Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(445,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.445");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.s (of order \(6\), 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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 445.6 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.6 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −2.67140 | + | 1.36514i | −0.890467 | + | 0.455047i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.45215 | − | 7.71135i | −0.890430 | − | 1.54227i | −0.839361 | − | 0.543575i | \(-0.817070\pi\) |
−0.0510696 | − | 0.998695i | \(-0.516263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.28143 | − | 3.95155i | −0.325918 | − | 0.564507i | 0.655779 | − | 0.754953i | \(-0.272340\pi\) |
−0.981698 | + | 0.190445i | \(0.939007\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.27278 | − | 7.29368i | 0.585864 | − | 0.810409i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.526632 | − | 0.912153i | −0.0478756 | − | 0.0829230i | 0.841095 | − | 0.540888i | \(-0.181912\pi\) |
−0.888970 | + | 0.457965i | \(0.848578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 16.8563i | − | 1.29664i | −0.761367 | − | 0.648321i | \(-0.775471\pi\) | ||
0.761367 | − | 0.648321i | \(-0.224529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 22.4206 | + | 14.5223i | 1.49470 | + | 0.968154i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.48650 | − | 6.03879i | 0.205088 | − | 0.355223i | −0.745073 | − | 0.666983i | \(-0.767585\pi\) |
0.950161 | + | 0.311760i | \(0.100919\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.6720 | − | 6.97862i | 0.930104 | − | 0.367296i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.4890 | + | 7.44171i | 0.547097 | + | 0.354367i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.67438 | −0.377147 | −0.188573 | − | 0.982059i | \(-0.560386\pi\) | ||||
−0.188573 | + | 0.982059i | \(0.560386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27.1433 | + | 47.0136i | −1.08573 | + | 1.88054i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.12881 | + | 26.6824i | −0.152919 | + | 0.988239i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −32.0106 | − | 18.4813i | −1.10381 | − | 0.637287i | −0.166593 | − | 0.986026i | \(-0.553277\pi\) |
−0.937220 | + | 0.348739i | \(0.886610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.57498 | − | 5.52812i | −0.308870 | − | 0.178326i | 0.337551 | − | 0.941307i | \(-0.390402\pi\) |
−0.646421 | + | 0.762981i | \(0.723735\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.65206 | + | 1.71780i | 0.0803656 | + | 0.0520546i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −20.3145 | + | 35.1858i | −0.580415 | + | 1.00531i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.0819i | − | 0.299510i | −0.988723 | − | 0.149755i | \(-0.952152\pi\) | ||
0.988723 | − | 0.149755i | \(-0.0478484\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 23.0113 | + | 45.0301i | 0.590033 | + | 1.15462i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.4835 | + | 10.6715i | −0.450818 | + | 0.260280i | −0.708176 | − | 0.706036i | \(-0.750482\pi\) |
0.257357 | + | 0.966316i | \(0.417148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.1871 | 1.19040 | 0.595199 | − | 0.803578i | \(-0.297073\pi\) | ||||
0.595199 | + | 0.803578i | \(0.297073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −79.7193 | − | 8.18769i | −1.77154 | − | 0.181949i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.8872 | + | 24.0533i | −0.295472 | + | 0.511772i | −0.975094 | − | 0.221790i | \(-0.928810\pi\) |
0.679623 | + | 0.733562i | \(0.262143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.0902 | − | 24.4049i | 0.287554 | − | 0.498059i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.07004 | + | 20.8916i | −0.0209811 | + | 0.409639i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4429 | + | 6.60656i | −0.215904 | + | 0.124652i | −0.604052 | − | 0.796945i | \(-0.706448\pi\) |
0.388148 | + | 0.921597i | \(0.373115\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.68929 | + | 8.12209i | −0.0852598 | + | 0.147674i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −37.6822 | + | 42.7674i | −0.661091 | + | 0.750306i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −23.2263 | + | 13.4097i | −0.393667 | + | 0.227284i | −0.683748 | − | 0.729718i | \(-0.739651\pi\) |
0.290081 | + | 0.957002i | \(0.406318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.965926 | + | 1.67303i | −0.0158349 | + | 0.0274268i | −0.873834 | − | 0.486224i | \(-0.838374\pi\) |
0.857999 | + | 0.513651i | \(0.171707\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −40.8508 | − | 4.19564i | −0.648426 | − | 0.0665975i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −129.985 | + | 75.0470i | −1.99977 | + | 1.15457i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 23.9413i | − | 0.357333i | −0.983910 | − | 0.178666i | \(-0.942822\pi\) | ||
0.983910 | − | 0.178666i | \(-0.0571782\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 23.1728 | − | 11.8418i | 0.335837 | − | 0.171620i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −102.629 | − | 59.2527i | −1.44547 | − | 0.834545i | −0.447267 | − | 0.894401i | \(-0.647603\pi\) |
−0.998207 | + | 0.0598559i | \(0.980936\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −46.1686 | + | 79.9664i | −0.632447 | + | 1.09543i | 0.354603 | + | 0.935017i | \(0.384616\pi\) |
−0.987050 | + | 0.160413i | \(0.948717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.33051 | − | 162.647i | 0.111073 | − | 2.16862i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.40295 | + | 4.16203i | −0.0312071 | + | 0.0540523i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38.4785i | 0.487070i | 0.969892 | + | 0.243535i | \(0.0783071\pi\) | ||||
−0.969892 | + | 0.243535i | \(0.921693\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −25.3956 | − | 76.9160i | −0.313526 | − | 0.949580i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 36.8320 | + | 63.7949i | 0.443759 | + | 0.768613i | 0.997965 | − | 0.0637666i | \(-0.0203113\pi\) |
−0.554206 | + | 0.832380i | \(0.686978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −62.0896 | −0.730466 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 110.743 | + | 5.67208i | 1.27291 | + | 0.0651963i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 86.6168 | − | 50.0082i | 0.973222 | − | 0.561890i | 0.0730051 | − | 0.997332i | \(-0.476741\pi\) |
0.900217 | + | 0.435442i | \(0.143408\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −66.6087 | + | 38.4566i | −0.731964 | + | 0.422599i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 33.1253 | + | 1.69663i | 0.356186 | + | 0.0182433i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −132.493 | − | 105.205i | −1.39466 | − | 1.10742i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 143.029i | 1.47452i | 0.675607 | + | 0.737262i | \(0.263882\pi\) | ||||
−0.675607 | + | 0.737262i | \(0.736118\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.42977 | − | 0.968498i | −0.0952502 | − | 0.00978281i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.5909 | + | 28.7362i | −0.164266 | + | 0.284517i | −0.936394 | − | 0.350950i | \(-0.885859\pi\) |
0.772128 | + | 0.635467i | \(0.219192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 140.802 | + | 81.2919i | 1.36701 | + | 0.789241i | 0.990545 | − | 0.137191i | \(-0.0438073\pi\) |
0.376462 | + | 0.926432i | \(0.377141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.23470 | − | 121.728i | 0.0593781 | − | 1.15931i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 126.606i | − | 1.18323i | −0.806220 | − | 0.591616i | \(-0.798490\pi\) | ||
0.806220 | − | 0.591616i | \(-0.201510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −91.6855 | − | 52.9346i | −0.841151 | − | 0.485639i | 0.0165041 | − | 0.999864i | \(-0.494746\pi\) |
−0.857655 | + | 0.514225i | \(0.828080\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.1283 | + | 29.6041i | 0.136291 | + | 0.266704i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −51.1065 | − | 29.5063i | −0.452270 | − | 0.261118i | 0.256519 | − | 0.966539i | \(-0.417425\pi\) |
−0.708788 | + | 0.705421i | \(0.750758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 38.6196 | + | 66.8912i | 0.335823 | + | 0.581663i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −122.945 | − | 88.8798i | −1.05081 | − | 0.759657i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −31.8168 | −0.267368 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 59.9453 | − | 103.828i | 0.495416 | − | 0.858085i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 34.8089 | − | 53.7405i | 0.282999 | − | 0.436914i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 260.777 | 2.08621 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −205.351 | + | 118.560i | −1.61694 | + | 0.933541i | −0.629234 | + | 0.777216i | \(0.716631\pi\) |
−0.987706 | + | 0.156325i | \(0.950035\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −136.741 | + | 69.8777i | −1.06001 | + | 0.541687i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 61.9051 | + | 107.223i | 0.472558 | + | 0.818494i | 0.999507 | − | 0.0314029i | \(-0.00999751\pi\) |
−0.526949 | + | 0.849897i | \(0.676664\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −67.8937 | − | 53.9105i | −0.510479 | − | 0.405342i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 224.140 | − | 86.9555i | 1.66029 | − | 0.644115i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −74.0078 | + | 128.185i | −0.540203 | + | 0.935658i | 0.458689 | + | 0.888597i | \(0.348319\pi\) |
−0.998892 | + | 0.0470616i | \(0.985014\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 151.636 | 1.09091 | 0.545453 | − | 0.838142i | \(-0.316358\pi\) | ||||
0.545453 | + | 0.838142i | \(0.316358\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.26209 | − | 83.2139i | 0.0302276 | − | 0.590170i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.3756 | + | 8.87709i | −0.107522 | + | 0.0620776i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 329.126i | 2.26984i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.32440 | + | 84.4303i | −0.0294177 | + | 0.574356i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 41.0582 | + | 71.1149i | 0.275559 | + | 0.477281i | 0.970276 | − | 0.242001i | \(-0.0778039\pi\) |
−0.694717 | + | 0.719283i | \(0.744471\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155.595 | − | 89.8330i | 1.03043 | − | 0.594921i | 0.113324 | − | 0.993558i | \(-0.463850\pi\) |
0.917109 | + | 0.398637i | \(0.130517\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −25.6615 | − | 57.2706i | −0.167722 | − | 0.374318i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 98.4480i | 0.635149i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 118.748 | + | 205.678i | 0.756358 | + | 1.31005i | 0.944696 | + | 0.327946i | \(0.106357\pi\) |
−0.188338 | + | 0.982104i | \(0.560310\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.5497 | − | 33.2699i | 0.135533 | − | 0.209245i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.7900 | + | 34.2772i | 0.122919 | + | 0.212902i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 223.745 | 1.37267 | 0.686335 | − | 0.727286i | \(-0.259219\pi\) | ||||
0.686335 | + | 0.727286i | \(0.259219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.43918 | − | 28.0989i | 0.00872233 | − | 0.170296i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.81572i | − | 0.0348247i | −0.999848 | − | 0.0174123i | \(-0.994457\pi\) | ||
0.999848 | − | 0.0174123i | \(-0.00554280\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −115.136 | −0.681281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 42.2806 | − | 165.691i | 0.247255 | − | 0.968950i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 282.198i | − | 1.63120i | −0.578613 | − | 0.815602i | \(-0.696406\pi\) | ||
0.578613 | − | 0.815602i | \(-0.303594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 247.702 | 1.41544 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 43.7407 | − | 67.5300i | 0.247123 | − | 0.381526i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.2455i | 0.141036i | 0.997510 | + | 0.0705181i | \(0.0224653\pi\) | ||||
−0.997510 | + | 0.0705181i | \(0.977535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −136.039 | + | 78.5424i | −0.751599 | + | 0.433936i | −0.826271 | − | 0.563272i | \(-0.809542\pi\) |
0.0746723 | + | 0.997208i | \(0.476209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.296451 | − | 5.78797i | 0.00161995 | − | 0.0316283i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −85.4561 | + | 49.3381i | −0.461925 | + | 0.266692i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.34440 | −0.0392749 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 114.857 | − | 44.5589i | 0.607707 | − | 0.235761i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −107.270 | − | 185.798i | −0.561625 | − | 0.972763i | −0.997355 | − | 0.0726857i | \(-0.976843\pi\) |
0.435730 | − | 0.900078i | \(-0.356490\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −268.141 | + | 154.811i | −1.38933 | + | 0.802132i | −0.993240 | − | 0.116079i | \(-0.962967\pi\) |
−0.396093 | + | 0.918211i | \(0.629634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 244.793 | − | 377.929i | 1.25535 | − | 1.93810i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 376.293 | 1.91012 | 0.955060 | − | 0.296414i | \(-0.0957908\pi\) | ||||
0.955060 | + | 0.296414i | \(0.0957908\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −37.6504 | − | 65.2123i | −0.189198 | − | 0.327700i | 0.755785 | − | 0.654820i | \(-0.227255\pi\) |
−0.944983 | + | 0.327119i | \(0.893922\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.6832 | + | 63.9568i | 0.162603 | + | 0.318193i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 168.655i | 0.830814i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 164.583 | + | 95.0221i | 0.802844 | + | 0.463522i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −45.7381 | + | 63.2682i | −0.220957 | + | 0.305643i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.6722 | − | 12.4444i | −0.0749866 | − | 0.0595426i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 279.402 | − | 161.313i | 1.32418 | − | 0.764516i | 0.339788 | − | 0.940502i | \(-0.389645\pi\) |
0.984393 | + | 0.175986i | \(0.0563113\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 355.051 | + | 18.1852i | 1.66690 | + | 0.0853763i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −227.893 | − | 394.722i | −1.05997 | − | 1.83592i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 50.4480i | 0.232479i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.1695 | − | 276.649i | 0.0647011 | − | 1.26324i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −101.792 | − | 58.7696i | −0.460597 | − | 0.265926i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 48.2068i | − | 0.216174i | −0.994141 | − | 0.108087i | \(-0.965527\pi\) | ||
0.994141 | − | 0.108087i | \(-0.0344725\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 199.781 | + | 445.867i | 0.887917 | + | 1.98163i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −137.892 | + | 79.6118i | −0.607453 | + | 0.350713i | −0.771968 | − | 0.635662i | \(-0.780727\pi\) |
0.164515 | + | 0.986375i | \(0.447394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.7008 | − | 53.1753i | 0.134065 | − | 0.232207i | −0.791175 | − | 0.611590i | \(-0.790530\pi\) |
0.925240 | + | 0.379383i | \(0.123864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.737485 | − | 14.3988i | 0.00319258 | − | 0.0623325i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −123.485 | + | 213.882i | −0.529977 | + | 0.917947i | 0.469412 | + | 0.882979i | \(0.344466\pi\) |
−0.999388 | + | 0.0349674i | \(0.988867\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 247.311 | 1.05239 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −52.5286 | − | 102.792i | −0.221640 | − | 0.433720i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 140.849 | − | 243.957i | 0.589325 | − | 1.02074i | −0.404996 | − | 0.914319i | \(-0.632727\pi\) |
0.994321 | − | 0.106423i | \(-0.0339396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −72.7517 | − | 42.0032i | −0.301874 | − | 0.174287i | 0.341410 | − | 0.939914i | \(-0.389095\pi\) |
−0.643285 | + | 0.765627i | \(0.722429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 172.843 | + | 170.805i | 0.711288 | + | 0.702901i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −250.926 | −1.02419 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −117.634 | − | 297.885i | −0.476251 | − | 1.20601i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −185.482 | − | 120.141i | −0.744908 | − | 0.482494i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0665 | − | 20.8998i | −0.0480738 | − | 0.0832663i | 0.840987 | − | 0.541055i | \(-0.181975\pi\) |
−0.889061 | + | 0.457789i | \(0.848642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.56821 | + | 7.91236i | 0.0180562 | + | 0.0312742i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 165.866 | − | 84.7611i | 0.650457 | − | 0.332397i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 109.226i | − | 0.425002i | −0.977161 | − | 0.212501i | \(-0.931839\pi\) | ||
0.977161 | − | 0.212501i | \(-0.0681609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −43.7905 | + | 25.2825i | −0.169075 | + | 0.0976157i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −303.582 | + | 136.027i | −1.16315 | + | 0.521177i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −374.488 | −1.42391 | −0.711955 | − | 0.702225i | \(-0.752190\pi\) | ||||
−0.711955 | + | 0.702225i | \(0.752190\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 101.891 | + | 58.8268i | 0.384494 | + | 0.221988i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −163.120 | + | 251.836i | −0.610936 | + | 0.943207i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −464.481 | − | 268.168i | −1.72670 | − | 0.996909i | −0.902632 | − | 0.430413i | \(-0.858368\pi\) |
−0.824065 | − | 0.566496i | \(-0.808299\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 123.546 | − | 213.989i | 0.455891 | − | 0.789626i | −0.542848 | − | 0.839831i | \(-0.682654\pi\) |
0.998739 | + | 0.0502050i | \(0.0159875\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 125.440 | − | 193.663i | 0.459487 | − | 0.709389i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 57.1781 | 0.207920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −224.160 | − | 388.257i | −0.809243 | − | 1.40165i | −0.913389 | − | 0.407087i | \(-0.866544\pi\) |
0.104147 | − | 0.994562i | \(-0.466789\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −90.8071 | + | 40.6883i | −0.325473 | + | 0.145836i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 303.885 | + | 175.448i | 1.08144 | + | 0.624371i | 0.931285 | − | 0.364291i | \(-0.118689\pi\) |
0.150158 | + | 0.988662i | \(0.452022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 82.4426 | + | 142.795i | 0.291316 | + | 0.504575i | 0.974121 | − | 0.226026i | \(-0.0725734\pi\) |
−0.682805 | + | 0.730601i | \(0.739240\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 497.561 | + | 100.173i | 1.74583 | + | 0.351485i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 84.3378 | + | 48.6924i | 0.293860 | + | 0.169660i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 120.189 | + | 208.173i | 0.415878 | + | 0.720321i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −195.255 | − | 382.088i | −0.670978 | − | 1.31302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −56.9902 | − | 32.9033i | −0.194506 | − | 0.112298i | 0.399584 | − | 0.916696i | \(-0.369154\pi\) |
−0.594090 | + | 0.804398i | \(0.702488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 206.814 | + | 119.404i | 0.701066 | + | 0.404760i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.5128 | − | 10.2857i | 0.0892688 | − | 0.0346321i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 146.218i | 0.489025i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −116.780 | − | 202.269i | −0.387973 | − | 0.671989i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.09188 | − | 99.4148i | 0.0168049 | − | 0.328102i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.2018 | 0.0563993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −256.227 | − | 147.933i | −0.834615 | − | 0.481865i | 0.0208149 | − | 0.999783i | \(-0.493374\pi\) |
−0.855430 | + | 0.517918i | \(0.826707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −487.113 | − | 24.9492i | −1.57642 | − | 0.0807417i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −102.633 | + | 177.766i | −0.330010 | + | 0.571594i | −0.982513 | − | 0.186192i | \(-0.940385\pi\) |
0.652504 | + | 0.757786i | \(0.273719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 182.485 | − | 316.073i | 0.583018 | − | 1.00982i | −0.412101 | − | 0.911138i | \(-0.635205\pi\) |
0.995119 | − | 0.0986790i | \(-0.0314617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 149.520 | + | 333.695i | 0.474666 | + | 1.05935i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −248.263 | − | 143.335i | −0.783164 | − | 0.452160i | 0.0543863 | − | 0.998520i | \(-0.482680\pi\) |
−0.837551 | + | 0.546360i | \(0.816013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.9314i | 0.122042i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 172.835 | + | 338.215i | 0.538427 | + | 1.05363i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4709 | − | 131.048i | 0.0602814 | − | 0.405722i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 792.477 | + | 457.537i | 2.43839 | + | 1.40781i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 317.192 | + | 16.2461i | 0.970006 | + | 0.0496823i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 126.730 | 0.385198 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −105.392 | + | 60.8478i | −0.318403 | + | 0.183830i | −0.650681 | − | 0.759351i | \(-0.725516\pi\) |
0.332277 | + | 0.943182i | \(0.392183\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −80.8275 | − | 58.4322i | −0.242725 | − | 0.175472i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −184.620 | + | 106.590i | −0.551103 | + | 0.318180i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.64151 | − | 1.52507i | 0.00783829 | − | 0.00452544i | −0.496076 | − | 0.868279i | \(-0.665226\pi\) |
0.503914 | + | 0.863754i | \(0.331893\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 176.806 | + | 9.05575i | 0.521552 | + | 0.0267131i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6451i | 0.0341500i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −352.163 | −1.02671 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −194.485 | − | 125.972i | −0.563723 | − | 0.365136i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −114.632 | − | 198.548i | −0.330352 | − | 0.572186i | 0.652229 | − | 0.758022i | \(-0.273834\pi\) |
−0.982581 | + | 0.185836i | \(0.940501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −102.794 | − | 178.045i | −0.294540 | − | 0.510158i | 0.680338 | − | 0.732899i | \(-0.261833\pi\) |
−0.974878 | + | 0.222741i | \(0.928500\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 449.769 | + | 69.5967i | 1.28139 | + | 0.198281i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −171.317 | − | 296.730i | −0.485318 | − | 0.840595i | 0.514540 | − | 0.857466i | \(-0.327963\pi\) |
−0.999858 | + | 0.0168717i | \(0.994629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1055.21i | 2.97241i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 84.9954 | − | 43.4344i | 0.238082 | − | 0.121665i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −177.982 | + | 308.274i | −0.495772 | + | 0.858702i | −0.999988 | − | 0.00487566i | \(-0.998448\pi\) |
0.504217 | + | 0.863577i | \(0.331781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 263.598 | − | 246.652i | 0.730188 | − | 0.683247i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.3977 | + | 359.201i | −0.0506825 | + | 0.989535i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 822.198 | 2.25260 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −238.486 | + | 413.069i | −0.649825 | + | 1.12553i | 0.333340 | + | 0.942807i | \(0.391824\pi\) |
−0.983165 | + | 0.182722i | \(0.941509\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.6253 | + | 191.082i | −0.0531851 | + | 0.517836i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 52.2123 | + | 30.1448i | 0.140734 | + | 0.0812528i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 113.432 | + | 65.4898i | 0.304106 | + | 0.175576i | 0.644286 | − | 0.764785i | \(-0.277155\pi\) |
−0.340180 | + | 0.940360i | \(0.610488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −696.639 | + | 355.997i | −1.85770 | + | 0.949325i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −311.528 | + | 539.582i | −0.826333 | + | 1.43125i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 121.104i | 0.319534i | 0.987155 | + | 0.159767i | \(0.0510743\pi\) | ||||
−0.987155 | + | 0.159767i | \(0.948926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 386.725 | − | 597.054i | 1.01503 | − | 1.56707i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −417.409 | + | 240.991i | −1.08984 | + | 0.629220i | −0.933534 | − | 0.358489i | \(-0.883292\pi\) |
−0.156307 | + | 0.987709i | \(0.549959\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 42.7931 | 0.111151 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 269.899 | − | 373.343i | 0.697412 | − | 0.964710i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −273.111 | + | 473.042i | −0.702085 | + | 1.21605i | 0.265649 | + | 0.964070i | \(0.414414\pi\) |
−0.967733 | + | 0.251977i | \(0.918919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.2432 | + | 52.3828i | −0.0773483 | + | 0.133971i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −311.747 | − | 201.926i | −0.793250 | − | 0.513806i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 296.721 | − | 171.312i | 0.751193 | − | 0.433702i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.6892 | − | 47.9590i | 0.0697460 | − | 0.120804i | −0.829043 | − | 0.559184i | \(-0.811114\pi\) |
0.898789 | + | 0.438381i | \(0.144448\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 254.967 | + | 51.3321i | 0.639015 | + | 0.128652i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −457.086 | + | 263.899i | −1.13987 | + | 0.658102i | −0.946397 | − | 0.323004i | \(-0.895307\pi\) |
−0.193469 | + | 0.981106i | \(0.561974\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −93.1839 | + | 161.399i | −0.231226 | + | 0.400494i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −480.061 | + | 538.276i | −1.18534 | + | 1.32908i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1084 | + | 5.83606i | −0.0248362 | + | 0.0143392i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 241.831i | − | 0.591275i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) | ||
0.955300 | − | 0.295637i | \(-0.0955320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.7136 | − | 443.465i | 0.0552643 | − | 1.07899i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 105.978 | + | 61.1867i | 0.256606 | + | 0.148152i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 327.963 | − | 568.049i | 0.790273 | − | 1.36879i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −405.080 | + | 207.004i | −0.971416 | + | 0.496413i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 62.5857 | − | 108.402i | 0.149369 | − | 0.258715i | −0.781625 | − | 0.623748i | \(-0.785609\pi\) |
0.930994 | + | 0.365033i | \(0.118942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 453.417i | − | 1.07700i | −0.842625 | − | 0.538500i | \(-0.818991\pi\) | ||
0.842625 | − | 0.538500i | \(-0.181009\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 102.213 | + | 228.116i | 0.241638 | + | 0.539282i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 189.270 | + | 327.825i | 0.445341 | + | 0.771354i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.81477 | 0.0206435 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.9559 | − | 44.7041i | 0.0674962 | − | 0.104205i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 696.599 | − | 402.182i | 1.61624 | − | 0.933136i | 0.628358 | − | 0.777925i | \(-0.283728\pi\) |
0.987881 | − | 0.155211i | \(-0.0496058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −53.8698 | + | 31.1017i | −0.124411 | + | 0.0718285i | −0.560914 | − | 0.827874i | \(-0.689550\pi\) |
0.436503 | + | 0.899703i | \(0.356217\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −449.304 | − | 879.229i | −1.03288 | − | 2.02122i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −153.293 | + | 60.5352i | −0.350786 | + | 0.138524i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 465.349i | − | 1.06002i | −0.847991 | − | 0.530011i | \(-0.822188\pi\) | ||
0.847991 | − | 0.530011i | \(-0.177812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −103.707 | − | 231.451i | −0.235164 | − | 0.524832i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 278.441 | − | 482.274i | 0.628535 | − | 1.08865i | −0.359311 | − | 0.933218i | \(-0.616988\pi\) |
0.987846 | − | 0.155437i | \(-0.0496785\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −771.262 | − | 445.288i | −1.73317 | − | 1.00065i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −206.765 | − | 133.926i | −0.462561 | − | 0.299611i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 445.457i | − | 0.992109i | −0.868291 | − | 0.496054i | \(-0.834782\pi\) | ||
0.868291 | − | 0.496054i | \(-0.165218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4681 | + | 11.2399i | 0.0431664 | + | 0.0249221i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −293.023 | + | 452.390i | −0.646850 | + | 0.998653i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 593.104 | + | 342.429i | 1.30353 | + | 0.752591i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −265.110 | − | 459.184i | −0.580110 | − | 1.00478i | −0.995466 | − | 0.0951208i | \(-0.969676\pi\) |
0.415356 | − | 0.909659i | \(-0.363657\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 146.735 | + | 117.961i | 0.319683 | + | 0.256996i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 738.736 | 1.60246 | 0.801232 | − | 0.598354i | \(-0.204178\pi\) | ||||
0.801232 | + | 0.598354i | \(0.204178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −450.313 | + | 779.964i | −0.972597 | + | 1.68459i | −0.284951 | + | 0.958542i | \(0.591977\pi\) |
−0.687646 | + | 0.726046i | \(0.741356\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −134.395 | − | 262.994i | −0.289023 | − | 0.565579i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7828 | −0.0445027 | −0.0222514 | − | 0.999752i | \(-0.507083\pi\) | ||||
−0.0222514 | + | 0.999752i | \(0.507083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −94.6052 | + | 54.6203i | −0.201717 | + | 0.116461i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −598.004 | − | 387.340i | −1.26965 | − | 0.822379i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.9568 | − | 46.6905i | −0.0569911 | − | 0.0987115i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −151.586 | + | 1020.25i | −0.319128 | + | 2.14788i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.1497 | + | 118.296i | −0.0254711 | + | 0.247999i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −379.098 | + | 656.617i | −0.791437 | + | 1.37081i | 0.133640 | + | 0.991030i | \(0.457333\pi\) |
−0.925077 | + | 0.379779i | \(0.876000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −186.800 | −0.388357 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −99.6603 | − | 64.5522i | −0.206336 | − | 0.133648i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1102.95 | − | 636.786i | 2.27411 | − | 1.31296i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 241.518i | 0.495930i | 0.968769 | + | 0.247965i | \(0.0797617\pi\) | ||||
−0.968769 | + | 0.247965i | \(0.920238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −597.713 | + | 305.444i | −1.22232 | + | 0.624629i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −71.9479 | − | 124.617i | −0.146533 | − | 0.253803i | 0.783411 | − | 0.621505i | \(-0.213478\pi\) |
−0.929944 | + | 0.367701i | \(0.880145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −223.210 | + | 128.870i | −0.452758 | + | 0.261400i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34.5143 | + | 77.0282i | 0.0697259 | + | 0.155612i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 540.723i | 1.08797i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −141.590 | − | 245.240i | −0.283747 | − | 0.491464i | 0.688558 | − | 0.725182i | \(-0.258244\pi\) |
−0.972304 | + | 0.233718i | \(0.924911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.93928 | + | 15.5361i | 0.0158469 | + | 0.0310103i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 269.400 | + | 466.614i | 0.535586 | + | 0.927661i | 0.999135 | + | 0.0415903i | \(0.0132424\pi\) |
−0.463549 | + | 0.886071i | \(0.653424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 295.460 | 0.585069 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 307.576 | − | 157.178i | 0.606659 | − | 0.310015i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 804.739i | 1.58102i | 0.612449 | + | 0.790510i | \(0.290184\pi\) | ||||
−0.612449 | + | 0.790510i | \(0.709816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 421.321 | 0.824504 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 113.242 | + | 500.345i | 0.220745 | + | 0.975332i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1447.69i | − | 2.81106i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.2537 | 0.0565836 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 385.241 | + | 753.865i | 0.742275 | + | 1.45253i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1019.07i | − | 1.95599i | −0.208620 | − | 0.977997i | \(-0.566897\pi\) | ||
0.208620 | − | 0.977997i | \(-0.433103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −586.614 | + | 338.682i | −1.12163 | + | 0.647575i | −0.941817 | − | 0.336126i | \(-0.890883\pi\) |
−0.179815 | + | 0.983700i | \(0.557550\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −661.711 | + | 338.148i | −1.26040 | + | 0.644091i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −66.7663 | + | 38.5475i | −0.126691 | + | 0.0731452i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −453.755 | −0.857760 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.6611 | + | 240.112i | −0.0464427 | + | 0.452189i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 179.882 | + | 311.565i | 0.337490 | + | 0.584550i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −976.303 | + | 563.669i | −1.82487 | + | 1.05359i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.4637 | − | 67.4409i | −0.0641781 | − | 0.125588i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.6813 | −0.0550674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −333.796 | − | 578.151i | −0.616998 | − | 1.06867i | −0.990030 | − | 0.140853i | \(-0.955015\pi\) |
0.373033 | − | 0.927818i | \(-0.378318\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 256.195 | − | 395.531i | 0.471813 | − | 0.728419i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 942.692i | 1.72971i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −387.363 | − | 223.644i | −0.708159 | − | 0.408856i | 0.102220 | − | 0.994762i | \(-0.467405\pi\) |
−0.810379 | + | 0.585906i | \(0.800739\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.10946 | + | 15.8667i | 0.0129498 | + | 0.0289011i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −694.665 | − | 103.212i | −1.26073 | − | 0.187317i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 152.050 | − | 87.7860i | 0.274954 | − | 0.158745i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 160.934 | − | 248.461i | 0.289971 | − | 0.447678i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −465.088 | − | 805.556i | −0.834988 | − | 1.44624i | −0.894041 | − | 0.447986i | \(-0.852141\pi\) |
0.0590530 | − | 0.998255i | \(-0.481192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 862.828i | − | 1.54352i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.6199 | − | 10.0261i | 0.0349730 | − | 0.0178719i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 615.916 | + | 355.599i | 1.09399 | + | 0.631615i | 0.934636 | − | 0.355606i | \(-0.115726\pi\) |
0.159354 | + | 0.987222i | \(0.449059\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 525.467i | 0.930029i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −245.999 | + | 275.830i | −0.433861 | + | 0.486473i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 424.190 | − | 244.906i | 0.745501 | − | 0.430415i | −0.0785653 | − | 0.996909i | \(-0.525034\pi\) |
0.824066 | + | 0.566494i | \(0.191701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −94.8843 | + | 164.344i | −0.166172 | + | 0.287819i | −0.937071 | − | 0.349139i | \(-0.886474\pi\) |
0.770899 | + | 0.636958i | \(0.219807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 540.203 | + | 349.901i | 0.942762 | + | 0.610648i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 235.451 | − | 407.813i | 0.409480 | − | 0.709241i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −852.111 | −1.47680 | −0.738398 | − | 0.674366i | \(-0.764417\pi\) | ||||
−0.738398 | + | 0.674366i | \(0.764417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 504.974 | − | 779.614i | 0.872148 | − | 1.34648i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 168.059 | − | 291.087i | 0.289258 | − | 0.501010i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0524 | + | 6.95845i | 0.0206730 | + | 0.0119356i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −138.015 | + | 1343.78i | −0.235922 | + | 2.29705i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −661.590 | −1.12707 | −0.563535 | − | 0.826092i | \(-0.690559\pi\) | ||||
−0.563535 | + | 0.826092i | \(0.690559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −207.787 | − | 30.8727i | −0.352780 | − | 0.0524154i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1005.23 | + | 513.694i | −1.70090 | + | 0.869194i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −359.755 | − | 623.113i | −0.606669 | − | 1.05078i | −0.991785 | − | 0.127914i | \(-0.959172\pi\) |
0.385116 | − | 0.922868i | \(-0.374161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 141.653 | + | 245.350i | 0.238072 | + | 0.412353i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 189.603 | + | 122.810i | 0.317593 | + | 0.205712i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 370.363i | 0.618302i | 0.951013 | + | 0.309151i | \(0.100045\pi\) | ||||
−0.951013 | + | 0.309151i | \(0.899955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 335.465 | − | 193.681i | 0.558178 | − | 0.322264i | −0.194236 | − | 0.980955i | \(-0.562223\pi\) |
0.752414 | + | 0.658691i | \(0.228889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −174.620 | − | 126.237i | −0.289586 | − | 0.209348i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1067.54 | −1.76453 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 834.955 | + | 482.061i | 1.37554 | + | 0.794170i | 0.991619 | − | 0.129194i | \(-0.0412391\pi\) |
0.383924 | + | 0.923365i | \(0.374572\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −230.238 | − | 450.546i | −0.378059 | − | 0.739813i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 405.450 | + | 234.087i | 0.663585 | + | 0.383121i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −75.7056 | + | 131.126i | −0.123500 | + | 0.213909i | −0.921146 | − | 0.389218i | \(-0.872745\pi\) |
0.797645 | + | 0.603127i | \(0.206079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −569.386 | − | 29.1631i | −0.925831 | − | 0.0474197i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 392.782 | 0.636600 | 0.318300 | − | 0.947990i | \(-0.396888\pi\) | ||||
0.318300 | + | 0.947990i | \(0.396888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 488.602 | + | 846.283i | 0.789341 | + | 1.36718i | 0.926371 | + | 0.376611i | \(0.122911\pi\) |
−0.137031 | + | 0.990567i | \(0.543756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.8149 | − | 231.454i | 0.0576729 | − | 0.372711i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −395.220 | − | 228.180i | −0.634382 | − | 0.366261i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −482.434 | − | 835.600i | −0.771895 | − | 1.33696i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 58.8551 | + | 11.8492i | 0.0938678 | + | 0.0188983i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −66.9210 | − | 38.6369i | −0.106393 | − | 0.0614258i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −365.773 | − | 633.537i | −0.579672 | − | 1.00402i | −0.995517 | − | 0.0945855i | \(-0.969847\pi\) |
0.415845 | − | 0.909436i | \(-0.363486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −526.181 | + | 812.355i | −0.831249 | + | 1.28334i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1828.51 | + | 1055.69i | 2.87954 | + | 1.66251i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −411.377 | − | 237.509i | −0.645804 | − | 0.372855i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −973.308 | + | 436.114i | −1.52317 | + | 0.682495i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 534.564i | 0.833952i | 0.908917 | + | 0.416976i | \(0.136910\pi\) | ||||
−0.908917 | + | 0.416976i | \(0.863090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −513.484 | − | 889.380i | −0.798575 | − | 1.38317i | −0.920544 | − | 0.390638i | \(-0.872254\pi\) |
0.121969 | − | 0.992534i | \(-0.461079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1147.64 | + | 743.355i | 1.77929 | + | 1.15249i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 83.2309 | 0.128641 | 0.0643206 | − | 0.997929i | \(-0.479512\pi\) | ||||
0.0643206 | + | 0.997929i | \(0.479512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.4635 | + | 14.1240i | 0.0376941 | + | 0.0217627i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −68.8687 | − | 134.767i | −0.105789 | − | 0.207015i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −512.059 | + | 886.913i | −0.784165 | + | 1.35821i | 0.145332 | + | 0.989383i | \(0.453575\pi\) |
−0.929497 | + | 0.368830i | \(0.879758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 551.221 | − | 954.743i | 0.841559 | − | 1.45762i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 339.812 | + | 758.384i | 0.517218 | + | 1.15431i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 476.919 | + | 275.349i | 0.723701 | + | 0.417829i | 0.816113 | − | 0.577892i | \(-0.196124\pi\) |
−0.0924121 | + | 0.995721i | \(0.529458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 439.526i | − | 0.664942i | −0.943114 | − | 0.332471i | \(-0.892118\pi\) | ||
0.943114 | − | 0.332471i | \(-0.107882\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 352.156 | + | 18.0369i | 0.531155 | + | 0.0272050i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −113.450 | + | 763.570i | −0.170601 | + | 1.14823i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 277.672 | + | 160.314i | 0.416300 | + | 0.240351i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 65.8091 | + | 128.780i | 0.0983694 | + | 0.192496i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.03475 | 0.00303242 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 388.654 | − | 224.389i | 0.577495 | − | 0.333417i | −0.182642 | − | 0.983179i | \(-0.558465\pi\) |
0.760137 | + | 0.649763i | \(0.225132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1142.37 | − | 918.360i | −1.69240 | − | 1.36053i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 199.246 | − | 115.035i | 0.294308 | − | 0.169919i | −0.345575 | − | 0.938391i | \(-0.612316\pi\) |
0.639883 | + | 0.768472i | \(0.278983\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 565.186 | − | 326.310i | 0.832379 | − | 0.480574i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 259.683 | − | 400.917i | 0.381326 | − | 0.588718i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 980.063i | 1.43494i | 0.696590 | + | 0.717469i | \(0.254700\pi\) | ||||
−0.696590 | + | 0.717469i | \(0.745300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1317.97 | 1.92405 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.42234 | + | 183.964i | −0.0137152 | + | 0.267778i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 111.362 | + | 192.885i | 0.161629 | + | 0.279950i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 102.099 | + | 176.841i | 0.147756 | + | 0.255921i | 0.930398 | − | 0.366551i | \(-0.119462\pi\) |
−0.782642 | + | 0.622472i | \(0.786128\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.6863 | + | 39.4718i | 0.0255213 | + | 0.0569578i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −675.106 | − | 1169.32i | −0.971375 | − | 1.68247i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 148.824i | 0.213521i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 37.8985 | − | 739.938i | 0.0542182 | − | 1.05857i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 170.159 | − | 294.724i | 0.242738 | − | 0.420434i | −0.718755 | − | 0.695263i | \(-0.755288\pi\) |
0.961493 | + | 0.274829i | \(0.0886212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −77.3360 | − | 195.838i | −0.110009 | − | 0.278575i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −660.667 | + | 337.614i | −0.937117 | + | 0.478886i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 151.403 | 0.214149 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.8318 | − | 44.7420i | 0.0364341 | − | 0.0631058i | −0.847233 | − | 0.531221i | \(-0.821733\pi\) |
0.883667 | + | 0.468115i | \(0.155067\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 280.650 | + | 202.889i | 0.394726 | + | 0.285357i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 83.0570 | + | 47.9530i | 0.116490 | + | 0.0672552i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 136.909 | + | 79.0443i | 0.191481 | + | 0.110551i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43.2277 | + | 843.986i | −0.0602897 | + | 1.17711i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −320.673 | + | 555.422i | −0.445999 | + | 0.772492i | −0.998121 | − | 0.0612706i | \(-0.980485\pi\) |
0.552122 | + | 0.833763i | \(0.313818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 741.846i | − | 1.02891i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 251.689 | + | 12.8912i | 0.348118 | + | 0.0178301i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1737.75 | − | 1003.29i | 2.39689 | − | 1.38385i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 494.140 | 0.679698 | 0.339849 | − | 0.940480i | \(-0.389624\pi\) | ||||
0.339849 | + | 0.940480i | \(0.389624\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −694.906 | − | 220.334i | −0.953232 | − | 0.302241i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 178.464 | − | 309.108i | 0.244137 | − | 0.422857i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 427.809 | − | 740.986i | 0.583641 | − | 1.01090i | −0.411403 | − | 0.911454i | \(-0.634961\pi\) |
0.995043 | − | 0.0994414i | \(-0.0317056\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 670.325 | − | 342.550i | 0.912007 | − | 0.466054i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8381 | + | 12.6082i | −0.0296311 | + | 0.0171075i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 544.175 | − | 942.539i | 0.736367 | − | 1.27543i | −0.217754 | − | 0.976004i | \(-0.569873\pi\) |
0.954121 | − | 0.299421i | \(-0.0967937\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 720.903 | + | 635.184i | 0.972878 | + | 0.857198i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 141.199 | − | 81.5216i | 0.190040 | − | 0.109719i | −0.401961 | − | 0.915657i | \(-0.631671\pi\) |
0.592001 | + | 0.805937i | \(0.298338\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 365.595 | − | 633.229i | 0.490731 | − | 0.849972i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 659.507 | + | 67.7356i | 0.882874 | + | 0.0906768i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −500.290 | + | 288.842i | −0.667943 | + | 0.385637i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 978.567i | − | 1.30302i | −0.758641 | − | 0.651509i | \(-0.774136\pi\) | ||
0.758641 | − | 0.651509i | \(-0.225864\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.7658 | + | 39.3594i | 0.0806983 | + | 0.0522701i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1385.47 | − | 799.901i | −1.83506 | − | 1.05947i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 713.647 | − | 1236.07i | 0.942731 | − | 1.63286i | 0.182499 | − | 0.983206i | \(-0.441581\pi\) |
0.760232 | − | 0.649652i | \(-0.225085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.0050 | − | 14.9009i | −0.0303096 | − | 0.0196322i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 317.545 | − | 550.005i | 0.417274 | − | 0.722740i | −0.578390 | − | 0.815760i | \(-0.696319\pi\) |
0.995664 | + | 0.0930206i | \(0.0296522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 483.066i | 0.633115i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −327.385 | + | 452.862i | −0.427954 | + | 0.591977i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 226.039 | + | 391.511i | 0.294706 | + | 0.510445i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −697.716 | −0.907302 | −0.453651 | − | 0.891179i | \(-0.649879\pi\) | ||||
−0.453651 | + | 0.891179i | \(0.649879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 149.108 | + | 291.785i | 0.193396 | + | 0.378450i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 819.856 | − | 473.344i | 1.06062 | − | 0.612347i | 0.135014 | − | 0.990844i | \(-0.456892\pi\) |
0.925603 | + | 0.378497i | \(0.123559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 519.793 | − | 300.103i | 0.670701 | − | 0.387229i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 82.4679 | − | 127.320i | 0.106136 | − | 0.163861i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −252.169 | + | 317.576i | −0.323708 | + | 0.407671i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 124.817i | 0.159817i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 625.293 | − | 777.815i | 0.798586 | − | 0.993378i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1057.37 | − | 1831.42i | 1.34697 | − | 2.33302i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −630.202 | − | 363.847i | −0.800765 | − | 0.462322i | 0.0429736 | − | 0.999076i | \(-0.486317\pi\) |
−0.843739 | + | 0.536754i | \(0.819650\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1000.41 | − | 511.230i | 1.26795 | − | 0.647946i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 269.266i | 0.340413i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.2012 | + | 16.2820i | 0.0355627 | + | 0.0205321i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −352.499 | − | 18.0544i | −0.443394 | − | 0.0227100i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 845.328 | + | 488.051i | 1.06064 | + | 0.612360i | 0.925609 | − | 0.378482i | \(-0.123554\pi\) |
0.135029 | + | 0.990842i | \(0.456887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 96.8351 | + | 167.723i | 0.121195 | + | 0.209917i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 91.9672 | − | 895.437i | 0.114815 | − | 1.11790i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 97.2555 | 0.121115 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 176.216 | − | 305.215i | 0.218902 | − | 0.379149i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1606.90 | + | 82.3032i | 1.99121 | + | 0.101987i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −729.554 | −0.901797 | −0.450899 | − | 0.892575i | \(-0.648896\pi\) | ||||
−0.450899 | + | 0.892575i | \(0.648896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −839.889 | + | 484.910i | −1.03562 | + | 0.597916i | −0.918590 | − | 0.395212i | \(-0.870671\pi\) |
−0.117031 | + | 0.993128i | \(0.537338\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.9175 | + | 740.308i | −0.0466389 | + | 0.910588i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −996.147 | − | 1725.38i | −1.22227 | − | 2.11703i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 904.578 | − | 357.216i | 1.10719 | − | 0.437228i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −70.7232 | + | 688.596i | −0.0863531 | + | 0.840776i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 161.947 | − | 280.500i | 0.197255 | − | 0.341656i | −0.750382 | − | 0.661004i | \(-0.770131\pi\) |
0.947637 | + | 0.319348i | \(0.103464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1235.10 | 1.50072 | 0.750362 | − | 0.661027i | \(-0.229879\pi\) | ||||
0.750362 | + | 0.661027i | \(0.229879\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −152.746 | + | 78.0562i | −0.185146 | + | 0.0946135i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 200.684 | − | 115.865i | 0.242665 | − | 0.140103i | −0.373736 | − | 0.927535i | \(-0.621923\pi\) |
0.616401 | + | 0.787432i | \(0.288590\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 127.878i | − | 0.154256i | −0.997021 | − | 0.0771281i | \(-0.975425\pi\) | ||
0.997021 | − | 0.0771281i | \(-0.0245751\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1128.85 | + | 731.180i | 1.35842 | + | 0.879880i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −98.2507 | − | 170.175i | −0.117948 | − | 0.204292i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.8471 | + | 25.8925i | −0.0537091 | + | 0.0310090i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 187.037 | − | 232.659i | 0.223461 | − | 0.277968i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 185.566i | 0.221175i | 0.993866 | + | 0.110587i | \(0.0352732\pi\) | ||||
−0.993866 | + | 0.110587i | \(0.964727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 262.618 | + | 454.868i | 0.312269 | + | 0.540866i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1051.31 | − | 53.8466i | −1.24711 | − | 0.0638750i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 512.605 | + | 887.858i | 0.606633 | + | 1.05072i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −547.044 | −0.645860 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −415.172 | − | 268.916i | −0.489013 | − | 0.316745i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 96.1282i | 0.112959i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1350.44 | −1.58316 | −0.791581 | − | 0.611064i | \(-0.790742\pi\) | ||||
−0.791581 | + | 0.611064i | \(0.790742\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1465.94 | + | 411.638i | −1.71455 | + | 0.481448i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 178.226i | − | 0.207965i | −0.994579 | − | 0.103983i | \(-0.966841\pi\) | ||
0.994579 | − | 0.103983i | \(-0.0331586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 319.958 | 0.372478 | 0.186239 | − | 0.982504i | \(-0.440370\pi\) | ||||
0.186239 | + | 0.982504i | \(0.440370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −291.772 | − | 14.9441i | −0.338876 | − | 0.0173567i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 757.163i | 0.877362i | 0.898643 | + | 0.438681i | \(0.144554\pi\) | ||||
−0.898643 | + | 0.438681i | \(0.855446\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2176.13 | + | 1256.39i | −2.51576 | + | 1.45247i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −605.258 | − | 392.039i | −0.698106 | − | 0.452179i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.0983 | − | 20.2640i | 0.0403893 | − | 0.0233188i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −403.563 | −0.463332 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1043.21 | + | 754.160i | 1.19497 | + | 0.863871i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −594.943 | − | 1030.47i | −0.679935 | − | 1.17768i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 689.070 | − | 397.835i | 0.785712 | − | 0.453631i | −0.0527385 | − | 0.998608i | \(-0.516795\pi\) |
0.838451 | + | 0.544977i | \(0.183462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 197.161 | + | 10.0983i | 0.224302 | + | 0.0114884i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 812.402 | 0.922136 | 0.461068 | − | 0.887365i | \(-0.347466\pi\) | ||||
0.461068 | + | 0.887365i | \(0.347466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 327.533 | + | 567.304i | 0.370932 | + | 0.642474i | 0.989709 | − | 0.143093i | \(-0.0457048\pi\) |
−0.618777 | + | 0.785567i | \(0.712372\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −715.488 | − | 36.6462i | −0.808461 | − | 0.0414082i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 464.445i | 0.523613i | 0.965120 | + | 0.261807i | \(0.0843183\pi\) | ||||
−0.965120 | + | 0.261807i | \(0.915682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 936.989 | + | 540.971i | 1.05398 | + | 0.608516i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −56.7850 | + | 63.6711i | −0.0637318 | + | 0.0714602i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −77.5551 | + | 521.982i | −0.0868478 | + | 0.584527i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 194.677 | − | 112.397i | 0.217516 | − | 0.125583i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −199.609 | − | 390.608i | −0.222529 | − | 0.435461i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 204.334 | + | 353.917i | 0.227290 | + | 0.393678i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 92.1350i | 0.102259i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 588.091 | + | 380.920i | 0.651263 | + | 0.421838i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1211.34 | + | 699.365i | 1.33849 | + | 0.772779i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1549.89i | 1.70881i | 0.519608 | + | 0.854405i | \(0.326078\pi\) | ||||
−0.519608 | + | 0.854405i | \(0.673922\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 122.113 | + | 272.528i | 0.134338 | + | 0.299811i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −276.396 | + | 159.577i | −0.303398 | + | 0.175167i | −0.643968 | − | 0.765052i | \(-0.722713\pi\) |
0.340570 | + | 0.940219i | \(0.389380\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.7938 | − | 67.1928i | 0.0424905 | − | 0.0735957i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −45.9529 | + | 23.4829i | −0.0502218 | + | 0.0256644i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 282.464 | − | 489.242i | 0.308030 | − | 0.533524i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1193.65 | −1.29886 | −0.649431 | − | 0.760421i | \(-0.724993\pi\) | ||||
−0.649431 | + | 0.760421i | \(0.724993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 886.434 | + | 45.4018i | 0.962469 | + | 0.0492962i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −998.784 | + | 1729.94i | −1.08211 | + | 1.87426i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 520.997 | + | 300.798i | 0.563240 | + | 0.325187i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1335.33 | − | 598.328i | 1.44049 | − | 0.645446i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1612.12 | 1.73533 | 0.867664 | − | 0.497152i | \(-0.165621\pi\) | ||||
0.867664 | + | 0.497152i | \(0.165621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 78.6888 | − | 529.613i | 0.0845207 | − | 0.568864i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.4990 | − | 614.992i | 0.0337610 | − | 0.659156i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.6984 | + | 56.6353i | 0.0349715 | + | 0.0605725i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −298.001 | − | 516.152i | −0.318037 | − | 0.550856i | 0.662041 | − | 0.749467i | \(-0.269690\pi\) |
−0.980078 | + | 0.198611i | \(0.936357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −56.0061 | + | 1093.47i | −0.0596444 | + | 1.16451i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1310.21i | − | 1.39236i | −0.717867 | − | 0.696180i | \(-0.754881\pi\) | ||
0.717867 | − | 0.696180i | \(-0.245119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 160.333 | − | 92.5685i | 0.170025 | − | 0.0981638i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −854.968 | − | 687.317i | −0.904728 | − | 0.727319i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.4917 | 0.0480377 | 0.0240188 | − | 0.999712i | \(-0.492354\pi\) | ||||
0.0240188 | + | 0.999712i | \(0.492354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1347.94 | + | 778.234i | 1.42038 | + | 0.820057i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 858.883 | + | 43.9907i | 0.903136 | + | 0.0462573i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 381.297 | + | 220.142i | 0.400102 | + | 0.230999i | 0.686528 | − | 0.727104i | \(-0.259134\pi\) |
−0.286426 | + | 0.958102i | \(0.592467\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −955.168 | + | 1654.40i | −1.00018 | + | 1.73236i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −53.1469 | − | 104.001i | −0.0555349 | − | 0.108674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 675.374 | 0.704248 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −419.380 | − | 726.387i | −0.436399 | − | 0.755866i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −923.423 | − | 667.565i | −0.958903 | − | 0.693214i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2387.61 | + | 1378.49i | 2.47421 | + | 1.42848i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 378.829 | + | 656.151i | 0.391757 | + | 0.678543i | 0.992681 | − | 0.120763i | \(-0.0385341\pi\) |
−0.600924 | + | 0.799306i | \(0.705201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 126.885 | + | 376.663i | 0.130944 | + | 0.388713i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1563.97 | − | 902.956i | −1.61068 | − | 0.929924i | −0.989214 | − | 0.146480i | \(-0.953205\pi\) |
−0.621463 | − | 0.783444i | \(-0.713461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −345.946 | − | 599.197i | −0.355546 | − | 0.615824i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2741.63 | − | 140.422i | −2.81192 | − | 0.144023i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1432.56 | − | 827.090i | −1.46629 | − | 0.846561i | −0.466997 | − | 0.884259i | \(-0.654664\pi\) |
−0.999289 | + | 0.0376982i | \(0.987997\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −91.2303 | − | 52.6719i | −0.0931873 | − | 0.0538017i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −869.526 | + | 389.612i | −0.886367 | + | 0.397158i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 673.714i | 0.685365i | 0.939451 | + | 0.342683i | \(0.111336\pi\) | ||||
−0.939451 | + | 0.342683i | \(0.888664\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1675.32 | − | 2901.73i | −1.70083 | − | 2.94592i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −338.548 | + | 173.005i | −0.343007 | + | 0.175283i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −444.017 | −0.448955 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −999.399 | − | 577.003i | −1.00848 | − | 0.582244i | −0.0977305 | − | 0.995213i | \(-0.531158\pi\) |
−0.910745 | + | 0.412969i | \(0.864492\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 198.477 | − | 306.423i | 0.199876 | − | 0.308583i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −335.250 | + | 580.670i | −0.336935 | + | 0.583588i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −476.239 | + | 824.870i | −0.477672 | + | 0.827352i | −0.999672 | − | 0.0255931i | \(-0.991853\pi\) |
0.522000 | + | 0.852945i | \(0.325186\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 295.691 | + | 45.7549i | 0.295987 | + | 0.0458007i |
(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 | 684.3.s.a.445.6 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.40 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.1 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.22 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.22 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.1 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.6 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.40 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.6 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.6 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.22 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.22 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.40 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.40 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.1 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.1 | 80 | 9.2 | odd | 6 |