Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(167.601091705\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37290 | −0.419474 | −0.209737 | − | 0.977758i | \(-0.567261\pi\) | ||||
−0.209737 | + | 0.977758i | \(0.567261\pi\) | |||||||
\(3\) | −13.1216 | −0.841748 | −0.420874 | − | 0.907119i | \(-0.638277\pi\) | ||||
−0.420874 | + | 0.907119i | \(0.638277\pi\) | |||||||
\(4\) | −26.3693 | −0.824042 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 31.1362 | 0.353091 | ||||||||
\(7\) | 161.256 | 1.24385 | 0.621927 | − | 0.783075i | \(-0.286350\pi\) | ||||
0.621927 | + | 0.783075i | \(0.286350\pi\) | |||||||
\(8\) | 138.505 | 0.765138 | ||||||||
\(9\) | −70.8249 | −0.291460 | ||||||||
\(10\) | 59.3226 | 0.187594 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 346.007 | 0.693635 | ||||||||
\(13\) | −854.616 | −1.40253 | −0.701265 | − | 0.712900i | \(-0.747381\pi\) | ||||
−0.701265 | + | 0.712900i | \(0.747381\pi\) | |||||||
\(14\) | −382.644 | −0.521765 | ||||||||
\(15\) | 328.039 | 0.376441 | ||||||||
\(16\) | 515.160 | 0.503086 | ||||||||
\(17\) | −773.382 | −0.649041 | −0.324520 | − | 0.945879i | \(-0.605203\pi\) | ||||
−0.324520 | + | 0.945879i | \(0.605203\pi\) | |||||||
\(18\) | 168.061 | 0.122260 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 659.233 | 0.368523 | ||||||||
\(21\) | −2115.92 | −1.04701 | ||||||||
\(22\) | −287.121 | −0.126476 | ||||||||
\(23\) | 3015.46 | 1.18860 | 0.594298 | − | 0.804245i | \(-0.297430\pi\) | ||||
0.594298 | + | 0.804245i | \(0.297430\pi\) | |||||||
\(24\) | −1817.40 | −0.644053 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2027.92 | 0.588325 | ||||||||
\(27\) | 4117.87 | 1.08708 | ||||||||
\(28\) | −4252.20 | −1.02499 | ||||||||
\(29\) | 1569.76 | 0.346607 | 0.173303 | − | 0.984868i | \(-0.444556\pi\) | ||||
0.173303 | + | 0.984868i | \(0.444556\pi\) | |||||||
\(30\) | −778.404 | −0.157907 | ||||||||
\(31\) | 5621.67 | 1.05066 | 0.525329 | − | 0.850899i | \(-0.323942\pi\) | ||||
0.525329 | + | 0.850899i | \(0.323942\pi\) | |||||||
\(32\) | −5654.58 | −0.976169 | ||||||||
\(33\) | −1587.71 | −0.253797 | ||||||||
\(34\) | 1835.16 | 0.272256 | ||||||||
\(35\) | −4031.39 | −0.556269 | ||||||||
\(36\) | 1867.61 | 0.240176 | ||||||||
\(37\) | −2170.05 | −0.260595 | −0.130297 | − | 0.991475i | \(-0.541593\pi\) | ||||
−0.130297 | + | 0.991475i | \(0.541593\pi\) | |||||||
\(38\) | 856.618 | 0.0962339 | ||||||||
\(39\) | 11213.9 | 1.18058 | ||||||||
\(40\) | −3462.62 | −0.342180 | ||||||||
\(41\) | 8714.50 | 0.809623 | 0.404811 | − | 0.914400i | \(-0.367337\pi\) | ||||
0.404811 | + | 0.914400i | \(0.367337\pi\) | |||||||
\(42\) | 5020.88 | 0.439194 | ||||||||
\(43\) | −2640.06 | −0.217742 | −0.108871 | − | 0.994056i | \(-0.534724\pi\) | ||||
−0.108871 | + | 0.994056i | \(0.534724\pi\) | |||||||
\(44\) | −3190.69 | −0.248458 | ||||||||
\(45\) | 1770.62 | 0.130345 | ||||||||
\(46\) | −7155.40 | −0.498585 | ||||||||
\(47\) | −7280.62 | −0.480755 | −0.240378 | − | 0.970679i | \(-0.577271\pi\) | ||||
−0.240378 | + | 0.970679i | \(0.577271\pi\) | |||||||
\(48\) | −6759.70 | −0.423472 | ||||||||
\(49\) | 9196.37 | 0.547175 | ||||||||
\(50\) | −1483.06 | −0.0838948 | ||||||||
\(51\) | 10148.0 | 0.546329 | ||||||||
\(52\) | 22535.6 | 1.15574 | ||||||||
\(53\) | 4281.20 | 0.209351 | 0.104676 | − | 0.994506i | \(-0.466620\pi\) | ||||
0.104676 | + | 0.994506i | \(0.466620\pi\) | |||||||
\(54\) | −9771.30 | −0.456003 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 22334.7 | 0.951721 | ||||||||
\(57\) | 4736.88 | 0.193110 | ||||||||
\(58\) | −3724.88 | −0.145393 | ||||||||
\(59\) | −15566.1 | −0.582170 | −0.291085 | − | 0.956697i | \(-0.594016\pi\) | ||||
−0.291085 | + | 0.956697i | \(0.594016\pi\) | |||||||
\(60\) | −8650.16 | −0.310203 | ||||||||
\(61\) | 1673.74 | 0.0575922 | 0.0287961 | − | 0.999585i | \(-0.490833\pi\) | ||||
0.0287961 | + | 0.999585i | \(0.490833\pi\) | |||||||
\(62\) | −13339.7 | −0.440723 | ||||||||
\(63\) | −11420.9 | −0.362535 | ||||||||
\(64\) | −3067.37 | −0.0936086 | ||||||||
\(65\) | 21365.4 | 0.627231 | ||||||||
\(66\) | 3767.48 | 0.106461 | ||||||||
\(67\) | −5693.31 | −0.154945 | −0.0774726 | − | 0.996994i | \(-0.524685\pi\) | ||||
−0.0774726 | + | 0.996994i | \(0.524685\pi\) | |||||||
\(68\) | 20393.6 | 0.534836 | ||||||||
\(69\) | −39567.5 | −1.00050 | ||||||||
\(70\) | 9566.10 | 0.233340 | ||||||||
\(71\) | −66500.3 | −1.56559 | −0.782795 | − | 0.622280i | \(-0.786207\pi\) | ||||
−0.782795 | + | 0.622280i | \(0.786207\pi\) | |||||||
\(72\) | −9809.58 | −0.223007 | ||||||||
\(73\) | −27566.1 | −0.605435 | −0.302718 | − | 0.953080i | \(-0.597894\pi\) | ||||
−0.302718 | + | 0.953080i | \(0.597894\pi\) | |||||||
\(74\) | 5149.32 | 0.109313 | ||||||||
\(75\) | −8200.97 | −0.168350 | ||||||||
\(76\) | 9519.33 | 0.189048 | ||||||||
\(77\) | 19511.9 | 0.375036 | ||||||||
\(78\) | −26609.5 | −0.495221 | ||||||||
\(79\) | −38949.0 | −0.702148 | −0.351074 | − | 0.936348i | \(-0.614183\pi\) | ||||
−0.351074 | + | 0.936348i | \(0.614183\pi\) | |||||||
\(80\) | −12879.0 | −0.224987 | ||||||||
\(81\) | −36822.4 | −0.623590 | ||||||||
\(82\) | −20678.7 | −0.339616 | ||||||||
\(83\) | −17829.9 | −0.284088 | −0.142044 | − | 0.989860i | \(-0.545367\pi\) | ||||
−0.142044 | + | 0.989860i | \(0.545367\pi\) | |||||||
\(84\) | 55795.5 | 0.862782 | ||||||||
\(85\) | 19334.6 | 0.290260 | ||||||||
\(86\) | 6264.60 | 0.0913370 | ||||||||
\(87\) | −20597.6 | −0.291756 | ||||||||
\(88\) | 16759.1 | 0.230698 | ||||||||
\(89\) | −107643. | −1.44049 | −0.720246 | − | 0.693719i | \(-0.755971\pi\) | ||||
−0.720246 | + | 0.693719i | \(0.755971\pi\) | |||||||
\(90\) | −4201.51 | −0.0546764 | ||||||||
\(91\) | −137812. | −1.74454 | ||||||||
\(92\) | −79515.7 | −0.979453 | ||||||||
\(93\) | −73765.1 | −0.884389 | ||||||||
\(94\) | 17276.2 | 0.201664 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 74196.8 | 0.821689 | ||||||||
\(97\) | 17058.2 | 0.184079 | 0.0920395 | − | 0.995755i | \(-0.470661\pi\) | ||||
0.0920395 | + | 0.995755i | \(0.470661\pi\) | |||||||
\(98\) | −21822.1 | −0.229526 | ||||||||
\(99\) | −8569.81 | −0.0878786 | ||||||||
\(100\) | −16480.8 | −0.164808 | ||||||||
\(101\) | −60004.0 | −0.585298 | −0.292649 | − | 0.956220i | \(-0.594537\pi\) | ||||
−0.292649 | + | 0.956220i | \(0.594537\pi\) | |||||||
\(102\) | −24080.2 | −0.229171 | ||||||||
\(103\) | 125218. | 1.16298 | 0.581492 | − | 0.813552i | \(-0.302469\pi\) | ||||
0.581492 | + | 0.813552i | \(0.302469\pi\) | |||||||
\(104\) | −118368. | −1.07313 | ||||||||
\(105\) | 52898.1 | 0.468238 | ||||||||
\(106\) | −10158.9 | −0.0878174 | ||||||||
\(107\) | 48206.6 | 0.407050 | 0.203525 | − | 0.979070i | \(-0.434760\pi\) | ||||
0.203525 | + | 0.979070i | \(0.434760\pi\) | |||||||
\(108\) | −108585. | −0.895803 | ||||||||
\(109\) | −218634. | −1.76259 | −0.881293 | − | 0.472570i | \(-0.843327\pi\) | ||||
−0.881293 | + | 0.472570i | \(0.843327\pi\) | |||||||
\(110\) | 7178.03 | 0.0565619 | ||||||||
\(111\) | 28474.4 | 0.219355 | ||||||||
\(112\) | 83072.5 | 0.625766 | ||||||||
\(113\) | −106273. | −0.782935 | −0.391467 | − | 0.920192i | \(-0.628032\pi\) | ||||
−0.391467 | + | 0.920192i | \(0.628032\pi\) | |||||||
\(114\) | −11240.2 | −0.0810047 | ||||||||
\(115\) | −75386.6 | −0.531556 | ||||||||
\(116\) | −41393.4 | −0.285619 | ||||||||
\(117\) | 60528.1 | 0.408782 | ||||||||
\(118\) | 36936.9 | 0.244205 | ||||||||
\(119\) | −124712. | −0.807312 | ||||||||
\(120\) | 45434.9 | 0.288029 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −3971.63 | −0.0241584 | ||||||||
\(123\) | −114348. | −0.681498 | ||||||||
\(124\) | −148240. | −0.865786 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 27100.7 | 0.152074 | ||||||||
\(127\) | 136934. | 0.753358 | 0.376679 | − | 0.926344i | \(-0.377066\pi\) | ||||
0.376679 | + | 0.926344i | \(0.377066\pi\) | |||||||
\(128\) | 188225. | 1.01544 | ||||||||
\(129\) | 34641.6 | 0.183284 | ||||||||
\(130\) | −50698.0 | −0.263107 | ||||||||
\(131\) | 171446. | 0.872868 | 0.436434 | − | 0.899736i | \(-0.356241\pi\) | ||||
0.436434 | + | 0.899736i | \(0.356241\pi\) | |||||||
\(132\) | 41866.8 | 0.209139 | ||||||||
\(133\) | −58213.3 | −0.285360 | ||||||||
\(134\) | 13509.7 | 0.0649955 | ||||||||
\(135\) | −102947. | −0.486159 | ||||||||
\(136\) | −107117. | −0.496606 | ||||||||
\(137\) | −190342. | −0.866430 | −0.433215 | − | 0.901291i | \(-0.642621\pi\) | ||||
−0.433215 | + | 0.901291i | \(0.642621\pi\) | |||||||
\(138\) | 93889.9 | 0.419683 | ||||||||
\(139\) | −130774. | −0.574098 | −0.287049 | − | 0.957916i | \(-0.592674\pi\) | ||||
−0.287049 | + | 0.957916i | \(0.592674\pi\) | |||||||
\(140\) | 106305. | 0.458389 | ||||||||
\(141\) | 95533.0 | 0.404675 | ||||||||
\(142\) | 157799. | 0.656724 | ||||||||
\(143\) | −103408. | −0.422879 | ||||||||
\(144\) | −36486.2 | −0.146630 | ||||||||
\(145\) | −39243.9 | −0.155007 | ||||||||
\(146\) | 65411.6 | 0.253964 | ||||||||
\(147\) | −120671. | −0.460584 | ||||||||
\(148\) | 57222.8 | 0.214741 | ||||||||
\(149\) | 152156. | 0.561466 | 0.280733 | − | 0.959786i | \(-0.409422\pi\) | ||||
0.280733 | + | 0.959786i | \(0.409422\pi\) | |||||||
\(150\) | 19460.1 | 0.0706183 | ||||||||
\(151\) | 163485. | 0.583494 | 0.291747 | − | 0.956496i | \(-0.405764\pi\) | ||||
0.291747 | + | 0.956496i | \(0.405764\pi\) | |||||||
\(152\) | −50000.2 | −0.175535 | ||||||||
\(153\) | 54774.7 | 0.189170 | ||||||||
\(154\) | −46299.9 | −0.157318 | ||||||||
\(155\) | −140542. | −0.469868 | ||||||||
\(156\) | −295703. | −0.972845 | ||||||||
\(157\) | 57420.1 | 0.185915 | 0.0929576 | − | 0.995670i | \(-0.470368\pi\) | ||||
0.0929576 | + | 0.995670i | \(0.470368\pi\) | |||||||
\(158\) | 92422.2 | 0.294533 | ||||||||
\(159\) | −56175.9 | −0.176221 | ||||||||
\(160\) | 141364. | 0.436556 | ||||||||
\(161\) | 486260. | 1.47844 | ||||||||
\(162\) | 87375.9 | 0.261580 | ||||||||
\(163\) | −69419.2 | −0.204650 | −0.102325 | − | 0.994751i | \(-0.532628\pi\) | ||||
−0.102325 | + | 0.994751i | \(0.532628\pi\) | |||||||
\(164\) | −229795. | −0.667163 | ||||||||
\(165\) | 39692.7 | 0.113501 | ||||||||
\(166\) | 42308.6 | 0.119168 | ||||||||
\(167\) | −461436. | −1.28032 | −0.640162 | − | 0.768240i | \(-0.721133\pi\) | ||||
−0.640162 | + | 0.768240i | \(0.721133\pi\) | |||||||
\(168\) | −293066. | −0.801109 | ||||||||
\(169\) | 359075. | 0.967093 | ||||||||
\(170\) | −45879.0 | −0.121756 | ||||||||
\(171\) | 25567.8 | 0.0668656 | ||||||||
\(172\) | 69616.5 | 0.179428 | ||||||||
\(173\) | 204310. | 0.519007 | 0.259504 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259504 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(174\) | 48876.2 | 0.122384 | ||||||||
\(175\) | 100785. | 0.248771 | ||||||||
\(176\) | 62334.4 | 0.151686 | ||||||||
\(177\) | 204251. | 0.490040 | ||||||||
\(178\) | 255426. | 0.604248 | ||||||||
\(179\) | −58332.8 | −0.136076 | −0.0680378 | − | 0.997683i | \(-0.521674\pi\) | ||||
−0.0680378 | + | 0.997683i | \(0.521674\pi\) | |||||||
\(180\) | −46690.1 | −0.107410 | ||||||||
\(181\) | 776342. | 1.76140 | 0.880698 | − | 0.473679i | \(-0.157074\pi\) | ||||
0.880698 | + | 0.473679i | \(0.157074\pi\) | |||||||
\(182\) | 327013. | 0.731791 | ||||||||
\(183\) | −21962.1 | −0.0484781 | ||||||||
\(184\) | 417656. | 0.909440 | ||||||||
\(185\) | 54251.3 | 0.116542 | ||||||||
\(186\) | 175037. | 0.370978 | ||||||||
\(187\) | −93579.2 | −0.195693 | ||||||||
\(188\) | 191985. | 0.396162 | ||||||||
\(189\) | 664030. | 1.35218 | ||||||||
\(190\) | −21415.4 | −0.0430371 | ||||||||
\(191\) | 125267. | 0.248459 | 0.124229 | − | 0.992254i | \(-0.460354\pi\) | ||||
0.124229 | + | 0.992254i | \(0.460354\pi\) | |||||||
\(192\) | 40248.6 | 0.0787949 | ||||||||
\(193\) | 682643. | 1.31917 | 0.659585 | − | 0.751630i | \(-0.270732\pi\) | ||||
0.659585 | + | 0.751630i | \(0.270732\pi\) | |||||||
\(194\) | −40477.5 | −0.0772163 | ||||||||
\(195\) | −280347. | −0.527970 | ||||||||
\(196\) | −242502. | −0.450895 | ||||||||
\(197\) | 576442. | 1.05825 | 0.529127 | − | 0.848543i | \(-0.322519\pi\) | ||||
0.529127 | + | 0.848543i | \(0.322519\pi\) | |||||||
\(198\) | 20335.3 | 0.0368628 | ||||||||
\(199\) | −410738. | −0.735245 | −0.367622 | − | 0.929975i | \(-0.619828\pi\) | ||||
−0.367622 | + | 0.929975i | \(0.619828\pi\) | |||||||
\(200\) | 86565.5 | 0.153028 | ||||||||
\(201\) | 74705.1 | 0.130425 | ||||||||
\(202\) | 142384. | 0.245517 | ||||||||
\(203\) | 253132. | 0.431129 | ||||||||
\(204\) | −267595. | −0.450197 | ||||||||
\(205\) | −217862. | −0.362074 | ||||||||
\(206\) | −297130. | −0.487842 | ||||||||
\(207\) | −213570. | −0.346429 | ||||||||
\(208\) | −440264. | −0.705594 | ||||||||
\(209\) | −43681.0 | −0.0691714 | ||||||||
\(210\) | −125522. | −0.196414 | ||||||||
\(211\) | 850360. | 1.31491 | 0.657456 | − | 0.753493i | \(-0.271633\pi\) | ||||
0.657456 | + | 0.753493i | \(0.271633\pi\) | |||||||
\(212\) | −112892. | −0.172514 | ||||||||
\(213\) | 872588. | 1.31783 | ||||||||
\(214\) | −114390. | −0.170747 | ||||||||
\(215\) | 66001.4 | 0.0973771 | ||||||||
\(216\) | 570344. | 0.831769 | ||||||||
\(217\) | 906526. | 1.30687 | ||||||||
\(218\) | 518796. | 0.739359 | ||||||||
\(219\) | 361710. | 0.509624 | ||||||||
\(220\) | 79767.2 | 0.111114 | ||||||||
\(221\) | 660944. | 0.910299 | ||||||||
\(222\) | −67567.1 | −0.0920138 | ||||||||
\(223\) | −1.18730e6 | −1.59882 | −0.799409 | − | 0.600787i | \(-0.794854\pi\) | ||||
−0.799409 | + | 0.600787i | \(0.794854\pi\) | |||||||
\(224\) | −911832. | −1.21421 | ||||||||
\(225\) | −44265.6 | −0.0582921 | ||||||||
\(226\) | 252175. | 0.328421 | ||||||||
\(227\) | 91416.9 | 0.117750 | 0.0588751 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588751 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(228\) | −124908. | −0.159131 | ||||||||
\(229\) | 274091. | 0.345387 | 0.172694 | − | 0.984976i | \(-0.444753\pi\) | ||||
0.172694 | + | 0.984976i | \(0.444753\pi\) | |||||||
\(230\) | 178885. | 0.222974 | ||||||||
\(231\) | −256027. | −0.315686 | ||||||||
\(232\) | 217419. | 0.265202 | ||||||||
\(233\) | −791866. | −0.955568 | −0.477784 | − | 0.878477i | \(-0.658560\pi\) | ||||
−0.477784 | + | 0.878477i | \(0.658560\pi\) | |||||||
\(234\) | −143627. | −0.171473 | ||||||||
\(235\) | 182016. | 0.215000 | ||||||||
\(236\) | 410468. | 0.479732 | ||||||||
\(237\) | 511071. | 0.591032 | ||||||||
\(238\) | 295930. | 0.338646 | ||||||||
\(239\) | −1.19500e6 | −1.35323 | −0.676617 | − | 0.736335i | \(-0.736555\pi\) | ||||
−0.676617 | + | 0.736335i | \(0.736555\pi\) | |||||||
\(240\) | 168993. | 0.189382 | ||||||||
\(241\) | −1.11921e6 | −1.24128 | −0.620639 | − | 0.784096i | \(-0.713127\pi\) | ||||
−0.620639 | + | 0.784096i | \(0.713127\pi\) | |||||||
\(242\) | −34741.7 | −0.0381340 | ||||||||
\(243\) | −517475. | −0.562178 | ||||||||
\(244\) | −44135.5 | −0.0474584 | ||||||||
\(245\) | −229909. | −0.244704 | ||||||||
\(246\) | 271336. | 0.285871 | ||||||||
\(247\) | 308516. | 0.321763 | ||||||||
\(248\) | 778628. | 0.803898 | ||||||||
\(249\) | 233956. | 0.239131 | ||||||||
\(250\) | 37076.6 | 0.0375189 | ||||||||
\(251\) | 480820. | 0.481724 | 0.240862 | − | 0.970559i | \(-0.422570\pi\) | ||||
0.240862 | + | 0.970559i | \(0.422570\pi\) | |||||||
\(252\) | 301162. | 0.298744 | ||||||||
\(253\) | 364871. | 0.358375 | ||||||||
\(254\) | −324931. | −0.316014 | ||||||||
\(255\) | −253699. | −0.244326 | ||||||||
\(256\) | −348484. | −0.332340 | ||||||||
\(257\) | 1.48286e6 | 1.40045 | 0.700227 | − | 0.713920i | \(-0.253082\pi\) | ||||
0.700227 | + | 0.713920i | \(0.253082\pi\) | |||||||
\(258\) | −82201.2 | −0.0768828 | ||||||||
\(259\) | −349933. | −0.324142 | ||||||||
\(260\) | −563391. | −0.516864 | ||||||||
\(261\) | −111178. | −0.101022 | ||||||||
\(262\) | −406824. | −0.366145 | ||||||||
\(263\) | 26645.2 | 0.0237536 | 0.0118768 | − | 0.999929i | \(-0.496219\pi\) | ||||
0.0118768 | + | 0.999929i | \(0.496219\pi\) | |||||||
\(264\) | −219905. | −0.194189 | ||||||||
\(265\) | −107030. | −0.0936247 | ||||||||
\(266\) | 138134. | 0.119701 | ||||||||
\(267\) | 1.41244e6 | 1.21253 | ||||||||
\(268\) | 150129. | 0.127681 | ||||||||
\(269\) | 1.79237e6 | 1.51024 | 0.755120 | − | 0.655587i | \(-0.227579\pi\) | ||||
0.755120 | + | 0.655587i | \(0.227579\pi\) | |||||||
\(270\) | 244283. | 0.203931 | ||||||||
\(271\) | 42086.2 | 0.0348110 | 0.0174055 | − | 0.999849i | \(-0.494459\pi\) | ||||
0.0174055 | + | 0.999849i | \(0.494459\pi\) | |||||||
\(272\) | −398416. | −0.326523 | ||||||||
\(273\) | 1.80830e6 | 1.46847 | ||||||||
\(274\) | 451663. | 0.363445 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 1.04337e6 | 0.824452 | ||||||||
\(277\) | 192387. | 0.150652 | 0.0753261 | − | 0.997159i | \(-0.476000\pi\) | ||||
0.0753261 | + | 0.997159i | \(0.476000\pi\) | |||||||
\(278\) | 310315. | 0.240819 | ||||||||
\(279\) | −398154. | −0.306225 | ||||||||
\(280\) | −558367. | −0.425622 | ||||||||
\(281\) | −662659. | −0.500639 | −0.250319 | − | 0.968163i | \(-0.580536\pi\) | ||||
−0.250319 | + | 0.968163i | \(0.580536\pi\) | |||||||
\(282\) | −226691. | −0.169750 | ||||||||
\(283\) | −896996. | −0.665770 | −0.332885 | − | 0.942967i | \(-0.608022\pi\) | ||||
−0.332885 | + | 0.942967i | \(0.608022\pi\) | |||||||
\(284\) | 1.75357e6 | 1.29011 | ||||||||
\(285\) | −118422. | −0.0863615 | ||||||||
\(286\) | 245378. | 0.177387 | ||||||||
\(287\) | 1.40526e6 | 1.00705 | ||||||||
\(288\) | 400485. | 0.284515 | ||||||||
\(289\) | −821737. | −0.578746 | ||||||||
\(290\) | 93122.0 | 0.0650215 | ||||||||
\(291\) | −223830. | −0.154948 | ||||||||
\(292\) | 726899. | 0.498904 | ||||||||
\(293\) | 2.17973e6 | 1.48332 | 0.741659 | − | 0.670777i | \(-0.234039\pi\) | ||||
0.741659 | + | 0.670777i | \(0.234039\pi\) | |||||||
\(294\) | 286340. | 0.193203 | ||||||||
\(295\) | 389153. | 0.260354 | ||||||||
\(296\) | −300563. | −0.199391 | ||||||||
\(297\) | 498262. | 0.327768 | ||||||||
\(298\) | −361052. | −0.235521 | ||||||||
\(299\) | −2.57706e6 | −1.66704 | ||||||||
\(300\) | 216254. | 0.138727 | ||||||||
\(301\) | −425724. | −0.270839 | ||||||||
\(302\) | −387935. | −0.244760 | ||||||||
\(303\) | 787346. | 0.492673 | ||||||||
\(304\) | −185973. | −0.115416 | ||||||||
\(305\) | −41843.6 | −0.0257560 | ||||||||
\(306\) | −129975. | −0.0793517 | ||||||||
\(307\) | −1.50259e6 | −0.909901 | −0.454950 | − | 0.890517i | \(-0.650343\pi\) | ||||
−0.454950 | + | 0.890517i | \(0.650343\pi\) | |||||||
\(308\) | −514517. | −0.309046 | ||||||||
\(309\) | −1.64306e6 | −0.978940 | ||||||||
\(310\) | 333492. | 0.197098 | ||||||||
\(311\) | −750226. | −0.439837 | −0.219918 | − | 0.975518i | \(-0.570579\pi\) | ||||
−0.219918 | + | 0.975518i | \(0.570579\pi\) | |||||||
\(312\) | 1.55318e6 | 0.903304 | ||||||||
\(313\) | −1.35177e6 | −0.779906 | −0.389953 | − | 0.920835i | \(-0.627509\pi\) | ||||
−0.389953 | + | 0.920835i | \(0.627509\pi\) | |||||||
\(314\) | −136252. | −0.0779866 | ||||||||
\(315\) | 285523. | 0.162130 | ||||||||
\(316\) | 1.02706e6 | 0.578599 | ||||||||
\(317\) | −2.40047e6 | −1.34168 | −0.670838 | − | 0.741604i | \(-0.734065\pi\) | ||||
−0.670838 | + | 0.741604i | \(0.734065\pi\) | |||||||
\(318\) | 133300. | 0.0739201 | ||||||||
\(319\) | 189941. | 0.104506 | ||||||||
\(320\) | 76684.2 | 0.0418631 | ||||||||
\(321\) | −632546. | −0.342633 | ||||||||
\(322\) | −1.15385e6 | −0.620168 | ||||||||
\(323\) | 279191. | 0.148900 | ||||||||
\(324\) | 970982. | 0.513864 | ||||||||
\(325\) | −534135. | −0.280506 | ||||||||
\(326\) | 164725. | 0.0858451 | ||||||||
\(327\) | 2.86881e6 | 1.48365 | ||||||||
\(328\) | 1.20700e6 | 0.619473 | ||||||||
\(329\) | −1.17404e6 | −0.597990 | ||||||||
\(330\) | −94186.9 | −0.0476108 | ||||||||
\(331\) | −461188. | −0.231371 | −0.115685 | − | 0.993286i | \(-0.536906\pi\) | ||||
−0.115685 | + | 0.993286i | \(0.536906\pi\) | |||||||
\(332\) | 470162. | 0.234101 | ||||||||
\(333\) | 153694. | 0.0759531 | ||||||||
\(334\) | 1.09494e6 | 0.537063 | ||||||||
\(335\) | 142333. | 0.0692936 | ||||||||
\(336\) | −1.09004e6 | −0.526738 | ||||||||
\(337\) | 3.24545e6 | 1.55668 | 0.778342 | − | 0.627840i | \(-0.216061\pi\) | ||||
0.778342 | + | 0.627840i | \(0.216061\pi\) | |||||||
\(338\) | −852049. | −0.405670 | ||||||||
\(339\) | 1.39446e6 | 0.659034 | ||||||||
\(340\) | −509839. | −0.239186 | ||||||||
\(341\) | 680222. | 0.316785 | ||||||||
\(342\) | −60669.9 | −0.0280484 | ||||||||
\(343\) | −1.22726e6 | −0.563248 | ||||||||
\(344\) | −365660. | −0.166603 | ||||||||
\(345\) | 989189. | 0.447437 | ||||||||
\(346\) | −484807. | −0.217710 | ||||||||
\(347\) | −1.12740e6 | −0.502636 | −0.251318 | − | 0.967905i | \(-0.580864\pi\) | ||||
−0.251318 | + | 0.967905i | \(0.580864\pi\) | |||||||
\(348\) | 543146. | 0.240419 | ||||||||
\(349\) | 1.75750e6 | 0.772380 | 0.386190 | − | 0.922419i | \(-0.373791\pi\) | ||||
0.386190 | + | 0.922419i | \(0.373791\pi\) | |||||||
\(350\) | −239152. | −0.104353 | ||||||||
\(351\) | −3.51920e6 | −1.52467 | ||||||||
\(352\) | −684204. | −0.294326 | ||||||||
\(353\) | 4.16035e6 | 1.77702 | 0.888512 | − | 0.458854i | \(-0.151740\pi\) | ||||
0.888512 | + | 0.458854i | \(0.151740\pi\) | |||||||
\(354\) | −484669. | −0.205559 | ||||||||
\(355\) | 1.66251e6 | 0.700153 | ||||||||
\(356\) | 2.83847e6 | 1.18702 | ||||||||
\(357\) | 1.63642e6 | 0.679553 | ||||||||
\(358\) | 138418. | 0.0570802 | ||||||||
\(359\) | −3.27805e6 | −1.34239 | −0.671197 | − | 0.741279i | \(-0.734219\pi\) | ||||
−0.671197 | + | 0.741279i | \(0.734219\pi\) | |||||||
\(360\) | 245240. | 0.0997320 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −1.84219e6 | −0.738859 | ||||||||
\(363\) | −192113. | −0.0765225 | ||||||||
\(364\) | 3.63400e6 | 1.43758 | ||||||||
\(365\) | 689152. | 0.270759 | ||||||||
\(366\) | 52113.9 | 0.0203353 | ||||||||
\(367\) | 184003. | 0.0713117 | 0.0356559 | − | 0.999364i | \(-0.488648\pi\) | ||||
0.0356559 | + | 0.999364i | \(0.488648\pi\) | |||||||
\(368\) | 1.55345e6 | 0.597966 | ||||||||
\(369\) | −617203. | −0.235973 | ||||||||
\(370\) | −128733. | −0.0488861 | ||||||||
\(371\) | 690367. | 0.260403 | ||||||||
\(372\) | 1.94514e6 | 0.728773 | ||||||||
\(373\) | −2.27618e6 | −0.847100 | −0.423550 | − | 0.905873i | \(-0.639216\pi\) | ||||
−0.423550 | + | 0.905873i | \(0.639216\pi\) | |||||||
\(374\) | 222054. | 0.0820881 | ||||||||
\(375\) | 205024. | 0.0752882 | ||||||||
\(376\) | −1.00840e6 | −0.367844 | ||||||||
\(377\) | −1.34154e6 | −0.486127 | ||||||||
\(378\) | −1.57568e6 | −0.567202 | ||||||||
\(379\) | 2.09363e6 | 0.748690 | 0.374345 | − | 0.927289i | \(-0.377868\pi\) | ||||
0.374345 | + | 0.927289i | \(0.377868\pi\) | |||||||
\(380\) | −237983. | −0.0845449 | ||||||||
\(381\) | −1.79678e6 | −0.634138 | ||||||||
\(382\) | −297247. | −0.104222 | ||||||||
\(383\) | −1.49234e6 | −0.519840 | −0.259920 | − | 0.965630i | \(-0.583696\pi\) | ||||
−0.259920 | + | 0.965630i | \(0.583696\pi\) | |||||||
\(384\) | −2.46980e6 | −0.854741 | ||||||||
\(385\) | −487798. | −0.167721 | ||||||||
\(386\) | −1.61985e6 | −0.553357 | ||||||||
\(387\) | 186982. | 0.0634631 | ||||||||
\(388\) | −449814. | −0.151689 | ||||||||
\(389\) | 4.53488e6 | 1.51947 | 0.759734 | − | 0.650234i | \(-0.225329\pi\) | ||||
0.759734 | + | 0.650234i | \(0.225329\pi\) | |||||||
\(390\) | 665236. | 0.221470 | ||||||||
\(391\) | −2.33210e6 | −0.771447 | ||||||||
\(392\) | 1.27374e6 | 0.418665 | ||||||||
\(393\) | −2.24963e6 | −0.734735 | ||||||||
\(394\) | −1.36784e6 | −0.443910 | ||||||||
\(395\) | 973725. | 0.314010 | ||||||||
\(396\) | 225980. | 0.0724157 | ||||||||
\(397\) | 1.08979e6 | 0.347030 | 0.173515 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173515 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(398\) | 974640. | 0.308416 | ||||||||
\(399\) | 763849. | 0.240201 | ||||||||
\(400\) | 321975. | 0.100617 | ||||||||
\(401\) | 4.34966e6 | 1.35081 | 0.675405 | − | 0.737447i | \(-0.263969\pi\) | ||||
0.675405 | + | 0.737447i | \(0.263969\pi\) | |||||||
\(402\) | −177268. | −0.0547098 | ||||||||
\(403\) | −4.80437e6 | −1.47358 | ||||||||
\(404\) | 1.58227e6 | 0.482310 | ||||||||
\(405\) | 920560. | 0.278878 | ||||||||
\(406\) | −600658. | −0.180847 | ||||||||
\(407\) | −262576. | −0.0785723 | ||||||||
\(408\) | 1.40554e6 | 0.418017 | ||||||||
\(409\) | 3.77403e6 | 1.11557 | 0.557785 | − | 0.829986i | \(-0.311651\pi\) | ||||
0.557785 | + | 0.829986i | \(0.311651\pi\) | |||||||
\(410\) | 516966. | 0.151881 | ||||||||
\(411\) | 2.49758e6 | 0.729315 | ||||||||
\(412\) | −3.30192e6 | −0.958348 | ||||||||
\(413\) | −2.51012e6 | −0.724135 | ||||||||
\(414\) | 506780. | 0.145318 | ||||||||
\(415\) | 445747. | 0.127048 | ||||||||
\(416\) | 4.83249e6 | 1.36911 | ||||||||
\(417\) | 1.71596e6 | 0.483246 | ||||||||
\(418\) | 103651. | 0.0290156 | ||||||||
\(419\) | 1.88686e6 | 0.525055 | 0.262527 | − | 0.964925i | \(-0.415444\pi\) | ||||
0.262527 | + | 0.964925i | \(0.415444\pi\) | |||||||
\(420\) | −1.39489e6 | −0.385848 | ||||||||
\(421\) | 2.56104e6 | 0.704224 | 0.352112 | − | 0.935958i | \(-0.385464\pi\) | ||||
0.352112 | + | 0.935958i | \(0.385464\pi\) | |||||||
\(422\) | −2.01782e6 | −0.551571 | ||||||||
\(423\) | 515649. | 0.140121 | ||||||||
\(424\) | 592966. | 0.160183 | ||||||||
\(425\) | −483364. | −0.129808 | ||||||||
\(426\) | −2.07057e6 | −0.552796 | ||||||||
\(427\) | 269900. | 0.0716364 | ||||||||
\(428\) | −1.27118e6 | −0.335426 | ||||||||
\(429\) | 1.35688e6 | 0.355957 | ||||||||
\(430\) | −156615. | −0.0408472 | ||||||||
\(431\) | 5.99609e6 | 1.55480 | 0.777400 | − | 0.629006i | \(-0.216538\pi\) | ||||
0.777400 | + | 0.629006i | \(0.216538\pi\) | |||||||
\(432\) | 2.12136e6 | 0.546897 | ||||||||
\(433\) | 693248. | 0.177692 | 0.0888461 | − | 0.996045i | \(-0.471682\pi\) | ||||
0.0888461 | + | 0.996045i | \(0.471682\pi\) | |||||||
\(434\) | −2.15110e6 | −0.548196 | ||||||||
\(435\) | 514941. | 0.130477 | ||||||||
\(436\) | 5.76522e6 | 1.45244 | ||||||||
\(437\) | −1.08858e6 | −0.272683 | ||||||||
\(438\) | −858302. | −0.213774 | ||||||||
\(439\) | 4.18152e6 | 1.03555 | 0.517777 | − | 0.855515i | \(-0.326760\pi\) | ||||
0.517777 | + | 0.855515i | \(0.326760\pi\) | |||||||
\(440\) | −418977. | −0.103171 | ||||||||
\(441\) | −651332. | −0.159480 | ||||||||
\(442\) | −1.56836e6 | −0.381847 | ||||||||
\(443\) | −959488. | −0.232290 | −0.116145 | − | 0.993232i | \(-0.537054\pi\) | ||||
−0.116145 | + | 0.993232i | \(0.537054\pi\) | |||||||
\(444\) | −750852. | −0.180758 | ||||||||
\(445\) | 2.69107e6 | 0.644207 | ||||||||
\(446\) | 2.81735e6 | 0.670662 | ||||||||
\(447\) | −1.99652e6 | −0.472613 | ||||||||
\(448\) | −494630. | −0.116436 | ||||||||
\(449\) | −867910. | −0.203170 | −0.101585 | − | 0.994827i | \(-0.532391\pi\) | ||||
−0.101585 | + | 0.994827i | \(0.532391\pi\) | |||||||
\(450\) | 105038. | 0.0244520 | ||||||||
\(451\) | 1.05445e6 | 0.244110 | ||||||||
\(452\) | 2.80234e6 | 0.645171 | ||||||||
\(453\) | −2.14518e6 | −0.491155 | ||||||||
\(454\) | −216923. | −0.0493932 | ||||||||
\(455\) | 3.44529e6 | 0.780184 | ||||||||
\(456\) | 656080. | 0.147756 | ||||||||
\(457\) | 4.28127e6 | 0.958919 | 0.479460 | − | 0.877564i | \(-0.340833\pi\) | ||||
0.479460 | + | 0.877564i | \(0.340833\pi\) | |||||||
\(458\) | −650391. | −0.144881 | ||||||||
\(459\) | −3.18469e6 | −0.705562 | ||||||||
\(460\) | 1.98789e6 | 0.438025 | ||||||||
\(461\) | 2.06835e6 | 0.453285 | 0.226642 | − | 0.973978i | \(-0.427225\pi\) | ||||
0.226642 | + | 0.973978i | \(0.427225\pi\) | |||||||
\(462\) | 607527. | 0.132422 | ||||||||
\(463\) | 2.45612e6 | 0.532471 | 0.266236 | − | 0.963908i | \(-0.414220\pi\) | ||||
0.266236 | + | 0.963908i | \(0.414220\pi\) | |||||||
\(464\) | 808676. | 0.174373 | ||||||||
\(465\) | 1.84413e6 | 0.395511 | ||||||||
\(466\) | 1.87902e6 | 0.400836 | ||||||||
\(467\) | 1.41736e6 | 0.300738 | 0.150369 | − | 0.988630i | \(-0.451954\pi\) | ||||
0.150369 | + | 0.988630i | \(0.451954\pi\) | |||||||
\(468\) | −1.59608e6 | −0.336854 | ||||||||
\(469\) | −918079. | −0.192729 | ||||||||
\(470\) | −431905. | −0.0901870 | ||||||||
\(471\) | −753441. | −0.156494 | ||||||||
\(472\) | −2.15598e6 | −0.445440 | ||||||||
\(473\) | −319447. | −0.0656516 | ||||||||
\(474\) | −1.21272e6 | −0.247922 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | 3.28858e6 | 0.665259 | ||||||||
\(477\) | −303215. | −0.0610176 | ||||||||
\(478\) | 2.83562e6 | 0.567646 | ||||||||
\(479\) | 915681. | 0.182350 | 0.0911749 | − | 0.995835i | \(-0.470938\pi\) | ||||
0.0911749 | + | 0.995835i | \(0.470938\pi\) | |||||||
\(480\) | −1.85492e6 | −0.367470 | ||||||||
\(481\) | 1.85456e6 | 0.365492 | ||||||||
\(482\) | 2.65578e6 | 0.520684 | ||||||||
\(483\) | −6.38049e6 | −1.24448 | ||||||||
\(484\) | −386073. | −0.0749129 | ||||||||
\(485\) | −426455. | −0.0823226 | ||||||||
\(486\) | 1.22792e6 | 0.235819 | ||||||||
\(487\) | −2.18548e6 | −0.417566 | −0.208783 | − | 0.977962i | \(-0.566950\pi\) | ||||
−0.208783 | + | 0.977962i | \(0.566950\pi\) | |||||||
\(488\) | 231821. | 0.0440660 | ||||||||
\(489\) | 910888. | 0.172263 | ||||||||
\(490\) | 545553. | 0.102647 | ||||||||
\(491\) | 9.04192e6 | 1.69261 | 0.846305 | − | 0.532699i | \(-0.178822\pi\) | ||||
0.846305 | + | 0.532699i | \(0.178822\pi\) | |||||||
\(492\) | 3.01527e6 | 0.561583 | ||||||||
\(493\) | −1.21402e6 | −0.224962 | ||||||||
\(494\) | −732079. | −0.134971 | ||||||||
\(495\) | 214245. | 0.0393005 | ||||||||
\(496\) | 2.89606e6 | 0.528571 | ||||||||
\(497\) | −1.07236e7 | −1.94737 | ||||||||
\(498\) | −555154. | −0.100309 | ||||||||
\(499\) | −4.20662e6 | −0.756279 | −0.378140 | − | 0.925749i | \(-0.623436\pi\) | ||||
−0.378140 | + | 0.925749i | \(0.623436\pi\) | |||||||
\(500\) | 412021. | 0.0737045 | ||||||||
\(501\) | 6.05475e6 | 1.07771 | ||||||||
\(502\) | −1.14094e6 | −0.202071 | ||||||||
\(503\) | −950827. | −0.167564 | −0.0837821 | − | 0.996484i | \(-0.526700\pi\) | ||||
−0.0837821 | + | 0.996484i | \(0.526700\pi\) | |||||||
\(504\) | −1.58185e6 | −0.277389 | ||||||||
\(505\) | 1.50010e6 | 0.261753 | ||||||||
\(506\) | −865803. | −0.150329 | ||||||||
\(507\) | −4.71162e6 | −0.814048 | ||||||||
\(508\) | −3.61085e6 | −0.620798 | ||||||||
\(509\) | −2.16476e6 | −0.370352 | −0.185176 | − | 0.982705i | \(-0.559286\pi\) | ||||
−0.185176 | + | 0.982705i | \(0.559286\pi\) | |||||||
\(510\) | 602004. | 0.102488 | ||||||||
\(511\) | −4.44518e6 | −0.753074 | ||||||||
\(512\) | −5.19628e6 | −0.876028 | ||||||||
\(513\) | −1.48655e6 | −0.249394 | ||||||||
\(514\) | −3.51869e6 | −0.587454 | ||||||||
\(515\) | −3.13045e6 | −0.520102 | ||||||||
\(516\) | −913477. | −0.151033 | ||||||||
\(517\) | −880955. | −0.144953 | ||||||||
\(518\) | 830357. | 0.135969 | ||||||||
\(519\) | −2.68086e6 | −0.436873 | ||||||||
\(520\) | 2.95921e6 | 0.479918 | ||||||||
\(521\) | 4.67888e6 | 0.755176 | 0.377588 | − | 0.925974i | \(-0.376754\pi\) | ||||
0.377588 | + | 0.925974i | \(0.376754\pi\) | |||||||
\(522\) | 263814. | 0.0423762 | ||||||||
\(523\) | 8.60530e6 | 1.37566 | 0.687831 | − | 0.725871i | \(-0.258563\pi\) | ||||
0.687831 | + | 0.725871i | \(0.258563\pi\) | |||||||
\(524\) | −4.52091e6 | −0.719279 | ||||||||
\(525\) | −1.32245e6 | −0.209402 | ||||||||
\(526\) | −63226.4 | −0.00996400 | ||||||||
\(527\) | −4.34770e6 | −0.681919 | ||||||||
\(528\) | −817924. | −0.127682 | ||||||||
\(529\) | 2.65667e6 | 0.412761 | ||||||||
\(530\) | 253972. | 0.0392731 | ||||||||
\(531\) | 1.10247e6 | 0.169680 | ||||||||
\(532\) | 1.53505e6 | 0.235148 | ||||||||
\(533\) | −7.44754e6 | −1.13552 | ||||||||
\(534\) | −3.35159e6 | −0.508625 | ||||||||
\(535\) | −1.20517e6 | −0.182038 | ||||||||
\(536\) | −788551. | −0.118554 | ||||||||
\(537\) | 765417. | 0.114541 | ||||||||
\(538\) | −4.25311e6 | −0.633506 | ||||||||
\(539\) | 1.11276e6 | 0.164980 | ||||||||
\(540\) | 2.71464e6 | 0.400615 | ||||||||
\(541\) | 4.94858e6 | 0.726922 | 0.363461 | − | 0.931609i | \(-0.381595\pi\) | ||||
0.363461 | + | 0.931609i | \(0.381595\pi\) | |||||||
\(542\) | −99866.5 | −0.0146023 | ||||||||
\(543\) | −1.01868e7 | −1.48265 | ||||||||
\(544\) | 4.37315e6 | 0.633574 | ||||||||
\(545\) | 5.46584e6 | 0.788253 | ||||||||
\(546\) | −4.29092e6 | −0.615984 | ||||||||
\(547\) | 5.10257e6 | 0.729156 | 0.364578 | − | 0.931173i | \(-0.381213\pi\) | ||||
0.364578 | + | 0.931173i | \(0.381213\pi\) | |||||||
\(548\) | 5.01919e6 | 0.713974 | ||||||||
\(549\) | −118543. | −0.0167859 | ||||||||
\(550\) | −179451. | −0.0252952 | ||||||||
\(551\) | −566682. | −0.0795171 | ||||||||
\(552\) | −5.48029e6 | −0.765519 | ||||||||
\(553\) | −6.28075e6 | −0.873370 | ||||||||
\(554\) | −456515. | −0.0631946 | ||||||||
\(555\) | −711861. | −0.0980986 | ||||||||
\(556\) | 3.44843e6 | 0.473081 | ||||||||
\(557\) | 5.90274e6 | 0.806150 | 0.403075 | − | 0.915167i | \(-0.367941\pi\) | ||||
0.403075 | + | 0.915167i | \(0.367941\pi\) | |||||||
\(558\) | 944781. | 0.128453 | ||||||||
\(559\) | 2.25623e6 | 0.305390 | ||||||||
\(560\) | −2.07681e6 | −0.279851 | ||||||||
\(561\) | 1.22790e6 | 0.164724 | ||||||||
\(562\) | 1.57243e6 | 0.210005 | ||||||||
\(563\) | 2.20840e6 | 0.293635 | 0.146817 | − | 0.989164i | \(-0.453097\pi\) | ||||
0.146817 | + | 0.989164i | \(0.453097\pi\) | |||||||
\(564\) | −2.51914e6 | −0.333469 | ||||||||
\(565\) | 2.65682e6 | 0.350139 | ||||||||
\(566\) | 2.12848e6 | 0.279273 | ||||||||
\(567\) | −5.93782e6 | −0.775656 | ||||||||
\(568\) | −9.21061e6 | −1.19789 | ||||||||
\(569\) | 455199. | 0.0589414 | 0.0294707 | − | 0.999566i | \(-0.490618\pi\) | ||||
0.0294707 | + | 0.999566i | \(0.490618\pi\) | |||||||
\(570\) | 281004. | 0.0362264 | ||||||||
\(571\) | −2.85732e6 | −0.366748 | −0.183374 | − | 0.983043i | \(-0.558702\pi\) | ||||
−0.183374 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(572\) | 2.72681e6 | 0.348470 | ||||||||
\(573\) | −1.64370e6 | −0.209140 | ||||||||
\(574\) | −3.33455e6 | −0.422433 | ||||||||
\(575\) | 1.88466e6 | 0.237719 | ||||||||
\(576\) | 217246. | 0.0272832 | ||||||||
\(577\) | −1.28731e7 | −1.60969 | −0.804846 | − | 0.593484i | \(-0.797752\pi\) | ||||
−0.804846 | + | 0.593484i | \(0.797752\pi\) | |||||||
\(578\) | 1.94990e6 | 0.242769 | ||||||||
\(579\) | −8.95734e6 | −1.11041 | ||||||||
\(580\) | 1.03484e6 | 0.127732 | ||||||||
\(581\) | −2.87517e6 | −0.353365 | ||||||||
\(582\) | 531127. | 0.0649967 | ||||||||
\(583\) | 518025. | 0.0631218 | ||||||||
\(584\) | −3.81803e6 | −0.463241 | ||||||||
\(585\) | −1.51320e6 | −0.182813 | ||||||||
\(586\) | −5.17229e6 | −0.622213 | ||||||||
\(587\) | −7.94013e6 | −0.951114 | −0.475557 | − | 0.879685i | \(-0.657753\pi\) | ||||
−0.475557 | + | 0.879685i | \(0.657753\pi\) | |||||||
\(588\) | 3.18201e6 | 0.379540 | ||||||||
\(589\) | −2.02942e6 | −0.241037 | ||||||||
\(590\) | −923421. | −0.109212 | ||||||||
\(591\) | −7.56381e6 | −0.890783 | ||||||||
\(592\) | −1.11792e6 | −0.131102 | ||||||||
\(593\) | 4.48562e6 | 0.523825 | 0.261912 | − | 0.965092i | \(-0.415647\pi\) | ||||
0.261912 | + | 0.965092i | \(0.415647\pi\) | |||||||
\(594\) | −1.18233e6 | −0.137490 | ||||||||
\(595\) | 3.11781e6 | 0.361041 | ||||||||
\(596\) | −4.01226e6 | −0.462672 | ||||||||
\(597\) | 5.38951e6 | 0.618891 | ||||||||
\(598\) | 6.11512e6 | 0.699281 | ||||||||
\(599\) | −5.08340e6 | −0.578878 | −0.289439 | − | 0.957196i | \(-0.593469\pi\) | ||||
−0.289439 | + | 0.957196i | \(0.593469\pi\) | |||||||
\(600\) | −1.13587e6 | −0.128811 | ||||||||
\(601\) | −7.95366e6 | −0.898216 | −0.449108 | − | 0.893477i | \(-0.648258\pi\) | ||||
−0.449108 | + | 0.893477i | \(0.648258\pi\) | |||||||
\(602\) | 1.01020e6 | 0.113610 | ||||||||
\(603\) | 403228. | 0.0451604 | ||||||||
\(604\) | −4.31100e6 | −0.480823 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | −1.86830e6 | −0.206664 | ||||||||
\(607\) | 1.07655e6 | 0.118594 | 0.0592969 | − | 0.998240i | \(-0.481114\pi\) | ||||
0.0592969 | + | 0.998240i | \(0.481114\pi\) | |||||||
\(608\) | 2.04130e6 | 0.223949 | ||||||||
\(609\) | −3.32148e6 | −0.362902 | ||||||||
\(610\) | 99290.7 | 0.0108040 | ||||||||
\(611\) | 6.22213e6 | 0.674274 | ||||||||
\(612\) | −1.44437e6 | −0.155884 | ||||||||
\(613\) | −1.63843e6 | −0.176107 | −0.0880534 | − | 0.996116i | \(-0.528065\pi\) | ||||
−0.0880534 | + | 0.996116i | \(0.528065\pi\) | |||||||
\(614\) | 3.56550e6 | 0.381680 | ||||||||
\(615\) | 2.85869e6 | 0.304775 | ||||||||
\(616\) | 2.70250e6 | 0.286955 | ||||||||
\(617\) | −1.01236e6 | −0.107058 | −0.0535292 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535292 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(618\) | 3.89881e6 | 0.410640 | ||||||||
\(619\) | 1.59040e7 | 1.66832 | 0.834161 | − | 0.551521i | \(-0.185952\pi\) | ||||
0.834161 | + | 0.551521i | \(0.185952\pi\) | |||||||
\(620\) | 3.70599e6 | 0.387191 | ||||||||
\(621\) | 1.24173e7 | 1.29210 | ||||||||
\(622\) | 1.78021e6 | 0.184500 | ||||||||
\(623\) | −1.73580e7 | −1.79176 | ||||||||
\(624\) | 5.77695e6 | 0.593932 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 3.20762e6 | 0.327150 | ||||||||
\(627\) | 573162. | 0.0582249 | ||||||||
\(628\) | −1.51413e6 | −0.153202 | ||||||||
\(629\) | 1.67828e6 | 0.169137 | ||||||||
\(630\) | −677518. | −0.0680095 | ||||||||
\(631\) | 1.80933e7 | 1.80902 | 0.904512 | − | 0.426448i | \(-0.140235\pi\) | ||||
0.904512 | + | 0.426448i | \(0.140235\pi\) | |||||||
\(632\) | −5.39462e6 | −0.537240 | ||||||||
\(633\) | −1.11580e7 | −1.10682 | ||||||||
\(634\) | 5.69608e6 | 0.562798 | ||||||||
\(635\) | −3.42335e6 | −0.336912 | ||||||||
\(636\) | 1.48132e6 | 0.145213 | ||||||||
\(637\) | −7.85936e6 | −0.767430 | ||||||||
\(638\) | −450710. | −0.0438375 | ||||||||
\(639\) | 4.70988e6 | 0.456308 | ||||||||
\(640\) | −4.70563e6 | −0.454117 | ||||||||
\(641\) | −1.44097e7 | −1.38519 | −0.692596 | − | 0.721326i | \(-0.743533\pi\) | ||||
−0.692596 | + | 0.721326i | \(0.743533\pi\) | |||||||
\(642\) | 1.50097e6 | 0.143726 | ||||||||
\(643\) | 2.24743e6 | 0.214367 | 0.107184 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107184 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(644\) | −1.28224e7 | −1.21830 | ||||||||
\(645\) | −866041. | −0.0819670 | ||||||||
\(646\) | −662493. | −0.0624597 | ||||||||
\(647\) | −2.00218e6 | −0.188036 | −0.0940181 | − | 0.995570i | \(-0.529971\pi\) | ||||
−0.0940181 | + | 0.995570i | \(0.529971\pi\) | |||||||
\(648\) | −5.10008e6 | −0.477133 | ||||||||
\(649\) | −1.88350e6 | −0.175531 | ||||||||
\(650\) | 1.26745e6 | 0.117665 | ||||||||
\(651\) | −1.18950e7 | −1.10005 | ||||||||
\(652\) | 1.83054e6 | 0.168640 | ||||||||
\(653\) | 1.28042e7 | 1.17508 | 0.587541 | − | 0.809194i | \(-0.300096\pi\) | ||||
0.587541 | + | 0.809194i | \(0.300096\pi\) | |||||||
\(654\) | −6.80741e6 | −0.622354 | ||||||||
\(655\) | −4.28614e6 | −0.390358 | ||||||||
\(656\) | 4.48936e6 | 0.407310 | ||||||||
\(657\) | 1.95236e6 | 0.176460 | ||||||||
\(658\) | 2.78589e6 | 0.250841 | ||||||||
\(659\) | 3.02033e6 | 0.270919 | 0.135460 | − | 0.990783i | \(-0.456749\pi\) | ||||
0.135460 | + | 0.990783i | \(0.456749\pi\) | |||||||
\(660\) | −1.04667e6 | −0.0935298 | ||||||||
\(661\) | 3.07171e6 | 0.273450 | 0.136725 | − | 0.990609i | \(-0.456342\pi\) | ||||
0.136725 | + | 0.990609i | \(0.456342\pi\) | |||||||
\(662\) | 1.09435e6 | 0.0970540 | ||||||||
\(663\) | −8.67262e6 | −0.766243 | ||||||||
\(664\) | −2.46952e6 | −0.217367 | ||||||||
\(665\) | 1.45533e6 | 0.127617 | ||||||||
\(666\) | −364700. | −0.0318603 | ||||||||
\(667\) | 4.73354e6 | 0.411976 | ||||||||
\(668\) | 1.21678e7 | 1.05504 | ||||||||
\(669\) | 1.55792e7 | 1.34580 | ||||||||
\(670\) | −337742. | −0.0290669 | ||||||||
\(671\) | 202523. | 0.0173647 | ||||||||
\(672\) | 1.19647e7 | 1.02206 | ||||||||
\(673\) | −1.86853e7 | −1.59024 | −0.795119 | − | 0.606453i | \(-0.792592\pi\) | ||||
−0.795119 | + | 0.606453i | \(0.792592\pi\) | |||||||
\(674\) | −7.70114e6 | −0.652988 | ||||||||
\(675\) | 2.57367e6 | 0.217417 | ||||||||
\(676\) | −9.46856e6 | −0.796925 | ||||||||
\(677\) | 2.29336e7 | 1.92309 | 0.961546 | − | 0.274643i | \(-0.0885596\pi\) | ||||
0.961546 | + | 0.274643i | \(0.0885596\pi\) | |||||||
\(678\) | −3.30892e6 | −0.276447 | ||||||||
\(679\) | 2.75073e6 | 0.228968 | ||||||||
\(680\) | 2.67793e6 | 0.222089 | ||||||||
\(681\) | −1.19953e6 | −0.0991161 | ||||||||
\(682\) | −1.61410e6 | −0.132883 | ||||||||
\(683\) | 1.11687e7 | 0.916113 | 0.458057 | − | 0.888923i | \(-0.348546\pi\) | ||||
0.458057 | + | 0.888923i | \(0.348546\pi\) | |||||||
\(684\) | −674205. | −0.0551001 | ||||||||
\(685\) | 4.75855e6 | 0.387479 | ||||||||
\(686\) | 2.91216e6 | 0.236268 | ||||||||
\(687\) | −3.59650e6 | −0.290729 | ||||||||
\(688\) | −1.36005e6 | −0.109543 | ||||||||
\(689\) | −3.65878e6 | −0.293621 | ||||||||
\(690\) | −2.34725e6 | −0.187688 | ||||||||
\(691\) | −1.19214e7 | −0.949801 | −0.474901 | − | 0.880039i | \(-0.657516\pi\) | ||||
−0.474901 | + | 0.880039i | \(0.657516\pi\) | |||||||
\(692\) | −5.38751e6 | −0.427684 | ||||||||
\(693\) | −1.38193e6 | −0.109308 | ||||||||
\(694\) | 2.67520e6 | 0.210843 | ||||||||
\(695\) | 3.26936e6 | 0.256744 | ||||||||
\(696\) | −2.85287e6 | −0.223233 | ||||||||
\(697\) | −6.73964e6 | −0.525478 | ||||||||
\(698\) | −4.17037e6 | −0.323993 | ||||||||
\(699\) | 1.03905e7 | 0.804348 | ||||||||
\(700\) | −2.65763e6 | −0.204998 | ||||||||
\(701\) | −2.85037e6 | −0.219082 | −0.109541 | − | 0.993982i | \(-0.534938\pi\) | ||||
−0.109541 | + | 0.993982i | \(0.534938\pi\) | |||||||
\(702\) | 8.35071e6 | 0.639559 | ||||||||
\(703\) | 783389. | 0.0597846 | ||||||||
\(704\) | −371151. | −0.0282241 | ||||||||
\(705\) | −2.38833e6 | −0.180976 | ||||||||
\(706\) | −9.87211e6 | −0.745415 | ||||||||
\(707\) | −9.67599e6 | −0.728026 | ||||||||
\(708\) | −5.38597e6 | −0.403814 | ||||||||
\(709\) | 1.01938e7 | 0.761590 | 0.380795 | − | 0.924659i | \(-0.375650\pi\) | ||||
0.380795 | + | 0.924659i | \(0.375650\pi\) | |||||||
\(710\) | −3.94497e6 | −0.293696 | ||||||||
\(711\) | 2.75856e6 | 0.204648 | ||||||||
\(712\) | −1.49091e7 | −1.10217 | ||||||||
\(713\) | 1.69519e7 | 1.24881 | ||||||||
\(714\) | −3.88306e6 | −0.285055 | ||||||||
\(715\) | 2.58521e6 | 0.189117 | ||||||||
\(716\) | 1.53820e6 | 0.112132 | ||||||||
\(717\) | 1.56802e7 | 1.13908 | ||||||||
\(718\) | 7.77850e6 | 0.563099 | ||||||||
\(719\) | 1.44249e7 | 1.04061 | 0.520307 | − | 0.853979i | \(-0.325818\pi\) | ||||
0.520307 | + | 0.853979i | \(0.325818\pi\) | |||||||
\(720\) | 912154. | 0.0655748 | ||||||||
\(721\) | 2.01921e7 | 1.44658 | ||||||||
\(722\) | −309239. | −0.0220776 | ||||||||
\(723\) | 1.46858e7 | 1.04484 | ||||||||
\(724\) | −2.04716e7 | −1.45146 | ||||||||
\(725\) | 981098. | 0.0693214 | ||||||||
\(726\) | 455865. | 0.0320992 | ||||||||
\(727\) | −2.94371e6 | −0.206566 | −0.103283 | − | 0.994652i | \(-0.532935\pi\) | ||||
−0.103283 | + | 0.994652i | \(0.532935\pi\) | |||||||
\(728\) | −1.90876e7 | −1.33482 | ||||||||
\(729\) | 1.57379e7 | 1.09680 | ||||||||
\(730\) | −1.63529e6 | −0.113576 | ||||||||
\(731\) | 2.04177e6 | 0.141323 | ||||||||
\(732\) | 579126. | 0.0399480 | ||||||||
\(733\) | 5.37045e6 | 0.369191 | 0.184595 | − | 0.982815i | \(-0.440903\pi\) | ||||
0.184595 | + | 0.982815i | \(0.440903\pi\) | |||||||
\(734\) | −436622. | −0.0299134 | ||||||||
\(735\) | 3.01677e6 | 0.205979 | ||||||||
\(736\) | −1.70512e7 | −1.16027 | ||||||||
\(737\) | −688891. | −0.0467177 | ||||||||
\(738\) | 1.46456e6 | 0.0989845 | ||||||||
\(739\) | 2.58078e7 | 1.73836 | 0.869180 | − | 0.494495i | \(-0.164647\pi\) | ||||
0.869180 | + | 0.494495i | \(0.164647\pi\) | |||||||
\(740\) | −1.43057e6 | −0.0960351 | ||||||||
\(741\) | −4.04821e6 | −0.270843 | ||||||||
\(742\) | −1.63817e6 | −0.109232 | ||||||||
\(743\) | −1.23720e7 | −0.822183 | −0.411091 | − | 0.911594i | \(-0.634852\pi\) | ||||
−0.411091 | + | 0.911594i | \(0.634852\pi\) | |||||||
\(744\) | −1.02168e7 | −0.676679 | ||||||||
\(745\) | −3.80390e6 | −0.251095 | ||||||||
\(746\) | 5.40115e6 | 0.355336 | ||||||||
\(747\) | 1.26280e6 | 0.0828005 | ||||||||
\(748\) | 2.46762e6 | 0.161259 | ||||||||
\(749\) | 7.77359e6 | 0.506311 | ||||||||
\(750\) | −486503. | −0.0315814 | ||||||||
\(751\) | −6.64194e6 | −0.429730 | −0.214865 | − | 0.976644i | \(-0.568931\pi\) | ||||
−0.214865 | + | 0.976644i | \(0.568931\pi\) | |||||||
\(752\) | −3.75069e6 | −0.241861 | ||||||||
\(753\) | −6.30910e6 | −0.405490 | ||||||||
\(754\) | 3.18334e6 | 0.203918 | ||||||||
\(755\) | −4.08713e6 | −0.260946 | ||||||||
\(756\) | −1.75100e7 | −1.11425 | ||||||||
\(757\) | −1.52835e7 | −0.969355 | −0.484678 | − | 0.874693i | \(-0.661063\pi\) | ||||
−0.484678 | + | 0.874693i | \(0.661063\pi\) | |||||||
\(758\) | −4.96798e6 | −0.314056 | ||||||||
\(759\) | −4.78767e6 | −0.301662 | ||||||||
\(760\) | 1.25001e6 | 0.0785015 | ||||||||
\(761\) | −1.33069e7 | −0.832941 | −0.416471 | − | 0.909149i | \(-0.636733\pi\) | ||||
−0.416471 | + | 0.909149i | \(0.636733\pi\) | |||||||
\(762\) | 4.26359e6 | 0.266004 | ||||||||
\(763\) | −3.52559e7 | −2.19240 | ||||||||
\(764\) | −3.30322e6 | −0.204740 | ||||||||
\(765\) | −1.36937e6 | −0.0845992 | ||||||||
\(766\) | 3.54117e6 | 0.218059 | ||||||||
\(767\) | 1.33030e7 | 0.816511 | ||||||||
\(768\) | 4.57265e6 | 0.279747 | ||||||||
\(769\) | 7.47042e6 | 0.455543 | 0.227771 | − | 0.973715i | \(-0.426856\pi\) | ||||
0.227771 | + | 0.973715i | \(0.426856\pi\) | |||||||
\(770\) | 1.15750e6 | 0.0703547 | ||||||||
\(771\) | −1.94575e7 | −1.17883 | ||||||||
\(772\) | −1.80008e7 | −1.08705 | ||||||||
\(773\) | 7.29605e6 | 0.439177 | 0.219588 | − | 0.975593i | \(-0.429529\pi\) | ||||
0.219588 | + | 0.975593i | \(0.429529\pi\) | |||||||
\(774\) | −443689. | −0.0266211 | ||||||||
\(775\) | 3.51354e6 | 0.210132 | ||||||||
\(776\) | 2.36264e6 | 0.140846 | ||||||||
\(777\) | 4.59166e6 | 0.272846 | ||||||||
\(778\) | −1.07608e7 | −0.637377 | ||||||||
\(779\) | −3.14593e6 | −0.185740 | ||||||||
\(780\) | 7.39256e6 | 0.435069 | ||||||||
\(781\) | −8.04654e6 | −0.472043 | ||||||||
\(782\) | 5.53386e6 | 0.323602 | ||||||||
\(783\) | 6.46405e6 | 0.376791 | ||||||||
\(784\) | 4.73761e6 | 0.275276 | ||||||||
\(785\) | −1.43550e6 | −0.0831438 | ||||||||
\(786\) | 5.33816e6 | 0.308202 | ||||||||
\(787\) | −2.75695e7 | −1.58669 | −0.793344 | − | 0.608774i | \(-0.791662\pi\) | ||||
−0.793344 | + | 0.608774i | \(0.791662\pi\) | |||||||
\(788\) | −1.52004e7 | −0.872046 | ||||||||
\(789\) | −349626. | −0.0199945 | ||||||||
\(790\) | −2.31055e6 | −0.131719 | ||||||||
\(791\) | −1.71371e7 | −0.973857 | ||||||||
\(792\) | −1.18696e6 | −0.0672393 | ||||||||
\(793\) | −1.43041e6 | −0.0807749 | ||||||||
\(794\) | −2.58597e6 | −0.145570 | ||||||||
\(795\) | 1.40440e6 | 0.0788084 | ||||||||
\(796\) | 1.08309e7 | 0.605872 | ||||||||
\(797\) | 3.54357e6 | 0.197604 | 0.0988020 | − | 0.995107i | \(-0.468499\pi\) | ||||
0.0988020 | + | 0.995107i | \(0.468499\pi\) | |||||||
\(798\) | −1.81254e6 | −0.100758 | ||||||||
\(799\) | 5.63070e6 | 0.312029 | ||||||||
\(800\) | −3.53411e6 | −0.195234 | ||||||||
\(801\) | 7.62380e6 | 0.419846 | ||||||||
\(802\) | −1.03213e7 | −0.566630 | ||||||||
\(803\) | −3.33549e6 | −0.182546 | ||||||||
\(804\) | −1.96992e6 | −0.107475 | ||||||||
\(805\) | −1.21565e7 | −0.661179 | ||||||||
\(806\) | 1.14003e7 | 0.618128 | ||||||||
\(807\) | −2.35186e7 | −1.27124 | ||||||||
\(808\) | −8.31084e6 | −0.447834 | ||||||||
\(809\) | −3.25812e7 | −1.75023 | −0.875117 | − | 0.483911i | \(-0.839216\pi\) | ||||
−0.875117 | + | 0.483911i | \(0.839216\pi\) | |||||||
\(810\) | −2.18440e6 | −0.116982 | ||||||||
\(811\) | −2.08727e7 | −1.11436 | −0.557181 | − | 0.830391i | \(-0.688117\pi\) | ||||
−0.557181 | + | 0.830391i | \(0.688117\pi\) | |||||||
\(812\) | −6.67492e6 | −0.355268 | ||||||||
\(813\) | −552236. | −0.0293021 | ||||||||
\(814\) | 623068. | 0.0329590 | ||||||||
\(815\) | 1.73548e6 | 0.0915221 | ||||||||
\(816\) | 5.22783e6 | 0.274850 | ||||||||
\(817\) | 953060. | 0.0499534 | ||||||||
\(818\) | −8.95540e6 | −0.467952 | ||||||||
\(819\) | 9.76049e6 | 0.508466 | ||||||||
\(820\) | 5.74489e6 | 0.298364 | ||||||||
\(821\) | 3.66310e6 | 0.189667 | 0.0948334 | − | 0.995493i | \(-0.469768\pi\) | ||||
0.0948334 | + | 0.995493i | \(0.469768\pi\) | |||||||
\(822\) | −5.92652e6 | −0.305929 | ||||||||
\(823\) | −78151.3 | −0.00402195 | −0.00201098 | − | 0.999998i | \(-0.500640\pi\) | ||||
−0.00201098 | + | 0.999998i | \(0.500640\pi\) | |||||||
\(824\) | 1.73433e7 | 0.889843 | ||||||||
\(825\) | −992317. | −0.0507593 | ||||||||
\(826\) | 5.95627e6 | 0.303756 | ||||||||
\(827\) | 2.65484e7 | 1.34981 | 0.674907 | − | 0.737903i | \(-0.264184\pi\) | ||||
0.674907 | + | 0.737903i | \(0.264184\pi\) | |||||||
\(828\) | 5.63169e6 | 0.285472 | ||||||||
\(829\) | −947687. | −0.0478937 | −0.0239469 | − | 0.999713i | \(-0.507623\pi\) | ||||
−0.0239469 | + | 0.999713i | \(0.507623\pi\) | |||||||
\(830\) | −1.05771e6 | −0.0532934 | ||||||||
\(831\) | −2.52441e6 | −0.126811 | ||||||||
\(832\) | 2.62142e6 | 0.131289 | ||||||||
\(833\) | −7.11231e6 | −0.355139 | ||||||||
\(834\) | −4.07181e6 | −0.202709 | ||||||||
\(835\) | 1.15359e7 | 0.572578 | ||||||||
\(836\) | 1.15184e6 | 0.0570002 | ||||||||
\(837\) | 2.31493e7 | 1.14215 | ||||||||
\(838\) | −4.47733e6 | −0.220247 | ||||||||
\(839\) | 2.73512e7 | 1.34144 | 0.670721 | − | 0.741709i | \(-0.265985\pi\) | ||||
0.670721 | + | 0.741709i | \(0.265985\pi\) | |||||||
\(840\) | 7.32664e6 | 0.358267 | ||||||||
\(841\) | −1.80470e7 | −0.879864 | ||||||||
\(842\) | −6.07709e6 | −0.295404 | ||||||||
\(843\) | 8.69511e6 | 0.421411 | ||||||||
\(844\) | −2.24234e7 | −1.08354 | ||||||||
\(845\) | −8.97687e6 | −0.432497 | ||||||||
\(846\) | −1.22359e6 | −0.0587771 | ||||||||
\(847\) | 2.36094e6 | 0.113078 | ||||||||
\(848\) | 2.20550e6 | 0.105322 | ||||||||
\(849\) | 1.17700e7 | 0.560410 | ||||||||
\(850\) | 1.14698e6 | 0.0544511 | ||||||||
\(851\) | −6.54371e6 | −0.309742 | ||||||||
\(852\) | −2.30096e7 | −1.08595 | ||||||||
\(853\) | −2.25067e7 | −1.05911 | −0.529553 | − | 0.848277i | \(-0.677640\pi\) | ||||
−0.529553 | + | 0.848277i | \(0.677640\pi\) | |||||||
\(854\) | −640447. | −0.0300496 | ||||||||
\(855\) | −639195. | −0.0299032 | ||||||||
\(856\) | 6.67685e6 | 0.311449 | ||||||||
\(857\) | −807631. | −0.0375630 | −0.0187815 | − | 0.999824i | \(-0.505979\pi\) | ||||
−0.0187815 | + | 0.999824i | \(0.505979\pi\) | |||||||
\(858\) | −3.21974e6 | −0.149315 | ||||||||
\(859\) | 2.14256e7 | 0.990719 | 0.495360 | − | 0.868688i | \(-0.335036\pi\) | ||||
0.495360 | + | 0.868688i | \(0.335036\pi\) | |||||||
\(860\) | −1.74041e6 | −0.0802428 | ||||||||
\(861\) | −1.84392e7 | −0.847685 | ||||||||
\(862\) | −1.42281e7 | −0.652198 | ||||||||
\(863\) | −1.90437e7 | −0.870410 | −0.435205 | − | 0.900331i | \(-0.643324\pi\) | ||||
−0.435205 | + | 0.900331i | \(0.643324\pi\) | |||||||
\(864\) | −2.32848e7 | −1.06118 | ||||||||
\(865\) | −5.10774e6 | −0.232107 | ||||||||
\(866\) | −1.64501e6 | −0.0745373 | ||||||||
\(867\) | 1.07825e7 | 0.487159 | ||||||||
\(868\) | −2.39045e7 | −1.07691 | ||||||||
\(869\) | −4.71283e6 | −0.211706 | ||||||||
\(870\) | −1.22190e6 | −0.0547317 | ||||||||
\(871\) | 4.86559e6 | 0.217315 | ||||||||
\(872\) | −3.02818e7 | −1.34862 | ||||||||
\(873\) | −1.20815e6 | −0.0536517 | ||||||||
\(874\) | 2.58310e6 | 0.114383 | ||||||||
\(875\) | −2.51962e6 | −0.111254 | ||||||||
\(876\) | −9.53804e6 | −0.419951 | ||||||||
\(877\) | 266272. | 0.0116903 | 0.00584516 | − | 0.999983i | \(-0.498139\pi\) | ||||
0.00584516 | + | 0.999983i | \(0.498139\pi\) | |||||||
\(878\) | −9.92234e6 | −0.434388 | ||||||||
\(879\) | −2.86015e7 | −1.24858 | ||||||||
\(880\) | −1.55836e6 | −0.0678361 | ||||||||
\(881\) | 3.54570e7 | 1.53908 | 0.769541 | − | 0.638597i | \(-0.220485\pi\) | ||||
0.769541 | + | 0.638597i | \(0.220485\pi\) | |||||||
\(882\) | 1.54555e6 | 0.0668977 | ||||||||
\(883\) | −3.84411e7 | −1.65918 | −0.829591 | − | 0.558371i | \(-0.811426\pi\) | ||||
−0.829591 | + | 0.558371i | \(0.811426\pi\) | |||||||
\(884\) | −1.74287e7 | −0.750125 | ||||||||
\(885\) | −5.10629e6 | −0.219153 | ||||||||
\(886\) | 2.27677e6 | 0.0974395 | ||||||||
\(887\) | −4.44852e7 | −1.89848 | −0.949241 | − | 0.314550i | \(-0.898146\pi\) | ||||
−0.949241 | + | 0.314550i | \(0.898146\pi\) | |||||||
\(888\) | 3.94385e6 | 0.167837 | ||||||||
\(889\) | 2.20814e7 | 0.937068 | ||||||||
\(890\) | −6.38566e6 | −0.270228 | ||||||||
\(891\) | −4.45551e6 | −0.188020 | ||||||||
\(892\) | 3.13084e7 | 1.31749 | ||||||||
\(893\) | 2.62830e6 | 0.110293 | ||||||||
\(894\) | 4.73756e6 | 0.198249 | ||||||||
\(895\) | 1.45832e6 | 0.0608548 | ||||||||
\(896\) | 3.03523e7 | 1.26305 | ||||||||
\(897\) | 3.38150e7 | 1.40323 | ||||||||
\(898\) | 2.05947e6 | 0.0852244 | ||||||||
\(899\) | 8.82465e6 | 0.364165 | ||||||||
\(900\) | 1.16725e6 | 0.0480351 | ||||||||
\(901\) | −3.31100e6 | −0.135877 | ||||||||
\(902\) | −2.50212e6 | −0.102398 | ||||||||
\(903\) | 5.58616e6 | 0.227978 | ||||||||
\(904\) | −1.47193e7 | −0.599053 | ||||||||
\(905\) | −1.94086e7 | −0.787720 | ||||||||
\(906\) | 5.09030e6 | 0.206027 | ||||||||
\(907\) | −211109. | −0.00852096 | −0.00426048 | − | 0.999991i | \(-0.501356\pi\) | ||||
−0.00426048 | + | 0.999991i | \(0.501356\pi\) | |||||||
\(908\) | −2.41060e6 | −0.0970311 | ||||||||
\(909\) | 4.24978e6 | 0.170591 | ||||||||
\(910\) | −8.17534e6 | −0.327267 | ||||||||
\(911\) | 2.18697e7 | 0.873066 | 0.436533 | − | 0.899688i | \(-0.356206\pi\) | ||||
0.436533 | + | 0.899688i | \(0.356206\pi\) | |||||||
\(912\) | 2.44025e6 | 0.0971511 | ||||||||
\(913\) | −2.15742e6 | −0.0856558 | ||||||||
\(914\) | −1.01590e7 | −0.402242 | ||||||||
\(915\) | 549052. | 0.0216801 | ||||||||
\(916\) | −7.22760e6 | −0.284613 | ||||||||
\(917\) | 2.76466e7 | 1.08572 | ||||||||
\(918\) | 7.55695e6 | 0.295965 | ||||||||
\(919\) | 1.88742e7 | 0.737192 | 0.368596 | − | 0.929590i | \(-0.379839\pi\) | ||||
0.368596 | + | 0.929590i | \(0.379839\pi\) | |||||||
\(920\) | −1.04414e7 | −0.406714 | ||||||||
\(921\) | 1.97163e7 | 0.765907 | ||||||||
\(922\) | −4.90799e6 | −0.190141 | ||||||||
\(923\) | 5.68322e7 | 2.19579 | ||||||||
\(924\) | 6.75126e6 | 0.260138 | ||||||||
\(925\) | −1.35628e6 | −0.0521190 | ||||||||
\(926\) | −5.82812e6 | −0.223358 | ||||||||
\(927\) | −8.86856e6 | −0.338964 | ||||||||
\(928\) | −8.87631e6 | −0.338347 | ||||||||
\(929\) | −5.37016e6 | −0.204149 | −0.102075 | − | 0.994777i | \(-0.532548\pi\) | ||||
−0.102075 | + | 0.994777i | \(0.532548\pi\) | |||||||
\(930\) | −4.37593e6 | −0.165906 | ||||||||
\(931\) | −3.31989e6 | −0.125531 | ||||||||
\(932\) | 2.08810e7 | 0.787428 | ||||||||
\(933\) | 9.84413e6 | 0.370232 | ||||||||
\(934\) | −3.36326e6 | −0.126152 | ||||||||
\(935\) | 2.33948e6 | 0.0875166 | ||||||||
\(936\) | 8.38342e6 | 0.312775 | ||||||||
\(937\) | 2.80796e7 | 1.04482 | 0.522411 | − | 0.852694i | \(-0.325033\pi\) | ||||
0.522411 | + | 0.852694i | \(0.325033\pi\) | |||||||
\(938\) | 2.17851e6 | 0.0808449 | ||||||||
\(939\) | 1.77373e7 | 0.656484 | ||||||||
\(940\) | −4.79963e6 | −0.177169 | ||||||||
\(941\) | 1.33996e7 | 0.493307 | 0.246654 | − | 0.969104i | \(-0.420669\pi\) | ||||
0.246654 | + | 0.969104i | \(0.420669\pi\) | |||||||
\(942\) | 1.78784e6 | 0.0656450 | ||||||||
\(943\) | 2.62782e7 | 0.962314 | ||||||||
\(944\) | −8.01904e6 | −0.292882 | ||||||||
\(945\) | −1.66007e7 | −0.604711 | ||||||||
\(946\) | 758016. | 0.0275392 | ||||||||
\(947\) | 1.81387e6 | 0.0657251 | 0.0328626 | − | 0.999460i | \(-0.489538\pi\) | ||||
0.0328626 | + | 0.999460i | \(0.489538\pi\) | |||||||
\(948\) | −1.34766e7 | −0.487035 | ||||||||
\(949\) | 2.35584e7 | 0.849142 | ||||||||
\(950\) | 535386. | 0.0192468 | ||||||||
\(951\) | 3.14979e7 | 1.12935 | ||||||||
\(952\) | −1.72732e7 | −0.617705 | ||||||||
\(953\) | −4.14362e7 | −1.47791 | −0.738954 | − | 0.673756i | \(-0.764680\pi\) | ||||
−0.738954 | + | 0.673756i | \(0.764680\pi\) | |||||||
\(954\) | 719500. | 0.0255953 | ||||||||
\(955\) | −3.13168e6 | −0.111114 | ||||||||
\(956\) | 3.15113e7 | 1.11512 | ||||||||
\(957\) | −2.49231e6 | −0.0879676 | ||||||||
\(958\) | −2.17282e6 | −0.0764910 | ||||||||
\(959\) | −3.06937e7 | −1.07771 | ||||||||
\(960\) | −1.00622e6 | −0.0352381 | ||||||||
\(961\) | 2.97404e6 | 0.103882 | ||||||||
\(962\) | −4.40069e6 | −0.153314 | ||||||||
\(963\) | −3.41423e6 | −0.118639 | ||||||||
\(964\) | 2.95128e7 | 1.02286 | ||||||||
\(965\) | −1.70661e7 | −0.589951 | ||||||||
\(966\) | 1.51403e7 | 0.522025 | ||||||||
\(967\) | 3.09184e7 | 1.06329 | 0.531644 | − | 0.846968i | \(-0.321575\pi\) | ||||
0.531644 | + | 0.846968i | \(0.321575\pi\) | |||||||
\(968\) | 2.02785e6 | 0.0695580 | ||||||||
\(969\) | −3.66342e6 | −0.125336 | ||||||||
\(970\) | 1.01194e6 | 0.0345322 | ||||||||
\(971\) | −1.72970e7 | −0.588738 | −0.294369 | − | 0.955692i | \(-0.595110\pi\) | ||||
−0.294369 | + | 0.955692i | \(0.595110\pi\) | |||||||
\(972\) | 1.36455e7 | 0.463258 | ||||||||
\(973\) | −2.10881e7 | −0.714094 | ||||||||
\(974\) | 5.18594e6 | 0.175158 | ||||||||
\(975\) | 7.00868e6 | 0.236115 | ||||||||
\(976\) | 862245. | 0.0289739 | ||||||||
\(977\) | −3.25532e7 | −1.09108 | −0.545541 | − | 0.838084i | \(-0.683676\pi\) | ||||
−0.545541 | + | 0.838084i | \(0.683676\pi\) | |||||||
\(978\) | −2.16145e6 | −0.0722600 | ||||||||
\(979\) | −1.30248e7 | −0.434324 | ||||||||
\(980\) | 6.06256e6 | 0.201646 | ||||||||
\(981\) | 1.54847e7 | 0.513724 | ||||||||
\(982\) | −2.14556e7 | −0.710006 | ||||||||
\(983\) | −5.93839e6 | −0.196013 | −0.0980066 | − | 0.995186i | \(-0.531247\pi\) | ||||
−0.0980066 | + | 0.995186i | \(0.531247\pi\) | |||||||
\(984\) | −1.58377e7 | −0.521440 | ||||||||
\(985\) | −1.44111e7 | −0.473266 | ||||||||
\(986\) | 2.88075e6 | 0.0943657 | ||||||||
\(987\) | 1.54052e7 | 0.503356 | ||||||||
\(988\) | −8.13537e6 | −0.265146 | ||||||||
\(989\) | −7.96099e6 | −0.258807 | ||||||||
\(990\) | −508383. | −0.0164855 | ||||||||
\(991\) | −3.47991e7 | −1.12560 | −0.562800 | − | 0.826593i | \(-0.690276\pi\) | ||||
−0.562800 | + | 0.826593i | \(0.690276\pi\) | |||||||
\(992\) | −3.17882e7 | −1.02562 | ||||||||
\(993\) | 6.05151e6 | 0.194756 | ||||||||
\(994\) | 2.54460e7 | 0.816870 | ||||||||
\(995\) | 1.02684e7 | 0.328811 | ||||||||
\(996\) | −6.16926e6 | −0.197054 | ||||||||
\(997\) | 2.57562e7 | 0.820623 | 0.410312 | − | 0.911945i | \(-0.365420\pi\) | ||||
0.410312 | + | 0.911945i | \(0.365420\pi\) | |||||||
\(998\) | 9.98191e6 | 0.317239 | ||||||||
\(999\) | −8.93599e6 | −0.283289 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1045.6.a.d.1.16 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.d.1.16 | ✓ | 37 | 1.1 | even | 1 | trivial |