Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(101,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.101");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.15 | ||
Character | \(\chi\) | \(=\) | 136.101 |
Dual form | 136.4.h.a.101.13 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98225 | + | 2.01760i | −0.700830 | + | 0.713329i | ||||
\(3\) | −0.0741700 | −0.0142740 | −0.00713702 | − | 0.999975i | \(-0.502272\pi\) | ||||
−0.00713702 | + | 0.999975i | \(0.502272\pi\) | |||||||
\(4\) | −0.141403 | − | 7.99875i | −0.0176754 | − | 0.999844i | ||||
\(5\) | 17.3656 | 1.55323 | 0.776614 | − | 0.629977i | \(-0.216936\pi\) | ||||
0.776614 | + | 0.629977i | \(0.216936\pi\) | |||||||
\(6\) | 0.147023 | − | 0.149645i | 0.0100037 | − | 0.0101821i | ||||
\(7\) | − | 22.3324i | − | 1.20583i | −0.797804 | − | 0.602917i | \(-0.794005\pi\) | ||
0.797804 | − | 0.602917i | \(-0.205995\pi\) | |||||||
\(8\) | 16.4186 | + | 15.5702i | 0.725605 | + | 0.688112i | ||||
\(9\) | −26.9945 | −0.999796 | ||||||||
\(10\) | −34.4229 | + | 35.0368i | −1.08855 | + | 1.10796i | ||||
\(11\) | −62.5853 | −1.71547 | −0.857735 | − | 0.514091i | \(-0.828129\pi\) | ||||
−0.857735 | + | 0.514091i | \(0.828129\pi\) | |||||||
\(12\) | 0.0104879 | + | 0.593268i | 0.000252300 | + | 0.0142718i | ||||
\(13\) | − | 75.3060i | − | 1.60663i | −0.595557 | − | 0.803313i | \(-0.703069\pi\) | ||
0.595557 | − | 0.803313i | \(-0.296931\pi\) | |||||||
\(14\) | 45.0578 | + | 44.2683i | 0.860157 | + | 0.845085i | ||||
\(15\) | −1.28801 | −0.0221708 | ||||||||
\(16\) | −63.9600 | + | 2.26210i | −0.999375 | + | 0.0353453i | ||||
\(17\) | 67.1809 | + | 19.9933i | 0.958456 | + | 0.285241i | ||||
\(18\) | 53.5097 | − | 54.4640i | 0.700687 | − | 0.713183i | ||||
\(19\) | − | 99.5556i | − | 1.20209i | −0.799217 | − | 0.601043i | \(-0.794752\pi\) | ||
0.799217 | − | 0.601043i | \(-0.205248\pi\) | |||||||
\(20\) | −2.45556 | − | 138.903i | −0.0274540 | − | 1.55299i | ||||
\(21\) | 1.65639i | 0.0172121i | ||||||||
\(22\) | 124.059 | − | 126.272i | 1.20225 | − | 1.22369i | ||||
\(23\) | 83.3842i | 0.755948i | 0.925816 | + | 0.377974i | \(0.123379\pi\) | ||||
−0.925816 | + | 0.377974i | \(0.876621\pi\) | |||||||
\(24\) | −1.21777 | − | 1.15484i | −0.0103573 | − | 0.00982213i | ||||
\(25\) | 176.565 | 1.41252 | ||||||||
\(26\) | 151.937 | + | 149.275i | 1.14605 | + | 1.12597i | ||||
\(27\) | 4.00477 | 0.0285452 | ||||||||
\(28\) | −178.631 | + | 3.15787i | −1.20565 | + | 0.0213136i | ||||
\(29\) | −93.0996 | −0.596143 | −0.298072 | − | 0.954543i | \(-0.596343\pi\) | ||||
−0.298072 | + | 0.954543i | \(0.596343\pi\) | |||||||
\(30\) | 2.55315 | − | 2.59868i | 0.0155380 | − | 0.0158151i | ||||
\(31\) | − | 127.204i | − | 0.736984i | −0.929631 | − | 0.368492i | \(-0.879874\pi\) | ||
0.929631 | − | 0.368492i | \(-0.120126\pi\) | |||||||
\(32\) | 122.220 | − | 133.530i | 0.675179 | − | 0.737654i | ||||
\(33\) | 4.64196 | 0.0244867 | ||||||||
\(34\) | −173.507 | + | 95.9123i | −0.875185 | + | 0.483789i | ||||
\(35\) | − | 387.816i | − | 1.87294i | ||||||
\(36\) | 3.81711 | + | 215.922i | 0.0176718 | + | 0.999640i | ||||
\(37\) | 221.411 | 0.983776 | 0.491888 | − | 0.870658i | \(-0.336307\pi\) | ||||
0.491888 | + | 0.870658i | \(0.336307\pi\) | |||||||
\(38\) | 200.863 | + | 197.344i | 0.857482 | + | 0.842457i | ||||
\(39\) | 5.58545i | 0.0229330i | ||||||||
\(40\) | 285.118 | + | 270.386i | 1.12703 | + | 1.06879i | ||||
\(41\) | − | 73.5978i | − | 0.280343i | −0.990127 | − | 0.140171i | \(-0.955235\pi\) | ||
0.990127 | − | 0.140171i | \(-0.0447653\pi\) | |||||||
\(42\) | −3.34194 | − | 3.28338i | −0.0122779 | − | 0.0120628i | ||||
\(43\) | − | 210.100i | − | 0.745114i | −0.928009 | − | 0.372557i | \(-0.878481\pi\) | ||
0.928009 | − | 0.372557i | \(-0.121519\pi\) | |||||||
\(44\) | 8.84977 | + | 500.604i | 0.0303217 | + | 1.71520i | ||||
\(45\) | −468.776 | −1.55291 | ||||||||
\(46\) | −168.236 | − | 165.288i | −0.539239 | − | 0.529791i | ||||
\(47\) | 163.391 | 0.507085 | 0.253542 | − | 0.967324i | \(-0.418404\pi\) | ||||
0.253542 | + | 0.967324i | \(0.418404\pi\) | |||||||
\(48\) | 4.74392 | − | 0.167780i | 0.0142651 | − | 0.000504520i | ||||
\(49\) | −155.735 | −0.454038 | ||||||||
\(50\) | −349.995 | + | 356.237i | −0.989934 | + | 1.00759i | ||||
\(51\) | −4.98281 | − | 1.48291i | −0.0136810 | − | 0.00407153i | ||||
\(52\) | −602.354 | + | 10.6485i | −1.60637 | + | 0.0283978i | ||||
\(53\) | 2.84772i | 0.00738046i | 0.999993 | + | 0.00369023i | \(0.00117464\pi\) | ||||
−0.999993 | + | 0.00369023i | \(0.998825\pi\) | |||||||
\(54\) | −7.93845 | + | 8.08003i | −0.0200053 | + | 0.0203621i | ||||
\(55\) | −1086.83 | −2.66452 | ||||||||
\(56\) | 347.719 | − | 366.665i | 0.829749 | − | 0.874959i | ||||
\(57\) | 7.38404i | 0.0171586i | ||||||||
\(58\) | 184.546 | − | 187.838i | 0.417795 | − | 0.425246i | ||||
\(59\) | 326.354i | 0.720131i | 0.932927 | + | 0.360065i | \(0.117246\pi\) | ||||
−0.932927 | + | 0.360065i | \(0.882754\pi\) | |||||||
\(60\) | 0.182129 | + | 10.3025i | 0.000391879 | + | 0.0221674i | ||||
\(61\) | 225.228 | 0.472745 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(62\) | 256.646 | + | 252.149i | 0.525712 | + | 0.516500i | ||||
\(63\) | 602.851i | 1.20559i | ||||||||
\(64\) | 27.1381 | + | 511.280i | 0.0530042 | + | 0.998594i | ||||
\(65\) | − | 1307.74i | − | 2.49546i | ||||||
\(66\) | −9.20150 | + | 9.36560i | −0.0171610 | + | 0.0174671i | ||||
\(67\) | − | 330.624i | − | 0.602868i | −0.953487 | − | 0.301434i | \(-0.902535\pi\) | ||
0.953487 | − | 0.301434i | \(-0.0974653\pi\) | |||||||
\(68\) | 150.422 | − | 540.190i | 0.268255 | − | 0.963348i | ||||
\(69\) | − | 6.18461i | − | 0.0107904i | ||||||
\(70\) | 782.456 | + | 768.746i | 1.33602 | + | 1.31261i | ||||
\(71\) | 636.622i | 1.06413i | 0.846704 | + | 0.532065i | \(0.178584\pi\) | ||||
−0.846704 | + | 0.532065i | \(0.821416\pi\) | |||||||
\(72\) | −443.211 | − | 420.310i | −0.725457 | − | 0.687972i | ||||
\(73\) | 1094.13i | 1.75422i | 0.480288 | + | 0.877111i | \(0.340532\pi\) | ||||
−0.480288 | + | 0.877111i | \(0.659468\pi\) | |||||||
\(74\) | −438.891 | + | 446.718i | −0.689460 | + | 0.701756i | ||||
\(75\) | −13.0958 | −0.0201623 | ||||||||
\(76\) | −796.320 | + | 14.0775i | −1.20190 | + | 0.0212474i | ||||
\(77\) | 1397.68i | 2.06857i | ||||||||
\(78\) | −11.2692 | − | 11.0717i | −0.0163588 | − | 0.0160721i | ||||
\(79\) | 18.7611i | 0.0267189i | 0.999911 | + | 0.0133595i | \(0.00425257\pi\) | ||||
−0.999911 | + | 0.0133595i | \(0.995747\pi\) | |||||||
\(80\) | −1110.71 | + | 39.2828i | −1.55226 | + | 0.0548993i | ||||
\(81\) | 728.554 | 0.999389 | ||||||||
\(82\) | 148.491 | + | 145.889i | 0.199976 | + | 0.196472i | ||||
\(83\) | − | 953.977i | − | 1.26160i | −0.775946 | − | 0.630799i | \(-0.782727\pi\) | ||
0.775946 | − | 0.630799i | \(-0.217273\pi\) | |||||||
\(84\) | 13.2491 | − | 0.234220i | 0.0172094 | − | 0.000304232i | ||||
\(85\) | 1166.64 | + | 347.196i | 1.48870 | + | 0.443044i | ||||
\(86\) | 423.897 | + | 416.469i | 0.531511 | + | 0.522198i | ||||
\(87\) | 6.90520 | 0.00850937 | ||||||||
\(88\) | −1027.56 | − | 974.465i | −1.24475 | − | 1.18044i | ||||
\(89\) | 797.377 | 0.949684 | 0.474842 | − | 0.880071i | \(-0.342505\pi\) | ||||
0.474842 | + | 0.880071i | \(0.342505\pi\) | |||||||
\(90\) | 929.230 | − | 945.802i | 1.08833 | − | 1.10774i | ||||
\(91\) | −1681.76 | −1.93733 | ||||||||
\(92\) | 666.969 | − | 11.7908i | 0.755830 | − | 0.0133617i | ||||
\(93\) | 9.43472i | 0.0105197i | ||||||||
\(94\) | −323.881 | + | 329.657i | −0.355380 | + | 0.361718i | ||||
\(95\) | − | 1728.84i | − | 1.86711i | ||||||
\(96\) | −9.06510 | + | 9.90390i | −0.00963753 | + | 0.0105293i | ||||
\(97\) | 1396.19i | 1.46146i | 0.682665 | + | 0.730732i | \(0.260821\pi\) | ||||
−0.682665 | + | 0.730732i | \(0.739179\pi\) | |||||||
\(98\) | 308.705 | − | 314.211i | 0.318203 | − | 0.323878i | ||||
\(99\) | 1689.46 | 1.71512 | ||||||||
\(100\) | −24.9668 | − | 1412.30i | −0.0249668 | − | 1.41230i | ||||
\(101\) | − | 783.768i | − | 0.772156i | −0.922466 | − | 0.386078i | \(-0.873830\pi\) | ||
0.922466 | − | 0.386078i | \(-0.126170\pi\) | |||||||
\(102\) | 12.8691 | − | 7.11382i | 0.0124924 | − | 0.00690562i | ||||
\(103\) | −1102.23 | −1.05443 | −0.527215 | − | 0.849732i | \(-0.676764\pi\) | ||||
−0.527215 | + | 0.849732i | \(0.676764\pi\) | |||||||
\(104\) | 1172.53 | − | 1236.42i | 1.10554 | − | 1.16578i | ||||
\(105\) | 28.7643i | 0.0267344i | ||||||||
\(106\) | −5.74555 | − | 5.64488i | −0.00526469 | − | 0.00517244i | ||||
\(107\) | −1224.33 | −1.10617 | −0.553085 | − | 0.833125i | \(-0.686550\pi\) | ||||
−0.553085 | + | 0.833125i | \(0.686550\pi\) | |||||||
\(108\) | −0.566289 | − | 32.0332i | −0.000504548 | − | 0.0285407i | ||||
\(109\) | −17.3959 | −0.0152864 | −0.00764321 | − | 0.999971i | \(-0.502433\pi\) | ||||
−0.00764321 | + | 0.999971i | \(0.502433\pi\) | |||||||
\(110\) | 2154.37 | − | 2192.79i | 1.86737 | − | 1.90068i | ||||
\(111\) | −16.4221 | −0.0140425 | ||||||||
\(112\) | 50.5181 | + | 1428.38i | 0.0426206 | + | 1.20508i | ||||
\(113\) | − | 1900.05i | − | 1.58179i | −0.611953 | − | 0.790894i | \(-0.709616\pi\) | ||
0.611953 | − | 0.790894i | \(-0.290384\pi\) | |||||||
\(114\) | −14.8980 | − | 14.6370i | −0.0122397 | − | 0.0120253i | ||||
\(115\) | 1448.02i | 1.17416i | ||||||||
\(116\) | 13.1646 | + | 744.680i | 0.0105371 | + | 0.596050i | ||||
\(117\) | 2032.85i | 1.60630i | ||||||||
\(118\) | −658.452 | − | 646.914i | −0.513690 | − | 0.504689i | ||||
\(119\) | 446.498 | − | 1500.31i | 0.343953 | − | 1.15574i | ||||
\(120\) | −21.1472 | − | 20.0545i | −0.0160873 | − | 0.0152560i | ||||
\(121\) | 2585.92 | 1.94284 | ||||||||
\(122\) | −446.457 | + | 454.419i | −0.331314 | + | 0.337223i | ||||
\(123\) | 5.45875i | 0.00400162i | ||||||||
\(124\) | −1017.47 | + | 17.9871i | −0.736869 | + | 0.0130265i | ||||
\(125\) | 895.453 | 0.640734 | ||||||||
\(126\) | −1216.31 | − | 1195.00i | −0.859981 | − | 0.844913i | ||||
\(127\) | −205.605 | −0.143658 | −0.0718288 | − | 0.997417i | \(-0.522884\pi\) | ||||
−0.0718288 | + | 0.997417i | \(0.522884\pi\) | |||||||
\(128\) | −1085.35 | − | 958.729i | −0.749473 | − | 0.662035i | ||||
\(129\) | 15.5831i | 0.0106358i | ||||||||
\(130\) | 2638.49 | + | 2592.25i | 1.78008 | + | 1.74889i | ||||
\(131\) | 1380.10 | 0.920454 | 0.460227 | − | 0.887801i | \(-0.347768\pi\) | ||||
0.460227 | + | 0.887801i | \(0.347768\pi\) | |||||||
\(132\) | −0.656388 | − | 37.1298i | −0.000432812 | − | 0.0244829i | ||||
\(133\) | −2223.31 | −1.44952 | ||||||||
\(134\) | 667.066 | + | 655.378i | 0.430043 | + | 0.422508i | ||||
\(135\) | 69.5454 | 0.0443371 | ||||||||
\(136\) | 791.713 | + | 1374.28i | 0.499183 | + | 0.866497i | ||||
\(137\) | −1194.79 | −0.745092 | −0.372546 | − | 0.928014i | \(-0.621515\pi\) | ||||
−0.372546 | + | 0.928014i | \(0.621515\pi\) | |||||||
\(138\) | 12.4781 | + | 12.2594i | 0.00769712 | + | 0.00756225i | ||||
\(139\) | 619.145 | 0.377807 | 0.188904 | − | 0.981996i | \(-0.439507\pi\) | ||||
0.188904 | + | 0.981996i | \(0.439507\pi\) | |||||||
\(140\) | −3102.04 | + | 54.8384i | −1.87264 | + | 0.0331049i | ||||
\(141\) | −12.1187 | −0.00723815 | ||||||||
\(142\) | −1284.45 | − | 1261.94i | −0.759074 | − | 0.745773i | ||||
\(143\) | 4713.05i | 2.75612i | ||||||||
\(144\) | 1726.57 | − | 61.0643i | 0.999172 | − | 0.0353381i | ||||
\(145\) | −1616.73 | −0.925947 | ||||||||
\(146\) | −2207.51 | − | 2168.83i | −1.25134 | − | 1.22941i | ||||
\(147\) | 11.5509 | 0.00648095 | ||||||||
\(148\) | −31.3082 | − | 1771.01i | −0.0173887 | − | 0.983622i | ||||
\(149\) | 167.437i | 0.0920602i | 0.998940 | + | 0.0460301i | \(0.0146570\pi\) | ||||
−0.998940 | + | 0.0460301i | \(0.985343\pi\) | |||||||
\(150\) | 25.9591 | − | 26.4221i | 0.0141304 | − | 0.0143824i | ||||
\(151\) | 1475.25 | 0.795061 | 0.397531 | − | 0.917589i | \(-0.369867\pi\) | ||||
0.397531 | + | 0.917589i | \(0.369867\pi\) | |||||||
\(152\) | 1550.10 | − | 1634.56i | 0.827169 | − | 0.872239i | ||||
\(153\) | −1813.51 | − | 539.710i | −0.958261 | − | 0.285183i | ||||
\(154\) | −2819.95 | − | 2770.54i | −1.47557 | − | 1.44972i | ||||
\(155\) | − | 2208.98i | − | 1.14470i | ||||||
\(156\) | 44.6766 | − | 0.789802i | 0.0229294 | − | 0.000405351i | ||||
\(157\) | 341.194i | 0.173441i | 0.996233 | + | 0.0867205i | \(0.0276387\pi\) | ||||
−0.996233 | + | 0.0867205i | \(0.972361\pi\) | |||||||
\(158\) | −37.8525 | − | 37.1892i | −0.0190594 | − | 0.0187254i | ||||
\(159\) | − | 0.211215i | − | 0.000105349i | ||||||
\(160\) | 2122.43 | − | 2318.82i | 1.04871 | − | 1.14574i | ||||
\(161\) | 1862.17 | 0.911548 | ||||||||
\(162\) | −1444.17 | + | 1469.93i | −0.700401 | + | 0.712893i | ||||
\(163\) | 1716.60 | 0.824875 | 0.412437 | − | 0.910986i | \(-0.364678\pi\) | ||||
0.412437 | + | 0.910986i | \(0.364678\pi\) | |||||||
\(164\) | −588.690 | + | 10.4070i | −0.280299 | + | 0.00495517i | ||||
\(165\) | 80.6104 | 0.0380334 | ||||||||
\(166\) | 1924.74 | + | 1891.02i | 0.899934 | + | 0.884165i | ||||
\(167\) | 3343.32i | 1.54918i | 0.632461 | + | 0.774592i | \(0.282045\pi\) | ||||
−0.632461 | + | 0.774592i | \(0.717955\pi\) | |||||||
\(168\) | −25.7904 | + | 27.1956i | −0.0118439 | + | 0.0124892i | ||||
\(169\) | −3474.00 | −1.58125 | ||||||||
\(170\) | −3013.06 | + | 1665.58i | −1.35936 | + | 0.751435i | ||||
\(171\) | 2687.45i | 1.20184i | ||||||||
\(172\) | −1680.53 | + | 29.7088i | −0.744997 | + | 0.0131702i | ||||
\(173\) | 1958.82 | 0.860846 | 0.430423 | − | 0.902627i | \(-0.358364\pi\) | ||||
0.430423 | + | 0.902627i | \(0.358364\pi\) | |||||||
\(174\) | −13.6878 | + | 13.9319i | −0.00596362 | + | 0.00606998i | ||||
\(175\) | − | 3943.11i | − | 1.70326i | ||||||
\(176\) | 4002.96 | − | 141.574i | 1.71440 | − | 0.0606339i | ||||
\(177\) | − | 24.2057i | − | 0.0102792i | ||||||
\(178\) | −1580.60 | + | 1608.79i | −0.665567 | + | 0.677437i | ||||
\(179\) | 1997.03i | 0.833883i | 0.908933 | + | 0.416941i | \(0.136898\pi\) | ||||
−0.908933 | + | 0.416941i | \(0.863102\pi\) | |||||||
\(180\) | 66.2865 | + | 3749.62i | 0.0274484 | + | 1.55267i | ||||
\(181\) | 537.433 | 0.220702 | 0.110351 | − | 0.993893i | \(-0.464803\pi\) | ||||
0.110351 | + | 0.993893i | \(0.464803\pi\) | |||||||
\(182\) | 3333.67 | − | 3393.12i | 1.35774 | − | 1.38195i | ||||
\(183\) | −16.7052 | −0.00674798 | ||||||||
\(184\) | −1298.31 | + | 1369.05i | −0.520177 | + | 0.548519i | ||||
\(185\) | 3844.94 | 1.52803 | ||||||||
\(186\) | −19.0355 | − | 18.7019i | −0.00750403 | − | 0.00737254i | ||||
\(187\) | −4204.53 | − | 1251.29i | −1.64420 | − | 0.489322i | ||||
\(188\) | −23.1040 | − | 1306.92i | −0.00896294 | − | 0.507006i | ||||
\(189\) | − | 89.4361i | − | 0.0344207i | ||||||
\(190\) | 3488.11 | + | 3426.99i | 1.33186 | + | 1.30853i | ||||
\(191\) | −1810.54 | −0.685894 | −0.342947 | − | 0.939355i | \(-0.611425\pi\) | ||||
−0.342947 | + | 0.939355i | \(0.611425\pi\) | |||||||
\(192\) | −2.01284 | − | 37.9217i | −0.000756583 | − | 0.0142540i | ||||
\(193\) | − | 2270.61i | − | 0.846851i | −0.905931 | − | 0.423425i | \(-0.860828\pi\) | ||
0.905931 | − | 0.423425i | \(-0.139172\pi\) | |||||||
\(194\) | −2816.96 | − | 2767.60i | −1.04250 | − | 1.02424i | ||||
\(195\) | 96.9948i | 0.0356202i | ||||||||
\(196\) | 22.0214 | + | 1245.69i | 0.00802531 | + | 0.453967i | ||||
\(197\) | −3414.23 | −1.23479 | −0.617396 | − | 0.786652i | \(-0.711812\pi\) | ||||
−0.617396 | + | 0.786652i | \(0.711812\pi\) | |||||||
\(198\) | −3348.92 | + | 3408.65i | −1.20201 | + | 1.22345i | ||||
\(199\) | − | 628.204i | − | 0.223780i | −0.993721 | − | 0.111890i | \(-0.964310\pi\) | ||
0.993721 | − | 0.111890i | \(-0.0356904\pi\) | |||||||
\(200\) | 2898.94 | + | 2749.15i | 1.02493 | + | 0.971970i | ||||
\(201\) | 24.5224i | 0.00860535i | ||||||||
\(202\) | 1581.33 | + | 1553.62i | 0.550801 | + | 0.541150i | ||||
\(203\) | 2079.13i | 0.718850i | ||||||||
\(204\) | −11.1568 | + | 40.0659i | −0.00382908 | + | 0.0137509i | ||||
\(205\) | − | 1278.07i | − | 0.435436i | ||||||
\(206\) | 2184.90 | − | 2223.86i | 0.738976 | − | 0.752155i | ||||
\(207\) | − | 2250.91i | − | 0.755794i | ||||||
\(208\) | 170.350 | + | 4816.57i | 0.0567867 | + | 1.60562i | ||||
\(209\) | 6230.72i | 2.06214i | ||||||||
\(210\) | −58.0348 | − | 57.0179i | −0.0190704 | − | 0.0187362i | ||||
\(211\) | −168.439 | −0.0549564 | −0.0274782 | − | 0.999622i | \(-0.508748\pi\) | ||||
−0.0274782 | + | 0.999622i | \(0.508748\pi\) | |||||||
\(212\) | 22.7782 | − | 0.402677i | 0.00737930 | − | 0.000130453i | ||||
\(213\) | − | 47.2183i | − | 0.0151894i | ||||||
\(214\) | 2426.92 | − | 2470.20i | 0.775237 | − | 0.789063i | ||||
\(215\) | − | 3648.51i | − | 1.15733i | ||||||
\(216\) | 65.7526 | + | 62.3551i | 0.0207125 | + | 0.0196423i | ||||
\(217\) | −2840.77 | −0.888681 | ||||||||
\(218\) | 34.4829 | − | 35.0978i | 0.0107132 | − | 0.0109042i | ||||
\(219\) | − | 81.1516i | − | 0.0250398i | ||||||
\(220\) | 153.682 | + | 8693.30i | 0.0470965 | + | 2.66410i | ||||
\(221\) | 1505.62 | − | 5059.12i | 0.458275 | − | 1.53988i | ||||
\(222\) | 32.5525 | − | 33.1331i | 0.00984137 | − | 0.0100169i | ||||
\(223\) | 5890.95 | 1.76900 | 0.884500 | − | 0.466540i | \(-0.154500\pi\) | ||||
0.884500 | + | 0.466540i | \(0.154500\pi\) | |||||||
\(224\) | −2982.03 | − | 2729.47i | −0.889489 | − | 0.814154i | ||||
\(225\) | −4766.28 | −1.41223 | ||||||||
\(226\) | 3833.55 | + | 3766.37i | 1.12833 | + | 1.10856i | ||||
\(227\) | 2963.13 | 0.866388 | 0.433194 | − | 0.901301i | \(-0.357386\pi\) | ||||
0.433194 | + | 0.901301i | \(0.357386\pi\) | |||||||
\(228\) | 59.0631 | − | 1.04413i | 0.0171559 | − | 0.000303286i | ||||
\(229\) | − | 4665.91i | − | 1.34643i | −0.739448 | − | 0.673213i | \(-0.764914\pi\) | ||
0.739448 | − | 0.673213i | \(-0.235086\pi\) | |||||||
\(230\) | −2921.52 | − | 2870.33i | −0.837561 | − | 0.822886i | ||||
\(231\) | − | 103.666i | − | 0.0295269i | ||||||
\(232\) | −1528.56 | − | 1449.58i | −0.432564 | − | 0.410213i | ||||
\(233\) | − | 92.7784i | − | 0.0260863i | −0.999915 | − | 0.0130432i | \(-0.995848\pi\) | ||
0.999915 | − | 0.0130432i | \(-0.00415189\pi\) | |||||||
\(234\) | −4101.47 | − | 4029.61i | −1.14582 | − | 1.12574i | ||||
\(235\) | 2837.38 | 0.787619 | ||||||||
\(236\) | 2610.43 | − | 46.1476i | 0.720018 | − | 0.0127286i | ||||
\(237\) | − | 1.39152i | − | 0.000381387i | ||||||
\(238\) | 2141.95 | + | 3874.83i | 0.583370 | + | 1.05533i | ||||
\(239\) | 3237.67 | 0.876266 | 0.438133 | − | 0.898910i | \(-0.355640\pi\) | ||||
0.438133 | + | 0.898910i | \(0.355640\pi\) | |||||||
\(240\) | 82.3811 | − | 2.91360i | 0.0221570 | − | 0.000783635i | ||||
\(241\) | 1681.04i | 0.449316i | 0.974438 | + | 0.224658i | \(0.0721265\pi\) | ||||
−0.974438 | + | 0.224658i | \(0.927873\pi\) | |||||||
\(242\) | −5125.93 | + | 5217.35i | −1.36160 | + | 1.38588i | ||||
\(243\) | −162.166 | −0.0428105 | ||||||||
\(244\) | −31.8480 | − | 1801.54i | −0.00835597 | − | 0.472671i | ||||
\(245\) | −2704.43 | −0.705224 | ||||||||
\(246\) | −11.0136 | − | 10.8206i | −0.00285447 | − | 0.00280445i | ||||
\(247\) | −7497.14 | −1.93130 | ||||||||
\(248\) | 1980.59 | − | 2088.51i | 0.507127 | − | 0.534759i | ||||
\(249\) | 70.7565i | 0.0180081i | ||||||||
\(250\) | −1775.01 | + | 1806.66i | −0.449046 | + | 0.457054i | ||||
\(251\) | 653.059i | 0.164226i | 0.996623 | + | 0.0821130i | \(0.0261668\pi\) | ||||
−0.996623 | + | 0.0821130i | \(0.973833\pi\) | |||||||
\(252\) | 4822.06 | − | 85.2452i | 1.20540 | − | 0.0213093i | ||||
\(253\) | − | 5218.62i | − | 1.29681i | ||||||
\(254\) | 407.560 | − | 414.829i | 0.100680 | − | 0.102475i | ||||
\(255\) | −86.5295 | − | 25.7516i | −0.0212498 | − | 0.00632402i | ||||
\(256\) | 4085.77 | − | 289.368i | 0.997501 | − | 0.0706465i | ||||
\(257\) | −1636.18 | −0.397130 | −0.198565 | − | 0.980088i | \(-0.563628\pi\) | ||||
−0.198565 | + | 0.980088i | \(0.563628\pi\) | |||||||
\(258\) | −31.4404 | − | 30.8895i | −0.00758681 | − | 0.00745387i | ||||
\(259\) | − | 4944.63i | − | 1.18627i | ||||||
\(260\) | −10460.3 | + | 184.918i | −2.49507 | + | 0.0441082i | ||||
\(261\) | 2513.18 | 0.596022 | ||||||||
\(262\) | −2735.69 | + | 2784.48i | −0.645081 | + | 0.656586i | ||||
\(263\) | 5502.33 | 1.29007 | 0.645034 | − | 0.764154i | \(-0.276843\pi\) | ||||
0.645034 | + | 0.764154i | \(0.276843\pi\) | |||||||
\(264\) | 76.2142 | + | 72.2761i | 0.0177677 | + | 0.0168496i | ||||
\(265\) | 49.4524i | 0.0114635i | ||||||||
\(266\) | 4407.15 | − | 4485.75i | 1.01586 | − | 1.03398i | ||||
\(267\) | −59.1415 | −0.0135558 | ||||||||
\(268\) | −2644.58 | + | 46.7513i | −0.602774 | + | 0.0106559i | ||||
\(269\) | −6822.32 | −1.54634 | −0.773168 | − | 0.634201i | \(-0.781329\pi\) | ||||
−0.773168 | + | 0.634201i | \(0.781329\pi\) | |||||||
\(270\) | −137.856 | + | 140.315i | −0.0310728 | + | 0.0316270i | ||||
\(271\) | 4780.17 | 1.07149 | 0.535747 | − | 0.844379i | \(-0.320030\pi\) | ||||
0.535747 | + | 0.844379i | \(0.320030\pi\) | |||||||
\(272\) | −4342.12 | − | 1126.80i | −0.967939 | − | 0.251186i | ||||
\(273\) | 124.736 | 0.0276534 | ||||||||
\(274\) | 2368.36 | − | 2410.60i | 0.522183 | − | 0.531495i | ||||
\(275\) | −11050.4 | −2.42313 | ||||||||
\(276\) | −49.4691 | + | 0.874524i | −0.0107887 | + | 0.000190725i | ||||
\(277\) | 3596.56 | 0.780132 | 0.390066 | − | 0.920787i | \(-0.372452\pi\) | ||||
0.390066 | + | 0.920787i | \(0.372452\pi\) | |||||||
\(278\) | −1227.30 | + | 1249.19i | −0.264779 | + | 0.269501i | ||||
\(279\) | 3433.81i | 0.736834i | ||||||||
\(280\) | 6038.36 | − | 6367.37i | 1.28879 | − | 1.35901i | ||||
\(281\) | −3084.37 | −0.654797 | −0.327398 | − | 0.944886i | \(-0.606172\pi\) | ||||
−0.327398 | + | 0.944886i | \(0.606172\pi\) | |||||||
\(282\) | 24.0222 | − | 24.4507i | 0.00507271 | − | 0.00516318i | ||||
\(283\) | −251.886 | −0.0529083 | −0.0264541 | − | 0.999650i | \(-0.508422\pi\) | ||||
−0.0264541 | + | 0.999650i | \(0.508422\pi\) | |||||||
\(284\) | 5092.18 | − | 90.0205i | 1.06396 | − | 0.0188089i | ||||
\(285\) | 128.228i | 0.0266512i | ||||||||
\(286\) | −9509.04 | − | 9342.42i | −1.96602 | − | 1.93157i | ||||
\(287\) | −1643.61 | −0.338047 | ||||||||
\(288\) | −3299.28 | + | 3604.57i | −0.675041 | + | 0.737504i | ||||
\(289\) | 4113.53 | + | 2686.34i | 0.837276 | + | 0.546781i | ||||
\(290\) | 3204.76 | − | 3261.91i | 0.648931 | − | 0.660504i | ||||
\(291\) | − | 103.556i | − | 0.0208610i | ||||||
\(292\) | 8751.67 | − | 154.714i | 1.75395 | − | 0.0310066i | ||||
\(293\) | 109.394i | 0.0218118i | 0.999941 | + | 0.0109059i | \(0.00347152\pi\) | ||||
−0.999941 | + | 0.0109059i | \(0.996528\pi\) | |||||||
\(294\) | −22.8967 | + | 23.3050i | −0.00454204 | + | 0.00462305i | ||||
\(295\) | 5667.34i | 1.11853i | ||||||||
\(296\) | 3635.25 | + | 3447.41i | 0.713833 | + | 0.676948i | ||||
\(297\) | −250.640 | −0.0489684 | ||||||||
\(298\) | −337.820 | − | 331.901i | −0.0656692 | − | 0.0645185i | ||||
\(299\) | 6279.33 | 1.21453 | ||||||||
\(300\) | 1.85179 | + | 104.750i | 0.000356378 | + | 0.0201592i | ||||
\(301\) | −4692.02 | −0.898484 | ||||||||
\(302\) | −2924.31 | + | 2976.46i | −0.557202 | + | 0.567140i | ||||
\(303\) | 58.1321i | 0.0110218i | ||||||||
\(304\) | 225.205 | + | 6367.58i | 0.0424881 | + | 1.20133i | ||||
\(305\) | 3911.22 | 0.734281 | ||||||||
\(306\) | 4683.75 | − | 2589.10i | 0.875006 | − | 0.483690i | ||||
\(307\) | 2337.41i | 0.434537i | 0.976112 | + | 0.217268i | \(0.0697147\pi\) | ||||
−0.976112 | + | 0.217268i | \(0.930285\pi\) | |||||||
\(308\) | 11179.7 | − | 197.636i | 2.06825 | − | 0.0365629i | ||||
\(309\) | 81.7527 | 0.0150510 | ||||||||
\(310\) | 4456.82 | + | 4378.73i | 0.816550 | + | 0.802243i | ||||
\(311\) | − | 3255.84i | − | 0.593640i | −0.954933 | − | 0.296820i | \(-0.904074\pi\) | ||
0.954933 | − | 0.296820i | \(-0.0959261\pi\) | |||||||
\(312\) | −86.9666 | + | 91.7051i | −0.0157805 | + | 0.0166403i | ||||
\(313\) | − | 8760.71i | − | 1.58206i | −0.611778 | − | 0.791029i | \(-0.709545\pi\) | ||
0.611778 | − | 0.791029i | \(-0.290455\pi\) | |||||||
\(314\) | −688.392 | − | 676.330i | −0.123720 | − | 0.121553i | ||||
\(315\) | 10468.9i | 1.87256i | ||||||||
\(316\) | 150.066 | − | 2.65289i | 0.0267147 | − | 0.000472268i | ||||
\(317\) | 8086.71 | 1.43279 | 0.716396 | − | 0.697694i | \(-0.245790\pi\) | ||||
0.716396 | + | 0.697694i | \(0.245790\pi\) | |||||||
\(318\) | 0.426148 | + | 0.418681i | 7.51484e−5 | + | 7.38316e-5i | ||||
\(319\) | 5826.67 | 1.02267 | ||||||||
\(320\) | 471.270 | + | 8878.70i | 0.0823276 | + | 1.55104i | ||||
\(321\) | 90.8085 | 0.0157895 | ||||||||
\(322\) | −3691.27 | + | 3757.10i | −0.638840 | + | 0.650233i | ||||
\(323\) | 1990.45 | − | 6688.23i | 0.342884 | − | 1.15215i | ||||
\(324\) | −103.020 | − | 5827.52i | −0.0176646 | − | 0.999233i | ||||
\(325\) | − | 13296.4i | − | 2.26939i | ||||||
\(326\) | −3402.73 | + | 3463.41i | −0.578097 | + | 0.588407i | ||||
\(327\) | 1.29025 | 0.000218199 | ||||||||
\(328\) | 1145.93 | − | 1208.37i | 0.192907 | − | 0.203418i | ||||
\(329\) | − | 3648.90i | − | 0.611461i | ||||||
\(330\) | −159.790 | + | 162.639i | −0.0266549 | + | 0.0271303i | ||||
\(331\) | − | 6473.73i | − | 1.07501i | −0.843260 | − | 0.537505i | \(-0.819367\pi\) | ||
0.843260 | − | 0.537505i | \(-0.180633\pi\) | |||||||
\(332\) | −7630.62 | + | 134.896i | −1.26140 | + | 0.0222993i | ||||
\(333\) | −5976.87 | −0.983576 | ||||||||
\(334\) | −6745.48 | − | 6627.28i | −1.10508 | − | 1.08571i | ||||
\(335\) | − | 5741.49i | − | 0.936391i | ||||||
\(336\) | −3.74693 | − | 105.943i | −0.000608368 | − | 0.0172014i | ||||
\(337\) | − | 8226.09i | − | 1.32968i | −0.746984 | − | 0.664842i | \(-0.768499\pi\) | ||
0.746984 | − | 0.664842i | \(-0.231501\pi\) | |||||||
\(338\) | 6886.32 | − | 7009.13i | 1.10818 | − | 1.12795i | ||||
\(339\) | 140.927i | 0.0225785i | ||||||||
\(340\) | 2612.17 | − | 9380.73i | 0.416661 | − | 1.49630i | ||||
\(341\) | 7961.10i | 1.26427i | ||||||||
\(342\) | −5422.20 | − | 5327.19i | −0.857307 | − | 0.842285i | ||||
\(343\) | − | 4182.07i | − | 0.658340i | ||||||
\(344\) | 3271.29 | − | 3449.53i | 0.512722 | − | 0.540658i | ||||
\(345\) | − | 107.400i | − | 0.0167600i | ||||||
\(346\) | −3882.86 | + | 3952.11i | −0.603306 | + | 0.614066i | ||||
\(347\) | 9552.28 | 1.47779 | 0.738895 | − | 0.673820i | \(-0.235348\pi\) | ||||
0.738895 | + | 0.673820i | \(0.235348\pi\) | |||||||
\(348\) | −0.976418 | − | 55.2330i | −0.000150407 | − | 0.00850804i | ||||
\(349\) | 7353.28i | 1.12783i | 0.825834 | + | 0.563914i | \(0.190705\pi\) | ||||
−0.825834 | + | 0.563914i | \(0.809295\pi\) | |||||||
\(350\) | 7955.61 | + | 7816.21i | 1.21499 | + | 1.19370i | ||||
\(351\) | − | 301.584i | − | 0.0458614i | ||||||
\(352\) | −7649.20 | + | 8356.99i | −1.15825 | + | 1.26542i | ||||
\(353\) | −5697.06 | −0.858991 | −0.429495 | − | 0.903069i | \(-0.641309\pi\) | ||||
−0.429495 | + | 0.903069i | \(0.641309\pi\) | |||||||
\(354\) | 48.8374 | + | 47.9817i | 0.00733243 | + | 0.00720395i | ||||
\(355\) | 11055.3i | 1.65284i | ||||||||
\(356\) | −112.752 | − | 6378.02i | −0.0167861 | − | 0.949535i | ||||
\(357\) | −33.1168 | + | 111.278i | −0.00490960 | + | 0.0164971i | ||||
\(358\) | −4029.20 | − | 3958.60i | −0.594832 | − | 0.584410i | ||||
\(359\) | −4654.57 | −0.684286 | −0.342143 | − | 0.939648i | \(-0.611153\pi\) | ||||
−0.342143 | + | 0.939648i | \(0.611153\pi\) | |||||||
\(360\) | −7696.63 | − | 7298.94i | −1.12680 | − | 1.06858i | ||||
\(361\) | −3052.32 | −0.445009 | ||||||||
\(362\) | −1065.32 | + | 1084.32i | −0.154674 | + | 0.157433i | ||||
\(363\) | −191.798 | −0.0277322 | ||||||||
\(364\) | 237.807 | + | 13452.0i | 0.0342430 | + | 1.93702i | ||||
\(365\) | 19000.2i | 2.72471i | ||||||||
\(366\) | 33.1137 | − | 33.7043i | 0.00472919 | − | 0.00481353i | ||||
\(367\) | 11694.9i | 1.66341i | 0.555220 | + | 0.831704i | \(0.312634\pi\) | ||||
−0.555220 | + | 0.831704i | \(0.687366\pi\) | |||||||
\(368\) | −188.623 | − | 5333.25i | −0.0267192 | − | 0.755475i | ||||
\(369\) | 1986.74i | 0.280285i | ||||||||
\(370\) | −7621.61 | + | 7757.54i | −1.07089 | + | 1.08999i | ||||
\(371\) | 63.5963 | 0.00889961 | ||||||||
\(372\) | 75.4660 | − | 1.33410i | 0.0105181 | − | 0.000185941i | ||||
\(373\) | − | 8084.20i | − | 1.12221i | −0.827745 | − | 0.561104i | \(-0.810377\pi\) | ||
0.827745 | − | 0.561104i | \(-0.189623\pi\) | |||||||
\(374\) | 10859.0 | − | 6002.70i | 1.50135 | − | 0.829926i | ||||
\(375\) | −66.4158 | −0.00914586 | ||||||||
\(376\) | 2682.64 | + | 2544.03i | 0.367943 | + | 0.348931i | ||||
\(377\) | 7010.96i | 0.957779i | ||||||||
\(378\) | 180.446 | + | 177.284i | 0.0245533 | + | 0.0241231i | ||||
\(379\) | 3912.91 | 0.530323 | 0.265162 | − | 0.964204i | \(-0.414575\pi\) | ||||
0.265162 | + | 0.964204i | \(0.414575\pi\) | |||||||
\(380\) | −13828.6 | + | 244.464i | −1.86682 | + | 0.0330020i | ||||
\(381\) | 15.2498 | 0.00205057 | ||||||||
\(382\) | 3588.93 | − | 3652.93i | 0.480695 | − | 0.489268i | ||||
\(383\) | 907.329 | 0.121050 | 0.0605252 | − | 0.998167i | \(-0.480722\pi\) | ||||
0.0605252 | + | 0.998167i | \(0.480722\pi\) | |||||||
\(384\) | 80.5006 | + | 71.1090i | 0.0106980 | + | 0.00944991i | ||||
\(385\) | 24271.6i | 3.21297i | ||||||||
\(386\) | 4581.18 | + | 4500.91i | 0.604083 | + | 0.593498i | ||||
\(387\) | 5671.54i | 0.744962i | ||||||||
\(388\) | 11167.8 | − | 197.426i | 1.46124 | − | 0.0258320i | ||||
\(389\) | 10732.1i | 1.39881i | 0.714724 | + | 0.699407i | \(0.246552\pi\) | ||||
−0.714724 | + | 0.699407i | \(0.753448\pi\) | |||||||
\(390\) | −195.697 | − | 192.268i | −0.0254089 | − | 0.0249637i | ||||
\(391\) | −1667.13 | + | 5601.82i | −0.215627 | + | 0.724543i | ||||
\(392\) | −2556.94 | − | 2424.82i | −0.329452 | − | 0.312429i | ||||
\(393\) | −102.362 | −0.0131386 | ||||||||
\(394\) | 6767.85 | − | 6888.55i | 0.865379 | − | 0.880813i | ||||
\(395\) | 325.799i | 0.0415006i | ||||||||
\(396\) | −238.895 | − | 13513.6i | −0.0303155 | − | 1.71485i | ||||
\(397\) | −9853.87 | −1.24572 | −0.622861 | − | 0.782333i | \(-0.714030\pi\) | ||||
−0.622861 | + | 0.782333i | \(0.714030\pi\) | |||||||
\(398\) | 1267.46 | + | 1245.25i | 0.159629 | + | 0.156832i | ||||
\(399\) | 164.903 | 0.0206904 | ||||||||
\(400\) | −11293.1 | + | 399.407i | −1.41164 | + | 0.0499259i | ||||
\(401\) | − | 7418.95i | − | 0.923902i | −0.886906 | − | 0.461951i | \(-0.847150\pi\) | ||
0.886906 | − | 0.461951i | \(-0.152850\pi\) | |||||||
\(402\) | −49.4763 | − | 48.6094i | −0.00613845 | − | 0.00603089i | ||||
\(403\) | −9579.22 | −1.18406 | ||||||||
\(404\) | −6269.16 | + | 110.827i | −0.772036 | + | 0.0136482i | ||||
\(405\) | 12651.8 | 1.55228 | ||||||||
\(406\) | −4194.86 | − | 4121.36i | −0.512777 | − | 0.503792i | ||||
\(407\) | −13857.1 | −1.68764 | ||||||||
\(408\) | −58.7214 | − | 101.930i | −0.00712535 | − | 0.0123684i | ||||
\(409\) | 1814.00 | 0.219307 | 0.109653 | − | 0.993970i | \(-0.465026\pi\) | ||||
0.109653 | + | 0.993970i | \(0.465026\pi\) | |||||||
\(410\) | 2578.63 | + | 2533.45i | 0.310609 | + | 0.305166i | ||||
\(411\) | 88.6175 | 0.0106355 | ||||||||
\(412\) | 155.860 | + | 8816.49i | 0.0186375 | + | 1.05427i | ||||
\(413\) | 7288.27 | 0.868359 | ||||||||
\(414\) | 4541.44 | + | 4461.86i | 0.539129 | + | 0.529683i | ||||
\(415\) | − | 16566.4i | − | 1.95955i | ||||||
\(416\) | −10055.6 | − | 9203.94i | −1.18513 | − | 1.08476i | ||||
\(417\) | −45.9220 | −0.00539283 | ||||||||
\(418\) | −12571.1 | − | 12350.8i | −1.47099 | − | 1.44521i | ||||
\(419\) | −10912.4 | −1.27233 | −0.636167 | − | 0.771552i | \(-0.719481\pi\) | ||||
−0.636167 | + | 0.771552i | \(0.719481\pi\) | |||||||
\(420\) | 230.078 | − | 4.06737i | 0.0267302 | − | 0.000472541i | ||||
\(421\) | 11131.8i | 1.28868i | 0.764740 | + | 0.644338i | \(0.222867\pi\) | ||||
−0.764740 | + | 0.644338i | \(0.777133\pi\) | |||||||
\(422\) | 333.887 | − | 339.841i | 0.0385150 | − | 0.0392019i | ||||
\(423\) | −4410.65 | −0.506982 | ||||||||
\(424\) | −44.3395 | + | 46.7554i | −0.00507858 | + | 0.00535529i | ||||
\(425\) | 11861.8 | + | 3530.11i | 1.35384 | + | 0.402907i | ||||
\(426\) | 95.2676 | + | 93.5983i | 0.0108350 | + | 0.0106452i | ||||
\(427\) | − | 5029.87i | − | 0.570053i | ||||||
\(428\) | 173.124 | + | 9793.10i | 0.0195520 | + | 1.10600i | ||||
\(429\) | − | 349.567i | − | 0.0393409i | ||||||
\(430\) | 7361.23 | + | 7232.24i | 0.825558 | + | 0.811093i | ||||
\(431\) | 4554.70i | 0.509031i | 0.967069 | + | 0.254516i | \(0.0819160\pi\) | ||||
−0.967069 | + | 0.254516i | \(0.918084\pi\) | |||||||
\(432\) | −256.145 | + | 9.05920i | −0.0285273 | + | 0.00100894i | ||||
\(433\) | 4519.31 | 0.501580 | 0.250790 | − | 0.968042i | \(-0.419310\pi\) | ||||
0.250790 | + | 0.968042i | \(0.419310\pi\) | |||||||
\(434\) | 5631.10 | − | 5731.52i | 0.622814 | − | 0.633922i | ||||
\(435\) | 119.913 | 0.0132170 | ||||||||
\(436\) | 2.45983 | + | 139.145i | 0.000270194 | + | 0.0152840i | ||||
\(437\) | 8301.36 | 0.908714 | ||||||||
\(438\) | 163.731 | + | 160.862i | 0.0178616 | + | 0.0175486i | ||||
\(439\) | − | 2602.30i | − | 0.282918i | −0.989944 | − | 0.141459i | \(-0.954821\pi\) | ||
0.989944 | − | 0.141459i | \(-0.0451793\pi\) | |||||||
\(440\) | −17844.2 | − | 16922.2i | −1.93339 | − | 1.83349i | ||||
\(441\) | 4203.99 | 0.453945 | ||||||||
\(442\) | 7222.77 | + | 13066.2i | 0.777268 | + | 1.40609i | ||||
\(443\) | 7533.16i | 0.807926i | 0.914775 | + | 0.403963i | \(0.132367\pi\) | ||||
−0.914775 | + | 0.403963i | \(0.867633\pi\) | |||||||
\(444\) | 2.32213 | + | 131.356i | 0.000248206 | + | 0.0140403i | ||||
\(445\) | 13847.0 | 1.47508 | ||||||||
\(446\) | −11677.3 | + | 11885.6i | −1.23977 | + | 1.26188i | ||||
\(447\) | − | 12.4188i | − | 0.00131407i | ||||||
\(448\) | 11418.1 | − | 606.059i | 1.20414 | − | 0.0639143i | ||||
\(449\) | − | 16145.6i | − | 1.69701i | −0.529186 | − | 0.848506i | \(-0.677503\pi\) | ||
0.529186 | − | 0.848506i | \(-0.322497\pi\) | |||||||
\(450\) | 9447.93 | − | 9616.43i | 0.989733 | − | 1.00738i | ||||
\(451\) | 4606.14i | 0.480920i | ||||||||
\(452\) | −15198.1 | + | 268.674i | −1.58154 | + | 0.0279588i | ||||
\(453\) | −109.419 | −0.0113487 | ||||||||
\(454\) | −5873.66 | + | 5978.41i | −0.607191 | + | 0.618019i | ||||
\(455\) | −29204.8 | −3.00911 | ||||||||
\(456\) | −114.971 | + | 121.235i | −0.0118070 | + | 0.0124504i | ||||
\(457\) | −4234.31 | −0.433419 | −0.216710 | − | 0.976236i | \(-0.569532\pi\) | ||||
−0.216710 | + | 0.976236i | \(0.569532\pi\) | |||||||
\(458\) | 9413.92 | + | 9248.97i | 0.960445 | + | 0.943616i | ||||
\(459\) | 269.044 | + | 80.0687i | 0.0273593 | + | 0.00814224i | ||||
\(460\) | 11582.3 | − | 204.755i | 1.17398 | − | 0.0207538i | ||||
\(461\) | − | 12098.5i | − | 1.22230i | −0.791514 | − | 0.611151i | \(-0.790707\pi\) | ||
0.791514 | − | 0.611151i | \(-0.209293\pi\) | |||||||
\(462\) | 209.156 | + | 205.491i | 0.0210624 | + | 0.0206933i | ||||
\(463\) | 1921.13 | 0.192835 | 0.0964174 | − | 0.995341i | \(-0.469262\pi\) | ||||
0.0964174 | + | 0.995341i | \(0.469262\pi\) | |||||||
\(464\) | 5954.65 | − | 210.601i | 0.595771 | − | 0.0210709i | ||||
\(465\) | 163.840i | 0.0163395i | ||||||||
\(466\) | 187.190 | + | 183.910i | 0.0186081 | + | 0.0182821i | ||||
\(467\) | − | 1205.99i | − | 0.119500i | −0.998213 | − | 0.0597501i | \(-0.980970\pi\) | ||
0.998213 | − | 0.0597501i | \(-0.0190304\pi\) | |||||||
\(468\) | 16260.2 | − | 287.452i | 1.60605 | − | 0.0283920i | ||||
\(469\) | −7383.62 | −0.726959 | ||||||||
\(470\) | −5624.39 | + | 5724.70i | −0.551986 | + | 0.561831i | ||||
\(471\) | − | 25.3064i | − | 0.00247570i | ||||||
\(472\) | −5081.40 | + | 5358.27i | −0.495530 | + | 0.522530i | ||||
\(473\) | 13149.2i | 1.27822i | ||||||||
\(474\) | 2.80752 | + | 2.75833i | 0.000272054 | + | 0.000267287i | ||||
\(475\) | − | 17578.0i | − | 1.69797i | ||||||
\(476\) | −12063.7 | − | 3359.28i | −1.16164 | − | 0.323471i | ||||
\(477\) | − | 76.8727i | − | 0.00737895i | ||||||
\(478\) | −6417.86 | + | 6532.32i | −0.614113 | + | 0.625066i | ||||
\(479\) | − | 4682.24i | − | 0.446633i | −0.974746 | − | 0.223316i | \(-0.928312\pi\) | ||
0.974746 | − | 0.223316i | \(-0.0716883\pi\) | |||||||
\(480\) | −157.421 | + | 171.987i | −0.0149693 | + | 0.0163544i | ||||
\(481\) | − | 16673.6i | − | 1.58056i | ||||||
\(482\) | −3391.66 | − | 3332.23i | −0.320510 | − | 0.314894i | ||||
\(483\) | −138.117 | −0.0130115 | ||||||||
\(484\) | −365.658 | − | 20684.1i | −0.0343405 | − | 1.94254i | ||||
\(485\) | 24245.8i | 2.26999i | ||||||||
\(486\) | 321.453 | − | 327.185i | 0.0300028 | − | 0.0305379i | ||||
\(487\) | 14671.6i | 1.36516i | 0.730809 | + | 0.682582i | \(0.239143\pi\) | ||||
−0.730809 | + | 0.682582i | \(0.760857\pi\) | |||||||
\(488\) | 3697.92 | + | 3506.84i | 0.343026 | + | 0.325302i | ||||
\(489\) | −127.320 | −0.0117743 | ||||||||
\(490\) | 5360.85 | − | 5456.46i | 0.494242 | − | 0.503057i | ||||
\(491\) | − | 20506.8i | − | 1.88484i | −0.334427 | − | 0.942422i | \(-0.608543\pi\) | ||
0.334427 | − | 0.942422i | \(-0.391457\pi\) | |||||||
\(492\) | 43.6632 | − | 0.771886i | 0.00400099 | − | 7.07303e-5i | ||||
\(493\) | −6254.51 | − | 1861.37i | −0.571377 | − | 0.170044i | ||||
\(494\) | 14861.2 | − | 15126.2i | 1.35351 | − | 1.37765i | ||||
\(495\) | 29338.5 | 2.66397 | ||||||||
\(496\) | 287.748 | + | 8135.97i | 0.0260489 | + | 0.736523i | ||||
\(497\) | 14217.3 | 1.28316 | ||||||||
\(498\) | −142.758 | − | 140.257i | −0.0128457 | − | 0.0126206i | ||||
\(499\) | 6913.78 | 0.620247 | 0.310124 | − | 0.950696i | \(-0.399630\pi\) | ||||
0.310124 | + | 0.950696i | \(0.399630\pi\) | |||||||
\(500\) | −126.620 | − | 7162.51i | −0.0113252 | − | 0.640634i | ||||
\(501\) | − | 247.974i | − | 0.0221131i | ||||||
\(502\) | −1317.61 | − | 1294.52i | −0.117147 | − | 0.115094i | ||||
\(503\) | 12839.4i | 1.13813i | 0.822293 | + | 0.569065i | \(0.192695\pi\) | ||||
−0.822293 | + | 0.569065i | \(0.807305\pi\) | |||||||
\(504\) | −9386.51 | + | 9897.95i | −0.829580 | + | 0.874781i | ||||
\(505\) | − | 13610.6i | − | 1.19933i | ||||||
\(506\) | 10529.1 | + | 10344.6i | 0.925049 | + | 0.908840i | ||||
\(507\) | 257.667 | 0.0225708 | ||||||||
\(508\) | 29.0733 | + | 1644.59i | 0.00253921 | + | 0.143635i | ||||
\(509\) | − | 7857.20i | − | 0.684213i | −0.939661 | − | 0.342106i | \(-0.888860\pi\) | ||
0.939661 | − | 0.342106i | \(-0.111140\pi\) | |||||||
\(510\) | 223.479 | − | 123.536i | 0.0194036 | − | 0.0107260i | ||||
\(511\) | 24434.5 | 2.11530 | ||||||||
\(512\) | −7515.16 | + | 8817.03i | −0.648684 | + | 0.761057i | ||||
\(513\) | − | 398.698i | − | 0.0343137i | ||||||
\(514\) | 3243.32 | − | 3301.16i | 0.278320 | − | 0.283284i | ||||
\(515\) | −19141.0 | −1.63777 | ||||||||
\(516\) | 124.645 | − | 2.20350i | 0.0106341 | − | 0.000187992i | ||||
\(517\) | −10225.9 | −0.869889 | ||||||||
\(518\) | 9976.28 | + | 9801.47i | 0.846202 | + | 0.831374i | ||||
\(519\) | −145.286 | −0.0122877 | ||||||||
\(520\) | 20361.7 | − | 21471.1i | 1.71715 | − | 1.81071i | ||||
\(521\) | − | 11238.7i | − | 0.945057i | −0.881315 | − | 0.472529i | \(-0.843341\pi\) | ||
0.881315 | − | 0.472529i | \(-0.156659\pi\) | |||||||
\(522\) | −4981.73 | + | 5070.58i | −0.417710 | + | 0.425159i | ||||
\(523\) | − | 16546.3i | − | 1.38340i | −0.722186 | − | 0.691699i | \(-0.756862\pi\) | ||
0.722186 | − | 0.691699i | \(-0.243138\pi\) | |||||||
\(524\) | −195.150 | − | 11039.0i | −0.0162694 | − | 0.920310i | ||||
\(525\) | 292.461i | 0.0243124i | ||||||||
\(526\) | −10907.0 | + | 11101.5i | −0.904119 | + | 0.920243i | ||||
\(527\) | 2543.23 | − | 8545.67i | 0.210218 | − | 0.706367i | ||||
\(528\) | −296.900 | + | 10.5006i | −0.0244714 | + | 0.000865490i | ||||
\(529\) | 5214.08 | 0.428543 | ||||||||
\(530\) | −99.7750 | − | 98.0268i | −0.00817726 | − | 0.00803398i | ||||
\(531\) | − | 8809.77i | − | 0.719984i | ||||||
\(532\) | 314.384 | + | 17783.7i | 0.0256208 | + | 1.44929i | ||||
\(533\) | −5542.36 | −0.450406 | ||||||||
\(534\) | 117.233 | − | 119.324i | 0.00950032 | − | 0.00966975i | ||||
\(535\) | −21261.2 | −1.71814 | ||||||||
\(536\) | 5147.88 | − | 5428.37i | 0.414840 | − | 0.437444i | ||||
\(537\) | − | 148.120i | − | 0.0119029i | ||||||
\(538\) | 13523.5 | − | 13764.7i | 1.08372 | − | 1.10305i | ||||
\(539\) | 9746.72 | 0.778889 | ||||||||
\(540\) | −9.83395 | − | 556.276i | −0.000783678 | − | 0.0443302i | ||||
\(541\) | −2403.44 | −0.191002 | −0.0955010 | − | 0.995429i | \(-0.530445\pi\) | ||||
−0.0955010 | + | 0.995429i | \(0.530445\pi\) | |||||||
\(542\) | −9475.48 | + | 9644.47i | −0.750935 | + | 0.764327i | ||||
\(543\) | −39.8614 | −0.00315031 | ||||||||
\(544\) | 10880.6 | − | 6527.04i | 0.857538 | − | 0.514420i | ||||
\(545\) | −302.090 | −0.0237433 | ||||||||
\(546\) | −247.258 | + | 251.668i | −0.0193804 | + | 0.0197260i | ||||
\(547\) | 20450.9 | 1.59857 | 0.799286 | − | 0.600951i | \(-0.205211\pi\) | ||||
0.799286 | + | 0.600951i | \(0.205211\pi\) | |||||||
\(548\) | 168.947 | + | 9556.81i | 0.0131698 | + | 0.744976i | ||||
\(549\) | −6079.91 | −0.472649 | ||||||||
\(550\) | 21904.5 | − | 22295.2i | 1.69820 | − | 1.72849i | ||||
\(551\) | 9268.58i | 0.716615i | ||||||||
\(552\) | 96.2955 | − | 101.542i | 0.00742502 | − | 0.00782958i | ||||
\(553\) | 418.981 | 0.0322186 | ||||||||
\(554\) | −7129.27 | + | 7256.42i | −0.546740 | + | 0.556491i | ||||
\(555\) | −285.179 | −0.0218111 | ||||||||
\(556\) | −87.5492 | − | 4952.39i | −0.00667790 | − | 0.377748i | ||||
\(557\) | 849.470i | 0.0646198i | 0.999478 | + | 0.0323099i | \(0.0102863\pi\) | ||||
−0.999478 | + | 0.0323099i | \(0.989714\pi\) | |||||||
\(558\) | −6928.04 | − | 6806.65i | −0.525605 | − | 0.516395i | ||||
\(559\) | −15821.8 | −1.19712 | ||||||||
\(560\) | 877.278 | + | 24804.7i | 0.0661995 | + | 1.87177i | ||||
\(561\) | 311.851 | + | 92.8081i | 0.0234694 | + | 0.00698460i | ||||
\(562\) | 6113.97 | − | 6223.01i | 0.458901 | − | 0.467085i | ||||
\(563\) | 1065.17i | 0.0797361i | 0.999205 | + | 0.0398680i | \(0.0126938\pi\) | ||||
−0.999205 | + | 0.0398680i | \(0.987306\pi\) | |||||||
\(564\) | 1.71362 | + | 96.9345i | 0.000127937 | + | 0.00723702i | ||||
\(565\) | − | 32995.6i | − | 2.45688i | ||||||
\(566\) | 499.299 | − | 508.204i | 0.0370797 | − | 0.0377410i | ||||
\(567\) | − | 16270.4i | − | 1.20510i | ||||||
\(568\) | −9912.33 | + | 10452.4i | −0.732240 | + | 0.772137i | ||||
\(569\) | 24782.8 | 1.82592 | 0.912961 | − | 0.408048i | \(-0.133790\pi\) | ||||
0.912961 | + | 0.408048i | \(0.133790\pi\) | |||||||
\(570\) | −258.714 | − | 254.180i | −0.0190111 | − | 0.0186780i | ||||
\(571\) | −12597.6 | −0.923280 | −0.461640 | − | 0.887067i | \(-0.652739\pi\) | ||||
−0.461640 | + | 0.887067i | \(0.652739\pi\) | |||||||
\(572\) | 37698.5 | − | 666.441i | 2.75569 | − | 0.0487156i | ||||
\(573\) | 134.288 | 0.00979048 | ||||||||
\(574\) | 3258.05 | − | 3316.15i | 0.236913 | − | 0.241139i | ||||
\(575\) | 14722.7i | 1.06779i | ||||||||
\(576\) | −732.580 | − | 13801.8i | −0.0529934 | − | 0.998391i | ||||
\(577\) | −25747.2 | −1.85766 | −0.928830 | − | 0.370505i | \(-0.879185\pi\) | ||||
−0.928830 | + | 0.370505i | \(0.879185\pi\) | |||||||
\(578\) | −13574.0 | + | 2974.48i | −0.976822 | + | 0.214052i | ||||
\(579\) | 168.411i | 0.0120880i | ||||||||
\(580\) | 228.611 | + | 12931.8i | 0.0163665 | + | 0.925802i | ||||
\(581\) | −21304.6 | −1.52128 | ||||||||
\(582\) | 208.934 | + | 205.273i | 0.0148807 | + | 0.0146200i | ||||
\(583\) | − | 178.225i | − | 0.0126610i | ||||||
\(584\) | −17035.8 | + | 17964.0i | −1.20710 | + | 1.27287i | ||||
\(585\) | 35301.7i | 2.49495i | ||||||||
\(586\) | −220.712 | − | 216.845i | −0.0155589 | − | 0.0152863i | ||||
\(587\) | 17172.8i | 1.20749i | 0.797176 | + | 0.603747i | \(0.206326\pi\) | ||||
−0.797176 | + | 0.603747i | \(0.793674\pi\) | |||||||
\(588\) | −1.63333 | − | 92.3925i | −0.000114554 | − | 0.00647994i | ||||
\(589\) | −12663.9 | −0.885918 | ||||||||
\(590\) | −11434.4 | − | 11234.1i | −0.797877 | − | 0.783897i | ||||
\(591\) | 253.234 | 0.0176255 | ||||||||
\(592\) | −14161.4 | + | 500.854i | −0.983161 | + | 0.0347719i | ||||
\(593\) | 5621.80 | 0.389308 | 0.194654 | − | 0.980872i | \(-0.437642\pi\) | ||||
0.194654 | + | 0.980872i | \(0.437642\pi\) | |||||||
\(594\) | 496.830 | − | 505.691i | 0.0343185 | − | 0.0349306i | ||||
\(595\) | 7753.72 | − | 26053.8i | 0.534238 | − | 1.79513i | ||||
\(596\) | 1339.29 | − | 23.6761i | 0.0920458 | − | 0.00162720i | ||||
\(597\) | 46.5939i | 0.00319424i | ||||||||
\(598\) | −12447.2 | + | 12669.2i | −0.851175 | + | 0.866355i | ||||
\(599\) | −4214.51 | −0.287479 | −0.143740 | − | 0.989616i | \(-0.545913\pi\) | ||||
−0.143740 | + | 0.989616i | \(0.545913\pi\) | |||||||
\(600\) | −215.014 | − | 203.904i | −0.0146299 | − | 0.0138739i | ||||
\(601\) | 16937.9i | 1.14960i | 0.818293 | + | 0.574801i | \(0.194921\pi\) | ||||
−0.818293 | + | 0.574801i | \(0.805079\pi\) | |||||||
\(602\) | 9300.75 | − | 9466.62i | 0.629685 | − | 0.640915i | ||||
\(603\) | 8925.03i | 0.602745i | ||||||||
\(604\) | −208.605 | − | 11800.2i | −0.0140530 | − | 0.794937i | ||||
\(605\) | 44906.1 | 3.01767 | ||||||||
\(606\) | −117.287 | − | 115.232i | −0.00786215 | − | 0.00772439i | ||||
\(607\) | 8620.85i | 0.576457i | 0.957562 | + | 0.288228i | \(0.0930663\pi\) | ||||
−0.957562 | + | 0.288228i | \(0.906934\pi\) | |||||||
\(608\) | −13293.6 | − | 12167.7i | −0.886723 | − | 0.811623i | ||||
\(609\) | − | 154.210i | − | 0.0102609i | ||||||
\(610\) | −7753.00 | + | 7891.27i | −0.514606 | + | 0.523784i | ||||
\(611\) | − | 12304.3i | − | 0.814696i | ||||||
\(612\) | −4060.56 | + | 14582.2i | −0.268200 | + | 0.963152i | ||||
\(613\) | − | 5413.39i | − | 0.356680i | −0.983969 | − | 0.178340i | \(-0.942927\pi\) | ||
0.983969 | − | 0.178340i | \(-0.0570727\pi\) | |||||||
\(614\) | −4715.94 | − | 4633.31i | −0.309967 | − | 0.304536i | ||||
\(615\) | 94.7946i | 0.00621543i | ||||||||
\(616\) | −21762.1 | + | 22947.9i | −1.42341 | + | 1.50097i | ||||
\(617\) | 1030.74i | 0.0672547i | 0.999434 | + | 0.0336274i | \(0.0107059\pi\) | ||||
−0.999434 | + | 0.0336274i | \(0.989294\pi\) | |||||||
\(618\) | −162.054 | + | 164.944i | −0.0105482 | + | 0.0107363i | ||||
\(619\) | −19679.7 | −1.27786 | −0.638929 | − | 0.769266i | \(-0.720622\pi\) | ||||
−0.638929 | + | 0.769266i | \(0.720622\pi\) | |||||||
\(620\) | −17669.0 | + | 312.356i | −1.14453 | + | 0.0202331i | ||||
\(621\) | 333.935i | 0.0215786i | ||||||||
\(622\) | 6568.98 | + | 6453.88i | 0.423460 | + | 0.416040i | ||||
\(623\) | − | 17807.3i | − | 1.14516i | ||||||
\(624\) | −12.6349 | − | 357.246i | −0.000810575 | − | 0.0229187i | ||||
\(625\) | −6520.49 | −0.417311 | ||||||||
\(626\) | 17675.6 | + | 17365.9i | 1.12853 | + | 1.10875i | ||||
\(627\) | − | 462.133i | − | 0.0294351i | ||||||
\(628\) | 2729.12 | − | 48.2460i | 0.173414 | − | 0.00306564i | ||||
\(629\) | 14874.6 | + | 4426.74i | 0.942906 | + | 0.280613i | ||||
\(630\) | −21122.0 | − | 20751.9i | −1.33575 | − | 1.31234i | ||||
\(631\) | −22362.5 | −1.41083 | −0.705417 | − | 0.708793i | \(-0.749240\pi\) | ||||
−0.705417 | + | 0.708793i | \(0.749240\pi\) | |||||||
\(632\) | −292.115 | + | 308.031i | −0.0183856 | + | 0.0193874i | ||||
\(633\) | 12.4931 | 0.000784449 | ||||||||
\(634\) | −16029.9 | + | 16315.7i | −1.00414 | + | 1.02205i | ||||
\(635\) | −3570.46 | −0.223133 | ||||||||
\(636\) | −1.68946 | + | 0.0298666i | −0.000105332 | + | 1.86209e-6i | ||||
\(637\) | 11727.8i | 0.729469i | ||||||||
\(638\) | −11549.9 | + | 11755.9i | −0.716715 | + | 0.729497i | ||||
\(639\) | − | 17185.3i | − | 1.06391i | ||||||
\(640\) | −18847.8 | − | 16648.9i | −1.16410 | − | 1.02829i | ||||
\(641\) | − | 3639.34i | − | 0.224252i | −0.993694 | − | 0.112126i | \(-0.964234\pi\) | ||
0.993694 | − | 0.112126i | \(-0.0357660\pi\) | |||||||
\(642\) | −180.005 | + | 183.215i | −0.0110658 | + | 0.0112631i | ||||
\(643\) | −12532.0 | −0.768607 | −0.384303 | − | 0.923207i | \(-0.625558\pi\) | ||||
−0.384303 | + | 0.923207i | \(0.625558\pi\) | |||||||
\(644\) | −263.317 | − | 14895.0i | −0.0161120 | − | 0.911406i | ||||
\(645\) | 270.610i | 0.0165198i | ||||||||
\(646\) | 9548.61 | + | 17273.6i | 0.581556 | + | 1.05205i | ||||
\(647\) | −10837.5 | −0.658528 | −0.329264 | − | 0.944238i | \(-0.606801\pi\) | ||||
−0.329264 | + | 0.944238i | \(0.606801\pi\) | |||||||
\(648\) | 11961.8 | + | 11343.7i | 0.725161 | + | 0.687691i | ||||
\(649\) | − | 20425.0i | − | 1.23536i | ||||||
\(650\) | 26826.8 | + | 26356.7i | 1.61882 | + | 1.59045i | ||||
\(651\) | 210.700 | 0.0126851 | ||||||||
\(652\) | −242.733 | − | 13730.7i | −0.0145800 | − | 0.824746i | ||||
\(653\) | 11538.7 | 0.691491 | 0.345745 | − | 0.938328i | \(-0.387626\pi\) | ||||
0.345745 | + | 0.938328i | \(0.387626\pi\) | |||||||
\(654\) | −2.55760 | + | 2.60321i | −0.000152920 | + | 0.000155648i | ||||
\(655\) | 23966.2 | 1.42967 | ||||||||
\(656\) | 166.486 | + | 4707.32i | 0.00990880 | + | 0.280167i | ||||
\(657\) | − | 29535.5i | − | 1.75386i | ||||||
\(658\) | 7362.02 | + | 7233.02i | 0.436172 | + | 0.428530i | ||||
\(659\) | 25213.1i | 1.49039i | 0.666849 | + | 0.745193i | \(0.267643\pi\) | ||||
−0.666849 | + | 0.745193i | \(0.732357\pi\) | |||||||
\(660\) | −11.3986 | − | 644.783i | −0.000672257 | − | 0.0380275i | ||||
\(661\) | 16257.2i | 0.956632i | 0.878188 | + | 0.478316i | \(0.158753\pi\) | ||||
−0.878188 | + | 0.478316i | \(0.841247\pi\) | |||||||
\(662\) | 13061.4 | + | 12832.5i | 0.766836 | + | 0.753399i | ||||
\(663\) | −111.672 | + | 375.235i | −0.00654143 | + | 0.0219803i | ||||
\(664\) | 14853.6 | − | 15662.9i | 0.868120 | − | 0.915421i | ||||
\(665\) | −38609.2 | −2.25143 | ||||||||
\(666\) | 11847.6 | − | 12058.9i | 0.689319 | − | 0.701613i | ||||
\(667\) | − | 7763.03i | − | 0.450653i | ||||||
\(668\) | 26742.4 | − | 472.757i | 1.54894 | − | 0.0273825i | ||||
\(669\) | −436.932 | −0.0252508 | ||||||||
\(670\) | 11584.0 | + | 11381.0i | 0.667955 | + | 0.656251i | ||||
\(671\) | −14095.9 | −0.810981 | ||||||||
\(672\) | 221.178 | + | 202.445i | 0.0126966 | + | 0.0116213i | ||||
\(673\) | 15342.7i | 0.878777i | 0.898297 | + | 0.439389i | \(0.144805\pi\) | ||||
−0.898297 | + | 0.439389i | \(0.855195\pi\) | |||||||
\(674\) | 16596.9 | + | 16306.1i | 0.948502 | + | 0.931882i | ||||
\(675\) | 707.102 | 0.0403205 | ||||||||
\(676\) | 491.235 | + | 27787.6i | 0.0279492 | + | 1.58100i | ||||
\(677\) | −8344.74 | −0.473729 | −0.236864 | − | 0.971543i | \(-0.576120\pi\) | ||||
−0.236864 | + | 0.971543i | \(0.576120\pi\) | |||||||
\(678\) | −284.334 | − | 279.352i | −0.0161059 | − | 0.0158237i | ||||
\(679\) | 31180.3 | 1.76228 | ||||||||
\(680\) | 13748.6 | + | 23865.2i | 0.775344 | + | 1.34587i | ||||
\(681\) | −219.776 | −0.0123669 | ||||||||
\(682\) | −16062.3 | − | 15780.9i | −0.901843 | − | 0.886041i | ||||
\(683\) | −6383.55 | −0.357628 | −0.178814 | − | 0.983883i | \(-0.557226\pi\) | ||||
−0.178814 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(684\) | 21496.3 | − | 380.015i | 1.20165 | − | 0.0212430i | ||||
\(685\) | −20748.2 | −1.15730 | ||||||||
\(686\) | 8437.74 | + | 8289.90i | 0.469613 | + | 0.461384i | ||||
\(687\) | 346.070i | 0.0192189i | ||||||||
\(688\) | 475.266 | + | 13438.0i | 0.0263363 | + | 0.744648i | ||||
\(689\) | 214.450 | 0.0118576 | ||||||||
\(690\) | 216.689 | + | 212.892i | 0.0119554 | + | 0.0117459i | ||||
\(691\) | 33017.1 | 1.81770 | 0.908850 | − | 0.417123i | \(-0.136962\pi\) | ||||
0.908850 | + | 0.417123i | \(0.136962\pi\) | |||||||
\(692\) | −276.984 | − | 15668.1i | −0.0152158 | − | 0.860711i | ||||
\(693\) | − | 37729.6i | − | 2.06815i | ||||||
\(694\) | −18935.0 | + | 19272.7i | −1.03568 | + | 1.05415i | ||||
\(695\) | 10751.8 | 0.586821 | ||||||||
\(696\) | 113.373 | + | 107.515i | 0.00617444 | + | 0.00585540i | ||||
\(697\) | 1471.46 | − | 4944.36i | 0.0799651 | − | 0.268696i | ||||
\(698\) | −14836.0 | − | 14576.0i | −0.804512 | − | 0.790415i | ||||
\(699\) | 6.88138i | 0.000372357i | ||||||||
\(700\) | −31539.9 | + | 557.569i | −1.70300 | + | 0.0301059i | ||||
\(701\) | 7053.95i | 0.380063i | 0.981778 | + | 0.190031i | \(0.0608590\pi\) | ||||
−0.981778 | + | 0.190031i | \(0.939141\pi\) | |||||||
\(702\) | 608.475 | + | 597.813i | 0.0327142 | + | 0.0321410i | ||||
\(703\) | − | 22042.7i | − | 1.18258i | ||||||
\(704\) | −1698.45 | − | 31998.6i | −0.0909271 | − | 1.71306i | ||||
\(705\) | −210.449 | −0.0112425 | ||||||||
\(706\) | 11293.0 | − | 11494.4i | 0.602006 | − | 0.612743i | ||||
\(707\) | −17503.4 | −0.931093 | ||||||||
\(708\) | −193.615 | + | 3.42277i | −0.0102776 | + | 0.000181689i | ||||
\(709\) | 29626.7 | 1.56933 | 0.784664 | − | 0.619922i | \(-0.212836\pi\) | ||||
0.784664 | + | 0.619922i | \(0.212836\pi\) | |||||||
\(710\) | −22305.2 | − | 21914.4i | −1.17901 | − | 1.15836i | ||||
\(711\) | − | 506.448i | − | 0.0267135i | ||||||
\(712\) | 13091.8 | + | 12415.3i | 0.689095 | + | 0.653489i | ||||
\(713\) | 10606.8 | 0.557121 | ||||||||
\(714\) | −158.868 | − | 287.397i | −0.00832704 | − | 0.0150638i | ||||
\(715\) | 81845.0i | 4.28088i | ||||||||
\(716\) | 15973.7 | − | 282.387i | 0.833752 | − | 0.0147392i | ||||
\(717\) | −240.138 | −0.0125079 | ||||||||
\(718\) | 9226.49 | − | 9391.04i | 0.479568 | − | 0.488121i | ||||
\(719\) | 26492.5i | 1.37414i | 0.726593 | + | 0.687068i | \(0.241103\pi\) | ||||
−0.726593 | + | 0.687068i | \(0.758897\pi\) | |||||||
\(720\) | 29982.9 | − | 1060.42i | 1.55194 | − | 0.0548882i | ||||
\(721\) | 24615.5i | 1.27147i | ||||||||
\(722\) | 6050.44 | − | 6158.35i | 0.311876 | − | 0.317438i | ||||
\(723\) | − | 124.683i | − | 0.00641355i | ||||||
\(724\) | −75.9948 | − | 4298.79i | −0.00390100 | − | 0.220667i | ||||
\(725\) | −16438.1 | −0.842063 | ||||||||
\(726\) | 380.190 | − | 386.971i | 0.0194355 | − | 0.0197821i | ||||
\(727\) | 23186.1 | 1.18284 | 0.591421 | − | 0.806363i | \(-0.298567\pi\) | ||||
0.591421 | + | 0.806363i | \(0.298567\pi\) | |||||||
\(728\) | −27612.1 | − | 26185.4i | −1.40573 | − | 1.33310i | ||||
\(729\) | −19658.9 | −0.998778 | ||||||||
\(730\) | −38334.8 | − | 37663.1i | −1.94361 | − | 1.90955i | ||||
\(731\) | 4200.59 | − | 14114.7i | 0.212537 | − | 0.714159i | ||||
\(732\) | 2.36217 | + | 133.620i | 0.000119273 | + | 0.00674693i | ||||
\(733\) | − | 31571.3i | − | 1.59088i | −0.606036 | − | 0.795438i | \(-0.707241\pi\) | ||
0.606036 | − | 0.795438i | \(-0.292759\pi\) | |||||||
\(734\) | −23595.7 | − | 23182.2i | −1.18656 | − | 1.16577i | ||||
\(735\) | 200.588 | 0.0100664 | ||||||||
\(736\) | 11134.3 | + | 10191.2i | 0.557628 | + | 0.510400i | ||||
\(737\) | 20692.2i | 1.03420i | ||||||||
\(738\) | −4008.43 | − | 3938.20i | −0.199936 | − | 0.196432i | ||||
\(739\) | 14205.3i | 0.707104i | 0.935415 | + | 0.353552i | \(0.115026\pi\) | ||||
−0.935415 | + | 0.353552i | \(0.884974\pi\) | |||||||
\(740\) | −543.687 | − | 30754.7i | −0.0270085 | − | 1.52779i | ||||
\(741\) | 556.063 | 0.0275675 | ||||||||
\(742\) | −126.064 | + | 128.312i | −0.00623711 | + | 0.00634835i | ||||
\(743\) | 13061.1i | 0.644906i | 0.946586 | + | 0.322453i | \(0.104507\pi\) | ||||
−0.946586 | + | 0.322453i | \(0.895493\pi\) | |||||||
\(744\) | −146.900 | + | 154.905i | −0.00723875 | + | 0.00763317i | ||||
\(745\) | 2907.65i | 0.142990i | ||||||||
\(746\) | 16310.7 | + | 16024.9i | 0.800504 | + | 0.786477i | ||||
\(747\) | 25752.1i | 1.26134i | ||||||||
\(748\) | −9414.20 | + | 33808.0i | −0.460184 | + | 1.65260i | ||||
\(749\) | 27342.2i | 1.33386i | ||||||||
\(750\) | 131.652 | − | 134.000i | 0.00640969 | − | 0.00652400i | ||||
\(751\) | 20340.6i | 0.988335i | 0.869367 | + | 0.494167i | \(0.164527\pi\) | ||||
−0.869367 | + | 0.494167i | \(0.835473\pi\) | |||||||
\(752\) | −10450.5 | + | 369.606i | −0.506768 | + | 0.0179231i | ||||
\(753\) | − | 48.4374i | − | 0.00234417i | ||||||
\(754\) | −14145.3 | − | 13897.4i | −0.683211 | − | 0.671240i | ||||
\(755\) | 25618.6 | 1.23491 | ||||||||
\(756\) | −715.377 | + | 12.6466i | −0.0344154 | + | 0.000608401i | ||||
\(757\) | 15960.2i | 0.766294i | 0.923687 | + | 0.383147i | \(0.125160\pi\) | ||||
−0.923687 | + | 0.383147i | \(0.874840\pi\) | |||||||
\(758\) | −7756.34 | + | 7894.67i | −0.371666 | + | 0.378295i | ||||
\(759\) | 387.066i | 0.0185107i | ||||||||
\(760\) | 26918.4 | − | 28385.1i | 1.28478 | − | 1.35479i | ||||
\(761\) | 4117.41 | 0.196131 | 0.0980657 | − | 0.995180i | \(-0.468734\pi\) | ||||
0.0980657 | + | 0.995180i | \(0.468734\pi\) | |||||||
\(762\) | −30.2288 | + | 30.7679i | −0.00143710 | + | 0.00146273i | ||||
\(763\) | 388.491i | 0.0184329i | ||||||||
\(764\) | 256.016 | + | 14482.0i | 0.0121235 | + | 0.685787i | ||||
\(765\) | −31492.8 | − | 9372.39i | −1.48840 | − | 0.442954i | ||||
\(766\) | −1798.55 | + | 1830.62i | −0.0848358 | + | 0.0863488i | ||||
\(767\) | 24576.4 | 1.15698 | ||||||||
\(768\) | −303.041 | + | 21.4624i | −0.0142384 | + | 0.00100841i | ||||
\(769\) | 10952.3 | 0.513588 | 0.256794 | − | 0.966466i | \(-0.417334\pi\) | ||||
0.256794 | + | 0.966466i | \(0.417334\pi\) | |||||||
\(770\) | −48970.2 | − | 48112.2i | −2.29190 | − | 2.25174i | ||||
\(771\) | 121.356 | 0.00566865 | ||||||||
\(772\) | −18162.0 | + | 321.072i | −0.846718 | + | 0.0149684i | ||||
\(773\) | 13654.4i | 0.635334i | 0.948202 | + | 0.317667i | \(0.102899\pi\) | ||||
−0.948202 | + | 0.317667i | \(0.897101\pi\) | |||||||
\(774\) | −11442.9 | − | 11242.4i | −0.531403 | − | 0.522092i | ||||
\(775\) | − | 22459.7i | − | 1.04100i | ||||||
\(776\) | −21739.0 | + | 22923.5i | −1.00565 | + | 1.06044i | ||||
\(777\) | 366.743i | 0.0169329i | ||||||||
\(778\) | −21653.0 | − | 21273.6i | −0.997814 | − | 0.980330i | ||||
\(779\) | −7327.07 | −0.336996 | ||||||||
\(780\) | 775.837 | − | 13.7154i | 0.0356147 | − | 0.000629602i | ||||
\(781\) | − | 39843.2i | − | 1.82548i | ||||||
\(782\) | −7997.57 | − | 14467.8i | −0.365719 | − | 0.661594i | ||||
\(783\) | −372.843 | −0.0170170 | ||||||||
\(784\) | 9960.81 | − | 352.288i | 0.453754 | − | 0.0160481i | ||||
\(785\) | 5925.04i | 0.269393i | ||||||||
\(786\) | 202.906 | − | 206.525i | 0.00920791 | − | 0.00937213i | ||||
\(787\) | 12703.7 | 0.575399 | 0.287699 | − | 0.957721i | \(-0.407110\pi\) | ||||
0.287699 | + | 0.957721i | \(0.407110\pi\) | |||||||
\(788\) | 482.784 | + | 27309.6i | 0.0218255 | + | 1.23460i | ||||
\(789\) | −408.108 | −0.0184145 | ||||||||
\(790\) | −657.331 | − | 645.814i | −0.0296035 | − | 0.0290848i | ||||
\(791\) | −42432.7 | −1.90738 | ||||||||
\(792\) | 27738.5 | + | 26305.2i | 1.24450 | + | 1.18020i | ||||
\(793\) | − | 16961.0i | − | 0.759525i | ||||||
\(794\) | 19532.8 | − | 19881.1i | 0.873039 | − | 0.888609i | ||||
\(795\) | − | 3.66789i | − | 0.000163631i | ||||||
\(796\) | −5024.85 | + | 88.8301i | −0.223745 | + | 0.00395540i | ||||
\(797\) | 23759.3i | 1.05596i | 0.849257 | + | 0.527979i | \(0.177050\pi\) | ||||
−0.849257 | + | 0.527979i | \(0.822950\pi\) | |||||||
\(798\) | −326.879 | + | 332.708i | −0.0145005 | + | 0.0147591i | ||||
\(799\) | 10976.7 | + | 3266.72i | 0.486019 | + | 0.144641i | ||||
\(800\) | 21579.8 | − | 23576.6i | 0.953702 | − | 1.04195i | ||||
\(801\) | −21524.8 | −0.949490 | ||||||||
\(802\) | 14968.5 | + | 14706.2i | 0.659045 | + | 0.647498i | ||||
\(803\) | − | 68476.4i | − | 3.00932i | ||||||
\(804\) | 196.149 | − | 3.46755i | 0.00860401 | − | 0.000152103i | ||||
\(805\) | 32337.7 | 1.41584 | ||||||||
\(806\) | 18988.4 | − | 19327.0i | 0.829823 | − | 0.844622i | ||||
\(807\) | 506.012 | 0.0220725 | ||||||||
\(808\) | 12203.4 | − | 12868.3i | 0.531330 | − | 0.560280i | ||||
\(809\) | − | 8146.86i | − | 0.354052i | −0.984206 | − | 0.177026i | \(-0.943352\pi\) | ||
0.984206 | − | 0.177026i | \(-0.0566477\pi\) | |||||||
\(810\) | −25079.0 | + | 25526.2i | −1.08788 | + | 1.10728i | ||||
\(811\) | 8350.91 | 0.361578 | 0.180789 | − | 0.983522i | \(-0.442135\pi\) | ||||
0.180789 | + | 0.983522i | \(0.442135\pi\) | |||||||
\(812\) | 16630.5 | − | 293.997i | 0.718738 | − | 0.0127060i | ||||
\(813\) | −354.546 | −0.0152945 | ||||||||
\(814\) | 27468.1 | − | 27958.0i | 1.18275 | − | 1.20384i | ||||
\(815\) | 29809.8 | 1.28122 | ||||||||
\(816\) | 322.055 | + | 83.5750i | 0.0138164 | + | 0.00358543i | ||||
\(817\) | −20916.6 | −0.895691 | ||||||||
\(818\) | −3595.79 | + | 3659.92i | −0.153697 | + | 0.156438i | ||||
\(819\) | 45398.3 | 1.93693 | ||||||||
\(820\) | −10223.0 | + | 180.724i | −0.435368 | + | 0.00769651i | ||||
\(821\) | 21197.4 | 0.901088 | 0.450544 | − | 0.892754i | \(-0.351230\pi\) | ||||
0.450544 | + | 0.892754i | \(0.351230\pi\) | |||||||
\(822\) | −175.662 | + | 178.794i | −0.00745365 | + | 0.00758658i | ||||
\(823\) | − | 36354.9i | − | 1.53979i | −0.638168 | − | 0.769897i | \(-0.720307\pi\) | ||
0.638168 | − | 0.769897i | \(-0.279693\pi\) | |||||||
\(824\) | −18097.1 | − | 17162.0i | −0.765099 | − | 0.725566i | ||||
\(825\) | 819.606 | 0.0345879 | ||||||||
\(826\) | −14447.1 | + | 14704.8i | −0.608572 | + | 0.619425i | ||||
\(827\) | −9957.18 | −0.418676 | −0.209338 | − | 0.977843i | \(-0.567131\pi\) | ||||
−0.209338 | + | 0.977843i | \(0.567131\pi\) | |||||||
\(828\) | −18004.5 | + | 318.287i | −0.755676 | + | 0.0133590i | ||||
\(829\) | 10099.2i | 0.423110i | 0.977366 | + | 0.211555i | \(0.0678528\pi\) | ||||
−0.977366 | + | 0.211555i | \(0.932147\pi\) | |||||||
\(830\) | 33424.3 | + | 32838.7i | 1.39780 | + | 1.37331i | ||||
\(831\) | −266.757 | −0.0111356 | ||||||||
\(832\) | 38502.5 | − | 2043.67i | 1.60437 | − | 0.0851579i | ||||
\(833\) | −10462.4 | − | 3113.66i | −0.435175 | − | 0.129510i | ||||
\(834\) | 91.0287 | − | 92.6522i | 0.00377946 | − | 0.00384686i | ||||
\(835\) | 58058.8i | 2.40624i | ||||||||
\(836\) | 49838.0 | − | 881.044i | 2.06182 | − | 0.0364492i | ||||
\(837\) | − | 509.423i | − | 0.0210373i | ||||||
\(838\) | 21631.1 | − | 22016.9i | 0.891689 | − | 0.907592i | ||||
\(839\) | 5391.05i | 0.221835i | 0.993830 | + | 0.110918i | \(0.0353790\pi\) | ||||
−0.993830 | + | 0.110918i | \(0.964621\pi\) | |||||||
\(840\) | −447.866 | + | 472.268i | −0.0183962 | + | 0.0193986i | ||||
\(841\) | −15721.5 | −0.644613 | ||||||||
\(842\) | −22459.6 | − | 22066.1i | −0.919250 | − | 0.903143i | ||||
\(843\) | 228.768 | 0.00934659 | ||||||||
\(844\) | 23.8178 | + | 1347.30i | 0.000971377 | + | 0.0549478i | ||||
\(845\) | −60328.1 | −2.45604 | ||||||||
\(846\) | 8743.00 | − | 8898.92i | 0.355308 | − | 0.361644i | ||||
\(847\) | − | 57749.7i | − | 2.34274i | ||||||
\(848\) | −6.44182 | − | 182.140i | −0.000260865 | − | 0.00737584i | ||||
\(849\) | 18.6824 | 0.000755215 | ||||||||
\(850\) | −30635.3 | + | 16934.7i | −1.23621 | + | 0.683360i | ||||
\(851\) | 18462.2i | 0.743683i | ||||||||
\(852\) | −377.687 | + | 6.67683i | −0.0151870 | + | 0.000268479i | ||||
\(853\) | −40811.4 | −1.63817 | −0.819084 | − | 0.573674i | \(-0.805518\pi\) | ||||
−0.819084 | + | 0.573674i | \(0.805518\pi\) | |||||||
\(854\) | 10148.3 | + | 9970.44i | 0.406635 | + | 0.399510i | ||||
\(855\) | 46669.3i | 1.86673i | ||||||||
\(856\) | −20101.7 | − | 19063.0i | −0.802643 | − | 0.761169i | ||||
\(857\) | 5699.01i | 0.227158i | 0.993529 | + | 0.113579i | \(0.0362315\pi\) | ||||
−0.993529 | + | 0.113579i | \(0.963768\pi\) | |||||||
\(858\) | 705.286 | + | 692.928i | 0.0280630 | + | 0.0275713i | ||||
\(859\) | 2828.67i | 0.112355i | 0.998421 | + | 0.0561774i | \(0.0178913\pi\) | ||||
−0.998421 | + | 0.0561774i | \(0.982109\pi\) | |||||||
\(860\) | −29183.5 | + | 515.912i | −1.15715 | + | 0.0204563i | ||||
\(861\) | 121.907 | 0.00482529 | ||||||||
\(862\) | −9189.56 | − | 9028.54i | −0.363106 | − | 0.356744i | ||||
\(863\) | 44058.3 | 1.73785 | 0.868924 | − | 0.494946i | \(-0.164812\pi\) | ||||
0.868924 | + | 0.494946i | \(0.164812\pi\) | |||||||
\(864\) | 489.465 | − | 534.756i | 0.0192731 | − | 0.0210564i | ||||
\(865\) | 34016.1 | 1.33709 | ||||||||
\(866\) | −8958.38 | + | 9118.15i | −0.351522 | + | 0.357791i | ||||
\(867\) | −305.101 | − | 199.246i | −0.0119513 | − | 0.00780477i | ||||
\(868\) | 401.694 | + | 22722.6i | 0.0157078 | + | 0.888542i | ||||
\(869\) | − | 1174.17i | − | 0.0458355i | ||||||
\(870\) | −237.697 | + | 241.936i | −0.00926286 | + | 0.00942806i | ||||
\(871\) | −24898.0 | −0.968583 | ||||||||
\(872\) | −285.615 | − | 270.857i | −0.0110919 | − | 0.0105188i | ||||
\(873\) | − | 37689.6i | − | 1.46117i | ||||||
\(874\) | −16455.3 | + | 16748.8i | −0.636854 | + | 0.648212i | ||||
\(875\) | − | 19997.6i | − | 0.772620i | ||||||
\(876\) | −649.112 | + | 11.4751i | −0.0250359 | + | 0.000442589i | ||||
\(877\) | 9130.12 | 0.351542 | 0.175771 | − | 0.984431i | \(-0.443758\pi\) | ||||
0.175771 | + | 0.984431i | \(0.443758\pi\) | |||||||
\(878\) | 5250.39 | + | 5158.39i | 0.201813 | + | 0.198277i | ||||
\(879\) | − | 8.11373i | − | 0.000311342i | ||||||
\(880\) | 69513.8 | − | 2458.52i | 2.66285 | − | 0.0941782i | ||||
\(881\) | − | 29609.9i | − | 1.13233i | −0.824292 | − | 0.566165i | \(-0.808427\pi\) | ||
0.824292 | − | 0.566165i | \(-0.191573\pi\) | |||||||
\(882\) | −8333.34 | + | 8481.96i | −0.318138 | + | 0.323812i | ||||
\(883\) | − | 456.368i | − | 0.0173930i | −0.999962 | − | 0.00869649i | \(-0.997232\pi\) | ||
0.999962 | − | 0.00869649i | \(-0.00276821\pi\) | |||||||
\(884\) | −40679.6 | − | 11327.7i | −1.54774 | − | 0.430985i | ||||
\(885\) | − | 420.347i | − | 0.0159659i | ||||||
\(886\) | −15198.9 | − | 14932.6i | −0.576316 | − | 0.566218i | ||||
\(887\) | 40199.2i | 1.52171i | 0.648921 | + | 0.760856i | \(0.275221\pi\) | ||||
−0.648921 | + | 0.760856i | \(0.724779\pi\) | |||||||
\(888\) | −269.626 | − | 255.695i | −0.0101893 | − | 0.00966278i | ||||
\(889\) | 4591.66i | 0.173227i | ||||||||
\(890\) | −27448.1 | + | 27937.6i | −1.03378 | + | 1.05221i | ||||
\(891\) | −45596.8 | −1.71442 | ||||||||
\(892\) | −833.000 | − | 47120.2i | −0.0312678 | − | 1.76872i | ||||
\(893\) | − | 16266.5i | − | 0.609559i | ||||||
\(894\) | 25.0562 | + | 24.6171i | 0.000937364 | + | 0.000920940i | ||||
\(895\) | 34679.6i | 1.29521i | ||||||||
\(896\) | −21410.7 | + | 24238.5i | −0.798305 | + | 0.903740i | ||||
\(897\) | −465.738 | −0.0173362 | ||||||||
\(898\) | 32575.3 | + | 32004.6i | 1.21053 | + | 1.18932i | ||||
\(899\) | 11842.6i | 0.439348i | ||||||||
\(900\) | 673.967 | + | 38124.3i | 0.0249618 | + | 1.41201i | ||||
\(901\) | −56.9353 | + | 191.312i | −0.00210521 | + | 0.00707384i | ||||
\(902\) | −9293.34 | − | 9130.50i | −0.343054 | − | 0.337043i | ||||
\(903\) | 348.008 | 0.0128250 | ||||||||
\(904\) | 29584.2 | − | 31196.2i | 1.08845 | − | 1.14775i | ||||
\(905\) | 9332.85 | 0.342801 | ||||||||
\(906\) | 216.896 | − | 220.764i | 0.00795353 | − | 0.00809537i | ||||
\(907\) | −20901.0 | −0.765168 | −0.382584 | − | 0.923921i | \(-0.624966\pi\) | ||||
−0.382584 | + | 0.923921i | \(0.624966\pi\) | |||||||
\(908\) | −418.997 | − | 23701.4i | −0.0153138 | − | 0.866253i | ||||
\(909\) | 21157.4i | 0.771999i | ||||||||
\(910\) | 57891.2 | − | 58923.6i | 2.10887 | − | 2.14648i | ||||
\(911\) | − | 44659.2i | − | 1.62418i | −0.583535 | − | 0.812088i | \(-0.698331\pi\) | ||
0.583535 | − | 0.812088i | \(-0.301669\pi\) | |||||||
\(912\) | −16.7034 | − | 472.284i | −0.000606476 | − | 0.0171479i | ||||
\(913\) | 59704.9i | 2.16423i | ||||||||
\(914\) | 8393.44 | − | 8543.13i | 0.303753 | − | 0.309170i | ||||
\(915\) | −290.095 | −0.0104812 | ||||||||
\(916\) | −37321.4 | + | 659.775i | −1.34622 | + | 0.0237987i | ||||
\(917\) | − | 30820.8i | − | 1.10992i | ||||||
\(918\) | −694.858 | + | 384.107i | −0.0249823 | + | 0.0138098i | ||||
\(919\) | 36085.5 | 1.29527 | 0.647633 | − | 0.761952i | \(-0.275759\pi\) | ||||
0.647633 | + | 0.761952i | \(0.275759\pi\) | |||||||
\(920\) | −22545.9 | + | 23774.4i | −0.807953 | + | 0.851975i | ||||
\(921\) | − | 173.365i | − | 0.00620259i | ||||||
\(922\) | 24409.8 | + | 23982.1i | 0.871903 | + | 0.856625i | ||||
\(923\) | 47941.5 | 1.70966 | ||||||||
\(924\) | −829.198 | + | 14.6587i | −0.0295223 | + | 0.000521900i | ||||
\(925\) | 39093.3 | 1.38960 | ||||||||
\(926\) | −3808.15 | + | 3876.07i | −0.135144 | + | 0.137555i | ||||
\(927\) | 29754.2 | 1.05422 | ||||||||
\(928\) | −11378.7 | + | 12431.6i | −0.402503 | + | 0.439747i | ||||
\(929\) | 4044.77i | 0.142847i | 0.997446 | + | 0.0714233i | \(0.0227541\pi\) | ||||
−0.997446 | + | 0.0714233i | \(0.977246\pi\) | |||||||
\(930\) | −330.563 | − | 324.771i | −0.0116555 | − | 0.0114512i | ||||
\(931\) | 15504.3i | 0.545792i | ||||||||
\(932\) | −742.111 | + | 13.1192i | −0.0260823 | + | 0.000461087i | ||||
\(933\) | 241.486i | 0.00847363i | ||||||||
\(934\) | 2433.21 | + | 2390.57i | 0.0852430 | + | 0.0837493i | ||||
\(935\) | −73014.3 | − | 21729.4i | −2.55382 | − | 0.760029i | ||||
\(936\) | −31651.8 | + | 33376.4i | −1.10531 | + | 1.16554i | ||||
\(937\) | 13027.9 | 0.454220 | 0.227110 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227110 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(938\) | 14636.1 | − | 14897.2i | 0.509475 | − | 0.518561i | ||||
\(939\) | 649.782i | 0.0225824i | ||||||||
\(940\) | −401.215 | − | 22695.5i | −0.0139215 | − | 0.787496i | ||||
\(941\) | −1461.82 | −0.0506420 | −0.0253210 | − | 0.999679i | \(-0.508061\pi\) | ||||
−0.0253210 | + | 0.999679i | \(0.508061\pi\) | |||||||
\(942\) | 51.0581 | + | 50.1634i | 0.00176599 | + | 0.00173505i | ||||
\(943\) | 6136.89 | 0.211924 | ||||||||
\(944\) | −738.246 | − | 20873.6i | −0.0254532 | − | 0.719681i | ||||
\(945\) | − | 1553.11i | − | 0.0534633i | ||||||
\(946\) | −26529.7 | − | 26064.9i | −0.911792 | − | 0.895815i | ||||
\(947\) | −25266.4 | −0.866997 | −0.433499 | − | 0.901154i | \(-0.642721\pi\) | ||||
−0.433499 | + | 0.901154i | \(0.642721\pi\) | |||||||
\(948\) | −11.1304 | + | 0.196765i | −0.000381327 | + | 6.74117e-6i | ||||
\(949\) | 82394.5 | 2.81838 | ||||||||
\(950\) | 35465.4 | + | 34843.9i | 1.21121 | + | 1.18999i | ||||
\(951\) | −599.792 | −0.0204517 | ||||||||
\(952\) | 30690.9 | − | 17680.8i | 1.04485 | − | 0.601932i | ||||
\(953\) | −47488.6 | −1.61417 | −0.807086 | − | 0.590433i | \(-0.798957\pi\) | ||||
−0.807086 | + | 0.590433i | \(0.798957\pi\) | |||||||
\(954\) | 155.098 | + | 152.381i | 0.00526362 | + | 0.00517139i | ||||
\(955\) | −31441.1 | −1.06535 | ||||||||
\(956\) | −457.818 | − | 25897.3i | −0.0154884 | − | 0.876129i | ||||
\(957\) | −432.164 | −0.0145976 | ||||||||
\(958\) | 9446.88 | + | 9281.35i | 0.318596 | + | 0.313013i | ||||
\(959\) | 26682.4i | 0.898458i | ||||||||
\(960\) | −34.9542 | − | 658.533i | −0.00117515 | − | 0.0221397i | ||||
\(961\) | 13610.2 | 0.456855 | ||||||||
\(962\) | 33640.6 | + | 33051.1i | 1.12746 | + | 1.10770i | ||||
\(963\) | 33050.1 | 1.10595 | ||||||||
\(964\) | 13446.2 | − | 237.704i | 0.449246 | − | 0.00794185i | ||||
\(965\) | − | 39430.6i | − | 1.31535i | ||||||
\(966\) | 273.782 | − | 278.665i | 0.00911882 | − | 0.00928145i | ||||
\(967\) | −37164.8 | −1.23592 | −0.617962 | − | 0.786208i | \(-0.712042\pi\) | ||||
−0.617962 | + | 0.786208i | \(0.712042\pi\) | |||||||
\(968\) | 42457.1 | + | 40263.3i | 1.40973 | + | 1.33689i | ||||
\(969\) | −147.632 | + | 496.066i | −0.00489433 | + | 0.0164458i | ||||
\(970\) | −48918.2 | − | 48061.1i | −1.61925 | − | 1.59087i | ||||
\(971\) | − | 38718.8i | − | 1.27965i | −0.768519 | − | 0.639827i | \(-0.779006\pi\) | ||
0.768519 | − | 0.639827i | \(-0.220994\pi\) | |||||||
\(972\) | 22.9308 | + | 1297.12i | 0.000756693 | + | 0.0428038i | ||||
\(973\) | − | 13827.0i | − | 0.455573i | ||||||
\(974\) | −29601.4 | − | 29082.8i | −0.973810 | − | 0.956747i | ||||
\(975\) | 986.194i | 0.0323933i | ||||||||
\(976\) | −14405.6 | + | 509.488i | −0.472450 | + | 0.0167093i | ||||
\(977\) | 20345.1 | 0.666219 | 0.333109 | − | 0.942888i | \(-0.391902\pi\) | ||||
0.333109 | + | 0.942888i | \(0.391902\pi\) | |||||||
\(978\) | 252.380 | − | 256.881i | 0.00825177 | − | 0.00839894i | ||||
\(979\) | −49904.1 | −1.62915 | ||||||||
\(980\) | 382.416 | + | 21632.1i | 0.0124651 | + | 0.705114i | ||||
\(981\) | 469.592 | 0.0152833 | ||||||||
\(982\) | 41374.4 | + | 40649.5i | 1.34451 | + | 1.32095i | ||||
\(983\) | − | 9685.74i | − | 0.314270i | −0.987577 | − | 0.157135i | \(-0.949774\pi\) | ||
0.987577 | − | 0.157135i | \(-0.0502258\pi\) | |||||||
\(984\) | −84.9938 | + | 89.6249i | −0.00275356 | + | 0.00290359i | ||||
\(985\) | −59290.3 | −1.91791 | ||||||||
\(986\) | 16153.5 | − | 8929.39i | 0.521736 | − | 0.288408i | ||||
\(987\) | 270.639i | 0.00872801i | ||||||||
\(988\) | 1060.12 | + | 59967.7i | 0.0341366 | + | 1.93100i | ||||
\(989\) | 17519.0 | 0.563267 | ||||||||
\(990\) | −58156.1 | + | 59193.3i | −1.86699 | + | 1.90029i | ||||
\(991\) | − | 41871.0i | − | 1.34216i | −0.741386 | − | 0.671078i | \(-0.765831\pi\) | ||
0.741386 | − | 0.671078i | \(-0.234169\pi\) | |||||||
\(992\) | −16985.5 | − | 15546.9i | −0.543639 | − | 0.497596i | ||||
\(993\) | 480.157i | 0.0153447i | ||||||||
\(994\) | −28182.2 | + | 28684.8i | −0.899279 | + | 0.915318i | ||||
\(995\) | − | 10909.1i | − | 0.347581i | ||||||
\(996\) | 565.964 | − | 10.0052i | 0.0180053 | − | 0.000318300i | ||||
\(997\) | −10315.0 | −0.327662 | −0.163831 | − | 0.986488i | \(-0.552385\pi\) | ||||
−0.163831 | + | 0.986488i | \(0.552385\pi\) | |||||||
\(998\) | −13704.8 | + | 13949.2i | −0.434688 | + | 0.442440i | ||||
\(999\) | 886.701 | 0.0280820 |
(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 | 136.4.h.a.101.15 | yes | 52 | |
4.3 | odd | 2 | 544.4.h.a.305.27 | 52 | |||
8.3 | odd | 2 | 544.4.h.a.305.25 | 52 | |||
8.5 | even | 2 | inner | 136.4.h.a.101.14 | yes | 52 | |
17.16 | even | 2 | inner | 136.4.h.a.101.16 | yes | 52 | |
68.67 | odd | 2 | 544.4.h.a.305.26 | 52 | |||
136.67 | odd | 2 | 544.4.h.a.305.28 | 52 | |||
136.101 | even | 2 | inner | 136.4.h.a.101.13 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.h.a.101.13 | ✓ | 52 | 136.101 | even | 2 | inner | |
136.4.h.a.101.14 | yes | 52 | 8.5 | even | 2 | inner | |
136.4.h.a.101.15 | yes | 52 | 1.1 | even | 1 | trivial | |
136.4.h.a.101.16 | yes | 52 | 17.16 | even | 2 | inner | |
544.4.h.a.305.25 | 52 | 8.3 | odd | 2 | |||
544.4.h.a.305.26 | 52 | 68.67 | odd | 2 | |||
544.4.h.a.305.27 | 52 | 4.3 | odd | 2 | |||
544.4.h.a.305.28 | 52 | 136.67 | odd | 2 |