Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,6,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(87.7299494377\) |
Analytic rank: | \(1\) |
Dimension: | \(111\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.1575 | −1.97238 | −0.986189 | − | 0.165623i | \(-0.947037\pi\) | ||||
−0.986189 | + | 0.165623i | \(0.947037\pi\) | |||||||
\(3\) | −27.7524 | −1.78032 | −0.890159 | − | 0.455651i | \(-0.849407\pi\) | ||||
−0.890159 | + | 0.455651i | \(0.849407\pi\) | |||||||
\(4\) | 92.4888 | 2.89028 | ||||||||
\(5\) | −19.1317 | −0.342239 | −0.171119 | − | 0.985250i | \(-0.554738\pi\) | ||||
−0.171119 | + | 0.985250i | \(0.554738\pi\) | |||||||
\(6\) | 309.646 | 3.51146 | ||||||||
\(7\) | −173.776 | −1.34043 | −0.670216 | − | 0.742166i | \(-0.733798\pi\) | ||||
−0.670216 | + | 0.742166i | \(0.733798\pi\) | |||||||
\(8\) | −674.902 | −3.72834 | ||||||||
\(9\) | 527.195 | 2.16953 | ||||||||
\(10\) | 213.461 | 0.675024 | ||||||||
\(11\) | −412.423 | −1.02769 | −0.513844 | − | 0.857884i | \(-0.671779\pi\) | ||||
−0.513844 | + | 0.857884i | \(0.671779\pi\) | |||||||
\(12\) | −2566.79 | −5.14561 | ||||||||
\(13\) | 68.8293 | 0.112957 | 0.0564787 | − | 0.998404i | \(-0.482013\pi\) | ||||
0.0564787 | + | 0.998404i | \(0.482013\pi\) | |||||||
\(14\) | 1938.90 | 2.64384 | ||||||||
\(15\) | 530.951 | 0.609293 | ||||||||
\(16\) | 4570.54 | 4.46342 | ||||||||
\(17\) | −1218.00 | −1.02217 | −0.511086 | − | 0.859530i | \(-0.670757\pi\) | ||||
−0.511086 | + | 0.859530i | \(0.670757\pi\) | |||||||
\(18\) | −5882.16 | −4.27913 | ||||||||
\(19\) | 3087.57 | 1.96215 | 0.981076 | − | 0.193621i | \(-0.0620231\pi\) | ||||
0.981076 | + | 0.193621i | \(0.0620231\pi\) | |||||||
\(20\) | −1769.47 | −0.989164 | ||||||||
\(21\) | 4822.70 | 2.38639 | ||||||||
\(22\) | 4601.59 | 2.02699 | ||||||||
\(23\) | −3329.84 | −1.31251 | −0.656257 | − | 0.754537i | \(-0.727861\pi\) | ||||
−0.656257 | + | 0.754537i | \(0.727861\pi\) | |||||||
\(24\) | 18730.1 | 6.63763 | ||||||||
\(25\) | −2758.98 | −0.882873 | ||||||||
\(26\) | −767.960 | −0.222795 | ||||||||
\(27\) | −7887.11 | −2.08213 | ||||||||
\(28\) | −16072.3 | −3.87422 | ||||||||
\(29\) | −8048.62 | −1.77716 | −0.888579 | − | 0.458723i | \(-0.848307\pi\) | ||||
−0.888579 | + | 0.458723i | \(0.848307\pi\) | |||||||
\(30\) | −5924.06 | −1.20176 | ||||||||
\(31\) | −537.597 | −0.100474 | −0.0502369 | − | 0.998737i | \(-0.515998\pi\) | ||||
−0.0502369 | + | 0.998737i | \(0.515998\pi\) | |||||||
\(32\) | −29398.8 | −5.07522 | ||||||||
\(33\) | 11445.7 | 1.82961 | ||||||||
\(34\) | 13589.8 | 2.01611 | ||||||||
\(35\) | 3324.63 | 0.458747 | ||||||||
\(36\) | 48759.7 | 6.27054 | ||||||||
\(37\) | −12341.0 | −1.48199 | −0.740994 | − | 0.671511i | \(-0.765645\pi\) | ||||
−0.740994 | + | 0.671511i | \(0.765645\pi\) | |||||||
\(38\) | −34449.4 | −3.87011 | ||||||||
\(39\) | −1910.18 | −0.201100 | ||||||||
\(40\) | 12912.0 | 1.27598 | ||||||||
\(41\) | 492.022 | 0.0457114 | 0.0228557 | − | 0.999739i | \(-0.492724\pi\) | ||||
0.0228557 | + | 0.999739i | \(0.492724\pi\) | |||||||
\(42\) | −53809.1 | −4.70687 | ||||||||
\(43\) | 3556.53 | 0.293329 | 0.146665 | − | 0.989186i | \(-0.453146\pi\) | ||||
0.146665 | + | 0.989186i | \(0.453146\pi\) | |||||||
\(44\) | −38144.5 | −2.97030 | ||||||||
\(45\) | −10086.2 | −0.742497 | ||||||||
\(46\) | 37152.6 | 2.58878 | ||||||||
\(47\) | 9225.08 | 0.609152 | 0.304576 | − | 0.952488i | \(-0.401485\pi\) | ||||
0.304576 | + | 0.952488i | \(0.401485\pi\) | |||||||
\(48\) | −126844. | −7.94631 | ||||||||
\(49\) | 13391.1 | 0.796756 | ||||||||
\(50\) | 30783.2 | 1.74136 | ||||||||
\(51\) | 33802.3 | 1.81979 | ||||||||
\(52\) | 6365.94 | 0.326478 | ||||||||
\(53\) | 33160.5 | 1.62155 | 0.810777 | − | 0.585355i | \(-0.199045\pi\) | ||||
0.810777 | + | 0.585355i | \(0.199045\pi\) | |||||||
\(54\) | 88000.0 | 4.10675 | ||||||||
\(55\) | 7890.36 | 0.351714 | ||||||||
\(56\) | 117282. | 4.99758 | ||||||||
\(57\) | −85687.5 | −3.49325 | ||||||||
\(58\) | 89802.1 | 3.50523 | ||||||||
\(59\) | 29971.0 | 1.12091 | 0.560456 | − | 0.828184i | \(-0.310626\pi\) | ||||
0.560456 | + | 0.828184i | \(0.310626\pi\) | |||||||
\(60\) | 49107.1 | 1.76103 | ||||||||
\(61\) | −11986.6 | −0.412451 | −0.206225 | − | 0.978504i | \(-0.566118\pi\) | ||||
−0.206225 | + | 0.978504i | \(0.566118\pi\) | |||||||
\(62\) | 5998.22 | 0.198172 | ||||||||
\(63\) | −91613.9 | −2.90810 | ||||||||
\(64\) | 181758. | 5.54682 | ||||||||
\(65\) | −1316.82 | −0.0386584 | ||||||||
\(66\) | −127705. | −3.60868 | ||||||||
\(67\) | −2225.90 | −0.0605784 | −0.0302892 | − | 0.999541i | \(-0.509643\pi\) | ||||
−0.0302892 | + | 0.999541i | \(0.509643\pi\) | |||||||
\(68\) | −112651. | −2.95436 | ||||||||
\(69\) | 92411.1 | 2.33669 | ||||||||
\(70\) | −37094.5 | −0.904823 | ||||||||
\(71\) | −83082.3 | −1.95597 | −0.977986 | − | 0.208669i | \(-0.933087\pi\) | ||||
−0.977986 | + | 0.208669i | \(0.933087\pi\) | |||||||
\(72\) | −355805. | −8.08874 | ||||||||
\(73\) | 27637.9 | 0.607014 | 0.303507 | − | 0.952829i | \(-0.401842\pi\) | ||||
0.303507 | + | 0.952829i | \(0.401842\pi\) | |||||||
\(74\) | 137694. | 2.92304 | ||||||||
\(75\) | 76568.2 | 1.57179 | ||||||||
\(76\) | 285566. | 5.67116 | ||||||||
\(77\) | 71669.2 | 1.37754 | ||||||||
\(78\) | 21312.7 | 0.396645 | ||||||||
\(79\) | −23679.0 | −0.426871 | −0.213435 | − | 0.976957i | \(-0.568465\pi\) | ||||
−0.213435 | + | 0.976957i | \(0.568465\pi\) | |||||||
\(80\) | −87442.4 | −1.52756 | ||||||||
\(81\) | 90777.6 | 1.53733 | ||||||||
\(82\) | −5489.71 | −0.0901602 | ||||||||
\(83\) | 43467.0 | 0.692572 | 0.346286 | − | 0.938129i | \(-0.387443\pi\) | ||||
0.346286 | + | 0.938129i | \(0.387443\pi\) | |||||||
\(84\) | 446046. | 6.89733 | ||||||||
\(85\) | 23302.4 | 0.349827 | ||||||||
\(86\) | −39681.8 | −0.578556 | ||||||||
\(87\) | 223368. | 3.16391 | ||||||||
\(88\) | 278345. | 3.83157 | ||||||||
\(89\) | −58454.3 | −0.782242 | −0.391121 | − | 0.920339i | \(-0.627913\pi\) | ||||
−0.391121 | + | 0.920339i | \(0.627913\pi\) | |||||||
\(90\) | 112536. | 1.46448 | ||||||||
\(91\) | −11960.9 | −0.151412 | ||||||||
\(92\) | −307973. | −3.79353 | ||||||||
\(93\) | 14919.6 | 0.178875 | ||||||||
\(94\) | −102928. | −1.20148 | ||||||||
\(95\) | −59070.5 | −0.671525 | ||||||||
\(96\) | 815887. | 9.03549 | ||||||||
\(97\) | 74835.0 | 0.807562 | 0.403781 | − | 0.914856i | \(-0.367696\pi\) | ||||
0.403781 | + | 0.914856i | \(0.367696\pi\) | |||||||
\(98\) | −149410. | −1.57150 | ||||||||
\(99\) | −217427. | −2.22960 | ||||||||
\(100\) | −255175. | −2.55175 | ||||||||
\(101\) | 106882. | 1.04256 | 0.521280 | − | 0.853386i | \(-0.325455\pi\) | ||||
0.521280 | + | 0.853386i | \(0.325455\pi\) | |||||||
\(102\) | −377148. | −3.58932 | ||||||||
\(103\) | 163475. | 1.51830 | 0.759152 | − | 0.650913i | \(-0.225614\pi\) | ||||
0.759152 | + | 0.650913i | \(0.225614\pi\) | |||||||
\(104\) | −46453.0 | −0.421144 | ||||||||
\(105\) | −92266.5 | −0.816716 | ||||||||
\(106\) | −369987. | −3.19832 | ||||||||
\(107\) | 131515. | 1.11050 | 0.555248 | − | 0.831685i | \(-0.312623\pi\) | ||||
0.555248 | + | 0.831685i | \(0.312623\pi\) | |||||||
\(108\) | −729469. | −6.01794 | ||||||||
\(109\) | 130163. | 1.04935 | 0.524674 | − | 0.851303i | \(-0.324187\pi\) | ||||
0.524674 | + | 0.851303i | \(0.324187\pi\) | |||||||
\(110\) | −88036.3 | −0.693714 | ||||||||
\(111\) | 342491. | 2.63841 | ||||||||
\(112\) | −794251. | −5.98291 | ||||||||
\(113\) | 136226. | 1.00360 | 0.501802 | − | 0.864982i | \(-0.332671\pi\) | ||||
0.501802 | + | 0.864982i | \(0.332671\pi\) | |||||||
\(114\) | 956054. | 6.89002 | ||||||||
\(115\) | 63705.6 | 0.449193 | ||||||||
\(116\) | −744407. | −5.13648 | ||||||||
\(117\) | 36286.5 | 0.245064 | ||||||||
\(118\) | −334400. | −2.21086 | ||||||||
\(119\) | 211659. | 1.37015 | ||||||||
\(120\) | −358340. | −2.27165 | ||||||||
\(121\) | 9041.53 | 0.0561408 | ||||||||
\(122\) | 133740. | 0.813509 | ||||||||
\(123\) | −13654.8 | −0.0813808 | ||||||||
\(124\) | −49721.7 | −0.290397 | ||||||||
\(125\) | 112571. | 0.644392 | ||||||||
\(126\) | 1.02218e6 | 5.73588 | ||||||||
\(127\) | 75340.2 | 0.414493 | 0.207247 | − | 0.978289i | \(-0.433550\pi\) | ||||
0.207247 | + | 0.978289i | \(0.433550\pi\) | |||||||
\(128\) | −1.08720e6 | −5.86522 | ||||||||
\(129\) | −98702.3 | −0.522219 | ||||||||
\(130\) | 14692.4 | 0.0762490 | ||||||||
\(131\) | 343851. | 1.75062 | 0.875310 | − | 0.483563i | \(-0.160658\pi\) | ||||
0.875310 | + | 0.483563i | \(0.160658\pi\) | |||||||
\(132\) | 1.05860e6 | 5.28808 | ||||||||
\(133\) | −536545. | −2.63013 | ||||||||
\(134\) | 24835.3 | 0.119484 | ||||||||
\(135\) | 150894. | 0.712586 | ||||||||
\(136\) | 822029. | 3.81101 | ||||||||
\(137\) | −25000.1 | −0.113800 | −0.0568998 | − | 0.998380i | \(-0.518122\pi\) | ||||
−0.0568998 | + | 0.998380i | \(0.518122\pi\) | |||||||
\(138\) | −1.03107e6 | −4.60884 | ||||||||
\(139\) | 33948.3 | 0.149033 | 0.0745163 | − | 0.997220i | \(-0.476259\pi\) | ||||
0.0745163 | + | 0.997220i | \(0.476259\pi\) | |||||||
\(140\) | 307491. | 1.32591 | ||||||||
\(141\) | −256018. | −1.08448 | ||||||||
\(142\) | 926987. | 3.85792 | ||||||||
\(143\) | −28386.8 | −0.116085 | ||||||||
\(144\) | 2.40957e6 | 9.68352 | ||||||||
\(145\) | 153984. | 0.608212 | ||||||||
\(146\) | −308369. | −1.19726 | ||||||||
\(147\) | −371635. | −1.41848 | ||||||||
\(148\) | −1.14140e6 | −4.28336 | ||||||||
\(149\) | −180925. | −0.667625 | −0.333812 | − | 0.942640i | \(-0.608335\pi\) | ||||
−0.333812 | + | 0.942640i | \(0.608335\pi\) | |||||||
\(150\) | −854307. | −3.10017 | ||||||||
\(151\) | −233727. | −0.834192 | −0.417096 | − | 0.908862i | \(-0.636952\pi\) | ||||
−0.417096 | + | 0.908862i | \(0.636952\pi\) | |||||||
\(152\) | −2.08381e6 | −7.31557 | ||||||||
\(153\) | −642123. | −2.21763 | ||||||||
\(154\) | −799645. | −2.71704 | ||||||||
\(155\) | 10285.2 | 0.0343860 | ||||||||
\(156\) | −176670. | −0.581235 | ||||||||
\(157\) | 119878. | 0.388142 | 0.194071 | − | 0.980988i | \(-0.437831\pi\) | ||||
0.194071 | + | 0.980988i | \(0.437831\pi\) | |||||||
\(158\) | 264198. | 0.841951 | ||||||||
\(159\) | −920284. | −2.88688 | ||||||||
\(160\) | 562450. | 1.73694 | ||||||||
\(161\) | 578647. | 1.75934 | ||||||||
\(162\) | −1.01285e6 | −3.03219 | ||||||||
\(163\) | 304780. | 0.898497 | 0.449249 | − | 0.893407i | \(-0.351692\pi\) | ||||
0.449249 | + | 0.893407i | \(0.351692\pi\) | |||||||
\(164\) | 45506.5 | 0.132119 | ||||||||
\(165\) | −218976. | −0.626163 | ||||||||
\(166\) | −484982. | −1.36601 | ||||||||
\(167\) | −340121. | −0.943719 | −0.471859 | − | 0.881674i | \(-0.656417\pi\) | ||||
−0.471859 | + | 0.881674i | \(0.656417\pi\) | |||||||
\(168\) | −3.25485e6 | −8.89728 | ||||||||
\(169\) | −366556. | −0.987241 | ||||||||
\(170\) | −259995. | −0.689991 | ||||||||
\(171\) | 1.62775e6 | 4.25695 | ||||||||
\(172\) | 328939. | 0.847803 | ||||||||
\(173\) | −100831. | −0.256141 | −0.128070 | − | 0.991765i | \(-0.540878\pi\) | ||||
−0.128070 | + | 0.991765i | \(0.540878\pi\) | |||||||
\(174\) | −2.49222e6 | −6.24042 | ||||||||
\(175\) | 479444. | 1.18343 | ||||||||
\(176\) | −1.88500e6 | −4.58700 | ||||||||
\(177\) | −831767. | −1.99558 | ||||||||
\(178\) | 652201. | 1.54288 | ||||||||
\(179\) | −149128. | −0.347878 | −0.173939 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173939 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(180\) | −932857. | −2.14602 | ||||||||
\(181\) | −380740. | −0.863838 | −0.431919 | − | 0.901912i | \(-0.642163\pi\) | ||||
−0.431919 | + | 0.901912i | \(0.642163\pi\) | |||||||
\(182\) | 133453. | 0.298641 | ||||||||
\(183\) | 332658. | 0.734294 | ||||||||
\(184\) | 2.24732e6 | 4.89350 | ||||||||
\(185\) | 236104. | 0.507194 | ||||||||
\(186\) | −166465. | −0.352809 | ||||||||
\(187\) | 502330. | 1.05047 | ||||||||
\(188\) | 853217. | 1.76062 | ||||||||
\(189\) | 1.37059e6 | 2.79095 | ||||||||
\(190\) | 659077. | 1.32450 | ||||||||
\(191\) | 335347. | 0.665138 | 0.332569 | − | 0.943079i | \(-0.392085\pi\) | ||||
0.332569 | + | 0.943079i | \(0.392085\pi\) | |||||||
\(192\) | −5.04423e6 | −9.87511 | ||||||||
\(193\) | 489983. | 0.946863 | 0.473432 | − | 0.880831i | \(-0.343015\pi\) | ||||
0.473432 | + | 0.880831i | \(0.343015\pi\) | |||||||
\(194\) | −834969. | −1.59282 | ||||||||
\(195\) | 36545.0 | 0.0688242 | ||||||||
\(196\) | 1.23853e6 | 2.30285 | ||||||||
\(197\) | 40123.1 | 0.0736596 | 0.0368298 | − | 0.999322i | \(-0.488274\pi\) | ||||
0.0368298 | + | 0.999322i | \(0.488274\pi\) | |||||||
\(198\) | 2.42594e6 | 4.39761 | ||||||||
\(199\) | 160586. | 0.287458 | 0.143729 | − | 0.989617i | \(-0.454091\pi\) | ||||
0.143729 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(200\) | 1.86204e6 | 3.29165 | ||||||||
\(201\) | 61773.9 | 0.107849 | ||||||||
\(202\) | −1.19253e6 | −2.05632 | ||||||||
\(203\) | 1.39866e6 | 2.38216 | ||||||||
\(204\) | 3.12634e6 | 5.25970 | ||||||||
\(205\) | −9413.23 | −0.0156442 | ||||||||
\(206\) | −1.82397e6 | −2.99467 | ||||||||
\(207\) | −1.75548e6 | −2.84754 | ||||||||
\(208\) | 314587. | 0.504177 | ||||||||
\(209\) | −1.27338e6 | −2.01648 | ||||||||
\(210\) | 1.02946e6 | 1.61087 | ||||||||
\(211\) | −415141. | −0.641932 | −0.320966 | − | 0.947091i | \(-0.604008\pi\) | ||||
−0.320966 | + | 0.947091i | \(0.604008\pi\) | |||||||
\(212\) | 3.06698e6 | 4.68674 | ||||||||
\(213\) | 2.30573e6 | 3.48225 | ||||||||
\(214\) | −1.46738e6 | −2.19032 | ||||||||
\(215\) | −68042.6 | −0.100389 | ||||||||
\(216\) | 5.32302e6 | 7.76290 | ||||||||
\(217\) | 93421.4 | 0.134678 | ||||||||
\(218\) | −1.45228e6 | −2.06971 | ||||||||
\(219\) | −767019. | −1.08068 | ||||||||
\(220\) | 729770. | 1.01655 | ||||||||
\(221\) | −83833.9 | −0.115462 | ||||||||
\(222\) | −3.82133e6 | −5.20394 | ||||||||
\(223\) | 775825. | 1.04472 | 0.522362 | − | 0.852724i | \(-0.325051\pi\) | ||||
0.522362 | + | 0.852724i | \(0.325051\pi\) | |||||||
\(224\) | 5.10880e6 | 6.80298 | ||||||||
\(225\) | −1.45452e6 | −1.91542 | ||||||||
\(226\) | −1.51993e6 | −1.97949 | ||||||||
\(227\) | 35942.4 | 0.0462959 | 0.0231479 | − | 0.999732i | \(-0.492631\pi\) | ||||
0.0231479 | + | 0.999732i | \(0.492631\pi\) | |||||||
\(228\) | −7.92514e6 | −10.0965 | ||||||||
\(229\) | −271606. | −0.342256 | −0.171128 | − | 0.985249i | \(-0.554741\pi\) | ||||
−0.171128 | + | 0.985249i | \(0.554741\pi\) | |||||||
\(230\) | −710793. | −0.885979 | ||||||||
\(231\) | −1.98899e6 | −2.45246 | ||||||||
\(232\) | 5.43202e6 | 6.62585 | ||||||||
\(233\) | 786471. | 0.949058 | 0.474529 | − | 0.880240i | \(-0.342618\pi\) | ||||
0.474529 | + | 0.880240i | \(0.342618\pi\) | |||||||
\(234\) | −404865. | −0.483360 | ||||||||
\(235\) | −176492. | −0.208475 | ||||||||
\(236\) | 2.77198e6 | 3.23974 | ||||||||
\(237\) | 657150. | 0.759965 | ||||||||
\(238\) | −2.36157e6 | −2.70246 | ||||||||
\(239\) | 153700. | 0.174052 | 0.0870260 | − | 0.996206i | \(-0.472264\pi\) | ||||
0.0870260 | + | 0.996206i | \(0.472264\pi\) | |||||||
\(240\) | 2.42674e6 | 2.71953 | ||||||||
\(241\) | 1.20367e6 | 1.33494 | 0.667472 | − | 0.744634i | \(-0.267376\pi\) | ||||
0.667472 | + | 0.744634i | \(0.267376\pi\) | |||||||
\(242\) | −100880. | −0.110731 | ||||||||
\(243\) | −602729. | −0.654796 | ||||||||
\(244\) | −1.10863e6 | −1.19210 | ||||||||
\(245\) | −256194. | −0.272681 | ||||||||
\(246\) | 152353. | 0.160514 | ||||||||
\(247\) | 212515. | 0.221640 | ||||||||
\(248\) | 362825. | 0.374600 | ||||||||
\(249\) | −1.20631e6 | −1.23300 | ||||||||
\(250\) | −1.25600e6 | −1.27098 | ||||||||
\(251\) | 35391.8 | 0.0354583 | 0.0177292 | − | 0.999843i | \(-0.494356\pi\) | ||||
0.0177292 | + | 0.999843i | \(0.494356\pi\) | |||||||
\(252\) | −8.47326e6 | −8.40523 | ||||||||
\(253\) | 1.37330e6 | 1.34885 | ||||||||
\(254\) | −840605. | −0.817538 | ||||||||
\(255\) | −646697. | −0.622803 | ||||||||
\(256\) | 6.31412e6 | 6.02161 | ||||||||
\(257\) | 49319.0 | 0.0465781 | 0.0232891 | − | 0.999729i | \(-0.492586\pi\) | ||||
0.0232891 | + | 0.999729i | \(0.492586\pi\) | |||||||
\(258\) | 1.10127e6 | 1.03001 | ||||||||
\(259\) | 2.14456e6 | 1.98650 | ||||||||
\(260\) | −121791. | −0.111733 | ||||||||
\(261\) | −4.24319e6 | −3.85560 | ||||||||
\(262\) | −3.83650e6 | −3.45288 | ||||||||
\(263\) | −1.68990e6 | −1.50651 | −0.753254 | − | 0.657730i | \(-0.771517\pi\) | ||||
−0.753254 | + | 0.657730i | \(0.771517\pi\) | |||||||
\(264\) | −7.72474e6 | −6.82140 | ||||||||
\(265\) | −634418. | −0.554959 | ||||||||
\(266\) | 5.98648e6 | 5.18761 | ||||||||
\(267\) | 1.62225e6 | 1.39264 | ||||||||
\(268\) | −205870. | −0.175088 | ||||||||
\(269\) | −1.26446e6 | −1.06543 | −0.532716 | − | 0.846294i | \(-0.678829\pi\) | ||||
−0.532716 | + | 0.846294i | \(0.678829\pi\) | |||||||
\(270\) | −1.68359e6 | −1.40549 | ||||||||
\(271\) | 107918. | 0.0892630 | 0.0446315 | − | 0.999004i | \(-0.485789\pi\) | ||||
0.0446315 | + | 0.999004i | \(0.485789\pi\) | |||||||
\(272\) | −5.56691e6 | −4.56239 | ||||||||
\(273\) | 331943. | 0.269561 | ||||||||
\(274\) | 278938. | 0.224456 | ||||||||
\(275\) | 1.13786e6 | 0.907317 | ||||||||
\(276\) | 8.54700e6 | 6.75369 | ||||||||
\(277\) | −2.33180e6 | −1.82596 | −0.912981 | − | 0.408003i | \(-0.866225\pi\) | ||||
−0.912981 | + | 0.408003i | \(0.866225\pi\) | |||||||
\(278\) | −378777. | −0.293949 | ||||||||
\(279\) | −283419. | −0.217981 | ||||||||
\(280\) | −2.24380e6 | −1.71037 | ||||||||
\(281\) | −920487. | −0.695428 | −0.347714 | − | 0.937601i | \(-0.613042\pi\) | ||||
−0.347714 | + | 0.937601i | \(0.613042\pi\) | |||||||
\(282\) | 2.85651e6 | 2.13901 | ||||||||
\(283\) | −182579. | −0.135514 | −0.0677570 | − | 0.997702i | \(-0.521584\pi\) | ||||
−0.0677570 | + | 0.997702i | \(0.521584\pi\) | |||||||
\(284\) | −7.68419e6 | −5.65330 | ||||||||
\(285\) | 1.63935e6 | 1.19553 | ||||||||
\(286\) | 316724. | 0.228963 | ||||||||
\(287\) | −85501.6 | −0.0612730 | ||||||||
\(288\) | −1.54989e7 | −11.0108 | ||||||||
\(289\) | 63660.5 | 0.0448359 | ||||||||
\(290\) | −1.71807e6 | −1.19962 | ||||||||
\(291\) | −2.07685e6 | −1.43772 | ||||||||
\(292\) | 2.55620e6 | 1.75444 | ||||||||
\(293\) | −1.82416e6 | −1.24135 | −0.620673 | − | 0.784069i | \(-0.713141\pi\) | ||||
−0.620673 | + | 0.784069i | \(0.713141\pi\) | |||||||
\(294\) | 4.14650e6 | 2.79778 | ||||||||
\(295\) | −573397. | −0.383619 | ||||||||
\(296\) | 8.32894e6 | 5.52536 | ||||||||
\(297\) | 3.25282e6 | 2.13978 | ||||||||
\(298\) | 2.01866e6 | 1.31681 | ||||||||
\(299\) | −229191. | −0.148258 | ||||||||
\(300\) | 7.08171e6 | 4.54292 | ||||||||
\(301\) | −618040. | −0.393188 | ||||||||
\(302\) | 2.60780e6 | 1.64534 | ||||||||
\(303\) | −2.96623e6 | −1.85609 | ||||||||
\(304\) | 1.41119e7 | 8.75792 | ||||||||
\(305\) | 229325. | 0.141157 | ||||||||
\(306\) | 7.16446e6 | 4.37401 | ||||||||
\(307\) | 2.88314e6 | 1.74590 | 0.872951 | − | 0.487808i | \(-0.162203\pi\) | ||||
0.872951 | + | 0.487808i | \(0.162203\pi\) | |||||||
\(308\) | 6.62860e6 | 3.98148 | ||||||||
\(309\) | −4.53683e6 | −2.70306 | ||||||||
\(310\) | −114756. | −0.0678222 | ||||||||
\(311\) | 2.79704e6 | 1.63983 | 0.819913 | − | 0.572488i | \(-0.194022\pi\) | ||||
0.819913 | + | 0.572488i | \(0.194022\pi\) | |||||||
\(312\) | 1.28918e6 | 0.749770 | ||||||||
\(313\) | −1.12104e6 | −0.646788 | −0.323394 | − | 0.946264i | \(-0.604824\pi\) | ||||
−0.323394 | + | 0.946264i | \(0.604824\pi\) | |||||||
\(314\) | −1.33753e6 | −0.765562 | ||||||||
\(315\) | 1.75273e6 | 0.995266 | ||||||||
\(316\) | −2.19005e6 | −1.23377 | ||||||||
\(317\) | −762781. | −0.426336 | −0.213168 | − | 0.977016i | \(-0.568378\pi\) | ||||
−0.213168 | + | 0.977016i | \(0.568378\pi\) | |||||||
\(318\) | 1.02680e7 | 5.69402 | ||||||||
\(319\) | 3.31943e6 | 1.82636 | ||||||||
\(320\) | −3.47735e6 | −1.89834 | ||||||||
\(321\) | −3.64987e6 | −1.97704 | ||||||||
\(322\) | −6.45623e6 | −3.47008 | ||||||||
\(323\) | −3.76065e6 | −2.00566 | ||||||||
\(324\) | 8.39591e6 | 4.44330 | ||||||||
\(325\) | −189898. | −0.0997271 | ||||||||
\(326\) | −3.40056e6 | −1.77218 | ||||||||
\(327\) | −3.61232e6 | −1.86817 | ||||||||
\(328\) | −332066. | −0.170428 | ||||||||
\(329\) | −1.60310e6 | −0.816526 | ||||||||
\(330\) | 2.44322e6 | 1.23503 | ||||||||
\(331\) | 1.60937e6 | 0.807397 | 0.403699 | − | 0.914892i | \(-0.367724\pi\) | ||||
0.403699 | + | 0.914892i | \(0.367724\pi\) | |||||||
\(332\) | 4.02022e6 | 2.00172 | ||||||||
\(333\) | −6.50610e6 | −3.21522 | ||||||||
\(334\) | 3.79489e6 | 1.86137 | ||||||||
\(335\) | 42585.2 | 0.0207323 | ||||||||
\(336\) | 2.20424e7 | 10.6515 | ||||||||
\(337\) | −448429. | −0.215090 | −0.107545 | − | 0.994200i | \(-0.534299\pi\) | ||||
−0.107545 | + | 0.994200i | \(0.534299\pi\) | |||||||
\(338\) | 4.08983e6 | 1.94721 | ||||||||
\(339\) | −3.78059e6 | −1.78673 | ||||||||
\(340\) | 2.15521e6 | 1.01110 | ||||||||
\(341\) | 221717. | 0.103256 | ||||||||
\(342\) | −1.81616e7 | −8.39631 | ||||||||
\(343\) | 593605. | 0.272435 | ||||||||
\(344\) | −2.40031e6 | −1.09363 | ||||||||
\(345\) | −1.76798e6 | −0.799707 | ||||||||
\(346\) | 1.12502e6 | 0.505206 | ||||||||
\(347\) | 763023. | 0.340184 | 0.170092 | − | 0.985428i | \(-0.445594\pi\) | ||||
0.170092 | + | 0.985428i | \(0.445594\pi\) | |||||||
\(348\) | 2.06591e7 | 9.14456 | ||||||||
\(349\) | −2.24983e6 | −0.988748 | −0.494374 | − | 0.869249i | \(-0.664603\pi\) | ||||
−0.494374 | + | 0.869249i | \(0.664603\pi\) | |||||||
\(350\) | −5.34937e6 | −2.33417 | ||||||||
\(351\) | −542864. | −0.235192 | ||||||||
\(352\) | 1.21247e7 | 5.21573 | ||||||||
\(353\) | −1.25844e6 | −0.537522 | −0.268761 | − | 0.963207i | \(-0.586614\pi\) | ||||
−0.268761 | + | 0.963207i | \(0.586614\pi\) | |||||||
\(354\) | 9.28041e6 | 3.93603 | ||||||||
\(355\) | 1.58951e6 | 0.669409 | ||||||||
\(356\) | −5.40637e6 | −2.26090 | ||||||||
\(357\) | −5.87403e6 | −2.43930 | ||||||||
\(358\) | 1.66389e6 | 0.686147 | ||||||||
\(359\) | −1.81972e6 | −0.745194 | −0.372597 | − | 0.927993i | \(-0.621533\pi\) | ||||
−0.372597 | + | 0.927993i | \(0.621533\pi\) | |||||||
\(360\) | 6.80717e6 | 2.76828 | ||||||||
\(361\) | 7.05699e6 | 2.85004 | ||||||||
\(362\) | 4.24809e6 | 1.70382 | ||||||||
\(363\) | −250924. | −0.0999484 | ||||||||
\(364\) | −1.10625e6 | −0.437622 | ||||||||
\(365\) | −528761. | −0.207744 | ||||||||
\(366\) | −3.71161e6 | −1.44830 | ||||||||
\(367\) | 3.95001e6 | 1.53085 | 0.765426 | − | 0.643524i | \(-0.222528\pi\) | ||||
0.765426 | + | 0.643524i | \(0.222528\pi\) | |||||||
\(368\) | −1.52192e7 | −5.85831 | ||||||||
\(369\) | 259392. | 0.0991723 | ||||||||
\(370\) | −2.63432e6 | −1.00038 | ||||||||
\(371\) | −5.76250e6 | −2.17358 | ||||||||
\(372\) | 1.37990e6 | 0.516999 | ||||||||
\(373\) | 2.65077e6 | 0.986505 | 0.493252 | − | 0.869886i | \(-0.335808\pi\) | ||||
0.493252 | + | 0.869886i | \(0.335808\pi\) | |||||||
\(374\) | −5.60472e6 | −2.07193 | ||||||||
\(375\) | −3.12410e6 | −1.14722 | ||||||||
\(376\) | −6.22602e6 | −2.27113 | ||||||||
\(377\) | −553981. | −0.200743 | ||||||||
\(378\) | −1.52923e7 | −5.50482 | ||||||||
\(379\) | −987497. | −0.353133 | −0.176566 | − | 0.984289i | \(-0.556499\pi\) | ||||
−0.176566 | + | 0.984289i | \(0.556499\pi\) | |||||||
\(380\) | −5.46337e6 | −1.94089 | ||||||||
\(381\) | −2.09087e6 | −0.737930 | ||||||||
\(382\) | −3.74162e6 | −1.31190 | ||||||||
\(383\) | 2.77254e6 | 0.965787 | 0.482893 | − | 0.875679i | \(-0.339586\pi\) | ||||
0.482893 | + | 0.875679i | \(0.339586\pi\) | |||||||
\(384\) | 3.01724e7 | 10.4420 | ||||||||
\(385\) | −1.37115e6 | −0.471449 | ||||||||
\(386\) | −5.46696e6 | −1.86757 | ||||||||
\(387\) | 1.87499e6 | 0.636386 | ||||||||
\(388\) | 6.92141e6 | 2.33408 | ||||||||
\(389\) | −1.22855e6 | −0.411642 | −0.205821 | − | 0.978590i | \(-0.565987\pi\) | ||||
−0.205821 | + | 0.978590i | \(0.565987\pi\) | |||||||
\(390\) | −407749. | −0.135747 | ||||||||
\(391\) | 4.05574e6 | 1.34162 | ||||||||
\(392\) | −9.03766e6 | −2.97058 | ||||||||
\(393\) | −9.54268e6 | −3.11666 | ||||||||
\(394\) | −447672. | −0.145285 | ||||||||
\(395\) | 453021. | 0.146092 | ||||||||
\(396\) | −2.01096e7 | −6.44415 | ||||||||
\(397\) | −628198. | −0.200042 | −0.100021 | − | 0.994985i | \(-0.531891\pi\) | ||||
−0.100021 | + | 0.994985i | \(0.531891\pi\) | |||||||
\(398\) | −1.79173e6 | −0.566975 | ||||||||
\(399\) | 1.48904e7 | 4.68247 | ||||||||
\(400\) | −1.26100e7 | −3.94063 | ||||||||
\(401\) | −504475. | −0.156667 | −0.0783337 | − | 0.996927i | \(-0.524960\pi\) | ||||
−0.0783337 | + | 0.996927i | \(0.524960\pi\) | |||||||
\(402\) | −689240. | −0.212719 | ||||||||
\(403\) | −37002.4 | −0.0113493 | ||||||||
\(404\) | 9.88539e6 | 3.01329 | ||||||||
\(405\) | −1.73673e6 | −0.526132 | ||||||||
\(406\) | −1.56054e7 | −4.69852 | ||||||||
\(407\) | 5.08970e6 | 1.52302 | ||||||||
\(408\) | −2.28133e7 | −6.78480 | ||||||||
\(409\) | 292189. | 0.0863687 | 0.0431843 | − | 0.999067i | \(-0.486250\pi\) | ||||
0.0431843 | + | 0.999067i | \(0.486250\pi\) | |||||||
\(410\) | 105028. | 0.0308563 | ||||||||
\(411\) | 693813. | 0.202599 | ||||||||
\(412\) | 1.51196e7 | 4.38832 | ||||||||
\(413\) | −5.20824e6 | −1.50250 | ||||||||
\(414\) | 1.95867e7 | 5.61642 | ||||||||
\(415\) | −831600. | −0.237025 | ||||||||
\(416\) | −2.02350e6 | −0.573284 | ||||||||
\(417\) | −942147. | −0.265325 | ||||||||
\(418\) | 1.42077e7 | 3.97726 | ||||||||
\(419\) | 811721. | 0.225877 | 0.112938 | − | 0.993602i | \(-0.463974\pi\) | ||||
0.112938 | + | 0.993602i | \(0.463974\pi\) | |||||||
\(420\) | −8.53363e6 | −2.36053 | ||||||||
\(421\) | −607784. | −0.167126 | −0.0835631 | − | 0.996502i | \(-0.526630\pi\) | ||||
−0.0835631 | + | 0.996502i | \(0.526630\pi\) | |||||||
\(422\) | 4.63192e6 | 1.26613 | ||||||||
\(423\) | 4.86342e6 | 1.32157 | ||||||||
\(424\) | −2.23801e7 | −6.04571 | ||||||||
\(425\) | 3.36043e6 | 0.902448 | ||||||||
\(426\) | −2.57261e7 | −6.86832 | ||||||||
\(427\) | 2.08299e6 | 0.552862 | ||||||||
\(428\) | 1.21637e7 | 3.20964 | ||||||||
\(429\) | 787801. | 0.206668 | ||||||||
\(430\) | 759182. | 0.198004 | ||||||||
\(431\) | 4.05571e6 | 1.05166 | 0.525828 | − | 0.850591i | \(-0.323756\pi\) | ||||
0.525828 | + | 0.850591i | \(0.323756\pi\) | |||||||
\(432\) | −3.60484e7 | −9.29343 | ||||||||
\(433\) | −1.44028e6 | −0.369171 | −0.184585 | − | 0.982817i | \(-0.559094\pi\) | ||||
−0.184585 | + | 0.982817i | \(0.559094\pi\) | |||||||
\(434\) | −1.04235e6 | −0.265636 | ||||||||
\(435\) | −4.27342e6 | −1.08281 | ||||||||
\(436\) | 1.20386e7 | 3.03291 | ||||||||
\(437\) | −1.02811e7 | −2.57535 | ||||||||
\(438\) | 8.55798e6 | 2.13150 | ||||||||
\(439\) | −4.89840e6 | −1.21309 | −0.606545 | − | 0.795049i | \(-0.707445\pi\) | ||||
−0.606545 | + | 0.795049i | \(0.707445\pi\) | |||||||
\(440\) | −5.32522e6 | −1.31131 | ||||||||
\(441\) | 7.05972e6 | 1.72859 | ||||||||
\(442\) | 935373. | 0.227735 | ||||||||
\(443\) | −6.73786e6 | −1.63122 | −0.815611 | − | 0.578601i | \(-0.803599\pi\) | ||||
−0.815611 | + | 0.578601i | \(0.803599\pi\) | |||||||
\(444\) | 3.16766e7 | 7.62573 | ||||||||
\(445\) | 1.11833e6 | 0.267714 | ||||||||
\(446\) | −8.65624e6 | −2.06059 | ||||||||
\(447\) | 5.02110e6 | 1.18858 | ||||||||
\(448\) | −3.15852e7 | −7.43514 | ||||||||
\(449\) | 3.90647e6 | 0.914468 | 0.457234 | − | 0.889347i | \(-0.348840\pi\) | ||||
0.457234 | + | 0.889347i | \(0.348840\pi\) | |||||||
\(450\) | 1.62287e7 | 3.77793 | ||||||||
\(451\) | −202921. | −0.0469771 | ||||||||
\(452\) | 1.25993e7 | 2.90069 | ||||||||
\(453\) | 6.48648e6 | 1.48513 | ||||||||
\(454\) | −401025. | −0.0913129 | ||||||||
\(455\) | 228832. | 0.0518189 | ||||||||
\(456\) | 5.78306e7 | 13.0240 | ||||||||
\(457\) | −7.34036e6 | −1.64409 | −0.822047 | − | 0.569419i | \(-0.807168\pi\) | ||||
−0.822047 | + | 0.569419i | \(0.807168\pi\) | |||||||
\(458\) | 3.03044e6 | 0.675059 | ||||||||
\(459\) | 9.60647e6 | 2.12830 | ||||||||
\(460\) | 5.89206e6 | 1.29829 | ||||||||
\(461\) | 4.09372e6 | 0.897152 | 0.448576 | − | 0.893745i | \(-0.351931\pi\) | ||||
0.448576 | + | 0.893745i | \(0.351931\pi\) | |||||||
\(462\) | 2.21921e7 | 4.83719 | ||||||||
\(463\) | 3.96085e6 | 0.858689 | 0.429345 | − | 0.903141i | \(-0.358745\pi\) | ||||
0.429345 | + | 0.903141i | \(0.358745\pi\) | |||||||
\(464\) | −3.67865e7 | −7.93221 | ||||||||
\(465\) | −285438. | −0.0612180 | ||||||||
\(466\) | −8.77501e6 | −1.87190 | ||||||||
\(467\) | 1.63277e6 | 0.346444 | 0.173222 | − | 0.984883i | \(-0.444582\pi\) | ||||
0.173222 | + | 0.984883i | \(0.444582\pi\) | |||||||
\(468\) | 3.35610e6 | 0.708304 | ||||||||
\(469\) | 386807. | 0.0812012 | ||||||||
\(470\) | 1.96920e6 | 0.411192 | ||||||||
\(471\) | −3.32690e6 | −0.691015 | ||||||||
\(472\) | −2.02275e7 | −4.17914 | ||||||||
\(473\) | −1.46679e6 | −0.301451 | ||||||||
\(474\) | −7.33213e6 | −1.49894 | ||||||||
\(475\) | −8.51854e6 | −1.73233 | ||||||||
\(476\) | 1.95761e7 | 3.96012 | ||||||||
\(477\) | 1.74821e7 | 3.51801 | ||||||||
\(478\) | −1.71490e6 | −0.343296 | ||||||||
\(479\) | 2.91116e6 | 0.579732 | 0.289866 | − | 0.957067i | \(-0.406389\pi\) | ||||
0.289866 | + | 0.957067i | \(0.406389\pi\) | |||||||
\(480\) | −1.56093e7 | −3.09230 | ||||||||
\(481\) | −849420. | −0.167402 | ||||||||
\(482\) | −1.34299e7 | −2.63302 | ||||||||
\(483\) | −1.60588e7 | −3.13218 | ||||||||
\(484\) | 836240. | 0.162262 | ||||||||
\(485\) | −1.43172e6 | −0.276379 | ||||||||
\(486\) | 6.72492e6 | 1.29151 | ||||||||
\(487\) | −2.89689e6 | −0.553490 | −0.276745 | − | 0.960943i | \(-0.589256\pi\) | ||||
−0.276745 | + | 0.960943i | \(0.589256\pi\) | |||||||
\(488\) | 8.08979e6 | 1.53776 | ||||||||
\(489\) | −8.45836e6 | −1.59961 | ||||||||
\(490\) | 2.85848e6 | 0.537830 | ||||||||
\(491\) | −2.70718e6 | −0.506773 | −0.253386 | − | 0.967365i | \(-0.581544\pi\) | ||||
−0.253386 | + | 0.967365i | \(0.581544\pi\) | |||||||
\(492\) | −1.26292e6 | −0.235213 | ||||||||
\(493\) | 9.80319e6 | 1.81656 | ||||||||
\(494\) | −2.37113e6 | −0.437158 | ||||||||
\(495\) | 4.15976e6 | 0.763054 | ||||||||
\(496\) | −2.45711e6 | −0.448457 | ||||||||
\(497\) | 1.44377e7 | 2.62185 | ||||||||
\(498\) | 1.34594e7 | 2.43194 | ||||||||
\(499\) | −330570. | −0.0594308 | −0.0297154 | − | 0.999558i | \(-0.509460\pi\) | ||||
−0.0297154 | + | 0.999558i | \(0.509460\pi\) | |||||||
\(500\) | 1.04115e7 | 1.86247 | ||||||||
\(501\) | 9.43918e6 | 1.68012 | ||||||||
\(502\) | −394882. | −0.0699372 | ||||||||
\(503\) | 494040. | 0.0870646 | 0.0435323 | − | 0.999052i | \(-0.486139\pi\) | ||||
0.0435323 | + | 0.999052i | \(0.486139\pi\) | |||||||
\(504\) | 6.18304e7 | 10.8424 | ||||||||
\(505\) | −2.04484e6 | −0.356804 | ||||||||
\(506\) | −1.53226e7 | −2.66045 | ||||||||
\(507\) | 1.01728e7 | 1.75760 | ||||||||
\(508\) | 6.96813e6 | 1.19800 | ||||||||
\(509\) | −3.92159e6 | −0.670915 | −0.335457 | − | 0.942055i | \(-0.608891\pi\) | ||||
−0.335457 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(510\) | 7.21550e6 | 1.22840 | ||||||||
\(511\) | −4.80281e6 | −0.813660 | ||||||||
\(512\) | −3.56591e7 | −6.01167 | ||||||||
\(513\) | −2.43520e7 | −4.08546 | ||||||||
\(514\) | −550275. | −0.0918696 | ||||||||
\(515\) | −3.12756e6 | −0.519623 | ||||||||
\(516\) | −9.12886e6 | −1.50936 | ||||||||
\(517\) | −3.80463e6 | −0.626018 | ||||||||
\(518\) | −2.39279e7 | −3.91814 | ||||||||
\(519\) | 2.79830e6 | 0.456011 | ||||||||
\(520\) | 888726. | 0.144132 | ||||||||
\(521\) | −5.05932e6 | −0.816578 | −0.408289 | − | 0.912853i | \(-0.633875\pi\) | ||||
−0.408289 | + | 0.912853i | \(0.633875\pi\) | |||||||
\(522\) | 4.73433e7 | 7.60470 | ||||||||
\(523\) | 3.22834e6 | 0.516090 | 0.258045 | − | 0.966133i | \(-0.416922\pi\) | ||||
0.258045 | + | 0.966133i | \(0.416922\pi\) | |||||||
\(524\) | 3.18024e7 | 5.05977 | ||||||||
\(525\) | −1.33057e7 | −2.10688 | ||||||||
\(526\) | 1.88550e7 | 2.97140 | ||||||||
\(527\) | 654792. | 0.102701 | ||||||||
\(528\) | 5.23132e7 | 8.16632 | ||||||||
\(529\) | 4.65151e6 | 0.722695 | ||||||||
\(530\) | 7.07849e6 | 1.09459 | ||||||||
\(531\) | 1.58006e7 | 2.43185 | ||||||||
\(532\) | −4.96245e7 | −7.60181 | ||||||||
\(533\) | 33865.5 | 0.00516345 | ||||||||
\(534\) | −1.81001e7 | −2.74681 | ||||||||
\(535\) | −2.51612e6 | −0.380055 | ||||||||
\(536\) | 1.50226e6 | 0.225857 | ||||||||
\(537\) | 4.13867e6 | 0.619334 | ||||||||
\(538\) | 1.41082e7 | 2.10143 | ||||||||
\(539\) | −5.52279e6 | −0.818816 | ||||||||
\(540\) | 1.39560e7 | 2.05957 | ||||||||
\(541\) | −2.41717e6 | −0.355071 | −0.177535 | − | 0.984114i | \(-0.556812\pi\) | ||||
−0.177535 | + | 0.984114i | \(0.556812\pi\) | |||||||
\(542\) | −1.20409e6 | −0.176060 | ||||||||
\(543\) | 1.05665e7 | 1.53791 | ||||||||
\(544\) | 3.58076e7 | 5.18774 | ||||||||
\(545\) | −2.49023e6 | −0.359128 | ||||||||
\(546\) | −3.70364e6 | −0.531676 | ||||||||
\(547\) | −299209. | −0.0427569 | ||||||||
\(548\) | −2.31223e6 | −0.328912 | ||||||||
\(549\) | −6.31929e6 | −0.894824 | ||||||||
\(550\) | −1.26957e7 | −1.78957 | ||||||||
\(551\) | −2.48507e7 | −3.48706 | ||||||||
\(552\) | −6.23684e7 | −8.71199 | ||||||||
\(553\) | 4.11485e6 | 0.572191 | ||||||||
\(554\) | 2.60169e7 | 3.60149 | ||||||||
\(555\) | −6.55245e6 | −0.902966 | ||||||||
\(556\) | 3.13984e6 | 0.430745 | ||||||||
\(557\) | −891752. | −0.121788 | −0.0608942 | − | 0.998144i | \(-0.519395\pi\) | ||||
−0.0608942 | + | 0.998144i | \(0.519395\pi\) | |||||||
\(558\) | 3.16223e6 | 0.429940 | ||||||||
\(559\) | 244794. | 0.0331337 | ||||||||
\(560\) | 1.51954e7 | 2.04758 | ||||||||
\(561\) | −1.39409e7 | −1.87018 | ||||||||
\(562\) | 1.02703e7 | 1.37165 | ||||||||
\(563\) | 1.21958e7 | 1.62158 | 0.810792 | − | 0.585335i | \(-0.199037\pi\) | ||||
0.810792 | + | 0.585335i | \(0.199037\pi\) | |||||||
\(564\) | −2.36788e7 | −3.13446 | ||||||||
\(565\) | −2.60623e6 | −0.343472 | ||||||||
\(566\) | 2.03712e6 | 0.267285 | ||||||||
\(567\) | −1.57750e7 | −2.06068 | ||||||||
\(568\) | 5.60724e7 | 7.29253 | ||||||||
\(569\) | −17154.0 | −0.00222119 | −0.00111059 | − | 0.999999i | \(-0.500354\pi\) | ||||
−0.00111059 | + | 0.999999i | \(0.500354\pi\) | |||||||
\(570\) | −1.82910e7 | −2.35803 | ||||||||
\(571\) | 2.64958e6 | 0.340085 | 0.170042 | − | 0.985437i | \(-0.445610\pi\) | ||||
0.170042 | + | 0.985437i | \(0.445610\pi\) | |||||||
\(572\) | −2.62546e6 | −0.335518 | ||||||||
\(573\) | −9.30670e6 | −1.18416 | ||||||||
\(574\) | 953980. | 0.120854 | ||||||||
\(575\) | 9.18696e6 | 1.15878 | ||||||||
\(576\) | 9.58222e7 | 12.0340 | ||||||||
\(577\) | −8.44674e6 | −1.05621 | −0.528104 | − | 0.849180i | \(-0.677097\pi\) | ||||
−0.528104 | + | 0.849180i | \(0.677097\pi\) | |||||||
\(578\) | −710290. | −0.0884333 | ||||||||
\(579\) | −1.35982e7 | −1.68572 | ||||||||
\(580\) | 1.42418e7 | 1.75790 | ||||||||
\(581\) | −7.55353e6 | −0.928345 | ||||||||
\(582\) | 2.31724e7 | 2.83572 | ||||||||
\(583\) | −1.36761e7 | −1.66645 | ||||||||
\(584\) | −1.86529e7 | −2.26315 | ||||||||
\(585\) | −694223. | −0.0838705 | ||||||||
\(586\) | 2.03530e7 | 2.44841 | ||||||||
\(587\) | −458654. | −0.0549402 | −0.0274701 | − | 0.999623i | \(-0.508745\pi\) | ||||
−0.0274701 | + | 0.999623i | \(0.508745\pi\) | |||||||
\(588\) | −3.43720e7 | −4.09979 | ||||||||
\(589\) | −1.65987e6 | −0.197145 | ||||||||
\(590\) | 6.39765e6 | 0.756642 | ||||||||
\(591\) | −1.11351e6 | −0.131137 | ||||||||
\(592\) | −5.64049e7 | −6.61474 | ||||||||
\(593\) | −7.42864e6 | −0.867506 | −0.433753 | − | 0.901032i | \(-0.642811\pi\) | ||||
−0.433753 | + | 0.901032i | \(0.642811\pi\) | |||||||
\(594\) | −3.62932e7 | −4.22046 | ||||||||
\(595\) | −4.04939e6 | −0.468919 | ||||||||
\(596\) | −1.67335e7 | −1.92962 | ||||||||
\(597\) | −4.45664e6 | −0.511766 | ||||||||
\(598\) | 2.55719e6 | 0.292422 | ||||||||
\(599\) | −1.04362e7 | −1.18843 | −0.594216 | − | 0.804305i | \(-0.702538\pi\) | ||||
−0.594216 | + | 0.804305i | \(0.702538\pi\) | |||||||
\(600\) | −5.16760e7 | −5.86018 | ||||||||
\(601\) | 2.64233e6 | 0.298401 | 0.149201 | − | 0.988807i | \(-0.452330\pi\) | ||||
0.149201 | + | 0.988807i | \(0.452330\pi\) | |||||||
\(602\) | 6.89575e6 | 0.775515 | ||||||||
\(603\) | −1.17348e6 | −0.131427 | ||||||||
\(604\) | −2.16171e7 | −2.41105 | ||||||||
\(605\) | −172980. | −0.0192135 | ||||||||
\(606\) | 3.30956e7 | 3.66091 | ||||||||
\(607\) | 6.72243e6 | 0.740550 | 0.370275 | − | 0.928922i | \(-0.379263\pi\) | ||||
0.370275 | + | 0.928922i | \(0.379263\pi\) | |||||||
\(608\) | −9.07708e7 | −9.95835 | ||||||||
\(609\) | −3.88160e7 | −4.24100 | ||||||||
\(610\) | −2.55868e6 | −0.278414 | ||||||||
\(611\) | 634956. | 0.0688083 | ||||||||
\(612\) | −5.93892e7 | −6.40957 | ||||||||
\(613\) | −1.84145e7 | −1.97928 | −0.989641 | − | 0.143562i | \(-0.954144\pi\) | ||||
−0.989641 | + | 0.143562i | \(0.954144\pi\) | |||||||
\(614\) | −3.21685e7 | −3.44358 | ||||||||
\(615\) | 261240. | 0.0278517 | ||||||||
\(616\) | −4.83696e7 | −5.13595 | ||||||||
\(617\) | 1.35918e7 | 1.43735 | 0.718675 | − | 0.695346i | \(-0.244749\pi\) | ||||
0.718675 | + | 0.695346i | \(0.244749\pi\) | |||||||
\(618\) | 5.06195e7 | 5.33146 | ||||||||
\(619\) | 1.12109e7 | 1.17602 | 0.588009 | − | 0.808855i | \(-0.299912\pi\) | ||||
0.588009 | + | 0.808855i | \(0.299912\pi\) | |||||||
\(620\) | 951262. | 0.0993851 | ||||||||
\(621\) | 2.62628e7 | 2.73283 | ||||||||
\(622\) | −3.12079e7 | −3.23436 | ||||||||
\(623\) | 1.01579e7 | 1.04854 | ||||||||
\(624\) | −8.73055e6 | −0.897595 | ||||||||
\(625\) | 6.46813e6 | 0.662337 | ||||||||
\(626\) | 1.25080e7 | 1.27571 | ||||||||
\(627\) | 3.53395e7 | 3.58997 | ||||||||
\(628\) | 1.10874e7 | 1.12184 | ||||||||
\(629\) | 1.50313e7 | 1.51485 | ||||||||
\(630\) | −1.95560e7 | −1.96304 | ||||||||
\(631\) | 7.62809e6 | 0.762680 | 0.381340 | − | 0.924435i | \(-0.375463\pi\) | ||||
0.381340 | + | 0.924435i | \(0.375463\pi\) | |||||||
\(632\) | 1.59810e7 | 1.59152 | ||||||||
\(633\) | 1.15212e7 | 1.14284 | ||||||||
\(634\) | 8.51070e6 | 0.840896 | ||||||||
\(635\) | −1.44139e6 | −0.141856 | ||||||||
\(636\) | −8.51160e7 | −8.34388 | ||||||||
\(637\) | 921698. | 0.0899995 | ||||||||
\(638\) | −3.70364e7 | −3.60228 | ||||||||
\(639\) | −4.38006e7 | −4.24354 | ||||||||
\(640\) | 2.08000e7 | 2.00731 | ||||||||
\(641\) | 1.83128e7 | 1.76039 | 0.880196 | − | 0.474611i | \(-0.157411\pi\) | ||||
0.880196 | + | 0.474611i | \(0.157411\pi\) | |||||||
\(642\) | 4.07233e7 | 3.89946 | ||||||||
\(643\) | 1.91637e6 | 0.182790 | 0.0913950 | − | 0.995815i | \(-0.470867\pi\) | ||||
0.0913950 | + | 0.995815i | \(0.470867\pi\) | |||||||
\(644\) | 5.35184e7 | 5.08497 | ||||||||
\(645\) | 1.88834e6 | 0.178724 | ||||||||
\(646\) | 4.19593e7 | 3.95592 | ||||||||
\(647\) | 3.57012e6 | 0.335291 | 0.167646 | − | 0.985847i | \(-0.446384\pi\) | ||||
0.167646 | + | 0.985847i | \(0.446384\pi\) | |||||||
\(648\) | −6.12659e7 | −5.73168 | ||||||||
\(649\) | −1.23607e7 | −1.15195 | ||||||||
\(650\) | 2.11878e6 | 0.196699 | ||||||||
\(651\) | −2.59267e6 | −0.239770 | ||||||||
\(652\) | 2.81887e7 | 2.59691 | ||||||||
\(653\) | −4.41723e6 | −0.405385 | −0.202692 | − | 0.979242i | \(-0.564969\pi\) | ||||
−0.202692 | + | 0.979242i | \(0.564969\pi\) | |||||||
\(654\) | 4.03043e7 | 3.68475 | ||||||||
\(655\) | −6.57846e6 | −0.599130 | ||||||||
\(656\) | 2.24881e6 | 0.204029 | ||||||||
\(657\) | 1.45706e7 | 1.31693 | ||||||||
\(658\) | 1.78865e7 | 1.61050 | ||||||||
\(659\) | −424525. | −0.0380794 | −0.0190397 | − | 0.999819i | \(-0.506061\pi\) | ||||
−0.0190397 | + | 0.999819i | \(0.506061\pi\) | |||||||
\(660\) | −2.02529e7 | −1.80978 | ||||||||
\(661\) | 5.28141e6 | 0.470161 | 0.235080 | − | 0.971976i | \(-0.424465\pi\) | ||||
0.235080 | + | 0.971976i | \(0.424465\pi\) | |||||||
\(662\) | −1.79565e7 | −1.59249 | ||||||||
\(663\) | 2.32659e6 | 0.205559 | ||||||||
\(664\) | −2.93360e7 | −2.58214 | ||||||||
\(665\) | 1.02650e7 | 0.900133 | ||||||||
\(666\) | 7.25916e7 | 6.34162 | ||||||||
\(667\) | 2.68006e7 | 2.33255 | ||||||||
\(668\) | −3.14574e7 | −2.72761 | ||||||||
\(669\) | −2.15310e7 | −1.85994 | ||||||||
\(670\) | −475143. | −0.0408919 | ||||||||
\(671\) | 4.94356e6 | 0.423871 | ||||||||
\(672\) | −1.41782e8 | −12.1115 | ||||||||
\(673\) | −1.33158e7 | −1.13326 | −0.566631 | − | 0.823972i | \(-0.691753\pi\) | ||||
−0.566631 | + | 0.823972i | \(0.691753\pi\) | |||||||
\(674\) | 5.00333e6 | 0.424238 | ||||||||
\(675\) | 2.17603e7 | 1.83826 | ||||||||
\(676\) | −3.39023e7 | −2.85340 | ||||||||
\(677\) | 5.07423e6 | 0.425499 | 0.212750 | − | 0.977107i | \(-0.431758\pi\) | ||||
0.212750 | + | 0.977107i | \(0.431758\pi\) | |||||||
\(678\) | 4.21817e7 | 3.52411 | ||||||||
\(679\) | −1.30045e7 | −1.08248 | ||||||||
\(680\) | −1.57268e7 | −1.30427 | ||||||||
\(681\) | −997487. | −0.0824213 | ||||||||
\(682\) | −2.47380e6 | −0.203659 | ||||||||
\(683\) | −1.06491e7 | −0.873496 | −0.436748 | − | 0.899584i | \(-0.643870\pi\) | ||||
−0.436748 | + | 0.899584i | \(0.643870\pi\) | |||||||
\(684\) | 1.50549e8 | 12.3038 | ||||||||
\(685\) | 478295. | 0.0389466 | ||||||||
\(686\) | −6.62312e6 | −0.537344 | ||||||||
\(687\) | 7.53773e6 | 0.609324 | ||||||||
\(688\) | 1.62553e7 | 1.30925 | ||||||||
\(689\) | 2.28241e6 | 0.183167 | ||||||||
\(690\) | 1.97262e7 | 1.57732 | ||||||||
\(691\) | −9.29758e6 | −0.740755 | −0.370378 | − | 0.928881i | \(-0.620772\pi\) | ||||
−0.370378 | + | 0.928881i | \(0.620772\pi\) | |||||||
\(692\) | −9.32573e6 | −0.740317 | ||||||||
\(693\) | 3.77837e7 | 2.98862 | ||||||||
\(694\) | −8.51339e6 | −0.670971 | ||||||||
\(695\) | −649490. | −0.0510047 | ||||||||
\(696\) | −1.50752e8 | −11.7961 | ||||||||
\(697\) | −599281. | −0.0467250 | ||||||||
\(698\) | 2.51024e7 | 1.95019 | ||||||||
\(699\) | −2.18264e7 | −1.68962 | ||||||||
\(700\) | 4.43432e7 | 3.42044 | ||||||||
\(701\) | 2.43226e7 | 1.86946 | 0.934729 | − | 0.355361i | \(-0.115642\pi\) | ||||
0.934729 | + | 0.355361i | \(0.115642\pi\) | |||||||
\(702\) | 6.05698e6 | 0.463888 | ||||||||
\(703\) | −3.81036e7 | −2.90789 | ||||||||
\(704\) | −7.49613e7 | −5.70040 | ||||||||
\(705\) | 4.89807e6 | 0.371152 | ||||||||
\(706\) | 1.40410e7 | 1.06020 | ||||||||
\(707\) | −1.85735e7 | −1.39748 | ||||||||
\(708\) | −7.69292e7 | −5.76777 | ||||||||
\(709\) | 1.61653e7 | 1.20772 | 0.603862 | − | 0.797089i | \(-0.293628\pi\) | ||||
0.603862 | + | 0.797089i | \(0.293628\pi\) | |||||||
\(710\) | −1.77349e7 | −1.32033 | ||||||||
\(711\) | −1.24835e7 | −0.926108 | ||||||||
\(712\) | 3.94509e7 | 2.91647 | ||||||||
\(713\) | 1.79011e6 | 0.131873 | ||||||||
\(714\) | 6.55393e7 | 4.81123 | ||||||||
\(715\) | 543088. | 0.0397288 | ||||||||
\(716\) | −1.37927e7 | −1.00546 | ||||||||
\(717\) | −4.26554e6 | −0.309868 | ||||||||
\(718\) | 2.03035e7 | 1.46981 | ||||||||
\(719\) | −2.51635e7 | −1.81530 | −0.907652 | − | 0.419723i | \(-0.862127\pi\) | ||||
−0.907652 | + | 0.419723i | \(0.862127\pi\) | |||||||
\(720\) | −4.60992e7 | −3.31408 | ||||||||
\(721\) | −2.84081e7 | −2.03518 | ||||||||
\(722\) | −7.87381e7 | −5.62137 | ||||||||
\(723\) | −3.34046e7 | −2.37663 | ||||||||
\(724\) | −3.52142e7 | −2.49673 | ||||||||
\(725\) | 2.22059e7 | 1.56900 | ||||||||
\(726\) | 2.79967e6 | 0.197136 | ||||||||
\(727\) | −1.21831e7 | −0.854913 | −0.427457 | − | 0.904036i | \(-0.640590\pi\) | ||||
−0.427457 | + | 0.904036i | \(0.640590\pi\) | |||||||
\(728\) | 8.07242e6 | 0.564514 | ||||||||
\(729\) | −5.33179e6 | −0.371582 | ||||||||
\(730\) | 5.89963e6 | 0.409749 | ||||||||
\(731\) | −4.33185e6 | −0.299833 | ||||||||
\(732\) | 3.07671e7 | 2.12231 | ||||||||
\(733\) | 1.20161e7 | 0.826046 | 0.413023 | − | 0.910721i | \(-0.364473\pi\) | ||||
0.413023 | + | 0.910721i | \(0.364473\pi\) | |||||||
\(734\) | −4.40721e7 | −3.01942 | ||||||||
\(735\) | 7.11001e6 | 0.485458 | ||||||||
\(736\) | 9.78934e7 | 6.66130 | ||||||||
\(737\) | 918010. | 0.0622556 | ||||||||
\(738\) | −2.89415e6 | −0.195605 | ||||||||
\(739\) | −4.56003e6 | −0.307154 | −0.153577 | − | 0.988137i | \(-0.549079\pi\) | ||||
−0.153577 | + | 0.988137i | \(0.549079\pi\) | |||||||
\(740\) | 2.18370e7 | 1.46593 | ||||||||
\(741\) | −5.89781e6 | −0.394589 | ||||||||
\(742\) | 6.42948e7 | 4.28713 | ||||||||
\(743\) | 1.05670e7 | 0.702233 | 0.351116 | − | 0.936332i | \(-0.385802\pi\) | ||||
0.351116 | + | 0.936332i | \(0.385802\pi\) | |||||||
\(744\) | −1.00693e7 | −0.666907 | ||||||||
\(745\) | 3.46140e6 | 0.228487 | ||||||||
\(746\) | −2.95758e7 | −1.94576 | ||||||||
\(747\) | 2.29156e7 | 1.50255 | ||||||||
\(748\) | 4.64599e7 | 3.03616 | ||||||||
\(749\) | −2.28542e7 | −1.48854 | ||||||||
\(750\) | 3.48571e7 | 2.26276 | ||||||||
\(751\) | −1.31974e7 | −0.853865 | −0.426933 | − | 0.904283i | \(-0.640406\pi\) | ||||
−0.426933 | + | 0.904283i | \(0.640406\pi\) | |||||||
\(752\) | 4.21636e7 | 2.71890 | ||||||||
\(753\) | −982206. | −0.0631270 | ||||||||
\(754\) | 6.18101e6 | 0.395942 | ||||||||
\(755\) | 4.47160e6 | 0.285493 | ||||||||
\(756\) | 1.26764e8 | 8.06663 | ||||||||
\(757\) | −3.35942e6 | −0.213071 | −0.106535 | − | 0.994309i | \(-0.533976\pi\) | ||||
−0.106535 | + | 0.994309i | \(0.533976\pi\) | |||||||
\(758\) | 1.10180e7 | 0.696511 | ||||||||
\(759\) | −3.81125e7 | −2.40139 | ||||||||
\(760\) | 3.98668e7 | 2.50367 | ||||||||
\(761\) | 1.18755e7 | 0.743342 | 0.371671 | − | 0.928365i | \(-0.378785\pi\) | ||||
0.371671 | + | 0.928365i | \(0.378785\pi\) | |||||||
\(762\) | 2.33288e7 | 1.45548 | ||||||||
\(763\) | −2.26191e7 | −1.40658 | ||||||||
\(764\) | 3.10159e7 | 1.92243 | ||||||||
\(765\) | 1.22849e7 | 0.758959 | ||||||||
\(766\) | −3.09345e7 | −1.90490 | ||||||||
\(767\) | 2.06288e6 | 0.126615 | ||||||||
\(768\) | −1.75232e8 | −10.7204 | ||||||||
\(769\) | 2.63124e7 | 1.60452 | 0.802260 | − | 0.596975i | \(-0.203631\pi\) | ||||
0.802260 | + | 0.596975i | \(0.203631\pi\) | |||||||
\(770\) | 1.52986e7 | 0.929875 | ||||||||
\(771\) | −1.36872e6 | −0.0829238 | ||||||||
\(772\) | 4.53179e7 | 2.73670 | ||||||||
\(773\) | 6.59751e6 | 0.397129 | 0.198564 | − | 0.980088i | \(-0.436372\pi\) | ||||
0.198564 | + | 0.980088i | \(0.436372\pi\) | |||||||
\(774\) | −2.09201e7 | −1.25519 | ||||||||
\(775\) | 1.48322e6 | 0.0887055 | ||||||||
\(776\) | −5.05063e7 | −3.01086 | ||||||||
\(777\) | −5.95168e7 | −3.53661 | ||||||||
\(778\) | 1.37075e7 | 0.811915 | ||||||||
\(779\) | 1.51915e6 | 0.0896928 | ||||||||
\(780\) | 3.38000e6 | 0.198921 | ||||||||
\(781\) | 3.42650e7 | 2.01013 | ||||||||
\(782\) | −4.52518e7 | −2.64617 | ||||||||
\(783\) | 6.34803e7 | 3.70028 | ||||||||
\(784\) | 6.12045e7 | 3.55626 | ||||||||
\(785\) | −2.29347e6 | −0.132837 | ||||||||
\(786\) | 1.06472e8 | 6.14723 | ||||||||
\(787\) | 2.24658e7 | 1.29296 | 0.646481 | − | 0.762930i | \(-0.276240\pi\) | ||||
0.646481 | + | 0.762930i | \(0.276240\pi\) | |||||||
\(788\) | 3.71094e6 | 0.212896 | ||||||||
\(789\) | 4.68988e7 | 2.68206 | ||||||||
\(790\) | −5.05456e6 | −0.288148 | ||||||||
\(791\) | −2.36727e7 | −1.34526 | ||||||||
\(792\) | 1.46742e8 | 8.31270 | ||||||||
\(793\) | −825031. | −0.0465894 | ||||||||
\(794\) | 7.00909e6 | 0.394558 | ||||||||
\(795\) | 1.76066e7 | 0.988002 | ||||||||
\(796\) | 1.48524e7 | 0.830832 | ||||||||
\(797\) | −1.47289e7 | −0.821344 | −0.410672 | − | 0.911783i | \(-0.634706\pi\) | ||||
−0.410672 | + | 0.911783i | \(0.634706\pi\) | |||||||
\(798\) | −1.66139e8 | −9.23560 | ||||||||
\(799\) | −1.12361e7 | −0.622658 | ||||||||
\(800\) | 8.11106e7 | 4.48077 | ||||||||
\(801\) | −3.08168e7 | −1.69710 | ||||||||
\(802\) | 5.62866e6 | 0.309007 | ||||||||
\(803\) | −1.13985e7 | −0.623820 | ||||||||
\(804\) | 5.71340e6 | 0.311713 | ||||||||
\(805\) | −1.10705e7 | −0.602113 | ||||||||
\(806\) | 412853. | 0.0223850 | ||||||||
\(807\) | 3.50919e7 | 1.89681 | ||||||||
\(808\) | −7.21348e7 | −3.88702 | ||||||||
\(809\) | −8.37974e6 | −0.450152 | −0.225076 | − | 0.974341i | \(-0.572263\pi\) | ||||
−0.225076 | + | 0.974341i | \(0.572263\pi\) | |||||||
\(810\) | 1.93775e7 | 1.03773 | ||||||||
\(811\) | 3.13647e7 | 1.67451 | 0.837257 | − | 0.546809i | \(-0.184158\pi\) | ||||
0.837257 | + | 0.546809i | \(0.184158\pi\) | |||||||
\(812\) | 1.29360e8 | 6.88510 | ||||||||
\(813\) | −2.99499e6 | −0.158916 | ||||||||
\(814\) | −5.67881e7 | −3.00397 | ||||||||
\(815\) | −5.83096e6 | −0.307501 | ||||||||
\(816\) | 1.54495e8 | 8.12249 | ||||||||
\(817\) | 1.09810e7 | 0.575557 | ||||||||
\(818\) | −3.26009e6 | −0.170352 | ||||||||
\(819\) | −6.30572e6 | −0.328492 | ||||||||
\(820\) | −870619. | −0.0452161 | ||||||||
\(821\) | 1.31639e7 | 0.681594 | 0.340797 | − | 0.940137i | \(-0.389303\pi\) | ||||
0.340797 | + | 0.940137i | \(0.389303\pi\) | |||||||
\(822\) | −7.74119e6 | −0.399603 | ||||||||
\(823\) | −2.47626e7 | −1.27437 | −0.637187 | − | 0.770709i | \(-0.719902\pi\) | ||||
−0.637187 | + | 0.770709i | \(0.719902\pi\) | |||||||
\(824\) | −1.10330e8 | −5.66076 | ||||||||
\(825\) | −3.15785e7 | −1.61531 | ||||||||
\(826\) | 5.81107e7 | 2.96351 | ||||||||
\(827\) | −1.56468e7 | −0.795539 | −0.397770 | − | 0.917485i | \(-0.630216\pi\) | ||||
−0.397770 | + | 0.917485i | \(0.630216\pi\) | |||||||
\(828\) | −1.62362e8 | −8.23017 | ||||||||
\(829\) | −3.67510e7 | −1.85730 | −0.928652 | − | 0.370951i | \(-0.879032\pi\) | ||||
−0.928652 | + | 0.370951i | \(0.879032\pi\) | |||||||
\(830\) | 9.27854e6 | 0.467503 | ||||||||
\(831\) | 6.47130e7 | 3.25079 | ||||||||
\(832\) | 1.25103e7 | 0.626555 | ||||||||
\(833\) | −1.63103e7 | −0.814422 | ||||||||
\(834\) | 1.05120e7 | 0.523322 | ||||||||
\(835\) | 6.50711e6 | 0.322977 | ||||||||
\(836\) | −1.17774e8 | −5.82818 | ||||||||
\(837\) | 4.24008e6 | 0.209200 | ||||||||
\(838\) | −9.05674e6 | −0.445515 | ||||||||
\(839\) | 1.31090e7 | 0.642931 | 0.321466 | − | 0.946921i | \(-0.395825\pi\) | ||||
0.321466 | + | 0.946921i | \(0.395825\pi\) | |||||||
\(840\) | 6.22708e7 | 3.04499 | ||||||||
\(841\) | 4.42691e7 | 2.15829 | ||||||||
\(842\) | 6.78133e6 | 0.329636 | ||||||||
\(843\) | 2.55457e7 | 1.23808 | ||||||||
\(844\) | −3.83959e7 | −1.85536 | ||||||||
\(845\) | 7.01284e6 | 0.337872 | ||||||||
\(846\) | −5.42634e7 | −2.60664 | ||||||||
\(847\) | −1.57120e6 | −0.0752528 | ||||||||
\(848\) | 1.51562e8 | 7.23768 | ||||||||
\(849\) | 5.06700e6 | 0.241258 | ||||||||
\(850\) | −3.74938e7 | −1.77997 | ||||||||
\(851\) | 4.10935e7 | 1.94513 | ||||||||
\(852\) | 2.13255e8 | 10.0647 | ||||||||
\(853\) | 2.86732e7 | 1.34928 | 0.674641 | − | 0.738146i | \(-0.264298\pi\) | ||||
0.674641 | + | 0.738146i | \(0.264298\pi\) | |||||||
\(854\) | −2.32408e7 | −1.09045 | ||||||||
\(855\) | −3.11417e7 | −1.45689 | ||||||||
\(856\) | −8.87600e7 | −4.14031 | ||||||||
\(857\) | 2.23024e7 | 1.03729 | 0.518644 | − | 0.854990i | \(-0.326437\pi\) | ||||
0.518644 | + | 0.854990i | \(0.326437\pi\) | |||||||
\(858\) | −8.78985e6 | −0.407627 | ||||||||
\(859\) | −3.25219e7 | −1.50381 | −0.751905 | − | 0.659271i | \(-0.770865\pi\) | ||||
−0.751905 | + | 0.659271i | \(0.770865\pi\) | |||||||
\(860\) | −6.29318e6 | −0.290151 | ||||||||
\(861\) | 2.37287e6 | 0.109085 | ||||||||
\(862\) | −4.52514e7 | −2.07426 | ||||||||
\(863\) | −2.35901e7 | −1.07821 | −0.539104 | − | 0.842239i | \(-0.681237\pi\) | ||||
−0.539104 | + | 0.842239i | \(0.681237\pi\) | |||||||
\(864\) | 2.31871e8 | 10.5673 | ||||||||
\(865\) | 1.92907e6 | 0.0876612 | ||||||||
\(866\) | 1.60699e7 | 0.728144 | ||||||||
\(867\) | −1.76673e6 | −0.0798221 | ||||||||
\(868\) | 8.64044e6 | 0.389257 | ||||||||
\(869\) | 9.76578e6 | 0.438690 | ||||||||
\(870\) | 4.76805e7 | 2.13571 | ||||||||
\(871\) | −153207. | −0.00684278 | ||||||||
\(872\) | −8.78470e7 | −3.91233 | ||||||||
\(873\) | 3.94527e7 | 1.75203 | ||||||||
\(874\) | 1.14711e8 | 5.07957 | ||||||||
\(875\) | −1.95621e7 | −0.863763 | ||||||||
\(876\) | −7.09407e7 | −3.12345 | ||||||||
\(877\) | −3.50444e7 | −1.53858 | −0.769290 | − | 0.638900i | \(-0.779390\pi\) | ||||
−0.769290 | + | 0.638900i | \(0.779390\pi\) | |||||||
\(878\) | 5.46537e7 | 2.39267 | ||||||||
\(879\) | 5.06247e7 | 2.20999 | ||||||||
\(880\) | 3.60632e7 | 1.56985 | ||||||||
\(881\) | 2.88177e6 | 0.125089 | 0.0625446 | − | 0.998042i | \(-0.480078\pi\) | ||||
0.0625446 | + | 0.998042i | \(0.480078\pi\) | |||||||
\(882\) | −7.87685e7 | −3.40942 | ||||||||
\(883\) | −3.10076e7 | −1.33834 | −0.669170 | − | 0.743110i | \(-0.733350\pi\) | ||||
−0.669170 | + | 0.743110i | \(0.733350\pi\) | |||||||
\(884\) | −7.75370e6 | −0.333717 | ||||||||
\(885\) | 1.59131e7 | 0.682964 | ||||||||
\(886\) | 7.51774e7 | 3.21739 | ||||||||
\(887\) | −3.08394e7 | −1.31612 | −0.658062 | − | 0.752964i | \(-0.728624\pi\) | ||||
−0.658062 | + | 0.752964i | \(0.728624\pi\) | |||||||
\(888\) | −2.31148e8 | −9.83689 | ||||||||
\(889\) | −1.30923e7 | −0.555600 | ||||||||
\(890\) | −1.24777e7 | −0.528032 | ||||||||
\(891\) | −3.74387e7 | −1.57989 | ||||||||
\(892\) | 7.17552e7 | 3.01954 | ||||||||
\(893\) | 2.84831e7 | 1.19525 | ||||||||
\(894\) | −5.60227e7 | −2.34434 | ||||||||
\(895\) | 2.85308e6 | 0.119057 | ||||||||
\(896\) | 1.88929e8 | 7.86193 | ||||||||
\(897\) | 6.36059e6 | 0.263947 | ||||||||
\(898\) | −4.35862e7 | −1.80368 | ||||||||
\(899\) | 4.32691e6 | 0.178558 | ||||||||
\(900\) | −1.34527e8 | −5.53609 | ||||||||
\(901\) | −4.03894e7 | −1.65751 | ||||||||
\(902\) | 2.26408e6 | 0.0926565 | ||||||||
\(903\) | 1.71521e7 | 0.699999 | ||||||||
\(904\) | −9.19389e7 | −3.74178 | ||||||||
\(905\) | 7.28422e6 | 0.295639 | ||||||||
\(906\) | −7.23726e7 | −2.92923 | ||||||||
\(907\) | 1.08662e7 | 0.438591 | 0.219296 | − | 0.975658i | \(-0.429624\pi\) | ||||
0.219296 | + | 0.975658i | \(0.429624\pi\) | |||||||
\(908\) | 3.32427e6 | 0.133808 | ||||||||
\(909\) | 5.63477e7 | 2.26186 | ||||||||
\(910\) | −2.55318e6 | −0.102207 | ||||||||
\(911\) | 4.02309e7 | 1.60607 | 0.803034 | − | 0.595933i | \(-0.203217\pi\) | ||||
0.803034 | + | 0.595933i | \(0.203217\pi\) | |||||||
\(912\) | −3.91638e8 | −15.5919 | ||||||||
\(913\) | −1.79268e7 | −0.711747 | ||||||||
\(914\) | 8.18997e7 | 3.24278 | ||||||||
\(915\) | −6.36431e6 | −0.251304 | ||||||||
\(916\) | −2.51206e7 | −0.989215 | ||||||||
\(917\) | −5.97530e7 | −2.34658 | ||||||||
\(918\) | −1.07184e8 | −4.19781 | ||||||||
\(919\) | 1.70270e7 | 0.665043 | 0.332521 | − | 0.943096i | \(-0.392101\pi\) | ||||
0.332521 | + | 0.943096i | \(0.392101\pi\) | |||||||
\(920\) | −4.29950e7 | −1.67475 | ||||||||
\(921\) | −8.00141e7 | −3.10826 | ||||||||
\(922\) | −4.56755e7 | −1.76952 | ||||||||
\(923\) | −5.71850e6 | −0.220942 | ||||||||
\(924\) | −1.83959e8 | −7.08830 | ||||||||
\(925\) | 3.40484e7 | 1.30841 | ||||||||
\(926\) | −4.41930e7 | −1.69366 | ||||||||
\(927\) | 8.61834e7 | 3.29401 | ||||||||
\(928\) | 2.36620e8 | 9.01946 | ||||||||
\(929\) | 1.01384e7 | 0.385416 | 0.192708 | − | 0.981256i | \(-0.438273\pi\) | ||||
0.192708 | + | 0.981256i | \(0.438273\pi\) | |||||||
\(930\) | 3.18476e6 | 0.120745 | ||||||||
\(931\) | 4.13459e7 | 1.56336 | ||||||||
\(932\) | 7.27398e7 | 2.74304 | ||||||||
\(933\) | −7.76246e7 | −2.91941 | ||||||||
\(934\) | −1.82176e7 | −0.683318 | ||||||||
\(935\) | −9.61044e6 | −0.359513 | ||||||||
\(936\) | −2.44898e7 | −0.913684 | ||||||||
\(937\) | −3.63635e7 | −1.35306 | −0.676529 | − | 0.736416i | \(-0.736517\pi\) | ||||
−0.676529 | + | 0.736416i | \(0.736517\pi\) | |||||||
\(938\) | −4.31578e6 | −0.160159 | ||||||||
\(939\) | 3.11117e7 | 1.15149 | ||||||||
\(940\) | −1.63235e7 | −0.602551 | ||||||||
\(941\) | 8.48490e6 | 0.312372 | 0.156186 | − | 0.987728i | \(-0.450080\pi\) | ||||
0.156186 | + | 0.987728i | \(0.450080\pi\) | |||||||
\(942\) | 3.71198e7 | 1.36294 | ||||||||
\(943\) | −1.63836e6 | −0.0599969 | ||||||||
\(944\) | 1.36984e8 | 5.00310 | ||||||||
\(945\) | −2.62217e7 | −0.955173 | ||||||||
\(946\) | 1.63657e7 | 0.594575 | ||||||||
\(947\) | 246640. | 0.00893693 | 0.00446847 | − | 0.999990i | \(-0.498578\pi\) | ||||
0.00446847 | + | 0.999990i | \(0.498578\pi\) | |||||||
\(948\) | 6.07791e7 | 2.19651 | ||||||||
\(949\) | 1.90230e6 | 0.0685667 | ||||||||
\(950\) | 9.50452e7 | 3.41681 | ||||||||
\(951\) | 2.11690e7 | 0.759013 | ||||||||
\(952\) | −1.42849e8 | −5.10839 | ||||||||
\(953\) | 1.84803e6 | 0.0659137 | 0.0329569 | − | 0.999457i | \(-0.489508\pi\) | ||||
0.0329569 | + | 0.999457i | \(0.489508\pi\) | |||||||
\(954\) | −1.95055e8 | −6.93884 | ||||||||
\(955\) | −6.41577e6 | −0.227636 | ||||||||
\(956\) | 1.42155e7 | 0.503058 | ||||||||
\(957\) | −9.21222e7 | −3.25151 | ||||||||
\(958\) | −3.24811e7 | −1.14345 | ||||||||
\(959\) | 4.34442e6 | 0.152541 | ||||||||
\(960\) | 9.65048e7 | 3.37964 | ||||||||
\(961\) | −2.83401e7 | −0.989905 | ||||||||
\(962\) | 9.47737e6 | 0.330179 | ||||||||
\(963\) | 6.93344e7 | 2.40925 | ||||||||
\(964\) | 1.11326e8 | 3.85836 | ||||||||
\(965\) | −9.37421e6 | −0.324053 | ||||||||
\(966\) | 1.79176e8 | 6.17784 | ||||||||
\(967\) | −3.71164e7 | −1.27644 | −0.638219 | − | 0.769855i | \(-0.720329\pi\) | ||||
−0.638219 | + | 0.769855i | \(0.720329\pi\) | |||||||
\(968\) | −6.10214e6 | −0.209312 | ||||||||
\(969\) | 1.04367e8 | 3.57071 | ||||||||
\(970\) | 1.59744e7 | 0.545124 | ||||||||
\(971\) | 5.58644e7 | 1.90146 | 0.950730 | − | 0.310020i | \(-0.100336\pi\) | ||||
0.950730 | + | 0.310020i | \(0.100336\pi\) | |||||||
\(972\) | −5.57457e7 | −1.89254 | ||||||||
\(973\) | −5.89940e6 | −0.199768 | ||||||||
\(974\) | 3.23219e7 | 1.09169 | ||||||||
\(975\) | 5.27014e6 | 0.177546 | ||||||||
\(976\) | −5.47854e7 | −1.84094 | ||||||||
\(977\) | 1.89734e7 | 0.635930 | 0.317965 | − | 0.948102i | \(-0.397000\pi\) | ||||
0.317965 | + | 0.948102i | \(0.397000\pi\) | |||||||
\(978\) | 9.43738e7 | 3.15504 | ||||||||
\(979\) | 2.41079e7 | 0.803900 | ||||||||
\(980\) | −2.36951e7 | −0.788123 | ||||||||
\(981\) | 6.86211e7 | 2.27659 | ||||||||
\(982\) | 3.02052e7 | 0.999548 | ||||||||
\(983\) | −4.34136e7 | −1.43299 | −0.716494 | − | 0.697593i | \(-0.754254\pi\) | ||||
−0.716494 | + | 0.697593i | \(0.754254\pi\) | |||||||
\(984\) | 9.21564e6 | 0.303416 | ||||||||
\(985\) | −767624. | −0.0252092 | ||||||||
\(986\) | −1.09379e8 | −3.58295 | ||||||||
\(987\) | 4.44898e7 | 1.45368 | ||||||||
\(988\) | 1.96553e7 | 0.640600 | ||||||||
\(989\) | −1.18427e7 | −0.384999 | ||||||||
\(990\) | −4.64124e7 | −1.50503 | ||||||||
\(991\) | −8.70314e6 | −0.281509 | −0.140754 | − | 0.990045i | \(-0.544953\pi\) | ||||
−0.140754 | + | 0.990045i | \(0.544953\pi\) | |||||||
\(992\) | 1.58047e7 | 0.509926 | ||||||||
\(993\) | −4.46640e7 | −1.43742 | ||||||||
\(994\) | −1.61088e8 | −5.17127 | ||||||||
\(995\) | −3.07228e6 | −0.0983791 | ||||||||
\(996\) | −1.11571e8 | −3.56370 | ||||||||
\(997\) | 2.13851e7 | 0.681355 | 0.340678 | − | 0.940180i | \(-0.389344\pi\) | ||||
0.340678 | + | 0.940180i | \(0.389344\pi\) | |||||||
\(998\) | 3.68832e6 | 0.117220 | ||||||||
\(999\) | 9.73345e7 | 3.08570 |
(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 | 547.6.a.a.1.2 | ✓ | 111 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.6.a.a.1.2 | ✓ | 111 | 1.1 | even | 1 | trivial |