Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(181,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.181");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.f (of order \(2\), degree \(1\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(1.72286 + 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.181 |
Dual form | 210.3.f.a.181.4 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −6.70141 | − | 2.02265i | −0.957344 | − | 0.288949i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | −5.00806 | −0.455278 | −0.227639 | − | 0.973746i | \(-0.573101\pi\) | ||||
−0.227639 | + | 0.973746i | \(0.573101\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | 9.06929i | 0.697638i | 0.937190 | + | 0.348819i | \(0.113417\pi\) | ||||
−0.937190 | + | 0.348819i | \(0.886583\pi\) | |||||||
\(14\) | 9.47723 | + | 2.86045i | 0.676945 | + | 0.204318i | ||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 19.7410i | − | 1.16123i | −0.814177 | − | 0.580617i | \(-0.802812\pi\) | ||
0.814177 | − | 0.580617i | \(-0.197188\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 25.6863i | 1.35191i | 0.736942 | + | 0.675956i | \(0.236269\pi\) | ||||
−0.736942 | + | 0.675956i | \(0.763731\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | −3.50333 | + | 11.6072i | −0.166825 | + | 0.552723i | ||||
\(22\) | 7.08246 | 0.321930 | ||||||||
\(23\) | −40.9686 | −1.78124 | −0.890621 | − | 0.454746i | \(-0.849730\pi\) | ||||
−0.890621 | + | 0.454746i | \(0.849730\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − | 12.8259i | − | 0.493304i | ||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −13.4028 | − | 4.04529i | −0.478672 | − | 0.144475i | ||||
\(29\) | −22.3071 | −0.769209 | −0.384604 | − | 0.923081i | \(-0.625662\pi\) | ||||
−0.384604 | + | 0.923081i | \(0.625662\pi\) | |||||||
\(30\) | 5.47723 | 0.182574 | ||||||||
\(31\) | 15.9015i | 0.512952i | 0.966551 | + | 0.256476i | \(0.0825614\pi\) | ||||
−0.966551 | + | 0.256476i | \(0.917439\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 8.67421i | 0.262855i | ||||||||
\(34\) | 27.9179i | 0.821116i | ||||||||
\(35\) | −4.52277 | + | 14.9848i | −0.129222 | + | 0.428137i | ||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −44.7506 | −1.20948 | −0.604738 | − | 0.796424i | \(-0.706722\pi\) | ||||
−0.604738 | + | 0.796424i | \(0.706722\pi\) | |||||||
\(38\) | − | 36.3259i | − | 0.955946i | ||||||
\(39\) | 15.7085 | 0.402781 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | − | 27.0829i | − | 0.660557i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||
0.943883 | − | 0.330279i | \(-0.107143\pi\) | |||||||
\(42\) | 4.95445 | − | 16.4150i | 0.117963 | − | 0.390834i | ||||
\(43\) | −30.6690 | −0.713233 | −0.356616 | − | 0.934251i | \(-0.616070\pi\) | ||||
−0.356616 | + | 0.934251i | \(0.616070\pi\) | |||||||
\(44\) | −10.0161 | −0.227639 | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | 57.9383 | 1.25953 | ||||||||
\(47\) | − | 58.1430i | − | 1.23709i | −0.785751 | − | 0.618543i | \(-0.787723\pi\) | ||
0.785751 | − | 0.618543i | \(-0.212277\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | 40.8178 | + | 27.1092i | 0.833016 | + | 0.553248i | ||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | −34.1924 | −0.670438 | ||||||||
\(52\) | 18.1386i | 0.348819i | ||||||||
\(53\) | 65.6199 | 1.23811 | 0.619055 | − | 0.785347i | \(-0.287516\pi\) | ||||
0.619055 | + | 0.785347i | \(0.287516\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 11.1984i | 0.203606i | ||||||||
\(56\) | 18.9545 | + | 5.72091i | 0.338472 | + | 0.102159i | ||||
\(57\) | 44.4900 | 0.780526 | ||||||||
\(58\) | 31.5469 | 0.543913 | ||||||||
\(59\) | 32.5746i | 0.552112i | 0.961142 | + | 0.276056i | \(0.0890275\pi\) | ||||
−0.961142 | + | 0.276056i | \(0.910973\pi\) | |||||||
\(60\) | −7.74597 | −0.129099 | ||||||||
\(61\) | − | 83.5349i | − | 1.36943i | −0.728813 | − | 0.684713i | \(-0.759928\pi\) | ||
0.728813 | − | 0.684713i | \(-0.240072\pi\) | |||||||
\(62\) | − | 22.4881i | − | 0.362712i | ||||||
\(63\) | 20.1042 | + | 6.06794i | 0.319115 | + | 0.0963165i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 20.2796 | 0.311993 | ||||||||
\(66\) | − | 12.2672i | − | 0.185866i | ||||||
\(67\) | 72.0585 | 1.07550 | 0.537750 | − | 0.843104i | \(-0.319274\pi\) | ||||
0.537750 | + | 0.843104i | \(0.319274\pi\) | |||||||
\(68\) | − | 39.4819i | − | 0.580617i | ||||||
\(69\) | 70.9597i | 1.02840i | ||||||||
\(70\) | 6.39617 | − | 21.1917i | 0.0913738 | − | 0.302739i | ||||
\(71\) | −24.8675 | −0.350246 | −0.175123 | − | 0.984547i | \(-0.556032\pi\) | ||||
−0.175123 | + | 0.984547i | \(0.556032\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | − | 67.8725i | − | 0.929760i | −0.885374 | − | 0.464880i | \(-0.846098\pi\) | ||
0.885374 | − | 0.464880i | \(-0.153902\pi\) | |||||||
\(74\) | 63.2870 | 0.855229 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 51.3726i | 0.675956i | ||||||||
\(77\) | 33.5610 | + | 10.1295i | 0.435858 | + | 0.131552i | ||||
\(78\) | −22.2151 | −0.284809 | ||||||||
\(79\) | 30.4452 | 0.385383 | 0.192691 | − | 0.981259i | \(-0.438278\pi\) | ||||
0.192691 | + | 0.981259i | \(0.438278\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 38.3009i | 0.467085i | ||||||||
\(83\) | − | 72.4623i | − | 0.873040i | −0.899695 | − | 0.436520i | \(-0.856211\pi\) | ||
0.899695 | − | 0.436520i | \(-0.143789\pi\) | |||||||
\(84\) | −7.00665 | + | 23.2144i | −0.0834125 | + | 0.276362i | ||||
\(85\) | −44.1421 | −0.519319 | ||||||||
\(86\) | 43.3725 | 0.504332 | ||||||||
\(87\) | 38.6370i | 0.444103i | ||||||||
\(88\) | 14.1649 | 0.160965 | ||||||||
\(89\) | 113.756i | 1.27815i | 0.769143 | + | 0.639076i | \(0.220683\pi\) | ||||
−0.769143 | + | 0.639076i | \(0.779317\pi\) | |||||||
\(90\) | − | 9.48683i | − | 0.105409i | ||||||
\(91\) | 18.3440 | − | 60.7770i | 0.201582 | − | 0.667880i | ||||
\(92\) | −81.9372 | −0.890621 | ||||||||
\(93\) | 27.5422 | 0.296153 | ||||||||
\(94\) | 82.2267i | 0.874752i | ||||||||
\(95\) | 57.4363 | 0.604593 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | − | 103.804i | − | 1.07014i | −0.844806 | − | 0.535072i | \(-0.820284\pi\) | ||
0.844806 | − | 0.535072i | \(-0.179716\pi\) | |||||||
\(98\) | −57.7251 | − | 38.3381i | −0.589032 | − | 0.391206i | ||||
\(99\) | 15.0242 | 0.151759 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | − | 155.379i | − | 1.53841i | −0.639003 | − | 0.769204i | \(-0.720653\pi\) | ||
0.639003 | − | 0.769204i | \(-0.279347\pi\) | |||||||
\(102\) | 48.3553 | 0.474071 | ||||||||
\(103\) | 65.9471i | 0.640264i | 0.947373 | + | 0.320132i | \(0.103727\pi\) | ||||
−0.947373 | + | 0.320132i | \(0.896273\pi\) | |||||||
\(104\) | − | 25.6518i | − | 0.246652i | ||||||
\(105\) | 25.9545 | + | 7.83368i | 0.247185 | + | 0.0746064i | ||||
\(106\) | −92.8005 | −0.875476 | ||||||||
\(107\) | −136.269 | −1.27354 | −0.636771 | − | 0.771053i | \(-0.719730\pi\) | ||||
−0.636771 | + | 0.771053i | \(0.719730\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | 166.003 | 1.52296 | 0.761482 | − | 0.648186i | \(-0.224472\pi\) | ||||
0.761482 | + | 0.648186i | \(0.224472\pi\) | |||||||
\(110\) | − | 15.8369i | − | 0.143971i | ||||||
\(111\) | 77.5104i | 0.698292i | ||||||||
\(112\) | −26.8056 | − | 8.09058i | −0.239336 | − | 0.0722374i | ||||
\(113\) | −25.5037 | −0.225696 | −0.112848 | − | 0.993612i | \(-0.535997\pi\) | ||||
−0.112848 | + | 0.993612i | \(0.535997\pi\) | |||||||
\(114\) | −62.9184 | −0.551915 | ||||||||
\(115\) | 91.6085i | 0.796596i | ||||||||
\(116\) | −44.6141 | −0.384604 | ||||||||
\(117\) | − | 27.2079i | − | 0.232546i | ||||||
\(118\) | − | 46.0674i | − | 0.390402i | ||||||
\(119\) | −39.9290 | + | 132.292i | −0.335538 | + | 1.11170i | ||||
\(120\) | 10.9545 | 0.0912871 | ||||||||
\(121\) | −95.9194 | −0.792722 | ||||||||
\(122\) | 118.136i | 0.968330i | ||||||||
\(123\) | −46.9089 | −0.381373 | ||||||||
\(124\) | 31.8030i | 0.256476i | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | −28.4317 | − | 8.58136i | −0.225648 | − | 0.0681060i | ||||
\(127\) | −230.306 | −1.81344 | −0.906718 | − | 0.421738i | \(-0.861420\pi\) | ||||
−0.906718 | + | 0.421738i | \(0.861420\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 53.1203i | 0.411785i | ||||||||
\(130\) | −28.6796 | −0.220612 | ||||||||
\(131\) | − | 40.9127i | − | 0.312311i | −0.987733 | − | 0.156155i | \(-0.950090\pi\) | ||
0.987733 | − | 0.156155i | \(-0.0499101\pi\) | |||||||
\(132\) | 17.3484i | 0.131427i | ||||||||
\(133\) | 51.9543 | − | 172.135i | 0.390634 | − | 1.29424i | ||||
\(134\) | −101.906 | −0.760493 | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | 55.8359i | 0.410558i | ||||||||
\(137\) | 158.300 | 1.15547 | 0.577737 | − | 0.816223i | \(-0.303936\pi\) | ||||
0.577737 | + | 0.816223i | \(0.303936\pi\) | |||||||
\(138\) | − | 100.352i | − | 0.727189i | ||||||
\(139\) | − | 141.584i | − | 1.01859i | −0.860592 | − | 0.509296i | \(-0.829906\pi\) | ||
0.860592 | − | 0.509296i | \(-0.170094\pi\) | |||||||
\(140\) | −9.04555 | + | 29.9696i | −0.0646111 | + | 0.214069i | ||||
\(141\) | −100.707 | −0.714232 | ||||||||
\(142\) | 35.1679 | 0.247661 | ||||||||
\(143\) | − | 45.4195i | − | 0.317619i | ||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 49.8801i | 0.344001i | ||||||||
\(146\) | 95.9861i | 0.657439i | ||||||||
\(147\) | 46.9545 | − | 70.6985i | 0.319418 | − | 0.480942i | ||||
\(148\) | −89.5013 | −0.604738 | ||||||||
\(149\) | −121.456 | −0.815139 | −0.407569 | − | 0.913174i | \(-0.633624\pi\) | ||||
−0.407569 | + | 0.913174i | \(0.633624\pi\) | |||||||
\(150\) | − | 12.2474i | − | 0.0816497i | ||||||
\(151\) | −219.093 | −1.45094 | −0.725472 | − | 0.688251i | \(-0.758379\pi\) | ||||
−0.725472 | + | 0.688251i | \(0.758379\pi\) | |||||||
\(152\) | − | 72.6519i | − | 0.477973i | ||||||
\(153\) | 59.2229i | 0.387078i | ||||||||
\(154\) | −47.4625 | − | 14.3253i | −0.308198 | − | 0.0930215i | ||||
\(155\) | 35.5569 | 0.229399 | ||||||||
\(156\) | 31.4169 | 0.201391 | ||||||||
\(157\) | 57.2815i | 0.364850i | 0.983220 | + | 0.182425i | \(0.0583947\pi\) | ||||
−0.983220 | + | 0.182425i | \(0.941605\pi\) | |||||||
\(158\) | −43.0560 | −0.272507 | ||||||||
\(159\) | − | 113.657i | − | 0.714824i | ||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 274.547 | + | 82.8649i | 1.70526 | + | 0.514689i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −8.52297 | −0.0522882 | −0.0261441 | − | 0.999658i | \(-0.508323\pi\) | ||||
−0.0261441 | + | 0.999658i | \(0.508323\pi\) | |||||||
\(164\) | − | 54.1657i | − | 0.330279i | ||||||
\(165\) | 19.3961 | 0.117552 | ||||||||
\(166\) | 102.477i | 0.617333i | ||||||||
\(167\) | 258.148i | 1.54580i | 0.634529 | + | 0.772899i | \(0.281194\pi\) | ||||
−0.634529 | + | 0.772899i | \(0.718806\pi\) | |||||||
\(168\) | 9.90890 | − | 32.8301i | 0.0589816 | − | 0.195417i | ||||
\(169\) | 86.7480 | 0.513301 | ||||||||
\(170\) | 62.4264 | 0.367214 | ||||||||
\(171\) | − | 77.0589i | − | 0.450637i | ||||||
\(172\) | −61.3380 | −0.356616 | ||||||||
\(173\) | 327.250i | 1.89162i | 0.324725 | + | 0.945808i | \(0.394728\pi\) | ||||
−0.324725 | + | 0.945808i | \(0.605272\pi\) | |||||||
\(174\) | − | 54.6409i | − | 0.314028i | ||||||
\(175\) | 33.5071 | + | 10.1132i | 0.191469 | + | 0.0577899i | ||||
\(176\) | −20.0322 | −0.113819 | ||||||||
\(177\) | 56.4208 | 0.318762 | ||||||||
\(178\) | − | 160.875i | − | 0.903791i | ||||||
\(179\) | −167.569 | −0.936141 | −0.468071 | − | 0.883691i | \(-0.655051\pi\) | ||||
−0.468071 | + | 0.883691i | \(0.655051\pi\) | |||||||
\(180\) | 13.4164i | 0.0745356i | ||||||||
\(181\) | − | 147.957i | − | 0.817442i | −0.912659 | − | 0.408721i | \(-0.865975\pi\) | ||
0.912659 | − | 0.408721i | \(-0.134025\pi\) | |||||||
\(182\) | −25.9423 | + | 85.9517i | −0.142540 | + | 0.472262i | ||||
\(183\) | −144.687 | −0.790638 | ||||||||
\(184\) | 115.877 | 0.629764 | ||||||||
\(185\) | 100.065i | 0.540894i | ||||||||
\(186\) | −38.9506 | −0.209412 | ||||||||
\(187\) | 98.8638i | 0.528684i | ||||||||
\(188\) | − | 116.286i | − | 0.618543i | ||||||
\(189\) | 10.5100 | − | 34.8216i | 0.0556083 | − | 0.184241i | ||||
\(190\) | −81.2273 | −0.427512 | ||||||||
\(191\) | 49.4939 | 0.259130 | 0.129565 | − | 0.991571i | \(-0.458642\pi\) | ||||
0.129565 | + | 0.991571i | \(0.458642\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | 172.674 | 0.894686 | 0.447343 | − | 0.894362i | \(-0.352370\pi\) | ||||
0.447343 | + | 0.894362i | \(0.352370\pi\) | |||||||
\(194\) | 146.801i | 0.756707i | ||||||||
\(195\) | − | 35.1252i | − | 0.180129i | ||||||
\(196\) | 81.6356 | + | 54.2183i | 0.416508 | + | 0.276624i | ||||
\(197\) | 75.6444 | 0.383982 | 0.191991 | − | 0.981397i | \(-0.438506\pi\) | ||||
0.191991 | + | 0.981397i | \(0.438506\pi\) | |||||||
\(198\) | −21.2474 | −0.107310 | ||||||||
\(199\) | − | 147.620i | − | 0.741808i | −0.928671 | − | 0.370904i | \(-0.879048\pi\) | ||
0.928671 | − | 0.370904i | \(-0.120952\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | − | 124.809i | − | 0.620940i | ||||||
\(202\) | 219.739i | 1.08782i | ||||||||
\(203\) | 149.489 | + | 45.1193i | 0.736398 | + | 0.222262i | ||||
\(204\) | −68.3847 | −0.335219 | ||||||||
\(205\) | −60.5591 | −0.295410 | ||||||||
\(206\) | − | 93.2634i | − | 0.452735i | ||||||
\(207\) | 122.906 | 0.593747 | ||||||||
\(208\) | 36.2772i | 0.174409i | ||||||||
\(209\) | − | 128.638i | − | 0.615495i | ||||||
\(210\) | −36.7051 | − | 11.0785i | −0.174786 | − | 0.0527547i | ||||
\(211\) | 156.882 | 0.743518 | 0.371759 | − | 0.928329i | \(-0.378755\pi\) | ||||
0.371759 | + | 0.928329i | \(0.378755\pi\) | |||||||
\(212\) | 131.240 | 0.619055 | ||||||||
\(213\) | 43.0717i | 0.202215i | ||||||||
\(214\) | 192.713 | 0.900530 | ||||||||
\(215\) | 68.5780i | 0.318967i | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 32.1631 | − | 106.563i | 0.148217 | − | 0.491072i | ||||
\(218\) | −234.764 | −1.07690 | ||||||||
\(219\) | −117.559 | −0.536797 | ||||||||
\(220\) | 22.3967i | 0.101803i | ||||||||
\(221\) | 179.037 | 0.810120 | ||||||||
\(222\) | − | 109.616i | − | 0.493767i | ||||||
\(223\) | 60.4029i | 0.270865i | 0.990787 | + | 0.135433i | \(0.0432424\pi\) | ||||
−0.990787 | + | 0.135433i | \(0.956758\pi\) | |||||||
\(224\) | 37.9089 | + | 11.4418i | 0.169236 | + | 0.0510795i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 36.0677 | 0.159592 | ||||||||
\(227\) | − | 313.611i | − | 1.38155i | −0.723071 | − | 0.690773i | \(-0.757270\pi\) | ||
0.723071 | − | 0.690773i | \(-0.242730\pi\) | |||||||
\(228\) | 88.9800 | 0.390263 | ||||||||
\(229\) | − | 110.368i | − | 0.481957i | −0.970530 | − | 0.240979i | \(-0.922532\pi\) | ||
0.970530 | − | 0.240979i | \(-0.0774684\pi\) | |||||||
\(230\) | − | 129.554i | − | 0.563278i | ||||||
\(231\) | 17.5449 | − | 58.1294i | 0.0759517 | − | 0.251643i | ||||
\(232\) | 63.0939 | 0.271956 | ||||||||
\(233\) | 38.4067 | 0.164835 | 0.0824177 | − | 0.996598i | \(-0.473736\pi\) | ||||
0.0824177 | + | 0.996598i | \(0.473736\pi\) | |||||||
\(234\) | 38.4777i | 0.164435i | ||||||||
\(235\) | −130.012 | −0.553242 | ||||||||
\(236\) | 65.1492i | 0.276056i | ||||||||
\(237\) | − | 52.7327i | − | 0.222501i | ||||||
\(238\) | 56.4681 | − | 187.090i | 0.237261 | − | 0.786091i | ||||
\(239\) | −125.129 | −0.523552 | −0.261776 | − | 0.965129i | \(-0.584308\pi\) | ||||
−0.261776 | + | 0.965129i | \(0.584308\pi\) | |||||||
\(240\) | −15.4919 | −0.0645497 | ||||||||
\(241\) | 154.625i | 0.641598i | 0.947147 | + | 0.320799i | \(0.103951\pi\) | ||||
−0.947147 | + | 0.320799i | \(0.896049\pi\) | |||||||
\(242\) | 135.650 | 0.560539 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 167.070i | − | 0.684713i | ||||||
\(245\) | 60.6179 | − | 91.2714i | 0.247420 | − | 0.372536i | ||||
\(246\) | 66.3392 | 0.269671 | ||||||||
\(247\) | −232.957 | −0.943144 | ||||||||
\(248\) | − | 44.9763i | − | 0.181356i | ||||||
\(249\) | −125.508 | −0.504050 | ||||||||
\(250\) | − | 15.8114i | − | 0.0632456i | ||||||
\(251\) | 152.655i | 0.608185i | 0.952642 | + | 0.304093i | \(0.0983532\pi\) | ||||
−0.952642 | + | 0.304093i | \(0.901647\pi\) | |||||||
\(252\) | 40.2085 | + | 12.1359i | 0.159557 | + | 0.0481582i | ||||
\(253\) | 205.173 | 0.810960 | ||||||||
\(254\) | 325.702 | 1.28229 | ||||||||
\(255\) | 76.4564i | 0.299829i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 20.1517i | 0.0784113i | 0.999231 | + | 0.0392057i | \(0.0124827\pi\) | ||||
−0.999231 | + | 0.0392057i | \(0.987517\pi\) | |||||||
\(258\) | − | 75.1234i | − | 0.291176i | ||||||
\(259\) | 299.892 | + | 90.5147i | 1.15789 | + | 0.349478i | ||||
\(260\) | 40.5591 | 0.155997 | ||||||||
\(261\) | 66.9212 | 0.256403 | ||||||||
\(262\) | 57.8593i | 0.220837i | ||||||||
\(263\) | −320.699 | −1.21939 | −0.609693 | − | 0.792637i | \(-0.708707\pi\) | ||||
−0.609693 | + | 0.792637i | \(0.708707\pi\) | |||||||
\(264\) | − | 24.5344i | − | 0.0929332i | ||||||
\(265\) | − | 146.730i | − | 0.553700i | ||||||
\(266\) | −73.4745 | + | 243.435i | −0.276220 | + | 0.915169i | ||||
\(267\) | 197.030 | 0.737942 | ||||||||
\(268\) | 144.117 | 0.537750 | ||||||||
\(269\) | − | 39.2134i | − | 0.145775i | −0.997340 | − | 0.0728874i | \(-0.976779\pi\) | ||
0.997340 | − | 0.0728874i | \(-0.0232214\pi\) | |||||||
\(270\) | −16.4317 | −0.0608581 | ||||||||
\(271\) | − | 299.071i | − | 1.10358i | −0.833982 | − | 0.551792i | \(-0.813944\pi\) | ||
0.833982 | − | 0.551792i | \(-0.186056\pi\) | |||||||
\(272\) | − | 78.9639i | − | 0.290308i | ||||||
\(273\) | −105.269 | − | 31.7727i | −0.385600 | − | 0.116383i | ||||
\(274\) | −223.870 | −0.817044 | ||||||||
\(275\) | 25.0403 | 0.0910556 | ||||||||
\(276\) | 141.919i | 0.514200i | ||||||||
\(277\) | −438.966 | −1.58472 | −0.792358 | − | 0.610056i | \(-0.791147\pi\) | ||||
−0.792358 | + | 0.610056i | \(0.791147\pi\) | |||||||
\(278\) | 200.230i | 0.720253i | ||||||||
\(279\) | − | 47.7045i | − | 0.170984i | ||||||
\(280\) | 12.7923 | − | 42.3834i | 0.0456869 | − | 0.151369i | ||||
\(281\) | −199.479 | −0.709889 | −0.354944 | − | 0.934887i | \(-0.615500\pi\) | ||||
−0.354944 | + | 0.934887i | \(0.615500\pi\) | |||||||
\(282\) | 142.421 | 0.505038 | ||||||||
\(283\) | 541.179i | 1.91229i | 0.292889 | + | 0.956147i | \(0.405384\pi\) | ||||
−0.292889 | + | 0.956147i | \(0.594616\pi\) | |||||||
\(284\) | −49.7349 | −0.175123 | ||||||||
\(285\) | − | 99.4827i | − | 0.349062i | ||||||
\(286\) | 64.2329i | 0.224591i | ||||||||
\(287\) | −54.7790 | + | 181.493i | −0.190868 | + | 0.632381i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −100.706 | −0.348462 | ||||||||
\(290\) | − | 70.5411i | − | 0.243245i | ||||||
\(291\) | −179.794 | −0.617848 | ||||||||
\(292\) | − | 135.745i | − | 0.464880i | ||||||
\(293\) | 378.757i | 1.29269i | 0.763047 | + | 0.646343i | \(0.223702\pi\) | ||||
−0.763047 | + | 0.646343i | \(0.776298\pi\) | |||||||
\(294\) | −66.4036 | + | 99.9828i | −0.225863 | + | 0.340078i | ||||
\(295\) | 72.8390 | 0.246912 | ||||||||
\(296\) | 126.574 | 0.427615 | ||||||||
\(297\) | − | 26.0226i | − | 0.0876183i | ||||||
\(298\) | 171.764 | 0.576390 | ||||||||
\(299\) | − | 371.556i | − | 1.24266i | ||||||
\(300\) | 17.3205i | 0.0577350i | ||||||||
\(301\) | 205.526 | + | 62.0326i | 0.682810 | + | 0.206088i | ||||
\(302\) | 309.844 | 1.02597 | ||||||||
\(303\) | −269.125 | −0.888200 | ||||||||
\(304\) | 102.745i | 0.337978i | ||||||||
\(305\) | −186.790 | −0.612426 | ||||||||
\(306\) | − | 83.7538i | − | 0.273705i | ||||||
\(307\) | 140.210i | 0.456710i | 0.973578 | + | 0.228355i | \(0.0733346\pi\) | ||||
−0.973578 | + | 0.228355i | \(0.926665\pi\) | |||||||
\(308\) | 67.1221 | + | 20.2591i | 0.217929 | + | 0.0657761i | ||||
\(309\) | 114.224 | 0.369656 | ||||||||
\(310\) | −50.2850 | −0.162210 | ||||||||
\(311\) | − | 249.886i | − | 0.803491i | −0.915751 | − | 0.401745i | \(-0.868404\pi\) | ||
0.915751 | − | 0.401745i | \(-0.131596\pi\) | |||||||
\(312\) | −44.4303 | −0.142405 | ||||||||
\(313\) | 517.894i | 1.65461i | 0.561750 | + | 0.827307i | \(0.310128\pi\) | ||||
−0.561750 | + | 0.827307i | \(0.689872\pi\) | |||||||
\(314\) | − | 81.0082i | − | 0.257988i | ||||||
\(315\) | 13.5683 | − | 44.9544i | 0.0430740 | − | 0.142712i | ||||
\(316\) | 60.8904 | 0.192691 | ||||||||
\(317\) | −180.043 | −0.567959 | −0.283980 | − | 0.958830i | \(-0.591655\pi\) | ||||
−0.283980 | + | 0.958830i | \(0.591655\pi\) | |||||||
\(318\) | 160.735i | 0.505457i | ||||||||
\(319\) | 111.715 | 0.350204 | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | 236.025i | 0.735280i | ||||||||
\(322\) | −388.268 | − | 117.189i | −1.20580 | − | 0.363940i | ||||
\(323\) | 507.073 | 1.56988 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | − | 45.3465i | − | 0.139528i | ||||||
\(326\) | 12.0533 | 0.0369733 | ||||||||
\(327\) | − | 287.526i | − | 0.879283i | ||||||
\(328\) | 76.6019i | 0.233542i | ||||||||
\(329\) | −117.603 | + | 389.640i | −0.357455 | + | 1.18432i | ||||
\(330\) | −27.4303 | −0.0831220 | ||||||||
\(331\) | 81.0283 | 0.244799 | 0.122399 | − | 0.992481i | \(-0.460941\pi\) | ||||
0.122399 | + | 0.992481i | \(0.460941\pi\) | |||||||
\(332\) | − | 144.925i | − | 0.436520i | ||||||
\(333\) | 134.252 | 0.403159 | ||||||||
\(334\) | − | 365.077i | − | 1.09304i | ||||||
\(335\) | − | 161.128i | − | 0.480978i | ||||||
\(336\) | −14.0133 | + | 46.4287i | −0.0417063 | + | 0.138181i | ||||
\(337\) | −372.937 | −1.10664 | −0.553318 | − | 0.832970i | \(-0.686639\pi\) | ||||
−0.553318 | + | 0.832970i | \(0.686639\pi\) | |||||||
\(338\) | −122.680 | −0.362959 | ||||||||
\(339\) | 44.1737i | 0.130306i | ||||||||
\(340\) | −88.2843 | −0.259660 | ||||||||
\(341\) | − | 79.6356i | − | 0.233536i | ||||||
\(342\) | 108.978i | 0.318649i | ||||||||
\(343\) | −218.705 | − | 264.230i | −0.637623 | − | 0.770349i | ||||
\(344\) | 86.7451 | 0.252166 | ||||||||
\(345\) | 158.671 | 0.459915 | ||||||||
\(346\) | − | 462.801i | − | 1.33758i | ||||||
\(347\) | 415.231 | 1.19663 | 0.598316 | − | 0.801260i | \(-0.295837\pi\) | ||||
0.598316 | + | 0.801260i | \(0.295837\pi\) | |||||||
\(348\) | 77.2739i | 0.222051i | ||||||||
\(349\) | − | 536.207i | − | 1.53641i | −0.640203 | − | 0.768206i | \(-0.721150\pi\) | ||
0.640203 | − | 0.768206i | \(-0.278850\pi\) | |||||||
\(350\) | −47.3861 | − | 14.3023i | −0.135389 | − | 0.0408636i | ||||
\(351\) | −47.1254 | −0.134260 | ||||||||
\(352\) | 28.3298 | 0.0804825 | ||||||||
\(353\) | − | 416.230i | − | 1.17912i | −0.807724 | − | 0.589560i | \(-0.799301\pi\) | ||
0.807724 | − | 0.589560i | \(-0.200699\pi\) | |||||||
\(354\) | −79.7911 | −0.225399 | ||||||||
\(355\) | 55.6053i | 0.156635i | ||||||||
\(356\) | 227.511i | 0.639076i | ||||||||
\(357\) | 229.137 | + | 69.1590i | 0.641840 | + | 0.193723i | ||||
\(358\) | 236.979 | 0.661952 | ||||||||
\(359\) | −270.563 | −0.753659 | −0.376829 | − | 0.926283i | \(-0.622986\pi\) | ||||
−0.376829 | + | 0.926283i | \(0.622986\pi\) | |||||||
\(360\) | − | 18.9737i | − | 0.0527046i | ||||||
\(361\) | −298.787 | −0.827664 | ||||||||
\(362\) | 209.243i | 0.578019i | ||||||||
\(363\) | 166.137i | 0.457678i | ||||||||
\(364\) | 36.6879 | − | 121.554i | 0.100791 | − | 0.333940i | ||||
\(365\) | −151.767 | −0.415801 | ||||||||
\(366\) | 204.618 | 0.559066 | ||||||||
\(367\) | 605.024i | 1.64857i | 0.566178 | + | 0.824283i | \(0.308422\pi\) | ||||
−0.566178 | + | 0.824283i | \(0.691578\pi\) | |||||||
\(368\) | −163.874 | −0.445311 | ||||||||
\(369\) | 81.2486i | 0.220186i | ||||||||
\(370\) | − | 141.514i | − | 0.382470i | ||||||
\(371\) | −439.746 | − | 132.726i | −1.18530 | − | 0.357751i | ||||
\(372\) | 55.0844 | 0.148076 | ||||||||
\(373\) | −21.5124 | −0.0576739 | −0.0288370 | − | 0.999584i | \(-0.509180\pi\) | ||||
−0.0288370 | + | 0.999584i | \(0.509180\pi\) | |||||||
\(374\) | − | 139.815i | − | 0.373836i | ||||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | 164.453i | 0.437376i | ||||||||
\(377\) | − | 202.309i | − | 0.536629i | ||||||
\(378\) | −14.8634 | + | 49.2451i | −0.0393210 | + | 0.130278i | ||||
\(379\) | 449.862 | 1.18697 | 0.593486 | − | 0.804844i | \(-0.297751\pi\) | ||||
0.593486 | + | 0.804844i | \(0.297751\pi\) | |||||||
\(380\) | 114.873 | 0.302297 | ||||||||
\(381\) | 398.902i | 1.04699i | ||||||||
\(382\) | −69.9949 | −0.183233 | ||||||||
\(383\) | 560.756i | 1.46412i | 0.681242 | + | 0.732058i | \(0.261440\pi\) | ||||
−0.681242 | + | 0.732058i | \(0.738560\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 22.6503 | − | 75.0448i | 0.0588320 | − | 0.194921i | ||||
\(386\) | −244.199 | −0.632639 | ||||||||
\(387\) | 92.0071 | 0.237744 | ||||||||
\(388\) | − | 207.608i | − | 0.535072i | ||||||
\(389\) | −582.222 | −1.49671 | −0.748357 | − | 0.663296i | \(-0.769157\pi\) | ||||
−0.748357 | + | 0.663296i | \(0.769157\pi\) | |||||||
\(390\) | 49.6746i | 0.127371i | ||||||||
\(391\) | 808.759i | 2.06844i | ||||||||
\(392\) | −115.450 | − | 76.6763i | −0.294516 | − | 0.195603i | ||||
\(393\) | −70.8629 | −0.180313 | ||||||||
\(394\) | −106.977 | −0.271516 | ||||||||
\(395\) | − | 68.0776i | − | 0.172348i | ||||||
\(396\) | 30.0483 | 0.0758796 | ||||||||
\(397\) | − | 726.563i | − | 1.83013i | −0.403304 | − | 0.915066i | \(-0.632138\pi\) | ||
0.403304 | − | 0.915066i | \(-0.367862\pi\) | |||||||
\(398\) | 208.766i | 0.524538i | ||||||||
\(399\) | −298.146 | − | 89.9875i | −0.747232 | − | 0.225533i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | −32.7962 | −0.0817860 | −0.0408930 | − | 0.999164i | \(-0.513020\pi\) | ||||
−0.0408930 | + | 0.999164i | \(0.513020\pi\) | |||||||
\(402\) | 176.507i | 0.439071i | ||||||||
\(403\) | −144.215 | −0.357855 | ||||||||
\(404\) | − | 310.758i | − | 0.769204i | ||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | −211.409 | − | 63.8083i | −0.520712 | − | 0.157163i | ||||
\(407\) | 224.114 | 0.550648 | ||||||||
\(408\) | 96.7106 | 0.237036 | ||||||||
\(409\) | 637.739i | 1.55926i | 0.626238 | + | 0.779632i | \(0.284594\pi\) | ||||
−0.626238 | + | 0.779632i | \(0.715406\pi\) | |||||||
\(410\) | 85.6435 | 0.208887 | ||||||||
\(411\) | − | 274.184i | − | 0.667114i | ||||||
\(412\) | 131.894i | 0.320132i | ||||||||
\(413\) | 65.8869 | − | 218.296i | 0.159532 | − | 0.528561i | ||||
\(414\) | −173.815 | −0.419843 | ||||||||
\(415\) | −162.031 | −0.390435 | ||||||||
\(416\) | − | 51.3037i | − | 0.123326i | ||||||
\(417\) | −245.231 | −0.588084 | ||||||||
\(418\) | 181.922i | 0.435221i | ||||||||
\(419\) | − | 344.535i | − | 0.822280i | −0.911572 | − | 0.411140i | \(-0.865131\pi\) | ||
0.911572 | − | 0.411140i | \(-0.134869\pi\) | |||||||
\(420\) | 51.9089 | + | 15.6674i | 0.123593 | + | 0.0373032i | ||||
\(421\) | 290.412 | 0.689814 | 0.344907 | − | 0.938637i | \(-0.387910\pi\) | ||||
0.344907 | + | 0.938637i | \(0.387910\pi\) | |||||||
\(422\) | −221.865 | −0.525746 | ||||||||
\(423\) | 174.429i | 0.412362i | ||||||||
\(424\) | −185.601 | −0.437738 | ||||||||
\(425\) | 98.7048i | 0.232247i | ||||||||
\(426\) | − | 60.9126i | − | 0.142987i | ||||||
\(427\) | −168.962 | + | 559.802i | −0.395695 | + | 1.31101i | ||||
\(428\) | −272.538 | −0.636771 | ||||||||
\(429\) | −78.6689 | −0.183377 | ||||||||
\(430\) | − | 96.9839i | − | 0.225544i | ||||||
\(431\) | −214.780 | −0.498329 | −0.249164 | − | 0.968461i | \(-0.580156\pi\) | ||||
−0.249164 | + | 0.968461i | \(0.580156\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | − | 425.041i | − | 0.981619i | −0.871267 | − | 0.490809i | \(-0.836701\pi\) | ||
0.871267 | − | 0.490809i | \(-0.163299\pi\) | |||||||
\(434\) | −45.4855 | + | 150.702i | −0.104805 | + | 0.347240i | ||||
\(435\) | 86.3949 | 0.198609 | ||||||||
\(436\) | 332.006 | 0.761482 | ||||||||
\(437\) | − | 1052.33i | − | 2.40808i | ||||||
\(438\) | 166.253 | 0.379573 | ||||||||
\(439\) | − | 204.200i | − | 0.465149i | −0.972579 | − | 0.232574i | \(-0.925285\pi\) | ||
0.972579 | − | 0.232574i | \(-0.0747149\pi\) | |||||||
\(440\) | − | 31.6737i | − | 0.0719857i | ||||||
\(441\) | −122.453 | − | 81.3275i | −0.277672 | − | 0.184416i | ||||
\(442\) | −253.196 | −0.572841 | ||||||||
\(443\) | 276.367 | 0.623854 | 0.311927 | − | 0.950106i | \(-0.399026\pi\) | ||||
0.311927 | + | 0.950106i | \(0.399026\pi\) | |||||||
\(444\) | 155.021i | 0.349146i | ||||||||
\(445\) | 254.365 | 0.571607 | ||||||||
\(446\) | − | 85.4227i | − | 0.191531i | ||||||
\(447\) | 210.367i | 0.470620i | ||||||||
\(448\) | −53.6113 | − | 16.1812i | −0.119668 | − | 0.0361187i | ||||
\(449\) | 195.290 | 0.434945 | 0.217472 | − | 0.976066i | \(-0.430219\pi\) | ||||
0.217472 | + | 0.976066i | \(0.430219\pi\) | |||||||
\(450\) | −21.2132 | −0.0471405 | ||||||||
\(451\) | 135.632i | 0.300737i | ||||||||
\(452\) | −51.0074 | −0.112848 | ||||||||
\(453\) | 379.480i | 0.837703i | ||||||||
\(454\) | 443.513i | 0.976901i | ||||||||
\(455\) | −135.902 | − | 41.0184i | −0.298685 | − | 0.0901502i | ||||
\(456\) | −125.837 | −0.275958 | ||||||||
\(457\) | 10.3428 | 0.0226319 | 0.0113159 | − | 0.999936i | \(-0.496398\pi\) | ||||
0.0113159 | + | 0.999936i | \(0.496398\pi\) | |||||||
\(458\) | 156.084i | 0.340795i | ||||||||
\(459\) | 102.577 | 0.223479 | ||||||||
\(460\) | 183.217i | 0.398298i | ||||||||
\(461\) | 527.572i | 1.14441i | 0.820111 | + | 0.572204i | \(0.193912\pi\) | ||||
−0.820111 | + | 0.572204i | \(0.806088\pi\) | |||||||
\(462\) | −24.8122 | + | 82.2074i | −0.0537060 | + | 0.177938i | ||||
\(463\) | 797.897 | 1.72332 | 0.861660 | − | 0.507486i | \(-0.169425\pi\) | ||||
0.861660 | + | 0.507486i | \(0.169425\pi\) | |||||||
\(464\) | −89.2282 | −0.192302 | ||||||||
\(465\) | − | 61.5863i | − | 0.132444i | ||||||
\(466\) | −54.3152 | −0.116556 | ||||||||
\(467\) | 169.651i | 0.363278i | 0.983365 | + | 0.181639i | \(0.0581403\pi\) | ||||
−0.983365 | + | 0.181639i | \(0.941860\pi\) | |||||||
\(468\) | − | 54.4157i | − | 0.116273i | ||||||
\(469\) | −482.894 | − | 145.749i | −1.02962 | − | 0.310765i | ||||
\(470\) | 183.864 | 0.391201 | ||||||||
\(471\) | 99.2144 | 0.210646 | ||||||||
\(472\) | − | 92.1348i | − | 0.195201i | ||||||
\(473\) | 153.592 | 0.324719 | ||||||||
\(474\) | 74.5753i | 0.157332i | ||||||||
\(475\) | − | 128.432i | − | 0.270382i | ||||||
\(476\) | −79.8580 | + | 264.585i | −0.167769 | + | 0.555850i | ||||
\(477\) | −196.860 | −0.412704 | ||||||||
\(478\) | 176.959 | 0.370207 | ||||||||
\(479\) | − | 704.272i | − | 1.47030i | −0.677906 | − | 0.735148i | \(-0.737113\pi\) | ||
0.677906 | − | 0.735148i | \(-0.262887\pi\) | |||||||
\(480\) | 21.9089 | 0.0456435 | ||||||||
\(481\) | − | 405.857i | − | 0.843777i | ||||||
\(482\) | − | 218.673i | − | 0.453678i | ||||||
\(483\) | 143.526 | − | 475.530i | 0.297156 | − | 0.984534i | ||||
\(484\) | −191.839 | −0.396361 | ||||||||
\(485\) | −232.113 | −0.478583 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −66.7966 | −0.137159 | −0.0685797 | − | 0.997646i | \(-0.521847\pi\) | ||||
−0.0685797 | + | 0.997646i | \(0.521847\pi\) | |||||||
\(488\) | 236.273i | 0.484165i | ||||||||
\(489\) | 14.7622i | 0.0301886i | ||||||||
\(490\) | −85.7267 | + | 129.077i | −0.174952 | + | 0.263423i | ||||
\(491\) | 546.122 | 1.11227 | 0.556133 | − | 0.831094i | \(-0.312285\pi\) | ||||
0.556133 | + | 0.831094i | \(0.312285\pi\) | |||||||
\(492\) | −93.8178 | −0.190687 | ||||||||
\(493\) | 440.363i | 0.893231i | ||||||||
\(494\) | 329.450 | 0.666904 | ||||||||
\(495\) | − | 33.5951i | − | 0.0678688i | ||||||
\(496\) | 63.6060i | 0.128238i | ||||||||
\(497\) | 166.647 | + | 50.2981i | 0.335306 | + | 0.101203i | ||||
\(498\) | 177.496 | 0.356417 | ||||||||
\(499\) | 714.060 | 1.43098 | 0.715491 | − | 0.698622i | \(-0.246203\pi\) | ||||
0.715491 | + | 0.698622i | \(0.246203\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 447.126 | 0.892467 | ||||||||
\(502\) | − | 215.886i | − | 0.430052i | ||||||
\(503\) | − | 878.751i | − | 1.74702i | −0.486807 | − | 0.873510i | \(-0.661838\pi\) | ||
0.486807 | − | 0.873510i | \(-0.338162\pi\) | |||||||
\(504\) | −56.8634 | − | 17.1627i | −0.112824 | − | 0.0340530i | ||||
\(505\) | −347.438 | −0.687997 | ||||||||
\(506\) | −290.158 | −0.573435 | ||||||||
\(507\) | − | 150.252i | − | 0.296355i | ||||||
\(508\) | −460.613 | −0.906718 | ||||||||
\(509\) | 510.558i | 1.00306i | 0.865140 | + | 0.501530i | \(0.167229\pi\) | ||||
−0.865140 | + | 0.501530i | \(0.832771\pi\) | |||||||
\(510\) | − | 108.126i | − | 0.212011i | ||||||
\(511\) | −137.282 | + | 454.841i | −0.268654 | + | 0.890100i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −133.470 | −0.260175 | ||||||||
\(514\) | − | 28.4988i | − | 0.0554452i | ||||||
\(515\) | 147.462 | 0.286335 | ||||||||
\(516\) | 106.241i | 0.205893i | ||||||||
\(517\) | 291.184i | 0.563218i | ||||||||
\(518\) | −424.112 | − | 128.007i | −0.818749 | − | 0.247118i | ||||
\(519\) | 566.813 | 1.09213 | ||||||||
\(520\) | −57.3592 | −0.110306 | ||||||||
\(521\) | − | 17.2889i | − | 0.0331841i | −0.999862 | − | 0.0165921i | \(-0.994718\pi\) | ||
0.999862 | − | 0.0165921i | \(-0.00528166\pi\) | |||||||
\(522\) | −94.6408 | −0.181304 | ||||||||
\(523\) | 287.840i | 0.550364i | 0.961392 | + | 0.275182i | \(0.0887381\pi\) | ||||
−0.961392 | + | 0.275182i | \(0.911262\pi\) | |||||||
\(524\) | − | 81.8254i | − | 0.156155i | ||||||
\(525\) | 17.5166 | − | 58.0359i | 0.0333650 | − | 0.110545i | ||||
\(526\) | 453.536 | 0.862237 | ||||||||
\(527\) | 313.911 | 0.595657 | ||||||||
\(528\) | 34.6968i | 0.0657137i | ||||||||
\(529\) | 1149.42 | 2.17282 | ||||||||
\(530\) | 207.508i | 0.391525i | ||||||||
\(531\) | − | 97.7238i | − | 0.184037i | ||||||
\(532\) | 103.909 | − | 344.269i | 0.195317 | − | 0.647122i | ||||
\(533\) | 245.622 | 0.460830 | ||||||||
\(534\) | −278.643 | −0.521804 | ||||||||
\(535\) | 304.707i | 0.569545i | ||||||||
\(536\) | −203.812 | −0.380247 | ||||||||
\(537\) | 290.239i | 0.540481i | ||||||||
\(538\) | 55.4562i | 0.103078i | ||||||||
\(539\) | −204.418 | − | 135.764i | −0.379254 | − | 0.251882i | ||||
\(540\) | 23.2379 | 0.0430331 | ||||||||
\(541\) | −228.274 | −0.421949 | −0.210974 | − | 0.977492i | \(-0.567664\pi\) | ||||
−0.210974 | + | 0.977492i | \(0.567664\pi\) | |||||||
\(542\) | 422.950i | 0.780351i | ||||||||
\(543\) | −256.269 | −0.471950 | ||||||||
\(544\) | 111.672i | 0.205279i | ||||||||
\(545\) | − | 371.194i | − | 0.681090i | ||||||
\(546\) | 148.873 | + | 44.9334i | 0.272661 | + | 0.0822955i | ||||
\(547\) | 876.996 | 1.60328 | 0.801642 | − | 0.597805i | \(-0.203960\pi\) | ||||
0.801642 | + | 0.597805i | \(0.203960\pi\) | |||||||
\(548\) | 316.600 | 0.577737 | ||||||||
\(549\) | 250.605i | 0.456475i | ||||||||
\(550\) | −35.4123 | −0.0643860 | ||||||||
\(551\) | − | 572.986i | − | 1.03990i | ||||||
\(552\) | − | 200.704i | − | 0.363595i | ||||||
\(553\) | −204.026 | − | 61.5799i | −0.368944 | − | 0.111356i | ||||
\(554\) | 620.792 | 1.12056 | ||||||||
\(555\) | 173.318 | 0.312286 | ||||||||
\(556\) | − | 283.168i | − | 0.509296i | ||||||
\(557\) | 561.224 | 1.00758 | 0.503792 | − | 0.863825i | \(-0.331938\pi\) | ||||
0.503792 | + | 0.863825i | \(0.331938\pi\) | |||||||
\(558\) | 67.4644i | 0.120904i | ||||||||
\(559\) | − | 278.146i | − | 0.497578i | ||||||
\(560\) | −18.0911 | + | 59.9392i | −0.0323055 | + | 0.107034i | ||||
\(561\) | 171.237 | 0.305236 | ||||||||
\(562\) | 282.105 | 0.501967 | ||||||||
\(563\) | − | 890.386i | − | 1.58150i | −0.612137 | − | 0.790752i | \(-0.709690\pi\) | ||
0.612137 | − | 0.790752i | \(-0.290310\pi\) | |||||||
\(564\) | −201.413 | −0.357116 | ||||||||
\(565\) | 57.0280i | 0.100935i | ||||||||
\(566\) | − | 765.343i | − | 1.35220i | ||||||
\(567\) | −60.3127 | − | 18.2038i | −0.106372 | − | 0.0321055i | ||||
\(568\) | 70.3358 | 0.123831 | ||||||||
\(569\) | 138.453 | 0.243327 | 0.121663 | − | 0.992571i | \(-0.461177\pi\) | ||||
0.121663 | + | 0.992571i | \(0.461177\pi\) | |||||||
\(570\) | 140.690i | 0.246824i | ||||||||
\(571\) | 476.343 | 0.834225 | 0.417113 | − | 0.908855i | \(-0.363042\pi\) | ||||
0.417113 | + | 0.908855i | \(0.363042\pi\) | |||||||
\(572\) | − | 90.8390i | − | 0.158810i | ||||||
\(573\) | − | 85.7259i | − | 0.149609i | ||||||
\(574\) | 77.4693 | − | 256.670i | 0.134964 | − | 0.447161i | ||||
\(575\) | 204.843 | 0.356248 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | − | 678.464i | − | 1.17585i | −0.808916 | − | 0.587924i | \(-0.799945\pi\) | ||
0.808916 | − | 0.587924i | \(-0.200055\pi\) | |||||||
\(578\) | 142.419 | 0.246400 | ||||||||
\(579\) | − | 299.081i | − | 0.516547i | ||||||
\(580\) | 99.7602i | 0.172000i | ||||||||
\(581\) | −146.566 | + | 485.600i | −0.252264 | + | 0.835800i | ||||
\(582\) | 254.267 | 0.436885 | ||||||||
\(583\) | −328.628 | −0.563684 | ||||||||
\(584\) | 191.972i | 0.328720i | ||||||||
\(585\) | −60.8387 | −0.103998 | ||||||||
\(586\) | − | 535.643i | − | 0.914067i | ||||||
\(587\) | − | 48.9046i | − | 0.0833128i | −0.999132 | − | 0.0416564i | \(-0.986737\pi\) | ||
0.999132 | − | 0.0416564i | \(-0.0132635\pi\) | |||||||
\(588\) | 93.9089 | − | 141.397i | 0.159709 | − | 0.240471i | ||||
\(589\) | −408.451 | −0.693465 | ||||||||
\(590\) | −103.010 | −0.174593 | ||||||||
\(591\) | − | 131.020i | − | 0.221692i | ||||||
\(592\) | −179.003 | −0.302369 | ||||||||
\(593\) | 487.761i | 0.822531i | 0.911516 | + | 0.411266i | \(0.134913\pi\) | ||||
−0.911516 | + | 0.411266i | \(0.865087\pi\) | |||||||
\(594\) | 36.8015i | 0.0619555i | ||||||||
\(595\) | 295.815 | + | 89.2839i | 0.497167 | + | 0.150057i | ||||
\(596\) | −242.911 | −0.407569 | ||||||||
\(597\) | −255.685 | −0.428283 | ||||||||
\(598\) | 525.459i | 0.878695i | ||||||||
\(599\) | −1083.77 | −1.80931 | −0.904653 | − | 0.426149i | \(-0.859870\pi\) | ||||
−0.904653 | + | 0.426149i | \(0.859870\pi\) | |||||||
\(600\) | − | 24.4949i | − | 0.0408248i | ||||||
\(601\) | 274.481i | 0.456707i | 0.973578 | + | 0.228353i | \(0.0733342\pi\) | ||||
−0.973578 | + | 0.228353i | \(0.926666\pi\) | |||||||
\(602\) | −290.657 | − | 87.7273i | −0.482819 | − | 0.145726i | ||||
\(603\) | −216.175 | −0.358500 | ||||||||
\(604\) | −438.185 | −0.725472 | ||||||||
\(605\) | 214.482i | 0.354516i | ||||||||
\(606\) | 380.600 | 0.628052 | ||||||||
\(607\) | 941.550i | 1.55115i | 0.631253 | + | 0.775577i | \(0.282541\pi\) | ||||
−0.631253 | + | 0.775577i | \(0.717459\pi\) | |||||||
\(608\) | − | 145.304i | − | 0.238986i | ||||||
\(609\) | 78.1489 | − | 258.922i | 0.128323 | − | 0.425159i | ||||
\(610\) | 264.161 | 0.433050 | ||||||||
\(611\) | 527.316 | 0.863038 | ||||||||
\(612\) | 118.446i | 0.193539i | ||||||||
\(613\) | −658.706 | −1.07456 | −0.537281 | − | 0.843404i | \(-0.680548\pi\) | ||||
−0.537281 | + | 0.843404i | \(0.680548\pi\) | |||||||
\(614\) | − | 198.287i | − | 0.322942i | ||||||
\(615\) | 104.891i | 0.170555i | ||||||||
\(616\) | −94.9249 | − | 28.6506i | −0.154099 | − | 0.0465108i | ||||
\(617\) | 355.965 | 0.576929 | 0.288464 | − | 0.957491i | \(-0.406855\pi\) | ||||
0.288464 | + | 0.957491i | \(0.406855\pi\) | |||||||
\(618\) | −161.537 | −0.261387 | ||||||||
\(619\) | 214.933i | 0.347226i | 0.984814 | + | 0.173613i | \(0.0555442\pi\) | ||||
−0.984814 | + | 0.173613i | \(0.944456\pi\) | |||||||
\(620\) | 71.1137 | 0.114700 | ||||||||
\(621\) | − | 212.879i | − | 0.342800i | ||||||
\(622\) | 353.392i | 0.568154i | ||||||||
\(623\) | 230.087 | − | 762.323i | 0.369322 | − | 1.22363i | ||||
\(624\) | 62.8339 | 0.100695 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 732.413i | − | 1.16999i | ||||||
\(627\) | −222.808 | −0.355356 | ||||||||
\(628\) | 114.563i | 0.182425i | ||||||||
\(629\) | 883.421i | 1.40448i | ||||||||
\(630\) | −19.1885 | + | 63.5752i | −0.0304579 | + | 0.100913i | ||||
\(631\) | 589.714 | 0.934570 | 0.467285 | − | 0.884107i | \(-0.345232\pi\) | ||||
0.467285 | + | 0.884107i | \(0.345232\pi\) | |||||||
\(632\) | −86.1121 | −0.136253 | ||||||||
\(633\) | − | 271.728i | − | 0.429270i | ||||||
\(634\) | 254.619 | 0.401608 | ||||||||
\(635\) | 514.980i | 0.810993i | ||||||||
\(636\) | − | 227.314i | − | 0.357412i | ||||||
\(637\) | −245.861 | + | 370.189i | −0.385967 | + | 0.581144i | ||||
\(638\) | −157.989 | −0.247631 | ||||||||
\(639\) | 74.6024 | 0.116749 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | −675.508 | −1.05383 | −0.526917 | − | 0.849917i | \(-0.676652\pi\) | ||||
−0.526917 | + | 0.849917i | \(0.676652\pi\) | |||||||
\(642\) | − | 333.789i | − | 0.519921i | ||||||
\(643\) | − | 733.747i | − | 1.14113i | −0.821252 | − | 0.570565i | \(-0.806724\pi\) | ||
0.821252 | − | 0.570565i | \(-0.193276\pi\) | |||||||
\(644\) | 549.095 | + | 165.730i | 0.852631 | + | 0.257345i | ||||
\(645\) | 118.781 | 0.184156 | ||||||||
\(646\) | −717.109 | −1.11008 | ||||||||
\(647\) | 645.060i | 0.997002i | 0.866889 | + | 0.498501i | \(0.166116\pi\) | ||||
−0.866889 | + | 0.498501i | \(0.833884\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | − | 163.135i | − | 0.251364i | ||||||
\(650\) | 64.1296i | 0.0986609i | ||||||||
\(651\) | −184.572 | − | 55.7082i | −0.283520 | − | 0.0855732i | ||||
\(652\) | −17.0459 | −0.0261441 | ||||||||
\(653\) | −610.744 | −0.935289 | −0.467644 | − | 0.883917i | \(-0.654897\pi\) | ||||
−0.467644 | + | 0.883917i | \(0.654897\pi\) | |||||||
\(654\) | 406.623i | 0.621747i | ||||||||
\(655\) | −91.4836 | −0.139670 | ||||||||
\(656\) | − | 108.331i | − | 0.165139i | ||||||
\(657\) | 203.617i | 0.309920i | ||||||||
\(658\) | 166.315 | − | 551.035i | 0.252759 | − | 0.837439i | ||||
\(659\) | 220.888 | 0.335187 | 0.167594 | − | 0.985856i | \(-0.446400\pi\) | ||||
0.167594 | + | 0.985856i | \(0.446400\pi\) | |||||||
\(660\) | 38.7922 | 0.0587761 | ||||||||
\(661\) | 306.043i | 0.463000i | 0.972835 | + | 0.231500i | \(0.0743634\pi\) | ||||
−0.972835 | + | 0.231500i | \(0.925637\pi\) | |||||||
\(662\) | −114.591 | −0.173099 | ||||||||
\(663\) | − | 310.100i | − | 0.467723i | ||||||
\(664\) | 204.954i | 0.308666i | ||||||||
\(665\) | −384.905 | − | 116.173i | −0.578804 | − | 0.174697i | ||||
\(666\) | −189.861 | −0.285076 | ||||||||
\(667\) | 913.888 | 1.37015 | ||||||||
\(668\) | 516.297i | 0.772899i | ||||||||
\(669\) | 104.621 | 0.156384 | ||||||||
\(670\) | 227.869i | 0.340103i | ||||||||
\(671\) | 418.348i | 0.623469i | ||||||||
\(672\) | 19.8178 | − | 65.6601i | 0.0294908 | − | 0.0977085i | ||||
\(673\) | −1025.63 | −1.52397 | −0.761986 | − | 0.647594i | \(-0.775775\pi\) | ||||
−0.761986 | + | 0.647594i | \(0.775775\pi\) | |||||||
\(674\) | 527.412 | 0.782510 | ||||||||
\(675\) | − | 25.9808i | − | 0.0384900i | ||||||
\(676\) | 173.496 | 0.256651 | ||||||||
\(677\) | 622.692i | 0.919781i | 0.887976 | + | 0.459891i | \(0.152111\pi\) | ||||
−0.887976 | + | 0.459891i | \(0.847889\pi\) | |||||||
\(678\) | − | 62.4711i | − | 0.0921402i | ||||||
\(679\) | −209.959 | + | 695.634i | −0.309218 | + | 1.02450i | ||||
\(680\) | 124.853 | 0.183607 | ||||||||
\(681\) | −543.190 | −0.797636 | ||||||||
\(682\) | 112.622i | 0.165135i | ||||||||
\(683\) | 170.676 | 0.249891 | 0.124946 | − | 0.992164i | \(-0.460124\pi\) | ||||
0.124946 | + | 0.992164i | \(0.460124\pi\) | |||||||
\(684\) | − | 154.118i | − | 0.225319i | ||||||
\(685\) | − | 353.970i | − | 0.516744i | ||||||
\(686\) | 309.295 | + | 373.677i | 0.450867 | + | 0.544719i | ||||
\(687\) | −191.163 | −0.278258 | ||||||||
\(688\) | −122.676 | −0.178308 | ||||||||
\(689\) | 595.126i | 0.863753i | ||||||||
\(690\) | −224.394 | −0.325209 | ||||||||
\(691\) | − | 1353.09i | − | 1.95816i | −0.203481 | − | 0.979079i | \(-0.565226\pi\) | ||
0.203481 | − | 0.979079i | \(-0.434774\pi\) | |||||||
\(692\) | 654.499i | 0.945808i | ||||||||
\(693\) | −100.683 | − | 30.3886i | −0.145286 | − | 0.0438508i | ||||
\(694\) | −587.226 | −0.846147 | ||||||||
\(695\) | −316.592 | −0.455528 | ||||||||
\(696\) | − | 109.282i | − | 0.157014i | ||||||
\(697\) | −534.642 | −0.767061 | ||||||||
\(698\) | 758.312i | 1.08641i | ||||||||
\(699\) | − | 66.5223i | − | 0.0951678i | ||||||
\(700\) | 67.0141 | + | 20.2265i | 0.0957344 | + | 0.0288949i | ||||
\(701\) | −631.426 | −0.900750 | −0.450375 | − | 0.892840i | \(-0.648710\pi\) | ||||
−0.450375 | + | 0.892840i | \(0.648710\pi\) | |||||||
\(702\) | 66.6454 | 0.0949365 | ||||||||
\(703\) | − | 1149.48i | − | 1.63510i | ||||||
\(704\) | −40.0644 | −0.0569097 | ||||||||
\(705\) | 225.187i | 0.319414i | ||||||||
\(706\) | 588.638i | 0.833764i | ||||||||
\(707\) | −314.277 | + | 1041.26i | −0.444522 | + | 1.47279i | ||||
\(708\) | 112.842 | 0.159381 | ||||||||
\(709\) | −294.907 | −0.415947 | −0.207974 | − | 0.978134i | \(-0.566687\pi\) | ||||
−0.207974 | + | 0.978134i | \(0.566687\pi\) | |||||||
\(710\) | − | 78.6378i | − | 0.110757i | ||||||
\(711\) | −91.3357 | −0.128461 | ||||||||
\(712\) | − | 321.749i | − | 0.451895i | ||||||
\(713\) | − | 651.462i | − | 0.913692i | ||||||
\(714\) | −324.049 | − | 97.8056i | −0.453850 | − | 0.136983i | ||||
\(715\) | −101.561 | −0.142044 | ||||||||
\(716\) | −335.139 | −0.468071 | ||||||||
\(717\) | 216.730i | 0.302273i | ||||||||
\(718\) | 382.634 | 0.532917 | ||||||||
\(719\) | 884.788i | 1.23058i | 0.788301 | + | 0.615290i | \(0.210961\pi\) | ||||
−0.788301 | + | 0.615290i | \(0.789039\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | 133.388 | − | 441.939i | 0.185004 | − | 0.612953i | ||||
\(722\) | 422.548 | 0.585247 | ||||||||
\(723\) | 267.818 | 0.370427 | ||||||||
\(724\) | − | 295.914i | − | 0.408721i | ||||||
\(725\) | 111.535 | 0.153842 | ||||||||
\(726\) | − | 234.954i | − | 0.323627i | ||||||
\(727\) | − | 361.739i | − | 0.497578i | −0.968558 | − | 0.248789i | \(-0.919967\pi\) | ||
0.968558 | − | 0.248789i | \(-0.0800325\pi\) | |||||||
\(728\) | −51.8846 | + | 171.903i | −0.0712700 | + | 0.236131i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 214.632 | 0.294016 | ||||||||
\(731\) | 605.436i | 0.828230i | ||||||||
\(732\) | −289.374 | −0.395319 | ||||||||
\(733\) | − | 819.923i | − | 1.11859i | −0.828970 | − | 0.559293i | \(-0.811073\pi\) | ||
0.828970 | − | 0.559293i | \(-0.188927\pi\) | |||||||
\(734\) | − | 855.633i | − | 1.16571i | ||||||
\(735\) | −158.087 | − | 104.993i | −0.215084 | − | 0.142848i | ||||
\(736\) | 231.753 | 0.314882 | ||||||||
\(737\) | −360.873 | −0.489651 | ||||||||
\(738\) | − | 114.903i | − | 0.155695i | ||||||
\(739\) | −802.663 | −1.08615 | −0.543074 | − | 0.839685i | \(-0.682740\pi\) | ||||
−0.543074 | + | 0.839685i | \(0.682740\pi\) | |||||||
\(740\) | 200.131i | 0.270447i | ||||||||
\(741\) | 403.493i | 0.544525i | ||||||||
\(742\) | 621.894 | + | 187.703i | 0.838132 | + | 0.252968i | ||||
\(743\) | −1061.48 | −1.42865 | −0.714323 | − | 0.699816i | \(-0.753265\pi\) | ||||
−0.714323 | + | 0.699816i | \(0.753265\pi\) | |||||||
\(744\) | −77.9012 | −0.104706 | ||||||||
\(745\) | 271.583i | 0.364541i | ||||||||
\(746\) | 30.4231 | 0.0407816 | ||||||||
\(747\) | 217.387i | 0.291013i | ||||||||
\(748\) | 197.728i | 0.264342i | ||||||||
\(749\) | 913.194 | + | 275.624i | 1.21922 | + | 0.367989i | ||||
\(750\) | −27.3861 | −0.0365148 | ||||||||
\(751\) | −1044.41 | −1.39069 | −0.695346 | − | 0.718675i | \(-0.744749\pi\) | ||||
−0.695346 | + | 0.718675i | \(0.744749\pi\) | |||||||
\(752\) | − | 232.572i | − | 0.309272i | ||||||
\(753\) | 264.405 | 0.351136 | ||||||||
\(754\) | 286.108i | 0.379454i | ||||||||
\(755\) | 489.906i | 0.648882i | ||||||||
\(756\) | 21.0200 | − | 69.6431i | 0.0278042 | − | 0.0921205i | ||||
\(757\) | −1267.83 | −1.67481 | −0.837406 | − | 0.546581i | \(-0.815929\pi\) | ||||
−0.837406 | + | 0.546581i | \(0.815929\pi\) | |||||||
\(758\) | −636.202 | −0.839316 | ||||||||
\(759\) | − | 355.370i | − | 0.468208i | ||||||
\(760\) | −162.455 | −0.213756 | ||||||||
\(761\) | − | 257.020i | − | 0.337740i | −0.985638 | − | 0.168870i | \(-0.945988\pi\) | ||
0.985638 | − | 0.168870i | \(-0.0540118\pi\) | |||||||
\(762\) | − | 564.133i | − | 0.740332i | ||||||
\(763\) | −1112.45 | − | 335.765i | −1.45800 | − | 0.440060i | ||||
\(764\) | 98.9878 | 0.129565 | ||||||||
\(765\) | 132.426 | 0.173106 | ||||||||
\(766\) | − | 793.029i | − | 1.03529i | ||||||
\(767\) | −295.428 | −0.385174 | ||||||||
\(768\) | − | 27.7128i | − | 0.0360844i | ||||||
\(769\) | 1192.50i | 1.55071i | 0.631524 | + | 0.775357i | \(0.282430\pi\) | ||||
−0.631524 | + | 0.775357i | \(0.717570\pi\) | |||||||
\(770\) | −32.0324 | + | 106.129i | −0.0416005 | + | 0.137830i | ||||
\(771\) | 34.9038 | 0.0452708 | ||||||||
\(772\) | 345.349 | 0.447343 | ||||||||
\(773\) | 1121.01i | 1.45021i | 0.688639 | + | 0.725104i | \(0.258208\pi\) | ||||
−0.688639 | + | 0.725104i | \(0.741792\pi\) | |||||||
\(774\) | −130.118 | −0.168111 | ||||||||
\(775\) | − | 79.5075i | − | 0.102590i | ||||||
\(776\) | 293.602i | 0.378353i | ||||||||
\(777\) | 156.776 | − | 519.429i | 0.201771 | − | 0.668506i | ||||
\(778\) | 823.386 | 1.05834 | ||||||||
\(779\) | 695.659 | 0.893015 | ||||||||
\(780\) | − | 70.2504i | − | 0.0900647i | ||||||
\(781\) | 124.538 | 0.159459 | ||||||||
\(782\) | − | 1143.76i | − | 1.46261i | ||||||
\(783\) | − | 115.911i | − | 0.148034i | ||||||
\(784\) | 163.271 | + | 108.437i | 0.208254 | + | 0.138312i | ||||
\(785\) | 128.085 | 0.163166 | ||||||||
\(786\) | 100.215 | 0.127500 | ||||||||
\(787\) | − | 1207.04i | − | 1.53372i | −0.641813 | − | 0.766861i | \(-0.721817\pi\) | ||
0.641813 | − | 0.766861i | \(-0.278183\pi\) | |||||||
\(788\) | 151.289 | 0.191991 | ||||||||
\(789\) | 555.466i | 0.704013i | ||||||||
\(790\) | 96.2762i | 0.121869i | ||||||||
\(791\) | 170.911 | + | 51.5850i | 0.216069 | + | 0.0652149i | ||||
\(792\) | −42.4948 | −0.0536550 | ||||||||
\(793\) | 757.603 | 0.955363 | ||||||||
\(794\) | 1027.51i | 1.29410i | ||||||||
\(795\) | −254.145 | −0.319679 | ||||||||
\(796\) | − | 295.240i | − | 0.370904i | ||||||
\(797\) | − | 378.901i | − | 0.475409i | −0.971338 | − | 0.237704i | \(-0.923605\pi\) | ||
0.971338 | − | 0.237704i | \(-0.0763950\pi\) | |||||||
\(798\) | 421.642 | + | 127.262i | 0.528373 | + | 0.159476i | ||||
\(799\) | −1147.80 | −1.43655 | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | − | 341.267i | − | 0.426051i | ||||||
\(802\) | 46.3808 | 0.0578314 | ||||||||
\(803\) | 339.909i | 0.423299i | ||||||||
\(804\) | − | 249.618i | − | 0.310470i | ||||||
\(805\) | 185.292 | − | 613.906i | 0.230176 | − | 0.762617i | ||||
\(806\) | 203.951 | 0.253041 | ||||||||
\(807\) | −67.9196 | −0.0841631 | ||||||||
\(808\) | 439.479i | 0.543909i | ||||||||
\(809\) | −403.691 | −0.499000 | −0.249500 | − | 0.968375i | \(-0.580266\pi\) | ||||
−0.249500 | + | 0.968375i | \(0.580266\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | 109.713i | 0.135281i | 0.997710 | + | 0.0676407i | \(0.0215471\pi\) | ||||
−0.997710 | + | 0.0676407i | \(0.978453\pi\) | |||||||
\(812\) | 298.977 | + | 90.2386i | 0.368199 | + | 0.111131i | ||||
\(813\) | −518.006 | −0.637154 | ||||||||
\(814\) | −316.945 | −0.389367 | ||||||||
\(815\) | 19.0579i | 0.0233840i | ||||||||
\(816\) | −136.769 | −0.167610 | ||||||||
\(817\) | − | 787.774i | − | 0.964228i | ||||||
\(818\) | − | 901.899i | − | 1.10257i | ||||||
\(819\) | −55.0319 | + | 182.331i | −0.0671940 | + | 0.222627i | ||||
\(820\) | −121.118 | −0.147705 | ||||||||
\(821\) | 426.293 | 0.519236 | 0.259618 | − | 0.965711i | \(-0.416403\pi\) | ||||
0.259618 | + | 0.965711i | \(0.416403\pi\) | |||||||
\(822\) | 387.754i | 0.471721i | ||||||||
\(823\) | −708.932 | −0.861400 | −0.430700 | − | 0.902495i | \(-0.641733\pi\) | ||||
−0.430700 | + | 0.902495i | \(0.641733\pi\) | |||||||
\(824\) | − | 186.527i | − | 0.226367i | ||||||
\(825\) | − | 43.3710i | − | 0.0525710i | ||||||
\(826\) | −93.1781 | + | 308.717i | −0.112806 | + | 0.373749i | ||||
\(827\) | −813.963 | −0.984236 | −0.492118 | − | 0.870528i | \(-0.663777\pi\) | ||||
−0.492118 | + | 0.870528i | \(0.663777\pi\) | |||||||
\(828\) | 245.811 | 0.296874 | ||||||||
\(829\) | 92.7107i | 0.111834i | 0.998435 | + | 0.0559172i | \(0.0178083\pi\) | ||||
−0.998435 | + | 0.0559172i | \(0.982192\pi\) | |||||||
\(830\) | 229.146 | 0.276079 | ||||||||
\(831\) | 760.312i | 0.914936i | ||||||||
\(832\) | 72.5543i | 0.0872047i | ||||||||
\(833\) | 535.161 | − | 805.783i | 0.642450 | − | 0.967326i | ||||
\(834\) | 346.809 | 0.415838 | ||||||||
\(835\) | 577.237 | 0.691302 | ||||||||
\(836\) | − | 257.277i | − | 0.307748i | ||||||
\(837\) | −82.6267 | −0.0987176 | ||||||||
\(838\) | 487.247i | 0.581440i | ||||||||
\(839\) | 852.206i | 1.01574i | 0.861434 | + | 0.507870i | \(0.169567\pi\) | ||||
−0.861434 | + | 0.507870i | \(0.830433\pi\) | |||||||
\(840\) | −73.4103 | − | 22.1570i | −0.0873932 | − | 0.0263774i | ||||
\(841\) | −343.395 | −0.408318 | ||||||||
\(842\) | −410.704 | −0.487772 | ||||||||
\(843\) | 345.507i | 0.409854i | ||||||||
\(844\) | 313.764 | 0.371759 | ||||||||
\(845\) | − | 193.974i | − | 0.229555i | ||||||
\(846\) | − | 246.680i | − | 0.291584i | ||||||
\(847\) | 642.795 | + | 194.011i | 0.758908 | + | 0.229057i | ||||
\(848\) | 262.479 | 0.309528 | ||||||||
\(849\) | 937.349 | 1.10406 | ||||||||
\(850\) | − | 139.590i | − | 0.164223i | ||||||
\(851\) | 1833.37 | 2.15437 | ||||||||
\(852\) | 86.1434i | 0.101107i | ||||||||
\(853\) | − | 1472.75i | − | 1.72655i | −0.504733 | − | 0.863275i | \(-0.668409\pi\) | ||
0.504733 | − | 0.863275i | \(-0.331591\pi\) | |||||||
\(854\) | 238.948 | − | 791.680i | 0.279798 | − | 0.927025i | ||||
\(855\) | −172.309 | −0.201531 | ||||||||
\(856\) | 385.427 | 0.450265 | ||||||||
\(857\) | − | 882.824i | − | 1.03013i | −0.857150 | − | 0.515066i | \(-0.827767\pi\) | ||
0.857150 | − | 0.515066i | \(-0.172233\pi\) | |||||||
\(858\) | 111.255 | 0.129667 | ||||||||
\(859\) | − | 700.963i | − | 0.816023i | −0.912977 | − | 0.408011i | \(-0.866222\pi\) | ||
0.912977 | − | 0.408011i | \(-0.133778\pi\) | |||||||
\(860\) | 137.156i | 0.159484i | ||||||||
\(861\) | 314.356 | + | 94.8801i | 0.365105 | + | 0.110198i | ||||
\(862\) | 303.744 | 0.352372 | ||||||||
\(863\) | 1246.07 | 1.44388 | 0.721938 | − | 0.691957i | \(-0.243251\pi\) | ||||
0.721938 | + | 0.691957i | \(0.243251\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 731.753 | 0.845957 | ||||||||
\(866\) | 601.099i | 0.694109i | ||||||||
\(867\) | 174.427i | 0.201185i | ||||||||
\(868\) | 64.3263 | − | 213.125i | 0.0741086 | − | 0.245536i | ||||
\(869\) | −152.471 | −0.175456 | ||||||||
\(870\) | −122.181 | −0.140438 | ||||||||
\(871\) | 653.519i | 0.750309i | ||||||||
\(872\) | −469.527 | −0.538449 | ||||||||
\(873\) | 311.412i | 0.356715i | ||||||||
\(874\) | 1488.22i | 1.70277i | ||||||||
\(875\) | 22.6139 | − | 74.9240i | 0.0258444 | − | 0.0856275i | ||||
\(876\) | −235.117 | −0.268399 | ||||||||
\(877\) | 957.986 | 1.09234 | 0.546172 | − | 0.837673i | \(-0.316084\pi\) | ||||
0.546172 | + | 0.837673i | \(0.316084\pi\) | |||||||
\(878\) | 288.783i | 0.328910i | ||||||||
\(879\) | 656.026 | 0.746333 | ||||||||
\(880\) | 44.7934i | 0.0509016i | ||||||||
\(881\) | 865.707i | 0.982642i | 0.870979 | + | 0.491321i | \(0.163486\pi\) | ||||
−0.870979 | + | 0.491321i | \(0.836514\pi\) | |||||||
\(882\) | 173.175 | + | 115.014i | 0.196344 | + | 0.130402i | ||||
\(883\) | 985.817 | 1.11644 | 0.558220 | − | 0.829693i | \(-0.311484\pi\) | ||||
0.558220 | + | 0.829693i | \(0.311484\pi\) | |||||||
\(884\) | 358.073 | 0.405060 | ||||||||
\(885\) | − | 126.161i | − | 0.142555i | ||||||
\(886\) | −390.843 | −0.441132 | ||||||||
\(887\) | − | 443.357i | − | 0.499838i | −0.968267 | − | 0.249919i | \(-0.919596\pi\) | ||
0.968267 | − | 0.249919i | \(-0.0804040\pi\) | |||||||
\(888\) | − | 219.232i | − | 0.246883i | ||||||
\(889\) | 1543.38 | + | 465.828i | 1.73608 | + | 0.523991i | ||||
\(890\) | −359.727 | −0.404187 | ||||||||
\(891\) | −45.0725 | −0.0505864 | ||||||||
\(892\) | 120.806i | 0.135433i | ||||||||
\(893\) | 1493.48 | 1.67243 | ||||||||
\(894\) | − | 297.504i | − | 0.332779i | ||||||
\(895\) | 374.696i | 0.418655i | ||||||||
\(896\) | 75.8178 | + | 22.8836i | 0.0846181 | + | 0.0255398i | ||||
\(897\) | −643.554 | −0.717451 | ||||||||
\(898\) | −276.182 | −0.307552 | ||||||||
\(899\) | − | 354.716i | − | 0.394567i | ||||||
\(900\) | 30.0000 | 0.0333333 | ||||||||
\(901\) | − | 1295.40i | − | 1.43774i | ||||||
\(902\) | − | 191.813i | − | 0.212653i | ||||||
\(903\) | 107.444 | − | 355.981i | 0.118985 | − | 0.394220i | ||||
\(904\) | 72.1354 | 0.0797958 | ||||||||
\(905\) | −330.842 | −0.365571 | ||||||||
\(906\) | − | 536.665i | − | 0.592346i | ||||||
\(907\) | 49.0514 | 0.0540810 | 0.0270405 | − | 0.999634i | \(-0.491392\pi\) | ||||
0.0270405 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(908\) | − | 627.222i | − | 0.690773i | ||||||
\(909\) | 466.138i | 0.512803i | ||||||||
\(910\) | 192.194 | + | 58.0087i | 0.211202 | + | 0.0637458i | ||||
\(911\) | −290.836 | −0.319249 | −0.159624 | − | 0.987178i | \(-0.551028\pi\) | ||||
−0.159624 | + | 0.987178i | \(0.551028\pi\) | |||||||
\(912\) | 177.960 | 0.195132 | ||||||||
\(913\) | 362.895i | 0.397476i | ||||||||
\(914\) | −14.6269 | −0.0160032 | ||||||||
\(915\) | 323.529i | 0.353584i | ||||||||
\(916\) | − | 220.736i | − | 0.240979i | ||||||
\(917\) | −82.7519 | + | 274.173i | −0.0902420 | + | 0.298989i | ||||
\(918\) | −145.066 | −0.158024 | ||||||||
\(919\) | −721.872 | −0.785498 | −0.392749 | − | 0.919646i | \(-0.628476\pi\) | ||||
−0.392749 | + | 0.919646i | \(0.628476\pi\) | |||||||
\(920\) | − | 259.108i | − | 0.281639i | ||||||
\(921\) | 242.851 | 0.263681 | ||||||||
\(922\) | − | 746.100i | − | 0.809219i | ||||||
\(923\) | − | 225.530i | − | 0.244345i | ||||||
\(924\) | 35.0897 | − | 116.259i | 0.0379759 | − | 0.125821i | ||||
\(925\) | 223.753 | 0.241895 | ||||||||
\(926\) | −1128.40 | −1.21857 | ||||||||
\(927\) | − | 197.841i | − | 0.213421i | ||||||
\(928\) | 126.188 | 0.135978 | ||||||||
\(929\) | 617.161i | 0.664329i | 0.943222 | + | 0.332164i | \(0.107779\pi\) | ||||
−0.943222 | + | 0.332164i | \(0.892221\pi\) | |||||||
\(930\) | 87.0962i | 0.0936518i | ||||||||
\(931\) | −696.335 | + | 1048.46i | −0.747943 | + | 1.12616i | ||||
\(932\) | 76.8133 | 0.0824177 | ||||||||
\(933\) | −432.815 | −0.463896 | ||||||||
\(934\) | − | 239.923i | − | 0.256877i | ||||||
\(935\) | 221.066 | 0.236435 | ||||||||
\(936\) | 76.9555i | 0.0822174i | ||||||||
\(937\) | − | 224.045i | − | 0.239108i | −0.992828 | − | 0.119554i | \(-0.961853\pi\) | ||
0.992828 | − | 0.119554i | \(-0.0381465\pi\) | |||||||
\(938\) | 682.915 | + | 206.120i | 0.728054 | + | 0.219744i | ||||
\(939\) | 897.019 | 0.955292 | ||||||||
\(940\) | −260.024 | −0.276621 | ||||||||
\(941\) | − | 522.371i | − | 0.555124i | −0.960708 | − | 0.277562i | \(-0.910474\pi\) | ||
0.960708 | − | 0.277562i | \(-0.0895264\pi\) | |||||||
\(942\) | −140.310 | −0.148949 | ||||||||
\(943\) | 1109.55i | 1.17661i | ||||||||
\(944\) | 130.298i | 0.138028i | ||||||||
\(945\) | −77.8634 | − | 23.5010i | −0.0823951 | − | 0.0248688i | ||||
\(946\) | −217.212 | −0.229611 | ||||||||
\(947\) | −728.427 | −0.769194 | −0.384597 | − | 0.923084i | \(-0.625660\pi\) | ||||
−0.384597 | + | 0.923084i | \(0.625660\pi\) | |||||||
\(948\) | − | 105.465i | − | 0.111250i | ||||||
\(949\) | 615.555 | 0.648636 | ||||||||
\(950\) | 181.630i | 0.191189i | ||||||||
\(951\) | 311.844i | 0.327911i | ||||||||
\(952\) | 112.936 | − | 374.179i | 0.118630 | − | 0.393045i | ||||
\(953\) | −1169.38 | −1.22705 | −0.613527 | − | 0.789674i | \(-0.710250\pi\) | ||||
−0.613527 | + | 0.789674i | \(0.710250\pi\) | |||||||
\(954\) | 278.402 | 0.291825 | ||||||||
\(955\) | − | 110.672i | − | 0.115887i | ||||||
\(956\) | −250.258 | −0.261776 | ||||||||
\(957\) | − | 193.496i | − | 0.202190i | ||||||
\(958\) | 995.991i | 1.03966i | ||||||||
\(959\) | −1060.83 | − | 320.185i | −1.10619 | − | 0.333874i | ||||
\(960\) | −30.9839 | −0.0322749 | ||||||||
\(961\) | 708.142 | 0.736880 | ||||||||
\(962\) | 573.968i | 0.596640i | ||||||||
\(963\) | 408.807 | 0.424514 | ||||||||
\(964\) | 309.250i | 0.320799i | ||||||||
\(965\) | − | 386.112i | − | 0.400116i | ||||||
\(966\) | −202.977 | + | 672.501i | −0.210121 | + | 0.696170i | ||||
\(967\) | 771.440 | 0.797767 | 0.398883 | − | 0.917002i | \(-0.369398\pi\) | ||||
0.398883 | + | 0.917002i | \(0.369398\pi\) | |||||||
\(968\) | 271.301 | 0.280270 | ||||||||
\(969\) | − | 878.275i | − | 0.906373i | ||||||
\(970\) | 328.257 | 0.338410 | ||||||||
\(971\) | − | 1380.71i | − | 1.42195i | −0.703220 | − | 0.710973i | \(-0.748255\pi\) | ||
0.703220 | − | 0.710973i | \(-0.251745\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −286.375 | + | 948.814i | −0.294321 | + | 0.975143i | ||||
\(974\) | 94.4647 | 0.0969864 | ||||||||
\(975\) | −78.5424 | −0.0805563 | ||||||||
\(976\) | − | 334.140i | − | 0.342356i | ||||||
\(977\) | 974.771 | 0.997718 | 0.498859 | − | 0.866683i | \(-0.333752\pi\) | ||||
0.498859 | + | 0.866683i | \(0.333752\pi\) | |||||||
\(978\) | − | 20.8769i | − | 0.0213466i | ||||||
\(979\) | − | 569.694i | − | 0.581915i | ||||||
\(980\) | 121.236 | − | 182.543i | 0.123710 | − | 0.186268i | ||||
\(981\) | −498.009 | −0.507655 | ||||||||
\(982\) | −772.333 | −0.786490 | ||||||||
\(983\) | − | 206.961i | − | 0.210540i | −0.994444 | − | 0.105270i | \(-0.966429\pi\) | ||
0.994444 | − | 0.105270i | \(-0.0335708\pi\) | |||||||
\(984\) | 132.678 | 0.134836 | ||||||||
\(985\) | − | 169.146i | − | 0.171722i | ||||||
\(986\) | − | 622.767i | − | 0.631610i | ||||||
\(987\) | 674.877 | + | 203.694i | 0.683766 | + | 0.206377i | ||||
\(988\) | −465.913 | −0.471572 | ||||||||
\(989\) | 1256.47 | 1.27044 | ||||||||
\(990\) | 47.5106i | 0.0479905i | ||||||||
\(991\) | −413.701 | −0.417459 | −0.208729 | − | 0.977973i | \(-0.566933\pi\) | ||||
−0.208729 | + | 0.977973i | \(0.566933\pi\) | |||||||
\(992\) | − | 89.9525i | − | 0.0906779i | ||||||
\(993\) | − | 140.345i | − | 0.141335i | ||||||
\(994\) | −235.675 | − | 71.1322i | −0.237097 | − | 0.0715616i | ||||
\(995\) | −330.088 | −0.331747 | ||||||||
\(996\) | −251.017 | −0.252025 | ||||||||
\(997\) | − | 542.511i | − | 0.544143i | −0.962277 | − | 0.272072i | \(-0.912291\pi\) | ||
0.962277 | − | 0.272072i | \(-0.0877088\pi\) | |||||||
\(998\) | −1009.83 | −1.01186 | ||||||||
\(999\) | − | 232.531i | − | 0.232764i |
(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 | 210.3.f.a.181.1 | ✓ | 8 | |
3.2 | odd | 2 | 630.3.f.c.181.7 | 8 | |||
4.3 | odd | 2 | 1680.3.s.a.1441.6 | 8 | |||
5.2 | odd | 4 | 1050.3.h.b.349.3 | 16 | |||
5.3 | odd | 4 | 1050.3.h.b.349.14 | 16 | |||
5.4 | even | 2 | 1050.3.f.b.601.8 | 8 | |||
7.6 | odd | 2 | inner | 210.3.f.a.181.4 | yes | 8 | |
21.20 | even | 2 | 630.3.f.c.181.5 | 8 | |||
28.27 | even | 2 | 1680.3.s.a.1441.4 | 8 | |||
35.13 | even | 4 | 1050.3.h.b.349.11 | 16 | |||
35.27 | even | 4 | 1050.3.h.b.349.6 | 16 | |||
35.34 | odd | 2 | 1050.3.f.b.601.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.f.a.181.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
210.3.f.a.181.4 | yes | 8 | 7.6 | odd | 2 | inner | |
630.3.f.c.181.5 | 8 | 21.20 | even | 2 | |||
630.3.f.c.181.7 | 8 | 3.2 | odd | 2 | |||
1050.3.f.b.601.6 | 8 | 35.34 | odd | 2 | |||
1050.3.f.b.601.8 | 8 | 5.4 | even | 2 | |||
1050.3.h.b.349.3 | 16 | 5.2 | odd | 4 | |||
1050.3.h.b.349.6 | 16 | 35.27 | even | 4 | |||
1050.3.h.b.349.11 | 16 | 35.13 | even | 4 | |||
1050.3.h.b.349.14 | 16 | 5.3 | odd | 4 | |||
1680.3.s.a.1441.4 | 8 | 28.27 | even | 2 | |||
1680.3.s.a.1441.6 | 8 | 4.3 | odd | 2 |