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 | 445.40 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.40 |
$q$-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 | ||||||||
\(3\) | 2.99550 | + | 0.164289i | 0.998499 | + | 0.0547630i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.18843 | − | 7.25458i | −0.837687 | − | 1.45092i | −0.891824 | − | 0.452383i | \(-0.850574\pi\) |
0.0541368 | − | 0.998534i | \(-0.482759\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.50755 | − | 7.80731i | −0.643936 | − | 1.11533i | −0.984546 | − | 0.175125i | \(-0.943967\pi\) |
0.340610 | − | 0.940205i | \(-0.389366\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.94602 | + | 0.984254i | 0.994002 | + | 0.109362i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.48869 | − | 2.57849i | −0.135336 | − | 0.234408i | 0.790390 | − | 0.612604i | \(-0.209878\pi\) |
−0.925726 | + | 0.378196i | \(0.876545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.56875i | 0.428366i | 0.976794 | + | 0.214183i | \(0.0687088\pi\) | ||||
−0.976794 | + | 0.214183i | \(0.931291\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.3546 | − | 22.4192i | −0.756973 | − | 1.49461i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.0392 | + | 22.5845i | −0.767010 | + | 1.32850i | 0.172167 | + | 0.985068i | \(0.444923\pi\) |
−0.939177 | + | 0.343433i | \(0.888410\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.0502 | − | 16.1243i | −0.528957 | − | 0.848649i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.2197 | − | 24.1273i | −0.581891 | − | 1.14892i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.9366 | 0.823332 | 0.411666 | − | 0.911335i | \(-0.364947\pi\) | ||||
0.411666 | + | 0.911335i | \(0.364947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −22.5860 | + | 39.1201i | −0.903439 | + | 1.56480i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.6361 | + | 4.41806i | 0.986521 | + | 0.163632i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13.6152 | − | 7.86072i | −0.469489 | − | 0.271059i | 0.246537 | − | 0.969133i | \(-0.420707\pi\) |
−0.716026 | + | 0.698074i | \(0.754041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16.0762 | − | 9.28158i | −0.518586 | − | 0.299406i | 0.217770 | − | 0.976000i | \(-0.430122\pi\) |
−0.736356 | + | 0.676594i | \(0.763455\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.03576 | − | 7.96844i | −0.122296 | − | 0.241468i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −37.7592 | + | 65.4008i | −1.07883 | + | 1.86859i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 32.1993i | − | 0.870251i | −0.900370 | − | 0.435126i | \(-0.856704\pi\) | ||
0.900370 | − | 0.435126i | \(-0.143296\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.914885 | + | 16.6812i | −0.0234586 | + | 0.427723i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −62.9342 | + | 36.3351i | −1.53498 | + | 0.886222i | −0.535860 | + | 0.844307i | \(0.680012\pi\) |
−0.999121 | + | 0.0419144i | \(0.986654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −63.1803 | −1.46931 | −0.734655 | − | 0.678441i | \(-0.762656\pi\) | ||||
−0.734655 | + | 0.678441i | \(0.762656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −30.3295 | − | 69.0221i | −0.673988 | − | 1.53382i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −20.3688 | + | 35.2799i | −0.433379 | + | 0.750635i | −0.997162 | − | 0.0752882i | \(-0.976012\pi\) |
0.563782 | + | 0.825923i | \(0.309346\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.1361 | + | 27.9485i | −0.329307 | + | 0.570377i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.7692 | + | 65.5097i | −0.838612 | + | 1.28450i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 73.4198 | − | 42.3890i | 1.38528 | − | 0.799792i | 0.392501 | − | 0.919752i | \(-0.371610\pi\) |
0.992779 | + | 0.119960i | \(0.0382767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.4706 | + | 21.5997i | −0.226738 | + | 0.392721i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −27.4562 | − | 49.9515i | −0.481688 | − | 0.876343i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.4480 | − | 7.76418i | 0.227931 | − | 0.131596i | −0.381686 | − | 0.924292i | \(-0.624656\pi\) |
0.609617 | + | 0.792696i | \(0.291323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.32790 | + | 14.4244i | −0.136523 | + | 0.236465i | −0.926178 | − | 0.377086i | \(-0.876926\pi\) |
0.789655 | + | 0.613551i | \(0.210259\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −32.6403 | − | 74.2809i | −0.518100 | − | 1.17906i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 40.3990 | − | 23.3244i | 0.621523 | − | 0.358836i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 63.1854i | − | 0.943065i | −0.881849 | − | 0.471533i | \(-0.843701\pi\) | ||
0.881849 | − | 0.471533i | \(-0.156299\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 56.7247 | + | 3.11108i | 0.822097 | + | 0.0450881i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 84.2994 | + | 48.6703i | 1.18732 | + | 0.685497i | 0.957695 | − | 0.287784i | \(-0.0929184\pi\) |
0.229620 | + | 0.973280i | \(0.426252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 20.4220 | − | 35.3719i | 0.279753 | − | 0.484547i | −0.691570 | − | 0.722309i | \(-0.743081\pi\) |
0.971323 | + | 0.237763i | \(0.0764140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −74.0832 | + | 113.473i | −0.987776 | + | 1.51298i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.4207 | + | 23.2454i | −0.174295 | + | 0.301888i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 107.749i | − | 1.36391i | −0.731394 | − | 0.681955i | \(-0.761130\pi\) | ||
0.731394 | − | 0.681955i | \(-0.238870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.0625 | + | 17.6103i | 0.976080 | + | 0.217411i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −57.3231 | − | 99.2866i | −0.690640 | − | 1.19622i | −0.971628 | − | 0.236512i | \(-0.923996\pi\) |
0.280988 | − | 0.959711i | \(-0.409338\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 218.455 | 2.57006 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −39.4928 | − | 25.7836i | −0.453940 | − | 0.296363i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.70957 | − | 1.56437i | 0.0304446 | − | 0.0175772i | −0.484700 | − | 0.874680i | \(-0.661071\pi\) |
0.515145 | + | 0.857103i | \(0.327738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 43.4770 | − | 25.1015i | 0.477769 | − | 0.275840i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −46.6313 | − | 30.4441i | −0.501411 | − | 0.327356i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −74.8808 | + | 140.446i | −0.788219 | + | 1.47837i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 120.628i | − | 1.24359i | −0.783181 | − | 0.621794i | \(-0.786404\pi\) | ||
0.783181 | − | 0.621794i | \(-0.213596\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.7800 | − | 24.5325i | −0.108889 | − | 0.247803i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.81674 | + | 15.2710i | −0.0872944 | + | 0.151198i | −0.906367 | − | 0.422492i | \(-0.861155\pi\) |
0.819072 | + | 0.573690i | \(0.194489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 100.731 | + | 58.1573i | 0.977976 | + | 0.564634i | 0.901658 | − | 0.432449i | \(-0.142351\pi\) |
0.0763172 | + | 0.997084i | \(0.475684\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −123.852 | + | 189.705i | −1.17954 | + | 1.80671i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.14531i | 0.0480870i | 0.999711 | + | 0.0240435i | \(0.00765403\pi\) | ||||
−0.999711 | + | 0.0240435i | \(0.992346\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.07991 | − | 5.24229i | −0.0833019 | − | 0.0480944i | 0.457770 | − | 0.889070i | \(-0.348648\pi\) |
−0.541072 | + | 0.840976i | \(0.681981\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.28999 | − | 96.4530i | 0.0476576 | − | 0.868946i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −177.083 | − | 102.239i | −1.56711 | − | 0.904772i | −0.996504 | − | 0.0835482i | \(-0.973375\pi\) |
−0.570607 | − | 0.821223i | \(-0.693292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −79.3149 | − | 137.377i | −0.689695 | − | 1.19459i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.48107 | + | 49.8182i | −0.0468468 | + | 0.425796i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 235.099 | 1.97562 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56.0676 | − | 97.1119i | 0.463369 | − | 0.802578i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −194.489 | + | 98.5023i | −1.58121 | + | 0.800832i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 168.978 | 1.35182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.6506 | − | 21.1602i | 0.288587 | − | 0.166616i | −0.348717 | − | 0.937228i | \(-0.613383\pi\) |
0.637305 | + | 0.770612i | \(0.280049\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −189.257 | − | 10.3798i | −1.46710 | − | 0.0804638i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 108.540 | + | 187.997i | 0.828552 | + | 1.43509i | 0.899174 | + | 0.437591i | \(0.144168\pi\) |
−0.0706218 | + | 0.997503i | \(0.522498\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −80.5859 | + | 151.146i | −0.605909 | + | 1.13644i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −79.5123 | − | 211.738i | −0.588980 | − | 1.56843i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −29.4674 | + | 51.0391i | −0.215091 | + | 0.372548i | −0.953301 | − | 0.302023i | \(-0.902338\pi\) |
0.738210 | + | 0.674571i | \(0.235671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.16605 | 0.0155831 | 0.00779155 | − | 0.999970i | \(-0.497520\pi\) | ||||
0.00779155 | + | 0.999970i | \(0.497520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −66.8109 | + | 102.334i | −0.473836 | + | 0.725776i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3590 | − | 8.29016i | 0.100412 | − | 0.0579731i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 131.697i | 0.908252i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −52.9272 | + | 81.0686i | −0.360049 | + | 0.551487i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −71.1507 | − | 123.237i | −0.477522 | − | 0.827092i | 0.522146 | − | 0.852856i | \(-0.325131\pi\) |
−0.999668 | + | 0.0257641i | \(0.991798\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −247.779 | + | 143.055i | −1.64092 | + | 0.947387i | −0.660416 | + | 0.750900i | \(0.729620\pi\) |
−0.980506 | + | 0.196487i | \(0.937047\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −138.878 | + | 189.208i | −0.907697 | + | 1.23665i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 155.501i | 1.00323i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −87.4600 | − | 151.485i | −0.557070 | − | 0.964874i | −0.997739 | − | 0.0672042i | \(-0.978592\pi\) |
0.440669 | − | 0.897670i | \(-0.354741\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 226.893 | − | 114.914i | 1.42700 | − | 0.722729i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −85.3579 | − | 147.844i | −0.530173 | − | 0.918287i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 280.563 | 1.72124 | 0.860622 | − | 0.509244i | \(-0.170075\pi\) | ||||
0.860622 | + | 0.509244i | \(0.170075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.9042 | + | 62.6530i | −0.247904 | + | 0.379715i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.68711i | − | 0.0340545i | −0.999855 | − | 0.0170273i | \(-0.994580\pi\) | ||
0.999855 | − | 0.0170273i | \(-0.00542021\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 137.989 | 0.816503 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −74.0386 | − | 154.140i | −0.432974 | − | 0.901406i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.03532i | 0.00598452i | 0.999996 | + | 0.00299226i | \(0.000952468\pi\) | ||||
−0.999996 | + | 0.00299226i | \(0.999048\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 407.230 | 2.32703 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 41.5589 | − | 21.0482i | 0.234796 | − | 0.118917i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 185.084i | − | 1.03399i | −0.855988 | − | 0.516996i | \(-0.827050\pi\) | ||
0.855988 | − | 0.516996i | \(-0.172950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 77.7940 | − | 44.9144i | 0.429801 | − | 0.248146i | −0.269461 | − | 0.963011i | \(-0.586845\pi\) |
0.699262 | + | 0.714866i | \(0.253512\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.3160 | + | 41.8399i | −0.149268 | + | 0.228634i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −233.592 | + | 134.865i | −1.26266 | + | 0.728998i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 77.6452 | 0.415215 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −85.5703 | − | 227.871i | −0.452753 | − | 1.20567i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 107.195 | + | 185.668i | 0.561233 | + | 0.972083i | 0.997389 | + | 0.0722127i | \(0.0230060\pi\) |
−0.436157 | + | 0.899871i | \(0.643661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.35082 | − | 4.24400i | 0.0380871 | − | 0.0219896i | −0.480836 | − | 0.876811i | \(-0.659667\pi\) |
0.518923 | + | 0.854821i | \(0.326333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 124.847 | − | 63.2310i | 0.640241 | − | 0.324261i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −182.684 | −0.927331 | −0.463666 | − | 0.886010i | \(-0.653466\pi\) | ||||
−0.463666 | + | 0.886010i | \(0.653466\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −117.295 | − | 203.161i | −0.589422 | − | 1.02091i | −0.994308 | − | 0.106541i | \(-0.966022\pi\) |
0.404886 | − | 0.914367i | \(-0.367311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3807 | − | 189.272i | 0.0516451 | − | 0.941650i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 141.731i | 0.698180i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 527.192 | + | 304.374i | 2.57167 | + | 1.48475i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 169.408 | + | 18.6385i | 0.818394 | + | 0.0900409i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.6148 | + | 49.9184i | −0.127344 | + | 0.238844i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −57.8006 | + | 33.3712i | −0.273936 | + | 0.158157i | −0.630675 | − | 0.776047i | \(-0.717222\pi\) |
0.356739 | + | 0.934204i | \(0.383889\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 244.523 | + | 159.641i | 1.14799 | + | 0.749489i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 264.627 | + | 458.347i | 1.23082 | + | 2.13185i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 167.349i | 0.771193i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 66.9852 | − | 102.601i | 0.305869 | − | 0.468500i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −125.768 | − | 72.6120i | −0.569084 | − | 0.328561i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 230.654i | − | 1.03432i | −0.855888 | − | 0.517161i | \(-0.826989\pi\) | ||
0.855888 | − | 0.517161i | \(-0.173011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −240.559 | + | 327.738i | −1.06915 | + | 1.45661i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −76.8934 | + | 44.3944i | −0.338737 | + | 0.195570i | −0.659713 | − | 0.751517i | \(-0.729322\pi\) |
0.320976 | + | 0.947087i | \(0.395989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 67.4283 | − | 116.789i | 0.294447 | − | 0.509997i | −0.680409 | − | 0.732832i | \(-0.738198\pi\) |
0.974856 | + | 0.222836i | \(0.0715313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −44.0207 | + | 67.4265i | −0.190566 | + | 0.291890i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 33.1778 | − | 57.4656i | 0.142394 | − | 0.246633i | −0.786004 | − | 0.618222i | \(-0.787853\pi\) |
0.928398 | + | 0.371588i | \(0.121187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 341.254 | 1.45215 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.7019 | − | 322.762i | 0.0746918 | − | 1.36186i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 157.173 | − | 272.231i | 0.657626 | − | 1.13904i | −0.323602 | − | 0.946193i | \(-0.604894\pi\) |
0.981228 | − | 0.192849i | \(-0.0617728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −43.9174 | − | 25.3557i | −0.182230 | − | 0.105210i | 0.406110 | − | 0.913824i | \(-0.366885\pi\) |
−0.588340 | + | 0.808614i | \(0.700218\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 233.938 | + | 65.7408i | 0.962709 | + | 0.270538i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 270.339 | 1.10343 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 89.7924 | − | 55.9669i | 0.363532 | − | 0.226587i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −155.400 | − | 306.830i | −0.624095 | − | 1.23225i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9851 | + | 19.0267i | 0.0437653 | + | 0.0758038i | 0.887078 | − | 0.461619i | \(-0.152731\pi\) |
−0.843313 | + | 0.537423i | \(0.819398\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.1908 | − | 48.8279i | −0.111426 | − | 0.192996i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 654.381 | + | 35.8897i | 2.56620 | + | 0.140744i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 410.241i | 1.59627i | 0.602479 | + | 0.798135i | \(0.294180\pi\) | ||||
−0.602479 | + | 0.798135i | \(0.705820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −251.390 | + | 145.140i | −0.970618 | + | 0.560386i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −114.065 | − | 83.7230i | −0.437029 | − | 0.320778i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 254.216 | 0.966600 | 0.483300 | − | 0.875455i | \(-0.339438\pi\) | ||||
0.483300 | + | 0.875455i | \(0.339438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −615.028 | − | 355.087i | −2.32086 | − | 1.33995i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.37352 | − | 4.24092i | 0.0313615 | − | 0.0158836i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.296857 | − | 0.171391i | −0.00110356 | − | 0.000637140i | 0.499448 | − | 0.866344i | \(-0.333536\pi\) |
−0.500552 | + | 0.865707i | \(0.666869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 177.957 | − | 308.230i | 0.656666 | − | 1.13738i | −0.324807 | − | 0.945780i | \(-0.605299\pi\) |
0.981473 | − | 0.191599i | \(-0.0613673\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 134.359 | − | 68.0486i | 0.492158 | − | 0.249262i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 134.494 | 0.489070 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −146.001 | − | 252.882i | −0.527081 | − | 0.912931i | −0.999502 | − | 0.0315577i | \(-0.989953\pi\) |
0.472421 | − | 0.881373i | \(-0.343380\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −134.682 | − | 98.8562i | −0.482732 | − | 0.354323i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 293.470 | + | 169.435i | 1.04438 | + | 0.602972i | 0.921070 | − | 0.389396i | \(-0.127316\pi\) |
0.123308 | + | 0.992368i | \(0.460650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 38.4339 | + | 66.5694i | 0.135809 | + | 0.235228i | 0.925906 | − | 0.377754i | \(-0.123303\pi\) |
−0.790097 | + | 0.612981i | \(0.789970\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −247.379 | + | 408.402i | −0.867996 | + | 1.43299i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 567.359 | + | 327.565i | 1.97686 | + | 1.14134i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −195.540 | − | 338.685i | −0.676610 | − | 1.17192i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.8178 | − | 361.341i | 0.0681025 | − | 1.24172i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.8270 | − | 7.98304i | −0.0471913 | − | 0.0272459i | 0.476219 | − | 0.879327i | \(-0.342007\pi\) |
−0.523410 | + | 0.852081i | \(0.675340\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −112.652 | − | 65.0395i | −0.381870 | − | 0.220473i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.2610 | − | 75.2580i | −0.0951548 | − | 0.253394i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 105.454i | 0.352687i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 284.789 | + | 493.268i | 0.946141 | + | 1.63877i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.9194 | + | 44.2959i | −0.0954435 | + | 0.146191i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 139.524 | 0.457454 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 392.315 | + | 226.503i | 1.27790 | + | 0.737795i | 0.976461 | − | 0.215692i | \(-0.0692006\pi\) |
0.301436 | + | 0.953486i | \(0.402534\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 292.186 | + | 190.759i | 0.945587 | + | 0.617344i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −179.030 | + | 310.089i | −0.575659 | + | 0.997071i | 0.420311 | + | 0.907380i | \(0.361921\pi\) |
−0.995970 | + | 0.0896903i | \(0.971412\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −289.612 | + | 501.622i | −0.925277 | + | 1.60263i | −0.134161 | + | 0.990959i | \(0.542834\pi\) |
−0.791115 | + | 0.611667i | \(0.790499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −402.165 | + | 547.912i | −1.27672 | + | 1.73940i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −276.153 | − | 159.437i | −0.871146 | − | 0.502956i | −0.00341721 | − | 0.999994i | \(-0.501088\pi\) |
−0.867729 | + | 0.497038i | \(0.834421\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.8088i | 0.146736i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.845318 | + | 15.4128i | −0.00263339 | + | 0.0480149i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 495.206 | − | 16.7304i | 1.53315 | − | 0.0517968i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −217.850 | − | 125.776i | −0.670308 | − | 0.387002i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.3376 | − | 17.1950i | −0.0805431 | − | 0.0525841i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 367.254 | 1.11627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 454.593 | − | 262.459i | 1.37339 | − | 0.792928i | 0.382038 | − | 0.924147i | \(-0.375222\pi\) |
0.991353 | + | 0.131219i | \(0.0418890\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.6923 | − | 288.056i | 0.0951721 | − | 0.865032i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −458.383 | + | 264.648i | −1.36831 | + | 0.789993i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −183.075 | + | 105.698i | −0.543249 | + | 0.313645i | −0.746395 | − | 0.665504i | \(-0.768217\pi\) |
0.203146 | + | 0.979149i | \(0.434884\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −513.656 | − | 335.350i | −1.51521 | − | 0.989234i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.2696i | 0.162081i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −150.804 | −0.439661 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −215.018 | − | 424.544i | −0.623241 | − | 1.23056i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −137.369 | − | 237.930i | −0.395875 | − | 0.685676i | 0.597337 | − | 0.801990i | \(-0.296225\pi\) |
−0.993213 | + | 0.116314i | \(0.962892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −50.0768 | − | 86.7355i | −0.143486 | − | 0.248526i | 0.785321 | − | 0.619089i | \(-0.212498\pi\) |
−0.928807 | + | 0.370563i | \(0.879165\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.6031 | + | 148.330i | −0.0700943 | + | 0.422592i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 285.912 | + | 495.215i | 0.809950 | + | 1.40287i | 0.912898 | + | 0.408187i | \(0.133839\pi\) |
−0.102948 | + | 0.994687i | \(0.532828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 815.409i | − | 2.29693i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 704.239 | + | 38.6242i | 1.97266 | + | 0.108191i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.1543 | − | 52.2287i | 0.0839951 | − | 0.145484i | −0.820967 | − | 0.570975i | \(-0.806565\pi\) |
0.904963 | + | 0.425491i | \(0.139899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −158.988 | + | 324.105i | −0.440410 | + | 0.897797i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 183.905 | − | 281.687i | 0.506625 | − | 0.775998i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −342.145 | −0.937382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 262.298 | − | 454.314i | 0.714709 | − | 1.23791i | −0.248363 | − | 0.968667i | \(-0.579893\pi\) |
0.963072 | − | 0.269245i | \(-0.0867741\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −598.774 | + | 263.111i | −1.62269 | + | 0.713038i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −661.887 | − | 382.141i | −1.78406 | − | 1.03003i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −525.452 | − | 303.370i | −1.40872 | − | 0.813324i | −0.413454 | − | 0.910525i | \(-0.635678\pi\) |
−0.995265 | + | 0.0972011i | \(0.969011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 506.173 | + | 27.7612i | 1.34979 | + | 0.0740298i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.7744 | − | 75.8195i | 0.116113 | − | 0.201113i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 488.868i | 1.28989i | 0.764229 | + | 0.644945i | \(0.223120\pi\) | ||||
−0.764229 | + | 0.644945i | \(0.776880\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 113.263 | − | 57.3641i | 0.297279 | − | 0.150562i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −153.679 | + | 88.7264i | −0.401250 | + | 0.231662i | −0.687023 | − | 0.726636i | \(-0.741083\pi\) |
0.285773 | + | 0.958297i | \(0.407750\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 224.847 | 0.584018 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −565.212 | − | 62.1855i | −1.46050 | − | 0.160686i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 335.243 | − | 580.659i | 0.861808 | − | 1.49270i | −0.00837339 | − | 0.999965i | \(-0.502665\pi\) |
0.870182 | − | 0.492731i | \(-0.164001\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −246.918 | + | 427.675i | −0.631504 | + | 1.09380i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 294.246 | + | 580.978i | 0.748719 | + | 1.47831i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −781.673 | + | 451.299i | −1.97892 | + | 1.14253i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −143.711 | + | 248.915i | −0.361992 | + | 0.626989i | −0.988289 | − | 0.152596i | \(-0.951237\pi\) |
0.626296 | + | 0.779585i | \(0.284570\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −266.227 | + | 439.518i | −0.667235 | + | 1.10155i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −116.457 | + | 67.2365i | −0.290417 | + | 0.167672i | −0.638130 | − | 0.769929i | \(-0.720292\pi\) |
0.347713 | + | 0.937601i | \(0.386958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 51.6868 | − | 89.5242i | 0.128255 | − | 0.222144i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −203.393 | − | 647.325i | −0.502204 | − | 1.59833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −83.0256 | + | 47.9348i | −0.203994 | + | 0.117776i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 599.099i | − | 1.46479i | −0.680880 | − | 0.732395i | \(-0.738402\pi\) | ||
0.680880 | − | 0.732395i | \(-0.261598\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −96.6548 | + | 148.046i | −0.235170 | + | 0.360210i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −121.235 | − | 69.9949i | −0.293547 | − | 0.169479i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −480.188 | + | 831.711i | −1.15708 | + | 2.00412i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.48840 | + | 0.355858i | 0.0155597 | + | 0.000853376i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −161.894 | + | 280.408i | −0.386381 | + | 0.669232i | −0.991960 | − | 0.126553i | \(-0.959609\pi\) |
0.605578 | + | 0.795786i | \(0.292942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 652.095i | − | 1.54892i | −0.632624 | − | 0.774459i | \(-0.718022\pi\) | ||
0.632624 | − | 0.774459i | \(-0.281978\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −216.944 | + | 295.566i | −0.512871 | + | 0.698738i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −589.005 | − | 1020.19i | −1.38589 | − | 2.40044i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 150.154 | 0.351648 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 44.3743 | − | 22.4741i | 0.103436 | − | 0.0523872i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 99.9113 | − | 57.6838i | 0.231813 | − | 0.133837i | −0.379595 | − | 0.925153i | \(-0.623937\pi\) |
0.611408 | + | 0.791315i | \(0.290603\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −60.5946 | + | 34.9843i | −0.139941 | + | 0.0807952i | −0.568336 | − | 0.822797i | \(-0.692413\pi\) |
0.428395 | + | 0.903592i | \(0.359079\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.6363 | + | 394.497i | −0.0497386 | + | 0.906889i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −190.317 | − | 305.341i | −0.435507 | − | 0.698720i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 449.021i | 1.02283i | 0.859335 | + | 0.511414i | \(0.170878\pi\) | ||||
−0.859335 | + | 0.511414i | \(0.829122\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −171.862 | + | 234.146i | −0.389710 | + | 0.530942i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −96.3807 | + | 166.936i | −0.217564 | + | 0.376831i | −0.954063 | − | 0.299607i | \(-0.903144\pi\) |
0.736499 | + | 0.676439i | \(0.236478\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.6977 | − | 13.1045i | −0.0510061 | − | 0.0294484i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −192.885 | − | 380.845i | −0.431511 | − | 0.852001i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 264.055i | − | 0.588096i | −0.955791 | − | 0.294048i | \(-0.904997\pi\) | ||
0.955791 | − | 0.294048i | \(-0.0950025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 187.379 | + | 108.183i | 0.415475 | + | 0.239875i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −765.725 | + | 387.815i | −1.69034 | + | 0.856104i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −364.201 | − | 210.272i | −0.800442 | − | 0.462135i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −225.519 | − | 390.610i | −0.493476 | − | 0.854726i | 0.506495 | − | 0.862243i | \(-0.330941\pi\) |
−0.999972 | + | 0.00751646i | \(0.997607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −447.092 | + | 543.955i | −0.974057 | + | 1.18509i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 599.782 | 1.30104 | 0.650522 | − | 0.759487i | \(-0.274550\pi\) | ||||
0.650522 | + | 0.759487i | \(0.274550\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.3790 | + | 68.2064i | −0.0850518 | + | 0.147314i | −0.905413 | − | 0.424531i | \(-0.860439\pi\) |
0.820361 | + | 0.571845i | \(0.193772\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.5471 | + | 465.803i | −0.0549400 | + | 1.00173i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 570.793 | 1.22225 | 0.611127 | − | 0.791532i | \(-0.290716\pi\) | ||||
0.611127 | + | 0.791532i | \(0.290716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −493.308 | + | 284.811i | −1.05183 | + | 0.607274i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −237.099 | − | 468.142i | −0.503395 | − | 0.993933i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 94.0560 | + | 162.910i | 0.198850 | + | 0.344418i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 857.778 | − | 28.9797i | 1.80585 | − | 0.0610099i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 698.537 | − | 306.949i | 1.46444 | − | 0.643498i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 462.338 | − | 800.793i | 0.965215 | − | 1.67180i | 0.256179 | − | 0.966629i | \(-0.417536\pi\) |
0.709036 | − | 0.705172i | \(-0.249130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 179.310 | 0.372786 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −231.400 | − | 456.891i | −0.479090 | − | 0.945943i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −875.105 | + | 505.242i | −1.80434 | + | 1.04174i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 236.919i | 0.486486i | 0.969965 | + | 0.243243i | \(0.0782113\pi\) | ||||
−0.969965 | + | 0.243243i | \(0.921789\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 840.425 | + | 46.0934i | 1.71866 | + | 0.0942605i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −276.148 | − | 478.302i | −0.562420 | − | 0.974139i | −0.997285 | − | 0.0736437i | \(-0.976537\pi\) |
0.434865 | − | 0.900496i | \(-0.356796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 355.061 | − | 204.995i | 0.720205 | − | 0.415811i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −132.822 | + | 180.957i | −0.268326 | + | 0.365569i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 877.535i | − | 1.76566i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 185.062 | + | 320.536i | 0.370865 | + | 0.642357i | 0.989699 | − | 0.143165i | \(-0.0457278\pi\) |
−0.618834 | + | 0.785522i | \(0.712395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.934328 | − | 17.0357i | 0.00186493 | − | 0.0340034i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −410.372 | − | 710.785i | −0.815848 | − | 1.41309i | −0.908717 | − | 0.417412i | \(-0.862937\pi\) |
0.0928687 | − | 0.995678i | \(-0.470396\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 147.713 | 0.292502 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 413.346 | + | 22.6701i | 0.815278 | + | 0.0447141i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 37.8132i | − | 0.0742891i | −0.999310 | − | 0.0371446i | \(-0.988174\pi\) | ||
0.999310 | − | 0.0371446i | \(-0.0118262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −368.213 | −0.720573 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −196.459 | − | 473.891i | −0.382961 | − | 0.923765i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 974.353i | − | 1.89195i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 121.292 | 0.234607 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.170092 | + | 3.10131i | −0.000327730 | + | 0.00597554i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 190.170i | 0.365009i | 0.983205 | + | 0.182504i | \(0.0584204\pi\) | ||||
−0.983205 | + | 0.182504i | \(0.941580\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 86.4225 | − | 49.8961i | 0.165244 | − | 0.0954035i | −0.415097 | − | 0.909777i | \(-0.636253\pi\) |
0.580341 | + | 0.814373i | \(0.302919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1219.86 | + | 66.9034i | 2.32354 | + | 0.127435i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 419.240 | − | 242.048i | 0.795522 | − | 0.459295i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −170.403 | −0.322124 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 127.948 | − | 56.2223i | 0.240956 | − | 0.105880i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −202.341 | − | 350.465i | −0.379627 | − | 0.657533i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.3271 | − | 21.5508i | 0.0697703 | − | 0.0402819i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.4073 | − | 554.420i | 0.0566245 | − | 1.03244i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 96.0865 | 0.178268 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 151.059 | + | 261.642i | 0.279222 | + | 0.483627i | 0.971192 | − | 0.238300i | \(-0.0765901\pi\) |
−0.691970 | + | 0.721927i | \(0.743257\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 240.411 | − | 121.760i | 0.442745 | − | 0.224236i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 87.8279i | 0.161152i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 313.718 | + | 181.125i | 0.573525 | + | 0.331125i | 0.758556 | − | 0.651608i | \(-0.225905\pi\) |
−0.185031 | + | 0.982733i | \(0.559239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −88.6988 | + | 120.844i | −0.161564 | + | 0.220116i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.0860 | + | 298.537i | 0.0183049 | + | 0.541810i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −841.229 | + | 485.684i | −1.52121 | + | 0.878271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −721.883 | + | 365.610i | −1.30069 | + | 0.658757i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 198.669 | + | 344.104i | 0.356676 | + | 0.617781i | 0.987403 | − | 0.158223i | \(-0.0505766\pi\) |
−0.630727 | + | 0.776005i | \(0.717243\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 351.836i | − | 0.629402i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 232.586 | + | 12.7563i | 0.414592 | + | 0.0227384i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 250.075 | + | 144.381i | 0.444182 | + | 0.256449i | 0.705370 | − | 0.708839i | \(-0.250781\pi\) |
−0.261188 | + | 0.965288i | \(0.584114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1712.89i | 3.03166i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −218.889 | − | 696.645i | −0.386048 | − | 1.22865i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 506.239 | − | 292.277i | 0.889700 | − | 0.513668i | 0.0158554 | − | 0.999874i | \(-0.494953\pi\) |
0.873844 | + | 0.486206i | \(0.161620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −523.855 | + | 907.343i | −0.917434 | + | 1.58904i | −0.114135 | + | 0.993465i | \(0.536410\pi\) |
−0.803298 | + | 0.595577i | \(0.796924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 290.601 | + | 573.779i | 0.507156 | + | 1.00136i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −427.703 | + | 740.803i | −0.743831 | + | 1.28835i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 514.036 | 0.890877 | 0.445438 | − | 0.895313i | \(-0.353048\pi\) | ||||
0.445438 | + | 0.895313i | \(0.353048\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.7166 | − | 11.5052i | 0.0392342 | − | 0.0198708i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −516.774 | + | 895.079i | −0.889456 | + | 1.54058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −218.599 | − | 126.208i | −0.374955 | − | 0.216481i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 384.367 | − | 168.897i | 0.657038 | − | 0.288713i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −506.000 | −0.862010 | −0.431005 | − | 0.902350i | \(-0.641841\pi\) | ||||
−0.431005 | + | 0.902350i | \(0.641841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9091 | + | 352.499i | 0.0202191 | + | 0.598470i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −547.230 | − | 30.0130i | −0.925940 | − | 0.0507834i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −110.508 | − | 191.405i | −0.186353 | − | 0.322774i | 0.757678 | − | 0.652628i | \(-0.226334\pi\) |
−0.944032 | + | 0.329855i | \(0.893000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −984.697 | − | 1705.55i | −1.65495 | − | 2.86646i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −317.980 | − | 627.838i | −0.532629 | − | 1.05165i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 149.926i | − | 0.250294i | −0.992138 | − | 0.125147i | \(-0.960060\pi\) | ||
0.992138 | − | 0.125147i | \(-0.0399402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −933.044 | + | 538.693i | −1.55249 | + | 0.896328i | −0.554547 | + | 0.832153i | \(0.687108\pi\) |
−0.997939 | + | 0.0641750i | \(0.979558\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 62.1905 | − | 565.257i | 0.103135 | − | 0.937409i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −939.342 | −1.55263 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 990.463 | + | 571.844i | 1.63174 | + | 0.942083i | 0.983558 | + | 0.180594i | \(0.0578019\pi\) |
0.648178 | + | 0.761489i | \(0.275531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.2848 | + | 424.553i | −0.0382344 | + | 0.697132i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −196.465 | − | 113.429i | −0.321546 | − | 0.185645i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −357.940 | + | 619.969i | −0.583914 | + | 1.01137i | 0.411095 | + | 0.911592i | \(0.365146\pi\) |
−0.995010 | + | 0.0997770i | \(0.968187\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1529.20 | + | 998.364i | 2.48650 | + | 1.62336i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1147.16 | −1.85925 | −0.929625 | − | 0.368506i | \(-0.879869\pi\) | ||||
−0.929625 | + | 0.368506i | \(0.879869\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 194.222 | + | 336.402i | 0.313767 | + | 0.543460i | 0.979175 | − | 0.203020i | \(-0.0650757\pi\) |
−0.665408 | + | 0.746480i | \(0.731742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 504.398 | + | 83.6633i | 0.812235 | + | 0.134724i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.4271 | − | 14.1030i | −0.0392088 | − | 0.0226372i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −143.103 | − | 247.862i | −0.228965 | − | 0.396579i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −87.9256 | + | 145.158i | −0.140232 | + | 0.231512i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 727.206 | + | 419.852i | 1.15613 | + | 0.667492i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −398.613 | − | 690.418i | −0.631717 | − | 1.09417i | −0.987201 | − | 0.159483i | \(-0.949017\pi\) |
0.355484 | − | 0.934682i | \(-0.384316\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −178.624 | + | 90.4673i | −0.282186 | + | 0.142918i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −307.017 | − | 177.256i | −0.483492 | − | 0.279144i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −155.638 | − | 89.8578i | −0.244330 | − | 0.141064i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 706.240 | + | 518.377i | 1.10523 | + | 0.811232i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 769.355i | − | 1.20024i | −0.799909 | − | 0.600121i | \(-0.795119\pi\) | ||
0.799909 | − | 0.600121i | \(-0.204881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 159.471 | + | 276.211i | 0.248010 | + | 0.429567i | 0.962974 | − | 0.269595i | \(-0.0868899\pi\) |
−0.714963 | + | 0.699162i | \(0.753557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 717.387 | + | 1416.45i | 1.11223 | + | 2.19605i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 585.103 | 0.904333 | 0.452166 | − | 0.891934i | \(-0.350651\pi\) | ||||
0.452166 | + | 0.891934i | \(0.350651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.0397 | − | 23.1169i | −0.0616945 | − | 0.0356193i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.4936 | + | 501.293i | −0.0422328 | + | 0.770035i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −89.3580 | + | 154.773i | −0.136842 | + | 0.237018i | −0.926300 | − | 0.376788i | \(-0.877029\pi\) |
0.789457 | + | 0.613805i | \(0.210362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 909.228 | − | 1574.83i | 1.38813 | − | 2.40432i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 217.510 | − | 296.337i | 0.331066 | − | 0.451046i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −118.419 | − | 68.3690i | −0.179694 | − | 0.103747i | 0.407455 | − | 0.913225i | \(-0.366416\pi\) |
−0.587149 | + | 0.809479i | \(0.699750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 633.064i | 0.957737i | 0.877887 | + | 0.478869i | \(0.158953\pi\) | ||||
−0.877887 | + | 0.478869i | \(0.841047\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −364.807 | − | 238.171i | −0.550237 | − | 0.359233i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1434.03 | − | 48.4482i | 2.15644 | − | 0.0728545i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −257.826 | − | 148.856i | −0.386545 | − | 0.223172i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.8939 | − | 690.923i | 0.0566425 | − | 1.03277i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.5907 | 0.0739057 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −293.528 | + | 169.468i | −0.436149 | + | 0.251811i | −0.701963 | − | 0.712214i | \(-0.747693\pi\) |
0.265814 | + | 0.964024i | \(0.414359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −774.437 | + | 942.219i | −1.14731 | + | 1.39588i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 90.2123 | − | 52.0841i | 0.133253 | − | 0.0769337i | −0.431892 | − | 0.901926i | \(-0.642154\pi\) |
0.565145 | + | 0.824992i | \(0.308820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −941.780 | + | 543.737i | −1.38701 | + | 0.800791i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −237.627 | + | 120.351i | −0.348939 | + | 0.176726i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 517.968i | − | 0.758371i | −0.925321 | − | 0.379186i | \(-0.876204\pi\) | ||
0.925321 | − | 0.379186i | \(-0.123796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 493.690 | 0.720715 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 221.169 | − | 338.764i | 0.321934 | − | 0.493107i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 236.054 | + | 408.857i | 0.342603 | + | 0.593406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.7261 | − | 77.4679i | −0.0647266 | − | 0.112110i | 0.831846 | − | 0.555006i | \(-0.187284\pi\) |
−0.896573 | + | 0.442897i | \(0.853951\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −142.941 | + | 194.744i | −0.206264 | + | 0.281016i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.07236 | − | 15.7138i | −0.0130538 | − | 0.0226098i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1895.12i | − | 2.71896i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 108.825 | − | 166.687i | 0.155687 | − | 0.238465i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 291.669 | − | 505.186i | 0.416076 | − | 0.720665i | −0.579465 | − | 0.814997i | \(-0.696738\pi\) |
0.995541 | + | 0.0943325i | \(0.0300717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −519.192 | + | 323.609i | −0.738538 | + | 0.460325i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1022.23 | + | 56.0643i | 1.44997 | + | 0.0795238i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 158.968 | 0.224848 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −426.312 | + | 738.395i | −0.601287 | + | 1.04146i | 0.391340 | + | 0.920246i | \(0.372012\pi\) |
−0.992627 | + | 0.121213i | \(0.961322\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 106.052 | − | 963.924i | 0.149159 | − | 1.35573i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −304.429 | − | 175.762i | −0.426969 | − | 0.246510i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −120.283 | − | 69.4456i | −0.168228 | − | 0.0971267i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 515.535 | − | 789.646i | 0.719017 | − | 1.10132i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −443.865 | + | 768.797i | −0.617337 | + | 1.06926i | 0.372633 | + | 0.927979i | \(0.378455\pi\) |
−0.989970 | + | 0.141280i | \(0.954878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1048.59i | − | 1.45435i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −127.389 | − | 83.1681i | −0.176195 | − | 0.115032i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 615.024 | − | 355.084i | 0.848309 | − | 0.489771i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −331.033 | −0.455341 | −0.227671 | − | 0.973738i | \(-0.573111\pi\) | ||||
−0.227671 | + | 0.973738i | \(0.573111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 689.961 | + | 235.360i | 0.946449 | + | 0.322853i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 823.819 | − | 1426.90i | 1.12698 | − | 1.95198i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −411.381 | + | 712.533i | −0.561229 | + | 0.972078i | 0.436160 | + | 0.899869i | \(0.356338\pi\) |
−0.997390 | + | 0.0722087i | \(0.976995\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 809.801 | + | 44.4138i | 1.10177 | + | 0.0604269i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −162.923 | + | 94.0635i | −0.221062 | + | 0.127630i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 351.505 | − | 608.824i | 0.475649 | − | 0.823849i | −0.523962 | − | 0.851742i | \(-0.675546\pi\) |
0.999611 | + | 0.0278931i | \(0.00887980\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 278.168 | − | 152.897i | 0.375395 | − | 0.206339i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −928.485 | + | 536.061i | −1.24964 | + | 0.721482i | −0.971038 | − | 0.238924i | \(-0.923205\pi\) |
−0.278605 | + | 0.960406i | \(0.589872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −596.020 | + | 1032.34i | −0.800027 | + | 1.38569i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −415.090 | − | 944.640i | −0.555677 | − | 1.26458i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40.1711 | − | 23.1928i | 0.0536329 | − | 0.0309650i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 120.921i | − | 0.161014i | −0.996754 | − | 0.0805068i | \(-0.974346\pi\) | ||
0.996754 | − | 0.0805068i | \(-0.0256539\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.7800 | + | 58.7993i | 0.0395484 | + | 0.0780867i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2075.62 | + | 1198.36i | 2.74916 | + | 1.58723i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −500.057 | + | 866.125i | −0.660578 | + | 1.14415i | 0.319887 | + | 0.947456i | \(0.396355\pi\) |
−0.980464 | + | 0.196698i | \(0.936978\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −76.4237 | − | 150.895i | −0.100690 | − | 0.198808i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 710.262 | − | 1230.21i | 0.933327 | − | 1.61657i | 0.155736 | − | 0.987799i | \(-0.450225\pi\) |
0.777591 | − | 0.628771i | \(-0.216442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 94.5195i | 0.123879i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1954.30 | + | 215.015i | 2.55464 | + | 0.281066i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.2368 | + | 74.8884i | 0.0563713 | + | 0.0976380i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 452.651 | 0.588623 | 0.294312 | − | 0.955709i | \(-0.404910\pi\) | ||||
0.294312 | + | 0.955709i | \(0.404910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −67.3981 | + | 1228.88i | −0.0874164 | + | 1.59387i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −158.416 | + | 91.4618i | −0.204937 | + | 0.118321i | −0.598956 | − | 0.800782i | \(-0.704418\pi\) |
0.394019 | + | 0.919102i | \(0.371084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 726.192 | − | 419.267i | 0.937022 | − | 0.540990i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −776.883 | + | 393.466i | −0.999850 | + | 0.506392i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1218.38 | + | 649.598i | 1.56403 | + | 0.833887i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 289.820i | − | 0.371088i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −327.926 | − | 269.532i | −0.418807 | − | 0.344229i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −732.641 | + | 1268.97i | −0.933301 | + | 1.61652i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 355.648 | + | 205.334i | 0.451904 | + | 0.260907i | 0.708634 | − | 0.705576i | \(-0.249312\pi\) |
−0.256730 | + | 0.966483i | \(0.582645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 761.503 | + | 41.7648i | 0.965149 | + | 0.0529339i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1843.39i | 2.33046i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −80.3257 | − | 46.3760i | −0.101293 | − | 0.0584818i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1783.98 | − | 1164.70i | −2.24400 | − | 1.46504i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1016.85 | + | 587.077i | 1.27584 | + | 0.736609i | 0.976081 | − | 0.217405i | \(-0.0697594\pi\) |
0.299762 | + | 0.954014i | \(0.403093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −531.186 | − | 920.040i | −0.664813 | − | 1.15149i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.7796 | − | 11.3280i | 0.0321843 | − | 0.0141423i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −121.608 | −0.151442 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −715.032 | + | 1238.47i | −0.888239 | + | 1.53847i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.861078 | − | 0.562171i | −0.00106701 | − | 0.000696618i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 500.592 | 0.618778 | 0.309389 | − | 0.950936i | \(-0.399875\pi\) | ||||
0.309389 | + | 0.950936i | \(0.399875\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 671.823 | − | 387.877i | 0.828389 | − | 0.478270i | −0.0249120 | − | 0.999690i | \(-0.507931\pi\) |
0.853301 | + | 0.521419i | \(0.174597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 583.707 | − | 894.065i | 0.717967 | − | 1.09971i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1175.12 | − | 2035.37i | −1.44186 | − | 2.49738i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 634.973 | + | 1018.74i | 0.777201 | + | 1.24693i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 413.652 | − | 181.766i | 0.505070 | − | 0.221936i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 724.841 | − | 1255.46i | 0.882875 | − | 1.52918i | 0.0347454 | − | 0.999396i | \(-0.488938\pi\) |
0.848130 | − | 0.529789i | \(-0.177729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0138 | 0.0267482 | 0.0133741 | − | 0.999911i | \(-0.495743\pi\) | ||||
0.0133741 | + | 0.999911i | \(0.495743\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 402.877 | + | 22.0959i | 0.488336 | + | 0.0267829i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −417.259 | + | 240.905i | −0.504546 | + | 0.291300i | −0.730589 | − | 0.682818i | \(-0.760754\pi\) |
0.226043 | + | 0.974117i | \(0.427421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1578.05i | − | 1.90355i | −0.306791 | − | 0.951777i | \(-0.599255\pi\) | ||
0.306791 | − | 0.951777i | \(-0.400745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −395.801 | − | 781.493i | −0.476295 | − | 0.940425i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −420.802 | − | 728.850i | −0.505164 | − | 0.874970i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.2576 | + | 23.8201i | −0.0494103 | + | 0.0285270i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −387.199 | − | 318.250i | −0.462604 | − | 0.380227i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 934.080i | 1.11333i | 0.830739 | + | 0.556663i | \(0.187918\pi\) | ||||
−0.830739 | + | 0.556663i | \(0.812082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −296.918 | − | 514.277i | −0.353054 | − | 0.611507i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 851.254 | + | 555.757i | 1.00979 | + | 0.659261i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −577.958 | − | 1001.05i | −0.683974 | − | 1.18468i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1010.91 | −1.19352 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 104.192 | + | 205.723i | 0.122723 | + | 0.242312i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 609.747i | − | 0.716506i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 293.146 | 0.343665 | 0.171832 | − | 0.985126i | \(-0.445031\pi\) | ||||
0.171832 | + | 0.985126i | \(0.445031\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −808.119 | + | 1182.73i | −0.945168 | + | 1.38331i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 801.284i | 0.934987i | 0.883996 | + | 0.467494i | \(0.154843\pi\) | ||||
−0.883996 | + | 0.467494i | \(0.845157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −850.247 | −0.989810 | −0.494905 | − | 0.868947i | \(-0.664797\pi\) | ||||
−0.494905 | + | 0.868947i | \(0.664797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1645.71 | + | 1074.43i | 1.91139 | + | 1.24789i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 57.6973i | 0.0668566i | 0.999441 | + | 0.0334283i | \(0.0106425\pi\) | ||||
−0.999441 | + | 0.0334283i | \(0.989357\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.51083 | − | 4.33638i | 0.00868304 | − | 0.00501316i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −530.098 | − | 1046.66i | −0.611416 | − | 1.20722i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −277.829 | + | 160.405i | −0.319712 | + | 0.184586i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 351.864 | 0.403977 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 118.729 | − | 1079.14i | 0.136001 | − | 1.23613i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −761.676 | − | 1319.26i | −0.870487 | − | 1.50773i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1377.56 | − | 795.333i | 1.57076 | − | 0.906879i | 0.574684 | − | 0.818375i | \(-0.305125\pi\) |
0.996076 | − | 0.0885036i | \(-0.0282085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.1073 | − | 26.1848i | −0.0456284 | − | 0.0297893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1154.00 | −1.30987 | −0.654936 | − | 0.755684i | \(-0.727304\pi\) | ||||
−0.654936 | + | 0.755684i | \(0.727304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 184.480 | + | 319.529i | 0.208924 | + | 0.361867i | 0.951376 | − | 0.308032i | \(-0.0996705\pi\) |
−0.742452 | + | 0.669899i | \(0.766337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −326.763 | − | 213.333i | −0.369224 | − | 0.241055i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1079.34i | 1.21685i | 0.793613 | + | 0.608423i | \(0.208198\pi\) | ||||
−0.793613 | + | 0.608423i | \(0.791802\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −330.409 | − | 190.762i | −0.371664 | − | 0.214580i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −72.2916 | − | 230.078i | −0.0811354 | − | 0.258225i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 773.574 | − | 26.1349i | 0.866265 | − | 0.0292664i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1342.71 | + | 775.214i | −1.50024 | + | 0.866161i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.3248 | + | 315.886i | −0.0193142 | + | 0.352158i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 145.920 | + | 252.741i | 0.162314 | + | 0.281135i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2210.87i | 2.45379i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 772.045 | + | 1524.37i | 0.854978 | + | 1.68812i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −651.670 | − | 376.242i | −0.720078 | − | 0.415737i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1159.72i | 1.27863i | 0.768945 | + | 0.639315i | \(0.220782\pi\) | ||||
−0.768945 | + | 0.639315i | \(0.779218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −93.9053 | + | 127.937i | −0.103306 | + | 0.140745i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 228.498 | − | 131.923i | 0.250821 | − | 0.144812i | −0.369319 | − | 0.929303i | \(-0.620409\pi\) |
0.620140 | + | 0.784491i | \(0.287076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −170.673 | + | 295.614i | −0.186936 | + | 0.323783i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 417.943 | + | 22.9222i | 0.456768 | + | 0.0250516i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 978.503 | − | 1694.82i | 1.06707 | − | 1.84822i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 197.600 | 0.215016 | 0.107508 | − | 0.994204i | \(-0.465713\pi\) | ||||
0.107508 | + | 0.994204i | \(0.465713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1137.97 | + | 742.942i | 1.23558 | + | 0.806669i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −271.033 | + | 469.442i | −0.293643 | + | 0.508605i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1259.64 | + | 727.253i | 1.36177 | + | 0.786219i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 843.904 | + | 619.422i | 0.910360 | + | 0.668201i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2727 | 0.0175164 | 0.00875820 | − | 0.999962i | \(-0.497212\pi\) | ||||
0.00875820 | + | 0.999962i | \(0.497212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 612.821 | − | 20.7039i | 0.658239 | − | 0.0222384i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −587.228 | + | 899.458i | −0.629398 | + | 0.964050i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −325.212 | − | 563.284i | −0.347820 | − | 0.602442i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 136.677 | + | 236.732i | 0.145867 | + | 0.252649i | 0.929696 | − | 0.368328i | \(-0.120070\pi\) |
−0.783829 | + | 0.620976i | \(0.786736\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −949.942 | + | 1455.03i | −1.01165 | + | 1.54955i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1205.09i | 1.28065i | 0.768104 | + | 0.640325i | \(0.221200\pi\) | ||||
−0.768104 | + | 0.640325i | \(0.778800\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1191.76 | + | 688.065i | −1.26380 | + | 0.729655i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1294.70 | + | 1575.20i | −1.37005 | + | 1.66688i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1029.74 | 1.08737 | 0.543686 | − | 0.839289i | \(-0.317028\pi\) | ||||
0.543686 | + | 0.839289i | \(0.317028\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 196.977 | + | 113.725i | 0.207563 | + | 0.119837i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −801.023 | − | 522.963i | −0.842296 | − | 0.549908i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −618.547 | − | 357.118i | −0.649052 | − | 0.374730i | 0.139041 | − | 0.990287i | \(-0.455598\pi\) |
−0.788093 | + | 0.615556i | \(0.788931\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 897.962 | − | 1555.32i | 0.940275 | − | 1.62860i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.69016 | + | 140.216i | −0.00803570 | + | 0.146516i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 531.304 | 0.554019 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −308.205 | − | 533.826i | −0.320712 | − | 0.555490i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.06430 | + | 46.0301i | −0.00525888 | + | 0.0477986i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −61.5768 | − | 35.5514i | −0.0638102 | − | 0.0368408i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 545.797 | + | 945.348i | 0.564423 | + | 0.977609i | 0.997103 | + | 0.0760618i | \(0.0242346\pi\) |
−0.432680 | + | 0.901548i | \(0.642432\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1486.14 | + | 31.2411i | 1.53368 | + | 0.0322406i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 997.067 | + | 575.657i | 1.02685 | + | 0.592850i | 0.916079 | − | 0.400997i | \(-0.131336\pi\) |
0.110766 | + | 0.993847i | \(0.464670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.76358 | − | 16.9110i | −0.0100345 | − | 0.0173803i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −631.906 | − | 412.551i | −0.648108 | − | 0.423130i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −742.979 | − | 428.959i | −0.760470 | − | 0.439057i | 0.0689947 | − | 0.997617i | \(-0.478021\pi\) |
−0.829464 | + | 0.558560i | \(0.811354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.06743 | − | 4.65773i | −0.00824048 | − | 0.00475764i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −76.0693 | − | 55.8345i | −0.0775426 | − | 0.0569159i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 877.350i | 0.892523i | 0.894903 | + | 0.446261i | \(0.147245\pi\) | ||||
−0.894903 | + | 0.446261i | \(0.852755\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 765.161 | + | 1325.30i | 0.776813 | + | 1.34548i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1100.11 | + | 60.3358i | 1.11460 | + | 0.0611305i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1196.42 | −1.20973 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −452.536 | − | 261.272i | −0.456646 | − | 0.263645i | 0.253987 | − | 0.967208i | \(-0.418258\pi\) |
−0.710633 | + | 0.703563i | \(0.751591\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1404.85 | − | 711.511i | 1.41475 | − | 0.716527i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −982.564 | + | 1701.85i | −0.987502 | + | 1.71040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 577.092 | − | 999.553i | 0.578829 | − | 1.00256i | −0.416785 | − | 0.909005i | \(-0.636843\pi\) |
0.995614 | − | 0.0935557i | \(-0.0298233\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 142.259 | − | 857.663i | 0.142401 | − | 0.858522i |
(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.445.40 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.39 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.2 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.29 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.29 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.2 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.40 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.39 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.40 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.40 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.29 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.29 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.39 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.39 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.2 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.2 | 80 | 9.2 | odd | 6 |