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: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.609213 | −0.107695 | −0.0538474 | − | 0.998549i | \(-0.517148\pi\) | ||||
−0.0538474 | + | 0.998549i | \(0.517148\pi\) | |||||||
\(3\) | 20.7237 | 1.32942 | 0.664712 | − | 0.747099i | \(-0.268554\pi\) | ||||
0.664712 | + | 0.747099i | \(0.268554\pi\) | |||||||
\(4\) | −31.6289 | −0.988402 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −12.6251 | −0.143172 | ||||||||
\(7\) | −114.174 | −0.880688 | −0.440344 | − | 0.897829i | \(-0.645143\pi\) | ||||
−0.440344 | + | 0.897829i | \(0.645143\pi\) | |||||||
\(8\) | 38.7636 | 0.214140 | ||||||||
\(9\) | 186.471 | 0.767370 | ||||||||
\(10\) | −15.2303 | −0.0481626 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −655.466 | −1.31401 | ||||||||
\(13\) | −557.016 | −0.914133 | −0.457066 | − | 0.889433i | \(-0.651100\pi\) | ||||
−0.457066 | + | 0.889433i | \(0.651100\pi\) | |||||||
\(14\) | 69.5563 | 0.0948454 | ||||||||
\(15\) | 518.092 | 0.594537 | ||||||||
\(16\) | 988.508 | 0.965340 | ||||||||
\(17\) | 1251.16 | 1.05000 | 0.525002 | − | 0.851101i | \(-0.324065\pi\) | ||||
0.525002 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(18\) | −113.601 | −0.0826417 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | −790.721 | −0.442027 | ||||||||
\(21\) | −2366.10 | −1.17081 | ||||||||
\(22\) | −73.7148 | −0.0324712 | ||||||||
\(23\) | 112.655 | 0.0444051 | 0.0222025 | − | 0.999753i | \(-0.492932\pi\) | ||||
0.0222025 | + | 0.999753i | \(0.492932\pi\) | |||||||
\(24\) | 803.324 | 0.284684 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 339.342 | 0.0984473 | ||||||||
\(27\) | −1171.49 | −0.309264 | ||||||||
\(28\) | 3611.19 | 0.870473 | ||||||||
\(29\) | 3058.85 | 0.675404 | 0.337702 | − | 0.941253i | \(-0.390350\pi\) | ||||
0.337702 | + | 0.941253i | \(0.390350\pi\) | |||||||
\(30\) | −315.629 | −0.0640285 | ||||||||
\(31\) | −2084.31 | −0.389546 | −0.194773 | − | 0.980848i | \(-0.562397\pi\) | ||||
−0.194773 | + | 0.980848i | \(0.562397\pi\) | |||||||
\(32\) | −1842.65 | −0.318102 | ||||||||
\(33\) | 2507.57 | 0.400837 | ||||||||
\(34\) | −762.224 | −0.113080 | ||||||||
\(35\) | −2854.35 | −0.393856 | ||||||||
\(36\) | −5897.86 | −0.758470 | ||||||||
\(37\) | −4134.99 | −0.496558 | −0.248279 | − | 0.968689i | \(-0.579865\pi\) | ||||
−0.248279 | + | 0.968689i | \(0.579865\pi\) | |||||||
\(38\) | −219.926 | −0.0247069 | ||||||||
\(39\) | −11543.4 | −1.21527 | ||||||||
\(40\) | 969.089 | 0.0957665 | ||||||||
\(41\) | 4338.04 | 0.403027 | 0.201513 | − | 0.979486i | \(-0.435414\pi\) | ||||
0.201513 | + | 0.979486i | \(0.435414\pi\) | |||||||
\(42\) | 1441.46 | 0.126090 | ||||||||
\(43\) | −12533.9 | −1.03375 | −0.516873 | − | 0.856062i | \(-0.672904\pi\) | ||||
−0.516873 | + | 0.856062i | \(0.672904\pi\) | |||||||
\(44\) | −3827.09 | −0.298014 | ||||||||
\(45\) | 4661.77 | 0.343178 | ||||||||
\(46\) | −68.6312 | −0.00478219 | ||||||||
\(47\) | −13727.7 | −0.906472 | −0.453236 | − | 0.891390i | \(-0.649731\pi\) | ||||
−0.453236 | + | 0.891390i | \(0.649731\pi\) | |||||||
\(48\) | 20485.5 | 1.28335 | ||||||||
\(49\) | −3771.31 | −0.224389 | ||||||||
\(50\) | −380.758 | −0.0215389 | ||||||||
\(51\) | 25928.6 | 1.39590 | ||||||||
\(52\) | 17617.8 | 0.903531 | ||||||||
\(53\) | 2552.04 | 0.124795 | 0.0623975 | − | 0.998051i | \(-0.480125\pi\) | ||||
0.0623975 | + | 0.998051i | \(0.480125\pi\) | |||||||
\(54\) | 713.688 | 0.0333061 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | −4425.79 | −0.188591 | ||||||||
\(57\) | 7481.25 | 0.304991 | ||||||||
\(58\) | −1863.49 | −0.0727374 | ||||||||
\(59\) | 11558.1 | 0.432272 | 0.216136 | − | 0.976363i | \(-0.430654\pi\) | ||||
0.216136 | + | 0.976363i | \(0.430654\pi\) | |||||||
\(60\) | −16386.7 | −0.587641 | ||||||||
\(61\) | 31983.1 | 1.10051 | 0.550257 | − | 0.834995i | \(-0.314530\pi\) | ||||
0.550257 | + | 0.834995i | \(0.314530\pi\) | |||||||
\(62\) | 1269.79 | 0.0419521 | ||||||||
\(63\) | −21290.1 | −0.675813 | ||||||||
\(64\) | −30509.7 | −0.931082 | ||||||||
\(65\) | −13925.4 | −0.408813 | ||||||||
\(66\) | −1527.64 | −0.0431680 | ||||||||
\(67\) | 31684.8 | 0.862312 | 0.431156 | − | 0.902277i | \(-0.358106\pi\) | ||||
0.431156 | + | 0.902277i | \(0.358106\pi\) | |||||||
\(68\) | −39572.8 | −1.03782 | ||||||||
\(69\) | 2334.63 | 0.0590332 | ||||||||
\(70\) | 1738.91 | 0.0424162 | ||||||||
\(71\) | 43305.0 | 1.01951 | 0.509755 | − | 0.860319i | \(-0.329736\pi\) | ||||
0.509755 | + | 0.860319i | \(0.329736\pi\) | |||||||
\(72\) | 7228.27 | 0.164325 | ||||||||
\(73\) | −10784.1 | −0.236852 | −0.118426 | − | 0.992963i | \(-0.537785\pi\) | ||||
−0.118426 | + | 0.992963i | \(0.537785\pi\) | |||||||
\(74\) | 2519.09 | 0.0534767 | ||||||||
\(75\) | 12952.3 | 0.265885 | ||||||||
\(76\) | −11418.0 | −0.226755 | ||||||||
\(77\) | −13815.0 | −0.265537 | ||||||||
\(78\) | 7032.41 | 0.130878 | ||||||||
\(79\) | −108908. | −1.96332 | −0.981661 | − | 0.190636i | \(-0.938945\pi\) | ||||
−0.981661 | + | 0.190636i | \(0.938945\pi\) | |||||||
\(80\) | 24712.7 | 0.431713 | ||||||||
\(81\) | −69590.0 | −1.17851 | ||||||||
\(82\) | −2642.79 | −0.0434039 | ||||||||
\(83\) | 45563.6 | 0.725977 | 0.362988 | − | 0.931794i | \(-0.381757\pi\) | ||||
0.362988 | + | 0.931794i | \(0.381757\pi\) | |||||||
\(84\) | 74837.2 | 1.15723 | ||||||||
\(85\) | 31279.0 | 0.469576 | ||||||||
\(86\) | 7635.80 | 0.111329 | ||||||||
\(87\) | 63390.6 | 0.897898 | ||||||||
\(88\) | 4690.39 | 0.0645658 | ||||||||
\(89\) | 72026.0 | 0.963860 | 0.481930 | − | 0.876210i | \(-0.339936\pi\) | ||||
0.481930 | + | 0.876210i | \(0.339936\pi\) | |||||||
\(90\) | −2840.01 | −0.0369585 | ||||||||
\(91\) | 63596.7 | 0.805066 | ||||||||
\(92\) | −3563.16 | −0.0438901 | ||||||||
\(93\) | −43194.7 | −0.517872 | ||||||||
\(94\) | 8363.13 | 0.0976223 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | −38186.4 | −0.422893 | ||||||||
\(97\) | 117684. | 1.26995 | 0.634977 | − | 0.772531i | \(-0.281010\pi\) | ||||
0.634977 | + | 0.772531i | \(0.281010\pi\) | |||||||
\(98\) | 2297.53 | 0.0241655 | ||||||||
\(99\) | 22563.0 | 0.231371 | ||||||||
\(100\) | −19768.0 | −0.197680 | ||||||||
\(101\) | −66340.4 | −0.647105 | −0.323552 | − | 0.946210i | \(-0.604877\pi\) | ||||
−0.323552 | + | 0.946210i | \(0.604877\pi\) | |||||||
\(102\) | −15796.1 | −0.150331 | ||||||||
\(103\) | 150322. | 1.39614 | 0.698071 | − | 0.716029i | \(-0.254042\pi\) | ||||
0.698071 | + | 0.716029i | \(0.254042\pi\) | |||||||
\(104\) | −21591.9 | −0.195753 | ||||||||
\(105\) | −59152.6 | −0.523601 | ||||||||
\(106\) | −1554.74 | −0.0134398 | ||||||||
\(107\) | 216512. | 1.82820 | 0.914098 | − | 0.405493i | \(-0.132900\pi\) | ||||
0.914098 | + | 0.405493i | \(0.132900\pi\) | |||||||
\(108\) | 37052.9 | 0.305677 | ||||||||
\(109\) | 41384.2 | 0.333633 | 0.166816 | − | 0.985988i | \(-0.446651\pi\) | ||||
0.166816 | + | 0.985988i | \(0.446651\pi\) | |||||||
\(110\) | −1842.87 | −0.0145216 | ||||||||
\(111\) | −85692.2 | −0.660137 | ||||||||
\(112\) | −112862. | −0.850163 | ||||||||
\(113\) | 119837. | 0.882867 | 0.441433 | − | 0.897294i | \(-0.354470\pi\) | ||||
0.441433 | + | 0.897294i | \(0.354470\pi\) | |||||||
\(114\) | −4557.68 | −0.0328459 | ||||||||
\(115\) | 2816.39 | 0.0198585 | ||||||||
\(116\) | −96748.0 | −0.667570 | ||||||||
\(117\) | −103867. | −0.701478 | ||||||||
\(118\) | −7041.37 | −0.0465535 | ||||||||
\(119\) | −142850. | −0.924725 | ||||||||
\(120\) | 20083.1 | 0.127314 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −19484.5 | −0.118520 | ||||||||
\(123\) | 89900.2 | 0.535794 | ||||||||
\(124\) | 65924.5 | 0.385028 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 12970.2 | 0.0727815 | ||||||||
\(127\) | 39095.9 | 0.215091 | 0.107545 | − | 0.994200i | \(-0.465701\pi\) | ||||
0.107545 | + | 0.994200i | \(0.465701\pi\) | |||||||
\(128\) | 77551.6 | 0.418375 | ||||||||
\(129\) | −259748. | −1.37429 | ||||||||
\(130\) | 8483.54 | 0.0440270 | ||||||||
\(131\) | −27724.1 | −0.141149 | −0.0705747 | − | 0.997506i | \(-0.522483\pi\) | ||||
−0.0705747 | + | 0.997506i | \(0.522483\pi\) | |||||||
\(132\) | −79311.4 | −0.396188 | ||||||||
\(133\) | −41216.8 | −0.202044 | ||||||||
\(134\) | −19302.8 | −0.0928665 | ||||||||
\(135\) | −29287.3 | −0.138307 | ||||||||
\(136\) | 48499.4 | 0.224848 | ||||||||
\(137\) | 35413.7 | 0.161202 | 0.0806010 | − | 0.996746i | \(-0.474316\pi\) | ||||
0.0806010 | + | 0.996746i | \(0.474316\pi\) | |||||||
\(138\) | −1422.29 | −0.00635756 | ||||||||
\(139\) | 173016. | 0.759535 | 0.379768 | − | 0.925082i | \(-0.376004\pi\) | ||||
0.379768 | + | 0.925082i | \(0.376004\pi\) | |||||||
\(140\) | 90279.8 | 0.389288 | ||||||||
\(141\) | −284489. | −1.20509 | ||||||||
\(142\) | −26382.0 | −0.109796 | ||||||||
\(143\) | −67398.9 | −0.275621 | ||||||||
\(144\) | 184328. | 0.740773 | ||||||||
\(145\) | 76471.3 | 0.302050 | ||||||||
\(146\) | 6569.81 | 0.0255077 | ||||||||
\(147\) | −78155.4 | −0.298308 | ||||||||
\(148\) | 130785. | 0.490799 | ||||||||
\(149\) | −55220.4 | −0.203767 | −0.101883 | − | 0.994796i | \(-0.532487\pi\) | ||||
−0.101883 | + | 0.994796i | \(0.532487\pi\) | |||||||
\(150\) | −7890.72 | −0.0286344 | ||||||||
\(151\) | 446154. | 1.59236 | 0.796182 | − | 0.605058i | \(-0.206850\pi\) | ||||
0.796182 | + | 0.605058i | \(0.206850\pi\) | |||||||
\(152\) | 13993.6 | 0.0491272 | ||||||||
\(153\) | 233305. | 0.805741 | ||||||||
\(154\) | 8416.31 | 0.0285970 | ||||||||
\(155\) | −52107.9 | −0.174210 | ||||||||
\(156\) | 365105. | 1.20118 | ||||||||
\(157\) | 282112. | 0.913424 | 0.456712 | − | 0.889615i | \(-0.349027\pi\) | ||||
0.456712 | + | 0.889615i | \(0.349027\pi\) | |||||||
\(158\) | 66348.1 | 0.211439 | ||||||||
\(159\) | 52887.6 | 0.165906 | ||||||||
\(160\) | −46066.2 | −0.142260 | ||||||||
\(161\) | −12862.3 | −0.0391070 | ||||||||
\(162\) | 42395.2 | 0.126920 | ||||||||
\(163\) | 305803. | 0.901515 | 0.450757 | − | 0.892647i | \(-0.351154\pi\) | ||||
0.450757 | + | 0.892647i | \(0.351154\pi\) | |||||||
\(164\) | −137207. | −0.398352 | ||||||||
\(165\) | 62689.1 | 0.179260 | ||||||||
\(166\) | −27757.9 | −0.0781839 | ||||||||
\(167\) | 156166. | 0.433306 | 0.216653 | − | 0.976249i | \(-0.430486\pi\) | ||||
0.216653 | + | 0.976249i | \(0.430486\pi\) | |||||||
\(168\) | −91718.6 | −0.250717 | ||||||||
\(169\) | −61026.2 | −0.164361 | ||||||||
\(170\) | −19055.6 | −0.0505708 | ||||||||
\(171\) | 67316.0 | 0.176047 | ||||||||
\(172\) | 396432. | 1.02176 | ||||||||
\(173\) | 610359. | 1.55050 | 0.775248 | − | 0.631657i | \(-0.217625\pi\) | ||||
0.775248 | + | 0.631657i | \(0.217625\pi\) | |||||||
\(174\) | −38618.4 | −0.0966989 | ||||||||
\(175\) | −71358.7 | −0.176138 | ||||||||
\(176\) | 119609. | 0.291061 | ||||||||
\(177\) | 239527. | 0.574674 | ||||||||
\(178\) | −43879.2 | −0.103803 | ||||||||
\(179\) | 16828.2 | 0.0392560 | 0.0196280 | − | 0.999807i | \(-0.493752\pi\) | ||||
0.0196280 | + | 0.999807i | \(0.493752\pi\) | |||||||
\(180\) | −147447. | −0.339198 | ||||||||
\(181\) | −417226. | −0.946618 | −0.473309 | − | 0.880896i | \(-0.656941\pi\) | ||||
−0.473309 | + | 0.880896i | \(0.656941\pi\) | |||||||
\(182\) | −38744.0 | −0.0867013 | ||||||||
\(183\) | 662807. | 1.46305 | ||||||||
\(184\) | 4366.93 | 0.00950892 | ||||||||
\(185\) | −103375. | −0.222068 | ||||||||
\(186\) | 26314.8 | 0.0557721 | ||||||||
\(187\) | 151390. | 0.316588 | ||||||||
\(188\) | 434193. | 0.895959 | ||||||||
\(189\) | 133754. | 0.272365 | ||||||||
\(190\) | −5498.15 | −0.0110492 | ||||||||
\(191\) | 837287. | 1.66070 | 0.830350 | − | 0.557242i | \(-0.188141\pi\) | ||||
0.830350 | + | 0.557242i | \(0.188141\pi\) | |||||||
\(192\) | −632273. | −1.23780 | ||||||||
\(193\) | 108159. | 0.209010 | 0.104505 | − | 0.994524i | \(-0.466674\pi\) | ||||
0.104505 | + | 0.994524i | \(0.466674\pi\) | |||||||
\(194\) | −71694.6 | −0.136767 | ||||||||
\(195\) | −288586. | −0.543486 | ||||||||
\(196\) | 119282. | 0.221787 | ||||||||
\(197\) | −326694. | −0.599757 | −0.299879 | − | 0.953977i | \(-0.596946\pi\) | ||||
−0.299879 | + | 0.953977i | \(0.596946\pi\) | |||||||
\(198\) | −13745.7 | −0.0249174 | ||||||||
\(199\) | 254361. | 0.455321 | 0.227661 | − | 0.973741i | \(-0.426892\pi\) | ||||
0.227661 | + | 0.973741i | \(0.426892\pi\) | |||||||
\(200\) | 24227.2 | 0.0428281 | ||||||||
\(201\) | 656626. | 1.14638 | ||||||||
\(202\) | 40415.5 | 0.0696898 | ||||||||
\(203\) | −349241. | −0.594820 | ||||||||
\(204\) | −820093. | −1.37971 | ||||||||
\(205\) | 108451. | 0.180239 | ||||||||
\(206\) | −91578.2 | −0.150357 | ||||||||
\(207\) | 21007.0 | 0.0340751 | ||||||||
\(208\) | −550615. | −0.882449 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | 36036.6 | 0.0563891 | ||||||||
\(211\) | 845329. | 1.30713 | 0.653566 | − | 0.756869i | \(-0.273272\pi\) | ||||
0.653566 | + | 0.756869i | \(0.273272\pi\) | |||||||
\(212\) | −80718.0 | −0.123348 | ||||||||
\(213\) | 897438. | 1.35536 | ||||||||
\(214\) | −131902. | −0.196887 | ||||||||
\(215\) | −313347. | −0.462306 | ||||||||
\(216\) | −45411.2 | −0.0662260 | ||||||||
\(217\) | 237974. | 0.343069 | ||||||||
\(218\) | −25211.8 | −0.0359305 | ||||||||
\(219\) | −223486. | −0.314876 | ||||||||
\(220\) | −95677.3 | −0.133276 | ||||||||
\(221\) | −696916. | −0.959842 | ||||||||
\(222\) | 52204.8 | 0.0710932 | ||||||||
\(223\) | −809537. | −1.09012 | −0.545060 | − | 0.838397i | \(-0.683493\pi\) | ||||
−0.545060 | + | 0.838397i | \(0.683493\pi\) | |||||||
\(224\) | 210382. | 0.280149 | ||||||||
\(225\) | 116544. | 0.153474 | ||||||||
\(226\) | −73006.4 | −0.0950801 | ||||||||
\(227\) | −309805. | −0.399047 | −0.199523 | − | 0.979893i | \(-0.563939\pi\) | ||||
−0.199523 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(228\) | −236623. | −0.301454 | ||||||||
\(229\) | −1.19087e6 | −1.50064 | −0.750319 | − | 0.661076i | \(-0.770100\pi\) | ||||
−0.750319 | + | 0.661076i | \(0.770100\pi\) | |||||||
\(230\) | −1715.78 | −0.00213866 | ||||||||
\(231\) | −286299. | −0.353012 | ||||||||
\(232\) | 118572. | 0.144631 | ||||||||
\(233\) | −60940.3 | −0.0735385 | −0.0367692 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367692 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(234\) | 63277.3 | 0.0755455 | ||||||||
\(235\) | −343194. | −0.405387 | ||||||||
\(236\) | −365570. | −0.427259 | ||||||||
\(237\) | −2.25697e6 | −2.61009 | ||||||||
\(238\) | 87026.1 | 0.0995880 | ||||||||
\(239\) | −855678. | −0.968982 | −0.484491 | − | 0.874796i | \(-0.660995\pi\) | ||||
−0.484491 | + | 0.874796i | \(0.660995\pi\) | |||||||
\(240\) | 512138. | 0.573930 | ||||||||
\(241\) | 1.55896e6 | 1.72898 | 0.864492 | − | 0.502646i | \(-0.167640\pi\) | ||||
0.864492 | + | 0.502646i | \(0.167640\pi\) | |||||||
\(242\) | −8919.49 | −0.00979043 | ||||||||
\(243\) | −1.15749e6 | −1.25748 | ||||||||
\(244\) | −1.01159e6 | −1.08775 | ||||||||
\(245\) | −94282.7 | −0.100350 | ||||||||
\(246\) | −54768.4 | −0.0577022 | ||||||||
\(247\) | −201083. | −0.209716 | ||||||||
\(248\) | −80795.4 | −0.0834176 | ||||||||
\(249\) | 944245. | 0.965131 | ||||||||
\(250\) | −9518.96 | −0.00963251 | ||||||||
\(251\) | −1.64608e6 | −1.64918 | −0.824588 | − | 0.565734i | \(-0.808593\pi\) | ||||
−0.824588 | + | 0.565734i | \(0.808593\pi\) | |||||||
\(252\) | 673382. | 0.667975 | ||||||||
\(253\) | 13631.3 | 0.0133886 | ||||||||
\(254\) | −23817.7 | −0.0231641 | ||||||||
\(255\) | 648216. | 0.624265 | ||||||||
\(256\) | 929065. | 0.886025 | ||||||||
\(257\) | −615662. | −0.581447 | −0.290723 | − | 0.956807i | \(-0.593896\pi\) | ||||
−0.290723 | + | 0.956807i | \(0.593896\pi\) | |||||||
\(258\) | 158242. | 0.148004 | ||||||||
\(259\) | 472108. | 0.437313 | ||||||||
\(260\) | 440445. | 0.404071 | ||||||||
\(261\) | 570387. | 0.518284 | ||||||||
\(262\) | 16889.9 | 0.0152011 | ||||||||
\(263\) | 550187. | 0.490480 | 0.245240 | − | 0.969462i | \(-0.421133\pi\) | ||||
0.245240 | + | 0.969462i | \(0.421133\pi\) | |||||||
\(264\) | 97202.2 | 0.0858353 | ||||||||
\(265\) | 63800.9 | 0.0558100 | ||||||||
\(266\) | 25109.8 | 0.0217590 | ||||||||
\(267\) | 1.49264e6 | 1.28138 | ||||||||
\(268\) | −1.00216e6 | −0.852311 | ||||||||
\(269\) | −187673. | −0.158132 | −0.0790661 | − | 0.996869i | \(-0.525194\pi\) | ||||
−0.0790661 | + | 0.996869i | \(0.525194\pi\) | |||||||
\(270\) | 17842.2 | 0.0148950 | ||||||||
\(271\) | 1.22230e6 | 1.01101 | 0.505505 | − | 0.862824i | \(-0.331306\pi\) | ||||
0.505505 | + | 0.862824i | \(0.331306\pi\) | |||||||
\(272\) | 1.23678e6 | 1.01361 | ||||||||
\(273\) | 1.31796e6 | 1.07027 | ||||||||
\(274\) | −21574.5 | −0.0173606 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | −73841.8 | −0.0583485 | ||||||||
\(277\) | −838965. | −0.656968 | −0.328484 | − | 0.944509i | \(-0.606538\pi\) | ||||
−0.328484 | + | 0.944509i | \(0.606538\pi\) | |||||||
\(278\) | −105403. | −0.0817980 | ||||||||
\(279\) | −388664. | −0.298926 | ||||||||
\(280\) | −110645. | −0.0843404 | ||||||||
\(281\) | 1.12952e6 | 0.853349 | 0.426675 | − | 0.904405i | \(-0.359685\pi\) | ||||
0.426675 | + | 0.904405i | \(0.359685\pi\) | |||||||
\(282\) | 173315. | 0.129781 | ||||||||
\(283\) | 700626. | 0.520020 | 0.260010 | − | 0.965606i | \(-0.416274\pi\) | ||||
0.260010 | + | 0.965606i | \(0.416274\pi\) | |||||||
\(284\) | −1.36969e6 | −1.00769 | ||||||||
\(285\) | 187031. | 0.136396 | ||||||||
\(286\) | 41060.3 | 0.0296830 | ||||||||
\(287\) | −495291. | −0.354941 | ||||||||
\(288\) | −343600. | −0.244102 | ||||||||
\(289\) | 145545. | 0.102506 | ||||||||
\(290\) | −46587.3 | −0.0325292 | ||||||||
\(291\) | 2.43884e6 | 1.68831 | ||||||||
\(292\) | 341088. | 0.234105 | ||||||||
\(293\) | 163837. | 0.111492 | 0.0557459 | − | 0.998445i | \(-0.482246\pi\) | ||||
0.0557459 | + | 0.998445i | \(0.482246\pi\) | |||||||
\(294\) | 47613.3 | 0.0321263 | ||||||||
\(295\) | 288953. | 0.193318 | ||||||||
\(296\) | −160287. | −0.106333 | ||||||||
\(297\) | −141750. | −0.0932467 | ||||||||
\(298\) | 33641.0 | 0.0219446 | ||||||||
\(299\) | −62750.9 | −0.0405921 | ||||||||
\(300\) | −409666. | −0.262801 | ||||||||
\(301\) | 1.43104e6 | 0.910408 | ||||||||
\(302\) | −271803. | −0.171489 | ||||||||
\(303\) | −1.37482e6 | −0.860277 | ||||||||
\(304\) | 356851. | 0.221464 | ||||||||
\(305\) | 799577. | 0.492165 | ||||||||
\(306\) | −142132. | −0.0867740 | ||||||||
\(307\) | −1.46111e6 | −0.884785 | −0.442393 | − | 0.896822i | \(-0.645870\pi\) | ||||
−0.442393 | + | 0.896822i | \(0.645870\pi\) | |||||||
\(308\) | 436954. | 0.262458 | ||||||||
\(309\) | 3.11522e6 | 1.85606 | ||||||||
\(310\) | 31744.8 | 0.0187615 | ||||||||
\(311\) | −412561. | −0.241873 | −0.120936 | − | 0.992660i | \(-0.538590\pi\) | ||||
−0.120936 | + | 0.992660i | \(0.538590\pi\) | |||||||
\(312\) | −447464. | −0.260239 | ||||||||
\(313\) | 2.78479e6 | 1.60669 | 0.803344 | − | 0.595516i | \(-0.203052\pi\) | ||||
0.803344 | + | 0.595516i | \(0.203052\pi\) | |||||||
\(314\) | −171867. | −0.0983710 | ||||||||
\(315\) | −532253. | −0.302233 | ||||||||
\(316\) | 3.44463e6 | 1.94055 | ||||||||
\(317\) | −1.13553e6 | −0.634674 | −0.317337 | − | 0.948313i | \(-0.602789\pi\) | ||||
−0.317337 | + | 0.948313i | \(0.602789\pi\) | |||||||
\(318\) | −32219.8 | −0.0178672 | ||||||||
\(319\) | 370121. | 0.203642 | ||||||||
\(320\) | −762742. | −0.416393 | ||||||||
\(321\) | 4.48693e6 | 2.43045 | ||||||||
\(322\) | 7835.90 | 0.00421162 | ||||||||
\(323\) | 451669. | 0.240887 | ||||||||
\(324\) | 2.20105e6 | 1.16484 | ||||||||
\(325\) | −348135. | −0.182827 | ||||||||
\(326\) | −186299. | −0.0970884 | ||||||||
\(327\) | 857633. | 0.443539 | ||||||||
\(328\) | 168158. | 0.0863043 | ||||||||
\(329\) | 1.56735e6 | 0.798319 | ||||||||
\(330\) | −38191.1 | −0.0193053 | ||||||||
\(331\) | 62356.8 | 0.0312834 | 0.0156417 | − | 0.999878i | \(-0.495021\pi\) | ||||
0.0156417 | + | 0.999878i | \(0.495021\pi\) | |||||||
\(332\) | −1.44112e6 | −0.717557 | ||||||||
\(333\) | −771055. | −0.381044 | ||||||||
\(334\) | −95138.3 | −0.0466648 | ||||||||
\(335\) | 792121. | 0.385638 | ||||||||
\(336\) | −2.33891e6 | −1.13023 | ||||||||
\(337\) | −1.12521e6 | −0.539706 | −0.269853 | − | 0.962902i | \(-0.586975\pi\) | ||||
−0.269853 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(338\) | 37178.0 | 0.0177008 | ||||||||
\(339\) | 2.48347e6 | 1.17370 | ||||||||
\(340\) | −989319. | −0.464129 | ||||||||
\(341\) | −252202. | −0.117453 | ||||||||
\(342\) | −41009.8 | −0.0189593 | ||||||||
\(343\) | 2.34951e6 | 1.07830 | ||||||||
\(344\) | −485858. | −0.221367 | ||||||||
\(345\) | 58365.9 | 0.0264004 | ||||||||
\(346\) | −371839. | −0.166980 | ||||||||
\(347\) | −122496. | −0.0546135 | −0.0273067 | − | 0.999627i | \(-0.508693\pi\) | ||||
−0.0273067 | + | 0.999627i | \(0.508693\pi\) | |||||||
\(348\) | −2.00497e6 | −0.887484 | ||||||||
\(349\) | 3.69774e6 | 1.62507 | 0.812536 | − | 0.582911i | \(-0.198087\pi\) | ||||
0.812536 | + | 0.582911i | \(0.198087\pi\) | |||||||
\(350\) | 43472.7 | 0.0189691 | ||||||||
\(351\) | 652540. | 0.282709 | ||||||||
\(352\) | −222960. | −0.0959115 | ||||||||
\(353\) | −2.44140e6 | −1.04280 | −0.521401 | − | 0.853312i | \(-0.674590\pi\) | ||||
−0.521401 | + | 0.853312i | \(0.674590\pi\) | |||||||
\(354\) | −145923. | −0.0618893 | ||||||||
\(355\) | 1.08262e6 | 0.455939 | ||||||||
\(356\) | −2.27810e6 | −0.952681 | ||||||||
\(357\) | −2.96038e6 | −1.22935 | ||||||||
\(358\) | −10252.0 | −0.00422767 | ||||||||
\(359\) | −3.74687e6 | −1.53438 | −0.767188 | − | 0.641422i | \(-0.778345\pi\) | ||||
−0.767188 | + | 0.641422i | \(0.778345\pi\) | |||||||
\(360\) | 180707. | 0.0734883 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 254180. | 0.101946 | ||||||||
\(363\) | 303415. | 0.120857 | ||||||||
\(364\) | −2.01149e6 | −0.795728 | ||||||||
\(365\) | −269602. | −0.105923 | ||||||||
\(366\) | −403791. | −0.157563 | ||||||||
\(367\) | −135654. | −0.0525738 | −0.0262869 | − | 0.999654i | \(-0.508368\pi\) | ||||
−0.0262869 | + | 0.999654i | \(0.508368\pi\) | |||||||
\(368\) | 111361. | 0.0428660 | ||||||||
\(369\) | 808918. | 0.309271 | ||||||||
\(370\) | 62977.3 | 0.0239155 | ||||||||
\(371\) | −291376. | −0.109905 | ||||||||
\(372\) | 1.36620e6 | 0.511866 | ||||||||
\(373\) | 3.31430e6 | 1.23344 | 0.616722 | − | 0.787181i | \(-0.288460\pi\) | ||||
0.616722 | + | 0.787181i | \(0.288460\pi\) | |||||||
\(374\) | −92229.1 | −0.0340948 | ||||||||
\(375\) | 323807. | 0.118907 | ||||||||
\(376\) | −532136. | −0.194112 | ||||||||
\(377\) | −1.70383e6 | −0.617409 | ||||||||
\(378\) | −81484.6 | −0.0293323 | ||||||||
\(379\) | 2.96745e6 | 1.06117 | 0.530585 | − | 0.847631i | \(-0.321972\pi\) | ||||
0.530585 | + | 0.847631i | \(0.321972\pi\) | |||||||
\(380\) | −285450. | −0.101408 | ||||||||
\(381\) | 810211. | 0.285947 | ||||||||
\(382\) | −510087. | −0.178849 | ||||||||
\(383\) | −40599.5 | −0.0141424 | −0.00707121 | − | 0.999975i | \(-0.502251\pi\) | ||||
−0.00707121 | + | 0.999975i | \(0.502251\pi\) | |||||||
\(384\) | 1.60715e6 | 0.556198 | ||||||||
\(385\) | −345376. | −0.118752 | ||||||||
\(386\) | −65891.7 | −0.0225093 | ||||||||
\(387\) | −2.33720e6 | −0.793266 | ||||||||
\(388\) | −3.72221e6 | −1.25522 | ||||||||
\(389\) | 1.75224e6 | 0.587109 | 0.293555 | − | 0.955942i | \(-0.405162\pi\) | ||||
0.293555 | + | 0.955942i | \(0.405162\pi\) | |||||||
\(390\) | 175810. | 0.0585305 | ||||||||
\(391\) | 140950. | 0.0466255 | ||||||||
\(392\) | −146189. | −0.0480508 | ||||||||
\(393\) | −574545. | −0.187648 | ||||||||
\(394\) | 199026. | 0.0645907 | ||||||||
\(395\) | −2.72270e6 | −0.878024 | ||||||||
\(396\) | −713641. | −0.228687 | ||||||||
\(397\) | 663352. | 0.211236 | 0.105618 | − | 0.994407i | \(-0.466318\pi\) | ||||
0.105618 | + | 0.994407i | \(0.466318\pi\) | |||||||
\(398\) | −154960. | −0.0490357 | ||||||||
\(399\) | −854164. | −0.268602 | ||||||||
\(400\) | 617818. | 0.193068 | ||||||||
\(401\) | −2.03063e6 | −0.630624 | −0.315312 | − | 0.948988i | \(-0.602109\pi\) | ||||
−0.315312 | + | 0.948988i | \(0.602109\pi\) | |||||||
\(402\) | −400026. | −0.123459 | ||||||||
\(403\) | 1.16100e6 | 0.356097 | ||||||||
\(404\) | 2.09827e6 | 0.639599 | ||||||||
\(405\) | −1.73975e6 | −0.527047 | ||||||||
\(406\) | 212762. | 0.0640589 | ||||||||
\(407\) | −500334. | −0.149718 | ||||||||
\(408\) | 1.00509e6 | 0.298919 | ||||||||
\(409\) | 4.46219e6 | 1.31898 | 0.659492 | − | 0.751712i | \(-0.270772\pi\) | ||||
0.659492 | + | 0.751712i | \(0.270772\pi\) | |||||||
\(410\) | −66069.8 | −0.0194108 | ||||||||
\(411\) | 733903. | 0.214306 | ||||||||
\(412\) | −4.75451e6 | −1.37995 | ||||||||
\(413\) | −1.31964e6 | −0.380697 | ||||||||
\(414\) | −12797.7 | −0.00366971 | ||||||||
\(415\) | 1.13909e6 | 0.324667 | ||||||||
\(416\) | 1.02638e6 | 0.290788 | ||||||||
\(417\) | 3.58552e6 | 1.00975 | ||||||||
\(418\) | −26611.1 | −0.00744940 | ||||||||
\(419\) | 1.44867e6 | 0.403121 | 0.201561 | − | 0.979476i | \(-0.435399\pi\) | ||||
0.201561 | + | 0.979476i | \(0.435399\pi\) | |||||||
\(420\) | 1.87093e6 | 0.517528 | ||||||||
\(421\) | −3.16817e6 | −0.871171 | −0.435585 | − | 0.900147i | \(-0.643459\pi\) | ||||
−0.435585 | + | 0.900147i | \(0.643459\pi\) | |||||||
\(422\) | −514986. | −0.140771 | ||||||||
\(423\) | −2.55982e6 | −0.695600 | ||||||||
\(424\) | 98926.0 | 0.0267237 | ||||||||
\(425\) | 781975. | 0.210001 | ||||||||
\(426\) | −546731. | −0.145965 | ||||||||
\(427\) | −3.65164e6 | −0.969210 | ||||||||
\(428\) | −6.84803e6 | −1.80699 | ||||||||
\(429\) | −1.39675e6 | −0.366418 | ||||||||
\(430\) | 190895. | 0.0497879 | ||||||||
\(431\) | 6.58226e6 | 1.70680 | 0.853398 | − | 0.521260i | \(-0.174538\pi\) | ||||
0.853398 | + | 0.521260i | \(0.174538\pi\) | |||||||
\(432\) | −1.15803e6 | −0.298545 | ||||||||
\(433\) | 76748.9 | 0.0196722 | 0.00983609 | − | 0.999952i | \(-0.496869\pi\) | ||||
0.00983609 | + | 0.999952i | \(0.496869\pi\) | |||||||
\(434\) | −144977. | −0.0369467 | ||||||||
\(435\) | 1.58477e6 | 0.401552 | ||||||||
\(436\) | −1.30894e6 | −0.329763 | ||||||||
\(437\) | 40668.6 | 0.0101872 | ||||||||
\(438\) | 136151. | 0.0339105 | ||||||||
\(439\) | −1.53842e6 | −0.380989 | −0.190495 | − | 0.981688i | \(-0.561009\pi\) | ||||
−0.190495 | + | 0.981688i | \(0.561009\pi\) | |||||||
\(440\) | 117260. | 0.0288747 | ||||||||
\(441\) | −703239. | −0.172189 | ||||||||
\(442\) | 424571. | 0.103370 | ||||||||
\(443\) | 7.10213e6 | 1.71941 | 0.859705 | − | 0.510791i | \(-0.170647\pi\) | ||||
0.859705 | + | 0.510791i | \(0.170647\pi\) | |||||||
\(444\) | 2.71035e6 | 0.652480 | ||||||||
\(445\) | 1.80065e6 | 0.431051 | ||||||||
\(446\) | 493181. | 0.117400 | ||||||||
\(447\) | −1.14437e6 | −0.270893 | ||||||||
\(448\) | 3.48341e6 | 0.819993 | ||||||||
\(449\) | 4.40451e6 | 1.03105 | 0.515527 | − | 0.856873i | \(-0.327596\pi\) | ||||
0.515527 | + | 0.856873i | \(0.327596\pi\) | |||||||
\(450\) | −71000.4 | −0.0165283 | ||||||||
\(451\) | 524903. | 0.121517 | ||||||||
\(452\) | −3.79031e6 | −0.872627 | ||||||||
\(453\) | 9.24595e6 | 2.11693 | ||||||||
\(454\) | 188737. | 0.0429752 | ||||||||
\(455\) | 1.58992e6 | 0.360036 | ||||||||
\(456\) | 290000. | 0.0653109 | ||||||||
\(457\) | 1.11602e6 | 0.249966 | 0.124983 | − | 0.992159i | \(-0.460112\pi\) | ||||
0.124983 | + | 0.992159i | \(0.460112\pi\) | |||||||
\(458\) | 725494. | 0.161611 | ||||||||
\(459\) | −1.46572e6 | −0.324728 | ||||||||
\(460\) | −89079.1 | −0.0196282 | ||||||||
\(461\) | 6.20830e6 | 1.36057 | 0.680284 | − | 0.732949i | \(-0.261856\pi\) | ||||
0.680284 | + | 0.732949i | \(0.261856\pi\) | |||||||
\(462\) | 174417. | 0.0380175 | ||||||||
\(463\) | 3.42480e6 | 0.742476 | 0.371238 | − | 0.928538i | \(-0.378933\pi\) | ||||
0.371238 | + | 0.928538i | \(0.378933\pi\) | |||||||
\(464\) | 3.02370e6 | 0.651994 | ||||||||
\(465\) | −1.07987e6 | −0.231600 | ||||||||
\(466\) | 37125.6 | 0.00791971 | ||||||||
\(467\) | 93071.3 | 0.0197480 | 0.00987401 | − | 0.999951i | \(-0.496857\pi\) | ||||
0.00987401 | + | 0.999951i | \(0.496857\pi\) | |||||||
\(468\) | 3.28520e6 | 0.693342 | ||||||||
\(469\) | −3.61758e6 | −0.759428 | ||||||||
\(470\) | 209078. | 0.0436580 | ||||||||
\(471\) | 5.84640e6 | 1.21433 | ||||||||
\(472\) | 448034. | 0.0925670 | ||||||||
\(473\) | −1.51660e6 | −0.311686 | ||||||||
\(474\) | 1.37498e6 | 0.281093 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | 4.51818e6 | 0.914000 | ||||||||
\(477\) | 475880. | 0.0957639 | ||||||||
\(478\) | 521291. | 0.104354 | ||||||||
\(479\) | −5.98996e6 | −1.19285 | −0.596424 | − | 0.802670i | \(-0.703412\pi\) | ||||
−0.596424 | + | 0.802670i | \(0.703412\pi\) | |||||||
\(480\) | −954660. | −0.189124 | ||||||||
\(481\) | 2.30326e6 | 0.453920 | ||||||||
\(482\) | −949737. | −0.186203 | ||||||||
\(483\) | −266554. | −0.0519898 | ||||||||
\(484\) | −463078. | −0.0898547 | ||||||||
\(485\) | 2.94210e6 | 0.567940 | ||||||||
\(486\) | 705158. | 0.135424 | ||||||||
\(487\) | 4.39175e6 | 0.839103 | 0.419551 | − | 0.907732i | \(-0.362187\pi\) | ||||
0.419551 | + | 0.907732i | \(0.362187\pi\) | |||||||
\(488\) | 1.23978e6 | 0.235665 | ||||||||
\(489\) | 6.33736e6 | 1.19850 | ||||||||
\(490\) | 57438.3 | 0.0108072 | ||||||||
\(491\) | 1.21644e6 | 0.227713 | 0.113856 | − | 0.993497i | \(-0.463680\pi\) | ||||
0.113856 | + | 0.993497i | \(0.463680\pi\) | |||||||
\(492\) | −2.84344e6 | −0.529580 | ||||||||
\(493\) | 3.82711e6 | 0.709176 | ||||||||
\(494\) | 122502. | 0.0225854 | ||||||||
\(495\) | 564074. | 0.103472 | ||||||||
\(496\) | −2.06036e6 | −0.376045 | ||||||||
\(497\) | −4.94430e6 | −0.897870 | ||||||||
\(498\) | −575247. | −0.103940 | ||||||||
\(499\) | 162759. | 0.0292613 | 0.0146307 | − | 0.999893i | \(-0.495343\pi\) | ||||
0.0146307 | + | 0.999893i | \(0.495343\pi\) | |||||||
\(500\) | −494201. | −0.0884053 | ||||||||
\(501\) | 3.23633e6 | 0.576048 | ||||||||
\(502\) | 1.00281e6 | 0.177607 | ||||||||
\(503\) | 4.48157e6 | 0.789788 | 0.394894 | − | 0.918727i | \(-0.370781\pi\) | ||||
0.394894 | + | 0.918727i | \(0.370781\pi\) | |||||||
\(504\) | −825281. | −0.144719 | ||||||||
\(505\) | −1.65851e6 | −0.289394 | ||||||||
\(506\) | −8304.38 | −0.00144189 | ||||||||
\(507\) | −1.26469e6 | −0.218506 | ||||||||
\(508\) | −1.23656e6 | −0.212596 | ||||||||
\(509\) | −6.49298e6 | −1.11084 | −0.555418 | − | 0.831571i | \(-0.687442\pi\) | ||||
−0.555418 | + | 0.831571i | \(0.687442\pi\) | |||||||
\(510\) | −394902. | −0.0672301 | ||||||||
\(511\) | 1.23126e6 | 0.208592 | ||||||||
\(512\) | −3.04765e6 | −0.513795 | ||||||||
\(513\) | −422908. | −0.0709501 | ||||||||
\(514\) | 375070. | 0.0626187 | ||||||||
\(515\) | 3.75805e6 | 0.624373 | ||||||||
\(516\) | 8.21553e6 | 1.35835 | ||||||||
\(517\) | −1.66106e6 | −0.273312 | ||||||||
\(518\) | −287615. | −0.0470963 | ||||||||
\(519\) | 1.26489e7 | 2.06127 | ||||||||
\(520\) | −539798. | −0.0875433 | ||||||||
\(521\) | −3.01994e6 | −0.487421 | −0.243710 | − | 0.969848i | \(-0.578365\pi\) | ||||
−0.243710 | + | 0.969848i | \(0.578365\pi\) | |||||||
\(522\) | −347487. | −0.0558165 | ||||||||
\(523\) | 661888. | 0.105811 | 0.0529055 | − | 0.998600i | \(-0.483152\pi\) | ||||
0.0529055 | + | 0.998600i | \(0.483152\pi\) | |||||||
\(524\) | 876881. | 0.139512 | ||||||||
\(525\) | −1.47882e6 | −0.234162 | ||||||||
\(526\) | −335181. | −0.0528221 | ||||||||
\(527\) | −2.60781e6 | −0.409025 | ||||||||
\(528\) | 2.47875e6 | 0.386944 | ||||||||
\(529\) | −6.42365e6 | −0.998028 | ||||||||
\(530\) | −38868.4 | −0.00601045 | ||||||||
\(531\) | 2.15525e6 | 0.331713 | ||||||||
\(532\) | 1.30364e6 | 0.199700 | ||||||||
\(533\) | −2.41636e6 | −0.368420 | ||||||||
\(534\) | −909338. | −0.137998 | ||||||||
\(535\) | 5.41280e6 | 0.817594 | ||||||||
\(536\) | 1.22822e6 | 0.184656 | ||||||||
\(537\) | 348743. | 0.0521879 | ||||||||
\(538\) | 114333. | 0.0170300 | ||||||||
\(539\) | −456328. | −0.0676559 | ||||||||
\(540\) | 926323. | 0.136703 | ||||||||
\(541\) | −4.71067e6 | −0.691974 | −0.345987 | − | 0.938239i | \(-0.612456\pi\) | ||||
−0.345987 | + | 0.938239i | \(0.612456\pi\) | |||||||
\(542\) | −744643. | −0.108880 | ||||||||
\(543\) | −8.64646e6 | −1.25846 | ||||||||
\(544\) | −2.30545e6 | −0.334009 | ||||||||
\(545\) | 1.03461e6 | 0.149205 | ||||||||
\(546\) | −802918. | −0.115263 | ||||||||
\(547\) | 7.59966e6 | 1.08599 | 0.542995 | − | 0.839736i | \(-0.317290\pi\) | ||||
0.542995 | + | 0.839736i | \(0.317290\pi\) | |||||||
\(548\) | −1.12010e6 | −0.159332 | ||||||||
\(549\) | 5.96392e6 | 0.844502 | ||||||||
\(550\) | −46071.8 | −0.00649424 | ||||||||
\(551\) | 1.10425e6 | 0.154948 | ||||||||
\(552\) | 90498.8 | 0.0126414 | ||||||||
\(553\) | 1.24344e7 | 1.72907 | ||||||||
\(554\) | 511109. | 0.0707520 | ||||||||
\(555\) | −2.14230e6 | −0.295222 | ||||||||
\(556\) | −5.47228e6 | −0.750726 | ||||||||
\(557\) | −1.25435e7 | −1.71309 | −0.856546 | − | 0.516070i | \(-0.827394\pi\) | ||||
−0.856546 | + | 0.516070i | \(0.827394\pi\) | |||||||
\(558\) | 236779. | 0.0321928 | ||||||||
\(559\) | 6.98157e6 | 0.944982 | ||||||||
\(560\) | −2.82155e6 | −0.380204 | ||||||||
\(561\) | 3.13737e6 | 0.420880 | ||||||||
\(562\) | −688117. | −0.0919013 | ||||||||
\(563\) | 1.28593e7 | 1.70980 | 0.854901 | − | 0.518792i | \(-0.173618\pi\) | ||||
0.854901 | + | 0.518792i | \(0.173618\pi\) | |||||||
\(564\) | 8.99807e6 | 1.19111 | ||||||||
\(565\) | 2.99593e6 | 0.394830 | ||||||||
\(566\) | −426831. | −0.0560035 | ||||||||
\(567\) | 7.94537e6 | 1.03790 | ||||||||
\(568\) | 1.67865e6 | 0.218318 | ||||||||
\(569\) | −9.15727e6 | −1.18573 | −0.592865 | − | 0.805302i | \(-0.702003\pi\) | ||||
−0.592865 | + | 0.805302i | \(0.702003\pi\) | |||||||
\(570\) | −113942. | −0.0146891 | ||||||||
\(571\) | −1.21179e6 | −0.155538 | −0.0777691 | − | 0.996971i | \(-0.524780\pi\) | ||||
−0.0777691 | + | 0.996971i | \(0.524780\pi\) | |||||||
\(572\) | 2.13175e6 | 0.272425 | ||||||||
\(573\) | 1.73517e7 | 2.20777 | ||||||||
\(574\) | 301738. | 0.0382253 | ||||||||
\(575\) | 70409.6 | 0.00888101 | ||||||||
\(576\) | −5.68917e6 | −0.714484 | ||||||||
\(577\) | 6.20841e6 | 0.776321 | 0.388160 | − | 0.921592i | \(-0.373111\pi\) | ||||
0.388160 | + | 0.921592i | \(0.373111\pi\) | |||||||
\(578\) | −88667.7 | −0.0110394 | ||||||||
\(579\) | 2.24145e6 | 0.277864 | ||||||||
\(580\) | −2.41870e6 | −0.298546 | ||||||||
\(581\) | −5.20217e6 | −0.639359 | ||||||||
\(582\) | −1.48578e6 | −0.181822 | ||||||||
\(583\) | 308796. | 0.0376271 | ||||||||
\(584\) | −418030. | −0.0507195 | ||||||||
\(585\) | −2.59668e6 | −0.313710 | ||||||||
\(586\) | −99811.6 | −0.0120071 | ||||||||
\(587\) | −1.08448e7 | −1.29906 | −0.649528 | − | 0.760338i | \(-0.725033\pi\) | ||||
−0.649528 | + | 0.760338i | \(0.725033\pi\) | |||||||
\(588\) | 2.47197e6 | 0.294849 | ||||||||
\(589\) | −752437. | −0.0893680 | ||||||||
\(590\) | −176034. | −0.0208193 | ||||||||
\(591\) | −6.77030e6 | −0.797332 | ||||||||
\(592\) | −4.08747e6 | −0.479347 | ||||||||
\(593\) | −1.09447e7 | −1.27811 | −0.639054 | − | 0.769162i | \(-0.720674\pi\) | ||||
−0.639054 | + | 0.769162i | \(0.720674\pi\) | |||||||
\(594\) | 86356.3 | 0.0100422 | ||||||||
\(595\) | −3.57125e6 | −0.413549 | ||||||||
\(596\) | 1.74656e6 | 0.201404 | ||||||||
\(597\) | 5.27130e6 | 0.605316 | ||||||||
\(598\) | 38228.7 | 0.00437156 | ||||||||
\(599\) | −1.27587e7 | −1.45292 | −0.726459 | − | 0.687210i | \(-0.758835\pi\) | ||||
−0.726459 | + | 0.687210i | \(0.758835\pi\) | |||||||
\(600\) | 502077. | 0.0569367 | ||||||||
\(601\) | −6.73618e6 | −0.760725 | −0.380363 | − | 0.924837i | \(-0.624201\pi\) | ||||
−0.380363 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(602\) | −871810. | −0.0980462 | ||||||||
\(603\) | 5.90830e6 | 0.661712 | ||||||||
\(604\) | −1.41113e7 | −1.57389 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 837557. | 0.0926473 | ||||||||
\(607\) | −4.75731e6 | −0.524071 | −0.262035 | − | 0.965058i | \(-0.584394\pi\) | ||||
−0.262035 | + | 0.965058i | \(0.584394\pi\) | |||||||
\(608\) | −665195. | −0.0729777 | ||||||||
\(609\) | −7.23756e6 | −0.790768 | ||||||||
\(610\) | −487113. | −0.0530036 | ||||||||
\(611\) | 7.64657e6 | 0.828636 | ||||||||
\(612\) | −7.37917e6 | −0.796396 | ||||||||
\(613\) | 266874. | 0.0286850 | 0.0143425 | − | 0.999897i | \(-0.495434\pi\) | ||||
0.0143425 | + | 0.999897i | \(0.495434\pi\) | |||||||
\(614\) | 890130. | 0.0952867 | ||||||||
\(615\) | 2.24750e6 | 0.239614 | ||||||||
\(616\) | −535520. | −0.0568623 | ||||||||
\(617\) | −2.11758e6 | −0.223937 | −0.111969 | − | 0.993712i | \(-0.535716\pi\) | ||||
−0.111969 | + | 0.993712i | \(0.535716\pi\) | |||||||
\(618\) | −1.89784e6 | −0.199888 | ||||||||
\(619\) | 1.96652e6 | 0.206287 | 0.103144 | − | 0.994666i | \(-0.467110\pi\) | ||||
0.103144 | + | 0.994666i | \(0.467110\pi\) | |||||||
\(620\) | 1.64811e6 | 0.172190 | ||||||||
\(621\) | −131975. | −0.0137329 | ||||||||
\(622\) | 251338. | 0.0260484 | ||||||||
\(623\) | −8.22349e6 | −0.848860 | ||||||||
\(624\) | −1.14108e7 | −1.17315 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.69653e6 | −0.173032 | ||||||||
\(627\) | 905231. | 0.0919582 | ||||||||
\(628\) | −8.92288e6 | −0.902830 | ||||||||
\(629\) | −5.17353e6 | −0.521388 | ||||||||
\(630\) | 324256. | 0.0325489 | ||||||||
\(631\) | 1.73409e7 | 1.73379 | 0.866896 | − | 0.498489i | \(-0.166112\pi\) | ||||
0.866896 | + | 0.498489i | \(0.166112\pi\) | |||||||
\(632\) | −4.22166e6 | −0.420427 | ||||||||
\(633\) | 1.75183e7 | 1.73773 | ||||||||
\(634\) | 691781. | 0.0683511 | ||||||||
\(635\) | 977397. | 0.0961915 | ||||||||
\(636\) | −1.67277e6 | −0.163981 | ||||||||
\(637\) | 2.10068e6 | 0.205122 | ||||||||
\(638\) | −225483. | −0.0219312 | ||||||||
\(639\) | 8.07511e6 | 0.782342 | ||||||||
\(640\) | 1.93879e6 | 0.187103 | ||||||||
\(641\) | −3.94482e6 | −0.379212 | −0.189606 | − | 0.981860i | \(-0.560721\pi\) | ||||
−0.189606 | + | 0.981860i | \(0.560721\pi\) | |||||||
\(642\) | −2.73350e6 | −0.261747 | ||||||||
\(643\) | −1.81584e7 | −1.73201 | −0.866005 | − | 0.500035i | \(-0.833321\pi\) | ||||
−0.866005 | + | 0.500035i | \(0.833321\pi\) | |||||||
\(644\) | 406820. | 0.0386534 | ||||||||
\(645\) | −6.49370e6 | −0.614600 | ||||||||
\(646\) | −275163. | −0.0259423 | ||||||||
\(647\) | 1.17027e7 | 1.09907 | 0.549537 | − | 0.835469i | \(-0.314804\pi\) | ||||
0.549537 | + | 0.835469i | \(0.314804\pi\) | |||||||
\(648\) | −2.69756e6 | −0.252367 | ||||||||
\(649\) | 1.39853e6 | 0.130335 | ||||||||
\(650\) | 212089. | 0.0196895 | ||||||||
\(651\) | 4.93171e6 | 0.456084 | ||||||||
\(652\) | −9.67220e6 | −0.891059 | ||||||||
\(653\) | −3.95039e6 | −0.362541 | −0.181271 | − | 0.983433i | \(-0.558021\pi\) | ||||
−0.181271 | + | 0.983433i | \(0.558021\pi\) | |||||||
\(654\) | −522482. | −0.0477669 | ||||||||
\(655\) | −693102. | −0.0631239 | ||||||||
\(656\) | 4.28819e6 | 0.389058 | ||||||||
\(657\) | −2.01092e6 | −0.181753 | ||||||||
\(658\) | −954851. | −0.0859748 | ||||||||
\(659\) | 1.24284e7 | 1.11481 | 0.557406 | − | 0.830240i | \(-0.311797\pi\) | ||||
0.557406 | + | 0.830240i | \(0.311797\pi\) | |||||||
\(660\) | −1.98279e6 | −0.177180 | ||||||||
\(661\) | −4.42595e6 | −0.394006 | −0.197003 | − | 0.980403i | \(-0.563121\pi\) | ||||
−0.197003 | + | 0.980403i | \(0.563121\pi\) | |||||||
\(662\) | −37988.6 | −0.00336905 | ||||||||
\(663\) | −1.44427e7 | −1.27604 | ||||||||
\(664\) | 1.76621e6 | 0.155461 | ||||||||
\(665\) | −1.03042e6 | −0.0903567 | ||||||||
\(666\) | 469737. | 0.0410364 | ||||||||
\(667\) | 344596. | 0.0299913 | ||||||||
\(668\) | −4.93935e6 | −0.428281 | ||||||||
\(669\) | −1.67766e7 | −1.44923 | ||||||||
\(670\) | −482571. | −0.0415311 | ||||||||
\(671\) | 3.86995e6 | 0.331818 | ||||||||
\(672\) | 4.35989e6 | 0.372437 | ||||||||
\(673\) | 1.16679e6 | 0.0993011 | 0.0496506 | − | 0.998767i | \(-0.484189\pi\) | ||||
0.0496506 | + | 0.998767i | \(0.484189\pi\) | |||||||
\(674\) | 685491. | 0.0581235 | ||||||||
\(675\) | −732182. | −0.0618529 | ||||||||
\(676\) | 1.93019e6 | 0.162455 | ||||||||
\(677\) | 1.01941e6 | 0.0854822 | 0.0427411 | − | 0.999086i | \(-0.486391\pi\) | ||||
0.0427411 | + | 0.999086i | \(0.486391\pi\) | |||||||
\(678\) | −1.51296e6 | −0.126402 | ||||||||
\(679\) | −1.34364e7 | −1.11843 | ||||||||
\(680\) | 1.21249e6 | 0.100555 | ||||||||
\(681\) | −6.42030e6 | −0.530503 | ||||||||
\(682\) | 153645. | 0.0126490 | ||||||||
\(683\) | −1.53024e7 | −1.25519 | −0.627594 | − | 0.778541i | \(-0.715960\pi\) | ||||
−0.627594 | + | 0.778541i | \(0.715960\pi\) | |||||||
\(684\) | −2.12913e6 | −0.174005 | ||||||||
\(685\) | 885344. | 0.0720917 | ||||||||
\(686\) | −1.43135e6 | −0.116128 | ||||||||
\(687\) | −2.46792e7 | −1.99498 | ||||||||
\(688\) | −1.23898e7 | −0.997917 | ||||||||
\(689\) | −1.42153e6 | −0.114079 | ||||||||
\(690\) | −35557.3 | −0.00284319 | ||||||||
\(691\) | 1.44395e7 | 1.15042 | 0.575211 | − | 0.818005i | \(-0.304920\pi\) | ||||
0.575211 | + | 0.818005i | \(0.304920\pi\) | |||||||
\(692\) | −1.93050e7 | −1.53251 | ||||||||
\(693\) | −2.57610e6 | −0.203765 | ||||||||
\(694\) | 74626.5 | 0.00588158 | ||||||||
\(695\) | 4.32539e6 | 0.339675 | ||||||||
\(696\) | 2.45725e6 | 0.192276 | ||||||||
\(697\) | 5.42758e6 | 0.423179 | ||||||||
\(698\) | −2.25271e6 | −0.175012 | ||||||||
\(699\) | −1.26291e6 | −0.0977638 | ||||||||
\(700\) | 2.25699e6 | 0.174095 | ||||||||
\(701\) | 1.06826e7 | 0.821074 | 0.410537 | − | 0.911844i | \(-0.365341\pi\) | ||||
0.410537 | + | 0.911844i | \(0.365341\pi\) | |||||||
\(702\) | −397536. | −0.0304462 | ||||||||
\(703\) | −1.49273e6 | −0.113918 | ||||||||
\(704\) | −3.69167e6 | −0.280732 | ||||||||
\(705\) | −7.11223e6 | −0.538931 | ||||||||
\(706\) | 1.48733e6 | 0.112304 | ||||||||
\(707\) | 7.57434e6 | 0.569897 | ||||||||
\(708\) | −7.57597e6 | −0.568009 | ||||||||
\(709\) | −4.42131e6 | −0.330321 | −0.165160 | − | 0.986267i | \(-0.552814\pi\) | ||||
−0.165160 | + | 0.986267i | \(0.552814\pi\) | |||||||
\(710\) | −659549. | −0.0491022 | ||||||||
\(711\) | −2.03081e7 | −1.50659 | ||||||||
\(712\) | 2.79198e6 | 0.206401 | ||||||||
\(713\) | −234809. | −0.0172978 | ||||||||
\(714\) | 1.80350e6 | 0.132395 | ||||||||
\(715\) | −1.68497e6 | −0.123262 | ||||||||
\(716\) | −532258. | −0.0388007 | ||||||||
\(717\) | −1.77328e7 | −1.28819 | ||||||||
\(718\) | 2.28264e6 | 0.165244 | ||||||||
\(719\) | −1.95698e7 | −1.41177 | −0.705885 | − | 0.708326i | \(-0.749451\pi\) | ||||
−0.705885 | + | 0.708326i | \(0.749451\pi\) | |||||||
\(720\) | 4.60820e6 | 0.331284 | ||||||||
\(721\) | −1.71629e7 | −1.22956 | ||||||||
\(722\) | −79393.3 | −0.00566814 | ||||||||
\(723\) | 3.23073e7 | 2.29856 | ||||||||
\(724\) | 1.31964e7 | 0.935639 | ||||||||
\(725\) | 1.91178e6 | 0.135081 | ||||||||
\(726\) | −184845. | −0.0130156 | ||||||||
\(727\) | −2.24777e7 | −1.57731 | −0.788654 | − | 0.614837i | \(-0.789222\pi\) | ||||
−0.788654 | + | 0.614837i | \(0.789222\pi\) | |||||||
\(728\) | 2.46524e6 | 0.172397 | ||||||||
\(729\) | −7.07705e6 | −0.493212 | ||||||||
\(730\) | 164245. | 0.0114074 | ||||||||
\(731\) | −1.56819e7 | −1.08544 | ||||||||
\(732\) | −2.09638e7 | −1.44608 | ||||||||
\(733\) | −1.36016e7 | −0.935040 | −0.467520 | − | 0.883982i | \(-0.654852\pi\) | ||||
−0.467520 | + | 0.883982i | \(0.654852\pi\) | |||||||
\(734\) | 82642.5 | 0.00566192 | ||||||||
\(735\) | −1.95388e6 | −0.133408 | ||||||||
\(736\) | −207584. | −0.0141254 | ||||||||
\(737\) | 3.83386e6 | 0.259997 | ||||||||
\(738\) | −492804. | −0.0333068 | ||||||||
\(739\) | 9.16190e6 | 0.617127 | 0.308563 | − | 0.951204i | \(-0.400152\pi\) | ||||
0.308563 | + | 0.951204i | \(0.400152\pi\) | |||||||
\(740\) | 3.26962e6 | 0.219492 | ||||||||
\(741\) | −4.16717e6 | −0.278802 | ||||||||
\(742\) | 177510. | 0.0118362 | ||||||||
\(743\) | 1.23617e7 | 0.821500 | 0.410750 | − | 0.911748i | \(-0.365267\pi\) | ||||
0.410750 | + | 0.911748i | \(0.365267\pi\) | |||||||
\(744\) | −1.67438e6 | −0.110897 | ||||||||
\(745\) | −1.38051e6 | −0.0911273 | ||||||||
\(746\) | −2.01912e6 | −0.132836 | ||||||||
\(747\) | 8.49628e6 | 0.557093 | ||||||||
\(748\) | −4.78830e6 | −0.312916 | ||||||||
\(749\) | −2.47201e7 | −1.61007 | ||||||||
\(750\) | −197268. | −0.0128057 | ||||||||
\(751\) | 9.61270e6 | 0.621936 | 0.310968 | − | 0.950420i | \(-0.399347\pi\) | ||||
0.310968 | + | 0.950420i | \(0.399347\pi\) | |||||||
\(752\) | −1.35700e7 | −0.875054 | ||||||||
\(753\) | −3.41128e7 | −2.19245 | ||||||||
\(754\) | 1.03800e6 | 0.0664917 | ||||||||
\(755\) | 1.11538e7 | 0.712127 | ||||||||
\(756\) | −4.23048e6 | −0.269206 | ||||||||
\(757\) | −2.55706e6 | −0.162182 | −0.0810908 | − | 0.996707i | \(-0.525840\pi\) | ||||
−0.0810908 | + | 0.996707i | \(0.525840\pi\) | |||||||
\(758\) | −1.80781e6 | −0.114283 | ||||||||
\(759\) | 282491. | 0.0177992 | ||||||||
\(760\) | 349841. | 0.0219703 | ||||||||
\(761\) | 6.00751e6 | 0.376039 | 0.188019 | − | 0.982165i | \(-0.439793\pi\) | ||||
0.188019 | + | 0.982165i | \(0.439793\pi\) | |||||||
\(762\) | −493591. | −0.0307950 | ||||||||
\(763\) | −4.72500e6 | −0.293826 | ||||||||
\(764\) | −2.64824e7 | −1.64144 | ||||||||
\(765\) | 5.83262e6 | 0.360338 | ||||||||
\(766\) | 24733.8 | 0.00152307 | ||||||||
\(767\) | −6.43806e6 | −0.395154 | ||||||||
\(768\) | 1.92536e7 | 1.17790 | ||||||||
\(769\) | −1.76926e7 | −1.07889 | −0.539443 | − | 0.842022i | \(-0.681365\pi\) | ||||
−0.539443 | + | 0.842022i | \(0.681365\pi\) | |||||||
\(770\) | 210408. | 0.0127890 | ||||||||
\(771\) | −1.27588e7 | −0.772989 | ||||||||
\(772\) | −3.42093e6 | −0.206586 | ||||||||
\(773\) | −2.65637e7 | −1.59897 | −0.799485 | − | 0.600686i | \(-0.794894\pi\) | ||||
−0.799485 | + | 0.600686i | \(0.794894\pi\) | |||||||
\(774\) | 1.42386e6 | 0.0854306 | ||||||||
\(775\) | −1.30270e6 | −0.0779092 | ||||||||
\(776\) | 4.56185e6 | 0.271948 | ||||||||
\(777\) | 9.78382e6 | 0.581374 | ||||||||
\(778\) | −1.06749e6 | −0.0632286 | ||||||||
\(779\) | 1.56603e6 | 0.0924607 | ||||||||
\(780\) | 9.12763e6 | 0.537182 | ||||||||
\(781\) | 5.23990e6 | 0.307394 | ||||||||
\(782\) | −85868.6 | −0.00502132 | ||||||||
\(783\) | −3.58342e6 | −0.208878 | ||||||||
\(784\) | −3.72797e6 | −0.216612 | ||||||||
\(785\) | 7.05280e6 | 0.408496 | ||||||||
\(786\) | 350021. | 0.0202087 | ||||||||
\(787\) | 2.44560e7 | 1.40750 | 0.703751 | − | 0.710446i | \(-0.251507\pi\) | ||||
0.703751 | + | 0.710446i | \(0.251507\pi\) | |||||||
\(788\) | 1.03330e7 | 0.592801 | ||||||||
\(789\) | 1.14019e7 | 0.652056 | ||||||||
\(790\) | 1.65870e6 | 0.0945586 | ||||||||
\(791\) | −1.36823e7 | −0.777530 | ||||||||
\(792\) | 874621. | 0.0495458 | ||||||||
\(793\) | −1.78151e7 | −1.00602 | ||||||||
\(794\) | −404123. | −0.0227490 | ||||||||
\(795\) | 1.32219e6 | 0.0741952 | ||||||||
\(796\) | −8.04515e6 | −0.450041 | ||||||||
\(797\) | 1.74911e6 | 0.0975376 | 0.0487688 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487688 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(798\) | 520368. | 0.0289270 | ||||||||
\(799\) | −1.71756e7 | −0.951799 | ||||||||
\(800\) | −1.15165e6 | −0.0636205 | ||||||||
\(801\) | 1.34307e7 | 0.739637 | ||||||||
\(802\) | 1.23709e6 | 0.0679149 | ||||||||
\(803\) | −1.30487e6 | −0.0714134 | ||||||||
\(804\) | −2.07683e7 | −1.13308 | ||||||||
\(805\) | −321558. | −0.0174892 | ||||||||
\(806\) | −707295. | −0.0383498 | ||||||||
\(807\) | −3.88927e6 | −0.210225 | ||||||||
\(808\) | −2.57159e6 | −0.138571 | ||||||||
\(809\) | −9.47251e6 | −0.508855 | −0.254427 | − | 0.967092i | \(-0.581887\pi\) | ||||
−0.254427 | + | 0.967092i | \(0.581887\pi\) | |||||||
\(810\) | 1.05988e6 | 0.0567602 | ||||||||
\(811\) | −8.05797e6 | −0.430203 | −0.215101 | − | 0.976592i | \(-0.569008\pi\) | ||||
−0.215101 | + | 0.976592i | \(0.569008\pi\) | |||||||
\(812\) | 1.10461e7 | 0.587921 | ||||||||
\(813\) | 2.53306e7 | 1.34406 | ||||||||
\(814\) | 304810. | 0.0161238 | ||||||||
\(815\) | 7.64507e6 | 0.403170 | ||||||||
\(816\) | 2.56307e7 | 1.34752 | ||||||||
\(817\) | −4.52473e6 | −0.237158 | ||||||||
\(818\) | −2.71842e6 | −0.142048 | ||||||||
\(819\) | 1.18589e7 | 0.617783 | ||||||||
\(820\) | −3.43018e6 | −0.178149 | ||||||||
\(821\) | −2.53676e7 | −1.31347 | −0.656736 | − | 0.754121i | \(-0.728063\pi\) | ||||
−0.656736 | + | 0.754121i | \(0.728063\pi\) | |||||||
\(822\) | −447104. | −0.0230796 | ||||||||
\(823\) | −2.45044e7 | −1.26109 | −0.630544 | − | 0.776154i | \(-0.717168\pi\) | ||||
−0.630544 | + | 0.776154i | \(0.717168\pi\) | |||||||
\(824\) | 5.82702e6 | 0.298970 | ||||||||
\(825\) | 1.56723e6 | 0.0801673 | ||||||||
\(826\) | 803941. | 0.0409991 | ||||||||
\(827\) | 2.50859e6 | 0.127546 | 0.0637729 | − | 0.997964i | \(-0.479687\pi\) | ||||
0.0637729 | + | 0.997964i | \(0.479687\pi\) | |||||||
\(828\) | −664426. | −0.0336799 | ||||||||
\(829\) | 2.57470e7 | 1.30119 | 0.650594 | − | 0.759426i | \(-0.274520\pi\) | ||||
0.650594 | + | 0.759426i | \(0.274520\pi\) | |||||||
\(830\) | −693949. | −0.0349649 | ||||||||
\(831\) | −1.73864e7 | −0.873390 | ||||||||
\(832\) | 1.69944e7 | 0.851133 | ||||||||
\(833\) | −4.71851e6 | −0.235609 | ||||||||
\(834\) | −2.18435e6 | −0.108744 | ||||||||
\(835\) | 3.90415e6 | 0.193780 | ||||||||
\(836\) | −1.38158e6 | −0.0683692 | ||||||||
\(837\) | 2.44176e6 | 0.120473 | ||||||||
\(838\) | −882552. | −0.0434140 | ||||||||
\(839\) | 4.72133e6 | 0.231558 | 0.115779 | − | 0.993275i | \(-0.463064\pi\) | ||||
0.115779 | + | 0.993275i | \(0.463064\pi\) | |||||||
\(840\) | −2.29297e6 | −0.112124 | ||||||||
\(841\) | −1.11546e7 | −0.543830 | ||||||||
\(842\) | 1.93009e6 | 0.0938205 | ||||||||
\(843\) | 2.34077e7 | 1.13446 | ||||||||
\(844\) | −2.67368e7 | −1.29197 | ||||||||
\(845\) | −1.52565e6 | −0.0735046 | ||||||||
\(846\) | 1.55948e6 | 0.0749124 | ||||||||
\(847\) | −1.67162e6 | −0.0800625 | ||||||||
\(848\) | 2.52271e6 | 0.120470 | ||||||||
\(849\) | 1.45196e7 | 0.691328 | ||||||||
\(850\) | −476390. | −0.0226160 | ||||||||
\(851\) | −465829. | −0.0220497 | ||||||||
\(852\) | −2.83849e7 | −1.33964 | ||||||||
\(853\) | 3.31831e7 | 1.56151 | 0.780754 | − | 0.624839i | \(-0.214835\pi\) | ||||
0.780754 | + | 0.624839i | \(0.214835\pi\) | |||||||
\(854\) | 2.22463e6 | 0.104379 | ||||||||
\(855\) | 1.68290e6 | 0.0787305 | ||||||||
\(856\) | 8.39278e6 | 0.391491 | ||||||||
\(857\) | −1.51606e7 | −0.705124 | −0.352562 | − | 0.935788i | \(-0.614689\pi\) | ||||
−0.352562 | + | 0.935788i | \(0.614689\pi\) | |||||||
\(858\) | 850921. | 0.0394613 | ||||||||
\(859\) | −3.64591e7 | −1.68586 | −0.842932 | − | 0.538020i | \(-0.819172\pi\) | ||||
−0.842932 | + | 0.538020i | \(0.819172\pi\) | |||||||
\(860\) | 9.91080e6 | 0.456944 | ||||||||
\(861\) | −1.02643e7 | −0.471867 | ||||||||
\(862\) | −4.01000e6 | −0.183813 | ||||||||
\(863\) | −2.98273e7 | −1.36328 | −0.681642 | − | 0.731685i | \(-0.738734\pi\) | ||||
−0.681642 | + | 0.731685i | \(0.738734\pi\) | |||||||
\(864\) | 2.15864e6 | 0.0983777 | ||||||||
\(865\) | 1.52590e7 | 0.693403 | ||||||||
\(866\) | −46756.5 | −0.00211859 | ||||||||
\(867\) | 3.01622e6 | 0.136275 | ||||||||
\(868\) | −7.52686e6 | −0.339090 | ||||||||
\(869\) | −1.31779e7 | −0.591964 | ||||||||
\(870\) | −965461. | −0.0432451 | ||||||||
\(871\) | −1.76490e7 | −0.788268 | ||||||||
\(872\) | 1.60420e6 | 0.0714442 | ||||||||
\(873\) | 2.19446e7 | 0.974524 | ||||||||
\(874\) | −24775.9 | −0.00109711 | ||||||||
\(875\) | −1.78397e6 | −0.0787711 | ||||||||
\(876\) | 7.06861e6 | 0.311224 | ||||||||
\(877\) | −916487. | −0.0402372 | −0.0201186 | − | 0.999798i | \(-0.506404\pi\) | ||||
−0.0201186 | + | 0.999798i | \(0.506404\pi\) | |||||||
\(878\) | 937225. | 0.0410306 | ||||||||
\(879\) | 3.39530e6 | 0.148220 | ||||||||
\(880\) | 2.99024e6 | 0.130166 | ||||||||
\(881\) | 3.07967e7 | 1.33680 | 0.668398 | − | 0.743804i | \(-0.266981\pi\) | ||||
0.668398 | + | 0.743804i | \(0.266981\pi\) | |||||||
\(882\) | 428423. | 0.0185439 | ||||||||
\(883\) | −4.44832e6 | −0.191997 | −0.0959984 | − | 0.995381i | \(-0.530604\pi\) | ||||
−0.0959984 | + | 0.995381i | \(0.530604\pi\) | |||||||
\(884\) | 2.20427e7 | 0.948710 | ||||||||
\(885\) | 5.98817e6 | 0.257002 | ||||||||
\(886\) | −4.32671e6 | −0.185171 | ||||||||
\(887\) | −2.81458e7 | −1.20117 | −0.600584 | − | 0.799561i | \(-0.705065\pi\) | ||||
−0.600584 | + | 0.799561i | \(0.705065\pi\) | |||||||
\(888\) | −3.32173e6 | −0.141362 | ||||||||
\(889\) | −4.46373e6 | −0.189428 | ||||||||
\(890\) | −1.09698e6 | −0.0464220 | ||||||||
\(891\) | −8.42039e6 | −0.355335 | ||||||||
\(892\) | 2.56047e7 | 1.07748 | ||||||||
\(893\) | −4.95572e6 | −0.207959 | ||||||||
\(894\) | 697165. | 0.0291737 | ||||||||
\(895\) | 420706. | 0.0175558 | ||||||||
\(896\) | −8.85437e6 | −0.368458 | ||||||||
\(897\) | −1.30043e6 | −0.0539642 | ||||||||
\(898\) | −2.68329e6 | −0.111039 | ||||||||
\(899\) | −6.37561e6 | −0.263101 | ||||||||
\(900\) | −3.68616e6 | −0.151694 | ||||||||
\(901\) | 3.19301e6 | 0.131035 | ||||||||
\(902\) | −319778. | −0.0130868 | ||||||||
\(903\) | 2.96565e7 | 1.21032 | ||||||||
\(904\) | 4.64531e6 | 0.189057 | ||||||||
\(905\) | −1.04306e7 | −0.423341 | ||||||||
\(906\) | −5.63276e6 | −0.227982 | ||||||||
\(907\) | 8.55681e6 | 0.345377 | 0.172689 | − | 0.984976i | \(-0.444755\pi\) | ||||
0.172689 | + | 0.984976i | \(0.444755\pi\) | |||||||
\(908\) | 9.79878e6 | 0.394419 | ||||||||
\(909\) | −1.23705e7 | −0.496569 | ||||||||
\(910\) | −968599. | −0.0387740 | ||||||||
\(911\) | 1.10075e7 | 0.439434 | 0.219717 | − | 0.975564i | \(-0.429487\pi\) | ||||
0.219717 | + | 0.975564i | \(0.429487\pi\) | |||||||
\(912\) | 7.39528e6 | 0.294420 | ||||||||
\(913\) | 5.51319e6 | 0.218890 | ||||||||
\(914\) | −679893. | −0.0269200 | ||||||||
\(915\) | 1.65702e7 | 0.654297 | ||||||||
\(916\) | 3.76659e7 | 1.48323 | ||||||||
\(917\) | 3.16537e6 | 0.124309 | ||||||||
\(918\) | 892938. | 0.0349715 | ||||||||
\(919\) | 2.27983e7 | 0.890458 | 0.445229 | − | 0.895417i | \(-0.353122\pi\) | ||||
0.445229 | + | 0.895417i | \(0.353122\pi\) | |||||||
\(920\) | 109173. | 0.00425252 | ||||||||
\(921\) | −3.02796e7 | −1.17626 | ||||||||
\(922\) | −3.78218e6 | −0.146526 | ||||||||
\(923\) | −2.41216e7 | −0.931968 | ||||||||
\(924\) | 9.05530e6 | 0.348918 | ||||||||
\(925\) | −2.58437e6 | −0.0993116 | ||||||||
\(926\) | −2.08643e6 | −0.0799607 | ||||||||
\(927\) | 2.80307e7 | 1.07136 | ||||||||
\(928\) | −5.63638e6 | −0.214848 | ||||||||
\(929\) | −1.70404e7 | −0.647799 | −0.323900 | − | 0.946091i | \(-0.604994\pi\) | ||||
−0.323900 | + | 0.946091i | \(0.604994\pi\) | |||||||
\(930\) | 657869. | 0.0249421 | ||||||||
\(931\) | −1.36144e6 | −0.0514784 | ||||||||
\(932\) | 1.92747e6 | 0.0726855 | ||||||||
\(933\) | −8.54978e6 | −0.321552 | ||||||||
\(934\) | −56700.3 | −0.00212676 | ||||||||
\(935\) | 3.78476e6 | 0.141582 | ||||||||
\(936\) | −4.02626e6 | −0.150215 | ||||||||
\(937\) | 1.60954e7 | 0.598898 | 0.299449 | − | 0.954112i | \(-0.403197\pi\) | ||||
0.299449 | + | 0.954112i | \(0.403197\pi\) | |||||||
\(938\) | 2.20388e6 | 0.0817864 | ||||||||
\(939\) | 5.77111e7 | 2.13597 | ||||||||
\(940\) | 1.08548e7 | 0.400685 | ||||||||
\(941\) | −4.32347e7 | −1.59169 | −0.795844 | − | 0.605501i | \(-0.792973\pi\) | ||||
−0.795844 | + | 0.605501i | \(0.792973\pi\) | |||||||
\(942\) | −3.56171e6 | −0.130777 | ||||||||
\(943\) | 488704. | 0.0178964 | ||||||||
\(944\) | 1.14253e7 | 0.417290 | ||||||||
\(945\) | 3.34385e6 | 0.121805 | ||||||||
\(946\) | 923932. | 0.0335670 | ||||||||
\(947\) | −3.07297e7 | −1.11348 | −0.556741 | − | 0.830686i | \(-0.687948\pi\) | ||||
−0.556741 | + | 0.830686i | \(0.687948\pi\) | |||||||
\(948\) | 7.13854e7 | 2.57982 | ||||||||
\(949\) | 6.00691e6 | 0.216514 | ||||||||
\(950\) | −137454. | −0.00494137 | ||||||||
\(951\) | −2.35324e7 | −0.843752 | ||||||||
\(952\) | −5.53737e6 | −0.198021 | ||||||||
\(953\) | 3.57437e7 | 1.27487 | 0.637437 | − | 0.770502i | \(-0.279995\pi\) | ||||
0.637437 | + | 0.770502i | \(0.279995\pi\) | |||||||
\(954\) | −289913. | −0.0103133 | ||||||||
\(955\) | 2.09322e7 | 0.742687 | ||||||||
\(956\) | 2.70641e7 | 0.957744 | ||||||||
\(957\) | 7.67027e6 | 0.270726 | ||||||||
\(958\) | 3.64916e6 | 0.128463 | ||||||||
\(959\) | −4.04333e6 | −0.141969 | ||||||||
\(960\) | −1.58068e7 | −0.553563 | ||||||||
\(961\) | −2.42848e7 | −0.848254 | ||||||||
\(962\) | −1.40317e6 | −0.0488848 | ||||||||
\(963\) | 4.03732e7 | 1.40290 | ||||||||
\(964\) | −4.93080e7 | −1.70893 | ||||||||
\(965\) | 2.70397e6 | 0.0934723 | ||||||||
\(966\) | 162389. | 0.00559903 | ||||||||
\(967\) | −2.23534e7 | −0.768738 | −0.384369 | − | 0.923180i | \(-0.625581\pi\) | ||||
−0.384369 | + | 0.923180i | \(0.625581\pi\) | |||||||
\(968\) | 567537. | 0.0194673 | ||||||||
\(969\) | 9.36024e6 | 0.320241 | ||||||||
\(970\) | −1.79237e6 | −0.0611642 | ||||||||
\(971\) | 2.85203e7 | 0.970747 | 0.485374 | − | 0.874307i | \(-0.338684\pi\) | ||||
0.485374 | + | 0.874307i | \(0.338684\pi\) | |||||||
\(972\) | 3.66101e7 | 1.24290 | ||||||||
\(973\) | −1.97539e7 | −0.668914 | ||||||||
\(974\) | −2.67551e6 | −0.0903670 | ||||||||
\(975\) | −7.21464e6 | −0.243054 | ||||||||
\(976\) | 3.16156e7 | 1.06237 | ||||||||
\(977\) | −1.27850e7 | −0.428514 | −0.214257 | − | 0.976777i | \(-0.568733\pi\) | ||||
−0.214257 | + | 0.976777i | \(0.568733\pi\) | |||||||
\(978\) | −3.86081e6 | −0.129072 | ||||||||
\(979\) | 8.71514e6 | 0.290615 | ||||||||
\(980\) | 2.98205e6 | 0.0991860 | ||||||||
\(981\) | 7.71695e6 | 0.256020 | ||||||||
\(982\) | −741072. | −0.0245235 | ||||||||
\(983\) | 3.98081e7 | 1.31398 | 0.656988 | − | 0.753901i | \(-0.271830\pi\) | ||||
0.656988 | + | 0.753901i | \(0.271830\pi\) | |||||||
\(984\) | 3.48485e6 | 0.114735 | ||||||||
\(985\) | −8.16735e6 | −0.268220 | ||||||||
\(986\) | −2.33153e6 | −0.0763745 | ||||||||
\(987\) | 3.24813e7 | 1.06130 | ||||||||
\(988\) | 6.36002e6 | 0.207284 | ||||||||
\(989\) | −1.41201e6 | −0.0459036 | ||||||||
\(990\) | −343642. | −0.0111434 | ||||||||
\(991\) | −1.86602e7 | −0.603576 | −0.301788 | − | 0.953375i | \(-0.597583\pi\) | ||||
−0.301788 | + | 0.953375i | \(0.597583\pi\) | |||||||
\(992\) | 3.84065e6 | 0.123916 | ||||||||
\(993\) | 1.29226e6 | 0.0415889 | ||||||||
\(994\) | 3.01213e6 | 0.0966959 | ||||||||
\(995\) | 6.35903e6 | 0.203626 | ||||||||
\(996\) | −2.98654e7 | −0.953937 | ||||||||
\(997\) | 4.30330e7 | 1.37108 | 0.685541 | − | 0.728034i | \(-0.259566\pi\) | ||||
0.685541 | + | 0.728034i | \(0.259566\pi\) | |||||||
\(998\) | −99155.0 | −0.00315129 | ||||||||
\(999\) | 4.84410e6 | 0.153568 |
(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.h.1.18 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.h.1.18 | ✓ | 40 | 1.1 | even | 1 | trivial |