Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1020,3,Mod(701,1020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1020, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1020.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1020.bc (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(27.7929869648\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 701.16 | ||
Character | \(\chi\) | \(=\) | 1020.701 |
Dual form | 1020.3.bc.a.761.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(341\) | \(511\) | \(817\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.36106 | + | 2.67349i | −0.453686 | + | 0.891162i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58114 | + | 1.58114i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.29057 | − | 6.29057i | −0.898652 | − | 0.898652i | 0.0966646 | − | 0.995317i | \(-0.469183\pi\) |
−0.995317 | + | 0.0966646i | \(0.969183\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.29505 | − | 7.27753i | −0.588338 | − | 0.808615i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.3064 | − | 12.3064i | 1.11877 | − | 1.11877i | 0.126845 | − | 0.991923i | \(-0.459515\pi\) |
0.991923 | − | 0.126845i | \(-0.0404851\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24.0578 | −1.85060 | −0.925300 | − | 0.379237i | \(-0.876187\pi\) | ||||
−0.925300 | + | 0.379237i | \(0.876187\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.37917 | + | 2.07513i | −0.425278 | + | 0.138342i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.72279 | + | 16.9125i | 0.101340 | + | 0.994852i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.8963i | 1.20507i | 0.798092 | + | 0.602535i | \(0.205843\pi\) | ||||
−0.798092 | + | 0.602535i | \(0.794157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 25.3796 | − | 8.25592i | 1.20855 | − | 0.393139i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.75727 | − | 3.75727i | 0.163360 | − | 0.163360i | −0.620694 | − | 0.784053i | \(-0.713149\pi\) |
0.784053 | + | 0.620694i | \(0.213149\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.6632 | − | 4.25109i | 0.987527 | − | 0.157448i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.5288 | + | 14.5288i | 0.500993 | + | 0.500993i | 0.911746 | − | 0.410754i | \(-0.134734\pi\) |
−0.410754 | + | 0.911746i | \(0.634734\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.0569 | − | 26.0569i | 0.840546 | − | 0.840546i | −0.148384 | − | 0.988930i | \(-0.547407\pi\) |
0.988930 | + | 0.148384i | \(0.0474070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.1513 | + | 49.6509i | 0.489434 | + | 1.50457i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 19.8925i | − | 0.568358i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.5048 | − | 34.5048i | 0.932563 | − | 0.932563i | −0.0653029 | − | 0.997865i | \(-0.520801\pi\) |
0.997865 | + | 0.0653029i | \(0.0208014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 32.7440 | − | 64.3182i | 0.839591 | − | 1.64918i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.5211 | − | 33.5211i | 0.817588 | − | 0.817588i | −0.168170 | − | 0.985758i | \(-0.553786\pi\) |
0.985758 | + | 0.168170i | \(0.0537857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57.1028i | 1.32797i | 0.747745 | + | 0.663986i | \(0.231137\pi\) | ||||
−0.747745 | + | 0.663986i | \(0.768863\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.13459 | − | 19.8790i | 0.0696575 | − | 0.441755i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 91.0534i | 1.93731i | 0.248415 | + | 0.968654i | \(0.420090\pi\) | ||||
−0.248415 | + | 0.968654i | \(0.579910\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 30.1425i | 0.615152i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −47.5601 | − | 18.4130i | −0.932551 | − | 0.361039i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 28.9108 | 0.545487 | 0.272743 | − | 0.962087i | \(-0.412069\pi\) | ||||
0.272743 | + | 0.962087i | \(0.412069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 38.9164 | 0.707571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −61.2130 | − | 31.1632i | −1.07391 | − | 0.546723i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −62.7773 | −1.06402 | −0.532011 | − | 0.846737i | \(-0.678564\pi\) | ||||
−0.532011 | + | 0.846737i | \(0.678564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.8695 | + | 37.8695i | 0.620812 | + | 0.620812i | 0.945739 | − | 0.324927i | \(-0.105340\pi\) |
−0.324927 | + | 0.945739i | \(0.605340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.4710 | + | 79.0886i | −0.197952 | + | 1.25538i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −38.0387 | − | 38.0387i | −0.585211 | − | 0.585211i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.4261 | 0.349644 | 0.174822 | − | 0.984600i | \(-0.444065\pi\) | ||||
0.174822 | + | 0.984600i | \(0.444065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.93115 | + | 15.1589i | 0.0714659 | + | 0.219694i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 72.3495 | + | 72.3495i | 1.01901 | + | 1.01901i | 0.999816 | + | 0.0191908i | \(0.00610901\pi\) |
0.0191908 | + | 0.999816i | \(0.493891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.89859 | + | 8.89859i | −0.121898 | + | 0.121898i | −0.765424 | − | 0.643526i | \(-0.777471\pi\) |
0.643526 | + | 0.765424i | \(0.277471\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.3674 | − | 6.80529i | −0.178232 | − | 0.0907371i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −154.829 | −2.01077 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 89.3154 | + | 89.3154i | 1.13058 | + | 1.13058i | 0.990082 | + | 0.140494i | \(0.0448690\pi\) |
0.140494 | + | 0.990082i | \(0.455131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −24.9250 | + | 77.0697i | −0.307716 | + | 0.951478i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −62.1090 | −0.748301 | −0.374150 | − | 0.927368i | \(-0.622066\pi\) | ||||
−0.374150 | + | 0.927368i | \(0.622066\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.0170 | + | 29.4649i | −0.282553 | + | 0.346646i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −58.6170 | + | 19.0680i | −0.673759 | + | 0.219172i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.26610i | − | 0.0816415i | −0.999166 | − | 0.0408208i | \(-0.987003\pi\) | ||
0.999166 | − | 0.0408208i | \(-0.0129973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 151.337 | + | 151.337i | 1.66305 | + | 1.66305i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 34.1978 | + | 105.128i | 0.367719 | + | 1.13041i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.2023 | + | 36.2023i | −0.381077 | + | 0.381077i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.821540 | + | 0.821540i | −0.00846948 | + | 0.00846948i | −0.711329 | − | 0.702859i | \(-0.751906\pi\) |
0.702859 | + | 0.711329i | \(0.251906\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −154.724 | − | 24.3974i | −1.56287 | − | 0.246438i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 174.692i | − | 1.72962i | −0.502098 | − | 0.864811i | \(-0.667438\pi\) | ||
0.502098 | − | 0.864811i | \(-0.332562\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 149.414 | 1.45062 | 0.725308 | − | 0.688424i | \(-0.241697\pi\) | ||||
0.725308 | + | 0.688424i | \(0.241697\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 53.1824 | + | 27.0749i | 0.506499 | + | 0.257856i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −94.8207 | − | 94.8207i | −0.886175 | − | 0.886175i | 0.107979 | − | 0.994153i | \(-0.465562\pi\) |
−0.994153 | + | 0.107979i | \(0.965562\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −44.4487 | − | 44.4487i | −0.407786 | − | 0.407786i | 0.473180 | − | 0.880966i | \(-0.343106\pi\) |
−0.880966 | + | 0.473180i | \(0.843106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 45.2851 | + | 139.211i | 0.407974 | + | 1.25415i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 37.2627 | − | 37.2627i | 0.329759 | − | 0.329759i | −0.522736 | − | 0.852495i | \(-0.675089\pi\) |
0.852495 | + | 0.522736i | \(0.175089\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.8815 | 0.103318 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 127.387 | + | 175.081i | 1.08878 | + | 1.49642i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 95.5518 | − | 117.226i | 0.802956 | − | 0.985096i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 181.897i | − | 1.50328i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 43.9940 | + | 135.242i | 0.357675 | + | 1.09953i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.90569 | + | 7.90569i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 29.1690i | 0.229677i | 0.993384 | + | 0.114839i | \(0.0366351\pi\) | ||||
−0.993384 | + | 0.114839i | \(0.963365\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −152.663 | − | 77.7202i | −1.18344 | − | 0.602482i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 149.091 | + | 149.091i | 1.13810 | + | 1.13810i | 0.988790 | + | 0.149312i | \(0.0477058\pi\) |
0.149312 | + | 0.988790i | \(0.452294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 144.031 | − | 144.031i | 1.08294 | − | 1.08294i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 48.8798 | + | 35.4367i | 0.362073 | + | 0.262494i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 106.362i | − | 0.776365i | −0.921582 | − | 0.388183i | \(-0.873103\pi\) | ||
0.921582 | − | 0.388183i | \(-0.126897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −114.652 | + | 114.652i | −0.824835 | + | 0.824835i | −0.986797 | − | 0.161962i | \(-0.948218\pi\) |
0.161962 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −243.430 | − | 123.929i | −1.72645 | − | 0.878929i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −296.066 | + | 296.066i | −2.07039 | + | 2.07039i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 45.9440i | 0.316856i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −80.5854 | − | 41.0256i | −0.548200 | − | 0.279086i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 156.483i | 1.05022i | 0.851033 | + | 0.525112i | \(0.175976\pi\) | ||||
−0.851033 | + | 0.525112i | \(0.824024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 285.404i | 1.89009i | 0.326933 | + | 0.945047i | \(0.393985\pi\) | ||||
−0.326933 | + | 0.945047i | \(0.606015\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 113.959 | − | 102.090i | 0.744829 | − | 0.667255i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 82.3993 | 0.531608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 159.247 | 1.01431 | 0.507155 | − | 0.861855i | \(-0.330697\pi\) | ||||
0.507155 | + | 0.861855i | \(0.330697\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −39.3493 | + | 77.2926i | −0.247480 | + | 0.486117i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −47.2707 | −0.293607 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −136.212 | − | 136.212i | −0.835658 | − | 0.835658i | 0.152626 | − | 0.988284i | \(-0.451227\pi\) |
−0.988284 | + | 0.152626i | \(0.951227\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −52.9674 | + | 104.042i | −0.321015 | + | 0.630560i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 102.681 | + | 102.681i | 0.614858 | + | 0.614858i | 0.944208 | − | 0.329350i | \(-0.106830\pi\) |
−0.329350 | + | 0.944208i | \(0.606830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 409.777 | 2.42472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 166.629 | − | 121.237i | 0.974438 | − | 0.708989i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 173.344 | + | 173.344i | 1.00199 | + | 1.00199i | 0.999998 | + | 0.00199190i | \(0.000634043\pi\) |
0.00199190 | + | 0.999998i | \(0.499366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 31.4528 | − | 31.4528i | 0.179730 | − | 0.179730i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 85.4435 | − | 167.834i | 0.482732 | − | 0.948216i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −108.141 | −0.604138 | −0.302069 | − | 0.953286i | \(-0.597677\pi\) | ||||
−0.302069 | + | 0.953286i | \(0.597677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.97525 | − | 3.97525i | −0.0219627 | − | 0.0219627i | 0.696040 | − | 0.718003i | \(-0.254944\pi\) |
−0.718003 | + | 0.696040i | \(0.754944\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −152.786 | + | 49.7010i | −0.834898 | + | 0.271590i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 109.114 | 0.589804 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 229.334 | + | 186.931i | 1.22638 | + | 0.999632i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −194.469 | − | 140.985i | −1.02893 | − | 0.745953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 184.990i | − | 0.968535i | −0.874920 | − | 0.484267i | \(-0.839086\pi\) | ||
0.874920 | − | 0.484267i | \(-0.160914\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −46.1304 | − | 46.1304i | −0.239018 | − | 0.239018i | 0.577426 | − | 0.816443i | \(-0.304057\pi\) |
−0.816443 | + | 0.577426i | \(0.804057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 153.469 | − | 49.9231i | 0.787019 | − | 0.256016i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −119.195 | + | 119.195i | −0.605053 | + | 0.605053i | −0.941649 | − | 0.336596i | \(-0.890724\pi\) |
0.336596 | + | 0.941649i | \(0.390724\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 76.3435 | − | 76.3435i | 0.383636 | − | 0.383636i | −0.488775 | − | 0.872410i | \(-0.662556\pi\) |
0.872410 | + | 0.488775i | \(0.162556\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −31.8843 | + | 62.6295i | −0.158628 | + | 0.311589i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 182.789i | − | 0.900436i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 106.003 | 0.517088 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −47.2386 | − | 7.44874i | −0.228206 | − | 0.0359843i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 281.772 | + | 281.772i | 1.34819 | + | 1.34819i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −95.7385 | − | 95.7385i | −0.453737 | − | 0.453737i | 0.442856 | − | 0.896593i | \(-0.353965\pi\) |
−0.896593 | + | 0.442856i | \(0.853965\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −291.897 | + | 94.9535i | −1.37041 | + | 0.445791i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −90.2874 | + | 90.2874i | −0.419942 | + | 0.419942i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −327.826 | −1.51072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.6788 | − | 35.9017i | −0.0533276 | − | 0.163935i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.4465 | − | 406.877i | −0.187541 | − | 1.84107i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.1312i | − | 0.0947589i | −0.998877 | − | 0.0473795i | \(-0.984913\pi\) | ||
0.998877 | − | 0.0473795i | \(-0.0150870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36.3877 | − | 26.4752i | 0.161723 | − | 0.117668i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.39210 | − | 8.39210i | 0.0369696 | − | 0.0369696i | −0.688380 | − | 0.725350i | \(-0.741678\pi\) |
0.725350 | + | 0.688380i | \(0.241678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 142.633i | − | 0.622852i | −0.950270 | − | 0.311426i | \(-0.899193\pi\) | ||
0.950270 | − | 0.311426i | \(-0.100807\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 210.731 | − | 413.933i | 0.912256 | − | 1.79192i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −93.7967 | − | 93.7967i | −0.402561 | − | 0.402561i | 0.476574 | − | 0.879135i | \(-0.341879\pi\) |
−0.879135 | + | 0.476574i | \(0.841879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −143.968 | + | 143.968i | −0.612630 | + | 0.612630i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −360.347 | + | 117.220i | −1.52045 | + | 0.494600i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 189.845i | − | 0.794331i | −0.917747 | − | 0.397166i | \(-0.869994\pi\) | ||
0.917747 | − | 0.397166i | \(-0.130006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 269.048 | − | 269.048i | 1.11638 | − | 1.11638i | 0.124116 | − | 0.992268i | \(-0.460391\pi\) |
0.992268 | − | 0.124116i | \(-0.0396095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −172.121 | − | 171.533i | −0.708315 | − | 0.705897i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −47.6594 | + | 47.6594i | −0.194528 | + | 0.194528i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 550.835i | − | 2.23010i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 84.5338 | − | 166.047i | 0.339493 | − | 0.666857i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 189.846i | − | 0.756358i | −0.925732 | − | 0.378179i | \(-0.876550\pi\) | ||
0.925732 | − | 0.378179i | \(-0.123450\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 92.4773i | − | 0.365523i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −46.0856 | − | 104.313i | −0.180728 | − | 0.409069i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.6062 | −0.0957441 | −0.0478721 | − | 0.998853i | \(-0.515244\pi\) | ||||
−0.0478721 | + | 0.998853i | \(0.515244\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −434.110 | −1.67610 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.8031 | − | 182.664i | 0.110357 | − | 0.699863i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 352.840 | 1.34160 | 0.670798 | − | 0.741640i | \(-0.265952\pi\) | ||||
0.670798 | + | 0.741640i | \(0.265952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45.7120 | + | 45.7120i | 0.172498 | + | 0.172498i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.4258 | + | 9.88957i | 0.0727558 | + | 0.0370396i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 344.160 | + | 344.160i | 1.27941 | + | 1.27941i | 0.941000 | + | 0.338406i | \(0.109888\pi\) |
0.338406 | + | 0.941000i | \(0.390112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 302.423 | 1.11595 | 0.557977 | − | 0.829857i | \(-0.311578\pi\) | ||||
0.557977 | + | 0.829857i | \(0.311578\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −610.576 | + | 198.619i | −2.23654 | + | 0.727543i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 61.5322 | + | 61.5322i | 0.223754 | + | 0.223754i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9001 | + | 20.9001i | −0.0754517 | + | 0.0754517i | −0.743826 | − | 0.668374i | \(-0.766991\pi\) |
0.668374 | + | 0.743826i | \(0.266991\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −327.603 | − | 51.6575i | −1.17420 | − | 0.185152i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −162.959 | −0.579926 | −0.289963 | − | 0.957038i | \(-0.593643\pi\) | ||||
−0.289963 | + | 0.957038i | \(0.593643\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.0296 | + | 31.0296i | 0.109645 | + | 0.109645i | 0.759801 | − | 0.650156i | \(-0.225296\pi\) |
−0.650156 | + | 0.759801i | \(0.725296\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −47.5129 | − | 146.060i | −0.166712 | − | 0.512490i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −421.734 | −1.46945 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −283.064 | + | 58.2732i | −0.979460 | + | 0.201637i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.07821 | − | 3.31454i | −0.00370520 | − | 0.0113902i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 314.503i | 1.07339i | 0.843777 | + | 0.536694i | \(0.180327\pi\) | ||||
−0.843777 | + | 0.536694i | \(0.819673\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −99.2596 | − | 99.2596i | −0.336473 | − | 0.336473i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 275.814 | − | 380.445i | 0.928666 | − | 1.28096i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −90.3917 | + | 90.3917i | −0.302313 | + | 0.302313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 359.209 | − | 359.209i | 1.19339 | − | 1.19339i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 467.036 | + | 237.766i | 1.54137 | + | 0.784705i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 119.754i | 0.392636i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −37.7267 | −0.122888 | −0.0614441 | − | 0.998111i | \(-0.519571\pi\) | ||||
−0.0614441 | + | 0.998111i | \(0.519571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −203.360 | + | 399.455i | −0.658124 | + | 1.29273i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −92.5674 | − | 92.5674i | −0.297644 | − | 0.297644i | 0.542446 | − | 0.840090i | \(-0.317498\pi\) |
−0.840090 | + | 0.542446i | \(0.817498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.2728 | − | 33.2728i | −0.106303 | − | 0.106303i | 0.651955 | − | 0.758258i | \(-0.273949\pi\) |
−0.758258 | + | 0.651955i | \(0.773949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −144.768 | + | 105.332i | −0.459582 | + | 0.334387i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 308.110 | − | 308.110i | 0.971955 | − | 0.971955i | −0.0276619 | − | 0.999617i | \(-0.508806\pi\) |
0.999617 | + | 0.0276619i | \(0.00880619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 357.595 | 1.12099 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 382.558 | − | 124.445i | 1.19177 | − | 0.387680i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −387.234 | + | 39.4455i | −1.19887 | + | 0.122122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 120.289i | − | 0.370120i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 179.330 | − | 58.3357i | 0.548410 | − | 0.178397i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 572.778 | − | 572.778i | 1.74097 | − | 1.74097i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 460.121i | 1.39009i | 0.718965 | + | 0.695047i | \(0.244616\pi\) | ||||
−0.718965 | + | 0.695047i | \(0.755384\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −433.815 | − | 68.4053i | −1.30275 | − | 0.205421i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 37.0400 | + | 37.0400i | 0.110567 | + | 0.110567i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −137.534 | + | 137.534i | −0.408114 | + | 0.408114i | −0.881081 | − | 0.472966i | \(-0.843183\pi\) |
0.472966 | + | 0.881081i | \(0.343183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 48.9046 | + | 150.338i | 0.144261 | + | 0.443475i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 641.336i | − | 1.88075i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −118.625 | + | 118.625i | −0.345844 | + | 0.345844i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.1715 | + | 31.7651i | −0.0468738 | + | 0.0920728i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −145.446 | + | 145.446i | −0.419152 | + | 0.419152i | −0.884912 | − | 0.465759i | \(-0.845781\pi\) |
0.465759 | + | 0.884912i | \(0.345781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 84.8581i | − | 0.243146i | −0.992582 | − | 0.121573i | \(-0.961206\pi\) | ||
0.992582 | − | 0.121573i | \(-0.0387939\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −641.459 | + | 102.272i | −1.82752 | + | 0.291373i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 66.9089i | 0.189544i | 0.995499 | + | 0.0947719i | \(0.0302122\pi\) | ||||
−0.995499 | + | 0.0947719i | \(0.969788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 228.789i | 0.644476i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 183.352 | + | 415.008i | 0.513590 | + | 1.16249i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 309.636 | 0.862496 | 0.431248 | − | 0.902233i | \(-0.358073\pi\) | ||||
0.431248 | + | 0.902233i | \(0.358073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −163.242 | −0.452194 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 486.299 | + | 247.572i | 1.33967 | + | 0.682018i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.1398 | −0.0770954 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 493.367 | + | 493.367i | 1.34432 | + | 1.34432i | 0.891704 | + | 0.452620i | \(0.149510\pi\) |
0.452620 | + | 0.891704i | \(0.350490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −421.447 | − | 66.4552i | −1.14213 | − | 0.180095i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −181.865 | − | 181.865i | −0.490203 | − | 0.490203i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −124.869 | −0.334770 | −0.167385 | − | 0.985892i | \(-0.553532\pi\) | ||||
−0.167385 | + | 0.985892i | \(0.553532\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.3757 | − | 31.8959i | −0.0276684 | − | 0.0850556i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −349.530 | − | 349.530i | −0.927137 | − | 0.927137i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 301.080 | − | 301.080i | 0.794405 | − | 0.794405i | −0.187802 | − | 0.982207i | \(-0.560136\pi\) |
0.982207 | + | 0.187802i | \(0.0601363\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −77.9828 | − | 39.7007i | −0.204679 | − | 0.104201i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 75.3731 | 0.196797 | 0.0983983 | − | 0.995147i | \(-0.468628\pi\) | ||||
0.0983983 | + | 0.995147i | \(0.468628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −244.806 | − | 244.806i | −0.635860 | − | 0.635860i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 415.567 | − | 302.362i | 1.07382 | − | 0.781297i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −486.743 | −1.25127 | −0.625634 | − | 0.780117i | \(-0.715160\pi\) | ||||
−0.625634 | + | 0.780117i | \(0.715160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 70.0178 | + | 57.0718i | 0.179074 | + | 0.145964i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −601.515 | + | 195.672i | −1.53057 | + | 0.497892i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 282.440i | 0.715039i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −318.769 | − | 318.769i | −0.802944 | − | 0.802944i | 0.180611 | − | 0.983555i | \(-0.442193\pi\) |
−0.983555 | + | 0.180611i | \(0.942193\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 189.030 | + | 581.099i | 0.473760 | + | 1.45639i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −116.374 | + | 116.374i | −0.290210 | + | 0.290210i | −0.837163 | − | 0.546953i | \(-0.815788\pi\) |
0.546953 | + | 0.837163i | \(0.315788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −626.872 | + | 626.872i | −1.55551 | + | 1.55551i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −161.268 | + | 82.4481i | −0.398192 | + | 0.203576i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 849.263i | − | 2.08664i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 250.502 | 0.612474 | 0.306237 | − | 0.951955i | \(-0.400930\pi\) | ||||
0.306237 | + | 0.951955i | \(0.400930\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 284.357 | + | 144.765i | 0.691867 | + | 0.352226i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 394.905 | + | 394.905i | 0.956186 | + | 0.956186i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −98.2029 | − | 98.2029i | −0.236633 | − | 0.236633i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −150.473 | − | 462.569i | −0.360846 | − | 1.10928i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −299.357 | + | 299.357i | −0.714457 | + | 0.714457i | −0.967464 | − | 0.253008i | \(-0.918580\pi\) |
0.253008 | + | 0.967464i | \(0.418580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −80.4125 | −0.191004 | −0.0955018 | − | 0.995429i | \(-0.530446\pi\) | ||||
−0.0955018 | + | 0.995429i | \(0.530446\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 662.644 | − | 482.132i | 1.56654 | − | 1.13979i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −84.5624 | + | 8.61393i | −0.198970 | + | 0.0202681i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 476.442i | − | 1.11579i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −388.565 | − | 1194.49i | −0.905746 | − | 2.78436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 325.077 | − | 325.077i | 0.754240 | − | 0.754240i | −0.221028 | − | 0.975268i | \(-0.570941\pi\) |
0.975268 | + | 0.221028i | \(0.0709411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 405.923i | 0.937467i | 0.883340 | + | 0.468734i | \(0.155290\pi\) | ||||
−0.883340 | + | 0.468734i | \(0.844710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −122.831 | − | 62.5325i | −0.282370 | − | 0.143753i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 86.0278 | + | 86.0278i | 0.196860 | + | 0.196860i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 208.410 | − | 208.410i | 0.474738 | − | 0.474738i | −0.428706 | − | 0.903444i | \(-0.641030\pi\) |
0.903444 | + | 0.428706i | \(0.141030\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 219.363 | − | 159.606i | 0.497421 | − | 0.361918i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 687.598i | 1.55214i | 0.630647 | + | 0.776070i | \(0.282790\pi\) | ||||
−0.630647 | + | 0.776070i | \(0.717210\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.4887 | − | 11.4887i | 0.0258173 | − | 0.0258173i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −418.356 | − | 212.983i | −0.935919 | − | 0.476471i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 104.129 | − | 104.129i | 0.231913 | − | 0.231913i | −0.581578 | − | 0.813491i | \(-0.697564\pi\) |
0.813491 | + | 0.581578i | \(0.197564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 825.051i | − | 1.82938i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −763.024 | − | 388.452i | −1.68438 | − | 0.857509i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 478.570i | 1.05180i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 40.8247i | − | 0.0893320i | −0.999002 | − | 0.0446660i | \(-0.985778\pi\) | ||
0.999002 | − | 0.0446660i | \(-0.0142224\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 117.832 | + | 443.618i | 0.256714 | + | 0.966488i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −298.234 | −0.646927 | −0.323464 | − | 0.946241i | \(-0.604847\pi\) | ||||
−0.323464 | + | 0.946241i | \(0.604847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 549.714 | 1.18729 | 0.593644 | − | 0.804728i | \(-0.297689\pi\) | ||||
0.593644 | + | 0.804728i | \(0.297689\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −112.150 | + | 220.293i | −0.241183 | + | 0.473749i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 672.000 | 1.43897 | 0.719486 | − | 0.694507i | \(-0.244377\pi\) | ||||
0.719486 | + | 0.694507i | \(0.244377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −147.364 | − | 147.364i | −0.314208 | − | 0.314208i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −216.744 | + | 425.744i | −0.460178 | + | 0.903915i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 702.732 | + | 702.732i | 1.48569 | + | 1.48569i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −114.482 | −0.241014 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −153.084 | − | 210.399i | −0.320931 | − | 0.441089i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −270.029 | − | 270.029i | −0.563735 | − | 0.563735i | 0.366632 | − | 0.930366i | \(-0.380511\pi\) |
−0.930366 | + | 0.366632i | \(0.880511\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −830.110 | + | 830.110i | −1.72580 | + | 1.72580i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 64.3382 | − | 126.378i | 0.133205 | − | 0.261651i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.59794 | −0.00535657 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −137.843 | − | 137.843i | −0.283046 | − | 0.283046i | 0.551277 | − | 0.834323i | \(-0.314141\pi\) |
−0.834323 | + | 0.551277i | \(0.814141\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 549.554 | − | 178.769i | 1.12383 | − | 0.365580i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.0629 | −0.0754844 | −0.0377422 | − | 0.999288i | \(-0.512017\pi\) | ||||
−0.0377422 | + | 0.999288i | \(0.512017\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −220.688 | + | 270.748i | −0.447643 | + | 0.549184i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −206.064 | − | 283.215i | −0.416291 | − | 0.572152i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 910.238i | − | 1.83147i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −300.616 | − | 300.616i | −0.602437 | − | 0.602437i | 0.338522 | − | 0.940959i | \(-0.390073\pi\) |
−0.940959 | + | 0.338522i | \(0.890073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −414.272 | + | 134.762i | −0.826890 | + | 0.268986i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 114.698 | − | 114.698i | 0.228028 | − | 0.228028i | −0.583841 | − | 0.811868i | \(-0.698451\pi\) |
0.811868 | + | 0.583841i | \(0.198451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 276.212 | − | 276.212i | 0.546954 | − | 0.546954i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −557.731 | + | 1095.53i | −1.10006 | + | 2.16082i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 515.736i | − | 1.01323i | −0.862171 | − | 0.506617i | \(-0.830896\pi\) | ||
0.862171 | − | 0.506617i | \(-0.169104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 111.954 | 0.219089 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 97.3344 | + | 610.490i | 0.189736 | + | 1.19004i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 236.244 | + | 236.244i | 0.458725 | + | 0.458725i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1120.54 | + | 1120.54i | 2.16740 | + | 2.16740i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −699.365 | + | 227.502i | −1.34752 | + | 0.438347i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −501.560 | + | 501.560i | −0.962686 | + | 0.962686i | −0.999328 | − | 0.0366423i | \(-0.988334\pi\) |
0.0366423 | + | 0.999328i | \(0.488334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 314.174 | 0.600715 | 0.300357 | − | 0.953827i | \(-0.402894\pi\) | ||||
0.300357 | + | 0.953827i | \(0.402894\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 41.2796 | + | 126.898i | 0.0786278 | + | 0.241710i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 485.578 | + | 395.797i | 0.921400 | + | 0.751038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 500.766i | 0.946627i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 332.409 | + | 456.864i | 0.626005 | + | 0.860384i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −806.444 | + | 806.444i | −1.51303 | + | 1.51303i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 299.849i | − | 0.560466i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 147.186 | − | 289.113i | 0.274089 | − | 0.538385i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 370.946 | + | 370.946i | 0.688212 | + | 0.688212i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 281.043 | − | 281.043i | 0.519489 | − | 0.519489i | −0.397928 | − | 0.917417i | \(-0.630271\pi\) |
0.917417 | + | 0.397928i | \(0.130271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.0383 | − | 5.21723i | 0.0295365 | − | 0.00960816i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 140.559i | − | 0.257906i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −75.3296 | + | 75.3296i | −0.137714 | + | 0.137714i | −0.772603 | − | 0.634889i | \(-0.781046\pi\) |
0.634889 | + | 0.772603i | \(0.281046\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 75.0759 | − | 476.118i | 0.136750 | − | 0.867246i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −332.656 | + | 332.656i | −0.603731 | + | 0.603731i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1123.69i | − | 2.03199i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −148.510 | + | 291.714i | −0.267586 | + | 0.525611i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 453.080i | − | 0.813430i | −0.913555 | − | 0.406715i | \(-0.866674\pi\) | ||
0.913555 | − | 0.406715i | \(-0.133326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1373.77i | − | 2.45754i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −811.894 | + | 358.697i | −1.44723 | + | 0.639388i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −174.265 | −0.309529 | −0.154764 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154764 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 117.835 | 0.208558 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 641.605 | − | 328.020i | 1.13158 | − | 0.578519i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −462.238 | −0.812369 | −0.406184 | − | 0.913791i | \(-0.633141\pi\) | ||||
−0.406184 | + | 0.913791i | \(0.633141\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 134.635 | + | 134.635i | 0.235788 | + | 0.235788i | 0.815103 | − | 0.579316i | \(-0.196680\pi\) |
−0.579316 | + | 0.815103i | \(0.696680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 494.568 | + | 251.782i | 0.863121 | + | 0.439410i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.7864 | + | 18.7864i | 0.0326719 | + | 0.0326719i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 868.124 | 1.50455 | 0.752274 | − | 0.658851i | \(-0.228957\pi\) | ||||
0.752274 | + | 0.658851i | \(0.228957\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 186.115 | − | 60.5429i | 0.321443 | − | 0.104565i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 390.701 | + | 390.701i | 0.672462 | + | 0.672462i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 355.789 | − | 355.789i | 0.610273 | − | 0.610273i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −75.4112 | + | 478.245i | −0.128908 | + | 0.817512i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 567.952 | 0.967551 | 0.483775 | − | 0.875192i | \(-0.339265\pi\) | ||||
0.483775 | + | 0.875192i | \(0.339265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 596.608 | + | 596.608i | 1.01292 | + | 1.01292i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −156.435 | − | 480.899i | −0.264696 | − | 0.813704i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −462.385 | −0.779739 | −0.389870 | − | 0.920870i | \(-0.627480\pi\) | ||||
−0.389870 | + | 0.920870i | \(0.627480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 336.432 | − | 34.2706i | 0.565432 | − | 0.0575976i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 100.195 | + | 308.011i | 0.167831 | + | 0.515931i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 161.307i | − | 0.269293i | −0.990894 | − | 0.134647i | \(-0.957010\pi\) | ||
0.990894 | − | 0.134647i | \(-0.0429899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −167.731 | − | 167.731i | −0.279087 | − | 0.279087i | 0.553658 | − | 0.832744i | \(-0.313232\pi\) |
−0.832744 | + | 0.553658i | \(0.813232\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −124.043 | − | 170.485i | −0.205709 | − | 0.282727i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 287.605 | − | 287.605i | 0.475379 | − | 0.475379i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −131.083 | + | 131.083i | −0.215953 | + | 0.215953i | −0.806791 | − | 0.590838i | \(-0.798797\pi\) |
0.590838 | + | 0.806791i | \(0.298797\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 488.683 | + | 248.786i | 0.802434 | + | 0.408515i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2190.55i | − | 3.58518i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −202.356 | −0.330108 | −0.165054 | − | 0.986285i | \(-0.552780\pi\) | ||||
−0.165054 | + | 0.986285i | \(0.552780\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −144.276 | + | 283.398i | −0.234596 | + | 0.460809i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −533.650 | − | 533.650i | −0.864911 | − | 0.864911i | 0.126993 | − | 0.991904i | \(-0.459467\pi\) |
−0.991904 | + | 0.126993i | \(0.959467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 577.426 | + | 577.426i | 0.932837 | + | 0.932837i | 0.997882 | − | 0.0650452i | \(-0.0207192\pi\) |
−0.0650452 | + | 0.997882i | \(0.520719\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 84.2085 | − | 116.154i | 0.135602 | − | 0.187043i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.7079 | + | 45.7079i | −0.0733674 | + | 0.0733674i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1136.82 | + | 369.806i | −1.81311 | + | 0.589802i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 643.006 | + | 524.118i | 1.02227 | + | 0.833255i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 98.8501i | 0.156656i | 0.996928 | + | 0.0783281i | \(0.0249582\pi\) | ||||
−0.996928 | + | 0.0783281i | \(0.975042\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 386.261 | − | 125.650i | 0.610207 | − | 0.198499i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.1202 | + | 46.1202i | −0.0726302 | + | 0.0726302i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 725.161i | − | 1.13840i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 143.432 | − | 909.619i | 0.224463 | − | 1.42350i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −352.845 | − | 352.845i | −0.550461 | − | 0.550461i | 0.376113 | − | 0.926574i | \(-0.377260\pi\) |
−0.926574 | + | 0.376113i | \(0.877260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −282.015 | + | 282.015i | −0.438593 | + | 0.438593i | −0.891538 | − | 0.452945i | \(-0.850373\pi\) |
0.452945 | + | 0.891538i | \(0.350373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −118.496 | − | 364.269i | −0.183714 | − | 0.564757i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1000.07i | 1.54570i | 0.634590 | + | 0.772849i | \(0.281169\pi\) | ||||
−0.634590 | + | 0.772849i | \(0.718831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −772.565 | + | 772.565i | −1.19039 | + | 1.19039i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 446.190 | − | 876.437i | 0.685391 | − | 1.34629i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 500.147 | − | 500.147i | 0.765923 | − | 0.765923i | −0.211463 | − | 0.977386i | \(-0.567823\pi\) |
0.977386 | + | 0.211463i | \(0.0678229\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 471.468i | 0.719799i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 111.878 | + | 17.6413i | 0.170286 | + | 0.0268513i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 153.605i | 0.233087i | 0.993186 | + | 0.116544i | \(0.0371815\pi\) | ||||
−0.993186 | + | 0.116544i | \(0.962819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 37.2209i | − | 0.0563100i | −0.999604 | − | 0.0281550i | \(-0.991037\pi\) | ||
0.999604 | − | 0.0281550i | \(-0.00896320\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1144.19 | + | 442.976i | 1.72578 | + | 0.668139i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 455.466 | 0.684911 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 109.177 | 0.163684 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 56.4941 | + | 28.7608i | 0.0844455 | + | 0.0429908i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 932.079 | 1.38909 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −297.412 | − | 297.412i | −0.441920 | − | 0.441920i | 0.450737 | − | 0.892657i | \(-0.351161\pi\) |
−0.892657 | + | 0.450737i | \(0.851161\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.2554 | + | 133.316i | 0.0314895 | + | 0.197505i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 518.454 | + | 518.454i | 0.765811 | + | 0.765811i | 0.977366 | − | 0.211555i | \(-0.0678528\pi\) |
−0.211555 | + | 0.977366i | \(0.567853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3359 | 0.0152222 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0140 | + | 33.8583i | 0.0161733 | + | 0.0497185i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −403.885 | − | 403.885i | −0.591339 | − | 0.591339i | 0.346654 | − | 0.937993i | \(-0.387318\pi\) |
−0.937993 | + | 0.346654i | \(0.887318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 168.173 | − | 168.173i | 0.245508 | − | 0.245508i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 381.327 | + | 194.132i | 0.555062 | + | 0.282579i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −695.530 | −1.00948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 818.051 | + | 818.051i | 1.18387 | + | 1.18387i | 0.978734 | + | 0.205132i | \(0.0657622\pi\) |
0.205132 | + | 0.978734i | \(0.434238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 819.827 | + | 1126.77i | 1.18301 | + | 1.62594i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −362.562 | −0.521672 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 624.675 | + | 509.175i | 0.896234 | + | 0.730524i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 378.427 | − | 123.101i | 0.541383 | − | 0.176111i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 701.073i | 1.00010i | 0.865995 | + | 0.500052i | \(0.166686\pi\) | ||||
−0.865995 | + | 0.500052i | \(0.833314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 790.034 | + | 790.034i | 1.12380 | + | 1.12380i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −188.948 | − | 580.846i | −0.268011 | − | 0.823894i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1098.91 | + | 1098.91i | −1.55433 | + | 1.55433i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 338.901 | − | 338.901i | 0.477999 | − | 0.477999i | −0.426492 | − | 0.904491i | \(-0.640251\pi\) |
0.904491 | + | 0.426492i | \(0.140251\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 177.067 | − | 1122.93i | 0.249039 | − | 1.57936i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 195.806i | − | 0.274623i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −936.243 | −1.30943 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 507.548 | + | 258.390i | 0.707877 | + | 0.360377i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −425.617 | − | 425.617i | −0.591957 | − | 0.591957i | 0.346203 | − | 0.938160i | \(-0.387471\pi\) |
−0.938160 | + | 0.346203i | \(0.887471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −939.896 | − | 939.896i | −1.30360 | − | 1.30360i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 353.107 | + | 1085.49i | 0.488391 | + | 1.50137i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −72.6439 | + | 72.6439i | −0.100199 | + | 0.100199i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −556.487 | −0.765456 | −0.382728 | − | 0.923861i | \(-0.625015\pi\) | ||||
−0.382728 | + | 0.923861i | \(0.625015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 692.856 | − | 226.696i | 0.950420 | − | 0.310968i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −965.750 | + | 98.3759i | −1.32114 | + | 0.134577i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1408.29i | 1.92128i | 0.277805 | + | 0.960638i | \(0.410393\pi\) | ||||
−0.277805 | + | 0.960638i | \(0.589607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −62.5495 | − | 192.284i | −0.0851014 | − | 0.261611i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 288.293 | − | 288.293i | 0.391170 | − | 0.391170i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 957.359i | 1.29548i | 0.761862 | + | 0.647740i | \(0.224286\pi\) | ||||
−0.761862 | + | 0.647740i | \(0.775714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1472.65 | + | 749.718i | 1.98738 | + | 1.01177i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −742.686 | − | 742.686i | −0.999578 | − | 0.999578i | 0.000422402 | − | 1.00000i | \(-0.499866\pi\) |
−1.00000 | 0.000422402i | \(0.999866\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −247.422 | + | 247.422i | −0.332110 | + | 0.332110i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 328.870 | + | 452.000i | 0.440254 | + | 0.605087i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1192.95i | 1.59273i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −920.718 | + | 920.718i | −1.22599 | + | 1.22599i | −0.260522 | + | 0.965468i | \(0.583895\pi\) |
−0.965468 | + | 0.260522i | \(0.916105\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 507.550 | + | 258.391i | 0.674037 | + | 0.343149i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −451.264 | + | 451.264i | −0.597700 | + | 0.597700i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 126.592i | 0.167228i | 0.996498 | + | 0.0836140i | \(0.0266463\pi\) | ||||
−0.996498 | + | 0.0836140i | \(0.973354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 247.237 | + | 125.867i | 0.325740 | + | 0.165833i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 263.944i | 0.346838i | 0.984848 | + | 0.173419i | \(0.0554815\pi\) | ||||
−0.984848 | + | 0.173419i | \(0.944518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 559.215i | 0.732916i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 341.603 | + | 18.7664i | 0.446540 | + | 0.0245312i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1510.28 | 1.96908 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 116.182 | 0.151082 | 0.0755409 | − | 0.997143i | \(-0.475932\pi\) | ||||
0.0755409 | + | 0.997143i | \(0.475932\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.4905 | − | 65.7844i | 0.0434377 | − | 0.0853235i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1333.03 | −1.72448 | −0.862242 | − | 0.506496i | \(-0.830940\pi\) | ||||
−0.862242 | + | 0.506496i | \(0.830940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 130.285 | + | 130.285i | 0.168109 | + | 0.168109i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 590.848 | − | 1160.59i | 0.760422 | − | 1.49368i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 767.511 | + | 767.511i | 0.985251 | + | 0.985251i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1780.73 | 2.28006 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 449.148 | + | 325.621i | 0.573624 | + | 0.415864i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 251.791 | + | 251.791i | 0.320753 | + | 0.320753i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −188.004 | + | 188.004i | −0.238886 | + | 0.238886i | −0.816389 | − | 0.577502i | \(-0.804027\pi\) |
0.577502 | + | 0.816389i | \(0.304027\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −480.235 | + | 943.312i | −0.608663 | + | 1.19558i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −468.807 | −0.592677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −911.058 | − | 911.058i | −1.14887 | − | 1.14887i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −184.427 | + | 59.9937i | −0.231984 | + | 0.0754638i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −313.441 | −0.393276 | −0.196638 | − | 0.980476i | \(-0.563002\pi\) | ||||
−0.196638 | + | 0.980476i | \(0.563002\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1539.94 | + | 156.866i | −1.92733 | + | 0.196328i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −52.8793 | + | 38.4743i | −0.0660166 | + | 0.0480329i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 219.020i | 0.272752i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −74.7416 | − | 74.7416i | −0.0928467 | − | 0.0928467i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1388.53 | + | 451.685i | −1.72061 | + | 0.559709i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 196.828 | − | 196.828i | 0.243298 | − | 0.243298i | −0.574915 | − | 0.818213i | \(-0.694965\pi\) |
0.818213 | + | 0.574915i | \(0.194965\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 655.686 | − | 655.686i | 0.808490 | − | 0.808490i | −0.175915 | − | 0.984405i | \(-0.556288\pi\) |
0.984405 | + | 0.175915i | \(0.0562884\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −411.615 | + | 808.524i | −0.506292 | + | 0.994495i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 430.741i | − | 0.528517i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1307.44 | −1.60030 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 300.024 | − | 1902.70i | 0.366330 | − | 2.32320i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −523.330 | − | 523.330i | −0.637430 | − | 0.637430i | 0.312491 | − | 0.949921i | \(-0.398837\pi\) |
−0.949921 | + | 0.312491i | \(0.898837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1018.42 | − | 1018.42i | −1.23744 | − | 1.23744i | −0.961042 | − | 0.276403i | \(-0.910858\pi\) |
−0.276403 | − | 0.961042i | \(-0.589142\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −248.254 | + | 80.7566i | −0.300914 | + | 0.0978868i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 746.034 | − | 746.034i | 0.902097 | − | 0.902097i | −0.0935204 | − | 0.995617i | \(-0.529812\pi\) |
0.995617 | + | 0.0935204i | \(0.0298120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −550.517 | −0.664074 | −0.332037 | − | 0.943266i | \(-0.607736\pi\) | ||||
−0.332037 | + | 0.943266i | \(0.607736\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.4299 | − | 84.3225i | −0.0330083 | − | 0.101471i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −509.784 | + | 51.9290i | −0.611985 | + | 0.0623398i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 324.707i | 0.388870i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 583.992 | − | 805.533i | 0.697720 | − | 0.962405i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −591.156 | + | 591.156i | −0.704596 | + | 0.704596i | −0.965394 | − | 0.260798i | \(-0.916014\pi\) |
0.260798 | + | 0.965394i | \(0.416014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 418.829i | − | 0.498013i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 221.797 | − | 435.669i | 0.263104 | − | 0.516808i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 647.915 | + | 647.915i | 0.766763 | + | 0.766763i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1144.24 | + | 1144.24i | −1.35093 | + | 1.35093i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −125.190 | + | 40.7241i | −0.147456 | + | 0.0479672i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 259.288i | − | 0.304686i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 177.160 | − | 177.160i | 0.207690 | − | 0.207690i | −0.595595 | − | 0.803285i | \(-0.703084\pi\) |
0.803285 | + | 0.595595i | \(0.203084\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 455.156 | + | 71.7705i | 0.532346 | + | 0.0839421i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 149.352 | − | 149.352i | 0.174272 | − | 0.174272i | −0.614581 | − | 0.788854i | \(-0.710675\pi\) |
0.788854 | + | 0.614581i | \(0.210675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 665.664i | 0.774929i | 0.921885 | + | 0.387464i | \(0.126649\pi\) | ||||
−0.921885 | + | 0.387464i | \(0.873351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 574.004 | − | 1127.50i | 0.666671 | − | 1.30952i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 57.4716i | − | 0.0665952i | −0.999445 | − | 0.0332976i | \(-0.989399\pi\) | ||
0.999445 | − | 0.0332976i | \(-0.0106009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 548.163i | 0.633714i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 229.474 | − | 836.081i | 0.264676 | − | 0.964337i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2198.31 | 2.52970 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −563.581 | −0.647051 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.3289 | + | 1.62869i | 0.0118315 | + | 0.00186563i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 99.4626 | 0.113672 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 626.865 | + | 626.865i | 0.714784 | + | 0.714784i | 0.967532 | − | 0.252748i | \(-0.0813345\pi\) |
−0.252748 | + | 0.967532i | \(0.581334\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −840.818 | − | 428.056i | −0.956562 | − | 0.486981i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −296.732 | − | 296.732i | −0.336813 | − | 0.336813i | 0.518353 | − | 0.855167i | \(-0.326545\pi\) |
−0.855167 | + | 0.518353i | \(0.826545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −773.255 | −0.875713 | −0.437857 | − | 0.899045i | \(-0.644262\pi\) | ||||
−0.437857 | + | 0.899045i | \(0.644262\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 400.467 | − | 130.271i | 0.452505 | − | 0.147199i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 617.167 | + | 617.167i | 0.695792 | + | 0.695792i | 0.963500 | − | 0.267708i | \(-0.0862663\pi\) |
−0.267708 | + | 0.963500i | \(0.586266\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 183.489 | − | 183.489i | 0.206400 | − | 0.206400i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 641.717 | + | 1255.19i | 0.720221 | + | 1.40875i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2084.79 | −2.33459 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −170.986 | − | 170.986i | −0.191045 | − | 0.191045i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −118.633 | − | 364.689i | −0.132255 | − | 0.406565i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 757.151 | 0.842215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.8072 | + | 488.953i | 0.0552799 | + | 0.542679i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 471.436 | + | 1449.24i | 0.522077 | + | 1.60492i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12.5708i | − | 0.0138904i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 876.313 | + | 876.313i | 0.966167 | + | 0.966167i | 0.999446 | − | 0.0332795i | \(-0.0105951\pi\) |
−0.0332795 | + | 0.999446i | \(0.510595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1271.33 | + | 925.001i | −1.39860 | + | 1.01760i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 183.047 | − | 183.047i | 0.200930 | − | 0.200930i | −0.599469 | − | 0.800398i | \(-0.704621\pi\) |
0.800398 | + | 0.599469i | \(0.204621\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −764.340 | + | 764.340i | −0.837175 | + | 0.837175i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −320.161 | − | 162.992i | −0.349902 | − | 0.178133i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1875.74i | − | 2.04552i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 237.681 | 0.258630 | 0.129315 | − | 0.991604i | \(-0.458722\pi\) | ||||
0.129315 | + | 0.991604i | \(0.458722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.3482 | − | 100.862i | 0.0557526 | − | 0.109513i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1740.57 | − | 1740.57i | −1.88577 | − | 1.88577i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 172.524 | + | 172.524i | 0.186513 | + | 0.186513i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −791.152 | − | 1087.36i | −0.853454 | − | 1.17299i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −608.555 | + | 608.555i | −0.655065 | + | 0.655065i | −0.954208 | − | 0.299143i | \(-0.903299\pi\) |
0.299143 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −690.152 | −0.741302 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 373.467 | − | 121.488i | 0.400286 | − | 0.130212i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 67.0447 | + | 658.173i | 0.0717055 | + | 0.703928i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1505.78i | − | 1.60703i | −0.595286 | − | 0.803514i | \(-0.702961\pi\) | ||
0.595286 | − | 0.803514i | \(-0.297039\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 134.240 | − | 43.6681i | 0.142961 | − | 0.0465049i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −811.174 | + | 811.174i | −0.862034 | + | 0.862034i | −0.991574 | − | 0.129540i | \(-0.958650\pi\) |
0.129540 | + | 0.991574i | \(0.458650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 251.896i | − | 0.267122i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −84.5649 | − | 530.399i | −0.0894866 | − | 0.561269i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −641.494 | − | 641.494i | −0.677396 | − | 0.677396i | 0.282014 | − | 0.959410i | \(-0.408998\pi\) |
−0.959410 | + | 0.282014i | \(0.908998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 214.080 | − | 214.080i | 0.225585 | − | 0.225585i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 404.372 | + | 1243.08i | 0.425207 | + | 1.30713i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 170.900i | − | 0.179329i | −0.995972 | − | 0.0896643i | \(-0.971421\pi\) | ||
0.995972 | − | 0.0896643i | \(-0.0285794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 292.495 | − | 292.495i | 0.306278 | − | 0.306278i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −486.708 | + | 956.026i | −0.508577 | + | 0.998982i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −669.077 | + | 669.077i | −0.697682 | + | 0.697682i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 396.928i | − | 0.413036i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −187.981 | + | 1192.14i | −0.195203 | + | 1.23794i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 145.877i | − | 0.151168i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 680.971i | − | 0.704210i | −0.935960 | − | 0.352105i | \(-0.885466\pi\) | ||
0.935960 | − | 0.352105i | \(-0.114534\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 421.590 | − | 1088.95i | 0.435078 | − | 1.12379i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 800.611 | 0.824522 | 0.412261 | − | 0.911066i | \(-0.364739\pi\) | ||||
0.412261 | + | 0.911066i | \(0.364739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1442.45 | 1.48248 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 321.591 | + | 163.720i | 0.329837 | + | 0.167918i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −498.800 | −0.510542 | −0.255271 | − | 0.966870i | \(-0.582165\pi\) | ||||
−0.255271 | + | 0.966870i | \(0.582165\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −89.4198 | − | 89.4198i | −0.0913379 | − | 0.0913379i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −88.1189 | + | 558.834i | −0.0898256 | + | 0.569658i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −123.849 | − | 123.849i | −0.125991 | − | 0.125991i | 0.641300 | − | 0.767290i | \(-0.278395\pi\) |
−0.767290 | + | 0.641300i | \(0.778395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −376.929 | −0.382669 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 751.730 | + | 2310.90i | 0.761631 | + | 2.34133i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 214.551 | + | 214.551i | 0.216937 | + | 0.216937i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 97.5355 | − | 97.5355i | 0.0984213 | − | 0.0984213i | −0.656182 | − | 0.754603i | \(-0.727829\pi\) |
0.754603 | + | 0.656182i | \(0.227829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1230.13 | − | 626.251i | −1.23880 | − | 0.630665i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 241.419 | 0.242632 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 580.961 | + | 580.961i | 0.582709 | + | 0.582709i | 0.935647 | − | 0.352937i | \(-0.114817\pi\) |
−0.352937 | + | 0.935647i | \(0.614817\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 773.327 | − | 1066.69i | 0.774101 | − | 1.06776i |
(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 | 1020.3.bc.a.701.16 | yes | 96 | |
3.2 | odd | 2 | inner | 1020.3.bc.a.701.9 | ✓ | 96 | |
17.13 | even | 4 | inner | 1020.3.bc.a.761.9 | yes | 96 | |
51.47 | odd | 4 | inner | 1020.3.bc.a.761.16 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1020.3.bc.a.701.9 | ✓ | 96 | 3.2 | odd | 2 | inner | |
1020.3.bc.a.701.16 | yes | 96 | 1.1 | even | 1 | trivial | |
1020.3.bc.a.761.9 | yes | 96 | 17.13 | even | 4 | inner | |
1020.3.bc.a.761.16 | yes | 96 | 51.47 | odd | 4 | inner |