||||||
\(249\) | 68958.0 | 0.0704833 | ||||||||
\(250\) | −720144. | −0.728734 | ||||||||
\(251\) | −1.05776e6 | −1.05975 | −0.529873 | − | 0.848077i | \(-0.677761\pi\) | ||||
−0.529873 | + | 0.848077i | \(0.677761\pi\) | |||||||
\(252\) | 63504.0 | 0.0629941 | ||||||||
\(253\) | 298356. | 0.293044 | ||||||||
\(254\) | 732496. | 0.712395 | ||||||||
\(255\) | −635688. | −0.612200 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.99438e6 | −1.88354 | −0.941771 | − | 0.336254i | \(-0.890840\pi\) | ||||
−0.941771 | + | 0.336254i | \(0.890840\pi\) | |||||||
\(258\) | 511776. | 0.478664 | ||||||||
\(259\) | 689822. | 0.638981 | ||||||||
\(260\) | −411264. | −0.377300 | ||||||||
\(261\) | −542862. | −0.493274 | ||||||||
\(262\) | 908592. | 0.817741 | ||||||||
\(263\) | −2.05939e6 | −1.83590 | −0.917951 | − | 0.396693i | \(-0.870158\pi\) | ||||
−0.917951 | + | 0.396693i | \(0.870158\pi\) | |||||||
\(264\) | 324864. | 0.286874 | ||||||||
\(265\) | −901692. | −0.788758 | ||||||||
\(266\) | −2744.00 | −0.00237783 | ||||||||
\(267\) | 688824. | 0.591330 | ||||||||
\(268\) | −635776. | −0.540713 | ||||||||
\(269\) | 610872. | 0.514718 | 0.257359 | − | 0.966316i | \(-0.417148\pi\) | ||||
0.257359 | + | 0.966316i | \(0.417148\pi\) | |||||||
\(270\) | −157464. | −0.131453 | ||||||||
\(271\) | −1.83771e6 | −1.52004 | −0.760019 | − | 0.649900i | \(-0.774811\pi\) | ||||
−0.760019 | + | 0.649900i | \(0.774811\pi\) | |||||||
\(272\) | −334848. | −0.274426 | ||||||||
\(273\) | −209916. | −0.170466 | ||||||||
\(274\) | −1.27961e6 | −1.02968 | ||||||||
\(275\) | −117876. | −0.0939926 | ||||||||
\(276\) | −76176.0 | −0.0601929 | ||||||||
\(277\) | −1.15727e6 | −0.906220 | −0.453110 | − | 0.891455i | \(-0.649686\pi\) | ||||
−0.453110 | + | 0.891455i | \(0.649686\pi\) | |||||||
\(278\) | −507776. | −0.394058 | ||||||||
\(279\) | −830898. | −0.639053 | ||||||||
\(280\) | 169344. | 0.129085 | ||||||||
\(281\) | −1.33204e6 | −1.00636 | −0.503179 | − | 0.864182i | \(-0.667836\pi\) | ||||
−0.503179 | + | 0.864182i | \(0.667836\pi\) | |||||||
\(282\) | −359640. | −0.269305 | ||||||||
\(283\) | 1.93125e6 | 1.43341 | 0.716707 | − | 0.697375i | \(-0.245649\pi\) | ||||
0.716707 | + | 0.697375i | \(0.245649\pi\) | |||||||
\(284\) | 961728. | 0.707549 | ||||||||
\(285\) | 6804.00 | 0.00496195 | ||||||||
\(286\) | −1.07386e6 | −0.776302 | ||||||||
\(287\) | −138474. | −0.0992347 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 291007. | 0.204955 | ||||||||
\(290\) | −1.44763e6 | −1.01080 | ||||||||
\(291\) | 171432. | 0.118675 | ||||||||
\(292\) | −123424. | −0.0847115 | ||||||||
\(293\) | 1.47079e6 | 1.00088 | 0.500438 | − | 0.865772i | \(-0.333172\pi\) | ||||
0.500438 | + | 0.865772i | \(0.333172\pi\) | |||||||
\(294\) | 86436.0 | 0.0583212 | ||||||||
\(295\) | −1.02838e6 | −0.688013 | ||||||||
\(296\) | −900992. | −0.597712 | ||||||||
\(297\) | −411156. | −0.270468 | ||||||||
\(298\) | −519960. | −0.339179 | ||||||||
\(299\) | 251804. | 0.162886 | ||||||||
\(300\) | 30096.0 | 0.0193066 | ||||||||
\(301\) | 696584. | 0.443157 | ||||||||
\(302\) | 1.30773e6 | 0.825088 | ||||||||
\(303\) | −604584. | −0.378312 | ||||||||
\(304\) | 3584.00 | 0.00222425 | ||||||||
\(305\) | −306612. | −0.188729 | ||||||||
\(306\) | 423792. | 0.258731 | ||||||||
\(307\) | 1.66333e6 | 1.00724 | 0.503619 | − | 0.863926i | \(-0.332002\pi\) | ||||
0.503619 | + | 0.863926i | \(0.332002\pi\) | |||||||
\(308\) | 442176. | 0.265594 | ||||||||
\(309\) | 54468.0 | 0.0324523 | ||||||||
\(310\) | −2.21573e6 | −1.30952 | ||||||||
\(311\) | 1.45701e6 | 0.854204 | 0.427102 | − | 0.904203i | \(-0.359535\pi\) | ||||
0.427102 | + | 0.904203i | \(0.359535\pi\) | |||||||
\(312\) | 274176. | 0.159457 | ||||||||
\(313\) | 740588. | 0.427283 | 0.213642 | − | 0.976912i | \(-0.431468\pi\) | ||||
0.213642 | + | 0.976912i | \(0.431468\pi\) | |||||||
\(314\) | −1.87758e6 | −1.07467 | ||||||||
\(315\) | −214326. | −0.121702 | ||||||||
\(316\) | 1.70355e6 | 0.959705 | ||||||||
\(317\) | −566826. | −0.316812 | −0.158406 | − | 0.987374i | \(-0.550635\pi\) | ||||
−0.158406 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(318\) | 601128. | 0.333349 | ||||||||
\(319\) | −3.77993e6 | −2.07973 | ||||||||
\(320\) | −221184. | −0.120748 | ||||||||
\(321\) | 1.64473e6 | 0.890907 | ||||||||
\(322\) | −103684. | −0.0557278 | ||||||||
\(323\) | −18312.0 | −0.00976629 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −99484.0 | −0.0522450 | ||||||||
\(326\) | −453392. | −0.236282 | ||||||||
\(327\) | −1.22647e6 | −0.634287 | ||||||||
\(328\) | 180864. | 0.0928255 | ||||||||
\(329\) | −489510. | −0.249328 | ||||||||
\(330\) | −1.09642e6 | −0.554231 | ||||||||
\(331\) | −2.83750e6 | −1.42353 | −0.711764 | − | 0.702419i | \(-0.752103\pi\) | ||||
−0.711764 | + | 0.702419i | \(0.752103\pi\) | |||||||
\(332\) | −122592. | −0.0610403 | ||||||||
\(333\) | 1.14032e6 | 0.563528 | ||||||||
\(334\) | 881544. | 0.432392 | ||||||||
\(335\) | 2.14574e6 | 1.04464 | ||||||||
\(336\) | −112896. | −0.0545545 | ||||||||
\(337\) | 1.24573e6 | 0.597517 | 0.298759 | − | 0.954329i | \(-0.403427\pi\) | ||||
0.298759 | + | 0.954329i | \(0.403427\pi\) | |||||||
\(338\) | 578868. | 0.275605 | ||||||||
\(339\) | 2.10497e6 | 0.994827 | ||||||||
\(340\) | 1.13011e6 | 0.530181 | ||||||||
\(341\) | −5.78551e6 | −2.69436 | ||||||||
\(342\) | −4536.00 | −0.00209705 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | −909824. | −0.414535 | ||||||||
\(345\) | 257094. | 0.116290 | ||||||||
\(346\) | 2.59114e6 | 1.16359 | ||||||||
\(347\) | 3.13938e6 | 1.39965 | 0.699826 | − | 0.714313i | \(-0.253261\pi\) | ||||
0.699826 | + | 0.714313i | \(0.253261\pi\) | |||||||
\(348\) | 965088. | 0.427188 | ||||||||
\(349\) | −2.87018e6 | −1.26138 | −0.630689 | − | 0.776036i | \(-0.717227\pi\) | ||||
−0.630689 | + | 0.776036i | \(0.717227\pi\) | |||||||
\(350\) | 40964.0 | 0.0178744 | ||||||||
\(351\) | −347004. | −0.150337 | ||||||||
\(352\) | −577536. | −0.248441 | ||||||||
\(353\) | −4.37219e6 | −1.86751 | −0.933754 | − | 0.357914i | \(-0.883488\pi\) | ||||
−0.933754 | + | 0.357914i | \(0.883488\pi\) | |||||||
\(354\) | 685584. | 0.290772 | ||||||||
\(355\) | −3.24583e6 | −1.36696 | ||||||||
\(356\) | −1.22458e6 | −0.512107 | ||||||||
\(357\) | 576828. | 0.239539 | ||||||||
\(358\) | −1.60939e6 | −0.663673 | ||||||||
\(359\) | −597504. | −0.244684 | −0.122342 | − | 0.992488i | \(-0.539040\pi\) | ||||
−0.122342 | + | 0.992488i | \(0.539040\pi\) | |||||||
\(360\) | 279936. | 0.113842 | ||||||||
\(361\) | −2.47590e6 | −0.999921 | ||||||||
\(362\) | −1.35260e6 | −0.542498 | ||||||||
\(363\) | −1.41340e6 | −0.562989 | ||||||||
\(364\) | 373184. | 0.147628 | ||||||||
\(365\) | 416556. | 0.163660 | ||||||||
\(366\) | 204408. | 0.0797618 | ||||||||
\(367\) | −879460. | −0.340840 | −0.170420 | − | 0.985371i | \(-0.554512\pi\) | ||||
−0.170420 | + | 0.985371i | \(0.554512\pi\) | |||||||
\(368\) | 135424. | 0.0521286 | ||||||||
\(369\) | −228906. | −0.0875168 | ||||||||
\(370\) | 3.04085e6 | 1.15476 | ||||||||
\(371\) | 818202. | 0.308621 | ||||||||
\(372\) | 1.47715e6 | 0.553437 | ||||||||
\(373\) | −671626. | −0.249951 | −0.124976 | − | 0.992160i | \(-0.539885\pi\) | ||||
−0.124976 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(374\) | 2.95085e6 | 1.09086 | ||||||||
\(375\) | −1.62032e6 | −0.595009 | ||||||||
\(376\) | 639360. | 0.233225 | ||||||||
\(377\) | −3.19015e6 | −1.15600 | ||||||||
\(378\) | 142884. | 0.0514344 | ||||||||
\(379\) | −1.46187e6 | −0.522769 | −0.261385 | − | 0.965235i | \(-0.584179\pi\) | ||||
−0.261385 | + | 0.965235i | \(0.584179\pi\) | |||||||
\(380\) | −12096.0 | −0.00429717 | ||||||||
\(381\) | 1.64812e6 | 0.581668 | ||||||||
\(382\) | −139968. | −0.0490761 | ||||||||
\(383\) | −2.94245e6 | −1.02497 | −0.512486 | − | 0.858696i | \(-0.671275\pi\) | ||||
−0.512486 | + | 0.858696i | \(0.671275\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −1.49234e6 | −0.513118 | ||||||||
\(386\) | −2.93506e6 | −1.00265 | ||||||||
\(387\) | 1.15150e6 | 0.390827 | ||||||||
\(388\) | −304768. | −0.102776 | ||||||||
\(389\) | 3.19939e6 | 1.07199 | 0.535997 | − | 0.844220i | \(-0.319936\pi\) | ||||
0.535997 | + | 0.844220i | \(0.319936\pi\) | |||||||
\(390\) | −925344. | −0.308065 | ||||||||
\(391\) | −691932. | −0.228887 | ||||||||
\(392\) | −153664. | −0.0505076 | ||||||||
\(393\) | 2.04433e6 | 0.667683 | ||||||||
\(394\) | 767880. | 0.249203 | ||||||||
\(395\) | −5.74949e6 | −1.85411 | ||||||||
\(396\) | 730944. | 0.234232 | ||||||||
\(397\) | −634420. | −0.202023 | −0.101011 | − | 0.994885i | \(-0.532208\pi\) | ||||
−0.101011 | + | 0.994885i | \(0.532208\pi\) | |||||||
\(398\) | −1.18165e6 | −0.373922 | ||||||||
\(399\) | −6174.00 | −0.00194149 | ||||||||
\(400\) | −53504.0 | −0.0167200 | ||||||||
\(401\) | −147642. | −0.0458510 | −0.0229255 | − | 0.999737i | \(-0.507298\pi\) | ||||
−0.0229255 | + | 0.999737i | \(0.507298\pi\) | |||||||
\(402\) | −1.43050e6 | −0.441491 | ||||||||
\(403\) | −4.88281e6 | −1.49764 | ||||||||
\(404\) | 1.07482e6 | 0.327628 | ||||||||
\(405\) | −354294. | −0.107331 | ||||||||
\(406\) | 1.31359e6 | 0.395499 | ||||||||
\(407\) | 7.93999e6 | 2.37593 | ||||||||
\(408\) | −753408. | −0.224068 | ||||||||
\(409\) | −5.10744e6 | −1.50971 | −0.754857 | − | 0.655889i | \(-0.772294\pi\) | ||||
−0.754857 | + | 0.655889i | \(0.772294\pi\) | |||||||
\(410\) | −610416. | −0.179335 | ||||||||
\(411\) | −2.87912e6 | −0.840727 | ||||||||
\(412\) | −96832.0 | −0.0281045 | ||||||||
\(413\) | 933156. | 0.269203 | ||||||||
\(414\) | −171396. | −0.0491473 | ||||||||
\(415\) | 413748. | 0.117928 | ||||||||
\(416\) | −487424. | −0.138094 | ||||||||
\(417\) | −1.14250e6 | −0.321747 | ||||||||
\(418\) | −31584.0 | −0.00884151 | ||||||||
\(419\) | −2.26352e6 | −0.629867 | −0.314934 | − | 0.949114i | \(-0.601982\pi\) | ||||
−0.314934 | + | 0.949114i | \(0.601982\pi\) | |||||||
\(420\) | 381024. | 0.105397 | ||||||||
\(421\) | −3.67663e6 | −1.01098 | −0.505492 | − | 0.862831i | \(-0.668689\pi\) | ||||
−0.505492 | + | 0.862831i | \(0.668689\pi\) | |||||||
\(422\) | 2.42382e6 | 0.662552 | ||||||||
\(423\) | −809190. | −0.219887 | ||||||||
\(424\) | −1.06867e6 | −0.288689 | ||||||||
\(425\) | 273372. | 0.0734145 | ||||||||
\(426\) | 2.16389e6 | 0.577711 | ||||||||
\(427\) | 278222. | 0.0738451 | ||||||||
\(428\) | −2.92397e6 | −0.771548 | ||||||||
\(429\) | −2.41618e6 | −0.633848 | ||||||||
\(430\) | 3.07066e6 | 0.800866 | ||||||||
\(431\) | 2.62430e6 | 0.680489 | 0.340244 | − | 0.940337i | \(-0.389490\pi\) | ||||
0.340244 | + | 0.940337i | \(0.389490\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 3.02994e6 | 0.776629 | 0.388315 | − | 0.921527i | \(-0.373057\pi\) | ||||
0.388315 | + | 0.921527i | \(0.373057\pi\) | |||||||
\(434\) | 2.01057e6 | 0.512383 | ||||||||
\(435\) | −3.25717e6 | −0.825311 | ||||||||
\(436\) | 2.18038e6 | 0.549309 | ||||||||
\(437\) | 7406.00 | 0.00185515 | ||||||||
\(438\) | −277704. | −0.0691667 | ||||||||
\(439\) | 2.80942e6 | 0.695753 | 0.347876 | − | 0.937540i | \(-0.386903\pi\) | ||||
0.347876 | + | 0.937540i | \(0.386903\pi\) | |||||||
\(440\) | 1.94918e6 | 0.479978 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 2.49043e6 | 0.606344 | ||||||||
\(443\) | −3.10168e6 | −0.750909 | −0.375454 | − | 0.926841i | \(-0.622513\pi\) | ||||
−0.375454 | + | 0.926841i | \(0.622513\pi\) | |||||||
\(444\) | −2.02723e6 | −0.488029 | ||||||||
\(445\) | 4.13294e6 | 0.989372 | ||||||||
\(446\) | 2.81078e6 | 0.669097 | ||||||||
\(447\) | −1.16991e6 | −0.276939 | ||||||||
\(448\) | 200704. | 0.0472456 | ||||||||
\(449\) | −5.66786e6 | −1.32679 | −0.663396 | − | 0.748268i | \(-0.730886\pi\) | ||||
−0.663396 | + | 0.748268i | \(0.730886\pi\) | |||||||
\(450\) | 67716.0 | 0.0157638 | ||||||||
\(451\) | −1.59386e6 | −0.368986 | ||||||||
\(452\) | −3.74218e6 | −0.861545 | ||||||||
\(453\) | 2.94239e6 | 0.673681 | ||||||||
\(454\) | −1.07359e6 | −0.244455 | ||||||||
\(455\) | −1.25950e6 | −0.285212 | ||||||||
\(456\) | 8064.00 | 0.00181609 | ||||||||
\(457\) | 6.09312e6 | 1.36474 | 0.682369 | − | 0.731008i | \(-0.260950\pi\) | ||||
0.682369 | + | 0.731008i | \(0.260950\pi\) | |||||||
\(458\) | −1.10386e6 | −0.245896 | ||||||||
\(459\) | 953532. | 0.211253 | ||||||||
\(460\) | −457056. | −0.100711 | ||||||||
\(461\) | −5.71469e6 | −1.25239 | −0.626196 | − | 0.779666i | \(-0.715389\pi\) | ||||
−0.626196 | + | 0.779666i | \(0.715389\pi\) | |||||||
\(462\) | 994896. | 0.216857 | ||||||||
\(463\) | −1.42574e6 | −0.309091 | −0.154546 | − | 0.987986i | \(-0.549391\pi\) | ||||
−0.154546 | + | 0.987986i | \(0.549391\pi\) | |||||||
\(464\) | −1.71571e6 | −0.369955 | ||||||||
\(465\) | −4.98539e6 | −1.06922 | ||||||||
\(466\) | −1.96822e6 | −0.419863 | ||||||||
\(467\) | 6.52861e6 | 1.38525 | 0.692625 | − | 0.721298i | \(-0.256454\pi\) | ||||
0.692625 | + | 0.721298i | \(0.256454\pi\) | |||||||
\(468\) | 616896. | 0.130196 | ||||||||
\(469\) | −1.94706e6 | −0.408741 | ||||||||
\(470\) | −2.15784e6 | −0.450583 | ||||||||
\(471\) | −4.22455e6 | −0.877461 | ||||||||
\(472\) | −1.21882e6 | −0.251816 | ||||||||
\(473\) | 8.01782e6 | 1.64780 | ||||||||
\(474\) | 3.83299e6 | 0.783596 | ||||||||
\(475\) | −2926.00 | −0.000595032 0 | ||||||||
\(476\) | −1.02547e6 | −0.207447 | ||||||||
\(477\) | 1.35254e6 | 0.272178 | ||||||||
\(478\) | 1.90622e6 | 0.381596 | ||||||||
\(479\) | −3.68276e6 | −0.733390 | −0.366695 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366695 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(480\) | −497664. | −0.0985901 | ||||||||
\(481\) | 6.70113e6 | 1.32064 | ||||||||
\(482\) | −3.64203e6 | −0.714046 | ||||||||
\(483\) | −233289. | −0.0455016 | ||||||||
\(484\) | 2.51272e6 | 0.487563 | ||||||||
\(485\) | 1.02859e6 | 0.198559 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 1.12249e6 | 0.214466 | 0.107233 | − | 0.994234i | \(-0.465801\pi\) | ||||
0.107233 | + | 0.994234i | \(0.465801\pi\) | |||||||
\(488\) | −363392. | −0.0690758 | ||||||||
\(489\) | −1.02013e6 | −0.192923 | ||||||||
\(490\) | 518616. | 0.0975789 | ||||||||
\(491\) | −8.07479e6 | −1.51157 | −0.755783 | − | 0.654822i | \(-0.772744\pi\) | ||||
−0.755783 | + | 0.654822i | \(0.772744\pi\) | |||||||
\(492\) | 406944. | 0.0757917 | ||||||||
\(493\) | 8.76622e6 | 1.62441 | ||||||||
\(494\) | −26656.0 | −0.00491448 | ||||||||
\(495\) | −2.46694e6 | −0.452527 | ||||||||
\(496\) | −2.62605e6 | −0.479290 | ||||||||
\(497\) | 2.94529e6 | 0.534857 | ||||||||
\(498\) | −275832. | −0.0498392 | ||||||||
\(499\) | 1.98616e6 | 0.357079 | 0.178539 | − | 0.983933i | \(-0.442863\pi\) | ||||
0.178539 | + | 0.983933i | \(0.442863\pi\) | |||||||
\(500\) | 2.88058e6 | 0.515293 | ||||||||
\(501\) | 1.98347e6 | 0.353047 | ||||||||
\(502\) | 4.23103e6 | 0.749354 | ||||||||
\(503\) | −1.85566e6 | −0.327022 | −0.163511 | − | 0.986541i | \(-0.552282\pi\) | ||||
−0.163511 | + | 0.986541i | \(0.552282\pi\) | |||||||
\(504\) | −254016. | −0.0445435 | ||||||||
\(505\) | −3.62750e6 | −0.632965 | ||||||||
\(506\) | −1.19342e6 | −0.207214 | ||||||||
\(507\) | 1.30245e6 | 0.225031 | ||||||||
\(508\) | −2.92998e6 | −0.503739 | ||||||||
\(509\) | −827808. | −0.141623 | −0.0708117 | − | 0.997490i | \(-0.522559\pi\) | ||||
−0.0708117 | + | 0.997490i | \(0.522559\pi\) | |||||||
\(510\) | 2.54275e6 | 0.432891 | ||||||||
\(511\) | −377986. | −0.0640359 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −10206.0 | −0.00171223 | ||||||||
\(514\) | 7.97753e6 | 1.33187 | ||||||||
\(515\) | 326808. | 0.0542968 | ||||||||
\(516\) | −2.04710e6 | −0.338466 | ||||||||
\(517\) | −5.63436e6 | −0.927082 | ||||||||
\(518\) | −2.75929e6 | −0.451827 | ||||||||
\(519\) | 5.83006e6 | 0.950067 | ||||||||
\(520\) | 1.64506e6 | 0.266792 | ||||||||
\(521\) | −9.85788e6 | −1.59107 | −0.795535 | − | 0.605908i | \(-0.792810\pi\) | ||||
−0.795535 | + | 0.605908i | \(0.792810\pi\) | |||||||
\(522\) | 2.17145e6 | 0.348797 | ||||||||
\(523\) | −9.92288e6 | −1.58629 | −0.793147 | − | 0.609030i | \(-0.791559\pi\) | ||||
−0.793147 | + | 0.609030i | \(0.791559\pi\) | |||||||
\(524\) | −3.63437e6 | −0.578230 | ||||||||
\(525\) | 92169.0 | 0.0145944 | ||||||||
\(526\) | 8.23757e6 | 1.29818 | ||||||||
\(527\) | 1.34175e7 | 2.10448 | ||||||||
\(528\) | −1.29946e6 | −0.202851 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 3.60677e6 | 0.557736 | ||||||||
\(531\) | 1.54256e6 | 0.237414 | ||||||||
\(532\) | 10976.0 | 0.00168138 | ||||||||
\(533\) | −1.34518e6 | −0.205098 | ||||||||
\(534\) | −2.75530e6 | −0.418134 | ||||||||
\(535\) | 9.86839e6 | 1.49060 | ||||||||
\(536\) | 2.54310e6 | 0.382342 | ||||||||
\(537\) | −3.62113e6 | −0.541887 | ||||||||
\(538\) | −2.44349e6 | −0.363961 | ||||||||
\(539\) | 1.35416e6 | 0.200770 | ||||||||
\(540\) | 629856. | 0.0929516 | ||||||||
\(541\) | 5.71216e6 | 0.839087 | 0.419544 | − | 0.907735i | \(-0.362190\pi\) | ||||
0.419544 | + | 0.907735i | \(0.362190\pi\) | |||||||
\(542\) | 7.35086e6 | 1.07483 | ||||||||
\(543\) | −3.04335e6 | −0.442948 | ||||||||
\(544\) | 1.33939e6 | 0.194049 | ||||||||
\(545\) | −7.35880e6 | −1.06124 | ||||||||
\(546\) | 839664. | 0.120538 | ||||||||
\(547\) | 3.60165e6 | 0.514675 | 0.257338 | − | 0.966322i | \(-0.417155\pi\) | ||||
0.257338 | + | 0.966322i | \(0.417155\pi\) | |||||||
\(548\) | 5.11843e6 | 0.728091 | ||||||||
\(549\) | 459918. | 0.0651253 | ||||||||
\(550\) | 471504. | 0.0664628 | ||||||||
\(551\) | −93828.0 | −0.0131660 | ||||||||
\(552\) | 304704. | 0.0425628 | ||||||||
\(553\) | 5.21713e6 | 0.725469 | ||||||||
\(554\) | 4.62906e6 | 0.640794 | ||||||||
\(555\) | 6.84191e6 | 0.942855 | ||||||||
\(556\) | 2.03110e6 | 0.278641 | ||||||||
\(557\) | 1.12908e7 | 1.54201 | 0.771003 | − | 0.636832i | \(-0.219755\pi\) | ||||
0.771003 | + | 0.636832i | \(0.219755\pi\) | |||||||
\(558\) | 3.32359e6 | 0.451879 | ||||||||
\(559\) | 6.76682e6 | 0.915914 | ||||||||
\(560\) | −677376. | −0.0912767 | ||||||||
\(561\) | 6.63941e6 | 0.890681 | ||||||||
\(562\) | 5.32817e6 | 0.711602 | ||||||||
\(563\) | −5.01085e6 | −0.666254 | −0.333127 | − | 0.942882i | \(-0.608104\pi\) | ||||
−0.333127 | + | 0.942882i | \(0.608104\pi\) | |||||||
\(564\) | 1.43856e6 | 0.190428 | ||||||||
\(565\) | 1.26298e7 | 1.66447 | ||||||||
\(566\) | −7.72498e6 | −1.01358 | ||||||||
\(567\) | 321489. | 0.0419961 | ||||||||
\(568\) | −3.84691e6 | −0.500313 | ||||||||
\(569\) | −2.99546e6 | −0.387867 | −0.193933 | − | 0.981015i | \(-0.562125\pi\) | ||||
−0.193933 | + | 0.981015i | \(0.562125\pi\) | |||||||
\(570\) | −27216.0 | −0.00350863 | ||||||||
\(571\) | 2.00434e6 | 0.257266 | 0.128633 | − | 0.991692i | \(-0.458941\pi\) | ||||
0.128633 | + | 0.991692i | \(0.458941\pi\) | |||||||
\(572\) | 4.29542e6 | 0.548929 | ||||||||
\(573\) | −314928. | −0.0400705 | ||||||||
\(574\) | 553896. | 0.0701695 | ||||||||
\(575\) | −110561. | −0.0139454 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 9.02687e6 | 1.12875 | 0.564375 | − | 0.825519i | \(-0.309117\pi\) | ||||
0.564375 | + | 0.825519i | \(0.309117\pi\) | |||||||
\(578\) | −1.16403e6 | −0.144925 | ||||||||
\(579\) | −6.60389e6 | −0.818660 | ||||||||
\(580\) | 5.79053e6 | 0.714740 | ||||||||
\(581\) | −375438. | −0.0461422 | ||||||||
\(582\) | −685728. | −0.0839159 | ||||||||
\(583\) | 9.41767e6 | 1.14755 | ||||||||
\(584\) | 493696. | 0.0599001 | ||||||||
\(585\) | −2.08202e6 | −0.251534 | ||||||||
\(586\) | −5.88314e6 | −0.707726 | ||||||||
\(587\) | 5.29598e6 | 0.634383 | 0.317191 | − | 0.948362i | \(-0.397260\pi\) | ||||
0.317191 | + | 0.948362i | \(0.397260\pi\) | |||||||
\(588\) | −345744. | −0.0412393 | ||||||||
\(589\) | −143612. | −0.0170570 | ||||||||
\(590\) | 4.11350e6 | 0.486499 | ||||||||
\(591\) | 1.72773e6 | 0.203473 | ||||||||
\(592\) | 3.60397e6 | 0.422646 | ||||||||
\(593\) | 1.05619e7 | 1.23340 | 0.616701 | − | 0.787197i | \(-0.288469\pi\) | ||||
0.616701 | + | 0.787197i | \(0.288469\pi\) | |||||||
\(594\) | 1.64462e6 | 0.191250 | ||||||||
\(595\) | 3.46097e6 | 0.400779 | ||||||||
\(596\) | 2.07984e6 | 0.239836 | ||||||||
\(597\) | −2.65871e6 | −0.305306 | ||||||||
\(598\) | −1.00722e6 | −0.115178 | ||||||||
\(599\) | −1.35753e7 | −1.54590 | −0.772952 | − | 0.634464i | \(-0.781221\pi\) | ||||
−0.772952 | + | 0.634464i | \(0.781221\pi\) | |||||||
\(600\) | −120384. | −0.0136518 | ||||||||
\(601\) | −1.51018e7 | −1.70547 | −0.852733 | − | 0.522347i | \(-0.825057\pi\) | ||||
−0.852733 | + | 0.522347i | \(0.825057\pi\) | |||||||
\(602\) | −2.78634e6 | −0.313359 | ||||||||
\(603\) | −3.21862e6 | −0.360476 | ||||||||
\(604\) | −5.23091e6 | −0.583425 | ||||||||
\(605\) | −8.48043e6 | −0.941953 | ||||||||
\(606\) | 2.41834e6 | 0.267507 | ||||||||
\(607\) | 3.43828e6 | 0.378764 | 0.189382 | − | 0.981903i | \(-0.439351\pi\) | ||||
0.189382 | + | 0.981903i | \(0.439351\pi\) | |||||||
\(608\) | −14336.0 | −0.00157278 | ||||||||
\(609\) | 2.95558e6 | 0.322924 | ||||||||
\(610\) | 1.22645e6 | 0.133452 | ||||||||
\(611\) | −4.75524e6 | −0.515311 | ||||||||
\(612\) | −1.69517e6 | −0.182951 | ||||||||
\(613\) | −6.27036e6 | −0.673971 | −0.336985 | − | 0.941510i | \(-0.609407\pi\) | ||||
−0.336985 | + | 0.941510i | \(0.609407\pi\) | |||||||
\(614\) | −6.65331e6 | −0.712225 | ||||||||
\(615\) | −1.37344e6 | −0.146427 | ||||||||
\(616\) | −1.76870e6 | −0.187803 | ||||||||
\(617\) | 1.14567e7 | 1.21157 | 0.605783 | − | 0.795630i | \(-0.292860\pi\) | ||||
0.605783 | + | 0.795630i | \(0.292860\pi\) | |||||||
\(618\) | −217872. | −0.0229472 | ||||||||
\(619\) | −820462. | −0.0860660 | −0.0430330 | − | 0.999074i | \(-0.513702\pi\) | ||||
−0.0430330 | + | 0.999074i | \(0.513702\pi\) | |||||||
\(620\) | 8.86291e6 | 0.925971 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | −5.82804e6 | −0.604013 | ||||||||
\(623\) | −3.75026e6 | −0.387117 | ||||||||
\(624\) | −1.09670e6 | −0.112753 | ||||||||
\(625\) | −9.06882e6 | −0.928647 | ||||||||
\(626\) | −2.96235e6 | −0.302135 | ||||||||
\(627\) | −71064.0 | −0.00721906 | ||||||||
\(628\) | 7.51030e6 | 0.759903 | ||||||||
\(629\) | −1.84140e7 | −1.85576 | ||||||||
\(630\) | 857304. | 0.0860565 | ||||||||
\(631\) | −8.69085e6 | −0.868938 | −0.434469 | − | 0.900687i | \(-0.643064\pi\) | ||||
−0.434469 | + | 0.900687i | \(0.643064\pi\) | |||||||
\(632\) | −6.81421e6 | −0.678614 | ||||||||
\(633\) | 5.45360e6 | 0.540971 | ||||||||
\(634\) | 2.26730e6 | 0.224020 | ||||||||
\(635\) | 9.88870e6 | 0.973206 | ||||||||
\(636\) | −2.40451e6 | −0.235713 | ||||||||
\(637\) | 1.14288e6 | 0.111596 | ||||||||
\(638\) | 1.51197e7 | 1.47059 | ||||||||
\(639\) | 4.86875e6 | 0.471699 | ||||||||
\(640\) | 884736. | 0.0853815 | ||||||||
\(641\) | −7.07488e6 | −0.680102 | −0.340051 | − | 0.940407i | \(-0.610444\pi\) | ||||
−0.340051 | + | 0.940407i | \(0.610444\pi\) | |||||||
\(642\) | −6.57893e6 | −0.629967 | ||||||||
\(643\) | −6.96165e6 | −0.664026 | −0.332013 | − | 0.943275i | \(-0.607728\pi\) | ||||
−0.332013 | + | 0.943275i | \(0.607728\pi\) | |||||||
\(644\) | 414736. | 0.0394055 | ||||||||
\(645\) | 6.90898e6 | 0.653905 | ||||||||
\(646\) | 73248.0 | 0.00690581 | ||||||||
\(647\) | 1.56651e6 | 0.147120 | 0.0735601 | − | 0.997291i | \(-0.476564\pi\) | ||||
0.0735601 | + | 0.997291i | \(0.476564\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 1.07408e7 | 1.00098 | ||||||||
\(650\) | 397936. | 0.0369428 | ||||||||
\(651\) | 4.52378e6 | 0.418359 | ||||||||
\(652\) | 1.81357e6 | 0.167076 | ||||||||
\(653\) | 608610. | 0.0558542 | 0.0279271 | − | 0.999610i | \(-0.491109\pi\) | ||||
0.0279271 | + | 0.999610i | \(0.491109\pi\) | |||||||
\(654\) | 4.90586e6 | 0.448509 | ||||||||
\(655\) | 1.22660e7 | 1.11712 | ||||||||
\(656\) | −723456. | −0.0656376 | ||||||||
\(657\) | −624834. | −0.0564743 | ||||||||
\(658\) | 1.95804e6 | 0.176302 | ||||||||
\(659\) | 1.62441e7 | 1.45707 | 0.728536 | − | 0.685007i | \(-0.240201\pi\) | ||||
0.728536 | + | 0.685007i | \(0.240201\pi\) | |||||||
\(660\) | 4.38566e6 | 0.391900 | ||||||||
\(661\) | −6.58633e6 | −0.586327 | −0.293163 | − | 0.956062i | \(-0.594708\pi\) | ||||
−0.293163 | + | 0.956062i | \(0.594708\pi\) | |||||||
\(662\) | 1.13500e7 | 1.00659 | ||||||||
\(663\) | 5.60347e6 | 0.495078 | ||||||||
\(664\) | 490368. | 0.0431620 | ||||||||
\(665\) | −37044.0 | −0.00324836 | ||||||||
\(666\) | −4.56127e6 | −0.398474 | ||||||||
\(667\) | −3.54536e6 | −0.308564 | ||||||||
\(668\) | −3.52618e6 | −0.305747 | ||||||||
\(669\) | 6.32425e6 | 0.546315 | ||||||||
\(670\) | −8.58298e6 | −0.738671 | ||||||||
\(671\) | 3.20239e6 | 0.274580 | ||||||||
\(672\) | 451584. | 0.0385758 | ||||||||
\(673\) | 1.96029e6 | 0.166833 | 0.0834165 | − | 0.996515i | \(-0.473417\pi\) | ||||
0.0834165 | + | 0.996515i | \(0.473417\pi\) | |||||||
\(674\) | −4.98294e6 | −0.422509 | ||||||||
\(675\) | 152361. | 0.0128711 | ||||||||
\(676\) | −2.31547e6 | −0.194882 | ||||||||
\(677\) | −1.79225e7 | −1.50289 | −0.751443 | − | 0.659798i | \(-0.770642\pi\) | ||||
−0.751443 | + | 0.659798i | \(0.770642\pi\) | |||||||
\(678\) | −8.41990e6 | −0.703449 | ||||||||
\(679\) | −933352. | −0.0776911 | ||||||||
\(680\) | −4.52045e6 | −0.374895 | ||||||||
\(681\) | −2.41558e6 | −0.199597 | ||||||||
\(682\) | 2.31420e7 | 1.90520 | ||||||||
\(683\) | −2.47564e6 | −0.203065 | −0.101532 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101532 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(684\) | 18144.0 | 0.00148283 | ||||||||
\(685\) | −1.72747e7 | −1.40664 | ||||||||
\(686\) | −470596. | −0.0381802 | ||||||||
\(687\) | −2.48369e6 | −0.200773 | ||||||||
\(688\) | 3.63930e6 | 0.293121 | ||||||||
\(689\) | 7.94825e6 | 0.637857 | ||||||||
\(690\) | −1.02838e6 | −0.0822298 | ||||||||
\(691\) | 6.03663e6 | 0.480950 | 0.240475 | − | 0.970655i | \(-0.422697\pi\) | ||||
0.240475 | + | 0.970655i | \(0.422697\pi\) | |||||||
\(692\) | −1.03645e7 | −0.822782 | ||||||||
\(693\) | 2.23852e6 | 0.177063 | ||||||||
\(694\) | −1.25575e7 | −0.989704 | ||||||||
\(695\) | −6.85498e6 | −0.538324 | ||||||||
\(696\) | −3.86035e6 | −0.302067 | ||||||||
\(697\) | 3.69641e6 | 0.288203 | ||||||||
\(698\) | 1.14807e7 | 0.891928 | ||||||||
\(699\) | −4.42849e6 | −0.342817 | ||||||||
\(700\) | −163856. | −0.0126391 | ||||||||
\(701\) | −1.37988e7 | −1.06059 | −0.530294 | − | 0.847814i | \(-0.677919\pi\) | ||||
−0.530294 | + | 0.847814i | \(0.677919\pi\) | |||||||
\(702\) | 1.38802e6 | 0.106305 | ||||||||
\(703\) | 197092. | 0.0150411 | ||||||||
\(704\) | 2.31014e6 | 0.175674 | ||||||||
\(705\) | −4.85514e6 | −0.367899 | ||||||||
\(706\) | 1.74888e7 | 1.32053 | ||||||||
\(707\) | 3.29162e6 | 0.247663 | ||||||||
\(708\) | −2.74234e6 | −0.205607 | ||||||||
\(709\) | −1.06221e7 | −0.793587 | −0.396794 | − | 0.917908i | \(-0.629877\pi\) | ||||
−0.396794 | + | 0.917908i | \(0.629877\pi\) | |||||||
\(710\) | 1.29833e7 | 0.966585 | ||||||||
\(711\) | 8.62423e6 | 0.639803 | ||||||||
\(712\) | 4.89830e6 | 0.362114 | ||||||||
\(713\) | −5.42648e6 | −0.399756 | ||||||||
\(714\) | −2.30731e6 | −0.169379 | ||||||||
\(715\) | −1.44971e7 | −1.06051 | ||||||||
\(716\) | 6.43757e6 | 0.469288 | ||||||||
\(717\) | 4.28900e6 | 0.311572 | ||||||||
\(718\) | 2.39002e6 | 0.173017 | ||||||||
\(719\) | −1.38913e7 | −1.00212 | −0.501061 | − | 0.865412i | \(-0.667057\pi\) | ||||
−0.501061 | + | 0.865412i | \(0.667057\pi\) | |||||||
\(720\) | −1.11974e6 | −0.0804984 | ||||||||
\(721\) | −296548. | −0.0212450 | ||||||||
\(722\) | 9.90361e6 | 0.707051 | ||||||||
\(723\) | −8.19457e6 | −0.583016 | ||||||||
\(724\) | 5.41040e6 | 0.383604 | ||||||||
\(725\) | 1.40072e6 | 0.0989705 | ||||||||
\(726\) | 5.65362e6 | 0.398093 | ||||||||
\(727\) | −1.68319e7 | −1.18113 | −0.590566 | − | 0.806989i | \(-0.701095\pi\) | ||||
−0.590566 | + | 0.806989i | \(0.701095\pi\) | |||||||
\(728\) | −1.49274e6 | −0.104389 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.66622e6 | −0.115725 | ||||||||
\(731\) | −1.85945e7 | −1.28704 | ||||||||
\(732\) | −817632. | −0.0564001 | ||||||||
\(733\) | −1.36596e7 | −0.939025 | −0.469513 | − | 0.882926i | \(-0.655570\pi\) | ||||
−0.469513 | + | 0.882926i | \(0.655570\pi\) | |||||||
\(734\) | 3.51784e6 | 0.241010 | ||||||||
\(735\) | 1.16689e6 | 0.0796728 | ||||||||
\(736\) | −541696. | −0.0368605 | ||||||||
\(737\) | −2.24111e7 | −1.51983 | ||||||||
\(738\) | 915624. | 0.0618837 | ||||||||
\(739\) | 375596. | 0.0252994 | 0.0126497 | − | 0.999920i | \(-0.495973\pi\) | ||||
0.0126497 | + | 0.999920i | \(0.495973\pi\) | |||||||
\(740\) | −1.21634e7 | −0.816536 | ||||||||
\(741\) | −59976.0 | −0.00401266 | ||||||||
\(742\) | −3.27281e6 | −0.218228 | ||||||||
\(743\) | −2.07706e7 | −1.38031 | −0.690156 | − | 0.723661i | \(-0.742458\pi\) | ||||
−0.690156 | + | 0.723661i | \(0.742458\pi\) | |||||||
\(744\) | −5.90861e6 | −0.391339 | ||||||||
\(745\) | −7.01946e6 | −0.463354 | ||||||||
\(746\) | 2.68650e6 | 0.176742 | ||||||||
\(747\) | −620622. | −0.0406936 | ||||||||
\(748\) | −1.18034e7 | −0.771352 | ||||||||
\(749\) | −8.95465e6 | −0.583236 | ||||||||
\(750\) | 6.48130e6 | 0.420735 | ||||||||
\(751\) | 2.52927e7 | 1.63642 | 0.818210 | − | 0.574919i | \(-0.194967\pi\) | ||||
0.818210 | + | 0.574919i | \(0.194967\pi\) | |||||||
\(752\) | −2.55744e6 | −0.164915 | ||||||||
\(753\) | 9.51982e6 | 0.611845 | ||||||||
\(754\) | 1.27606e7 | 0.817416 | ||||||||
\(755\) | 1.76543e7 | 1.12716 | ||||||||
\(756\) | −571536. | −0.0363696 | ||||||||
\(757\) | 2.10396e7 | 1.33444 | 0.667219 | − | 0.744862i | \(-0.267485\pi\) | ||||
0.667219 | + | 0.744862i | \(0.267485\pi\) | |||||||
\(758\) | 5.84747e6 | 0.369654 | ||||||||
\(759\) | −2.68520e6 | −0.169189 | ||||||||
\(760\) | 48384.0 | 0.00303856 | ||||||||
\(761\) | 1.55777e7 | 0.975082 | 0.487541 | − | 0.873100i | \(-0.337894\pi\) | ||||
0.487541 | + | 0.873100i | \(0.337894\pi\) | |||||||
\(762\) | −6.59246e6 | −0.411302 | ||||||||
\(763\) | 6.67743e6 | 0.415239 | ||||||||
\(764\) | 559872. | 0.0347021 | ||||||||
\(765\) | 5.72119e6 | 0.353454 | ||||||||
\(766\) | 1.17698e7 | 0.724764 | ||||||||
\(767\) | 9.06494e6 | 0.556387 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 1.22003e7 | 0.743970 | 0.371985 | − | 0.928239i | \(-0.378677\pi\) | ||||
0.371985 | + | 0.928239i | \(0.378677\pi\) | |||||||
\(770\) | 5.96938e6 | 0.362829 | ||||||||
\(771\) | 1.79494e7 | 1.08746 | ||||||||
\(772\) | 1.17403e7 | 0.708981 | ||||||||
\(773\) | 2.20997e7 | 1.33027 | 0.665133 | − | 0.746725i | \(-0.268375\pi\) | ||||
0.665133 | + | 0.746725i | \(0.268375\pi\) | |||||||
\(774\) | −4.60598e6 | −0.276357 | ||||||||
\(775\) | 2.14392e6 | 0.128220 | ||||||||
\(776\) | 1.21907e6 | 0.0726733 | ||||||||
\(777\) | −6.20840e6 | −0.368916 | ||||||||
\(778\) | −1.27975e7 | −0.758015 | ||||||||
\(779\) | −39564.0 | −0.00233591 | ||||||||
\(780\) | 3.70138e6 | 0.217835 | ||||||||
\(781\) | 3.39009e7 | 1.98877 | ||||||||
\(782\) | 2.76773e6 | 0.161848 | ||||||||
\(783\) | 4.88576e6 | 0.284792 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | −2.53473e7 | −1.46811 | ||||||||
\(786\) | −8.17733e6 | −0.472123 | ||||||||
\(787\) | 1.21476e7 | 0.699122 | 0.349561 | − | 0.936914i | \(-0.386331\pi\) | ||||
0.349561 | + | 0.936914i | \(0.386331\pi\) | |||||||
\(788\) | −3.07152e6 | −0.176213 | ||||||||
\(789\) | 1.85345e7 | 1.05996 | ||||||||
\(790\) | 2.29980e7 | 1.31106 | ||||||||
\(791\) | −1.14604e7 | −0.651267 | ||||||||
\(792\) | −2.92378e6 | −0.165627 | ||||||||
\(793\) | 2.70273e6 | 0.152623 | ||||||||
\(794\) | 2.53768e6 | 0.142852 | ||||||||
\(795\) | 8.11523e6 | 0.455389 | ||||||||
\(796\) | 4.72659e6 | 0.264402 | ||||||||
\(797\) | 1.80768e7 | 1.00803 | 0.504016 | − | 0.863694i | \(-0.331855\pi\) | ||||
0.504016 | + | 0.863694i | \(0.331855\pi\) | |||||||
\(798\) | 24696.0 | 0.00137284 | ||||||||
\(799\) | 1.30669e7 | 0.724113 | ||||||||
\(800\) | 214016. | 0.0118228 | ||||||||
\(801\) | −6.19942e6 | −0.341405 | ||||||||
\(802\) | 590568. | 0.0324216 | ||||||||
\(803\) | −4.35070e6 | −0.238106 | ||||||||
\(804\) | 5.72198e6 | 0.312181 | ||||||||
\(805\) | −1.39973e6 | −0.0761300 | ||||||||
\(806\) | 1.95312e7 | 1.05899 | ||||||||
\(807\) | −5.49785e6 | −0.297173 | ||||||||
\(808\) | −4.29926e6 | −0.231668 | ||||||||
\(809\) | −3.50042e7 | −1.88039 | −0.940197 | − | 0.340630i | \(-0.889359\pi\) | ||||
−0.940197 | + | 0.340630i | \(0.889359\pi\) | |||||||
\(810\) | 1.41718e6 | 0.0758947 | ||||||||
\(811\) | 9.45753e6 | 0.504924 | 0.252462 | − | 0.967607i | \(-0.418760\pi\) | ||||
0.252462 | + | 0.967607i | \(0.418760\pi\) | |||||||
\(812\) | −5.25437e6 | −0.279660 | ||||||||
\(813\) | 1.65394e7 | 0.877595 | ||||||||
\(814\) | −3.17600e7 | −1.68004 | ||||||||
\(815\) | −6.12079e6 | −0.322785 | ||||||||
\(816\) | 3.01363e6 | 0.158440 | ||||||||
\(817\) | 199024. | 0.0104316 | ||||||||
\(818\) | 2.04298e7 | 1.06753 | ||||||||
\(819\) | 1.88924e6 | 0.0984189 | ||||||||
\(820\) | 2.44166e6 | 0.126809 | ||||||||
\(821\) | −3.41482e7 | −1.76812 | −0.884058 | − | 0.467378i | \(-0.845199\pi\) | ||||
−0.884058 | + | 0.467378i | \(0.845199\pi\) | |||||||
\(822\) | 1.15165e7 | 0.594484 | ||||||||
\(823\) | 9.87880e6 | 0.508399 | 0.254200 | − | 0.967152i | \(-0.418188\pi\) | ||||
0.254200 | + | 0.967152i | \(0.418188\pi\) | |||||||
\(824\) | 387328. | 0.0198729 | ||||||||
\(825\) | 1.06088e6 | 0.0542667 | ||||||||
\(826\) | −3.73262e6 | −0.190355 | ||||||||
\(827\) | −2.42903e7 | −1.23501 | −0.617503 | − | 0.786569i | \(-0.711856\pi\) | ||||
−0.617503 | + | 0.786569i | \(0.711856\pi\) | |||||||
\(828\) | 685584. | 0.0347524 | ||||||||
\(829\) | −8.88732e6 | −0.449143 | −0.224572 | − | 0.974458i | \(-0.572098\pi\) | ||||
−0.224572 | + | 0.974458i | \(0.572098\pi\) | |||||||
\(830\) | −1.65499e6 | −0.0833874 | ||||||||
\(831\) | 1.04154e7 | 0.523207 | ||||||||
\(832\) | 1.94970e6 | 0.0976469 | ||||||||
\(833\) | −3.14051e6 | −0.156815 | ||||||||
\(834\) | 4.56998e6 | 0.227510 | ||||||||
\(835\) | 1.19008e7 | 0.590693 | ||||||||
\(836\) | 126336. | 0.00625189 | ||||||||
\(837\) | 7.47808e6 | 0.368958 | ||||||||
\(838\) | 9.05407e6 | 0.445383 | ||||||||
\(839\) | −1.77347e7 | −0.869797 | −0.434898 | − | 0.900479i | \(-0.643216\pi\) | ||||
−0.434898 | + | 0.900479i | \(0.643216\pi\) | |||||||
\(840\) | −1.52410e6 | −0.0745271 | ||||||||
\(841\) | 2.44057e7 | 1.18987 | ||||||||
\(842\) | 1.47065e7 | 0.714874 | ||||||||
\(843\) | 1.19884e7 | 0.581021 | ||||||||
\(844\) | −9.69530e6 | −0.468495 | ||||||||
\(845\) | 7.81472e6 | 0.376506 | ||||||||
\(846\) | 3.23676e6 | 0.155484 | ||||||||
\(847\) | 7.69520e6 | 0.368563 | ||||||||
\(848\) | 4.27469e6 | 0.204134 | ||||||||
\(849\) | −1.73812e7 | −0.827582 | ||||||||
\(850\) | −1.09349e6 | −0.0519119 | ||||||||
\(851\) | 7.44726e6 | 0.352511 | ||||||||
\(852\) | −8.65555e6 | −0.408504 | ||||||||
\(853\) | −9.61944e6 | −0.452665 | −0.226333 | − | 0.974050i | \(-0.572674\pi\) | ||||
−0.226333 | + | 0.974050i | \(0.572674\pi\) | |||||||
\(854\) | −1.11289e6 | −0.0522164 | ||||||||
\(855\) | −61236.0 | −0.00286478 | ||||||||
\(856\) | 1.16959e7 | 0.545567 | ||||||||
\(857\) | −1.39472e7 | −0.648687 | −0.324344 | − | 0.945939i | \(-0.605143\pi\) | ||||
−0.324344 | + | 0.945939i | \(0.605143\pi\) | |||||||
\(858\) | 9.66470e6 | 0.448198 | ||||||||
\(859\) | 6.76628e6 | 0.312872 | 0.156436 | − | 0.987688i | \(-0.449999\pi\) | ||||
0.156436 | + | 0.987688i | \(0.449999\pi\) | |||||||
\(860\) | −1.22826e7 | −0.566298 | ||||||||
\(861\) | 1.24627e6 | 0.0572932 | ||||||||
\(862\) | −1.04972e7 | −0.481178 | ||||||||
\(863\) | −3.07028e7 | −1.40330 | −0.701650 | − | 0.712522i | \(-0.747553\pi\) | ||||
−0.701650 | + | 0.712522i | \(0.747553\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 3.49803e7 | 1.58958 | ||||||||
\(866\) | −1.21197e7 | −0.549160 | ||||||||
\(867\) | −2.61906e6 | −0.118331 | ||||||||
\(868\) | −8.04227e6 | −0.362309 | ||||||||
\(869\) | 6.00502e7 | 2.69752 | ||||||||
\(870\) | 1.30287e7 | 0.583583 | ||||||||
\(871\) | −1.89143e7 | −0.844784 | ||||||||
\(872\) | −8.72154e6 | −0.388420 | ||||||||
\(873\) | −1.54289e6 | −0.0685171 | ||||||||
\(874\) | −29624.0 | −0.00131179 | ||||||||
\(875\) | 8.82176e6 | 0.389525 | ||||||||
\(876\) | 1.11082e6 | 0.0489082 | ||||||||
\(877\) | −6.06173e6 | −0.266132 | −0.133066 | − | 0.991107i | \(-0.542482\pi\) | ||||
−0.133066 | + | 0.991107i | \(0.542482\pi\) | |||||||
\(878\) | −1.12377e7 | −0.491972 | ||||||||
\(879\) | −1.32371e7 | −0.577856 | ||||||||
\(880\) | −7.79674e6 | −0.339396 | ||||||||
\(881\) | 5.92432e6 | 0.257157 | 0.128579 | − | 0.991699i | \(-0.458959\pi\) | ||||
0.128579 | + | 0.991699i | \(0.458959\pi\) | |||||||
\(882\) | −777924. | −0.0336718 | ||||||||
\(883\) | 4.36075e7 | 1.88217 | 0.941087 | − | 0.338166i | \(-0.109806\pi\) | ||||
0.941087 | + | 0.338166i | \(0.109806\pi\) | |||||||
\(884\) | −9.96173e6 | −0.428750 | ||||||||
\(885\) | 9.25538e6 | 0.397225 | ||||||||
\(886\) | 1.24067e7 | 0.530973 | ||||||||
\(887\) | −9.69254e6 | −0.413646 | −0.206823 | − | 0.978378i | \(-0.566312\pi\) | ||||
−0.206823 | + | 0.978378i | \(0.566312\pi\) | |||||||
\(888\) | 8.10893e6 | 0.345089 | ||||||||
\(889\) | −8.97308e6 | −0.380791 | ||||||||
\(890\) | −1.65318e7 | −0.699591 | ||||||||
\(891\) | 3.70040e6 | 0.156155 | ||||||||
\(892\) | −1.12431e7 | −0.473123 | ||||||||
\(893\) | −139860. | −0.00586901 | ||||||||
\(894\) | 4.67964e6 | 0.195825 | ||||||||
\(895\) | −2.17268e7 | −0.906647 | ||||||||
\(896\) | −802816. | −0.0334077 | ||||||||
\(897\) | −2.26624e6 | −0.0940425 | ||||||||
\(898\) | 2.26714e7 | 0.938184 | ||||||||
\(899\) | 6.87491e7 | 2.83706 | ||||||||
\(900\) | −270864. | −0.0111467 | ||||||||
\(901\) | −2.18410e7 | −0.896314 | ||||||||
\(902\) | 6.37546e6 | 0.260913 | ||||||||
\(903\) | −6.26926e6 | −0.255857 | ||||||||
\(904\) | 1.49687e7 | 0.609205 | ||||||||
\(905\) | −1.82601e7 | −0.741108 | ||||||||
\(906\) | −1.17696e7 | −0.476365 | ||||||||
\(907\) | −4.13096e6 | −0.166737 | −0.0833686 | − | 0.996519i | \(-0.526568\pi\) | ||||
−0.0833686 | + | 0.996519i | \(0.526568\pi\) | |||||||
\(908\) | 4.29437e6 | 0.172856 | ||||||||
\(909\) | 5.44126e6 | 0.218419 | ||||||||
\(910\) | 5.03798e6 | 0.201676 | ||||||||
\(911\) | 3.79068e7 | 1.51329 | 0.756644 | − | 0.653827i | \(-0.226838\pi\) | ||||
0.756644 | + | 0.653827i | \(0.226838\pi\) | |||||||
\(912\) | −32256.0 | −0.00128417 | ||||||||
\(913\) | −4.32137e6 | −0.171571 | ||||||||
\(914\) | −2.43725e7 | −0.965016 | ||||||||
\(915\) | 2.75951e6 | 0.108963 | ||||||||
\(916\) | 4.41546e6 | 0.173875 | ||||||||
\(917\) | −1.11303e7 | −0.437101 | ||||||||
\(918\) | −3.81413e6 | −0.149379 | ||||||||
\(919\) | −4.32179e7 | −1.68801 | −0.844004 | − | 0.536337i | \(-0.819808\pi\) | ||||
−0.844004 | + | 0.536337i | \(0.819808\pi\) | |||||||
\(920\) | 1.82822e6 | 0.0712131 | ||||||||
\(921\) | −1.49700e7 | −0.581529 | ||||||||
\(922\) | 2.28588e7 | 0.885575 | ||||||||
\(923\) | 2.86114e7 | 1.10544 | ||||||||
\(924\) | −3.97958e6 | −0.153341 | ||||||||
\(925\) | −2.94230e6 | −0.113066 | ||||||||
\(926\) | 5.70294e6 | 0.218560 | ||||||||
\(927\) | −490212. | −0.0187363 | ||||||||
\(928\) | 6.86285e6 | 0.261598 | ||||||||
\(929\) | −3.08783e7 | −1.17385 | −0.586927 | − | 0.809640i | \(-0.699662\pi\) | ||||
−0.586927 | + | 0.809640i | \(0.699662\pi\) | |||||||
\(930\) | 1.99416e7 | 0.756052 | ||||||||
\(931\) | 33614.0 | 0.00127100 | ||||||||
\(932\) | 7.87286e6 | 0.296888 | ||||||||
\(933\) | −1.31131e7 | −0.493175 | ||||||||
\(934\) | −2.61144e7 | −0.979520 | ||||||||
\(935\) | 3.98364e7 | 1.49022 | ||||||||
\(936\) | −2.46758e6 | −0.0920624 | ||||||||
\(937\) | 8.44029e6 | 0.314057 | 0.157029 | − | 0.987594i | \(-0.449809\pi\) | ||||
0.157029 | + | 0.987594i | \(0.449809\pi\) | |||||||
\(938\) | 7.78826e6 | 0.289023 | ||||||||
\(939\) | −6.66529e6 | −0.246692 | ||||||||
\(940\) | 8.63136e6 | 0.318610 | ||||||||
\(941\) | −2.11969e7 | −0.780367 | −0.390183 | − | 0.920737i | \(-0.627588\pi\) | ||||
−0.390183 | + | 0.920737i | \(0.627588\pi\) | |||||||
\(942\) | 1.68982e7 | 0.620459 | ||||||||
\(943\) | −1.49495e6 | −0.0547455 | ||||||||
\(944\) | 4.87526e6 | 0.178061 | ||||||||
\(945\) | 1.92893e6 | 0.0702648 | ||||||||
\(946\) | −3.20713e7 | −1.16517 | ||||||||
\(947\) | 6.75954e6 | 0.244930 | 0.122465 | − | 0.992473i | \(-0.460920\pi\) | ||||
0.122465 | + | 0.992473i | \(0.460920\pi\) | |||||||
\(948\) | −1.53320e7 | −0.554086 | ||||||||
\(949\) | −3.67186e6 | −0.132349 | ||||||||
\(950\) | 11704.0 | 0.000420751 0 | ||||||||
\(951\) | 5.10143e6 | 0.182911 | ||||||||
\(952\) | 4.10189e6 | 0.146687 | ||||||||
\(953\) | −2.24168e7 | −0.799543 | −0.399771 | − | 0.916615i | \(-0.630911\pi\) | ||||
−0.399771 | + | 0.916615i | \(0.630911\pi\) | |||||||
\(954\) | −5.41015e6 | −0.192459 | ||||||||
\(955\) | −1.88957e6 | −0.0670431 | ||||||||
\(956\) | −7.62490e6 | −0.269829 | ||||||||
\(957\) | 3.40194e7 | 1.20073 | ||||||||
\(958\) | 1.47311e7 | 0.518585 | ||||||||
\(959\) | 1.56752e7 | 0.550385 | ||||||||
\(960\) | 1.99066e6 | 0.0697137 | ||||||||
\(961\) | 7.65974e7 | 2.67550 | ||||||||
\(962\) | −2.68045e7 | −0.933835 | ||||||||
\(963\) | −1.48026e7 | −0.514366 | ||||||||
\(964\) | 1.45681e7 | 0.504907 | ||||||||
\(965\) | −3.96234e7 | −1.36972 | ||||||||
\(966\) | 933156. | 0.0321745 | ||||||||
\(967\) | −3.40977e7 | −1.17263 | −0.586313 | − | 0.810085i | \(-0.699421\pi\) | ||||
−0.586313 | + | 0.810085i | \(0.699421\pi\) | |||||||
\(968\) | −1.00509e7 | −0.344759 | ||||||||
\(969\) | 164808. | 0.00563857 | ||||||||
\(970\) | −4.11437e6 | −0.140402 | ||||||||
\(971\) | 5.25978e7 | 1.79027 | 0.895137 | − | 0.445791i | \(-0.147078\pi\) | ||||
0.895137 | + | 0.445791i | \(0.147078\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 6.22026e6 | 0.210633 | ||||||||
\(974\) | −4.48995e6 | −0.151651 | ||||||||
\(975\) | 895356. | 0.0301637 | ||||||||
\(976\) | 1.45357e6 | 0.0488440 | ||||||||
\(977\) | 1.10581e6 | 0.0370632 | 0.0185316 | − | 0.999828i | \(-0.494101\pi\) | ||||
0.0185316 | + | 0.999828i | \(0.494101\pi\) | |||||||
\(978\) | 4.08053e6 | 0.136417 | ||||||||
\(979\) | −4.31663e7 | −1.43942 | ||||||||
\(980\) | −2.07446e6 | −0.0689987 | ||||||||
\(981\) | 1.10382e7 | 0.366206 | ||||||||
\(982\) | 3.22992e7 | 1.06884 | ||||||||
\(983\) | 1.47662e7 | 0.487399 | 0.243700 | − | 0.969851i | \(-0.421639\pi\) | ||||
0.243700 | + | 0.969851i | \(0.421639\pi\) | |||||||
\(984\) | −1.62778e6 | −0.0535929 | ||||||||
\(985\) | 1.03664e7 | 0.340437 | ||||||||
\(986\) | −3.50649e7 | −1.14863 | ||||||||
\(987\) | 4.40559e6 | 0.143950 | ||||||||
\(988\) | 106624. | 0.00347506 | ||||||||
\(989\) | 7.52026e6 | 0.244479 | ||||||||
\(990\) | 9.86774e6 | 0.319985 | ||||||||
\(991\) | 3.14816e7 | 1.01829 | 0.509147 | − | 0.860680i | \(-0.329961\pi\) | ||||
0.509147 | + | 0.860680i | \(0.329961\pi\) | |||||||
\(992\) | 1.05042e7 | 0.338909 | ||||||||
\(993\) | 2.55375e7 | 0.821874 | ||||||||
\(994\) | −1.17812e7 | −0.378201 | ||||||||
\(995\) | −1.59522e7 | −0.510816 | ||||||||
\(996\) | 1.10333e6 | 0.0352417 | ||||||||
\(997\) | −5.60269e7 | −1.78509 | −0.892543 | − | 0.450963i | \(-0.851081\pi\) | ||||
−0.892543 | + | 0.450963i | \(0.851081\pi\) | |||||||
\(998\) | −7.94466e6 | −0.252493 | ||||||||
\(999\) | −1.02629e7 | −0.325353 |
(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 | 966.6.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |