Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 160) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −6.32456 | −0.405720 | −0.202860 | − | 0.979208i | \(-0.565024\pi\) | ||||
−0.202860 | + | 0.979208i | \(0.565024\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44.2719 | 0.341494 | 0.170747 | − | 0.985315i | \(-0.445382\pi\) | ||||
0.170747 | + | 0.985315i | \(0.445382\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −203.000 | −0.835391 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 720.999 | 1.79661 | 0.898304 | − | 0.439375i | \(-0.144800\pi\) | ||||
0.898304 | + | 0.439375i | \(0.144800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 146.000 | 0.239604 | 0.119802 | − | 0.992798i | \(-0.461774\pi\) | ||||
0.119802 | + | 0.992798i | \(0.461774\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 158.114 | 0.181444 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −702.000 | −0.589135 | −0.294567 | − | 0.955631i | \(-0.595176\pi\) | ||||
−0.294567 | + | 0.955631i | \(0.595176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2732.21 | −1.73632 | −0.868160 | − | 0.496285i | \(-0.834697\pi\) | ||||
−0.868160 | + | 0.496285i | \(0.834697\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −280.000 | −0.138551 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4091.99 | −1.61293 | −0.806463 | − | 0.591284i | \(-0.798621\pi\) | ||||
−0.806463 | + | 0.591284i | \(0.798621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2820.75 | 0.744656 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4010.00 | 0.885420 | 0.442710 | − | 0.896665i | \(-0.354017\pi\) | ||||
0.442710 | + | 0.896665i | \(0.354017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4566.33 | 0.853420 | 0.426710 | − | 0.904388i | \(-0.359672\pi\) | ||||
0.426710 | + | 0.904388i | \(0.359672\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4560.00 | −0.728920 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1106.80 | −0.152721 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14778.0 | 1.77464 | 0.887322 | − | 0.461150i | \(-0.152563\pi\) | ||||
0.887322 | + | 0.461150i | \(0.152563\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −923.385 | −0.0972123 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4350.00 | −0.404138 | −0.202069 | − | 0.979371i | \(-0.564767\pi\) | ||||
−0.202069 | + | 0.979371i | \(0.564767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12427.8 | −1.02499 | −0.512497 | − | 0.858689i | \(-0.671279\pi\) | ||||
−0.512497 | + | 0.858689i | \(0.671279\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5075.00 | 0.373598 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6014.65 | 0.397160 | 0.198580 | − | 0.980085i | \(-0.436367\pi\) | ||||
0.198580 | + | 0.980085i | \(0.436367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14847.0 | −0.883382 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4439.84 | 0.239024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 18154.0 | 0.887734 | 0.443867 | − | 0.896093i | \(-0.353606\pi\) | ||||
0.443867 | + | 0.896093i | \(0.353606\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18025.0 | −0.803467 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17280.0 | 0.704460 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 19707.3 | 0.737051 | 0.368525 | − | 0.929618i | \(-0.379863\pi\) | ||||
0.368525 | + | 0.929618i | \(0.379863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42130.0 | 1.44966 | 0.724831 | − | 0.688927i | \(-0.241918\pi\) | ||||
0.724831 | + | 0.688927i | \(0.241918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8987.19 | −0.285281 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3650.00 | −0.107154 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16184.5 | −0.440467 | −0.220233 | − | 0.975447i | \(-0.570682\pi\) | ||||
−0.220233 | + | 0.975447i | \(0.570682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 25880.0 | 0.654397 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45448.3 | 1.06997 | 0.534985 | − | 0.844862i | \(-0.320317\pi\) | ||||
0.534985 | + | 0.844862i | \(0.320317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26266.0 | 0.576882 | 0.288441 | − | 0.957498i | \(-0.406863\pi\) | ||||
0.288441 | + | 0.957498i | \(0.406863\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3952.85 | −0.0811441 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31920.0 | 0.613530 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8677.29 | −0.156429 | −0.0782143 | − | 0.996937i | \(-0.524922\pi\) | ||||
−0.0782143 | + | 0.996937i | \(0.524922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31489.0 | 0.533269 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 98757.9 | 1.57354 | 0.786768 | − | 0.617249i | \(-0.211753\pi\) | ||||
0.786768 | + | 0.617249i | \(0.211753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17550.0 | 0.263469 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −25361.5 | −0.359233 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 30570.0 | 0.409091 | 0.204546 | − | 0.978857i | \(-0.434428\pi\) | ||||
0.204546 | + | 0.978857i | \(0.434428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6463.70 | 0.0818234 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28880.0 | −0.346250 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 68305.2 | 0.776506 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66882.0 | 0.721739 | 0.360869 | − | 0.932616i | \(-0.382480\pi\) | ||||
0.360869 | + | 0.932616i | \(0.382480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −146363. | −1.50087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −42798.0 | −0.417465 | −0.208732 | − | 0.977973i | \(-0.566934\pi\) | ||||
−0.208732 | + | 0.977973i | \(0.566934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10505.1 | 0.0975678 | 0.0487839 | − | 0.998809i | \(-0.484465\pi\) | ||||
0.0487839 | + | 0.998809i | \(0.484465\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7000.00 | 0.0619619 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −66856.9 | −0.564529 | −0.282265 | − | 0.959337i | \(-0.591086\pi\) | ||||
−0.282265 | + | 0.959337i | \(0.591086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 111714. | 0.900620 | 0.450310 | − | 0.892872i | \(-0.351314\pi\) | ||||
0.450310 | + | 0.892872i | \(0.351314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −93464.3 | −0.720009 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 216834. | 1.59746 | 0.798732 | − | 0.601686i | \(-0.205504\pi\) | ||||
0.798732 | + | 0.601686i | \(0.205504\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 102300. | 0.721323 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −29638.0 | −0.200163 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −31078.9 | −0.201186 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 358789. | 2.22780 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 27511.8 | 0.163967 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 62277.9 | 0.342629 | 0.171315 | − | 0.985216i | \(-0.445199\pi\) | ||||
0.171315 | + | 0.985216i | \(0.445199\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 78600.0 | 0.415861 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −176189. | −0.897019 | −0.448510 | − | 0.893778i | \(-0.648045\pi\) | ||||
−0.448510 | + | 0.893778i | \(0.648045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −120960. | −0.592943 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −70518.8 | −0.333020 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 99802.0 | 0.454295 | 0.227147 | − | 0.973860i | \(-0.427060\pi\) | ||||
0.227147 | + | 0.973860i | \(0.427060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 271475. | 1.19177 | 0.595886 | − | 0.803069i | \(-0.296801\pi\) | ||||
0.595886 | + | 0.803069i | \(0.296801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −38040.0 | −0.161136 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 105266. | 0.430475 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −100250. | −0.395972 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 93900.7 | 0.358406 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 413626. | 1.52631 | 0.763154 | − | 0.646217i | \(-0.223650\pi\) | ||||
0.763154 | + | 0.646217i | \(0.223650\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 172496. | 0.615654 | 0.307827 | − | 0.951442i | \(-0.400398\pi\) | ||||
0.307827 | + | 0.951442i | \(0.400398\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 142506. | 0.492158 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −114158. | −0.381661 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −179358. | −0.580726 | −0.290363 | − | 0.956917i | \(-0.593776\pi\) | ||||
−0.290363 | + | 0.956917i | \(0.593776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −114816. | −0.360172 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −181160. | −0.550805 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −465924. | −1.37355 | −0.686777 | − | 0.726868i | \(-0.740975\pi\) | ||||
−0.686777 | + | 0.726868i | \(0.740975\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 114000. | 0.325983 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −609567. | −1.69134 | −0.845669 | − | 0.533708i | \(-0.820798\pi\) | ||||
−0.845669 | + | 0.533708i | \(0.820798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −349977. | −0.942590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 554638. | 1.45051 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −591086. | −1.50153 | −0.750767 | − | 0.660567i | \(-0.770316\pi\) | ||||
−0.750767 | + | 0.660567i | \(0.770316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27669.9 | 0.0682988 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −124640. | −0.299037 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −211215. | −0.492711 | −0.246355 | − | 0.969180i | \(-0.579233\pi\) | ||||
−0.246355 | + | 0.969180i | \(0.579233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 97538.0 | 0.221298 | 0.110649 | − | 0.993860i | \(-0.464707\pi\) | ||||
0.110649 | + | 0.993860i | \(0.464707\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −266454. | −0.588158 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −369450. | −0.793645 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −506142. | −1.05844 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 124880. | 0.254295 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 307158. | 0.609227 | 0.304613 | − | 0.952476i | \(-0.401473\pi\) | ||||
0.304613 | + | 0.952476i | \(0.401473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12434.0 | 0.0240280 | 0.0120140 | − | 0.999928i | \(-0.496176\pi\) | ||||
0.0120140 | + | 0.999928i | \(0.496176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23084.6 | 0.0434747 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 378858. | 0.695522 | 0.347761 | − | 0.937583i | \(-0.386942\pi\) | ||||
0.347761 | + | 0.937583i | \(0.386942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 767194. | 1.37332 | 0.686661 | − | 0.726978i | \(-0.259076\pi\) | ||||
0.686661 | + | 0.726978i | \(0.259076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 102360. | 0.178706 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 177530. | 0.302366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 108750. | 0.180736 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 830673. | 1.34742 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.96992e6 | −3.11948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 864529. | 1.33682 | 0.668411 | − | 0.743793i | \(-0.266975\pi\) | ||||
0.668411 | + | 0.743793i | \(0.266975\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −287440. | −0.434108 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 310694. | 0.458391 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 202160. | 0.291438 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −166121. | −0.234053 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −102492. | −0.141159 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −639710. | −0.861432 | −0.430716 | − | 0.902488i | \(-0.641739\pi\) | ||||
−0.430716 | + | 0.902488i | \(0.641739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −126875. | −0.167078 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 980515. | 1.26296 | 0.631480 | − | 0.775392i | \(-0.282448\pi\) | ||||
0.631480 | + | 0.775392i | \(0.282448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01261e6 | 1.27601 | 0.638004 | − | 0.770033i | \(-0.279760\pi\) | ||||
0.638004 | + | 0.770033i | \(0.279760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −201880. | −0.248922 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −706326. | −0.852345 | −0.426172 | − | 0.904642i | \(-0.640138\pi\) | ||||
−0.426172 | + | 0.904642i | \(0.640138\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −150366. | −0.177616 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 54880.0 | 0.0634663 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.19390e6 | −1.35199 | −0.675994 | − | 0.736907i | \(-0.736285\pi\) | ||||
−0.675994 | + | 0.736907i | \(0.736285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 404410. | 0.448517 | 0.224259 | − | 0.974530i | \(-0.428004\pi\) | ||||
0.224259 | + | 0.974530i | \(0.428004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −884597. | −0.961014 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 371175. | 0.395060 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −398902. | −0.416030 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −624600. | −0.638416 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.43258e6 | −1.43527 | −0.717634 | − | 0.696420i | \(-0.754775\pi\) | ||||
−0.717634 | + | 0.696420i | \(0.754775\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.95032e6 | −2.89780 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −110996. | −0.106895 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −987982. | −0.933074 | −0.466537 | − | 0.884502i | \(-0.654499\pi\) | ||||
−0.466537 | + | 0.884502i | \(0.654499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 654250. | 0.606030 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −814030. | −0.739672 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.06222e6 | 1.83842 | 0.919210 | − | 0.393767i | \(-0.128828\pi\) | ||||
0.919210 | + | 0.393767i | \(0.128828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −453850. | −0.397007 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −193342. | −0.165977 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 780386. | 0.657550 | 0.328775 | − | 0.944408i | \(-0.393364\pi\) | ||||
0.328775 | + | 0.944408i | \(0.393364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −562291. | −0.465091 | −0.232545 | − | 0.972586i | \(-0.574705\pi\) | ||||
−0.232545 | + | 0.972586i | \(0.574705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −40880.0 | −0.0331974 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 450625. | 0.359321 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −386758. | −0.302859 | −0.151429 | − | 0.988468i | \(-0.548388\pi\) | ||||
−0.151429 | + | 0.988468i | \(0.548388\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −926965. | −0.712940 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.55485e6 | 1.17469 | 0.587344 | − | 0.809337i | \(-0.300173\pi\) | ||||
0.587344 | + | 0.809337i | \(0.300173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.75157e6 | 1.30005 | 0.650026 | − | 0.759912i | \(-0.274758\pi\) | ||||
0.650026 | + | 0.759912i | \(0.274758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −432000. | −0.315044 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −192583. | −0.138011 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −927053. | −0.652920 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −422999. | −0.292824 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.55309e6 | −1.05689 | −0.528444 | − | 0.848968i | \(-0.677224\pi\) | ||||
−0.528444 | + | 0.848968i | \(0.677224\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −492683. | −0.329619 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.03376e6 | 1.33785 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −597430. | −0.386464 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −550200. | −0.350029 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 270678. | 0.169374 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.05325e6 | −0.648309 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.60409e6 | −1.57692 | −0.788461 | − | 0.615085i | \(-0.789122\pi\) | ||||
−0.788461 | + | 0.615085i | \(0.789122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −66440.0 | −0.0395853 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −302124. | −0.177127 | −0.0885634 | − | 0.996071i | \(-0.528228\pi\) | ||||
−0.0885634 | + | 0.996071i | \(0.528228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.09455e6 | 1.20846 | 0.604228 | − | 0.796812i | \(-0.293482\pi\) | ||||
0.604228 | + | 0.796812i | \(0.293482\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 224680. | 0.127581 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.07624e6 | −0.601534 | −0.300767 | − | 0.953698i | \(-0.597243\pi\) | ||||
−0.300767 | + | 0.953698i | \(0.597243\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.89121e6 | 1.59075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 422840. | 0.229041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.91801e6 | 1.02293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 91250.0 | 0.0479208 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −706541. | −0.365400 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 266280. | 0.135628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −313002. | −0.157028 | −0.0785141 | − | 0.996913i | \(-0.525018\pi\) | ||||
−0.0785141 | + | 0.996913i | \(0.525018\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.99993e6 | −1.48252 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 404613. | 0.196983 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55400e6 | 0.745378 | 0.372689 | − | 0.927956i | \(-0.378436\pi\) | ||||
0.372689 | + | 0.927956i | \(0.378436\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.37138e6 | −0.648124 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.29232e6 | 1.53326 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.40138e6 | −0.643163 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −647000. | −0.292655 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.22208e6 | 0.990684 | 0.495342 | − | 0.868698i | \(-0.335043\pi\) | ||||
0.495342 | + | 0.868698i | \(0.335043\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 774570. | 0.340406 | 0.170203 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170203 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 411830. | 0.178423 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.26217e6 | −0.966249 | −0.483125 | − | 0.875552i | \(-0.660498\pi\) | ||||
−0.483125 | + | 0.875552i | \(0.660498\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.13621e6 | −0.478505 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 196560. | 0.0816253 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −869601. | −0.356110 | −0.178055 | − | 0.984021i | \(-0.556980\pi\) | ||||
−0.178055 | + | 0.984021i | \(0.556980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.98886e6 | 2.01481 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.26918e6 | −0.903863 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −656650. | −0.257989 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.25361e6 | −0.485844 | −0.242922 | − | 0.970046i | \(-0.578106\pi\) | ||||
−0.242922 | + | 0.970046i | \(0.578106\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 883050. | 0.337613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 803712. | 0.303156 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −175206. | −0.0652044 | −0.0326022 | − | 0.999468i | \(-0.510379\pi\) | ||||
−0.0326022 | + | 0.999468i | \(0.510379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 98821.2 | 0.0362887 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 585460. | 0.212150 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 796945. | 0.284990 | 0.142495 | − | 0.989795i | \(-0.454487\pi\) | ||||
0.142495 | + | 0.989795i | \(0.454487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −393880. | −0.139012 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.36129e6 | −1.17087 | −0.585436 | − | 0.810719i | \(-0.699077\pi\) | ||||
−0.585436 | + | 0.810719i | \(0.699077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −798000. | −0.274379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.52283e6 | 0.856271 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.51959e6 | 1.84941 | 0.924705 | − | 0.380685i | \(-0.124312\pi\) | ||||
0.924705 | + | 0.380685i | \(0.124312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.87258e6 | 0.950232 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.11432e6 | 0.363939 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 216932. | 0.0699570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.74738e6 | 0.556430 | 0.278215 | − | 0.960519i | \(-0.410257\pi\) | ||||
0.278215 | + | 0.960519i | \(0.410257\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 765018. | 0.240569 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 541122. | 0.168048 | 0.0840242 | − | 0.996464i | \(-0.473223\pi\) | ||||
0.0840242 | + | 0.996464i | \(0.473223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 666684. | 0.204483 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −787225. | −0.238485 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.06549e7 | 3.18834 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.79699e6 | 1.12236 | 0.561179 | − | 0.827694i | \(-0.310348\pi\) | ||||
0.561179 | + | 0.827694i | \(0.310348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −631203. | −0.184317 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 872480. | 0.251698 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.46895e6 | −0.703707 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.71696e6 | −0.483526 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.88108e6 | 1.07998 | 0.539992 | − | 0.841670i | \(-0.318427\pi\) | ||||
0.539992 | + | 0.841670i | \(0.318427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.66081e6 | 1.83156 | 0.915781 | − | 0.401677i | \(-0.131573\pi\) | ||||
0.915781 | + | 0.401677i | \(0.131573\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.22097e6 | −0.331784 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −438750. | −0.117827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.86517e6 | 0.495051 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −665760. | −0.174652 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.65337e6 | −1.20663 | −0.603315 | − | 0.797503i | \(-0.706154\pi\) | ||||
−0.603315 | + | 0.797503i | \(0.706154\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.23873e6 | −1.59910 | −0.799552 | − | 0.600597i | \(-0.794930\pi\) | ||||
−0.799552 | + | 0.600597i | \(0.794930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 634037. | 0.160654 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.11802e7 | 2.80056 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.75743e6 | −1.17818 | −0.589089 | − | 0.808068i | \(-0.700513\pi\) | ||||
−0.589089 | + | 0.808068i | \(0.700513\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.01394e6 | 0.737969 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.77073e6 | −1.39708 | −0.698541 | − | 0.715570i | \(-0.746167\pi\) | ||||
−0.698541 | + | 0.715570i | \(0.746167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −764250. | −0.182951 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.61600e6 | −0.619254 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.22765e6 | −0.989654 | −0.494827 | − | 0.868991i | \(-0.664769\pi\) | ||||
−0.494827 | + | 0.868991i | \(0.664769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.13635e6 | −0.726077 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.09096e6 | −0.249783 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −161592. | −0.0365925 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.31374e6 | 0.966192 | 0.483096 | − | 0.875567i | \(-0.339512\pi\) | ||||
0.483096 | + | 0.875567i | \(0.339512\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.98017e6 | −0.438703 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.94820e6 | 1.30357 | 0.651784 | − | 0.758405i | \(-0.274021\pi\) | ||||
0.651784 | + | 0.758405i | \(0.274021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.39722e6 | 1.82047 | 0.910234 | − | 0.414094i | \(-0.135902\pi\) | ||||
0.910234 | + | 0.414094i | \(0.135902\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 722000. | 0.154848 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.30976e6 | −1.12663 | −0.563317 | − | 0.826241i | \(-0.690475\pi\) | ||||
−0.563317 | + | 0.826241i | \(0.690475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −716520. | −0.150417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.13436e6 | 0.235613 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.96040e6 | −1.84151 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.70763e6 | −0.347264 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.68526e6 | −0.741605 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.83653e6 | 1.16229 | 0.581147 | − | 0.813799i | \(-0.302604\pi\) | ||||
0.581147 | + | 0.813799i | \(0.302604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.15759e6 | 0.425212 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.14576e6 | 0.223473 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.67205e6 | −0.322771 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.75327e6 | −1.67243 | −0.836215 | − | 0.548402i | \(-0.815236\pi\) | ||||
−0.836215 | + | 0.548402i | \(0.815236\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.94676e6 | 0.557279 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.16834e6 | 0.967492 | 0.483746 | − | 0.875209i | \(-0.339276\pi\) | ||||
0.483746 | + | 0.875209i | \(0.339276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.81502e6 | −0.521632 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.65907e6 | 0.671209 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.01208e6 | 0.365388 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.36171e6 | 0.963943 | 0.481972 | − | 0.876187i | \(-0.339921\pi\) | ||||
0.481972 | + | 0.876187i | \(0.339921\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.85524e6 | 0.686210 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.26635e6 | −0.928089 | −0.464045 | − | 0.885812i | \(-0.653602\pi\) | ||||
−0.464045 | + | 0.885812i | \(0.653602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.06995e6 | 0.186696 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.21345e6 | 0.382428 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.46847e6 | −0.935559 | −0.467780 | − | 0.883845i | \(-0.654946\pi\) | ||||
−0.467780 | + | 0.883845i | \(0.654946\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.16285e6 | 0.197002 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.70688e6 | −1.29296 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −262627. | −0.0436337 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.33656e6 | 0.713541 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.73836e6 | 0.609203 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.05762e6 | −0.493503 | −0.246751 | − | 0.969079i | \(-0.579363\pi\) | ||||
−0.246751 | + | 0.969079i | \(0.579363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.64117e6 | 1.54126 | 0.770629 | − | 0.637284i | \(-0.219942\pi\) | ||||
0.770629 | + | 0.637284i | \(0.219942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −175000. | −0.0277102 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.20556e6 | −0.502780 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.03080e7 | 1.60153 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00058e6 | −0.615726 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −635100. | −0.0968332 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.67142e6 | 0.252465 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.33584e6 | 0.199903 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.07047e7 | −1.58709 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.15820e6 | 0.610819 | 0.305409 | − | 0.952221i | \(-0.401207\pi\) | ||||
0.305409 | + | 0.952221i | \(0.401207\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −616884. | −0.0897851 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.79285e6 | −0.402769 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.32628e6 | −0.761125 | −0.380562 | − | 0.924755i | \(-0.624270\pi\) | ||||
−0.380562 | + | 0.924755i | \(0.624270\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.55239e6 | −1.21103 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.09562e7 | −1.53737 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −384160. | −0.0534194 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.33661e6 | 0.321998 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −999102. | −0.136449 | −0.0682247 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682247 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.81445e6 | −0.245593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.20112e6 | 0.429432 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.31886e6 | −0.707208 | −0.353604 | − | 0.935395i | \(-0.615044\pi\) | ||||
−0.353604 | + | 0.935395i | \(0.615044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.42085e6 | −0.714408 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.39408e6 | 0.182108 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.56759e6 | 0.850404 | 0.425202 | − | 0.905099i | \(-0.360203\pi\) | ||||
0.425202 | + | 0.905099i | \(0.360203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 164173. | 0.0210723 | 0.0105361 | − | 0.999944i | \(-0.496646\pi\) | ||||
0.0105361 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.94264e6 | −0.247176 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.55749e6 | −0.322585 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.27762e6 | 1.16010 | 0.580052 | − | 0.814579i | \(-0.303032\pi\) | ||||
0.580052 | + | 0.814579i | \(0.303032\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −78639.5 | −0.00974865 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.37220e6 | 0.537353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.30890e7 | 1.59491 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 740950. | 0.0895157 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.44474e6 | 0.652202 | 0.326101 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326101 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.24762e7 | −1.48181 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.39611e6 | −0.282187 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.50978e7 | −1.76310 | −0.881548 | − | 0.472094i | \(-0.843498\pi\) | ||||
−0.881548 | + | 0.472094i | \(0.843498\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 776972. | 0.0899731 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.85216e6 | −0.557185 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.98593e6 | −0.795531 | −0.397765 | − | 0.917487i | \(-0.630214\pi\) | ||||
−0.397765 | + | 0.917487i | \(0.630214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.16941e6 | 0.696719 | 0.348359 | − | 0.937361i | \(-0.386739\pi\) | ||||
0.348359 | + | 0.937361i | \(0.386739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.28546e6 | 0.367962 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.96972e6 | −0.996301 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00769e7 | 1.11009 | 0.555043 | − | 0.831822i | \(-0.312702\pi\) | ||||
0.555043 | + | 0.831822i | \(0.312702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.12280e6 | −0.122676 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 878139. | 0.0951613 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.26885e6 | −0.566324 | −0.283162 | − | 0.959072i | \(-0.591383\pi\) | ||||
−0.283162 | + | 0.959072i | \(0.591383\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −687795. | −0.0733283 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.38112e7 | −1.46056 | −0.730280 | − | 0.683148i | \(-0.760610\pi\) | ||||
−0.730280 | + | 0.683148i | \(0.760610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.20903e6 | 0.336625 | 0.168313 | − | 0.985734i | \(-0.446168\pi\) | ||||
0.168313 | + | 0.985734i | \(0.446168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.15425e7 | −1.20108 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.35339e6 | 0.139702 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.24589e7 | 1.26564 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.03742e7 | −1.04551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.07204e6 | 0.607102 | 0.303551 | − | 0.952815i | \(-0.401828\pi\) | ||||
0.303551 | + | 0.952815i | \(0.401828\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.46776e6 | −0.542376 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.55695e6 | −0.153229 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.16766e6 | −0.211662 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.22600e6 | −0.893843 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.02767e6 | −0.194918 | −0.0974591 | − | 0.995240i | \(-0.531072\pi\) | ||||
−0.0974591 | + | 0.995240i | \(0.531072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.19769e7 | −1.14240 | −0.571199 | − | 0.820811i | \(-0.693522\pi\) | ||||
−0.571199 | + | 0.820811i | \(0.693522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.96500e6 | −0.185979 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.44768e6 | 0.135961 | 0.0679803 | − | 0.997687i | \(-0.478344\pi\) | ||||
0.0679803 | + | 0.997687i | \(0.478344\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.42090e7 | 1.32419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.27857e6 | −0.118242 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.82477e6 | −0.442785 | −0.221393 | − | 0.975185i | \(-0.571060\pi\) | ||||
−0.221393 | + | 0.975185i | \(0.571060\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.40474e6 | 0.401159 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.33200e6 | −0.481922 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.37616e6 | 0.392536 | 0.196268 | − | 0.980550i | \(-0.437118\pi\) | ||||
0.196268 | + | 0.980550i | \(0.437118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.34953e6 | 0.654268 | 0.327134 | − | 0.944978i | \(-0.393917\pi\) | ||||
0.327134 | + | 0.944978i | \(0.393917\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 648216. | 0.0572712 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.02400e6 | 0.265172 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.64089e7 | −1.42812 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.04588e6 | 0.349500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.03757e7 | 2.60447 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.75692e7 | −1.49525 | −0.747626 | − | 0.664119i | \(-0.768807\pi\) | ||||
−0.747626 | + | 0.664119i | \(0.768807\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.76297e6 | 0.148931 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.60338e6 | −0.469871 | −0.234935 | − | 0.972011i | \(-0.575488\pi\) | ||||
−0.234935 | + | 0.972011i | \(0.575488\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.96099e6 | 0.246469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.20132e6 | −0.512409 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.05809e6 | 0.414892 | 0.207446 | − | 0.978246i | \(-0.433485\pi\) | ||||
0.207446 | + | 0.978246i | \(0.433485\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.49505e6 | −0.203167 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.40431e6 | −0.517703 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.65048e6 | 0.212705 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.47421e7 | 1.17453 | 0.587267 | − | 0.809393i | \(-0.300204\pi\) | ||||
0.587267 | + | 0.809393i | \(0.300204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.47976e6 | −0.512538 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.78688e6 | −0.532977 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.05370e6 | 0.238092 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.46720e6 | 0.345814 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.83317e6 | 0.678925 | 0.339462 | − | 0.940620i | \(-0.389755\pi\) | ||||
0.339462 | + | 0.940620i | \(0.389755\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.03766e7 | −3.08135 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 951000. | 0.0720622 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.89475e6 | −0.142562 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.93101e6 | 0.144268 | 0.0721338 | − | 0.997395i | \(-0.477019\pi\) | ||||
0.0721338 | + | 0.997395i | \(0.477019\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.76149e6 | 0.130679 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.86854e7 | −1.37650 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.63165e6 | −0.192514 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.55088e6 | 0.548529 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.22373e6 | 0.521122 | 0.260561 | − | 0.965457i | \(-0.416093\pi\) | ||||
0.260561 | + | 0.965457i | \(0.416093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 465080. | 0.0333188 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.55771e6 | −0.181973 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.50625e6 | 0.177084 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.81106e6 | −0.688462 | −0.344231 | − | 0.938885i | \(-0.611860\pi\) | ||||
−0.344231 | + | 0.938885i | \(0.611860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.05715e6 | −0.143366 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.72428e6 | 0.603860 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.40813e7 | 1.65547 | 0.827733 | − | 0.561122i | \(-0.189630\pi\) | ||||
0.827733 | + | 0.561122i | \(0.189630\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.34752e6 | −0.160284 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.16690e7 | −0.791346 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.40518e7 | −1.62008 | −0.810040 | − | 0.586374i | \(-0.800555\pi\) | ||||
−0.810040 | + | 0.586374i | \(0.800555\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.52288e6 | 0.168792 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.70160e6 | 0.312445 | 0.156223 | − | 0.987722i | \(-0.450068\pi\) | ||||
0.156223 | + | 0.987722i | \(0.450068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.03406e7 | −0.682586 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.00479e7 | −1.31452 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.95988e6 | −0.192783 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.31282e7 | −1.49638 | −0.748189 | − | 0.663485i | \(-0.769077\pi\) | ||||
−0.748189 | + | 0.663485i | \(0.769077\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.06040e6 | 0.582318 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.31240e6 | −0.275329 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.26635e7 | 0.803181 | 0.401591 | − | 0.915819i | \(-0.368458\pi\) | ||||
0.401591 | + | 0.915819i | \(0.368458\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.86595e7 | 1.17570 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.33524e6 | −0.271363 | −0.135682 | − | 0.990752i | \(-0.543322\pi\) | ||||
−0.135682 | + | 0.990752i | \(0.543322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.94579e6 | 0.307556 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.56265e6 | −0.220100 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.87727e6 | 0.176600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −364270. | −0.0222130 | −0.0111065 | − | 0.999938i | \(-0.503535\pi\) | ||||
−0.0111065 | + | 0.999938i | \(0.503535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.24855e6 | 0.378567 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.03051e6 | 0.0620300 | 0.0310150 | − | 0.999519i | \(-0.490126\pi\) | ||||
0.0310150 | + | 0.999519i | \(0.490126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.85396e6 | 0.170684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.13784e6 | −0.245879 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.18851e7 | 0.701713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.27682e7 | 1.92231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.13112e7 | 0.659333 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.48395e6 | 0.259709 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.95300e7 | 1.12400 | 0.561999 | − | 0.827138i | \(-0.310032\pi\) | ||||
0.561999 | + | 0.827138i | \(0.310032\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.30426e7 | −0.745885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.59965e6 | 0.545524 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.15098e6 | 0.347345 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.87040e6 | 0.161074 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.86344e6 | −0.438497 | −0.219249 | − | 0.975669i | \(-0.570361\pi\) | ||||
−0.219249 | + | 0.975669i | \(0.570361\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.22229e6 | −0.233981 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.20571e6 | −0.341751 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.89378e7 | 1.03643 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.52900e6 | 0.246327 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.93559e6 | −0.266781 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.05014e7 | −0.564127 | −0.282064 | − | 0.959396i | \(-0.591019\pi\) | ||||
−0.282064 | + | 0.959396i | \(0.591019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.87803e7 | −1.00265 | −0.501325 | − | 0.865259i | \(-0.667154\pi\) | ||||
−0.501325 | + | 0.865259i | \(0.667154\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.55624e6 | 0.188697 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.16481e7 | 0.614272 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.39552e7 | 1.77972 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.31213e6 | −0.0683545 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.00558e7 | −1.03844 | −0.519220 | − | 0.854641i | \(-0.673777\pi\) | ||||
−0.519220 | + | 0.854641i | \(0.673777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.02444e7 | 0.527212 | 0.263606 | − | 0.964630i | \(-0.415088\pi\) | ||||
0.263606 | + | 0.964630i | \(0.415088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.85000e6 | −0.145784 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −827524. | −0.0420743 | −0.0210371 | − | 0.999779i | \(-0.506697\pi\) | ||||
−0.0210371 | + | 0.999779i | \(0.506697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.80328e7 | 1.92208 | 0.961041 | − | 0.276407i | \(-0.0891436\pi\) | ||||
0.961041 | + | 0.276407i | \(0.0891436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.44607e6 | 0.122876 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.04226e7 | 0.520431 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.52392e7 | 0.756389 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.28805e7 | 0.635504 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.57628e7 | −1.75399 | −0.876993 | − | 0.480503i | \(-0.840454\pi\) | ||||
−0.876993 | + | 0.480503i | \(0.840454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.43105e6 | −0.216031 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.83373e6 | −0.476595 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.74942e6 | 0.421539 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.58843e7 | 0.760779 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.10779e7 | −0.527457 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.04714e7 | −2.86237 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −970214. | −0.0456557 | −0.0228278 | − | 0.999739i | \(-0.507267\pi\) | ||||
−0.0228278 | + | 0.999739i | \(0.507267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.38660e7 | −0.648686 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.86468e6 | 0.0867267 | 0.0433633 | − | 0.999059i | \(-0.486193\pi\) | ||||
0.0433633 | + | 0.999059i | \(0.486193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.05785e6 | −0.0489147 | −0.0244573 | − | 0.999701i | \(-0.507786\pi\) | ||||
−0.0244573 | + | 0.999701i | \(0.507786\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.21800e6 | 0.0559937 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.24333e6 | 0.376769 | 0.188385 | − | 0.982095i | \(-0.439675\pi\) | ||||
0.188385 | + | 0.982095i | \(0.439675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.47772e7 | 0.671507 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.86320e6 | 0.264903 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.25632e6 | −0.281041 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.36294e6 | −0.105538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.35770e7 | −0.602934 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −691748. | −0.0305441 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.40362e7 | 1.05528 | 0.527640 | − | 0.849468i | \(-0.323077\pi\) | ||||
0.527640 | + | 0.849468i | \(0.323077\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.82263e6 | 0.428801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.68605e7 | 1.60000 | 0.800002 | − | 0.599997i | \(-0.204831\pi\) | ||||
0.800002 | + | 0.599997i | \(0.204831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.67403e7 | −0.722541 | −0.361271 | − | 0.932461i | \(-0.617657\pi\) | ||||
−0.361271 | + | 0.932461i | \(0.617657\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.11600e6 | 0.133733 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.25364e6 | −0.394915 | −0.197457 | − | 0.980311i | \(-0.563268\pi\) | ||||
−0.197457 | + | 0.980311i | \(0.563268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.75716e6 | 0.117006 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.27035e7 | 0.958075 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.64333e7 | −0.689597 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.28037e6 | 0.220347 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.77848e6 | 0.156796 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.83110e7 | 0.755635 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.27441e7 | −0.522995 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.47977e6 | 0.142014 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.43845e6 | −0.0989675 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.03030e7 | 0.415859 | 0.207929 | − | 0.978144i | \(-0.433328\pi\) | ||||
0.207929 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.68799e6 | 0.348746 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.82374e7 | −1.52649 | −0.763243 | − | 0.646111i | \(-0.776394\pi\) | ||||
−0.763243 | + | 0.646111i | \(0.776394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.12044e7 | 2.82703 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.66134e6 | 0.263032 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.80024e6 | −0.306327 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.72150e6 | 0.301587 | 0.150794 | − | 0.988565i | \(-0.451817\pi\) | ||||
0.150794 | + | 0.988565i | \(0.451817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.64697e7 | 0.639790 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.63545e6 | 0.256369 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.23625e6 | 0.354929 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.13253e6 | −0.0815073 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.39039e6 | 0.128888 | 0.0644438 | − | 0.997921i | \(-0.479473\pi\) | ||||
0.0644438 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.05651e7 | 1.53383 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.91080e6 | 0.0718640 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.26535e7 | 0.473351 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.67490e6 | −0.285577 | −0.142789 | − | 0.989753i | \(-0.545607\pi\) | ||||
−0.142789 | + | 0.989753i | \(0.545607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.32471e7 | −0.490295 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.55115e7 | −1.67551 | −0.837756 | − | 0.546045i | \(-0.816133\pi\) | ||||
−0.837756 | + | 0.546045i | \(0.816133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.78001e7 | 0.651845 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.12200e6 | −0.113724 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.28294e7 | −0.827218 | −0.413609 | − | 0.910455i | \(-0.635732\pi\) | ||||
−0.413609 | + | 0.910455i | \(0.635732\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.83484e6 | 0.138223 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.80673e6 | 0.244055 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.64478e7 | 1.65666 | 0.828330 | − | 0.560241i | \(-0.189291\pi\) | ||||
0.828330 | + | 0.560241i | \(0.189291\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.67896e6 | −0.272454 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.82856e7 | −0.645401 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.41842e6 | 0.155139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.77779e6 | −0.271674 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.35719e7 | 0.471603 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −310850. | −0.0107456 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.63000e7 | 0.904460 | 0.452230 | − | 0.891901i | \(-0.350629\pi\) | ||||
0.452230 | + | 0.891901i | \(0.350629\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.21306e7 | −0.415022 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.19967e7 | 0.748704 | 0.374352 | − | 0.927287i | \(-0.377865\pi\) | ||||
0.374352 | + | 0.927287i | \(0.377865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.20187e7 | 0.406983 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −577116. | −0.0194425 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.46750e7 | 1.49737 | 0.748683 | − | 0.662929i | \(-0.230687\pi\) | ||||
0.748683 | + | 0.662929i | \(0.230687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.20409e7 | 0.734977 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.26779e7 | −0.752369 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.02740e7 | −0.669201 | −0.334600 | − | 0.942360i | \(-0.608601\pi\) | ||||
−0.334600 | + | 0.942360i | \(0.608601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.47145e6 | −0.311047 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.68410e6 | −0.0550270 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.08542e7 | 1.65324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.49135e7 | 0.482386 | 0.241193 | − | 0.970477i | \(-0.422461\pi\) | ||||
0.241193 | + | 0.970477i | \(0.422461\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.97960e6 | 0.0637095 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.91798e7 | −0.614168 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.17032e7 | −1.01010 | −0.505052 | − | 0.863089i | \(-0.668527\pi\) | ||||
−0.505052 | + | 0.863089i | \(0.668527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.16851e7 | 1.32150 |
(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 | 320.6.a.s.1.1 | 2 | ||
4.3 | odd | 2 | inner | 320.6.a.s.1.2 | 2 | ||
8.3 | odd | 2 | 160.6.a.d.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 160.6.a.d.1.2 | yes | 2 | ||
40.3 | even | 4 | 800.6.c.i.449.2 | 4 | |||
40.13 | odd | 4 | 800.6.c.i.449.3 | 4 | |||
40.19 | odd | 2 | 800.6.a.h.1.2 | 2 | |||
40.27 | even | 4 | 800.6.c.i.449.4 | 4 | |||
40.29 | even | 2 | 800.6.a.h.1.1 | 2 | |||
40.37 | odd | 4 | 800.6.c.i.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.d.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
160.6.a.d.1.2 | yes | 2 | 8.5 | even | 2 | ||
320.6.a.s.1.1 | 2 | 1.1 | even | 1 | trivial | ||
320.6.a.s.1.2 | 2 | 4.3 | odd | 2 | inner | ||
800.6.a.h.1.1 | 2 | 40.29 | even | 2 | |||
800.6.a.h.1.2 | 2 | 40.19 | odd | 2 | |||
800.6.c.i.449.1 | 4 | 40.37 | odd | 4 | |||
800.6.c.i.449.2 | 4 | 40.3 | even | 4 | |||
800.6.c.i.449.3 | 4 | 40.13 | odd | 4 | |||
800.6.c.i.449.4 | 4 | 40.27 | even | 4 |