Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,6,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1075.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(172.412606299\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.78745 | −0.669533 | −0.334767 | − | 0.942301i | \(-0.608657\pi\) | ||||
−0.334767 | + | 0.942301i | \(0.608657\pi\) | |||||||
\(3\) | −2.98047 | −0.191197 | −0.0955987 | − | 0.995420i | \(-0.530477\pi\) | ||||
−0.0955987 | + | 0.995420i | \(0.530477\pi\) | |||||||
\(4\) | −17.6552 | −0.551725 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 11.2884 | 0.128013 | ||||||||
\(7\) | −10.8305 | −0.0835419 | −0.0417710 | − | 0.999127i | \(-0.513300\pi\) | ||||
−0.0417710 | + | 0.999127i | \(0.513300\pi\) | |||||||
\(8\) | 188.067 | 1.03893 | ||||||||
\(9\) | −234.117 | −0.963444 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −146.993 | −0.366281 | −0.183140 | − | 0.983087i | \(-0.558626\pi\) | ||||
−0.183140 | + | 0.983087i | \(0.558626\pi\) | |||||||
\(12\) | 52.6209 | 0.105488 | ||||||||
\(13\) | −212.624 | −0.348942 | −0.174471 | − | 0.984662i | \(-0.555822\pi\) | ||||
−0.174471 | + | 0.984662i | \(0.555822\pi\) | |||||||
\(14\) | 41.0201 | 0.0559341 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −147.327 | −0.143874 | ||||||||
\(17\) | −1714.81 | −1.43911 | −0.719556 | − | 0.694434i | \(-0.755655\pi\) | ||||
−0.719556 | + | 0.694434i | \(0.755655\pi\) | |||||||
\(18\) | 886.706 | 0.645057 | ||||||||
\(19\) | −945.260 | −0.600714 | −0.300357 | − | 0.953827i | \(-0.597106\pi\) | ||||
−0.300357 | + | 0.953827i | \(0.597106\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 32.2801 | 0.0159730 | ||||||||
\(22\) | 556.728 | 0.245237 | ||||||||
\(23\) | 672.673 | 0.265145 | 0.132573 | − | 0.991173i | \(-0.457676\pi\) | ||||
0.132573 | + | 0.991173i | \(0.457676\pi\) | |||||||
\(24\) | −560.528 | −0.198641 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 805.303 | 0.233628 | ||||||||
\(27\) | 1422.03 | 0.375405 | ||||||||
\(28\) | 191.215 | 0.0460922 | ||||||||
\(29\) | −7059.06 | −1.55866 | −0.779330 | − | 0.626613i | \(-0.784441\pi\) | ||||
−0.779330 | + | 0.626613i | \(0.784441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2752.37 | −0.514403 | −0.257201 | − | 0.966358i | \(-0.582800\pi\) | ||||
−0.257201 | + | 0.966358i | \(0.582800\pi\) | |||||||
\(32\) | −5460.14 | −0.942603 | ||||||||
\(33\) | 438.108 | 0.0700320 | ||||||||
\(34\) | 6494.78 | 0.963534 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4133.38 | 0.531556 | ||||||||
\(37\) | 6574.22 | 0.789478 | 0.394739 | − | 0.918793i | \(-0.370835\pi\) | ||||
0.394739 | + | 0.918793i | \(0.370835\pi\) | |||||||
\(38\) | 3580.13 | 0.402198 | ||||||||
\(39\) | 633.720 | 0.0667169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8613.44 | −0.800234 | −0.400117 | − | 0.916464i | \(-0.631030\pi\) | ||||
−0.400117 | + | 0.916464i | \(0.631030\pi\) | |||||||
\(42\) | −122.259 | −0.0106945 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | 2595.19 | 0.202087 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2547.72 | −0.177524 | ||||||||
\(47\) | −10163.7 | −0.671131 | −0.335565 | − | 0.942017i | \(-0.608927\pi\) | ||||
−0.335565 | + | 0.942017i | \(0.608927\pi\) | |||||||
\(48\) | 439.103 | 0.0275083 | ||||||||
\(49\) | −16689.7 | −0.993021 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5110.96 | 0.275155 | ||||||||
\(52\) | 3753.92 | 0.192520 | ||||||||
\(53\) | 16377.9 | 0.800881 | 0.400440 | − | 0.916323i | \(-0.368857\pi\) | ||||
0.400440 | + | 0.916323i | \(0.368857\pi\) | |||||||
\(54\) | −5385.88 | −0.251346 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2036.86 | −0.0867944 | ||||||||
\(57\) | 2817.32 | 0.114855 | ||||||||
\(58\) | 26735.8 | 1.04358 | ||||||||
\(59\) | 5594.08 | 0.209218 | 0.104609 | − | 0.994513i | \(-0.466641\pi\) | ||||
0.104609 | + | 0.994513i | \(0.466641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38842.8 | −1.33655 | −0.668277 | − | 0.743913i | \(-0.732968\pi\) | ||||
−0.668277 | + | 0.743913i | \(0.732968\pi\) | |||||||
\(62\) | 10424.5 | 0.344410 | ||||||||
\(63\) | 2535.61 | 0.0804879 | ||||||||
\(64\) | 25394.5 | 0.774978 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1659.31 | −0.0468887 | ||||||||
\(67\) | −47654.4 | −1.29693 | −0.648464 | − | 0.761246i | \(-0.724588\pi\) | ||||
−0.648464 | + | 0.761246i | \(0.724588\pi\) | |||||||
\(68\) | 30275.4 | 0.793995 | ||||||||
\(69\) | −2004.88 | −0.0506951 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46426.3 | 1.09300 | 0.546498 | − | 0.837461i | \(-0.315961\pi\) | ||||
0.546498 | + | 0.837461i | \(0.315961\pi\) | |||||||
\(72\) | −44029.6 | −1.00095 | ||||||||
\(73\) | −77983.9 | −1.71276 | −0.856382 | − | 0.516343i | \(-0.827293\pi\) | ||||
−0.856382 | + | 0.516343i | \(0.827293\pi\) | |||||||
\(74\) | −24899.6 | −0.528582 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16688.8 | 0.331429 | ||||||||
\(77\) | 1592.01 | 0.0305998 | ||||||||
\(78\) | −2400.18 | −0.0446692 | ||||||||
\(79\) | −16199.8 | −0.292039 | −0.146019 | − | 0.989282i | \(-0.546646\pi\) | ||||
−0.146019 | + | 0.989282i | \(0.546646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 52652.0 | 0.891667 | ||||||||
\(82\) | 32623.0 | 0.535783 | ||||||||
\(83\) | −11904.1 | −0.189671 | −0.0948355 | − | 0.995493i | \(-0.530233\pi\) | ||||
−0.0948355 | + | 0.995493i | \(0.530233\pi\) | |||||||
\(84\) | −569.912 | −0.00881271 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7003.00 | −0.102103 | ||||||||
\(87\) | 21039.3 | 0.298012 | ||||||||
\(88\) | −27644.5 | −0.380541 | ||||||||
\(89\) | 11983.9 | 0.160370 | 0.0801849 | − | 0.996780i | \(-0.474449\pi\) | ||||
0.0801849 | + | 0.996780i | \(0.474449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2302.83 | 0.0291513 | ||||||||
\(92\) | −11876.2 | −0.146287 | ||||||||
\(93\) | 8203.37 | 0.0983524 | ||||||||
\(94\) | 38494.5 | 0.449344 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16273.8 | 0.180223 | ||||||||
\(97\) | −138286. | −1.49228 | −0.746139 | − | 0.665791i | \(-0.768094\pi\) | ||||
−0.746139 | + | 0.665791i | \(0.768094\pi\) | |||||||
\(98\) | 63211.4 | 0.664860 | ||||||||
\(99\) | 34413.5 | 0.352891 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −107338. | −1.04701 | −0.523505 | − | 0.852022i | \(-0.675376\pi\) | ||||
−0.523505 | + | 0.852022i | \(0.675376\pi\) | |||||||
\(102\) | −19357.5 | −0.184225 | ||||||||
\(103\) | −184140. | −1.71024 | −0.855118 | − | 0.518434i | \(-0.826515\pi\) | ||||
−0.855118 | + | 0.518434i | \(0.826515\pi\) | |||||||
\(104\) | −39987.5 | −0.362527 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −62030.4 | −0.536216 | ||||||||
\(107\) | −224246. | −1.89350 | −0.946748 | − | 0.321975i | \(-0.895653\pi\) | ||||
−0.946748 | + | 0.321975i | \(0.895653\pi\) | |||||||
\(108\) | −25106.3 | −0.207121 | ||||||||
\(109\) | 45034.5 | 0.363061 | 0.181530 | − | 0.983385i | \(-0.441895\pi\) | ||||
0.181530 | + | 0.983385i | \(0.441895\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19594.3 | −0.150946 | ||||||||
\(112\) | 1595.63 | 0.0120195 | ||||||||
\(113\) | −54906.7 | −0.404510 | −0.202255 | − | 0.979333i | \(-0.564827\pi\) | ||||
−0.202255 | + | 0.979333i | \(0.564827\pi\) | |||||||
\(114\) | −10670.5 | −0.0768991 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 124629. | 0.859953 | ||||||||
\(117\) | 49778.8 | 0.336186 | ||||||||
\(118\) | −21187.3 | −0.140078 | ||||||||
\(119\) | 18572.3 | 0.120226 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139444. | −0.865838 | ||||||||
\(122\) | 147115. | 0.894867 | ||||||||
\(123\) | 25672.1 | 0.153003 | ||||||||
\(124\) | 48593.7 | 0.283809 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9603.49 | −0.0538893 | ||||||||
\(127\) | 178360. | 0.981272 | 0.490636 | − | 0.871365i | \(-0.336765\pi\) | ||||
0.490636 | + | 0.871365i | \(0.336765\pi\) | |||||||
\(128\) | 78544.2 | 0.423730 | ||||||||
\(129\) | −5510.89 | −0.0291573 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 155441. | 0.791384 | 0.395692 | − | 0.918383i | \(-0.370505\pi\) | ||||
0.395692 | + | 0.918383i | \(0.370505\pi\) | |||||||
\(132\) | −7734.89 | −0.0386384 | ||||||||
\(133\) | 10237.7 | 0.0501848 | ||||||||
\(134\) | 180489. | 0.868336 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −322499. | −1.49514 | ||||||||
\(137\) | −72863.2 | −0.331671 | −0.165835 | − | 0.986153i | \(-0.553032\pi\) | ||||
−0.165835 | + | 0.986153i | \(0.553032\pi\) | |||||||
\(138\) | 7593.40 | 0.0339421 | ||||||||
\(139\) | 33628.0 | 0.147626 | 0.0738132 | − | 0.997272i | \(-0.476483\pi\) | ||||
0.0738132 | + | 0.997272i | \(0.476483\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30292.6 | 0.128318 | ||||||||
\(142\) | −175837. | −0.731797 | ||||||||
\(143\) | 31254.2 | 0.127811 | ||||||||
\(144\) | 34491.7 | 0.138614 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 295360. | 1.14675 | ||||||||
\(147\) | 49743.2 | 0.189863 | ||||||||
\(148\) | −116069. | −0.435575 | ||||||||
\(149\) | −322095. | −1.18855 | −0.594277 | − | 0.804261i | \(-0.702562\pi\) | ||||
−0.594277 | + | 0.804261i | \(0.702562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 252170. | 0.900018 | 0.450009 | − | 0.893024i | \(-0.351421\pi\) | ||||
0.450009 | + | 0.893024i | \(0.351421\pi\) | |||||||
\(152\) | −177772. | −0.624100 | ||||||||
\(153\) | 401467. | 1.38650 | ||||||||
\(154\) | −6029.66 | −0.0204876 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11188.5 | −0.0368094 | ||||||||
\(157\) | −435261. | −1.40929 | −0.704646 | − | 0.709559i | \(-0.748894\pi\) | ||||
−0.704646 | + | 0.709559i | \(0.748894\pi\) | |||||||
\(158\) | 61355.8 | 0.195530 | ||||||||
\(159\) | −48813.8 | −0.153126 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7285.40 | −0.0221508 | ||||||||
\(162\) | −199417. | −0.597001 | ||||||||
\(163\) | 166832. | 0.491825 | 0.245913 | − | 0.969292i | \(-0.420912\pi\) | ||||
0.245913 | + | 0.969292i | \(0.420912\pi\) | |||||||
\(164\) | 152072. | 0.441509 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 45086.2 | 0.126991 | ||||||||
\(167\) | −380682. | −1.05626 | −0.528130 | − | 0.849163i | \(-0.677107\pi\) | ||||
−0.528130 | + | 0.849163i | \(0.677107\pi\) | |||||||
\(168\) | 6070.81 | 0.0165949 | ||||||||
\(169\) | −326084. | −0.878239 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 221301. | 0.578754 | ||||||||
\(172\) | −32644.5 | −0.0841373 | ||||||||
\(173\) | −323531. | −0.821864 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(174\) | −79685.4 | −0.199529 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21656.0 | 0.0526982 | ||||||||
\(177\) | −16673.0 | −0.0400019 | ||||||||
\(178\) | −45388.4 | −0.107373 | ||||||||
\(179\) | −722793. | −1.68609 | −0.843046 | − | 0.537841i | \(-0.819240\pi\) | ||||
−0.843046 | + | 0.537841i | \(0.819240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 554674. | 1.25847 | 0.629233 | − | 0.777217i | \(-0.283369\pi\) | ||||
0.629233 | + | 0.777217i | \(0.283369\pi\) | |||||||
\(182\) | −8721.85 | −0.0195178 | ||||||||
\(183\) | 115770. | 0.255545 | ||||||||
\(184\) | 126507. | 0.275468 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −31069.9 | −0.0658502 | ||||||||
\(187\) | 252065. | 0.527120 | ||||||||
\(188\) | 179442. | 0.370280 | ||||||||
\(189\) | −15401.4 | −0.0313621 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −465840. | −0.923961 | −0.461980 | − | 0.886890i | \(-0.652861\pi\) | ||||
−0.461980 | + | 0.886890i | \(0.652861\pi\) | |||||||
\(192\) | −75687.5 | −0.148174 | ||||||||
\(193\) | 685918. | 1.32550 | 0.662749 | − | 0.748842i | \(-0.269390\pi\) | ||||
0.662749 | + | 0.748842i | \(0.269390\pi\) | |||||||
\(194\) | 523752. | 0.999129 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 294660. | 0.547875 | ||||||||
\(197\) | −706923. | −1.29780 | −0.648898 | − | 0.760875i | \(-0.724770\pi\) | ||||
−0.648898 | + | 0.760875i | \(0.724770\pi\) | |||||||
\(198\) | −130339. | −0.236272 | ||||||||
\(199\) | 832627. | 1.49045 | 0.745225 | − | 0.666813i | \(-0.232342\pi\) | ||||
0.745225 | + | 0.666813i | \(0.232342\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 142033. | 0.247969 | ||||||||
\(202\) | 406538. | 0.701008 | ||||||||
\(203\) | 76453.3 | 0.130214 | ||||||||
\(204\) | −90235.0 | −0.151810 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 697423. | 1.14506 | ||||||||
\(207\) | −157484. | −0.255453 | ||||||||
\(208\) | 31325.2 | 0.0502037 | ||||||||
\(209\) | 138946. | 0.220030 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 586051. | 0.906211 | 0.453106 | − | 0.891457i | \(-0.350316\pi\) | ||||
0.453106 | + | 0.891457i | \(0.350316\pi\) | |||||||
\(212\) | −289155. | −0.441866 | ||||||||
\(213\) | −138372. | −0.208978 | ||||||||
\(214\) | 849319. | 1.26776 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 267437. | 0.390020 | ||||||||
\(217\) | 29809.7 | 0.0429742 | ||||||||
\(218\) | −170566. | −0.243081 | ||||||||
\(219\) | 232429. | 0.327476 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 364610. | 0.502167 | ||||||||
\(222\) | 74212.4 | 0.101063 | ||||||||
\(223\) | −294899. | −0.397110 | −0.198555 | − | 0.980090i | \(-0.563625\pi\) | ||||
−0.198555 | + | 0.980090i | \(0.563625\pi\) | |||||||
\(224\) | 59136.2 | 0.0787469 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 207956. | 0.270833 | ||||||||
\(227\) | 1.07718e6 | 1.38747 | 0.693734 | − | 0.720232i | \(-0.255965\pi\) | ||||
0.693734 | + | 0.720232i | \(0.255965\pi\) | |||||||
\(228\) | −49740.4 | −0.0633683 | ||||||||
\(229\) | 951704. | 1.19926 | 0.599630 | − | 0.800277i | \(-0.295314\pi\) | ||||
0.599630 | + | 0.800277i | \(0.295314\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4744.94 | −0.00585061 | ||||||||
\(232\) | −1.32757e6 | −1.61934 | ||||||||
\(233\) | 151423. | 0.182727 | 0.0913635 | − | 0.995818i | \(-0.470877\pi\) | ||||
0.0913635 | + | 0.995818i | \(0.470877\pi\) | |||||||
\(234\) | −188535. | −0.225088 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −98764.6 | −0.115431 | ||||||||
\(237\) | 48282.9 | 0.0558371 | ||||||||
\(238\) | −70341.9 | −0.0804955 | ||||||||
\(239\) | 424064. | 0.480216 | 0.240108 | − | 0.970746i | \(-0.422817\pi\) | ||||
0.240108 | + | 0.970746i | \(0.422817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 246268. | 0.273127 | 0.136564 | − | 0.990631i | \(-0.456394\pi\) | ||||
0.136564 | + | 0.990631i | \(0.456394\pi\) | |||||||
\(242\) | 528138. | 0.579707 | ||||||||
\(243\) | −502482. | −0.545890 | ||||||||
\(244\) | 685778. | 0.737410 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −97231.9 | −0.102440 | ||||||||
\(247\) | 200985. | 0.209614 | ||||||||
\(248\) | −517630. | −0.534429 | ||||||||
\(249\) | 35479.8 | 0.0362646 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 490250. | 0.491172 | 0.245586 | − | 0.969375i | \(-0.421020\pi\) | ||||
0.245586 | + | 0.969375i | \(0.421020\pi\) | |||||||
\(252\) | −44766.7 | −0.0444072 | ||||||||
\(253\) | −98878.1 | −0.0971178 | ||||||||
\(254\) | −675532. | −0.656994 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.11011e6 | −1.05868 | ||||||||
\(257\) | −877949. | −0.829157 | −0.414578 | − | 0.910014i | \(-0.636071\pi\) | ||||
−0.414578 | + | 0.910014i | \(0.636071\pi\) | |||||||
\(258\) | 20872.2 | 0.0195218 | ||||||||
\(259\) | −71202.3 | −0.0659545 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.65264e6 | 1.50168 | ||||||||
\(262\) | −588725. | −0.529858 | ||||||||
\(263\) | 543206. | 0.484256 | 0.242128 | − | 0.970244i | \(-0.422155\pi\) | ||||
0.242128 | + | 0.970244i | \(0.422155\pi\) | |||||||
\(264\) | 82393.5 | 0.0727584 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −38774.7 | −0.0336004 | ||||||||
\(267\) | −35717.6 | −0.0306623 | ||||||||
\(268\) | 841348. | 0.715548 | ||||||||
\(269\) | 1.04690e6 | 0.882113 | 0.441056 | − | 0.897479i | \(-0.354604\pi\) | ||||
0.441056 | + | 0.897479i | \(0.354604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.95842e6 | −1.61988 | −0.809939 | − | 0.586515i | \(-0.800500\pi\) | ||||
−0.809939 | + | 0.586515i | \(0.800500\pi\) | |||||||
\(272\) | 252638. | 0.207051 | ||||||||
\(273\) | −6863.52 | −0.00557366 | ||||||||
\(274\) | 275966. | 0.222064 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 35396.6 | 0.0279698 | ||||||||
\(277\) | −2.30455e6 | −1.80462 | −0.902311 | − | 0.431086i | \(-0.858131\pi\) | ||||
−0.902311 | + | 0.431086i | \(0.858131\pi\) | |||||||
\(278\) | −127364. | −0.0988407 | ||||||||
\(279\) | 644377. | 0.495598 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −613724. | −0.463668 | −0.231834 | − | 0.972755i | \(-0.574473\pi\) | ||||
−0.231834 | + | 0.972755i | \(0.574473\pi\) | |||||||
\(282\) | −114732. | −0.0859135 | ||||||||
\(283\) | 2.11228e6 | 1.56778 | 0.783889 | − | 0.620901i | \(-0.213233\pi\) | ||||
0.783889 | + | 0.620901i | \(0.213233\pi\) | |||||||
\(284\) | −819667. | −0.603033 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −118374. | −0.0855737 | ||||||||
\(287\) | 93288.1 | 0.0668531 | ||||||||
\(288\) | 1.27831e6 | 0.908145 | ||||||||
\(289\) | 1.52073e6 | 1.07105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 412158. | 0.285320 | ||||||||
\(292\) | 1.37682e6 | 0.944975 | ||||||||
\(293\) | −1.74950e6 | −1.19054 | −0.595272 | − | 0.803525i | \(-0.702956\pi\) | ||||
−0.595272 | + | 0.803525i | \(0.702956\pi\) | |||||||
\(294\) | −188400. | −0.127120 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.23639e6 | 0.820214 | ||||||||
\(297\) | −209029. | −0.137504 | ||||||||
\(298\) | 1.21992e6 | 0.795776 | ||||||||
\(299\) | −143026. | −0.0925205 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20025.6 | −0.0127400 | ||||||||
\(302\) | −955082. | −0.602592 | ||||||||
\(303\) | 319919. | 0.200186 | ||||||||
\(304\) | 139262. | 0.0864269 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.52054e6 | −0.928310 | ||||||||
\(307\) | −485962. | −0.294277 | −0.147139 | − | 0.989116i | \(-0.547006\pi\) | ||||
−0.147139 | + | 0.989116i | \(0.547006\pi\) | |||||||
\(308\) | −28107.3 | −0.0168827 | ||||||||
\(309\) | 548825. | 0.326993 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.09644e6 | 1.22908 | 0.614541 | − | 0.788885i | \(-0.289341\pi\) | ||||
0.614541 | + | 0.788885i | \(0.289341\pi\) | |||||||
\(312\) | 119182. | 0.0693143 | ||||||||
\(313\) | 1.34798e6 | 0.777716 | 0.388858 | − | 0.921298i | \(-0.372870\pi\) | ||||
0.388858 | + | 0.921298i | \(0.372870\pi\) | |||||||
\(314\) | 1.64853e6 | 0.943567 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 286010. | 0.161125 | ||||||||
\(317\) | −2.00382e6 | −1.11998 | −0.559991 | − | 0.828499i | \(-0.689195\pi\) | ||||
−0.559991 | + | 0.828499i | \(0.689195\pi\) | |||||||
\(318\) | 184880. | 0.102523 | ||||||||
\(319\) | 1.03763e6 | 0.570908 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 668358. | 0.362032 | ||||||||
\(322\) | 27593.1 | 0.0148307 | ||||||||
\(323\) | 1.62095e6 | 0.864494 | ||||||||
\(324\) | −929583. | −0.491955 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −631869. | −0.329293 | ||||||||
\(327\) | −134224. | −0.0694162 | ||||||||
\(328\) | −1.61990e6 | −0.831388 | ||||||||
\(329\) | 110078. | 0.0560676 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −758888. | −0.380722 | −0.190361 | − | 0.981714i | \(-0.560966\pi\) | ||||
−0.190361 | + | 0.981714i | \(0.560966\pi\) | |||||||
\(332\) | 210169. | 0.104646 | ||||||||
\(333\) | −1.53914e6 | −0.760618 | ||||||||
\(334\) | 1.44181e6 | 0.707202 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4755.72 | −0.00229810 | ||||||||
\(337\) | −280895. | −0.134732 | −0.0673658 | − | 0.997728i | \(-0.521459\pi\) | ||||
−0.0673658 | + | 0.997728i | \(0.521459\pi\) | |||||||
\(338\) | 1.23503e6 | 0.588010 | ||||||||
\(339\) | 163648. | 0.0773413 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 404579. | 0.188416 | ||||||||
\(342\) | −838168. | −0.387495 | ||||||||
\(343\) | 362787. | 0.166501 | ||||||||
\(344\) | 347735. | 0.158436 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.22536e6 | 0.550266 | ||||||||
\(347\) | 765330. | 0.341213 | 0.170606 | − | 0.985339i | \(-0.445427\pi\) | ||||
0.170606 | + | 0.985339i | \(0.445427\pi\) | |||||||
\(348\) | −371454. | −0.164421 | ||||||||
\(349\) | −2.25701e6 | −0.991906 | −0.495953 | − | 0.868349i | \(-0.665181\pi\) | ||||
−0.495953 | + | 0.868349i | \(0.665181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −302358. | −0.130995 | ||||||||
\(352\) | 802602. | 0.345258 | ||||||||
\(353\) | 4.13031e6 | 1.76419 | 0.882096 | − | 0.471071i | \(-0.156132\pi\) | ||||
0.882096 | + | 0.471071i | \(0.156132\pi\) | |||||||
\(354\) | 63148.2 | 0.0267826 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −211578. | −0.0884801 | ||||||||
\(357\) | −55354.4 | −0.0229869 | ||||||||
\(358\) | 2.73754e6 | 1.12889 | ||||||||
\(359\) | 2.18583e6 | 0.895116 | 0.447558 | − | 0.894255i | \(-0.352294\pi\) | ||||
0.447558 | + | 0.894255i | \(0.352294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.58258e6 | −0.639143 | ||||||||
\(362\) | −2.10080e6 | −0.842585 | ||||||||
\(363\) | 415609. | 0.165546 | ||||||||
\(364\) | −40656.9 | −0.0160835 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −438473. | −0.171096 | ||||||||
\(367\) | 970044. | 0.375947 | 0.187973 | − | 0.982174i | \(-0.439808\pi\) | ||||
0.187973 | + | 0.982174i | \(0.439808\pi\) | |||||||
\(368\) | −99102.7 | −0.0381475 | ||||||||
\(369\) | 2.01655e6 | 0.770980 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −177381. | −0.0669071 | ||||||||
\(372\) | −144832. | −0.0542635 | ||||||||
\(373\) | 1.00486e6 | 0.373969 | 0.186984 | − | 0.982363i | \(-0.440129\pi\) | ||||
0.186984 | + | 0.982363i | \(0.440129\pi\) | |||||||
\(374\) | −954685. | −0.352924 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.91145e6 | −0.697259 | ||||||||
\(377\) | 1.50092e6 | 0.543883 | ||||||||
\(378\) | 58332.0 | 0.0209980 | ||||||||
\(379\) | 2.83101e6 | 1.01238 | 0.506190 | − | 0.862422i | \(-0.331054\pi\) | ||||
0.506190 | + | 0.862422i | \(0.331054\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −531599. | −0.187617 | ||||||||
\(382\) | 1.76435e6 | 0.618623 | ||||||||
\(383\) | 4.39503e6 | 1.53096 | 0.765482 | − | 0.643458i | \(-0.222501\pi\) | ||||
0.765482 | + | 0.643458i | \(0.222501\pi\) | |||||||
\(384\) | −234099. | −0.0810160 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.59788e6 | −0.887465 | ||||||||
\(387\) | −432882. | −0.146924 | ||||||||
\(388\) | 2.44147e6 | 0.823327 | ||||||||
\(389\) | 1.76227e6 | 0.590470 | 0.295235 | − | 0.955425i | \(-0.404602\pi\) | ||||
0.295235 | + | 0.955425i | \(0.404602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.15351e6 | −0.381574 | ||||||||
\(392\) | −3.13878e6 | −1.03168 | ||||||||
\(393\) | −463288. | −0.151311 | ||||||||
\(394\) | 2.67744e6 | 0.868918 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −607577. | −0.194699 | ||||||||
\(397\) | 2.47331e6 | 0.787595 | 0.393798 | − | 0.919197i | \(-0.371161\pi\) | ||||
0.393798 | + | 0.919197i | \(0.371161\pi\) | |||||||
\(398\) | −3.15353e6 | −0.997906 | ||||||||
\(399\) | −30513.1 | −0.00959520 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.64980e6 | −0.512355 | −0.256177 | − | 0.966630i | \(-0.582463\pi\) | ||||
−0.256177 | + | 0.966630i | \(0.582463\pi\) | |||||||
\(402\) | −537941. | −0.166024 | ||||||||
\(403\) | 585220. | 0.179497 | ||||||||
\(404\) | 1.89508e6 | 0.577662 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −289563. | −0.0871823 | ||||||||
\(407\) | −966364. | −0.289171 | ||||||||
\(408\) | 961201. | 0.285867 | ||||||||
\(409\) | −1.68762e6 | −0.498845 | −0.249422 | − | 0.968395i | \(-0.580241\pi\) | ||||
−0.249422 | + | 0.968395i | \(0.580241\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 217167. | 0.0634145 | ||||||||
\(412\) | 3.25104e6 | 0.943580 | ||||||||
\(413\) | −60586.8 | −0.0174785 | ||||||||
\(414\) | 596463. | 0.171034 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.16096e6 | 0.328914 | ||||||||
\(417\) | −100227. | −0.0282258 | ||||||||
\(418\) | −526253. | −0.147317 | ||||||||
\(419\) | 5.53289e6 | 1.53963 | 0.769816 | − | 0.638266i | \(-0.220348\pi\) | ||||
0.769816 | + | 0.638266i | \(0.220348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.66009e6 | 1.55639 | 0.778194 | − | 0.628024i | \(-0.216136\pi\) | ||||
0.778194 | + | 0.628024i | \(0.216136\pi\) | |||||||
\(422\) | −2.21964e6 | −0.606738 | ||||||||
\(423\) | 2.37949e6 | 0.646597 | ||||||||
\(424\) | 3.08013e6 | 0.832060 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 524079. | 0.139918 | ||||||||
\(427\) | 420688. | 0.111658 | ||||||||
\(428\) | 3.95910e6 | 1.04469 | ||||||||
\(429\) | −93152.2 | −0.0244371 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.71981e6 | 1.74247 | 0.871233 | − | 0.490871i | \(-0.163321\pi\) | ||||
0.871233 | + | 0.490871i | \(0.163321\pi\) | |||||||
\(432\) | −209504. | −0.0540110 | ||||||||
\(433\) | 909356. | 0.233085 | 0.116542 | − | 0.993186i | \(-0.462819\pi\) | ||||
0.116542 | + | 0.993186i | \(0.462819\pi\) | |||||||
\(434\) | −112903. | −0.0287726 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −795094. | −0.200310 | ||||||||
\(437\) | −635851. | −0.159276 | ||||||||
\(438\) | −880313. | −0.219256 | ||||||||
\(439\) | −3.11990e6 | −0.772644 | −0.386322 | − | 0.922364i | \(-0.626255\pi\) | ||||
−0.386322 | + | 0.922364i | \(0.626255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.90734e6 | 0.956719 | ||||||||
\(442\) | −1.38094e6 | −0.336218 | ||||||||
\(443\) | −3.60692e6 | −0.873228 | −0.436614 | − | 0.899649i | \(-0.643822\pi\) | ||||
−0.436614 | + | 0.899649i | \(0.643822\pi\) | |||||||
\(444\) | 345941. | 0.0832808 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.11691e6 | 0.265878 | ||||||||
\(447\) | 959996. | 0.227248 | ||||||||
\(448\) | −275036. | −0.0647432 | ||||||||
\(449\) | 6.14057e6 | 1.43745 | 0.718726 | − | 0.695294i | \(-0.244726\pi\) | ||||
0.718726 | + | 0.695294i | \(0.244726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.26611e6 | 0.293110 | ||||||||
\(452\) | 969389. | 0.223178 | ||||||||
\(453\) | −751586. | −0.172081 | ||||||||
\(454\) | −4.07976e6 | −0.928955 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 529845. | 0.119326 | ||||||||
\(457\) | 2.84240e6 | 0.636642 | 0.318321 | − | 0.947983i | \(-0.396881\pi\) | ||||
0.318321 | + | 0.947983i | \(0.396881\pi\) | |||||||
\(458\) | −3.60453e6 | −0.802944 | ||||||||
\(459\) | −2.43852e6 | −0.540251 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.87847e6 | −1.06913 | −0.534566 | − | 0.845127i | \(-0.679525\pi\) | ||||
−0.534566 | + | 0.845127i | \(0.679525\pi\) | |||||||
\(462\) | 17971.2 | 0.00391718 | ||||||||
\(463\) | −6.64392e6 | −1.44036 | −0.720182 | − | 0.693786i | \(-0.755942\pi\) | ||||
−0.720182 | + | 0.693786i | \(0.755942\pi\) | |||||||
\(464\) | 1.03999e6 | 0.224250 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −573508. | −0.122342 | ||||||||
\(467\) | −569835. | −0.120908 | −0.0604542 | − | 0.998171i | \(-0.519255\pi\) | ||||
−0.0604542 | + | 0.998171i | \(0.519255\pi\) | |||||||
\(468\) | −878856. | −0.185482 | ||||||||
\(469\) | 516122. | 0.108348 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.29728e6 | 0.269453 | ||||||||
\(472\) | 1.05206e6 | 0.217363 | ||||||||
\(473\) | −271790. | −0.0558573 | ||||||||
\(474\) | −182869. | −0.0373848 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −327899. | −0.0663319 | ||||||||
\(477\) | −3.83433e6 | −0.771603 | ||||||||
\(478\) | −1.60612e6 | −0.321520 | ||||||||
\(479\) | −3.00681e6 | −0.598779 | −0.299390 | − | 0.954131i | \(-0.596783\pi\) | ||||
−0.299390 | + | 0.954131i | \(0.596783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.39784e6 | −0.275482 | ||||||||
\(482\) | −932727. | −0.182868 | ||||||||
\(483\) | 21713.9 | 0.00423517 | ||||||||
\(484\) | 2.46192e6 | 0.477705 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.90313e6 | 0.365491 | ||||||||
\(487\) | 316355. | 0.0604438 | 0.0302219 | − | 0.999543i | \(-0.490379\pi\) | ||||
0.0302219 | + | 0.999543i | \(0.490379\pi\) | |||||||
\(488\) | −7.30504e6 | −1.38859 | ||||||||
\(489\) | −497239. | −0.0940357 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.00469e7 | −1.88074 | −0.940368 | − | 0.340158i | \(-0.889519\pi\) | ||||
−0.940368 | + | 0.340158i | \(0.889519\pi\) | |||||||
\(492\) | −453247. | −0.0844154 | ||||||||
\(493\) | 1.21050e7 | 2.24309 | ||||||||
\(494\) | −761221. | −0.140344 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 405498. | 0.0740091 | ||||||||
\(497\) | −502822. | −0.0913110 | ||||||||
\(498\) | −134378. | −0.0242804 | ||||||||
\(499\) | 1.04539e7 | 1.87944 | 0.939719 | − | 0.341949i | \(-0.111087\pi\) | ||||
0.939719 | + | 0.341949i | \(0.111087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.13461e6 | 0.201954 | ||||||||
\(502\) | −1.85680e6 | −0.328856 | ||||||||
\(503\) | 6.03763e6 | 1.06401 | 0.532006 | − | 0.846741i | \(-0.321438\pi\) | ||||
0.532006 | + | 0.846741i | \(0.321438\pi\) | |||||||
\(504\) | 476864. | 0.0836215 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 374496. | 0.0650236 | ||||||||
\(507\) | 971885. | 0.167917 | ||||||||
\(508\) | −3.14899e6 | −0.541393 | ||||||||
\(509\) | −136721. | −0.0233905 | −0.0116953 | − | 0.999932i | \(-0.503723\pi\) | ||||
−0.0116953 | + | 0.999932i | \(0.503723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 844606. | 0.143088 | ||||||||
\(512\) | 1.69106e6 | 0.285091 | ||||||||
\(513\) | −1.34419e6 | −0.225511 | ||||||||
\(514\) | 3.32519e6 | 0.555148 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 97296.0 | 0.0160868 | ||||||||
\(517\) | 1.49399e6 | 0.245822 | ||||||||
\(518\) | 269675. | 0.0441588 | ||||||||
\(519\) | 964274. | 0.157138 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.40395e6 | 1.51781 | 0.758903 | − | 0.651204i | \(-0.225736\pi\) | ||||
0.758903 | + | 0.651204i | \(0.225736\pi\) | |||||||
\(522\) | −6.25931e6 | −1.00543 | ||||||||
\(523\) | 21599.2 | 0.00345290 | 0.00172645 | − | 0.999999i | \(-0.499450\pi\) | ||||
0.00172645 | + | 0.999999i | \(0.499450\pi\) | |||||||
\(524\) | −2.74434e6 | −0.436627 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.05736e6 | −0.324225 | ||||||||
\(527\) | 4.71981e6 | 0.740283 | ||||||||
\(528\) | −64545.0 | −0.0100758 | ||||||||
\(529\) | −5.98385e6 | −0.929698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.30967e6 | −0.201569 | ||||||||
\(532\) | −180748. | −0.0276882 | ||||||||
\(533\) | 1.83142e6 | 0.279235 | ||||||||
\(534\) | 135279. | 0.0205294 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.96220e6 | −1.34742 | ||||||||
\(537\) | 2.15426e6 | 0.322376 | ||||||||
\(538\) | −3.96508e6 | −0.590604 | ||||||||
\(539\) | 2.45327e6 | 0.363725 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.40079e6 | −1.08714 | −0.543570 | − | 0.839364i | \(-0.682928\pi\) | ||||
−0.543570 | + | 0.839364i | \(0.682928\pi\) | |||||||
\(542\) | 7.41741e6 | 1.08456 | ||||||||
\(543\) | −1.65319e6 | −0.240615 | ||||||||
\(544\) | 9.36313e6 | 1.35651 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 25995.2 | 0.00373175 | ||||||||
\(547\) | −4.12820e6 | −0.589919 | −0.294960 | − | 0.955510i | \(-0.595306\pi\) | ||||
−0.294960 | + | 0.955510i | \(0.595306\pi\) | |||||||
\(548\) | 1.28642e6 | 0.182991 | ||||||||
\(549\) | 9.09376e6 | 1.28769 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.67265e6 | 0.936309 | ||||||||
\(552\) | −377052. | −0.0526688 | ||||||||
\(553\) | 175452. | 0.0243975 | ||||||||
\(554\) | 8.72836e6 | 1.20825 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −593709. | −0.0814492 | ||||||||
\(557\) | 4.99309e6 | 0.681916 | 0.340958 | − | 0.940078i | \(-0.389249\pi\) | ||||
0.340958 | + | 0.940078i | \(0.389249\pi\) | |||||||
\(558\) | −2.44055e6 | −0.331819 | ||||||||
\(559\) | −393142. | −0.0532132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −751274. | −0.100784 | ||||||||
\(562\) | 2.32445e6 | 0.310441 | ||||||||
\(563\) | −6.88378e6 | −0.915285 | −0.457642 | − | 0.889136i | \(-0.651306\pi\) | ||||
−0.457642 | + | 0.889136i | \(0.651306\pi\) | |||||||
\(564\) | −534823. | −0.0707965 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.00014e6 | −1.04968 | ||||||||
\(567\) | −570249. | −0.0744916 | ||||||||
\(568\) | 8.73125e6 | 1.13555 | ||||||||
\(569\) | −9.36390e6 | −1.21248 | −0.606242 | − | 0.795280i | \(-0.707324\pi\) | ||||
−0.606242 | + | 0.795280i | \(0.707324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.30552e7 | 1.67569 | 0.837846 | − | 0.545907i | \(-0.183815\pi\) | ||||
0.837846 | + | 0.545907i | \(0.183815\pi\) | |||||||
\(572\) | −551799. | −0.0705165 | ||||||||
\(573\) | 1.38842e6 | 0.176659 | ||||||||
\(574\) | −353324. | −0.0447603 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.94527e6 | −0.746648 | ||||||||
\(577\) | −1.07959e7 | −1.34996 | −0.674978 | − | 0.737838i | \(-0.735847\pi\) | ||||
−0.674978 | + | 0.737838i | \(0.735847\pi\) | |||||||
\(578\) | −5.75969e6 | −0.717100 | ||||||||
\(579\) | −2.04436e6 | −0.253432 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 128928. | 0.0158455 | ||||||||
\(582\) | −1.56103e6 | −0.191031 | ||||||||
\(583\) | −2.40743e6 | −0.293347 | ||||||||
\(584\) | −1.46662e7 | −1.77944 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.62615e6 | 0.797108 | ||||||||
\(587\) | 5.25307e6 | 0.629242 | 0.314621 | − | 0.949217i | \(-0.398123\pi\) | ||||
0.314621 | + | 0.949217i | \(0.398123\pi\) | |||||||
\(588\) | −878227. | −0.104752 | ||||||||
\(589\) | 2.60171e6 | 0.309009 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.10697e6 | 0.248135 | ||||||||
\(592\) | −968559. | −0.113585 | ||||||||
\(593\) | −2.99811e6 | −0.350116 | −0.175058 | − | 0.984558i | \(-0.556011\pi\) | ||||
−0.175058 | + | 0.984558i | \(0.556011\pi\) | |||||||
\(594\) | 791686. | 0.0920634 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.68666e6 | 0.655755 | ||||||||
\(597\) | −2.48162e6 | −0.284970 | ||||||||
\(598\) | 541705. | 0.0619455 | ||||||||
\(599\) | −1.24700e7 | −1.42004 | −0.710019 | − | 0.704183i | \(-0.751314\pi\) | ||||
−0.710019 | + | 0.704183i | \(0.751314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.04108e6 | −0.569295 | −0.284647 | − | 0.958632i | \(-0.591877\pi\) | ||||
−0.284647 | + | 0.958632i | \(0.591877\pi\) | |||||||
\(602\) | 75846.2 | 0.00852987 | ||||||||
\(603\) | 1.11567e7 | 1.24952 | ||||||||
\(604\) | −4.45212e6 | −0.496563 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.21168e6 | −0.134031 | ||||||||
\(607\) | 6.79133e6 | 0.748140 | 0.374070 | − | 0.927400i | \(-0.377962\pi\) | ||||
0.374070 | + | 0.927400i | \(0.377962\pi\) | |||||||
\(608\) | 5.16126e6 | 0.566235 | ||||||||
\(609\) | −227867. | −0.0248965 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.16105e6 | 0.234186 | ||||||||
\(612\) | −7.08798e6 | −0.764969 | ||||||||
\(613\) | −483060. | −0.0519218 | −0.0259609 | − | 0.999663i | \(-0.508265\pi\) | ||||
−0.0259609 | + | 0.999663i | \(0.508265\pi\) | |||||||
\(614\) | 1.84056e6 | 0.197028 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 299404. | 0.0317911 | ||||||||
\(617\) | −5.47210e6 | −0.578683 | −0.289342 | − | 0.957226i | \(-0.593436\pi\) | ||||
−0.289342 | + | 0.957226i | \(0.593436\pi\) | |||||||
\(618\) | −2.07865e6 | −0.218932 | ||||||||
\(619\) | −9.25381e6 | −0.970720 | −0.485360 | − | 0.874314i | \(-0.661311\pi\) | ||||
−0.485360 | + | 0.874314i | \(0.661311\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 956563. | 0.0995370 | ||||||||
\(622\) | −7.94016e6 | −0.822911 | ||||||||
\(623\) | −129792. | −0.0133976 | ||||||||
\(624\) | −93363.9 | −0.00959881 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.10539e6 | −0.520707 | ||||||||
\(627\) | −414126. | −0.0420692 | ||||||||
\(628\) | 7.68463e6 | 0.777542 | ||||||||
\(629\) | −1.12736e7 | −1.13615 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.73727e6 | 0.173698 | 0.0868490 | − | 0.996221i | \(-0.472320\pi\) | ||||
0.0868490 | + | 0.996221i | \(0.472320\pi\) | |||||||
\(632\) | −3.04664e6 | −0.303409 | ||||||||
\(633\) | −1.74671e6 | −0.173265 | ||||||||
\(634\) | 7.58937e6 | 0.749865 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 861818. | 0.0844836 | ||||||||
\(637\) | 3.54863e6 | 0.346507 | ||||||||
\(638\) | −3.92998e6 | −0.382242 | ||||||||
\(639\) | −1.08692e7 | −1.05304 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.39085e7 | 1.33701 | 0.668506 | − | 0.743707i | \(-0.266934\pi\) | ||||
0.668506 | + | 0.743707i | \(0.266934\pi\) | |||||||
\(642\) | −2.53137e6 | −0.242392 | ||||||||
\(643\) | −9.27278e6 | −0.884468 | −0.442234 | − | 0.896900i | \(-0.645814\pi\) | ||||
−0.442234 | + | 0.896900i | \(0.645814\pi\) | |||||||
\(644\) | 128625. | 0.0122211 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.13925e6 | −0.578808 | ||||||||
\(647\) | 8.98311e6 | 0.843657 | 0.421828 | − | 0.906676i | \(-0.361388\pi\) | ||||
0.421828 | + | 0.906676i | \(0.361388\pi\) | |||||||
\(648\) | 9.90210e6 | 0.926381 | ||||||||
\(649\) | −822289. | −0.0766325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −88846.9 | −0.00821655 | ||||||||
\(652\) | −2.94546e6 | −0.271352 | ||||||||
\(653\) | −2.57150e6 | −0.235995 | −0.117998 | − | 0.993014i | \(-0.537647\pi\) | ||||
−0.117998 | + | 0.993014i | \(0.537647\pi\) | |||||||
\(654\) | 508367. | 0.0464765 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.26899e6 | 0.115133 | ||||||||
\(657\) | 1.82573e7 | 1.65015 | ||||||||
\(658\) | −416916. | −0.0375391 | ||||||||
\(659\) | −1.46805e7 | −1.31683 | −0.658413 | − | 0.752657i | \(-0.728772\pi\) | ||||
−0.658413 | + | 0.752657i | \(0.728772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.36060e7 | −1.21123 | −0.605617 | − | 0.795756i | \(-0.707074\pi\) | ||||
−0.605617 | + | 0.795756i | \(0.707074\pi\) | |||||||
\(662\) | 2.87425e6 | 0.254906 | ||||||||
\(663\) | −1.08671e6 | −0.0960131 | ||||||||
\(664\) | −2.23876e6 | −0.197055 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.82940e6 | 0.509259 | ||||||||
\(667\) | −4.74843e6 | −0.413272 | ||||||||
\(668\) | 6.72102e6 | 0.582766 | ||||||||
\(669\) | 878937. | 0.0759263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.70962e6 | 0.489554 | ||||||||
\(672\) | −176254. | −0.0150562 | ||||||||
\(673\) | −7.41285e6 | −0.630882 | −0.315441 | − | 0.948945i | \(-0.602152\pi\) | ||||
−0.315441 | + | 0.948945i | \(0.602152\pi\) | |||||||
\(674\) | 1.06388e6 | 0.0902073 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.75708e6 | 0.484547 | ||||||||
\(677\) | −1.02447e7 | −0.859066 | −0.429533 | − | 0.903051i | \(-0.641322\pi\) | ||||
−0.429533 | + | 0.903051i | \(0.641322\pi\) | |||||||
\(678\) | −619809. | −0.0517825 | ||||||||
\(679\) | 1.49771e6 | 0.124668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.21050e6 | −0.265280 | ||||||||
\(682\) | −1.53232e6 | −0.126151 | ||||||||
\(683\) | −1.68904e7 | −1.38544 | −0.692722 | − | 0.721204i | \(-0.743589\pi\) | ||||
−0.692722 | + | 0.721204i | \(0.743589\pi\) | |||||||
\(684\) | −3.90712e6 | −0.319313 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.37404e6 | −0.111478 | ||||||||
\(687\) | −2.83653e6 | −0.229295 | ||||||||
\(688\) | −272407. | −0.0219405 | ||||||||
\(689\) | −3.48233e6 | −0.279461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.55786e7 | 1.24117 | 0.620587 | − | 0.784138i | \(-0.286894\pi\) | ||||
0.620587 | + | 0.784138i | \(0.286894\pi\) | |||||||
\(692\) | 5.71200e6 | 0.453443 | ||||||||
\(693\) | −372716. | −0.0294812 | ||||||||
\(694\) | −2.89865e6 | −0.228453 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.95680e6 | 0.309614 | ||||||||
\(697\) | 1.47704e7 | 1.15163 | ||||||||
\(698\) | 8.54832e6 | 0.664114 | ||||||||
\(699\) | −451313. | −0.0349369 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.98268e6 | −0.767277 | −0.383638 | − | 0.923483i | \(-0.625329\pi\) | ||||
−0.383638 | + | 0.923483i | \(0.625329\pi\) | |||||||
\(702\) | 1.14517e6 | 0.0877054 | ||||||||
\(703\) | −6.21435e6 | −0.474250 | ||||||||
\(704\) | −3.73281e6 | −0.283860 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.56433e7 | −1.18118 | ||||||||
\(707\) | 1.16253e6 | 0.0874693 | ||||||||
\(708\) | 294365. | 0.0220701 | ||||||||
\(709\) | 7.97811e6 | 0.596052 | 0.298026 | − | 0.954558i | \(-0.403672\pi\) | ||||
0.298026 | + | 0.954558i | \(0.403672\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.79264e6 | 0.281363 | ||||||||
\(712\) | 2.25377e6 | 0.166613 | ||||||||
\(713\) | −1.85145e6 | −0.136392 | ||||||||
\(714\) | 209652. | 0.0153905 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.27611e7 | 0.930260 | ||||||||
\(717\) | −1.26391e6 | −0.0918160 | ||||||||
\(718\) | −8.27871e6 | −0.599310 | ||||||||
\(719\) | −1.13203e7 | −0.816647 | −0.408323 | − | 0.912837i | \(-0.633886\pi\) | ||||
−0.408323 | + | 0.912837i | \(0.633886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.99434e6 | 0.142876 | ||||||||
\(722\) | 5.99395e6 | 0.427928 | ||||||||
\(723\) | −733994. | −0.0522212 | ||||||||
\(724\) | −9.79289e6 | −0.694328 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.57410e6 | −0.110839 | ||||||||
\(727\) | −7.31325e6 | −0.513186 | −0.256593 | − | 0.966520i | \(-0.582600\pi\) | ||||
−0.256593 | + | 0.966520i | \(0.582600\pi\) | |||||||
\(728\) | 433085. | 0.0302862 | ||||||||
\(729\) | −1.12968e7 | −0.787294 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.17069e6 | −0.219463 | ||||||||
\(732\) | −2.04394e6 | −0.140991 | ||||||||
\(733\) | −3.97186e6 | −0.273045 | −0.136522 | − | 0.990637i | \(-0.543593\pi\) | ||||
−0.136522 | + | 0.990637i | \(0.543593\pi\) | |||||||
\(734\) | −3.67400e6 | −0.251709 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.67289e6 | −0.249927 | ||||||||
\(737\) | 7.00485e6 | 0.475040 | ||||||||
\(738\) | −7.63759e6 | −0.516197 | ||||||||
\(739\) | −2.00272e7 | −1.34899 | −0.674495 | − | 0.738279i | \(-0.735639\pi\) | ||||
−0.674495 | + | 0.738279i | \(0.735639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −599030. | −0.0400777 | ||||||||
\(742\) | 671822. | 0.0447965 | ||||||||
\(743\) | −1.61504e7 | −1.07327 | −0.536637 | − | 0.843813i | \(-0.680306\pi\) | ||||
−0.536637 | + | 0.843813i | \(0.680306\pi\) | |||||||
\(744\) | 1.54278e6 | 0.102181 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.80587e6 | −0.250384 | ||||||||
\(747\) | 2.78695e6 | 0.182737 | ||||||||
\(748\) | −4.45027e6 | −0.290825 | ||||||||
\(749\) | 2.42870e6 | 0.158186 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.43119e7 | 1.57297 | 0.786484 | − | 0.617611i | \(-0.211899\pi\) | ||||
0.786484 | + | 0.617611i | \(0.211899\pi\) | |||||||
\(752\) | 1.49738e6 | 0.0965581 | ||||||||
\(753\) | −1.46118e6 | −0.0939107 | ||||||||
\(754\) | −5.68468e6 | −0.364148 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 271914. | 0.0173033 | ||||||||
\(757\) | −5.71154e6 | −0.362254 | −0.181127 | − | 0.983460i | \(-0.557975\pi\) | ||||
−0.181127 | + | 0.983460i | \(0.557975\pi\) | |||||||
\(758\) | −1.07223e7 | −0.677822 | ||||||||
\(759\) | 294703. | 0.0185687 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.33266e6 | −0.584176 | −0.292088 | − | 0.956391i | \(-0.594350\pi\) | ||||
−0.292088 | + | 0.956391i | \(0.594350\pi\) | |||||||
\(762\) | 2.01340e6 | 0.125616 | ||||||||
\(763\) | −487747. | −0.0303308 | ||||||||
\(764\) | 8.22451e6 | 0.509773 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.66460e7 | −1.02503 | ||||||||
\(767\) | −1.18943e6 | −0.0730049 | ||||||||
\(768\) | 3.30864e6 | 0.202417 | ||||||||
\(769\) | −1.06417e7 | −0.648928 | −0.324464 | − | 0.945898i | \(-0.605184\pi\) | ||||
−0.324464 | + | 0.945898i | \(0.605184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.61670e6 | 0.158533 | ||||||||
\(772\) | −1.21100e7 | −0.731311 | ||||||||
\(773\) | 6.61915e6 | 0.398431 | 0.199216 | − | 0.979956i | \(-0.436161\pi\) | ||||
0.199216 | + | 0.979956i | \(0.436161\pi\) | |||||||
\(774\) | 1.63952e6 | 0.0983703 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.60070e7 | −1.55037 | ||||||||
\(777\) | 212217. | 0.0126103 | ||||||||
\(778\) | −6.67450e6 | −0.395339 | ||||||||
\(779\) | 8.14194e6 | 0.480711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.82434e6 | −0.400344 | ||||||||
\(782\) | 4.36886e6 | 0.255477 | ||||||||
\(783\) | −1.00382e7 | −0.585130 | ||||||||
\(784\) | 2.45884e6 | 0.142870 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.75468e6 | 0.101307 | ||||||||
\(787\) | −1.82917e7 | −1.05273 | −0.526367 | − | 0.850258i | \(-0.676446\pi\) | ||||
−0.526367 | + | 0.850258i | \(0.676446\pi\) | |||||||
\(788\) | 1.24809e7 | 0.716027 | ||||||||
\(789\) | −1.61901e6 | −0.0925884 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 594669. | 0.0337935 | ||||||||
\(792\) | 6.47203e6 | 0.366630 | ||||||||
\(793\) | 8.25891e6 | 0.466380 | ||||||||
\(794\) | −9.36756e6 | −0.527321 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.47002e7 | −0.822319 | ||||||||
\(797\) | 1.38959e7 | 0.774889 | 0.387444 | − | 0.921893i | \(-0.373358\pi\) | ||||
0.387444 | + | 0.921893i | \(0.373358\pi\) | |||||||
\(798\) | 115567. | 0.00642430 | ||||||||
\(799\) | 1.74289e7 | 0.965833 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.80563e6 | −0.154507 | ||||||||
\(802\) | 6.24854e6 | 0.343038 | ||||||||
\(803\) | 1.14631e7 | 0.627353 | ||||||||
\(804\) | −2.50761e6 | −0.136811 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.21649e6 | −0.120179 | ||||||||
\(807\) | −3.12025e6 | −0.168658 | ||||||||
\(808\) | −2.01867e7 | −1.08777 | ||||||||
\(809\) | −2.37890e7 | −1.27792 | −0.638961 | − | 0.769239i | \(-0.720636\pi\) | ||||
−0.638961 | + | 0.769239i | \(0.720636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.19292e6 | −0.330631 | −0.165315 | − | 0.986241i | \(-0.552864\pi\) | ||||
−0.165315 | + | 0.986241i | \(0.552864\pi\) | |||||||
\(812\) | −1.34980e6 | −0.0718421 | ||||||||
\(813\) | 5.83701e6 | 0.309716 | ||||||||
\(814\) | 3.66006e6 | 0.193609 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −752981. | −0.0395875 | ||||||||
\(817\) | −1.74779e6 | −0.0916080 | ||||||||
\(818\) | 6.39177e6 | 0.333993 | ||||||||
\(819\) | −539131. | −0.0280857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.66592e7 | −0.862575 | −0.431288 | − | 0.902215i | \(-0.641941\pi\) | ||||
−0.431288 | + | 0.902215i | \(0.641941\pi\) | |||||||
\(822\) | −822509. | −0.0424581 | ||||||||
\(823\) | 2.43775e6 | 0.125455 | 0.0627277 | − | 0.998031i | \(-0.480020\pi\) | ||||
0.0627277 | + | 0.998031i | \(0.480020\pi\) | |||||||
\(824\) | −3.46307e7 | −1.77682 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 229470. | 0.0117024 | ||||||||
\(827\) | 1.14098e7 | 0.580116 | 0.290058 | − | 0.957009i | \(-0.406325\pi\) | ||||
0.290058 | + | 0.957009i | \(0.406325\pi\) | |||||||
\(828\) | 2.78041e6 | 0.140940 | ||||||||
\(829\) | −1.29460e7 | −0.654259 | −0.327129 | − | 0.944980i | \(-0.606081\pi\) | ||||
−0.327129 | + | 0.944980i | \(0.606081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.86864e6 | 0.345039 | ||||||||
\(832\) | −5.39947e6 | −0.270423 | ||||||||
\(833\) | 2.86197e7 | 1.42907 | ||||||||
\(834\) | 379606. | 0.0188981 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.45313e6 | −0.121396 | ||||||||
\(837\) | −3.91397e6 | −0.193109 | ||||||||
\(838\) | −2.09556e7 | −1.03083 | ||||||||
\(839\) | 1.34123e7 | 0.657804 | 0.328902 | − | 0.944364i | \(-0.393321\pi\) | ||||
0.328902 | + | 0.944364i | \(0.393321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.93191e7 | 1.42942 | ||||||||
\(842\) | −2.14373e7 | −1.04205 | ||||||||
\(843\) | 1.82919e6 | 0.0886522 | ||||||||
\(844\) | −1.03469e7 | −0.499980 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.01221e6 | −0.432918 | ||||||||
\(847\) | 1.51025e6 | 0.0723338 | ||||||||
\(848\) | −2.41290e6 | −0.115226 | ||||||||
\(849\) | −6.29558e6 | −0.299755 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.42230e6 | 0.209327 | ||||||||
\(852\) | 2.44299e6 | 0.115298 | ||||||||
\(853\) | −3.55781e7 | −1.67421 | −0.837105 | − | 0.547042i | \(-0.815754\pi\) | ||||
−0.837105 | + | 0.547042i | \(0.815754\pi\) | |||||||
\(854\) | −1.59334e6 | −0.0747589 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.21731e7 | −1.96721 | ||||||||
\(857\) | 1.51251e7 | 0.703469 | 0.351735 | − | 0.936100i | \(-0.385592\pi\) | ||||
0.351735 | + | 0.936100i | \(0.385592\pi\) | |||||||
\(858\) | 352810. | 0.0163615 | ||||||||
\(859\) | 5.71909e6 | 0.264450 | 0.132225 | − | 0.991220i | \(-0.457788\pi\) | ||||
0.132225 | + | 0.991220i | \(0.457788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −278042. | −0.0127821 | ||||||||
\(862\) | −2.54510e7 | −1.16664 | ||||||||
\(863\) | −3.51869e7 | −1.60825 | −0.804125 | − | 0.594460i | \(-0.797366\pi\) | ||||
−0.804125 | + | 0.594460i | \(0.797366\pi\) | |||||||
\(864\) | −7.76450e6 | −0.353858 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.44414e6 | −0.156058 | ||||||||
\(867\) | −4.53250e6 | −0.204781 | ||||||||
\(868\) | −526296. | −0.0237099 | ||||||||
\(869\) | 2.38125e6 | 0.106968 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.01325e7 | 0.452553 | ||||||||
\(872\) | 8.46949e6 | 0.377195 | ||||||||
\(873\) | 3.23751e7 | 1.43773 | ||||||||
\(874\) | 2.40825e6 | 0.106641 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.10358e6 | −0.180677 | ||||||||
\(877\) | −2.79568e7 | −1.22740 | −0.613702 | − | 0.789537i | \(-0.710320\pi\) | ||||
−0.613702 | + | 0.789537i | \(0.710320\pi\) | |||||||
\(878\) | 1.18165e7 | 0.517310 | ||||||||
\(879\) | 5.21434e6 | 0.227629 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.91377e7 | 1.69885 | 0.849425 | − | 0.527709i | \(-0.176949\pi\) | ||||
0.849425 | + | 0.527709i | \(0.176949\pi\) | |||||||
\(882\) | −1.47989e7 | −0.640555 | ||||||||
\(883\) | −4.10119e7 | −1.77014 | −0.885071 | − | 0.465456i | \(-0.845890\pi\) | ||||
−0.885071 | + | 0.465456i | \(0.845890\pi\) | |||||||
\(884\) | −6.43728e6 | −0.277058 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.36610e7 | 0.584655 | ||||||||
\(887\) | 4.27594e7 | 1.82483 | 0.912415 | − | 0.409267i | \(-0.134215\pi\) | ||||
0.912415 | + | 0.409267i | \(0.134215\pi\) | |||||||
\(888\) | −3.68503e6 | −0.156823 | ||||||||
\(889\) | −1.93174e6 | −0.0819774 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.73947e6 | −0.326601 | ||||||||
\(892\) | 5.20650e6 | 0.219095 | ||||||||
\(893\) | 9.60734e6 | 0.403157 | ||||||||
\(894\) | −3.63594e6 | −0.152150 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −850675. | −0.0353992 | ||||||||
\(897\) | 426286. | 0.0176897 | ||||||||
\(898\) | −2.32571e7 | −0.962421 | ||||||||
\(899\) | 1.94292e7 | 0.801779 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.80850e7 | −1.15256 | ||||||||
\(902\) | −4.79534e6 | −0.196247 | ||||||||
\(903\) | 59685.9 | 0.00243586 | ||||||||
\(904\) | −1.03261e7 | −0.420258 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.84660e6 | 0.115214 | ||||||||
\(907\) | 3.87469e7 | 1.56394 | 0.781968 | − | 0.623319i | \(-0.214216\pi\) | ||||
0.781968 | + | 0.623319i | \(0.214216\pi\) | |||||||
\(908\) | −1.90178e7 | −0.765501 | ||||||||
\(909\) | 2.51297e7 | 1.00874 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.26167e7 | −0.902885 | −0.451443 | − | 0.892300i | \(-0.649090\pi\) | ||||
−0.451443 | + | 0.892300i | \(0.649090\pi\) | |||||||
\(912\) | −415067. | −0.0165246 | ||||||||
\(913\) | 1.74982e6 | 0.0694729 | ||||||||
\(914\) | −1.07655e7 | −0.426253 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.68025e7 | −0.661662 | ||||||||
\(917\) | −1.68351e6 | −0.0661138 | ||||||||
\(918\) | 9.23579e6 | 0.361716 | ||||||||
\(919\) | −3.75628e7 | −1.46713 | −0.733566 | − | 0.679618i | \(-0.762146\pi\) | ||||
−0.733566 | + | 0.679618i | \(0.762146\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.44840e6 | 0.0562650 | ||||||||
\(922\) | 1.84770e7 | 0.715820 | ||||||||
\(923\) | −9.87135e6 | −0.381392 | ||||||||
\(924\) | 83772.9 | 0.00322793 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.51635e7 | 0.964371 | ||||||||
\(927\) | 4.31104e7 | 1.64772 | ||||||||
\(928\) | 3.85434e7 | 1.46920 | ||||||||
\(929\) | −2.92453e7 | −1.11177 | −0.555887 | − | 0.831258i | \(-0.687621\pi\) | ||||
−0.555887 | + | 0.831258i | \(0.687621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.57761e7 | 0.596521 | ||||||||
\(932\) | −2.67341e6 | −0.100815 | ||||||||
\(933\) | −6.24838e6 | −0.234997 | ||||||||
\(934\) | 2.15822e6 | 0.0809522 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.36174e6 | 0.349275 | ||||||||
\(937\) | 1.98213e6 | 0.0737536 | 0.0368768 | − | 0.999320i | \(-0.488259\pi\) | ||||
0.0368768 | + | 0.999320i | \(0.488259\pi\) | |||||||
\(938\) | −1.95479e6 | −0.0725425 | ||||||||
\(939\) | −4.01760e6 | −0.148697 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.31164e7 | 1.21918 | 0.609592 | − | 0.792715i | \(-0.291333\pi\) | ||||
0.609592 | + | 0.792715i | \(0.291333\pi\) | |||||||
\(942\) | −4.91340e6 | −0.180408 | ||||||||
\(943\) | −5.79402e6 | −0.212178 | ||||||||
\(944\) | −824157. | −0.0301010 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.02939e6 | 0.0373983 | ||||||||
\(947\) | −6.56401e6 | −0.237845 | −0.118923 | − | 0.992904i | \(-0.537944\pi\) | ||||
−0.118923 | + | 0.992904i | \(0.537944\pi\) | |||||||
\(948\) | −852445. | −0.0308067 | ||||||||
\(949\) | 1.65812e7 | 0.597656 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.97233e6 | 0.214137 | ||||||||
\(952\) | 3.49284e6 | 0.124907 | ||||||||
\(953\) | −564124. | −0.0201207 | −0.0100603 | − | 0.999949i | \(-0.503202\pi\) | ||||
−0.0100603 | + | 0.999949i | \(0.503202\pi\) | |||||||
\(954\) | 1.45224e7 | 0.516614 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.48693e6 | −0.264947 | ||||||||
\(957\) | −3.09263e6 | −0.109156 | ||||||||
\(958\) | 1.13881e7 | 0.400903 | ||||||||
\(959\) | 789147. | 0.0277084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.10536e7 | −0.735390 | ||||||||
\(962\) | 5.29424e6 | 0.184445 | ||||||||
\(963\) | 5.24997e7 | 1.82428 | ||||||||
\(964\) | −4.34791e6 | −0.150691 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −82240.5 | −0.00283559 | ||||||||
\(967\) | −8.57276e6 | −0.294818 | −0.147409 | − | 0.989076i | \(-0.547093\pi\) | ||||
−0.147409 | + | 0.989076i | \(0.547093\pi\) | |||||||
\(968\) | −2.62248e7 | −0.899547 | ||||||||
\(969\) | −4.83118e6 | −0.165289 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.06221e7 | −0.701917 | −0.350958 | − | 0.936391i | \(-0.614144\pi\) | ||||
−0.350958 | + | 0.936391i | \(0.614144\pi\) | |||||||
\(972\) | 8.87143e6 | 0.301181 | ||||||||
\(973\) | −364209. | −0.0123330 | ||||||||
\(974\) | −1.19818e6 | −0.0404691 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.72259e6 | 0.192295 | ||||||||
\(977\) | 4.10422e6 | 0.137561 | 0.0687803 | − | 0.997632i | \(-0.478089\pi\) | ||||
0.0687803 | + | 0.997632i | \(0.478089\pi\) | |||||||
\(978\) | 1.88327e6 | 0.0629600 | ||||||||
\(979\) | −1.76155e6 | −0.0587404 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.05433e7 | −0.349788 | ||||||||
\(982\) | 3.80521e7 | 1.25922 | ||||||||
\(983\) | 2.18189e7 | 0.720193 | 0.360096 | − | 0.932915i | \(-0.382744\pi\) | ||||
0.360096 | + | 0.932915i | \(0.382744\pi\) | |||||||
\(984\) | 4.82807e6 | 0.158959 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.58470e7 | −1.50182 | ||||||||
\(987\) | −328085. | −0.0107200 | ||||||||
\(988\) | −3.54843e6 | −0.115650 | ||||||||
\(989\) | 1.24377e6 | 0.0404343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.69387e7 | −0.871349 | −0.435675 | − | 0.900104i | \(-0.643490\pi\) | ||||
−0.435675 | + | 0.900104i | \(0.643490\pi\) | |||||||
\(992\) | 1.50283e7 | 0.484878 | ||||||||
\(993\) | 2.26185e6 | 0.0727930 | ||||||||
\(994\) | 1.90441e6 | 0.0611357 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −626404. | −0.0200081 | ||||||||
\(997\) | 5.10386e7 | 1.62615 | 0.813076 | − | 0.582158i | \(-0.197791\pi\) | ||||
0.813076 | + | 0.582158i | \(0.197791\pi\) | |||||||
\(998\) | −3.95937e7 | −1.25835 | ||||||||
\(999\) | 9.34877e6 | 0.296374 |
(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 | 1075.6.a.j.1.14 | yes | 37 | |
5.4 | even | 2 | 1075.6.a.i.1.24 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1075.6.a.i.1.24 | ✓ | 37 | 5.4 | even | 2 | ||
1075.6.a.j.1.14 | yes | 37 | 1.1 | even | 1 | trivial |