Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(296,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.296");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 296.10 | ||
Character | \(\chi\) | \(=\) | 531.296 |
Dual form | 531.5.b.a.296.67 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 6.40563i | − 1.60141i | −0.599061 | − | 0.800703i | \(-0.704459\pi\) | ||||
0.599061 | − | 0.800703i | \(-0.295541\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −25.0320 | −1.56450 | ||||||||
\(5\) | 18.5372i | 0.741489i | 0.928735 | + | 0.370745i | \(0.120897\pi\) | ||||
−0.928735 | + | 0.370745i | \(0.879103\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.7242 | 0.606616 | 0.303308 | − | 0.952893i | \(-0.401909\pi\) | ||||
0.303308 | + | 0.952893i | \(0.401909\pi\) | |||||||
\(8\) | 57.8559i | 0.903998i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 118.743 | 1.18743 | ||||||||
\(11\) | 32.7748i | 0.270866i | 0.990787 | + | 0.135433i | \(0.0432425\pi\) | ||||
−0.990787 | + | 0.135433i | \(0.956757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −137.661 | −0.814562 | −0.407281 | − | 0.913303i | \(-0.633523\pi\) | ||||
−0.407281 | + | 0.913303i | \(0.633523\pi\) | |||||||
\(14\) | − 190.402i | − 0.971439i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −29.9096 | −0.116834 | ||||||||
\(17\) | − 443.487i | − 1.53456i | −0.641314 | − | 0.767278i | \(-0.721610\pi\) | ||||
0.641314 | − | 0.767278i | \(-0.278390\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −630.893 | −1.74763 | −0.873813 | − | 0.486262i | \(-0.838360\pi\) | ||||
−0.873813 | + | 0.486262i | \(0.838360\pi\) | |||||||
\(20\) | − 464.025i | − 1.16006i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 209.943 | 0.433766 | ||||||||
\(23\) | 445.913i | 0.842937i | 0.906843 | + | 0.421468i | \(0.138485\pi\) | ||||
−0.906843 | + | 0.421468i | \(0.861515\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 281.371 | 0.450194 | ||||||||
\(26\) | 881.805i | 1.30445i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −744.057 | −0.949052 | ||||||||
\(29\) | 606.766i | 0.721481i | 0.932666 | + | 0.360741i | \(0.117476\pi\) | ||||
−0.932666 | + | 0.360741i | \(0.882524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1621.00 | 1.68679 | 0.843393 | − | 0.537297i | \(-0.180555\pi\) | ||||
0.843393 | + | 0.537297i | \(0.180555\pi\) | |||||||
\(32\) | 1117.28i | 1.09110i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2840.81 | −2.45745 | ||||||||
\(35\) | 551.004i | 0.449799i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 873.840 | 0.638305 | 0.319153 | − | 0.947703i | \(-0.396602\pi\) | ||||
0.319153 | + | 0.947703i | \(0.396602\pi\) | |||||||
\(38\) | 4041.26i | 2.79866i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1072.49 | −0.670305 | ||||||||
\(41\) | 1861.83i | 1.10758i | 0.832658 | + | 0.553788i | \(0.186818\pi\) | ||||
−0.832658 | + | 0.553788i | \(0.813182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2797.58 | 1.51302 | 0.756511 | − | 0.653981i | \(-0.226903\pi\) | ||||
0.756511 | + | 0.653981i | \(0.226903\pi\) | |||||||
\(44\) | − 820.420i | − 0.423770i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2856.35 | 1.34988 | ||||||||
\(47\) | − 1713.95i | − 0.775895i | −0.921682 | − | 0.387947i | \(-0.873184\pi\) | ||||
0.921682 | − | 0.387947i | \(-0.126816\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1517.47 | −0.632017 | ||||||||
\(50\) | − 1802.36i | − 0.720943i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3445.94 | 1.27439 | ||||||||
\(53\) | 3467.53i | 1.23444i | 0.786792 | + | 0.617219i | \(0.211741\pi\) | ||||
−0.786792 | + | 0.617219i | \(0.788259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −607.554 | −0.200844 | ||||||||
\(56\) | 1719.72i | 0.548380i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3886.71 | 1.15538 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4806.75 | 1.29179 | 0.645895 | − | 0.763426i | \(-0.276484\pi\) | ||||
0.645895 | + | 0.763426i | \(0.276484\pi\) | |||||||
\(62\) | − 10383.5i | − 2.70123i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6678.35 | 1.63046 | ||||||||
\(65\) | − 2551.85i | − 0.603989i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3864.25 | −0.860827 | −0.430414 | − | 0.902632i | \(-0.641632\pi\) | ||||
−0.430414 | + | 0.902632i | \(0.641632\pi\) | |||||||
\(68\) | 11101.4i | 2.40082i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3529.52 | 0.720311 | ||||||||
\(71\) | 9178.02i | 1.82067i | 0.413867 | + | 0.910337i | \(0.364178\pi\) | ||||
−0.413867 | + | 0.910337i | \(0.635822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3348.84 | −0.628418 | −0.314209 | − | 0.949354i | \(-0.601739\pi\) | ||||
−0.314209 | + | 0.949354i | \(0.601739\pi\) | |||||||
\(74\) | − 5597.49i | − 1.02219i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15792.5 | 2.73417 | ||||||||
\(77\) | 974.203i | 0.164312i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7875.77 | 1.26194 | 0.630971 | − | 0.775807i | \(-0.282657\pi\) | ||||
0.630971 | + | 0.775807i | \(0.282657\pi\) | |||||||
\(80\) | − 554.441i | − 0.0866314i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11926.2 | 1.77368 | ||||||||
\(83\) | − 1055.87i | − 0.153270i | −0.997059 | − | 0.0766348i | \(-0.975582\pi\) | ||||
0.997059 | − | 0.0766348i | \(-0.0244176\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8221.02 | 1.13786 | ||||||||
\(86\) | − 17920.2i | − 2.42296i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1896.21 | −0.244862 | ||||||||
\(89\) | 13370.5i | 1.68799i | 0.536353 | + | 0.843994i | \(0.319802\pi\) | ||||
−0.536353 | + | 0.843994i | \(0.680198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4091.86 | −0.494126 | ||||||||
\(92\) | − 11162.1i | − 1.31878i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10978.9 | −1.24252 | ||||||||
\(95\) | − 11695.0i | − 1.29585i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1572.85 | −0.167164 | −0.0835822 | − | 0.996501i | \(-0.526636\pi\) | ||||
−0.0835822 | + | 0.996501i | \(0.526636\pi\) | |||||||
\(98\) | 9720.37i | 1.01212i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7043.30 | −0.704330 | ||||||||
\(101\) | − 12809.2i | − 1.25569i | −0.778340 | − | 0.627843i | \(-0.783938\pi\) | ||||
0.778340 | − | 0.627843i | \(-0.216062\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 413.910 | 0.0390150 | 0.0195075 | − | 0.999810i | \(-0.493790\pi\) | ||||
0.0195075 | + | 0.999810i | \(0.493790\pi\) | |||||||
\(104\) | − 7964.50i | − 0.736363i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22211.7 | 1.97684 | ||||||||
\(107\) | 15603.9i | 1.36291i | 0.731861 | + | 0.681454i | \(0.238652\pi\) | ||||
−0.731861 | + | 0.681454i | \(0.761348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 23274.9 | 1.95900 | 0.979502 | − | 0.201436i | \(-0.0645608\pi\) | ||||
0.979502 | + | 0.201436i | \(0.0645608\pi\) | |||||||
\(110\) | 3891.76i | 0.321633i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −889.038 | −0.0708735 | ||||||||
\(113\) | 20189.0i | 1.58109i | 0.612402 | + | 0.790546i | \(0.290203\pi\) | ||||
−0.612402 | + | 0.790546i | \(0.709797\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8266.00 | −0.625028 | ||||||||
\(116\) | − 15188.6i | − 1.12876i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2902.95 | 0.208485 | ||||||||
\(119\) | − 13182.3i | − 0.930887i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13566.8 | 0.926632 | ||||||||
\(122\) | − 30790.3i | − 2.06868i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −40577.0 | −2.63898 | ||||||||
\(125\) | 16801.6i | 1.07530i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12135.4 | −0.752393 | −0.376197 | − | 0.926540i | \(-0.622768\pi\) | ||||
−0.376197 | + | 0.926540i | \(0.622768\pi\) | |||||||
\(128\) | − 24902.5i | − 1.51993i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16346.2 | −0.967232 | ||||||||
\(131\) | − 29285.0i | − 1.70649i | −0.521514 | − | 0.853243i | \(-0.674633\pi\) | ||||
0.521514 | − | 0.853243i | \(-0.325367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18752.8 | −1.06014 | ||||||||
\(134\) | 24753.0i | 1.37853i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25658.3 | 1.38724 | ||||||||
\(137\) | 4399.11i | 0.234382i | 0.993109 | + | 0.117191i | \(0.0373889\pi\) | ||||
−0.993109 | + | 0.117191i | \(0.962611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16380.4 | −0.847802 | −0.423901 | − | 0.905709i | \(-0.639340\pi\) | ||||
−0.423901 | + | 0.905709i | \(0.639340\pi\) | |||||||
\(140\) | − 13792.7i | − 0.703712i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 58791.0 | 2.91564 | ||||||||
\(143\) | − 4511.81i | − 0.220637i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11247.8 | −0.534971 | ||||||||
\(146\) | 21451.4i | 1.00635i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21874.0 | −0.998630 | ||||||||
\(149\) | − 22971.4i | − 1.03470i | −0.855773 | − | 0.517352i | \(-0.826918\pi\) | ||||
0.855773 | − | 0.517352i | \(-0.173082\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13853.9 | −0.607600 | −0.303800 | − | 0.952736i | \(-0.598255\pi\) | ||||
−0.303800 | + | 0.952736i | \(0.598255\pi\) | |||||||
\(152\) | − 36500.9i | − 1.57985i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6240.38 | 0.263130 | ||||||||
\(155\) | 30048.9i | 1.25073i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8382.97 | 0.340094 | 0.170047 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170047 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(158\) | − 50449.3i | − 2.02088i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20711.3 | −0.809037 | ||||||||
\(161\) | 13254.4i | 0.511339i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4249.18 | 0.159930 | 0.0799651 | − | 0.996798i | \(-0.474519\pi\) | ||||
0.0799651 | + | 0.996798i | \(0.474519\pi\) | |||||||
\(164\) | − 46605.5i | − 1.73281i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6763.54 | −0.245447 | ||||||||
\(167\) | 40728.5i | 1.46038i | 0.683245 | + | 0.730189i | \(0.260568\pi\) | ||||
−0.683245 | + | 0.730189i | \(0.739432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9610.43 | −0.336488 | ||||||||
\(170\) | − 52660.8i | − 1.82217i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −70029.0 | −2.36713 | ||||||||
\(173\) | 11562.3i | 0.386324i | 0.981167 | + | 0.193162i | \(0.0618742\pi\) | ||||
−0.981167 | + | 0.193162i | \(0.938126\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8363.53 | 0.273095 | ||||||||
\(176\) | − 980.280i | − 0.0316464i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 85646.7 | 2.70315 | ||||||||
\(179\) | 26376.1i | 0.823199i | 0.911365 | + | 0.411599i | \(0.135030\pi\) | ||||
−0.911365 | + | 0.411599i | \(0.864970\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −33691.5 | −1.02840 | −0.514201 | − | 0.857670i | \(-0.671911\pi\) | ||||
−0.514201 | + | 0.857670i | \(0.671911\pi\) | |||||||
\(182\) | 26210.9i | 0.791297i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −25798.7 | −0.762013 | ||||||||
\(185\) | 16198.6i | 0.473296i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14535.2 | 0.415659 | ||||||||
\(188\) | 42903.7i | 1.21389i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −74913.8 | −2.07518 | ||||||||
\(191\) | − 60835.4i | − 1.66759i | −0.552073 | − | 0.833796i | \(-0.686163\pi\) | ||||
0.552073 | − | 0.833796i | \(-0.313837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 37876.5 | 1.01685 | 0.508423 | − | 0.861108i | \(-0.330229\pi\) | ||||
0.508423 | + | 0.861108i | \(0.330229\pi\) | |||||||
\(194\) | 10075.1i | 0.267698i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 37985.5 | 0.988793 | ||||||||
\(197\) | − 52067.4i | − 1.34163i | −0.741623 | − | 0.670816i | \(-0.765944\pi\) | ||||
0.741623 | − | 0.670816i | \(-0.234056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 58282.8 | 1.47175 | 0.735875 | − | 0.677117i | \(-0.236771\pi\) | ||||
0.735875 | + | 0.677117i | \(0.236771\pi\) | |||||||
\(200\) | 16279.0i | 0.406974i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −82051.2 | −2.01086 | ||||||||
\(203\) | 18035.6i | 0.437662i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −34513.3 | −0.821255 | ||||||||
\(206\) | − 2651.35i | − 0.0624789i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4117.38 | 0.0951688 | ||||||||
\(209\) | − 20677.4i | − 0.473372i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 48803.8 | 1.09620 | 0.548098 | − | 0.836414i | \(-0.315352\pi\) | ||||
0.548098 | + | 0.836414i | \(0.315352\pi\) | |||||||
\(212\) | − 86799.5i | − 1.93128i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 99952.9 | 2.18257 | ||||||||
\(215\) | 51859.3i | 1.12189i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 48182.9 | 1.02323 | ||||||||
\(218\) | − 149090.i | − 3.13716i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15208.3 | 0.314221 | ||||||||
\(221\) | 61050.9i | 1.24999i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 76803.9 | 1.54445 | 0.772225 | − | 0.635349i | \(-0.219144\pi\) | ||||
0.772225 | + | 0.635349i | \(0.219144\pi\) | |||||||
\(224\) | 33210.3i | 0.661877i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 129323. | 2.53197 | ||||||||
\(227\) | − 28589.3i | − 0.554820i | −0.960752 | − | 0.277410i | \(-0.910524\pi\) | ||||
0.960752 | − | 0.277410i | \(-0.0894760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −76462.1 | −1.45806 | −0.729030 | − | 0.684482i | \(-0.760028\pi\) | ||||
−0.729030 | + | 0.684482i | \(0.760028\pi\) | |||||||
\(230\) | 52948.9i | 1.00092i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −35105.0 | −0.652218 | ||||||||
\(233\) | 40137.7i | 0.739335i | 0.929164 | + | 0.369667i | \(0.120528\pi\) | ||||
−0.929164 | + | 0.369667i | \(0.879472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31771.9 | 0.575317 | ||||||||
\(236\) | − 11344.2i | − 0.203681i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −84440.8 | −1.49073 | ||||||||
\(239\) | − 26767.6i | − 0.468612i | −0.972163 | − | 0.234306i | \(-0.924718\pi\) | ||||
0.972163 | − | 0.234306i | \(-0.0752818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1680.86 | 0.0289399 | 0.0144699 | − | 0.999895i | \(-0.495394\pi\) | ||||
0.0144699 | + | 0.999895i | \(0.495394\pi\) | |||||||
\(242\) | − 86903.9i | − 1.48391i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −120323. | −2.02101 | ||||||||
\(245\) | − 28129.7i | − 0.468634i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 86849.4 | 1.42355 | ||||||||
\(248\) | 93784.4i | 1.52485i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 107625. | 1.72200 | ||||||||
\(251\) | 43157.9i | 0.685036i | 0.939511 | + | 0.342518i | \(0.111280\pi\) | ||||
−0.939511 | + | 0.342518i | \(0.888720\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14614.7 | −0.228323 | ||||||||
\(254\) | 77734.5i | 1.20489i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −52662.3 | −0.803562 | ||||||||
\(257\) | 50727.5i | 0.768028i | 0.923327 | + | 0.384014i | \(0.125459\pi\) | ||||
−0.923327 | + | 0.384014i | \(0.874541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25974.2 | 0.387206 | ||||||||
\(260\) | 63878.1i | 0.944943i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −187589. | −2.73278 | ||||||||
\(263\) | 45750.0i | 0.661424i | 0.943732 | + | 0.330712i | \(0.107289\pi\) | ||||
−0.943732 | + | 0.330712i | \(0.892711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −64278.5 | −0.915322 | ||||||||
\(266\) | 120123.i | 1.69771i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 96730.1 | 1.34677 | ||||||||
\(269\) | 38115.8i | 0.526746i | 0.964694 | + | 0.263373i | \(0.0848349\pi\) | ||||
−0.964694 | + | 0.263373i | \(0.915165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22465.1 | −0.305893 | −0.152947 | − | 0.988234i | \(-0.548876\pi\) | ||||
−0.152947 | + | 0.988234i | \(0.548876\pi\) | |||||||
\(272\) | 13264.5i | 0.179289i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 28179.1 | 0.375341 | ||||||||
\(275\) | 9221.88i | 0.121942i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −107669. | −1.40323 | −0.701615 | − | 0.712556i | \(-0.747538\pi\) | ||||
−0.701615 | + | 0.712556i | \(0.747538\pi\) | |||||||
\(278\) | 104927.i | 1.35768i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −31878.8 | −0.406617 | ||||||||
\(281\) | − 38399.3i | − 0.486307i | −0.969988 | − | 0.243153i | \(-0.921818\pi\) | ||||
0.969988 | − | 0.243153i | \(-0.0781818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31777.5 | −0.396777 | −0.198389 | − | 0.980123i | \(-0.563571\pi\) | ||||
−0.198389 | + | 0.980123i | \(0.563571\pi\) | |||||||
\(284\) | − 229745.i | − 2.84845i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28901.0 | −0.353330 | ||||||||
\(287\) | 55341.5i | 0.671873i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −113160. | −1.35486 | ||||||||
\(290\) | 72048.9i | 0.856705i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 83828.2 | 0.983161 | ||||||||
\(293\) | − 5251.78i | − 0.0611746i | −0.999532 | − | 0.0305873i | \(-0.990262\pi\) | ||||
0.999532 | − | 0.0305873i | \(-0.00973776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8400.84 | −0.0965337 | ||||||||
\(296\) | 50556.8i | 0.577027i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −147147. | −1.65698 | ||||||||
\(299\) | − 61384.9i | − 0.686624i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 83155.7 | 0.917823 | ||||||||
\(302\) | 88742.8i | 0.973015i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18869.7 | 0.204183 | ||||||||
\(305\) | 89103.9i | 0.957849i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5997.74 | 0.0636371 | 0.0318186 | − | 0.999494i | \(-0.489870\pi\) | ||||
0.0318186 | + | 0.999494i | \(0.489870\pi\) | |||||||
\(308\) | − 24386.3i | − 0.257066i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 192482. | 2.00293 | ||||||||
\(311\) | 53405.2i | 0.552157i | 0.961135 | + | 0.276079i | \(0.0890350\pi\) | ||||
−0.961135 | + | 0.276079i | \(0.910965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 57812.3 | 0.590108 | 0.295054 | − | 0.955481i | \(-0.404662\pi\) | ||||
0.295054 | + | 0.955481i | \(0.404662\pi\) | |||||||
\(314\) | − 53698.2i | − 0.544628i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −197147. | −1.97431 | ||||||||
\(317\) | 95275.8i | 0.948121i | 0.880492 | + | 0.474061i | \(0.157212\pi\) | ||||
−0.880492 | + | 0.474061i | \(0.842788\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19886.6 | −0.195425 | ||||||||
\(320\) | 123798.i | 1.20897i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 84902.8 | 0.818861 | ||||||||
\(323\) | 279793.i | 2.68183i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −38733.9 | −0.366711 | ||||||||
\(326\) | − 27218.7i | − 0.256113i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −107718. | −1.00125 | ||||||||
\(329\) | − 50945.8i | − 0.470670i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −132376. | −1.20824 | −0.604121 | − | 0.796892i | \(-0.706476\pi\) | ||||
−0.604121 | + | 0.796892i | \(0.706476\pi\) | |||||||
\(332\) | 26430.7i | 0.239791i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 260891. | 2.33866 | ||||||||
\(335\) | − 71632.5i | − 0.638294i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18547.6 | −0.163316 | −0.0816580 | − | 0.996660i | \(-0.526022\pi\) | ||||
−0.0816580 | + | 0.996660i | \(0.526022\pi\) | |||||||
\(338\) | 61560.8i | 0.538854i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −205789. | −1.78018 | ||||||||
\(341\) | 53128.0i | 0.456893i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −116473. | −0.990008 | ||||||||
\(344\) | 161856.i | 1.36777i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 74063.6 | 0.618661 | ||||||||
\(347\) | 107681.i | 0.894297i | 0.894460 | + | 0.447149i | \(0.147561\pi\) | ||||
−0.894460 | + | 0.447149i | \(0.852439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −150396. | −1.23476 | −0.617382 | − | 0.786663i | \(-0.711807\pi\) | ||||
−0.617382 | + | 0.786663i | \(0.711807\pi\) | |||||||
\(350\) | − 53573.6i | − 0.437336i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −36618.7 | −0.295541 | ||||||||
\(353\) | 120299.i | 0.965413i | 0.875782 | + | 0.482707i | \(0.160346\pi\) | ||||
−0.875782 | + | 0.482707i | \(0.839654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −170135. | −1.35001 | ||||||||
\(356\) | − 334692.i | − 2.64086i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 168956. | 1.31828 | ||||||||
\(359\) | − 37128.9i | − 0.288086i | −0.989571 | − | 0.144043i | \(-0.953990\pi\) | ||||
0.989571 | − | 0.144043i | \(-0.0460104\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 267705. | 2.05420 | ||||||||
\(362\) | 215815.i | 1.64689i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 102428. | 0.773062 | ||||||||
\(365\) | − 62078.2i | − 0.465965i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 229188. | 1.70161 | 0.850803 | − | 0.525484i | \(-0.176116\pi\) | ||||
0.850803 | + | 0.525484i | \(0.176116\pi\) | |||||||
\(368\) | − 13337.1i | − 0.0984839i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 103762. | 0.757940 | ||||||||
\(371\) | 103070.i | 0.748829i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −67878.4 | −0.487881 | −0.243941 | − | 0.969790i | \(-0.578440\pi\) | ||||
−0.243941 | + | 0.969790i | \(0.578440\pi\) | |||||||
\(374\) | − 93107.0i | − 0.665639i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 99162.2 | 0.701407 | ||||||||
\(377\) | − 83528.0i | − 0.587692i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −165620. | −1.15302 | −0.576508 | − | 0.817091i | \(-0.695585\pi\) | ||||
−0.576508 | + | 0.817091i | \(0.695585\pi\) | |||||||
\(380\) | 292750.i | 2.02735i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −389689. | −2.67049 | ||||||||
\(383\) | 58913.9i | 0.401624i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) | ||||
−0.979630 | + | 0.200812i | \(0.935642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18059.0 | −0.121835 | ||||||||
\(386\) | − 242623.i | − 1.62838i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 39371.6 | 0.261529 | ||||||||
\(389\) | 78199.0i | 0.516776i | 0.966041 | + | 0.258388i | \(0.0831912\pi\) | ||||
−0.966041 | + | 0.258388i | \(0.916809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 197757. | 1.29353 | ||||||||
\(392\) | − 87794.7i | − 0.571342i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −333524. | −2.14850 | ||||||||
\(395\) | 145995.i | 0.935716i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −122506. | −0.777277 | −0.388638 | − | 0.921390i | \(-0.627054\pi\) | ||||
−0.388638 | + | 0.921390i | \(0.627054\pi\) | |||||||
\(398\) | − 373338.i | − 2.35687i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8415.70 | −0.0525981 | ||||||||
\(401\) | − 103707.i | − 0.644939i | −0.946580 | − | 0.322469i | \(-0.895487\pi\) | ||||
0.946580 | − | 0.322469i | \(-0.104513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −223149. | −1.37399 | ||||||||
\(404\) | 320642.i | 1.96452i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 115529. | 0.700875 | ||||||||
\(407\) | 28639.9i | 0.172895i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −55315.2 | −0.330672 | −0.165336 | − | 0.986237i | \(-0.552871\pi\) | ||||
−0.165336 | + | 0.986237i | \(0.552871\pi\) | |||||||
\(410\) | 221079.i | 1.31516i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10361.0 | −0.0610391 | ||||||||
\(413\) | 13470.6i | 0.0789747i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19573.0 | 0.113648 | ||||||||
\(416\) | − 153806.i | − 0.888767i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −132452. | −0.758062 | ||||||||
\(419\) | 142368.i | 0.810931i | 0.914110 | + | 0.405466i | \(0.132891\pi\) | ||||
−0.914110 | + | 0.405466i | \(0.867109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 109029. | 0.615145 | 0.307573 | − | 0.951525i | \(-0.400483\pi\) | ||||
0.307573 | + | 0.951525i | \(0.400483\pi\) | |||||||
\(422\) | − 312619.i | − 1.75546i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −200617. | −1.11593 | ||||||||
\(425\) | − 124784.i | − 0.690848i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 142877. | 0.783621 | ||||||||
\(428\) | − 390598.i | − 2.13227i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 332191. | 1.79660 | ||||||||
\(431\) | 101136.i | 0.544440i | 0.962235 | + | 0.272220i | \(0.0877579\pi\) | ||||
−0.962235 | + | 0.272220i | \(0.912242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −187634. | −1.00078 | −0.500388 | − | 0.865801i | \(-0.666809\pi\) | ||||
−0.500388 | + | 0.865801i | \(0.666809\pi\) | |||||||
\(434\) | − 308642.i | − 1.63861i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −582619. | −3.06487 | ||||||||
\(437\) | − 281324.i | − 1.47314i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 237768. | 1.23374 | 0.616870 | − | 0.787065i | \(-0.288400\pi\) | ||||
0.616870 | + | 0.787065i | \(0.288400\pi\) | |||||||
\(440\) | − 35150.5i | − 0.181563i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 391069. | 2.00175 | ||||||||
\(443\) | − 175383.i | − 0.893675i | −0.894615 | − | 0.446837i | \(-0.852550\pi\) | ||||
0.894615 | − | 0.446837i | \(-0.147450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −247853. | −1.25162 | ||||||||
\(446\) | − 491977.i | − 2.47329i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 198508. | 0.989060 | ||||||||
\(449\) | − 294798.i | − 1.46229i | −0.682224 | − | 0.731143i | \(-0.738987\pi\) | ||||
0.682224 | − | 0.731143i | \(-0.261013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −61021.2 | −0.300005 | ||||||||
\(452\) | − 505371.i | − 2.47362i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −183132. | −0.888492 | ||||||||
\(455\) | − 75851.8i | − 0.366389i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 372380. | 1.78301 | 0.891505 | − | 0.453011i | \(-0.149650\pi\) | ||||
0.891505 | + | 0.453011i | \(0.149650\pi\) | |||||||
\(458\) | 489787.i | 2.33495i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 206915. | 0.977858 | ||||||||
\(461\) | − 41703.3i | − 0.196231i | −0.995175 | − | 0.0981156i | \(-0.968719\pi\) | ||||
0.995175 | − | 0.0981156i | \(-0.0312815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −44181.8 | −0.206102 | −0.103051 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103051 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(464\) | − 18148.1i | − 0.0842938i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 257107. | 1.18398 | ||||||||
\(467\) | 216232.i | 0.991485i | 0.868469 | + | 0.495743i | \(0.165104\pi\) | ||||
−0.868469 | + | 0.495743i | \(0.834896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −114862. | −0.522191 | ||||||||
\(470\) | − 203519.i | − 0.921317i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −26219.6 | −0.117691 | ||||||||
\(473\) | 91690.0i | 0.409826i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −177515. | −0.786771 | ||||||||
\(476\) | 329979.i | 1.45637i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −171463. | −0.750439 | ||||||||
\(479\) | − 153685.i | − 0.669825i | −0.942249 | − | 0.334913i | \(-0.891293\pi\) | ||||
0.942249 | − | 0.334913i | \(-0.108707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −120294. | −0.519940 | ||||||||
\(482\) | − 10766.9i | − 0.0463445i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −339605. | −1.44972 | ||||||||
\(485\) | − 29156.3i | − 0.123951i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −345723. | −1.45771 | −0.728853 | − | 0.684670i | \(-0.759946\pi\) | ||||
−0.728853 | + | 0.684670i | \(0.759946\pi\) | |||||||
\(488\) | 278099.i | 1.16778i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −180189. | −0.750473 | ||||||||
\(491\) | 20495.1i | 0.0850133i | 0.999096 | + | 0.0425067i | \(0.0135344\pi\) | ||||
−0.999096 | + | 0.0425067i | \(0.986466\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 269093. | 1.10715 | ||||||||
\(494\) | − 556325.i | − 2.27968i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48483.5 | −0.197074 | ||||||||
\(497\) | 272809.i | 1.10445i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 259780. | 1.04329 | 0.521645 | − | 0.853162i | \(-0.325318\pi\) | ||||
0.521645 | + | 0.853162i | \(0.325318\pi\) | |||||||
\(500\) | − 420579.i | − 1.68231i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 276454. | 1.09702 | ||||||||
\(503\) | − 204298.i | − 0.807473i | −0.914875 | − | 0.403736i | \(-0.867711\pi\) | ||||
0.914875 | − | 0.403736i | \(-0.132289\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 237448. | 0.931077 | ||||||||
\(506\) | 93616.4i | 0.365638i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 303773. | 1.17712 | ||||||||
\(509\) | − 392891.i | − 1.51648i | −0.651976 | − | 0.758239i | \(-0.726060\pi\) | ||||
0.651976 | − | 0.758239i | \(-0.273940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −99541.4 | −0.381208 | ||||||||
\(512\) | − 61104.6i | − 0.233096i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 324941. | 1.22993 | ||||||||
\(515\) | 7672.74i | 0.0289292i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 56174.4 | 0.210163 | ||||||||
\(518\) | − 166381.i | − 0.620074i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 147640. | 0.546005 | ||||||||
\(521\) | 249929.i | 0.920748i | 0.887725 | + | 0.460374i | \(0.152285\pi\) | ||||
−0.887725 | + | 0.460374i | \(0.847715\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −361636. | −1.32211 | −0.661056 | − | 0.750337i | \(-0.729891\pi\) | ||||
−0.661056 | + | 0.750337i | \(0.729891\pi\) | |||||||
\(524\) | 733063.i | 2.66980i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 293058. | 1.05921 | ||||||||
\(527\) | − 718893.i | − 2.58847i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 81002.2 | 0.289458 | ||||||||
\(530\) | 411744.i | 1.46580i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 469420. | 1.65859 | ||||||||
\(533\) | − 256302.i | − 0.902190i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −289254. | −1.01058 | ||||||||
\(536\) | − 223570.i | − 0.778186i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 244156. | 0.843534 | ||||||||
\(539\) | − 49734.9i | − 0.171192i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 397532. | 1.35824 | 0.679121 | − | 0.734026i | \(-0.262361\pi\) | ||||
0.679121 | + | 0.734026i | \(0.262361\pi\) | |||||||
\(542\) | 143903.i | 0.489860i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 495501. | 1.67435 | ||||||||
\(545\) | 431452.i | 1.45258i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −364724. | −1.21896 | −0.609480 | − | 0.792801i | \(-0.708622\pi\) | ||||
−0.609480 | + | 0.792801i | \(0.708622\pi\) | |||||||
\(548\) | − 110119.i | − 0.366691i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 59071.9 | 0.195279 | ||||||||
\(551\) | − 382804.i | − 1.26088i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 234101. | 0.765513 | ||||||||
\(554\) | 689684.i | 2.24714i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 410034. | 1.32639 | ||||||||
\(557\) | 74648.2i | 0.240607i | 0.992737 | + | 0.120304i | \(0.0383868\pi\) | ||||
−0.992737 | + | 0.120304i | \(0.961613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −385117. | −1.23245 | ||||||||
\(560\) | − 16480.3i | − 0.0525520i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −245971. | −0.778775 | ||||||||
\(563\) | 522150.i | 1.64732i | 0.567083 | + | 0.823661i | \(0.308072\pi\) | ||||
−0.567083 | + | 0.823661i | \(0.691928\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −374248. | −1.17236 | ||||||||
\(566\) | 203555.i | 0.635402i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −531002. | −1.64589 | ||||||||
\(569\) | 67984.0i | 0.209982i | 0.994473 | + | 0.104991i | \(0.0334814\pi\) | ||||
−0.994473 | + | 0.104991i | \(0.966519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −368588. | −1.13050 | −0.565248 | − | 0.824921i | \(-0.691219\pi\) | ||||
−0.565248 | + | 0.824921i | \(0.691219\pi\) | |||||||
\(572\) | 112940.i | 0.345188i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 354497. | 1.07594 | ||||||||
\(575\) | 125467.i | 0.379485i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −137388. | −0.412665 | −0.206332 | − | 0.978482i | \(-0.566153\pi\) | ||||
−0.206332 | + | 0.978482i | \(0.566153\pi\) | |||||||
\(578\) | 724858.i | 2.16969i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 281554. | 0.836963 | ||||||||
\(581\) | − 31385.0i | − 0.0929758i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −113648. | −0.334367 | ||||||||
\(584\) | − 193750.i | − 0.568088i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −33640.9 | −0.0979654 | ||||||||
\(587\) | 95419.4i | 0.276924i | 0.990368 | + | 0.138462i | \(0.0442159\pi\) | ||||
−0.990368 | + | 0.138462i | \(0.955784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.02268e6 | −2.94787 | ||||||||
\(590\) | 53812.6i | 0.154590i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26136.2 | −0.0745760 | ||||||||
\(593\) | − 577212.i | − 1.64144i | −0.571329 | − | 0.820721i | \(-0.693572\pi\) | ||||
0.571329 | − | 0.820721i | \(-0.306428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 244363. | 0.690242 | ||||||||
\(596\) | 575022.i | 1.61880i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −393209. | −1.09956 | ||||||||
\(599\) | 470493.i | 1.31129i | 0.755068 | + | 0.655647i | \(0.227604\pi\) | ||||
−0.755068 | + | 0.655647i | \(0.772396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 528715. | 1.46377 | 0.731885 | − | 0.681429i | \(-0.238641\pi\) | ||||
0.731885 | + | 0.681429i | \(0.238641\pi\) | |||||||
\(602\) | − 532664.i | − 1.46981i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 346791. | 0.950592 | ||||||||
\(605\) | 251491.i | 0.687087i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −432534. | −1.17393 | −0.586967 | − | 0.809611i | \(-0.699678\pi\) | ||||
−0.586967 | + | 0.809611i | \(0.699678\pi\) | |||||||
\(608\) | − 704886.i | − 1.90683i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 570766. | 1.53391 | ||||||||
\(611\) | 235944.i | 0.632015i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −339482. | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(614\) | − 38419.3i | − 0.101909i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −56363.4 | −0.148537 | ||||||||
\(617\) | 267332.i | 0.702232i | 0.936332 | + | 0.351116i | \(0.114198\pi\) | ||||
−0.936332 | + | 0.351116i | \(0.885802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 165165. | 0.431060 | 0.215530 | − | 0.976497i | \(-0.430852\pi\) | ||||
0.215530 | + | 0.976497i | \(0.430852\pi\) | |||||||
\(620\) | − 752185.i | − 1.95678i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 342094. | 0.884228 | ||||||||
\(623\) | 397429.i | 1.02396i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −135598. | −0.347131 | ||||||||
\(626\) | − 370324.i | − 0.945002i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −209843. | −0.532077 | ||||||||
\(629\) | − 387537.i | − 0.979516i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 564821. | 1.41857 | 0.709287 | − | 0.704919i | \(-0.249017\pi\) | ||||
0.709287 | + | 0.704919i | \(0.249017\pi\) | |||||||
\(632\) | 455660.i | 1.14079i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 610301. | 1.51833 | ||||||||
\(635\) | − 224956.i | − 0.557892i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 208897. | 0.514817 | ||||||||
\(638\) | 127386.i | 0.312954i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 461622. | 1.12701 | ||||||||
\(641\) | 425875.i | 1.03649i | 0.855232 | + | 0.518246i | \(0.173415\pi\) | ||||
−0.855232 | + | 0.518246i | \(0.826585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34160.8 | −0.0826239 | −0.0413119 | − | 0.999146i | \(-0.513154\pi\) | ||||
−0.0413119 | + | 0.999146i | \(0.513154\pi\) | |||||||
\(644\) | − 331785.i | − 0.799991i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.79225e6 | 4.29470 | ||||||||
\(647\) | 341938.i | 0.816844i | 0.912793 | + | 0.408422i | \(0.133921\pi\) | ||||
−0.912793 | + | 0.408422i | \(0.866079\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14853.1 | −0.0352637 | ||||||||
\(650\) | 248115.i | 0.587253i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −106366. | −0.250211 | ||||||||
\(653\) | − 175603.i | − 0.411818i | −0.978571 | − | 0.205909i | \(-0.933985\pi\) | ||||
0.978571 | − | 0.205909i | \(-0.0660150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 542863. | 1.26534 | ||||||||
\(656\) | − 55686.7i | − 0.129403i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −326340. | −0.753734 | ||||||||
\(659\) | − 53477.9i | − 0.123141i | −0.998103 | − | 0.0615707i | \(-0.980389\pi\) | ||||
0.998103 | − | 0.0615707i | \(-0.0196110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 105581. | 0.241647 | 0.120824 | − | 0.992674i | \(-0.461446\pi\) | ||||
0.120824 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(662\) | 847953.i | 1.93489i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 61088.5 | 0.138555 | ||||||||
\(665\) | − 347624.i | − 0.786081i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −270565. | −0.608163 | ||||||||
\(668\) | − 1.01952e6i | − 2.28476i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −458851. | −1.02217 | ||||||||
\(671\) | 157540.i | 0.349902i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −298173. | −0.658322 | −0.329161 | − | 0.944274i | \(-0.606766\pi\) | ||||
−0.329161 | + | 0.944274i | \(0.606766\pi\) | |||||||
\(674\) | 118809.i | 0.261535i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 240569. | 0.526436 | ||||||||
\(677\) | 32750.2i | 0.0714557i | 0.999362 | + | 0.0357279i | \(0.0113750\pi\) | ||||
−0.999362 | + | 0.0357279i | \(0.988625\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46751.7 | −0.101405 | ||||||||
\(680\) | 475634.i | 1.02862i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 340318. | 0.731671 | ||||||||
\(683\) | 202267.i | 0.433594i | 0.976217 | + | 0.216797i | \(0.0695609\pi\) | ||||
−0.976217 | + | 0.216797i | \(0.930439\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −81547.4 | −0.173792 | ||||||||
\(686\) | 746085.i | 1.58540i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −83674.3 | −0.176773 | ||||||||
\(689\) | − 477344.i | − 1.00553i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 540120. | 1.13119 | 0.565593 | − | 0.824684i | \(-0.308647\pi\) | ||||
0.565593 | + | 0.824684i | \(0.308647\pi\) | |||||||
\(692\) | − 289428.i | − 0.604404i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 689767. | 1.43213 | ||||||||
\(695\) | − 303647.i | − 0.628636i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 825699. | 1.69964 | ||||||||
\(698\) | 963378.i | 1.97736i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −209356. | −0.427257 | ||||||||
\(701\) | − 265495.i | − 0.540281i | −0.962821 | − | 0.270141i | \(-0.912930\pi\) | ||||
0.962821 | − | 0.270141i | \(-0.0870702\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −551300. | −1.11552 | ||||||||
\(704\) | 218881.i | 0.441635i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 770591. | 1.54602 | ||||||||
\(707\) | − 380744.i | − 0.761719i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −483177. | −0.961200 | −0.480600 | − | 0.876940i | \(-0.659581\pi\) | ||||
−0.480600 | + | 0.876940i | \(0.659581\pi\) | |||||||
\(710\) | 1.08982e6i | 2.16191i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −773565. | −1.52594 | ||||||||
\(713\) | 722826.i | 1.42185i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 83636.5 | 0.163600 | ||||||||
\(716\) | − 660248.i | − 1.28790i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −237834. | −0.461343 | ||||||||
\(719\) | − 416279.i | − 0.805242i | −0.915367 | − | 0.402621i | \(-0.868099\pi\) | ||||
0.915367 | − | 0.402621i | \(-0.131901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12303.1 | 0.0236671 | ||||||||
\(722\) | − 1.71482e6i | − 3.28961i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 843366. | 1.60894 | ||||||||
\(725\) | 170726.i | 0.324807i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 283110. | 0.535656 | 0.267828 | − | 0.963467i | \(-0.413694\pi\) | ||||
0.267828 | + | 0.963467i | \(0.413694\pi\) | |||||||
\(728\) | − 236738.i | − 0.446689i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −397649. | −0.746199 | ||||||||
\(731\) | − 1.24069e6i | − 2.32182i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −961667. | −1.78985 | −0.894925 | − | 0.446217i | \(-0.852771\pi\) | ||||
−0.894925 | + | 0.446217i | \(0.852771\pi\) | |||||||
\(734\) | − 1.46809e6i | − 2.72496i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −498212. | −0.919726 | ||||||||
\(737\) | − 126650.i | − 0.233169i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 360059. | 0.659302 | 0.329651 | − | 0.944103i | \(-0.393069\pi\) | ||||
0.329651 | + | 0.944103i | \(0.393069\pi\) | |||||||
\(740\) | − 405483.i | − 0.740474i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 660225. | 1.19918 | ||||||||
\(743\) | 912337.i | 1.65264i | 0.563203 | + | 0.826319i | \(0.309569\pi\) | ||||
−0.563203 | + | 0.826319i | \(0.690431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 425827. | 0.767221 | ||||||||
\(746\) | 434804.i | 0.781296i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −363845. | −0.650300 | ||||||||
\(749\) | 463814.i | 0.826762i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −165236. | −0.292971 | −0.146485 | − | 0.989213i | \(-0.546796\pi\) | ||||
−0.146485 | + | 0.989213i | \(0.546796\pi\) | |||||||
\(752\) | 51263.6i | 0.0906511i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −535049. | −0.941133 | ||||||||
\(755\) | − 256813.i | − 0.450529i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 930347. | 1.62350 | 0.811752 | − | 0.584002i | \(-0.198514\pi\) | ||||
0.811752 | + | 0.584002i | \(0.198514\pi\) | |||||||
\(758\) | 1.06090e6i | 1.84645i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 676625. | 1.17144 | ||||||||
\(761\) | − 544322.i | − 0.939910i | −0.882690 | − | 0.469955i | \(-0.844270\pi\) | ||||
0.882690 | − | 0.469955i | \(-0.155730\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 691828. | 1.18836 | ||||||||
\(764\) | 1.52283e6i | 2.60895i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 377380. | 0.643164 | ||||||||
\(767\) | − 62386.3i | − 0.106047i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −809294. | −1.36853 | −0.684264 | − | 0.729234i | \(-0.739876\pi\) | ||||
−0.684264 | + | 0.729234i | \(0.739876\pi\) | |||||||
\(770\) | 115679.i | 0.195108i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −948125. | −1.59086 | ||||||||
\(773\) | − 1.00316e6i | − 1.67885i | −0.543474 | − | 0.839426i | \(-0.682891\pi\) | ||||
0.543474 | − | 0.839426i | \(-0.317109\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 456103. | 0.759381 | ||||||||
\(776\) | − 90998.6i | − 0.151116i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 500914. | 0.827568 | ||||||||
\(779\) | − 1.17462e6i | − 1.93563i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −300808. | −0.493159 | ||||||||
\(782\) | − 1.26676e6i | − 2.07147i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 45387.0 | 0.0738413 | ||||||||
\(785\) | 155397.i | 0.252176i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −652885. | −1.05411 | −0.527057 | − | 0.849830i | \(-0.676704\pi\) | ||||
−0.527057 | + | 0.849830i | \(0.676704\pi\) | |||||||
\(788\) | 1.30335e6i | 2.09899i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 935189. | 1.49846 | ||||||||
\(791\) | 600100.i | 0.959116i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −661703. | −1.05224 | ||||||||
\(794\) | 784726.i | 1.24474i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.45894e6 | −2.30256 | ||||||||
\(797\) | 378935.i | 0.596552i | 0.954480 | + | 0.298276i | \(0.0964115\pi\) | ||||
−0.954480 | + | 0.298276i | \(0.903588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −760115. | −1.19065 | ||||||||
\(800\) | 314371.i | 0.491205i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −664307. | −1.03281 | ||||||||
\(803\) | − 109757.i | − 0.170217i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −245700. | −0.379152 | ||||||||
\(806\) | 1.42941e6i | 2.20032i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 741090. | 1.13514 | ||||||||
\(809\) | 142668.i | 0.217987i | 0.994042 | + | 0.108993i | \(0.0347628\pi\) | ||||
−0.994042 | + | 0.108993i | \(0.965237\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −616812. | −0.937802 | −0.468901 | − | 0.883251i | \(-0.655350\pi\) | ||||
−0.468901 | + | 0.883251i | \(0.655350\pi\) | |||||||
\(812\) | − 451468.i | − 0.684723i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 183457. | 0.276875 | ||||||||
\(815\) | 78768.1i | 0.118586i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.76497e6 | −2.64420 | ||||||||
\(818\) | 354328.i | 0.529540i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 863937. | 1.28486 | ||||||||
\(821\) | 466894.i | 0.692679i | 0.938109 | + | 0.346340i | \(0.112576\pi\) | ||||
−0.938109 | + | 0.346340i | \(0.887424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −337365. | −0.498081 | −0.249040 | − | 0.968493i | \(-0.580115\pi\) | ||||
−0.249040 | + | 0.968493i | \(0.580115\pi\) | |||||||
\(824\) | 23947.1i | 0.0352695i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 86287.8 | 0.126471 | ||||||||
\(827\) | − 1.23300e6i | − 1.80282i | −0.432966 | − | 0.901410i | \(-0.642533\pi\) | ||||
0.432966 | − | 0.901410i | \(-0.357467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.02212e6 | 1.48728 | 0.743642 | − | 0.668578i | \(-0.233097\pi\) | ||||
0.743642 | + | 0.668578i | \(0.233097\pi\) | |||||||
\(830\) | − 125377.i | − 0.181996i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −919348. | −1.32811 | ||||||||
\(833\) | 672980.i | 0.969866i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −754993. | −1.08285 | ||||||||
\(836\) | 517597.i | 0.740592i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 911956. | 1.29863 | ||||||||
\(839\) | − 444263.i | − 0.631126i | −0.948905 | − | 0.315563i | \(-0.897807\pi\) | ||||
0.948905 | − | 0.315563i | \(-0.102193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 339116. | 0.479465 | ||||||||
\(842\) | − 698398.i | − 0.985097i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.22166e6 | −1.71500 | ||||||||
\(845\) | − 178151.i | − 0.249502i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 403262. | 0.562109 | ||||||||
\(848\) | − 103712.i | − 0.144225i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −799323. | −1.10633 | ||||||||
\(851\) | 389657.i | 0.538051i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −531236. | −0.730112 | −0.365056 | − | 0.930986i | \(-0.618950\pi\) | ||||
−0.365056 | + | 0.930986i | \(0.618950\pi\) | |||||||
\(854\) | − 915215.i | − 1.25490i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −902779. | −1.23207 | ||||||||
\(857\) | − 994021.i | − 1.35342i | −0.736248 | − | 0.676712i | \(-0.763404\pi\) | ||||
0.736248 | − | 0.676712i | \(-0.236596\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −320156. | −0.433885 | −0.216943 | − | 0.976184i | \(-0.569608\pi\) | ||||
−0.216943 | + | 0.976184i | \(0.569608\pi\) | |||||||
\(860\) | − 1.29814e6i | − 1.75520i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 647838. | 0.871870 | ||||||||
\(863\) | 1.28196e6i | 1.72129i | 0.509209 | + | 0.860643i | \(0.329938\pi\) | ||||
−0.509209 | + | 0.860643i | \(0.670062\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −214333. | −0.286455 | ||||||||
\(866\) | 1.20192e6i | 1.60265i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.20612e6 | −1.60085 | ||||||||
\(869\) | 258127.i | 0.341817i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 531957. | 0.701197 | ||||||||
\(872\) | 1.34659e6i | 1.77094i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.80205e6 | −2.35909 | ||||||||
\(875\) | 499414.i | 0.652296i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 911572. | 1.18520 | 0.592600 | − | 0.805497i | \(-0.298102\pi\) | ||||
0.592600 | + | 0.805497i | \(0.298102\pi\) | |||||||
\(878\) | − 1.52305e6i | − 1.97572i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18171.7 | 0.0234655 | ||||||||
\(881\) | − 1.17613e6i | − 1.51532i | −0.652649 | − | 0.757660i | \(-0.726342\pi\) | ||||
0.652649 | − | 0.757660i | \(-0.273658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.15237e6 | −1.47799 | −0.738994 | − | 0.673712i | \(-0.764699\pi\) | ||||
−0.738994 | + | 0.673712i | \(0.764699\pi\) | |||||||
\(884\) | − 1.52823e6i | − 1.95562i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.12344e6 | −1.43114 | ||||||||
\(887\) | 453852.i | 0.576855i | 0.957502 | + | 0.288428i | \(0.0931325\pi\) | ||||
−0.957502 | + | 0.288428i | \(0.906868\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −360713. | −0.456414 | ||||||||
\(890\) | 1.58765e6i | 2.00436i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.92256e6 | −2.41630 | ||||||||
\(893\) | 1.08132e6i | 1.35597i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −488940. | −0.610393 | ||||||||
\(896\) | − 740205.i | − 0.922011i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.88837e6 | −2.34171 | ||||||||
\(899\) | 983568.i | 1.21698i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.53781e6 | 1.89431 | ||||||||
\(902\) | 390879.i | 0.480429i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.16805e6 | −1.42930 | ||||||||
\(905\) | − 624546.i | − 0.762549i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −645880. | −0.785122 | −0.392561 | − | 0.919726i | \(-0.628411\pi\) | ||||
−0.392561 | + | 0.919726i | \(0.628411\pi\) | |||||||
\(908\) | 715649.i | 0.868017i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −485878. | −0.586738 | ||||||||
\(911\) | 1.28705e6i | 1.55082i | 0.631461 | + | 0.775408i | \(0.282456\pi\) | ||||
−0.631461 | + | 0.775408i | \(0.717544\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34606.0 | 0.0415155 | ||||||||
\(914\) | − 2.38533e6i | − 2.85532i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.91400e6 | 2.28114 | ||||||||
\(917\) | − 870473.i | − 1.03518i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.26310e6 | −1.49558 | −0.747788 | − | 0.663938i | \(-0.768884\pi\) | ||||
−0.747788 | + | 0.663938i | \(0.768884\pi\) | |||||||
\(920\) | − 478237.i | − 0.565024i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −267135. | −0.314246 | ||||||||
\(923\) | − 1.26346e6i | − 1.48305i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 245873. | 0.287361 | ||||||||
\(926\) | 283012.i | 0.330052i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −677929. | −0.787206 | ||||||||
\(929\) | − 363947.i | − 0.421703i | −0.977518 | − | 0.210851i | \(-0.932376\pi\) | ||||
0.977518 | − | 0.210851i | \(-0.0676236\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 957363. | 1.10453 | ||||||||
\(932\) | − 1.00473e6i | − 1.15669i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.38510e6 | 1.58777 | ||||||||
\(935\) | 269442.i | 0.308207i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.01683e6 | 1.15817 | 0.579083 | − | 0.815268i | \(-0.303411\pi\) | ||||
0.579083 | + | 0.815268i | \(0.303411\pi\) | |||||||
\(938\) | 735761.i | 0.836241i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −795316. | −0.900086 | ||||||||
\(941\) | − 1.20432e6i | − 1.36007i | −0.733180 | − | 0.680034i | \(-0.761965\pi\) | ||||
0.733180 | − | 0.680034i | \(-0.238035\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −830217. | −0.933616 | ||||||||
\(944\) | − 13554.7i | − 0.0152105i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 587332. | 0.656298 | ||||||||
\(947\) | − 1.23315e6i | − 1.37504i | −0.726165 | − | 0.687520i | \(-0.758699\pi\) | ||||
0.726165 | − | 0.687520i | \(-0.241301\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 461005. | 0.511885 | ||||||||
\(950\) | 1.13710e6i | 1.25994i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 762673. | 0.841520 | ||||||||
\(953\) | − 943059.i | − 1.03837i | −0.854661 | − | 0.519186i | \(-0.826235\pi\) | ||||
0.854661 | − | 0.519186i | \(-0.173765\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.12772e6 | 1.23650 | ||||||||
\(956\) | 670048.i | 0.733145i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −984451. | −1.07266 | ||||||||
\(959\) | 130760.i | 0.142180i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.70412e6 | 1.84525 | ||||||||
\(962\) | 770557.i | 0.832635i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −42075.3 | −0.0452765 | ||||||||
\(965\) | 702125.i | 0.753980i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 613188. | 0.655753 | 0.327877 | − | 0.944721i | \(-0.393667\pi\) | ||||
0.327877 | + | 0.944721i | \(0.393667\pi\) | |||||||
\(968\) | 784920.i | 0.837673i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −186764. | −0.198495 | ||||||||
\(971\) | 1.73048e6i | 1.83539i | 0.397288 | + | 0.917694i | \(0.369951\pi\) | ||||
−0.397288 | + | 0.917694i | \(0.630049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −486893. | −0.514290 | ||||||||
\(974\) | 2.21457e6i | 2.33438i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −143768. | −0.150925 | ||||||||
\(977\) | 871924.i | 0.913460i | 0.889605 | + | 0.456730i | \(0.150979\pi\) | ||||
−0.889605 | + | 0.456730i | \(0.849021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −438217. | −0.457218 | ||||||||
\(980\) | 704145.i | 0.733179i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 131284. | 0.136141 | ||||||||
\(983\) | 398184.i | 0.412075i | 0.978544 | + | 0.206038i | \(0.0660570\pi\) | ||||
−0.978544 | + | 0.206038i | \(0.933943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 965186. | 0.994806 | ||||||||
\(986\) | − 1.72371e6i | − 1.77300i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.17402e6 | −2.22715 | ||||||||
\(989\) | 1.24748e6i | 1.27538i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −392895. | −0.400064 | −0.200032 | − | 0.979789i | \(-0.564105\pi\) | ||||
−0.200032 | + | 0.979789i | \(0.564105\pi\) | |||||||
\(992\) | 1.81112e6i | 1.84045i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.74751e6 | 1.76867 | ||||||||
\(995\) | 1.08040e6i | 1.09129i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 983000. | 0.988925 | 0.494462 | − | 0.869199i | \(-0.335365\pi\) | ||||
0.494462 | + | 0.869199i | \(0.335365\pi\) | |||||||
\(998\) | − 1.66406e6i | − 1.67073i | ||||||||
\(999\) | 0 | 0 |
(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 | 531.5.b.a.296.10 | ✓ | 76 | |
3.2 | odd | 2 | inner | 531.5.b.a.296.67 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
531.5.b.a.296.10 | ✓ | 76 | 1.1 | even | 1 | trivial | |
531.5.b.a.296.67 | yes | 76 | 3.2 | odd | 2 | inner |