Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(91.4187772934\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 12189x^{2} - 95210x + 4841400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-104.052\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 42.1343 | 0.325006 | 0.162503 | − | 0.986708i | \(-0.448043\pi\) | ||||
0.162503 | + | 0.986708i | \(0.448043\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −210.758 | −0.525173 | −0.262587 | − | 0.964908i | \(-0.584576\pi\) | ||||
−0.262587 | + | 0.964908i | \(0.584576\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −674.620 | −1.10714 | −0.553568 | − | 0.832804i | \(-0.686734\pi\) | ||||
−0.553568 | + | 0.832804i | \(0.686734\pi\) | |||||||
\(14\) | −168.537 | −0.229814 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1996.35 | −1.67538 | −0.837690 | − | 0.546145i | \(-0.816095\pi\) | ||||
−0.837690 | + | 0.546145i | \(0.816095\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | −379.209 | −0.187642 | ||||||||
\(22\) | 843.032 | 0.371353 | ||||||||
\(23\) | 2914.64 | 1.14886 | 0.574428 | − | 0.818555i | \(-0.305225\pi\) | ||||
0.574428 | + | 0.818555i | \(0.305225\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2698.48 | 0.782863 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 674.149 | 0.162503 | ||||||||
\(29\) | 7863.10 | 1.73620 | 0.868098 | − | 0.496393i | \(-0.165343\pi\) | ||||
0.868098 | + | 0.496393i | \(0.165343\pi\) | |||||||
\(30\) | −900.000 | −0.182574 | ||||||||
\(31\) | −8458.62 | −1.58087 | −0.790434 | − | 0.612548i | \(-0.790145\pi\) | ||||
−0.790434 | + | 0.612548i | \(0.790145\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 1896.82 | 0.303209 | ||||||||
\(34\) | 7985.38 | 1.18467 | ||||||||
\(35\) | −1053.36 | −0.145347 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −8801.15 | −1.05690 | −0.528451 | − | 0.848964i | \(-0.677227\pi\) | ||||
−0.528451 | + | 0.848964i | \(0.677227\pi\) | |||||||
\(38\) | −1444.00 | −0.162221 | ||||||||
\(39\) | 6071.58 | 0.639205 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | 717.020 | 0.0666149 | 0.0333075 | − | 0.999445i | \(-0.489396\pi\) | ||||
0.0333075 | + | 0.999445i | \(0.489396\pi\) | |||||||
\(42\) | 1516.84 | 0.132683 | ||||||||
\(43\) | −11462.2 | −0.945362 | −0.472681 | − | 0.881234i | \(-0.656714\pi\) | ||||
−0.472681 | + | 0.881234i | \(0.656714\pi\) | |||||||
\(44\) | −3372.13 | −0.262587 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | −11658.6 | −0.812364 | ||||||||
\(47\) | −6461.06 | −0.426638 | −0.213319 | − | 0.976983i | \(-0.568427\pi\) | ||||
−0.213319 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −15031.7 | −0.894371 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 17967.1 | 0.967282 | ||||||||
\(52\) | −10793.9 | −0.553568 | ||||||||
\(53\) | 7494.65 | 0.366489 | 0.183245 | − | 0.983067i | \(-0.441340\pi\) | ||||
0.183245 | + | 0.983067i | \(0.441340\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 5268.95 | 0.234865 | ||||||||
\(56\) | −2696.60 | −0.114907 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | −31452.4 | −1.22768 | ||||||||
\(59\) | −32213.5 | −1.20478 | −0.602389 | − | 0.798202i | \(-0.705785\pi\) | ||||
−0.602389 | + | 0.798202i | \(0.705785\pi\) | |||||||
\(60\) | 3600.00 | 0.129099 | ||||||||
\(61\) | 7348.69 | 0.252863 | 0.126432 | − | 0.991975i | \(-0.459648\pi\) | ||||
0.126432 | + | 0.991975i | \(0.459648\pi\) | |||||||
\(62\) | 33834.5 | 1.11784 | ||||||||
\(63\) | 3412.88 | 0.108335 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 16865.5 | 0.495126 | ||||||||
\(66\) | −7587.29 | −0.214401 | ||||||||
\(67\) | −10250.8 | −0.278980 | −0.139490 | − | 0.990223i | \(-0.544546\pi\) | ||||
−0.139490 | + | 0.990223i | \(0.544546\pi\) | |||||||
\(68\) | −31941.5 | −0.837690 | ||||||||
\(69\) | −26231.8 | −0.663292 | ||||||||
\(70\) | 4213.43 | 0.102776 | ||||||||
\(71\) | 28256.7 | 0.665236 | 0.332618 | − | 0.943062i | \(-0.392068\pi\) | ||||
0.332618 | + | 0.943062i | \(0.392068\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 37170.4 | 0.816375 | 0.408188 | − | 0.912898i | \(-0.366161\pi\) | ||||
0.408188 | + | 0.912898i | \(0.366161\pi\) | |||||||
\(74\) | 35204.6 | 0.747343 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 5776.00 | 0.114708 | ||||||||
\(77\) | −8880.15 | −0.170684 | ||||||||
\(78\) | −24286.3 | −0.451986 | ||||||||
\(79\) | −7304.46 | −0.131680 | −0.0658401 | − | 0.997830i | \(-0.520973\pi\) | ||||
−0.0658401 | + | 0.997830i | \(0.520973\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −2868.08 | −0.0471039 | ||||||||
\(83\) | −94295.6 | −1.50244 | −0.751219 | − | 0.660053i | \(-0.770534\pi\) | ||||
−0.751219 | + | 0.660053i | \(0.770534\pi\) | |||||||
\(84\) | −6067.34 | −0.0938211 | ||||||||
\(85\) | 49908.7 | 0.749253 | ||||||||
\(86\) | 45848.9 | 0.668472 | ||||||||
\(87\) | −70767.9 | −1.00239 | ||||||||
\(88\) | 13488.5 | 0.185677 | ||||||||
\(89\) | −57710.2 | −0.772284 | −0.386142 | − | 0.922439i | \(-0.626193\pi\) | ||||
−0.386142 | + | 0.922439i | \(0.626193\pi\) | |||||||
\(90\) | 8100.00 | 0.105409 | ||||||||
\(91\) | −28424.7 | −0.359825 | ||||||||
\(92\) | 46634.3 | 0.574428 | ||||||||
\(93\) | 76127.6 | 0.912714 | ||||||||
\(94\) | 25844.2 | 0.301678 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −151919. | −1.63939 | −0.819695 | − | 0.572800i | \(-0.805857\pi\) | ||||
−0.819695 | + | 0.572800i | \(0.805857\pi\) | |||||||
\(98\) | 60126.8 | 0.632416 | ||||||||
\(99\) | −17071.4 | −0.175058 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 71256.4 | 0.695057 | 0.347528 | − | 0.937669i | \(-0.387021\pi\) | ||||
0.347528 | + | 0.937669i | \(0.387021\pi\) | |||||||
\(102\) | −71868.5 | −0.683971 | ||||||||
\(103\) | −71251.3 | −0.661759 | −0.330879 | − | 0.943673i | \(-0.607345\pi\) | ||||
−0.330879 | + | 0.943673i | \(0.607345\pi\) | |||||||
\(104\) | 43175.7 | 0.391432 | ||||||||
\(105\) | 9480.22 | 0.0839161 | ||||||||
\(106\) | −29978.6 | −0.259147 | ||||||||
\(107\) | 77968.5 | 0.658355 | 0.329177 | − | 0.944268i | \(-0.393229\pi\) | ||||
0.329177 | + | 0.944268i | \(0.393229\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 185434. | 1.49494 | 0.747468 | − | 0.664297i | \(-0.231269\pi\) | ||||
0.747468 | + | 0.664297i | \(0.231269\pi\) | |||||||
\(110\) | −21075.8 | −0.166074 | ||||||||
\(111\) | 79210.3 | 0.610203 | ||||||||
\(112\) | 10786.4 | 0.0812514 | ||||||||
\(113\) | 224770. | 1.65593 | 0.827965 | − | 0.560780i | \(-0.189499\pi\) | ||||
0.827965 | + | 0.560780i | \(0.189499\pi\) | |||||||
\(114\) | 12996.0 | 0.0936586 | ||||||||
\(115\) | −72866.0 | −0.513784 | ||||||||
\(116\) | 125810. | 0.868098 | ||||||||
\(117\) | −54644.2 | −0.369045 | ||||||||
\(118\) | 128854. | 0.851907 | ||||||||
\(119\) | −84114.7 | −0.544508 | ||||||||
\(120\) | −14400.0 | −0.0912871 | ||||||||
\(121\) | −116632. | −0.724193 | ||||||||
\(122\) | −29394.8 | −0.178801 | ||||||||
\(123\) | −6453.18 | −0.0384602 | ||||||||
\(124\) | −135338. | −0.790434 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −13651.5 | −0.0766046 | ||||||||
\(127\) | −167574. | −0.921930 | −0.460965 | − | 0.887418i | \(-0.652497\pi\) | ||||
−0.460965 | + | 0.887418i | \(0.652497\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 103160. | 0.545805 | ||||||||
\(130\) | −67462.0 | −0.350107 | ||||||||
\(131\) | 12110.8 | 0.0616588 | 0.0308294 | − | 0.999525i | \(-0.490185\pi\) | ||||
0.0308294 | + | 0.999525i | \(0.490185\pi\) | |||||||
\(132\) | 30349.2 | 0.151604 | ||||||||
\(133\) | 15210.5 | 0.0745614 | ||||||||
\(134\) | 41003.4 | 0.197268 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | 127766. | 0.592337 | ||||||||
\(137\) | 312481. | 1.42240 | 0.711200 | − | 0.702990i | \(-0.248152\pi\) | ||||
0.711200 | + | 0.702990i | \(0.248152\pi\) | |||||||
\(138\) | 104927. | 0.469018 | ||||||||
\(139\) | −22038.4 | −0.0967483 | −0.0483741 | − | 0.998829i | \(-0.515404\pi\) | ||||
−0.0483741 | + | 0.998829i | \(0.515404\pi\) | |||||||
\(140\) | −16853.7 | −0.0726735 | ||||||||
\(141\) | 58149.5 | 0.246319 | ||||||||
\(142\) | −113027. | −0.470393 | ||||||||
\(143\) | 142182. | 0.581438 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −196577. | −0.776450 | ||||||||
\(146\) | −148681. | −0.577264 | ||||||||
\(147\) | 135285. | 0.516365 | ||||||||
\(148\) | −140818. | −0.528451 | ||||||||
\(149\) | 143488. | 0.529481 | 0.264741 | − | 0.964320i | \(-0.414714\pi\) | ||||
0.264741 | + | 0.964320i | \(0.414714\pi\) | |||||||
\(150\) | 22500.0 | 0.0816497 | ||||||||
\(151\) | 60288.0 | 0.215173 | 0.107587 | − | 0.994196i | \(-0.465688\pi\) | ||||
0.107587 | + | 0.994196i | \(0.465688\pi\) | |||||||
\(152\) | −23104.0 | −0.0811107 | ||||||||
\(153\) | −161704. | −0.558460 | ||||||||
\(154\) | 35520.6 | 0.120692 | ||||||||
\(155\) | 211466. | 0.706985 | ||||||||
\(156\) | 97145.3 | 0.319603 | ||||||||
\(157\) | 268382. | 0.868968 | 0.434484 | − | 0.900680i | \(-0.356931\pi\) | ||||
0.434484 | + | 0.900680i | \(0.356931\pi\) | |||||||
\(158\) | 29217.8 | 0.0931119 | ||||||||
\(159\) | −67451.8 | −0.211593 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 122806. | 0.373385 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | 578510. | 1.70546 | 0.852730 | − | 0.522351i | \(-0.174945\pi\) | ||||
0.852730 | + | 0.522351i | \(0.174945\pi\) | |||||||
\(164\) | 11472.3 | 0.0333075 | ||||||||
\(165\) | −47420.6 | −0.135599 | ||||||||
\(166\) | 377183. | 1.06238 | ||||||||
\(167\) | 526620. | 1.46119 | 0.730593 | − | 0.682813i | \(-0.239243\pi\) | ||||
0.730593 | + | 0.682813i | \(0.239243\pi\) | |||||||
\(168\) | 24269.4 | 0.0663415 | ||||||||
\(169\) | 83819.3 | 0.225750 | ||||||||
\(170\) | −199635. | −0.529802 | ||||||||
\(171\) | 29241.0 | 0.0764719 | ||||||||
\(172\) | −183396. | −0.472681 | ||||||||
\(173\) | −719527. | −1.82781 | −0.913907 | − | 0.405924i | \(-0.866950\pi\) | ||||
−0.913907 | + | 0.405924i | \(0.866950\pi\) | |||||||
\(174\) | 283071. | 0.708799 | ||||||||
\(175\) | 26334.0 | 0.0650011 | ||||||||
\(176\) | −53954.1 | −0.131293 | ||||||||
\(177\) | 289921. | 0.695579 | ||||||||
\(178\) | 230841. | 0.546088 | ||||||||
\(179\) | 81155.9 | 0.189316 | 0.0946580 | − | 0.995510i | \(-0.469824\pi\) | ||||
0.0946580 | + | 0.995510i | \(0.469824\pi\) | |||||||
\(180\) | −32400.0 | −0.0745356 | ||||||||
\(181\) | 395071. | 0.896351 | 0.448176 | − | 0.893946i | \(-0.352074\pi\) | ||||
0.448176 | + | 0.893946i | \(0.352074\pi\) | |||||||
\(182\) | 113699. | 0.254435 | ||||||||
\(183\) | −66138.2 | −0.145991 | ||||||||
\(184\) | −186537. | −0.406182 | ||||||||
\(185\) | 220029. | 0.472661 | ||||||||
\(186\) | −304510. | −0.645386 | ||||||||
\(187\) | 420746. | 0.879865 | ||||||||
\(188\) | −103377. | −0.213319 | ||||||||
\(189\) | −30715.9 | −0.0625474 | ||||||||
\(190\) | 36100.0 | 0.0725476 | ||||||||
\(191\) | 882496. | 1.75037 | 0.875184 | − | 0.483790i | \(-0.160740\pi\) | ||||
0.875184 | + | 0.483790i | \(0.160740\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 315735. | 0.610140 | 0.305070 | − | 0.952330i | \(-0.401320\pi\) | ||||
0.305070 | + | 0.952330i | \(0.401320\pi\) | |||||||
\(194\) | 607675. | 1.15922 | ||||||||
\(195\) | −151790. | −0.285861 | ||||||||
\(196\) | −240507. | −0.447186 | ||||||||
\(197\) | −462680. | −0.849406 | −0.424703 | − | 0.905333i | \(-0.639622\pi\) | ||||
−0.424703 | + | 0.905333i | \(0.639622\pi\) | |||||||
\(198\) | 68285.6 | 0.123784 | ||||||||
\(199\) | 985520. | 1.76414 | 0.882069 | − | 0.471119i | \(-0.156150\pi\) | ||||
0.882069 | + | 0.471119i | \(0.156150\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 92257.6 | 0.161069 | ||||||||
\(202\) | −285025. | −0.491479 | ||||||||
\(203\) | 331306. | 0.564274 | ||||||||
\(204\) | 287474. | 0.483641 | ||||||||
\(205\) | −17925.5 | −0.0297911 | ||||||||
\(206\) | 285005. | 0.467934 | ||||||||
\(207\) | 236086. | 0.382952 | ||||||||
\(208\) | −172703. | −0.276784 | ||||||||
\(209\) | −76083.6 | −0.120483 | ||||||||
\(210\) | −37920.9 | −0.0593377 | ||||||||
\(211\) | −349548. | −0.540506 | −0.270253 | − | 0.962789i | \(-0.587107\pi\) | ||||
−0.270253 | + | 0.962789i | \(0.587107\pi\) | |||||||
\(212\) | 119914. | 0.183245 | ||||||||
\(213\) | −254310. | −0.384074 | ||||||||
\(214\) | −311874. | −0.465527 | ||||||||
\(215\) | 286556. | 0.422779 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −356398. | −0.513791 | ||||||||
\(218\) | −741736. | −1.05708 | ||||||||
\(219\) | −334533. | −0.471334 | ||||||||
\(220\) | 84303.2 | 0.117432 | ||||||||
\(221\) | 1.34678e6 | 1.85487 | ||||||||
\(222\) | −316841. | −0.431479 | ||||||||
\(223\) | 276536. | 0.372383 | 0.186192 | − | 0.982513i | \(-0.440385\pi\) | ||||
0.186192 | + | 0.982513i | \(0.440385\pi\) | |||||||
\(224\) | −43145.6 | −0.0574534 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −899079. | −1.17092 | ||||||||
\(227\) | 528814. | 0.681143 | 0.340571 | − | 0.940219i | \(-0.389379\pi\) | ||||
0.340571 | + | 0.940219i | \(0.389379\pi\) | |||||||
\(228\) | −51984.0 | −0.0662266 | ||||||||
\(229\) | −104956. | −0.132256 | −0.0661282 | − | 0.997811i | \(-0.521065\pi\) | ||||
−0.0661282 | + | 0.997811i | \(0.521065\pi\) | |||||||
\(230\) | 291464. | 0.363300 | ||||||||
\(231\) | 79921.3 | 0.0985446 | ||||||||
\(232\) | −503238. | −0.613838 | ||||||||
\(233\) | −881192. | −1.06336 | −0.531681 | − | 0.846945i | \(-0.678439\pi\) | ||||
−0.531681 | + | 0.846945i | \(0.678439\pi\) | |||||||
\(234\) | 218577. | 0.260954 | ||||||||
\(235\) | 161526. | 0.190798 | ||||||||
\(236\) | −515415. | −0.602389 | ||||||||
\(237\) | 65740.1 | 0.0760256 | ||||||||
\(238\) | 336459. | 0.385026 | ||||||||
\(239\) | 1.24460e6 | 1.40940 | 0.704701 | − | 0.709505i | \(-0.251081\pi\) | ||||
0.704701 | + | 0.709505i | \(0.251081\pi\) | |||||||
\(240\) | 57600.0 | 0.0645497 | ||||||||
\(241\) | 708069. | 0.785295 | 0.392647 | − | 0.919689i | \(-0.371559\pi\) | ||||
0.392647 | + | 0.919689i | \(0.371559\pi\) | |||||||
\(242\) | 466528. | 0.512082 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 117579. | 0.126432 | ||||||||
\(245\) | 375792. | 0.399975 | ||||||||
\(246\) | 25812.7 | 0.0271954 | ||||||||
\(247\) | −243538. | −0.253994 | ||||||||
\(248\) | 541352. | 0.558921 | ||||||||
\(249\) | 848661. | 0.867433 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | 308105. | 0.308684 | 0.154342 | − | 0.988017i | \(-0.450674\pi\) | ||||
0.154342 | + | 0.988017i | \(0.450674\pi\) | |||||||
\(252\) | 54606.1 | 0.0541676 | ||||||||
\(253\) | −614284. | −0.603348 | ||||||||
\(254\) | 670297. | 0.651903 | ||||||||
\(255\) | −449178. | −0.432581 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.61211e6 | −1.52252 | −0.761259 | − | 0.648448i | \(-0.775418\pi\) | ||||
−0.761259 | + | 0.648448i | \(0.775418\pi\) | |||||||
\(258\) | −412640. | −0.385942 | ||||||||
\(259\) | −370830. | −0.343499 | ||||||||
\(260\) | 269848. | 0.247563 | ||||||||
\(261\) | 636911. | 0.578732 | ||||||||
\(262\) | −48443.3 | −0.0435994 | ||||||||
\(263\) | 460120. | 0.410187 | 0.205094 | − | 0.978742i | \(-0.434250\pi\) | ||||
0.205094 | + | 0.978742i | \(0.434250\pi\) | |||||||
\(264\) | −121397. | −0.107200 | ||||||||
\(265\) | −187366. | −0.163899 | ||||||||
\(266\) | −60842.0 | −0.0527229 | ||||||||
\(267\) | 519392. | 0.445879 | ||||||||
\(268\) | −164014. | −0.139490 | ||||||||
\(269\) | 1.76187e6 | 1.48455 | 0.742274 | − | 0.670096i | \(-0.233747\pi\) | ||||
0.742274 | + | 0.670096i | \(0.233747\pi\) | |||||||
\(270\) | −72900.0 | −0.0608581 | ||||||||
\(271\) | 219007. | 0.181148 | 0.0905741 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905741 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(272\) | −511065. | −0.418845 | ||||||||
\(273\) | 255822. | 0.207745 | ||||||||
\(274\) | −1.24992e6 | −1.00579 | ||||||||
\(275\) | −131724. | −0.105035 | ||||||||
\(276\) | −419708. | −0.331646 | ||||||||
\(277\) | −812005. | −0.635857 | −0.317928 | − | 0.948115i | \(-0.602987\pi\) | ||||
−0.317928 | + | 0.948115i | \(0.602987\pi\) | |||||||
\(278\) | 88153.6 | 0.0684114 | ||||||||
\(279\) | −685148. | −0.526956 | ||||||||
\(280\) | 67414.9 | 0.0513879 | ||||||||
\(281\) | 537890. | 0.406376 | 0.203188 | − | 0.979140i | \(-0.434870\pi\) | ||||
0.203188 | + | 0.979140i | \(0.434870\pi\) | |||||||
\(282\) | −232598. | −0.174174 | ||||||||
\(283\) | −992700. | −0.736804 | −0.368402 | − | 0.929667i | \(-0.620095\pi\) | ||||
−0.368402 | + | 0.929667i | \(0.620095\pi\) | |||||||
\(284\) | 452107. | 0.332618 | ||||||||
\(285\) | 81225.0 | 0.0592349 | ||||||||
\(286\) | −568726. | −0.411139 | ||||||||
\(287\) | 30211.2 | 0.0216502 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 2.56554e6 | 1.80690 | ||||||||
\(290\) | 786310. | 0.549033 | ||||||||
\(291\) | 1.36727e6 | 0.946502 | ||||||||
\(292\) | 594726. | 0.408188 | ||||||||
\(293\) | 1.48491e6 | 1.01049 | 0.505245 | − | 0.862976i | \(-0.331402\pi\) | ||||
0.505245 | + | 0.862976i | \(0.331402\pi\) | |||||||
\(294\) | −541141. | −0.365126 | ||||||||
\(295\) | 805336. | 0.538793 | ||||||||
\(296\) | 563273. | 0.373671 | ||||||||
\(297\) | 153643. | 0.101070 | ||||||||
\(298\) | −573953. | −0.374400 | ||||||||
\(299\) | −1.96628e6 | −1.27194 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | −482954. | −0.307248 | ||||||||
\(302\) | −241152. | −0.152150 | ||||||||
\(303\) | −641307. | −0.401291 | ||||||||
\(304\) | 92416.0 | 0.0573539 | ||||||||
\(305\) | −183717. | −0.113084 | ||||||||
\(306\) | 646816. | 0.394891 | ||||||||
\(307\) | −103155. | −0.0624663 | −0.0312332 | − | 0.999512i | \(-0.509943\pi\) | ||||
−0.0312332 | + | 0.999512i | \(0.509943\pi\) | |||||||
\(308\) | −142082. | −0.0853421 | ||||||||
\(309\) | 641262. | 0.382067 | ||||||||
\(310\) | −845862. | −0.499914 | ||||||||
\(311\) | −1.84732e6 | −1.08303 | −0.541515 | − | 0.840691i | \(-0.682149\pi\) | ||||
−0.541515 | + | 0.840691i | \(0.682149\pi\) | |||||||
\(312\) | −388581. | −0.225993 | ||||||||
\(313\) | −1.96273e6 | −1.13240 | −0.566200 | − | 0.824268i | \(-0.691587\pi\) | ||||
−0.566200 | + | 0.824268i | \(0.691587\pi\) | |||||||
\(314\) | −1.07353e6 | −0.614453 | ||||||||
\(315\) | −85322.0 | −0.0484490 | ||||||||
\(316\) | −116871. | −0.0658401 | ||||||||
\(317\) | 1.09872e6 | 0.614101 | 0.307051 | − | 0.951693i | \(-0.400658\pi\) | ||||
0.307051 | + | 0.951693i | \(0.400658\pi\) | |||||||
\(318\) | 269807. | 0.149619 | ||||||||
\(319\) | −1.65721e6 | −0.911803 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | −701717. | −0.380101 | ||||||||
\(322\) | −491226. | −0.264023 | ||||||||
\(323\) | −720681. | −0.384359 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −421638. | −0.221427 | ||||||||
\(326\) | −2.31404e6 | −1.20594 | ||||||||
\(327\) | −1.66890e6 | −0.863102 | ||||||||
\(328\) | −45889.3 | −0.0235519 | ||||||||
\(329\) | −272232. | −0.138660 | ||||||||
\(330\) | 189682. | 0.0958830 | ||||||||
\(331\) | −945619. | −0.474402 | −0.237201 | − | 0.971461i | \(-0.576230\pi\) | ||||
−0.237201 | + | 0.971461i | \(0.576230\pi\) | |||||||
\(332\) | −1.50873e6 | −0.751219 | ||||||||
\(333\) | −712893. | −0.352301 | ||||||||
\(334\) | −2.10648e6 | −1.03322 | ||||||||
\(335\) | 256271. | 0.124764 | ||||||||
\(336\) | −97077.5 | −0.0469105 | ||||||||
\(337\) | −1.16967e6 | −0.561033 | −0.280516 | − | 0.959849i | \(-0.590506\pi\) | ||||
−0.280516 | + | 0.959849i | \(0.590506\pi\) | |||||||
\(338\) | −335277. | −0.159629 | ||||||||
\(339\) | −2.02293e6 | −0.956051 | ||||||||
\(340\) | 798538. | 0.374627 | ||||||||
\(341\) | 1.78272e6 | 0.830229 | ||||||||
\(342\) | −116964. | −0.0540738 | ||||||||
\(343\) | −1.34150e6 | −0.615682 | ||||||||
\(344\) | 733583. | 0.334236 | ||||||||
\(345\) | 655794. | 0.296633 | ||||||||
\(346\) | 2.87811e6 | 1.29246 | ||||||||
\(347\) | 1.19758e6 | 0.533926 | 0.266963 | − | 0.963707i | \(-0.413980\pi\) | ||||
0.266963 | + | 0.963707i | \(0.413980\pi\) | |||||||
\(348\) | −1.13229e6 | −0.501196 | ||||||||
\(349\) | −313078. | −0.137590 | −0.0687952 | − | 0.997631i | \(-0.521916\pi\) | ||||
−0.0687952 | + | 0.997631i | \(0.521916\pi\) | |||||||
\(350\) | −105336. | −0.0459628 | ||||||||
\(351\) | 491798. | 0.213068 | ||||||||
\(352\) | 215816. | 0.0928384 | ||||||||
\(353\) | 2.31376e6 | 0.988282 | 0.494141 | − | 0.869382i | \(-0.335483\pi\) | ||||
0.494141 | + | 0.869382i | \(0.335483\pi\) | |||||||
\(354\) | −1.15968e6 | −0.491849 | ||||||||
\(355\) | −706418. | −0.297503 | ||||||||
\(356\) | −923363. | −0.386142 | ||||||||
\(357\) | 757032. | 0.314372 | ||||||||
\(358\) | −324623. | −0.133867 | ||||||||
\(359\) | 1.47275e6 | 0.603104 | 0.301552 | − | 0.953450i | \(-0.402495\pi\) | ||||
0.301552 | + | 0.953450i | \(0.402495\pi\) | |||||||
\(360\) | 129600. | 0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −1.58028e6 | −0.633816 | ||||||||
\(363\) | 1.04969e6 | 0.418113 | ||||||||
\(364\) | −454795. | −0.179913 | ||||||||
\(365\) | −929259. | −0.365094 | ||||||||
\(366\) | 264553. | 0.103231 | ||||||||
\(367\) | 1.99818e6 | 0.774408 | 0.387204 | − | 0.921994i | \(-0.373441\pi\) | ||||
0.387204 | + | 0.921994i | \(0.373441\pi\) | |||||||
\(368\) | 746148. | 0.287214 | ||||||||
\(369\) | 58078.6 | 0.0222050 | ||||||||
\(370\) | −880115. | −0.334222 | ||||||||
\(371\) | 315782. | 0.119111 | ||||||||
\(372\) | 1.21804e6 | 0.456357 | ||||||||
\(373\) | −4.08612e6 | −1.52068 | −0.760342 | − | 0.649523i | \(-0.774969\pi\) | ||||
−0.760342 | + | 0.649523i | \(0.774969\pi\) | |||||||
\(374\) | −1.68298e6 | −0.622158 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | 413508. | 0.150839 | ||||||||
\(377\) | −5.30460e6 | −1.92220 | ||||||||
\(378\) | 122864. | 0.0442277 | ||||||||
\(379\) | 4.69794e6 | 1.68000 | 0.840000 | − | 0.542587i | \(-0.182555\pi\) | ||||
0.840000 | + | 0.542587i | \(0.182555\pi\) | |||||||
\(380\) | −144400. | −0.0512989 | ||||||||
\(381\) | 1.50817e6 | 0.532277 | ||||||||
\(382\) | −3.52998e6 | −1.23770 | ||||||||
\(383\) | 970394. | 0.338027 | 0.169013 | − | 0.985614i | \(-0.445942\pi\) | ||||
0.169013 | + | 0.985614i | \(0.445942\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 222004. | 0.0763323 | ||||||||
\(386\) | −1.26294e6 | −0.431434 | ||||||||
\(387\) | −928441. | −0.315121 | ||||||||
\(388\) | −2.43070e6 | −0.819695 | ||||||||
\(389\) | 4.51520e6 | 1.51288 | 0.756438 | − | 0.654065i | \(-0.226938\pi\) | ||||
0.756438 | + | 0.654065i | \(0.226938\pi\) | |||||||
\(390\) | 607158. | 0.202134 | ||||||||
\(391\) | −5.81863e6 | −1.92477 | ||||||||
\(392\) | 962029. | 0.316208 | ||||||||
\(393\) | −108997. | −0.0355987 | ||||||||
\(394\) | 1.85072e6 | 0.600621 | ||||||||
\(395\) | 182611. | 0.0588892 | ||||||||
\(396\) | −273142. | −0.0875288 | ||||||||
\(397\) | 5.34819e6 | 1.70306 | 0.851531 | − | 0.524305i | \(-0.175675\pi\) | ||||
0.851531 | + | 0.524305i | \(0.175675\pi\) | |||||||
\(398\) | −3.94208e6 | −1.24743 | ||||||||
\(399\) | −136894. | −0.0430481 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 1.64514e6 | 0.510907 | 0.255453 | − | 0.966821i | \(-0.417775\pi\) | ||||
0.255453 | + | 0.966821i | \(0.417775\pi\) | |||||||
\(402\) | −369030. | −0.113893 | ||||||||
\(403\) | 5.70636e6 | 1.75023 | ||||||||
\(404\) | 1.14010e6 | 0.347528 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −1.32523e6 | −0.399002 | ||||||||
\(407\) | 1.85491e6 | 0.555057 | ||||||||
\(408\) | −1.14990e6 | −0.341986 | ||||||||
\(409\) | 368225. | 0.108844 | 0.0544221 | − | 0.998518i | \(-0.482668\pi\) | ||||
0.0544221 | + | 0.998518i | \(0.482668\pi\) | |||||||
\(410\) | 71702.0 | 0.0210655 | ||||||||
\(411\) | −2.81233e6 | −0.821223 | ||||||||
\(412\) | −1.14002e6 | −0.330879 | ||||||||
\(413\) | −1.35729e6 | −0.391560 | ||||||||
\(414\) | −944344. | −0.270788 | ||||||||
\(415\) | 2.35739e6 | 0.671910 | ||||||||
\(416\) | 690811. | 0.195716 | ||||||||
\(417\) | 198346. | 0.0558577 | ||||||||
\(418\) | 304335. | 0.0851943 | ||||||||
\(419\) | 1.01367e6 | 0.282073 | 0.141036 | − | 0.990004i | \(-0.454957\pi\) | ||||
0.141036 | + | 0.990004i | \(0.454957\pi\) | |||||||
\(420\) | 151684. | 0.0419581 | ||||||||
\(421\) | −5.53535e6 | −1.52209 | −0.761044 | − | 0.648700i | \(-0.775313\pi\) | ||||
−0.761044 | + | 0.648700i | \(0.775313\pi\) | |||||||
\(422\) | 1.39819e6 | 0.382196 | ||||||||
\(423\) | −523346. | −0.142213 | ||||||||
\(424\) | −479657. | −0.129574 | ||||||||
\(425\) | −1.24772e6 | −0.335076 | ||||||||
\(426\) | 1.01724e6 | 0.271581 | ||||||||
\(427\) | 309632. | 0.0821820 | ||||||||
\(428\) | 1.24750e6 | 0.329177 | ||||||||
\(429\) | −1.27963e6 | −0.335693 | ||||||||
\(430\) | −1.14622e6 | −0.298950 | ||||||||
\(431\) | 1.29691e6 | 0.336292 | 0.168146 | − | 0.985762i | \(-0.446222\pi\) | ||||
0.168146 | + | 0.985762i | \(0.446222\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −6.89054e6 | −1.76617 | −0.883087 | − | 0.469210i | \(-0.844539\pi\) | ||||
−0.883087 | + | 0.469210i | \(0.844539\pi\) | |||||||
\(434\) | 1.42559e6 | 0.363305 | ||||||||
\(435\) | 1.76920e6 | 0.448284 | ||||||||
\(436\) | 2.96694e6 | 0.747468 | ||||||||
\(437\) | 1.05219e6 | 0.263566 | ||||||||
\(438\) | 1.33813e6 | 0.333284 | ||||||||
\(439\) | −146297. | −0.0362304 | −0.0181152 | − | 0.999836i | \(-0.505767\pi\) | ||||
−0.0181152 | + | 0.999836i | \(0.505767\pi\) | |||||||
\(440\) | −337213. | −0.0830371 | ||||||||
\(441\) | −1.21757e6 | −0.298124 | ||||||||
\(442\) | −5.38710e6 | −1.31159 | ||||||||
\(443\) | −828057. | −0.200471 | −0.100235 | − | 0.994964i | \(-0.531960\pi\) | ||||
−0.100235 | + | 0.994964i | \(0.531960\pi\) | |||||||
\(444\) | 1.26737e6 | 0.305101 | ||||||||
\(445\) | 1.44275e6 | 0.345376 | ||||||||
\(446\) | −1.10615e6 | −0.263315 | ||||||||
\(447\) | −1.29139e6 | −0.305696 | ||||||||
\(448\) | 172582. | 0.0406257 | ||||||||
\(449\) | −595290. | −0.139352 | −0.0696759 | − | 0.997570i | \(-0.522197\pi\) | ||||
−0.0696759 | + | 0.997570i | \(0.522197\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | −151118. | −0.0349844 | ||||||||
\(452\) | 3.59632e6 | 0.827965 | ||||||||
\(453\) | −542592. | −0.124230 | ||||||||
\(454\) | −2.11526e6 | −0.481641 | ||||||||
\(455\) | 710617. | 0.160919 | ||||||||
\(456\) | 207936. | 0.0468293 | ||||||||
\(457\) | −5.83354e6 | −1.30660 | −0.653299 | − | 0.757100i | \(-0.726615\pi\) | ||||
−0.653299 | + | 0.757100i | \(0.726615\pi\) | |||||||
\(458\) | 419822. | 0.0935194 | ||||||||
\(459\) | 1.45534e6 | 0.322427 | ||||||||
\(460\) | −1.16586e6 | −0.256892 | ||||||||
\(461\) | 1.90531e6 | 0.417556 | 0.208778 | − | 0.977963i | \(-0.433051\pi\) | ||||
0.208778 | + | 0.977963i | \(0.433051\pi\) | |||||||
\(462\) | −319685. | −0.0696816 | ||||||||
\(463\) | 3.17108e6 | 0.687471 | 0.343735 | − | 0.939067i | \(-0.388308\pi\) | ||||
0.343735 | + | 0.939067i | \(0.388308\pi\) | |||||||
\(464\) | 2.01295e6 | 0.434049 | ||||||||
\(465\) | −1.90319e6 | −0.408178 | ||||||||
\(466\) | 3.52477e6 | 0.751910 | ||||||||
\(467\) | −667129. | −0.141553 | −0.0707763 | − | 0.997492i | \(-0.522548\pi\) | ||||
−0.0707763 | + | 0.997492i | \(0.522548\pi\) | |||||||
\(468\) | −874308. | −0.184523 | ||||||||
\(469\) | −431913. | −0.0906700 | ||||||||
\(470\) | −646106. | −0.134915 | ||||||||
\(471\) | −2.41544e6 | −0.501699 | ||||||||
\(472\) | 2.06166e6 | 0.425954 | ||||||||
\(473\) | 2.41576e6 | 0.496479 | ||||||||
\(474\) | −262961. | −0.0537582 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | −1.34584e6 | −0.272254 | ||||||||
\(477\) | 607066. | 0.122163 | ||||||||
\(478\) | −4.97840e6 | −0.996597 | ||||||||
\(479\) | −960007. | −0.191177 | −0.0955885 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955885 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(480\) | −230400. | −0.0456435 | ||||||||
\(481\) | 5.93743e6 | 1.17013 | ||||||||
\(482\) | −2.83227e6 | −0.555287 | ||||||||
\(483\) | −1.10526e6 | −0.215574 | ||||||||
\(484\) | −1.86611e6 | −0.362097 | ||||||||
\(485\) | 3.79797e6 | 0.733157 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −7.75364e6 | −1.48144 | −0.740719 | − | 0.671815i | \(-0.765515\pi\) | ||||
−0.740719 | + | 0.671815i | \(0.765515\pi\) | |||||||
\(488\) | −470316. | −0.0894006 | ||||||||
\(489\) | −5.20659e6 | −0.984648 | ||||||||
\(490\) | −1.50317e6 | −0.282825 | ||||||||
\(491\) | 5.73211e6 | 1.07303 | 0.536514 | − | 0.843892i | \(-0.319741\pi\) | ||||
0.536514 | + | 0.843892i | \(0.319741\pi\) | |||||||
\(492\) | −103251. | −0.0192301 | ||||||||
\(493\) | −1.56975e7 | −2.90879 | ||||||||
\(494\) | 974151. | 0.179601 | ||||||||
\(495\) | 426785. | 0.0782882 | ||||||||
\(496\) | −2.16541e6 | −0.395217 | ||||||||
\(497\) | 1.19058e6 | 0.216205 | ||||||||
\(498\) | −3.39464e6 | −0.613367 | ||||||||
\(499\) | −4.65684e6 | −0.837221 | −0.418610 | − | 0.908166i | \(-0.637483\pi\) | ||||
−0.418610 | + | 0.908166i | \(0.637483\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | −4.73958e6 | −0.843617 | ||||||||
\(502\) | −1.23242e6 | −0.218273 | ||||||||
\(503\) | −9.48419e6 | −1.67140 | −0.835700 | − | 0.549186i | \(-0.814938\pi\) | ||||
−0.835700 | + | 0.549186i | \(0.814938\pi\) | |||||||
\(504\) | −218424. | −0.0383023 | ||||||||
\(505\) | −1.78141e6 | −0.310839 | ||||||||
\(506\) | 2.45714e6 | 0.426632 | ||||||||
\(507\) | −754373. | −0.130337 | ||||||||
\(508\) | −2.68119e6 | −0.460965 | ||||||||
\(509\) | −3.53012e6 | −0.603941 | −0.301971 | − | 0.953317i | \(-0.597644\pi\) | ||||
−0.301971 | + | 0.953317i | \(0.597644\pi\) | |||||||
\(510\) | 1.79671e6 | 0.305881 | ||||||||
\(511\) | 1.56615e6 | 0.265327 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | 6.44845e6 | 1.07658 | ||||||||
\(515\) | 1.78128e6 | 0.295948 | ||||||||
\(516\) | 1.65056e6 | 0.272903 | ||||||||
\(517\) | 1.36172e6 | 0.224059 | ||||||||
\(518\) | 1.48332e6 | 0.242891 | ||||||||
\(519\) | 6.47575e6 | 1.05529 | ||||||||
\(520\) | −1.07939e6 | −0.175054 | ||||||||
\(521\) | 862947. | 0.139280 | 0.0696402 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696402 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(522\) | −2.54764e6 | −0.409225 | ||||||||
\(523\) | −1.68744e6 | −0.269758 | −0.134879 | − | 0.990862i | \(-0.543065\pi\) | ||||
−0.134879 | + | 0.990862i | \(0.543065\pi\) | |||||||
\(524\) | 193773. | 0.0308294 | ||||||||
\(525\) | −237006. | −0.0375284 | ||||||||
\(526\) | −1.84048e6 | −0.290046 | ||||||||
\(527\) | 1.68863e7 | 2.64855 | ||||||||
\(528\) | 485586. | 0.0758022 | ||||||||
\(529\) | 2.05879e6 | 0.319870 | ||||||||
\(530\) | 749465. | 0.115894 | ||||||||
\(531\) | −2.60929e6 | −0.401593 | ||||||||
\(532\) | 243368. | 0.0372807 | ||||||||
\(533\) | −483716. | −0.0737518 | ||||||||
\(534\) | −2.07757e6 | −0.315284 | ||||||||
\(535\) | −1.94921e6 | −0.294425 | ||||||||
\(536\) | 656054. | 0.0986342 | ||||||||
\(537\) | −730403. | −0.109302 | ||||||||
\(538\) | −7.04750e6 | −1.04973 | ||||||||
\(539\) | 3.16805e6 | 0.469700 | ||||||||
\(540\) | 291600. | 0.0430331 | ||||||||
\(541\) | 6.74968e6 | 0.991494 | 0.495747 | − | 0.868467i | \(-0.334894\pi\) | ||||
0.495747 | + | 0.868467i | \(0.334894\pi\) | |||||||
\(542\) | −876026. | −0.128091 | ||||||||
\(543\) | −3.55564e6 | −0.517509 | ||||||||
\(544\) | 2.04426e6 | 0.296168 | ||||||||
\(545\) | −4.63585e6 | −0.668556 | ||||||||
\(546\) | −1.02329e6 | −0.146898 | ||||||||
\(547\) | 1.12662e7 | 1.60994 | 0.804968 | − | 0.593318i | \(-0.202182\pi\) | ||||
0.804968 | + | 0.593318i | \(0.202182\pi\) | |||||||
\(548\) | 4.99969e6 | 0.711200 | ||||||||
\(549\) | 595244. | 0.0842877 | ||||||||
\(550\) | 526895. | 0.0742707 | ||||||||
\(551\) | 2.83858e6 | 0.398311 | ||||||||
\(552\) | 1.67883e6 | 0.234509 | ||||||||
\(553\) | −307769. | −0.0427968 | ||||||||
\(554\) | 3.24802e6 | 0.449619 | ||||||||
\(555\) | −1.98026e6 | −0.272891 | ||||||||
\(556\) | −352615. | −0.0483741 | ||||||||
\(557\) | 8.62465e6 | 1.17789 | 0.588944 | − | 0.808174i | \(-0.299544\pi\) | ||||
0.588944 | + | 0.808174i | \(0.299544\pi\) | |||||||
\(558\) | 2.74059e6 | 0.372614 | ||||||||
\(559\) | 7.73265e6 | 1.04664 | ||||||||
\(560\) | −269660. | −0.0363367 | ||||||||
\(561\) | −3.78671e6 | −0.507990 | ||||||||
\(562\) | −2.15156e6 | −0.287351 | ||||||||
\(563\) | −1.46836e7 | −1.95237 | −0.976184 | − | 0.216945i | \(-0.930391\pi\) | ||||
−0.976184 | + | 0.216945i | \(0.930391\pi\) | |||||||
\(564\) | 930392. | 0.123160 | ||||||||
\(565\) | −5.61924e6 | −0.740554 | ||||||||
\(566\) | 3.97080e6 | 0.520999 | ||||||||
\(567\) | 276443. | 0.0361117 | ||||||||
\(568\) | −1.80843e6 | −0.235196 | ||||||||
\(569\) | −9.50758e6 | −1.23109 | −0.615545 | − | 0.788102i | \(-0.711064\pi\) | ||||
−0.615545 | + | 0.788102i | \(0.711064\pi\) | |||||||
\(570\) | −324900. | −0.0418854 | ||||||||
\(571\) | 1.01310e6 | 0.130035 | 0.0650177 | − | 0.997884i | \(-0.479290\pi\) | ||||
0.0650177 | + | 0.997884i | \(0.479290\pi\) | |||||||
\(572\) | 2.27491e6 | 0.290719 | ||||||||
\(573\) | −7.94246e6 | −1.01058 | ||||||||
\(574\) | −120845. | −0.0153090 | ||||||||
\(575\) | 1.82165e6 | 0.229771 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 8.07864e6 | 1.01018 | 0.505090 | − | 0.863067i | \(-0.331459\pi\) | ||||
0.505090 | + | 0.863067i | \(0.331459\pi\) | |||||||
\(578\) | −1.02622e7 | −1.27767 | ||||||||
\(579\) | −2.84161e6 | −0.352264 | ||||||||
\(580\) | −3.14524e6 | −0.388225 | ||||||||
\(581\) | −3.97308e6 | −0.488301 | ||||||||
\(582\) | −5.46908e6 | −0.669278 | ||||||||
\(583\) | −1.57956e6 | −0.192470 | ||||||||
\(584\) | −2.37890e6 | −0.288632 | ||||||||
\(585\) | 1.36611e6 | 0.165042 | ||||||||
\(586\) | −5.93965e6 | −0.714524 | ||||||||
\(587\) | 8.79577e6 | 1.05361 | 0.526803 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526803 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(588\) | 2.16456e6 | 0.258183 | ||||||||
\(589\) | −3.05356e6 | −0.362676 | ||||||||
\(590\) | −3.22135e6 | −0.380984 | ||||||||
\(591\) | 4.16412e6 | 0.490405 | ||||||||
\(592\) | −2.25309e6 | −0.264226 | ||||||||
\(593\) | −5.79734e6 | −0.677006 | −0.338503 | − | 0.940965i | \(-0.609920\pi\) | ||||
−0.338503 | + | 0.940965i | \(0.609920\pi\) | |||||||
\(594\) | −614570. | −0.0714670 | ||||||||
\(595\) | 2.10287e6 | 0.243512 | ||||||||
\(596\) | 2.29581e6 | 0.264741 | ||||||||
\(597\) | −8.86968e6 | −1.01853 | ||||||||
\(598\) | 7.86510e6 | 0.899397 | ||||||||
\(599\) | −1.53091e7 | −1.74334 | −0.871670 | − | 0.490093i | \(-0.836963\pi\) | ||||
−0.871670 | + | 0.490093i | \(0.836963\pi\) | |||||||
\(600\) | 360000. | 0.0408248 | ||||||||
\(601\) | 5.77032e6 | 0.651649 | 0.325824 | − | 0.945430i | \(-0.394358\pi\) | ||||
0.325824 | + | 0.945430i | \(0.394358\pi\) | |||||||
\(602\) | 1.93181e6 | 0.217257 | ||||||||
\(603\) | −830318. | −0.0929933 | ||||||||
\(604\) | 964607. | 0.107587 | ||||||||
\(605\) | 2.91580e6 | 0.323869 | ||||||||
\(606\) | 2.56523e6 | 0.283756 | ||||||||
\(607\) | 5.92237e6 | 0.652415 | 0.326208 | − | 0.945298i | \(-0.394229\pi\) | ||||
0.326208 | + | 0.945298i | \(0.394229\pi\) | |||||||
\(608\) | −369664. | −0.0405554 | ||||||||
\(609\) | −2.98176e6 | −0.325783 | ||||||||
\(610\) | 734869. | 0.0799624 | ||||||||
\(611\) | 4.35876e6 | 0.472346 | ||||||||
\(612\) | −2.58726e6 | −0.279230 | ||||||||
\(613\) | 1.00960e7 | 1.08517 | 0.542583 | − | 0.840002i | \(-0.317446\pi\) | ||||
0.542583 | + | 0.840002i | \(0.317446\pi\) | |||||||
\(614\) | 412622. | 0.0441704 | ||||||||
\(615\) | 161330. | 0.0171999 | ||||||||
\(616\) | 568330. | 0.0603460 | ||||||||
\(617\) | −8.99298e6 | −0.951022 | −0.475511 | − | 0.879710i | \(-0.657737\pi\) | ||||
−0.475511 | + | 0.879710i | \(0.657737\pi\) | |||||||
\(618\) | −2.56505e6 | −0.270162 | ||||||||
\(619\) | −7.72814e6 | −0.810678 | −0.405339 | − | 0.914166i | \(-0.632847\pi\) | ||||
−0.405339 | + | 0.914166i | \(0.632847\pi\) | |||||||
\(620\) | 3.38345e6 | 0.353493 | ||||||||
\(621\) | −2.12477e6 | −0.221097 | ||||||||
\(622\) | 7.38927e6 | 0.765818 | ||||||||
\(623\) | −2.43158e6 | −0.250997 | ||||||||
\(624\) | 1.55432e6 | 0.159801 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 7.85093e6 | 0.800728 | ||||||||
\(627\) | 684753. | 0.0695609 | ||||||||
\(628\) | 4.29411e6 | 0.434484 | ||||||||
\(629\) | 1.75701e7 | 1.77071 | ||||||||
\(630\) | 341288. | 0.0342586 | ||||||||
\(631\) | −3.74241e6 | −0.374178 | −0.187089 | − | 0.982343i | \(-0.559905\pi\) | ||||
−0.187089 | + | 0.982343i | \(0.559905\pi\) | |||||||
\(632\) | 467485. | 0.0465560 | ||||||||
\(633\) | 3.14593e6 | 0.312061 | ||||||||
\(634\) | −4.39489e6 | −0.434235 | ||||||||
\(635\) | 4.18936e6 | 0.412300 | ||||||||
\(636\) | −1.07923e6 | −0.105796 | ||||||||
\(637\) | 1.01407e7 | 0.990190 | ||||||||
\(638\) | 6.62884e6 | 0.644742 | ||||||||
\(639\) | 2.28879e6 | 0.221745 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | 1.45395e7 | 1.39767 | 0.698833 | − | 0.715285i | \(-0.253703\pi\) | ||||
0.698833 | + | 0.715285i | \(0.253703\pi\) | |||||||
\(642\) | 2.80687e6 | 0.268772 | ||||||||
\(643\) | 1.77387e7 | 1.69198 | 0.845990 | − | 0.533199i | \(-0.179010\pi\) | ||||
0.845990 | + | 0.533199i | \(0.179010\pi\) | |||||||
\(644\) | 1.96490e6 | 0.186692 | ||||||||
\(645\) | −2.57900e6 | −0.244091 | ||||||||
\(646\) | 2.88272e6 | 0.271783 | ||||||||
\(647\) | −697833. | −0.0655377 | −0.0327688 | − | 0.999463i | \(-0.510433\pi\) | ||||
−0.0327688 | + | 0.999463i | \(0.510433\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 6.78924e6 | 0.632717 | ||||||||
\(650\) | 1.68655e6 | 0.156573 | ||||||||
\(651\) | 3.20759e6 | 0.296637 | ||||||||
\(652\) | 9.25616e6 | 0.852730 | ||||||||
\(653\) | 1.21909e7 | 1.11880 | 0.559399 | − | 0.828898i | \(-0.311032\pi\) | ||||
0.559399 | + | 0.828898i | \(0.311032\pi\) | |||||||
\(654\) | 6.67562e6 | 0.610305 | ||||||||
\(655\) | −302770. | −0.0275747 | ||||||||
\(656\) | 183557. | 0.0166537 | ||||||||
\(657\) | 3.01080e6 | 0.272125 | ||||||||
\(658\) | 1.08893e6 | 0.0980472 | ||||||||
\(659\) | 2.75765e6 | 0.247358 | 0.123679 | − | 0.992322i | \(-0.460531\pi\) | ||||
0.123679 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(660\) | −758729. | −0.0677995 | ||||||||
\(661\) | −1.45968e7 | −1.29943 | −0.649716 | − | 0.760177i | \(-0.725112\pi\) | ||||
−0.649716 | + | 0.760177i | \(0.725112\pi\) | |||||||
\(662\) | 3.78248e6 | 0.335453 | ||||||||
\(663\) | −1.21210e7 | −1.07091 | ||||||||
\(664\) | 6.03492e6 | 0.531192 | ||||||||
\(665\) | −380262. | −0.0333449 | ||||||||
\(666\) | 2.85157e6 | 0.249114 | ||||||||
\(667\) | 2.29181e7 | 1.99464 | ||||||||
\(668\) | 8.42591e6 | 0.730593 | ||||||||
\(669\) | −2.48883e6 | −0.214996 | ||||||||
\(670\) | −1.02508e6 | −0.0882211 | ||||||||
\(671\) | −1.54880e6 | −0.132797 | ||||||||
\(672\) | 388310. | 0.0331708 | ||||||||
\(673\) | −1.07005e7 | −0.910677 | −0.455339 | − | 0.890318i | \(-0.650482\pi\) | ||||
−0.455339 | + | 0.890318i | \(0.650482\pi\) | |||||||
\(674\) | 4.67867e6 | 0.396710 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | 1.34111e6 | 0.112875 | ||||||||
\(677\) | 1.43643e7 | 1.20452 | 0.602259 | − | 0.798301i | \(-0.294268\pi\) | ||||
0.602259 | + | 0.798301i | \(0.294268\pi\) | |||||||
\(678\) | 8.09171e6 | 0.676030 | ||||||||
\(679\) | −6.40100e6 | −0.532811 | ||||||||
\(680\) | −3.19415e6 | −0.264901 | ||||||||
\(681\) | −4.75932e6 | −0.393258 | ||||||||
\(682\) | −7.13089e6 | −0.587060 | ||||||||
\(683\) | 2.26535e7 | 1.85816 | 0.929081 | − | 0.369877i | \(-0.120600\pi\) | ||||
0.929081 | + | 0.369877i | \(0.120600\pi\) | |||||||
\(684\) | 467856. | 0.0382360 | ||||||||
\(685\) | −7.81201e6 | −0.636116 | ||||||||
\(686\) | 5.36601e6 | 0.435353 | ||||||||
\(687\) | 944600. | 0.0763583 | ||||||||
\(688\) | −2.93433e6 | −0.236341 | ||||||||
\(689\) | −5.05604e6 | −0.405754 | ||||||||
\(690\) | −2.62318e6 | −0.209751 | ||||||||
\(691\) | 2.27355e7 | 1.81138 | 0.905691 | − | 0.423938i | \(-0.139353\pi\) | ||||
0.905691 | + | 0.423938i | \(0.139353\pi\) | |||||||
\(692\) | −1.15124e7 | −0.913907 | ||||||||
\(693\) | −719292. | −0.0568947 | ||||||||
\(694\) | −4.79032e6 | −0.377543 | ||||||||
\(695\) | 550960. | 0.0432672 | ||||||||
\(696\) | 4.52914e6 | 0.354399 | ||||||||
\(697\) | −1.43142e6 | −0.111605 | ||||||||
\(698\) | 1.25231e6 | 0.0972912 | ||||||||
\(699\) | 7.93073e6 | 0.613932 | ||||||||
\(700\) | 421343. | 0.0325006 | ||||||||
\(701\) | −8.41277e6 | −0.646613 | −0.323306 | − | 0.946294i | \(-0.604794\pi\) | ||||
−0.323306 | + | 0.946294i | \(0.604794\pi\) | |||||||
\(702\) | −1.96719e6 | −0.150662 | ||||||||
\(703\) | −3.17721e6 | −0.242470 | ||||||||
\(704\) | −863265. | −0.0656466 | ||||||||
\(705\) | −1.45374e6 | −0.110157 | ||||||||
\(706\) | −9.25502e6 | −0.698821 | ||||||||
\(707\) | 3.00234e6 | 0.225897 | ||||||||
\(708\) | 4.63874e6 | 0.347790 | ||||||||
\(709\) | 6.70103e6 | 0.500640 | 0.250320 | − | 0.968163i | \(-0.419464\pi\) | ||||
0.250320 | + | 0.968163i | \(0.419464\pi\) | |||||||
\(710\) | 2.82567e6 | 0.210366 | ||||||||
\(711\) | −591661. | −0.0438934 | ||||||||
\(712\) | 3.69345e6 | 0.273044 | ||||||||
\(713\) | −2.46539e7 | −1.81619 | ||||||||
\(714\) | −3.02813e6 | −0.222295 | ||||||||
\(715\) | −3.55454e6 | −0.260027 | ||||||||
\(716\) | 1.29849e6 | 0.0946580 | ||||||||
\(717\) | −1.12014e7 | −0.813718 | ||||||||
\(718\) | −5.89099e6 | −0.426459 | ||||||||
\(719\) | 1.19095e7 | 0.859153 | 0.429577 | − | 0.903030i | \(-0.358663\pi\) | ||||
0.429577 | + | 0.903030i | \(0.358663\pi\) | |||||||
\(720\) | −518400. | −0.0372678 | ||||||||
\(721\) | −3.00213e6 | −0.215075 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | −6.37262e6 | −0.453390 | ||||||||
\(724\) | 6.32113e6 | 0.448176 | ||||||||
\(725\) | 4.91444e6 | 0.347239 | ||||||||
\(726\) | −4.19875e6 | −0.295651 | ||||||||
\(727\) | −1.67973e7 | −1.17870 | −0.589351 | − | 0.807877i | \(-0.700617\pi\) | ||||
−0.589351 | + | 0.807877i | \(0.700617\pi\) | |||||||
\(728\) | 1.81918e6 | 0.127218 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 3.71704e6 | 0.258160 | ||||||||
\(731\) | 2.28826e7 | 1.58384 | ||||||||
\(732\) | −1.05821e6 | −0.0729953 | ||||||||
\(733\) | −9.75964e6 | −0.670925 | −0.335462 | − | 0.942054i | \(-0.608893\pi\) | ||||
−0.335462 | + | 0.942054i | \(0.608893\pi\) | |||||||
\(734\) | −7.99273e6 | −0.547589 | ||||||||
\(735\) | −3.38213e6 | −0.230926 | ||||||||
\(736\) | −2.98459e6 | −0.203091 | ||||||||
\(737\) | 2.16045e6 | 0.146513 | ||||||||
\(738\) | −232314. | −0.0157013 | ||||||||
\(739\) | 1.33048e7 | 0.896185 | 0.448093 | − | 0.893987i | \(-0.352103\pi\) | ||||
0.448093 | + | 0.893987i | \(0.352103\pi\) | |||||||
\(740\) | 3.52046e6 | 0.236331 | ||||||||
\(741\) | 2.19184e6 | 0.146644 | ||||||||
\(742\) | −1.26313e6 | −0.0842243 | ||||||||
\(743\) | −9.23873e6 | −0.613960 | −0.306980 | − | 0.951716i | \(-0.599319\pi\) | ||||
−0.306980 | + | 0.951716i | \(0.599319\pi\) | |||||||
\(744\) | −4.87217e6 | −0.322693 | ||||||||
\(745\) | −3.58721e6 | −0.236791 | ||||||||
\(746\) | 1.63445e7 | 1.07529 | ||||||||
\(747\) | −7.63795e6 | −0.500812 | ||||||||
\(748\) | 6.73194e6 | 0.439932 | ||||||||
\(749\) | 3.28515e6 | 0.213969 | ||||||||
\(750\) | −562500. | −0.0365148 | ||||||||
\(751\) | 3.55337e6 | 0.229901 | 0.114950 | − | 0.993371i | \(-0.463329\pi\) | ||||
0.114950 | + | 0.993371i | \(0.463329\pi\) | |||||||
\(752\) | −1.65403e6 | −0.106659 | ||||||||
\(753\) | −2.77294e6 | −0.178219 | ||||||||
\(754\) | 2.12184e7 | 1.35920 | ||||||||
\(755\) | −1.50720e6 | −0.0962284 | ||||||||
\(756\) | −491455. | −0.0312737 | ||||||||
\(757\) | −7.04959e6 | −0.447120 | −0.223560 | − | 0.974690i | \(-0.571768\pi\) | ||||
−0.223560 | + | 0.974690i | \(0.571768\pi\) | |||||||
\(758\) | −1.87917e7 | −1.18794 | ||||||||
\(759\) | 5.52856e6 | 0.348343 | ||||||||
\(760\) | 577600. | 0.0362738 | ||||||||
\(761\) | −1.95250e7 | −1.22216 | −0.611081 | − | 0.791568i | \(-0.709265\pi\) | ||||
−0.611081 | + | 0.791568i | \(0.709265\pi\) | |||||||
\(762\) | −6.03267e6 | −0.376376 | ||||||||
\(763\) | 7.81313e6 | 0.485863 | ||||||||
\(764\) | 1.41199e7 | 0.875184 | ||||||||
\(765\) | 4.04260e6 | 0.249751 | ||||||||
\(766\) | −3.88158e6 | −0.239021 | ||||||||
\(767\) | 2.17318e7 | 1.33385 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 2.03020e7 | 1.23801 | 0.619004 | − | 0.785388i | \(-0.287537\pi\) | ||||
0.619004 | + | 0.785388i | \(0.287537\pi\) | |||||||
\(770\) | −888015. | −0.0539751 | ||||||||
\(771\) | 1.45090e7 | 0.879026 | ||||||||
\(772\) | 5.05176e6 | 0.305070 | ||||||||
\(773\) | −3.15938e7 | −1.90175 | −0.950873 | − | 0.309581i | \(-0.899811\pi\) | ||||
−0.950873 | + | 0.309581i | \(0.899811\pi\) | |||||||
\(774\) | 3.71376e6 | 0.222824 | ||||||||
\(775\) | −5.28664e6 | −0.316173 | ||||||||
\(776\) | 9.72280e6 | 0.579612 | ||||||||
\(777\) | 3.33747e6 | 0.198319 | ||||||||
\(778\) | −1.80608e7 | −1.06977 | ||||||||
\(779\) | 258844. | 0.0152825 | ||||||||
\(780\) | −2.42863e6 | −0.142931 | ||||||||
\(781\) | −5.95533e6 | −0.349364 | ||||||||
\(782\) | 2.32745e7 | 1.36102 | ||||||||
\(783\) | −5.73220e6 | −0.334131 | ||||||||
\(784\) | −3.84811e6 | −0.223593 | ||||||||
\(785\) | −6.70954e6 | −0.388614 | ||||||||
\(786\) | 435989. | 0.0251721 | ||||||||
\(787\) | 2.27199e7 | 1.30758 | 0.653792 | − | 0.756674i | \(-0.273177\pi\) | ||||
0.653792 | + | 0.756674i | \(0.273177\pi\) | |||||||
\(788\) | −7.40288e6 | −0.424703 | ||||||||
\(789\) | −4.14108e6 | −0.236822 | ||||||||
\(790\) | −730446. | −0.0416409 | ||||||||
\(791\) | 9.47052e6 | 0.538186 | ||||||||
\(792\) | 1.09257e6 | 0.0618922 | ||||||||
\(793\) | −4.95758e6 | −0.279954 | ||||||||
\(794\) | −2.13927e7 | −1.20425 | ||||||||
\(795\) | 1.68630e6 | 0.0946272 | ||||||||
\(796\) | 1.57683e7 | 0.882069 | ||||||||
\(797\) | 2.21510e7 | 1.23523 | 0.617616 | − | 0.786480i | \(-0.288099\pi\) | ||||
0.617616 | + | 0.786480i | \(0.288099\pi\) | |||||||
\(798\) | 547578. | 0.0304396 | ||||||||
\(799\) | 1.28985e7 | 0.714780 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −4.67452e6 | −0.257428 | ||||||||
\(802\) | −6.58055e6 | −0.361265 | ||||||||
\(803\) | −7.83395e6 | −0.428738 | ||||||||
\(804\) | 1.47612e6 | 0.0805345 | ||||||||
\(805\) | −3.07016e6 | −0.166983 | ||||||||
\(806\) | −2.28254e7 | −1.23760 | ||||||||
\(807\) | −1.58569e7 | −0.857104 | ||||||||
\(808\) | −4.56041e6 | −0.245740 | ||||||||
\(809\) | −856575. | −0.0460145 | −0.0230072 | − | 0.999735i | \(-0.507324\pi\) | ||||
−0.0230072 | + | 0.999735i | \(0.507324\pi\) | |||||||
\(810\) | 656100. | 0.0351364 | ||||||||
\(811\) | −2.41826e7 | −1.29107 | −0.645536 | − | 0.763730i | \(-0.723366\pi\) | ||||
−0.645536 | + | 0.763730i | \(0.723366\pi\) | |||||||
\(812\) | 5.30090e6 | 0.282137 | ||||||||
\(813\) | −1.97106e6 | −0.104586 | ||||||||
\(814\) | −7.41965e6 | −0.392484 | ||||||||
\(815\) | −1.44627e7 | −0.762705 | ||||||||
\(816\) | 4.59958e6 | 0.241820 | ||||||||
\(817\) | −4.13787e6 | −0.216881 | ||||||||
\(818\) | −1.47290e6 | −0.0769645 | ||||||||
\(819\) | −2.30240e6 | −0.119942 | ||||||||
\(820\) | −286808. | −0.0148956 | ||||||||
\(821\) | −2.37506e7 | −1.22975 | −0.614875 | − | 0.788625i | \(-0.710793\pi\) | ||||
−0.614875 | + | 0.788625i | \(0.710793\pi\) | |||||||
\(822\) | 1.12493e7 | 0.580692 | ||||||||
\(823\) | −1.16602e7 | −0.600077 | −0.300038 | − | 0.953927i | \(-0.596999\pi\) | ||||
−0.300038 | + | 0.953927i | \(0.596999\pi\) | |||||||
\(824\) | 4.56008e6 | 0.233967 | ||||||||
\(825\) | 1.18551e6 | 0.0606418 | ||||||||
\(826\) | 5.42917e6 | 0.276875 | ||||||||
\(827\) | 1.08538e7 | 0.551848 | 0.275924 | − | 0.961180i | \(-0.411016\pi\) | ||||
0.275924 | + | 0.961180i | \(0.411016\pi\) | |||||||
\(828\) | 3.77738e6 | 0.191476 | ||||||||
\(829\) | 5.41419e6 | 0.273619 | 0.136810 | − | 0.990597i | \(-0.456315\pi\) | ||||
0.136810 | + | 0.990597i | \(0.456315\pi\) | |||||||
\(830\) | −9.42956e6 | −0.475112 | ||||||||
\(831\) | 7.30805e6 | 0.367112 | ||||||||
\(832\) | −2.76324e6 | −0.138392 | ||||||||
\(833\) | 3.00085e7 | 1.49841 | ||||||||
\(834\) | −793383. | −0.0394973 | ||||||||
\(835\) | −1.31655e7 | −0.653463 | ||||||||
\(836\) | −1.21734e6 | −0.0602415 | ||||||||
\(837\) | 6.16634e6 | 0.304238 | ||||||||
\(838\) | −4.05468e6 | −0.199456 | ||||||||
\(839\) | 3.29355e7 | 1.61532 | 0.807660 | − | 0.589648i | \(-0.200734\pi\) | ||||
0.807660 | + | 0.589648i | \(0.200734\pi\) | |||||||
\(840\) | −606734. | −0.0296688 | ||||||||
\(841\) | 4.13171e7 | 2.01437 | ||||||||
\(842\) | 2.21414e7 | 1.07628 | ||||||||
\(843\) | −4.84101e6 | −0.234621 | ||||||||
\(844\) | −5.59277e6 | −0.270253 | ||||||||
\(845\) | −2.09548e6 | −0.100958 | ||||||||
\(846\) | 2.09338e6 | 0.100559 | ||||||||
\(847\) | −4.91421e6 | −0.235367 | ||||||||
\(848\) | 1.91863e6 | 0.0916223 | ||||||||
\(849\) | 8.93430e6 | 0.425394 | ||||||||
\(850\) | 4.99087e6 | 0.236935 | ||||||||
\(851\) | −2.56522e7 | −1.21423 | ||||||||
\(852\) | −4.06897e6 | −0.192037 | ||||||||
\(853\) | 2.54608e7 | 1.19812 | 0.599059 | − | 0.800705i | \(-0.295541\pi\) | ||||
0.599059 | + | 0.800705i | \(0.295541\pi\) | |||||||
\(854\) | −1.23853e6 | −0.0581114 | ||||||||
\(855\) | −731025. | −0.0341993 | ||||||||
\(856\) | −4.98999e6 | −0.232763 | ||||||||
\(857\) | −3.36988e7 | −1.56734 | −0.783669 | − | 0.621178i | \(-0.786654\pi\) | ||||
−0.783669 | + | 0.621178i | \(0.786654\pi\) | |||||||
\(858\) | 5.11854e6 | 0.237371 | ||||||||
\(859\) | −7.66604e6 | −0.354477 | −0.177239 | − | 0.984168i | \(-0.556716\pi\) | ||||
−0.177239 | + | 0.984168i | \(0.556716\pi\) | |||||||
\(860\) | 4.58489e6 | 0.211389 | ||||||||
\(861\) | −271900. | −0.0124998 | ||||||||
\(862\) | −5.18764e6 | −0.237794 | ||||||||
\(863\) | −1.84147e7 | −0.841662 | −0.420831 | − | 0.907139i | \(-0.638262\pi\) | ||||
−0.420831 | + | 0.907139i | \(0.638262\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 1.79882e7 | 0.817423 | ||||||||
\(866\) | 2.75621e7 | 1.24887 | ||||||||
\(867\) | −2.30899e7 | −1.04321 | ||||||||
\(868\) | −5.70237e6 | −0.256895 | ||||||||
\(869\) | 1.53947e6 | 0.0691549 | ||||||||
\(870\) | −7.07679e6 | −0.316984 | ||||||||
\(871\) | 6.91543e6 | 0.308868 | ||||||||
\(872\) | −1.18678e7 | −0.528540 | ||||||||
\(873\) | −1.23054e7 | −0.546463 | ||||||||
\(874\) | −4.20874e6 | −0.186369 | ||||||||
\(875\) | −658349. | −0.0290694 | ||||||||
\(876\) | −5.35253e6 | −0.235667 | ||||||||
\(877\) | 2.92849e7 | 1.28571 | 0.642857 | − | 0.765987i | \(-0.277749\pi\) | ||||
0.642857 | + | 0.765987i | \(0.277749\pi\) | |||||||
\(878\) | 585187. | 0.0256188 | ||||||||
\(879\) | −1.33642e7 | −0.583406 | ||||||||
\(880\) | 1.34885e6 | 0.0587161 | ||||||||
\(881\) | −1.17884e6 | −0.0511699 | −0.0255849 | − | 0.999673i | \(-0.508145\pi\) | ||||
−0.0255849 | + | 0.999673i | \(0.508145\pi\) | |||||||
\(882\) | 4.87027e6 | 0.210805 | ||||||||
\(883\) | −8.64064e6 | −0.372944 | −0.186472 | − | 0.982460i | \(-0.559705\pi\) | ||||
−0.186472 | + | 0.982460i | \(0.559705\pi\) | |||||||
\(884\) | 2.15484e7 | 0.927437 | ||||||||
\(885\) | −7.24803e6 | −0.311073 | ||||||||
\(886\) | 3.31223e6 | 0.141754 | ||||||||
\(887\) | 2.42978e7 | 1.03695 | 0.518475 | − | 0.855093i | \(-0.326500\pi\) | ||||
0.518475 | + | 0.855093i | \(0.326500\pi\) | |||||||
\(888\) | −5.06946e6 | −0.215739 | ||||||||
\(889\) | −7.06063e6 | −0.299633 | ||||||||
\(890\) | −5.77102e6 | −0.244218 | ||||||||
\(891\) | −1.38278e6 | −0.0583526 | ||||||||
\(892\) | 4.42458e6 | 0.186192 | ||||||||
\(893\) | −2.33244e6 | −0.0978774 | ||||||||
\(894\) | 5.16558e6 | 0.216160 | ||||||||
\(895\) | −2.02890e6 | −0.0846647 | ||||||||
\(896\) | −690329. | −0.0287267 | ||||||||
\(897\) | 1.76965e7 | 0.734355 | ||||||||
\(898\) | 2.38116e6 | 0.0985366 | ||||||||
\(899\) | −6.65110e7 | −2.74469 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | −1.49619e7 | −0.614009 | ||||||||
\(902\) | 604471. | 0.0247377 | ||||||||
\(903\) | 4.34658e6 | 0.177390 | ||||||||
\(904\) | −1.43853e7 | −0.585459 | ||||||||
\(905\) | −9.87676e6 | −0.400860 | ||||||||
\(906\) | 2.17037e6 | 0.0878441 | ||||||||
\(907\) | −1.76213e7 | −0.711247 | −0.355624 | − | 0.934629i | \(-0.615732\pi\) | ||||
−0.355624 | + | 0.934629i | \(0.615732\pi\) | |||||||
\(908\) | 8.46102e6 | 0.340571 | ||||||||
\(909\) | 5.77177e6 | 0.231686 | ||||||||
\(910\) | −2.84247e6 | −0.113787 | ||||||||
\(911\) | 3.91841e6 | 0.156428 | 0.0782140 | − | 0.996937i | \(-0.475078\pi\) | ||||
0.0782140 | + | 0.996937i | \(0.475078\pi\) | |||||||
\(912\) | −831744. | −0.0331133 | ||||||||
\(913\) | 1.98736e7 | 0.789040 | ||||||||
\(914\) | 2.33342e7 | 0.923904 | ||||||||
\(915\) | 1.65346e6 | 0.0652890 | ||||||||
\(916\) | −1.67929e6 | −0.0661282 | ||||||||
\(917\) | 510281. | 0.0200395 | ||||||||
\(918\) | −5.82135e6 | −0.227990 | ||||||||
\(919\) | −3.27348e7 | −1.27856 | −0.639280 | − | 0.768974i | \(-0.720768\pi\) | ||||
−0.639280 | + | 0.768974i | \(0.720768\pi\) | |||||||
\(920\) | 4.66343e6 | 0.181650 | ||||||||
\(921\) | 928399. | 0.0360650 | ||||||||
\(922\) | −7.62126e6 | −0.295256 | ||||||||
\(923\) | −1.90625e7 | −0.736507 | ||||||||
\(924\) | 1.27874e6 | 0.0492723 | ||||||||
\(925\) | −5.50072e6 | −0.211380 | ||||||||
\(926\) | −1.26843e7 | −0.486115 | ||||||||
\(927\) | −5.77136e6 | −0.220586 | ||||||||
\(928\) | −8.05181e6 | −0.306919 | ||||||||
\(929\) | −3.89116e7 | −1.47924 | −0.739622 | − | 0.673023i | \(-0.764996\pi\) | ||||
−0.739622 | + | 0.673023i | \(0.764996\pi\) | |||||||
\(930\) | 7.61276e6 | 0.288626 | ||||||||
\(931\) | −5.42644e6 | −0.205183 | ||||||||
\(932\) | −1.40991e7 | −0.531681 | ||||||||
\(933\) | 1.66258e7 | 0.625287 | ||||||||
\(934\) | 2.66852e6 | 0.100093 | ||||||||
\(935\) | −1.05186e7 | −0.393488 | ||||||||
\(936\) | 3.49723e6 | 0.130477 | ||||||||
\(937\) | −3.76135e7 | −1.39957 | −0.699785 | − | 0.714354i | \(-0.746721\pi\) | ||||
−0.699785 | + | 0.714354i | \(0.746721\pi\) | |||||||
\(938\) | 1.72765e6 | 0.0641134 | ||||||||
\(939\) | 1.76646e7 | 0.653792 | ||||||||
\(940\) | 2.58442e6 | 0.0953991 | ||||||||
\(941\) | 1.01083e7 | 0.372137 | 0.186068 | − | 0.982537i | \(-0.440425\pi\) | ||||
0.186068 | + | 0.982537i | \(0.440425\pi\) | |||||||
\(942\) | 9.66174e6 | 0.354755 | ||||||||
\(943\) | 2.08986e6 | 0.0765310 | ||||||||
\(944\) | −8.24664e6 | −0.301195 | ||||||||
\(945\) | 767898. | 0.0279720 | ||||||||
\(946\) | −9.66303e6 | −0.351063 | ||||||||
\(947\) | −313348. | −0.0113541 | −0.00567705 | − | 0.999984i | \(-0.501807\pi\) | ||||
−0.00567705 | + | 0.999984i | \(0.501807\pi\) | |||||||
\(948\) | 1.05184e6 | 0.0380128 | ||||||||
\(949\) | −2.50759e7 | −0.903838 | ||||||||
\(950\) | −902500. | −0.0324443 | ||||||||
\(951\) | −9.88851e6 | −0.354552 | ||||||||
\(952\) | 5.38334e6 | 0.192513 | ||||||||
\(953\) | −5.17010e7 | −1.84402 | −0.922012 | − | 0.387160i | \(-0.873456\pi\) | ||||
−0.922012 | + | 0.387160i | \(0.873456\pi\) | |||||||
\(954\) | −2.42827e6 | −0.0863824 | ||||||||
\(955\) | −2.20624e7 | −0.782788 | ||||||||
\(956\) | 1.99136e7 | 0.704701 | ||||||||
\(957\) | 1.49149e7 | 0.526430 | ||||||||
\(958\) | 3.84003e6 | 0.135183 | ||||||||
\(959\) | 1.31662e7 | 0.462288 | ||||||||
\(960\) | 921600. | 0.0322749 | ||||||||
\(961\) | 4.29191e7 | 1.49914 | ||||||||
\(962\) | −2.37497e7 | −0.827410 | ||||||||
\(963\) | 6.31545e6 | 0.219452 | ||||||||
\(964\) | 1.13291e7 | 0.392647 | ||||||||
\(965\) | −7.89337e6 | −0.272863 | ||||||||
\(966\) | 4.42103e6 | 0.152434 | ||||||||
\(967\) | 4.12743e7 | 1.41943 | 0.709714 | − | 0.704490i | \(-0.248824\pi\) | ||||
0.709714 | + | 0.704490i | \(0.248824\pi\) | |||||||
\(968\) | 7.46445e6 | 0.256041 | ||||||||
\(969\) | 6.48613e6 | 0.221910 | ||||||||
\(970\) | −1.51919e7 | −0.518421 | ||||||||
\(971\) | −3.75197e6 | −0.127706 | −0.0638531 | − | 0.997959i | \(-0.520339\pi\) | ||||
−0.0638531 | + | 0.997959i | \(0.520339\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −928574. | −0.0314437 | ||||||||
\(974\) | 3.10146e7 | 1.04753 | ||||||||
\(975\) | 3.79474e6 | 0.127841 | ||||||||
\(976\) | 1.88127e6 | 0.0632158 | ||||||||
\(977\) | −4.56688e7 | −1.53068 | −0.765338 | − | 0.643629i | \(-0.777428\pi\) | ||||
−0.765338 | + | 0.643629i | \(0.777428\pi\) | |||||||
\(978\) | 2.08264e7 | 0.696251 | ||||||||
\(979\) | 1.21629e7 | 0.405583 | ||||||||
\(980\) | 6.01268e6 | 0.199987 | ||||||||
\(981\) | 1.50201e7 | 0.498312 | ||||||||
\(982\) | −2.29284e7 | −0.758745 | ||||||||
\(983\) | 5.01976e7 | 1.65691 | 0.828455 | − | 0.560055i | \(-0.189220\pi\) | ||||
0.828455 | + | 0.560055i | \(0.189220\pi\) | |||||||
\(984\) | 413004. | 0.0135977 | ||||||||
\(985\) | 1.15670e7 | 0.379866 | ||||||||
\(986\) | 6.27899e7 | 2.05682 | ||||||||
\(987\) | 2.45009e6 | 0.0800552 | ||||||||
\(988\) | −3.89661e6 | −0.126997 | ||||||||
\(989\) | −3.34083e7 | −1.08608 | ||||||||
\(990\) | −1.70714e6 | −0.0553581 | ||||||||
\(991\) | −4.10710e7 | −1.32847 | −0.664235 | − | 0.747524i | \(-0.731242\pi\) | ||||
−0.664235 | + | 0.747524i | \(0.731242\pi\) | |||||||
\(992\) | 8.66163e6 | 0.279460 | ||||||||
\(993\) | 8.51057e6 | 0.273896 | ||||||||
\(994\) | −4.76231e6 | −0.152880 | ||||||||
\(995\) | −2.46380e7 | −0.788947 | ||||||||
\(996\) | 1.35786e7 | 0.433716 | ||||||||
\(997\) | 2.13194e6 | 0.0679260 | 0.0339630 | − | 0.999423i | \(-0.489187\pi\) | ||||
0.0339630 | + | 0.999423i | \(0.489187\pi\) | |||||||
\(998\) | 1.86274e7 | 0.592004 | ||||||||
\(999\) | 6.41604e6 | 0.203401 |
(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 | 570.6.a.h.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.h.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |