Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.32 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.31 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.34967 | + | 3.15947i | 0.918709 | + | 0.394934i | ||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | 44.0354 | + | 46.4422i | 0.688054 | + | 0.725660i | ||||
\(5\) | 111.509 | + | 56.4858i | 0.892075 | + | 0.451887i | ||||
\(6\) | −114.570 | − | 49.2513i | −0.530417 | − | 0.228015i | ||||
\(7\) | −231.647 | −0.675355 | −0.337677 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337677 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(8\) | 176.913 | + | 480.464i | 0.345533 | + | 0.938406i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 641.092 | + | 767.464i | 0.641092 | + | 0.767464i | ||||
\(11\) | 1432.15i | 1.07599i | 0.842947 | + | 0.537996i | \(0.180819\pi\) | ||||
−0.842947 | + | 0.537996i | \(0.819181\pi\) | |||||||
\(12\) | −686.445 | − | 723.963i | −0.397248 | − | 0.418960i | ||||
\(13\) | − | 1704.35i | − | 0.775762i | −0.921710 | − | 0.387881i | \(-0.873207\pi\) | ||
0.921710 | − | 0.387881i | \(-0.126793\pi\) | |||||||
\(14\) | −1702.53 | − | 731.882i | −0.620455 | − | 0.266721i | ||||
\(15\) | −1738.26 | − | 880.527i | −0.515040 | − | 0.260897i | ||||
\(16\) | −217.760 | + | 4090.21i | −0.0531641 | + | 0.998586i | ||||
\(17\) | 7567.92i | 1.54039i | 0.637810 | + | 0.770194i | \(0.279840\pi\) | ||||
−0.637810 | + | 0.770194i | \(0.720160\pi\) | |||||||
\(18\) | 1785.97 | + | 767.752i | 0.306236 | + | 0.131645i | ||||
\(19\) | 5564.86i | 0.811322i | 0.914024 | + | 0.405661i | \(0.132959\pi\) | ||||
−0.914024 | + | 0.405661i | \(0.867041\pi\) | |||||||
\(20\) | 2287.04 | + | 7666.12i | 0.285880 | + | 0.958265i | ||||
\(21\) | 3611.02 | 0.389916 | ||||||||
\(22\) | −4524.83 | + | 10525.8i | −0.424946 | + | 0.988524i | ||||
\(23\) | −14468.9 | −1.18920 | −0.594598 | − | 0.804023i | \(-0.702689\pi\) | ||||
−0.594598 | + | 0.804023i | \(0.702689\pi\) | |||||||
\(24\) | −2757.80 | − | 7489.69i | −0.199494 | − | 0.541789i | ||||
\(25\) | 9243.70 | + | 12597.4i | 0.591597 | + | 0.806234i | ||||
\(26\) | 5384.85 | − | 12526.4i | 0.306375 | − | 0.712699i | ||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | −10200.7 | − | 10758.2i | −0.464680 | − | 0.490078i | ||||
\(29\) | 25708.4 | 1.05410 | 0.527049 | − | 0.849835i | \(-0.323298\pi\) | ||||
0.527049 | + | 0.849835i | \(0.323298\pi\) | |||||||
\(30\) | −9993.64 | − | 11963.6i | −0.370135 | − | 0.443095i | ||||
\(31\) | − | 40919.0i | − | 1.37354i | −0.726876 | − | 0.686769i | \(-0.759029\pi\) | ||
0.726876 | − | 0.686769i | \(-0.240971\pi\) | |||||||
\(32\) | −14523.4 | + | 29373.7i | −0.443218 | + | 0.896414i | ||||
\(33\) | − | 22324.9i | − | 0.621225i | ||||||
\(34\) | −23910.7 | + | 55621.8i | −0.608352 | + | 1.41517i | ||||
\(35\) | −25830.8 | − | 13084.8i | −0.602467 | − | 0.305184i | ||||
\(36\) | 10700.6 | + | 11285.5i | 0.229351 | + | 0.241887i | ||||
\(37\) | − | 66045.9i | − | 1.30389i | −0.758267 | − | 0.651944i | \(-0.773954\pi\) | ||
0.758267 | − | 0.651944i | \(-0.226046\pi\) | |||||||
\(38\) | −17582.0 | + | 40899.9i | −0.320419 | + | 0.745369i | ||||
\(39\) | 26568.2i | 0.447886i | ||||||||
\(40\) | −7411.94 | + | 63569.4i | −0.115812 | + | 0.993271i | ||||
\(41\) | 106267. | 1.54187 | 0.770934 | − | 0.636915i | \(-0.219790\pi\) | ||||
0.770934 | + | 0.636915i | \(0.219790\pi\) | |||||||
\(42\) | 26539.8 | + | 11408.9i | 0.358220 | + | 0.153991i | ||||
\(43\) | 58344.7 | 0.733830 | 0.366915 | − | 0.930254i | \(-0.380414\pi\) | ||||
0.366915 | + | 0.930254i | \(0.380414\pi\) | |||||||
\(44\) | −66512.0 | + | 63065.2i | −0.780804 | + | 0.740341i | ||||
\(45\) | 27096.8 | + | 13726.1i | 0.297358 | + | 0.150629i | ||||
\(46\) | −106342. | − | 45714.3i | −1.09253 | − | 0.469654i | ||||
\(47\) | 75013.4 | 0.722512 | 0.361256 | − | 0.932467i | \(-0.382348\pi\) | ||||
0.361256 | + | 0.932467i | \(0.382348\pi\) | |||||||
\(48\) | 3394.54 | − | 63760.0i | 0.0306943 | − | 0.576534i | ||||
\(49\) | −63988.8 | −0.543896 | ||||||||
\(50\) | 28137.0 | + | 121792.i | 0.225096 | + | 0.974337i | ||||
\(51\) | − | 117972.i | − | 0.889343i | ||||||
\(52\) | 79153.7 | − | 75051.7i | 0.562939 | − | 0.533766i | ||||
\(53\) | − | 81861.1i | − | 0.549857i | −0.961465 | − | 0.274929i | \(-0.911346\pi\) | ||
0.961465 | − | 0.274929i | \(-0.0886542\pi\) | |||||||
\(54\) | −27840.5 | − | 11968.1i | −0.176806 | − | 0.0760051i | ||||
\(55\) | −80896.0 | + | 159698.i | −0.486227 | + | 0.959866i | ||||
\(56\) | −40981.3 | − | 111298.i | −0.233358 | − | 0.633757i | ||||
\(57\) | − | 86747.5i | − | 0.468417i | ||||||
\(58\) | 188948. | + | 81225.0i | 0.968410 | + | 0.416300i | ||||
\(59\) | − | 199623.i | − | 0.971974i | −0.873966 | − | 0.485987i | \(-0.838460\pi\) | ||
0.873966 | − | 0.485987i | \(-0.161540\pi\) | |||||||
\(60\) | −35651.4 | − | 119503.i | −0.165053 | − | 0.553255i | ||||
\(61\) | 168043. | 0.740339 | 0.370170 | − | 0.928964i | \(-0.379300\pi\) | ||||
0.370170 | + | 0.928964i | \(0.379300\pi\) | |||||||
\(62\) | 129283. | − | 300742.i | 0.542457 | − | 1.26188i | ||||
\(63\) | −56290.2 | −0.225118 | ||||||||
\(64\) | −199547. | + | 170001.i | −0.761213 | + | 0.648502i | ||||
\(65\) | 96271.5 | − | 190051.i | 0.350556 | − | 0.692038i | ||||
\(66\) | 70535.1 | − | 164081.i | 0.245343 | − | 0.570725i | ||||
\(67\) | −36855.0 | −0.122538 | −0.0612691 | − | 0.998121i | \(-0.519515\pi\) | ||||
−0.0612691 | + | 0.998121i | \(0.519515\pi\) | |||||||
\(68\) | −351471. | + | 333257.i | −1.11780 | + | 1.05987i | ||||
\(69\) | 225548. | 0.686582 | ||||||||
\(70\) | −148507. | − | 177780.i | −0.432965 | − | 0.518310i | ||||
\(71\) | − | 449616.i | − | 1.25622i | −0.778123 | − | 0.628112i | \(-0.783828\pi\) | ||
0.778123 | − | 0.628112i | \(-0.216172\pi\) | |||||||
\(72\) | 42989.9 | + | 116753.i | 0.115178 | + | 0.312802i | ||||
\(73\) | 58511.3i | 0.150408i | 0.997168 | + | 0.0752041i | \(0.0239608\pi\) | ||||
−0.997168 | + | 0.0752041i | \(0.976039\pi\) | |||||||
\(74\) | 208670. | − | 485416.i | 0.514950 | − | 1.19789i | ||||
\(75\) | −144095. | − | 196374.i | −0.341559 | − | 0.465479i | ||||
\(76\) | −258444. | + | 245051.i | −0.588744 | + | 0.558233i | ||||
\(77\) | − | 331752.i | − | 0.726677i | ||||||
\(78\) | −83941.4 | + | 195267.i | −0.176886 | + | 0.411477i | ||||
\(79\) | 649187.i | 1.31670i | 0.752710 | + | 0.658352i | \(0.228746\pi\) | ||||
−0.752710 | + | 0.658352i | \(0.771254\pi\) | |||||||
\(80\) | −255321. | + | 443796.i | −0.498674 | + | 0.866790i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 781028. | + | 335748.i | 1.41653 | + | 0.608936i | ||||
\(83\) | 452757. | 0.791828 | 0.395914 | − | 0.918288i | \(-0.370428\pi\) | ||||
0.395914 | + | 0.918288i | \(0.370428\pi\) | |||||||
\(84\) | 159013. | + | 167704.i | 0.268283 | + | 0.282947i | ||||
\(85\) | −427480. | + | 843895.i | −0.696080 | + | 1.37414i | ||||
\(86\) | 428814. | + | 184338.i | 0.674177 | + | 0.289815i | ||||
\(87\) | −400754. | −0.608584 | ||||||||
\(88\) | −688095. | + | 253365.i | −1.00972 | + | 0.371791i | ||||
\(89\) | −286863. | −0.406915 | −0.203458 | − | 0.979084i | \(-0.565218\pi\) | ||||
−0.203458 | + | 0.979084i | \(0.565218\pi\) | |||||||
\(90\) | 155785. | + | 186494.i | 0.213697 | + | 0.255821i | ||||
\(91\) | 394807.i | 0.523914i | ||||||||
\(92\) | −637146. | − | 671970.i | −0.818230 | − | 0.862951i | ||||
\(93\) | 637865.i | 0.793012i | ||||||||
\(94\) | 551324. | + | 237003.i | 0.663779 | + | 0.285345i | ||||
\(95\) | −314336. | + | 620534.i | −0.366626 | + | 0.723760i | ||||
\(96\) | 226397. | − | 457890.i | 0.255892 | − | 0.517545i | ||||
\(97\) | 386394.i | 0.423365i | 0.977338 | + | 0.211683i | \(0.0678943\pi\) | ||||
−0.977338 | + | 0.211683i | \(0.932106\pi\) | |||||||
\(98\) | −470297. | − | 202171.i | −0.499682 | − | 0.214803i | ||||
\(99\) | 348011.i | 0.358664i | ||||||||
\(100\) | −178001. | + | 984030.i | −0.178001 | + | 0.984030i | ||||
\(101\) | −881482. | −0.855558 | −0.427779 | − | 0.903883i | \(-0.640704\pi\) | ||||
−0.427779 | + | 0.903883i | \(0.640704\pi\) | |||||||
\(102\) | 372730. | − | 867057.i | 0.351232 | − | 0.817048i | ||||
\(103\) | 17661.6 | 0.0161628 | 0.00808142 | − | 0.999967i | \(-0.497428\pi\) | ||||
0.00808142 | + | 0.999967i | \(0.497428\pi\) | |||||||
\(104\) | 818878. | − | 301522.i | 0.727980 | − | 0.268052i | ||||
\(105\) | 402662. | + | 203971.i | 0.347835 | + | 0.176198i | ||||
\(106\) | 258638. | − | 601652.i | 0.217157 | − | 0.505159i | ||||
\(107\) | 2.08551e6 | 1.70239 | 0.851197 | − | 0.524847i | \(-0.175877\pi\) | ||||
0.851197 | + | 0.524847i | \(0.175877\pi\) | |||||||
\(108\) | −166806. | − | 175923.i | −0.132416 | − | 0.139653i | ||||
\(109\) | −1.58327e6 | −1.22257 | −0.611287 | − | 0.791409i | \(-0.709348\pi\) | ||||
−0.611287 | + | 0.791409i | \(0.709348\pi\) | |||||||
\(110\) | −1.09912e6 | + | 918138.i | −0.825785 | + | 0.689811i | ||||
\(111\) | 1.02955e6i | 0.752800i | ||||||||
\(112\) | 50443.4 | − | 947483.i | 0.0359046 | − | 0.674400i | ||||
\(113\) | 232817.i | 0.161354i | 0.996740 | + | 0.0806768i | \(0.0257082\pi\) | ||||
−0.996740 | + | 0.0806768i | \(0.974292\pi\) | |||||||
\(114\) | 274077. | − | 637566.i | 0.184994 | − | 0.430339i | ||||
\(115\) | −1.61342e6 | − | 817290.i | −1.06085 | − | 0.537382i | ||||
\(116\) | 1.13208e6 | + | 1.19396e6i | 0.725276 | + | 0.764917i | ||||
\(117\) | − | 414157.i | − | 0.258587i | ||||||
\(118\) | 630704. | − | 1.46716e6i | 0.383866 | − | 0.892961i | ||||
\(119\) | − | 1.75308e6i | − | 1.04031i | ||||||
\(120\) | 115541. | − | 990948.i | 0.0668638 | − | 0.573465i | ||||
\(121\) | −279481. | −0.157760 | ||||||||
\(122\) | 1.23506e6 | + | 530927.i | 0.680156 | + | 0.292385i | ||||
\(123\) | −1.65654e6 | −0.890198 | ||||||||
\(124\) | 1.90037e6 | − | 1.80189e6i | 0.996721 | − | 0.945067i | ||||
\(125\) | 319185. | + | 1.92687e6i | 0.163422 | + | 0.986556i | ||||
\(126\) | −413714. | − | 177847.i | −0.206818 | − | 0.0889069i | ||||
\(127\) | 1.40476e6 | 0.685789 | 0.342894 | − | 0.939374i | \(-0.388593\pi\) | ||||
0.342894 | + | 0.939374i | \(0.388593\pi\) | |||||||
\(128\) | −2.00372e6 | + | 618985.i | −0.955449 | + | 0.295155i | ||||
\(129\) | −909503. | −0.423677 | ||||||||
\(130\) | 1.30803e6 | − | 1.09264e6i | 0.595369 | − | 0.497335i | ||||
\(131\) | 1.22135e6i | 0.543281i | 0.962399 | + | 0.271641i | \(0.0875662\pi\) | ||||
−0.962399 | + | 0.271641i | \(0.912434\pi\) | |||||||
\(132\) | 1.03682e6 | − | 983089.i | 0.450798 | − | 0.427436i | ||||
\(133\) | − | 1.28908e6i | − | 0.547930i | ||||||
\(134\) | −270872. | − | 116442.i | −0.112577 | − | 0.0483945i | ||||
\(135\) | −422397. | − | 213968.i | −0.171680 | − | 0.0869656i | ||||
\(136\) | −3.63611e6 | + | 1.33886e6i | −1.44551 | + | 0.532255i | ||||
\(137\) | − | 4.07260e6i | − | 1.58383i | −0.610628 | − | 0.791917i | \(-0.709083\pi\) | ||
0.610628 | − | 0.791917i | \(-0.290917\pi\) | |||||||
\(138\) | 1.65771e6 | + | 712615.i | 0.630770 | + | 0.271155i | ||||
\(139\) | 1.82029e6i | 0.677791i | 0.940824 | + | 0.338895i | \(0.110053\pi\) | ||||
−0.940824 | + | 0.338895i | \(0.889947\pi\) | |||||||
\(140\) | −529785. | − | 1.77583e6i | −0.193070 | − | 0.647169i | ||||
\(141\) | −1.16934e6 | −0.417143 | ||||||||
\(142\) | 1.42055e6 | − | 3.30453e6i | 0.496126 | − | 1.15410i | ||||
\(143\) | 2.44088e6 | 0.834714 | ||||||||
\(144\) | −52915.7 | + | 993920.i | −0.0177214 | + | 0.332862i | ||||
\(145\) | 2.86673e6 | + | 1.45216e6i | 0.940335 | + | 0.476333i | ||||
\(146\) | −184865. | + | 430039.i | −0.0594013 | + | 0.138181i | ||||
\(147\) | 997487. | 0.314018 | ||||||||
\(148\) | 3.06732e6 | − | 2.90836e6i | 0.946179 | − | 0.897145i | ||||
\(149\) | −5.35411e6 | −1.61856 | −0.809280 | − | 0.587423i | \(-0.800143\pi\) | ||||
−0.809280 | + | 0.587423i | \(0.800143\pi\) | |||||||
\(150\) | −438612. | − | 1.89855e6i | −0.129959 | − | 0.562533i | ||||
\(151\) | − | 712681.i | − | 0.206997i | −0.994630 | − | 0.103499i | \(-0.966996\pi\) | ||
0.994630 | − | 0.103499i | \(-0.0330037\pi\) | |||||||
\(152\) | −2.67371e6 | + | 984496.i | −0.761350 | + | 0.280339i | ||||
\(153\) | 1.83900e6i | 0.513462i | ||||||||
\(154\) | 1.04816e6 | − | 2.43827e6i | 0.286990 | − | 0.667605i | ||||
\(155\) | 2.31135e6 | − | 4.56286e6i | 0.620683 | − | 1.22530i | ||||
\(156\) | −1.23388e6 | + | 1.16994e6i | −0.325013 | + | 0.308170i | ||||
\(157\) | − | 2.12365e6i | − | 0.548763i | −0.961621 | − | 0.274381i | \(-0.911527\pi\) | ||
0.961621 | − | 0.274381i | \(-0.0884731\pi\) | |||||||
\(158\) | −2.05109e6 | + | 4.77131e6i | −0.520012 | + | 1.20967i | ||||
\(159\) | 1.27609e6i | 0.317460i | ||||||||
\(160\) | −3.27869e6 | + | 2.45508e6i | −0.800461 | + | 0.599384i | ||||
\(161\) | 3.35168e6 | 0.803129 | ||||||||
\(162\) | 433991. | + | 186564.i | 0.102079 | + | 0.0438816i | ||||
\(163\) | −4.83687e6 | −1.11687 | −0.558433 | − | 0.829550i | \(-0.688597\pi\) | ||||
−0.558433 | + | 0.829550i | \(0.688597\pi\) | |||||||
\(164\) | 4.67952e6 | + | 4.93528e6i | 1.06089 | + | 1.11887i | ||||
\(165\) | 1.26104e6 | − | 2.48944e6i | 0.280723 | − | 0.554179i | ||||
\(166\) | 3.32762e6 | + | 1.43047e6i | 0.727460 | + | 0.312720i | ||||
\(167\) | 6.50373e6 | 1.39641 | 0.698205 | − | 0.715898i | \(-0.253982\pi\) | ||||
0.698205 | + | 0.715898i | \(0.253982\pi\) | |||||||
\(168\) | 638836. | + | 1.73496e6i | 0.134729 | + | 0.365900i | ||||
\(169\) | 1.92201e6 | 0.398194 | ||||||||
\(170\) | −5.80811e6 | + | 4.85174e6i | −1.18219 | + | 0.987530i | ||||
\(171\) | 1.35226e6i | 0.270441i | ||||||||
\(172\) | 2.56923e6 | + | 2.70966e6i | 0.504915 | + | 0.532511i | ||||
\(173\) | 5.13552e6i | 0.991851i | 0.868365 | + | 0.495926i | \(0.165171\pi\) | ||||
−0.868365 | + | 0.495926i | \(0.834829\pi\) | |||||||
\(174\) | −2.94541e6 | − | 1.26617e6i | −0.559112 | − | 0.240351i | ||||
\(175\) | −2.14127e6 | − | 2.91815e6i | −0.399538 | − | 0.544494i | ||||
\(176\) | −5.85777e6 | − | 311864.i | −1.07447 | − | 0.0572042i | ||||
\(177\) | 3.11181e6i | 0.561169i | ||||||||
\(178\) | −2.10835e6 | − | 906335.i | −0.373837 | − | 0.160705i | ||||
\(179\) | 7.09855e6i | 1.23769i | 0.785515 | + | 0.618843i | \(0.212398\pi\) | ||||
−0.785515 | + | 0.618843i | \(0.787602\pi\) | |||||||
\(180\) | 555750. | + | 1.86287e6i | 0.0952933 | + | 0.319422i | ||||
\(181\) | 9.46363e6 | 1.59596 | 0.797980 | − | 0.602683i | \(-0.205902\pi\) | ||||
0.797980 | + | 0.602683i | \(0.205902\pi\) | |||||||
\(182\) | −1.24738e6 | + | 2.90170e6i | −0.206912 | + | 0.481325i | ||||
\(183\) | −2.61953e6 | −0.427435 | ||||||||
\(184\) | −2.55975e6 | − | 6.95181e6i | −0.410907 | − | 1.11595i | ||||
\(185\) | 3.73066e6 | − | 7.36473e6i | 0.589210 | − | 1.16317i | ||||
\(186\) | −2.01532e6 | + | 4.68810e6i | −0.313188 | + | 0.728548i | ||||
\(187\) | −1.08384e7 | −1.65744 | ||||||||
\(188\) | 3.30325e6 | + | 3.48379e6i | 0.497127 | + | 0.524298i | ||||
\(189\) | 877477. | 0.129972 | ||||||||
\(190\) | −4.27083e6 | + | 3.56759e6i | −0.622660 | + | 0.520132i | ||||
\(191\) | − | 1.18644e7i | − | 1.70273i | −0.524570 | − | 0.851367i | \(-0.675774\pi\) | ||
0.524570 | − | 0.851367i | \(-0.324226\pi\) | |||||||
\(192\) | 3.11064e6 | − | 2.65005e6i | 0.439487 | − | 0.374413i | ||||
\(193\) | − | 5.29387e6i | − | 0.736379i | −0.929751 | − | 0.368189i | \(-0.879978\pi\) | ||
0.929751 | − | 0.368189i | \(-0.120022\pi\) | |||||||
\(194\) | −1.22080e6 | + | 2.83987e6i | −0.167201 | + | 0.388949i | ||||
\(195\) | −1.50072e6 | + | 2.96260e6i | −0.202394 | + | 0.399548i | ||||
\(196\) | −2.81777e6 | − | 2.97178e6i | −0.374230 | − | 0.394683i | ||||
\(197\) | − | 5.56867e6i | − | 0.728371i | −0.931326 | − | 0.364186i | \(-0.881347\pi\) | ||
0.931326 | − | 0.364186i | \(-0.118653\pi\) | |||||||
\(198\) | −1.09953e6 | + | 2.55777e6i | −0.141649 | + | 0.329508i | ||||
\(199\) | − | 6.63937e6i | − | 0.842496i | −0.906946 | − | 0.421248i | \(-0.861592\pi\) | ||
0.906946 | − | 0.421248i | \(-0.138408\pi\) | |||||||
\(200\) | −4.41727e6 | + | 6.66991e6i | −0.552159 | + | 0.833739i | ||||
\(201\) | 574512. | 0.0707475 | ||||||||
\(202\) | −6.47861e6 | − | 2.78502e6i | −0.786009 | − | 0.337889i | ||||
\(203\) | −5.95527e6 | −0.711890 | ||||||||
\(204\) | 5.47889e6 | − | 5.19496e6i | 0.645360 | − | 0.611916i | ||||
\(205\) | 1.18498e7 | + | 6.00258e6i | 1.37546 | + | 0.696749i | ||||
\(206\) | 129807. | + | 55801.3i | 0.0148490 | + | 0.00638326i | ||||
\(207\) | −3.51595e6 | −0.396399 | ||||||||
\(208\) | 6.97114e6 | + | 371139.i | 0.774665 | + | 0.0412427i | ||||
\(209\) | −7.96969e6 | −0.872976 | ||||||||
\(210\) | 2.31499e6 | + | 2.77132e6i | 0.249972 | + | 0.299247i | ||||
\(211\) | 2.67302e6i | 0.284548i | 0.989827 | + | 0.142274i | \(0.0454414\pi\) | ||||
−0.989827 | + | 0.142274i | \(0.954559\pi\) | |||||||
\(212\) | 3.80181e6 | − | 3.60479e6i | 0.399009 | − | 0.378331i | ||||
\(213\) | 7.00883e6i | 0.725281i | ||||||||
\(214\) | 1.53278e7 | + | 6.58910e6i | 1.56400 | + | 0.672334i | ||||
\(215\) | 6.50598e6 | + | 3.29565e6i | 0.654632 | + | 0.331608i | ||||
\(216\) | −670146. | − | 1.82000e6i | −0.0664979 | − | 0.180596i | ||||
\(217\) | 9.47876e6i | 0.927625i | ||||||||
\(218\) | −1.16365e7 | − | 5.00229e6i | −1.12319 | − | 0.482836i | ||||
\(219\) | − | 912101.i | − | 0.0868382i | ||||||
\(220\) | −1.09790e7 | + | 3.27537e6i | −1.03109 | + | 0.307604i | ||||
\(221\) | 1.28984e7 | 1.19497 | ||||||||
\(222\) | −3.25285e6 | + | 7.56688e6i | −0.297307 | + | 0.691605i | ||||
\(223\) | 8.78893e6 | 0.792540 | 0.396270 | − | 0.918134i | \(-0.370304\pi\) | ||||
0.396270 | + | 0.918134i | \(0.370304\pi\) | |||||||
\(224\) | 3.36429e6 | − | 6.80432e6i | 0.299330 | − | 0.605397i | ||||
\(225\) | 2.24622e6 | + | 3.06117e6i | 0.197199 | + | 0.268745i | ||||
\(226\) | −735579. | + | 1.71113e6i | −0.0637241 | + | 0.148237i | ||||
\(227\) | −1.92283e6 | −0.164385 | −0.0821926 | − | 0.996616i | \(-0.526192\pi\) | ||||
−0.0821926 | + | 0.996616i | \(0.526192\pi\) | |||||||
\(228\) | 4.02875e6 | − | 3.81997e6i | 0.339911 | − | 0.322296i | ||||
\(229\) | −1.88248e7 | −1.56756 | −0.783780 | − | 0.621039i | \(-0.786711\pi\) | ||||
−0.783780 | + | 0.621039i | \(0.786711\pi\) | |||||||
\(230\) | −9.27593e6 | − | 1.11044e7i | −0.762384 | − | 0.912664i | ||||
\(231\) | 5.17150e6i | 0.419547i | ||||||||
\(232\) | 4.54815e6 | + | 1.23520e7i | 0.364226 | + | 0.989172i | ||||
\(233\) | − | 9.64495e6i | − | 0.762487i | −0.924475 | − | 0.381243i | \(-0.875496\pi\) | ||
0.924475 | − | 0.381243i | \(-0.124504\pi\) | |||||||
\(234\) | 1.30852e6 | − | 3.04392e6i | 0.102125 | − | 0.237566i | ||||
\(235\) | 8.36470e6 | + | 4.23719e6i | 0.644535 | + | 0.326494i | ||||
\(236\) | 9.27093e6 | − | 8.79048e6i | 0.705322 | − | 0.668770i | ||||
\(237\) | − | 1.01198e7i | − | 0.760200i | ||||||
\(238\) | 5.53883e6 | − | 1.28846e7i | 0.410853 | − | 0.955741i | ||||
\(239\) | 1.55315e7i | 1.13768i | 0.822448 | + | 0.568841i | \(0.192608\pi\) | ||||
−0.822448 | + | 0.568841i | \(0.807392\pi\) | |||||||
\(240\) | 3.98006e6 | − | 6.91810e6i | 0.287910 | − | 0.500441i | ||||
\(241\) | −1.93206e7 | −1.38028 | −0.690142 | − | 0.723674i | \(-0.742452\pi\) | ||||
−0.690142 | + | 0.723674i | \(0.742452\pi\) | |||||||
\(242\) | −2.05409e6 | − | 883013.i | −0.144935 | − | 0.0623047i | ||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | 7.39984e6 | + | 7.80429e6i | 0.509393 | + | 0.537234i | ||||
\(245\) | −7.13535e6 | − | 3.61446e6i | −0.485196 | − | 0.245779i | ||||
\(246\) | −1.21750e7 | − | 5.23379e6i | −0.817833 | − | 0.351570i | ||||
\(247\) | 9.48445e6 | 0.629392 | ||||||||
\(248\) | 1.96601e7 | − | 7.23912e6i | 1.28894 | − | 0.474603i | ||||
\(249\) | −7.05778e6 | −0.457162 | ||||||||
\(250\) | −3.74199e6 | + | 1.51703e7i | −0.239487 | + | 0.970900i | ||||
\(251\) | − | 2.66294e7i | − | 1.68400i | −0.539481 | − | 0.841998i | \(-0.681380\pi\) | ||
0.539481 | − | 0.841998i | \(-0.318620\pi\) | |||||||
\(252\) | −2.47876e6 | − | 2.61424e6i | −0.154893 | − | 0.163359i | ||||
\(253\) | − | 2.07216e7i | − | 1.27957i | ||||||
\(254\) | 1.03245e7 | + | 4.43830e6i | 0.630041 | + | 0.270842i | ||||
\(255\) | 6.66376e6 | − | 1.31550e7i | 0.401882 | − | 0.793361i | ||||
\(256\) | −1.66824e7 | − | 1.78137e6i | −0.994347 | − | 0.106178i | ||||
\(257\) | 2.66861e7i | 1.57212i | 0.618152 | + | 0.786059i | \(0.287882\pi\) | ||||
−0.618152 | + | 0.786059i | \(0.712118\pi\) | |||||||
\(258\) | −6.68455e6 | − | 2.87355e6i | −0.389236 | − | 0.167325i | ||||
\(259\) | 1.52993e7i | 0.880587i | ||||||||
\(260\) | 1.30657e7 | − | 3.89791e6i | 0.743386 | − | 0.221775i | ||||
\(261\) | 6.24714e6 | 0.351366 | ||||||||
\(262\) | −3.85881e6 | + | 8.97650e6i | −0.214560 | + | 0.499118i | ||||
\(263\) | 1.09464e7 | 0.601735 | 0.300868 | − | 0.953666i | \(-0.402724\pi\) | ||||
0.300868 | + | 0.953666i | \(0.402724\pi\) | |||||||
\(264\) | 1.07263e7 | − | 3.94958e6i | 0.582961 | − | 0.214654i | ||||
\(265\) | 4.62399e6 | − | 9.12828e6i | 0.248473 | − | 0.490514i | ||||
\(266\) | 4.07282e6 | − | 9.47432e6i | 0.216396 | − | 0.503389i | ||||
\(267\) | 4.47175e6 | 0.234933 | ||||||||
\(268\) | −1.62292e6 | − | 1.71163e6i | −0.0843129 | − | 0.0889210i | ||||
\(269\) | −3.06782e7 | −1.57606 | −0.788030 | − | 0.615636i | \(-0.788899\pi\) | ||||
−0.788030 | + | 0.615636i | \(0.788899\pi\) | |||||||
\(270\) | −2.42845e6 | − | 2.90715e6i | −0.123378 | − | 0.147698i | ||||
\(271\) | 5.50607e6i | 0.276652i | 0.990387 | + | 0.138326i | \(0.0441722\pi\) | ||||
−0.990387 | + | 0.138326i | \(0.955828\pi\) | |||||||
\(272\) | −3.09544e7 | − | 1.64799e6i | −1.53821 | − | 0.0818933i | ||||
\(273\) | − | 6.15443e6i | − | 0.302482i | ||||||
\(274\) | 1.28673e7 | − | 2.99323e7i | 0.625511 | − | 1.45508i | ||||
\(275\) | −1.80413e7 | + | 1.32383e7i | −0.867502 | + | 0.636554i | ||||
\(276\) | 9.93213e6 | + | 1.04750e7i | 0.472406 | + | 0.498225i | ||||
\(277\) | 2.32026e7i | 1.09168i | 0.837888 | + | 0.545842i | \(0.183790\pi\) | ||||
−0.837888 | + | 0.545842i | \(0.816210\pi\) | |||||||
\(278\) | −5.75115e6 | + | 1.33785e7i | −0.267683 | + | 0.622693i | ||||
\(279\) | − | 9.94333e6i | − | 0.457846i | ||||||
\(280\) | 1.71695e6 | − | 1.47256e7i | 0.0782139 | − | 0.670811i | ||||
\(281\) | 2.25844e7 | 1.01786 | 0.508932 | − | 0.860807i | \(-0.330040\pi\) | ||||
0.508932 | + | 0.860807i | \(0.330040\pi\) | |||||||
\(282\) | −8.59429e6 | − | 3.69451e6i | −0.383233 | − | 0.164744i | ||||
\(283\) | 1.85815e7 | 0.819828 | 0.409914 | − | 0.912124i | \(-0.365559\pi\) | ||||
0.409914 | + | 0.912124i | \(0.365559\pi\) | |||||||
\(284\) | 2.08812e7 | − | 1.97991e7i | 0.911591 | − | 0.864350i | ||||
\(285\) | 4.90001e6 | − | 9.67317e6i | 0.211671 | − | 0.417863i | ||||
\(286\) | 1.79396e7 | + | 7.71188e6i | 0.766859 | + | 0.329657i | ||||
\(287\) | −2.46164e7 | −1.04131 | ||||||||
\(288\) | −3.52918e6 | + | 7.13781e6i | −0.147739 | + | 0.298805i | ||||
\(289\) | −3.31359e7 | −1.37279 | ||||||||
\(290\) | 1.64815e7 | + | 1.97303e7i | 0.675774 | + | 0.808982i | ||||
\(291\) | − | 6.02328e6i | − | 0.244430i | ||||||
\(292\) | −2.71740e6 | + | 2.57657e6i | −0.109145 | + | 0.103489i | ||||
\(293\) | 2.41469e7i | 0.959972i | 0.877276 | + | 0.479986i | \(0.159358\pi\) | ||||
−0.877276 | + | 0.479986i | \(0.840642\pi\) | |||||||
\(294\) | 7.33120e6 | + | 3.15153e6i | 0.288492 | + | 0.124017i | ||||
\(295\) | 1.12759e7 | − | 2.22598e7i | 0.439222 | − | 0.867074i | ||||
\(296\) | 3.17327e7 | − | 1.16844e7i | 1.22358 | − | 0.450537i | ||||
\(297\) | − | 5.42496e6i | − | 0.207075i | ||||||
\(298\) | −3.93510e7 | − | 1.69162e7i | −1.48699 | − | 0.639225i | ||||
\(299\) | 2.46601e7i | 0.922532i | ||||||||
\(300\) | 2.77476e6 | − | 1.53395e7i | 0.102769 | − | 0.568130i | ||||
\(301\) | −1.35154e7 | −0.495596 | ||||||||
\(302\) | 2.25170e6 | − | 5.23797e6i | 0.0817502 | − | 0.190170i | ||||
\(303\) | 1.37409e7 | 0.493957 | ||||||||
\(304\) | −2.27614e7 | − | 1.21180e6i | −0.810174 | − | 0.0431332i | ||||
\(305\) | 1.87384e7 | + | 9.49204e6i | 0.660438 | + | 0.334549i | ||||
\(306\) | −5.81029e6 | + | 1.35161e7i | −0.202784 | + | 0.471723i | ||||
\(307\) | −4.12727e7 | −1.42642 | −0.713210 | − | 0.700950i | \(-0.752759\pi\) | ||||
−0.713210 | + | 0.700950i | \(0.752759\pi\) | |||||||
\(308\) | 1.54073e7 | − | 1.46088e7i | 0.527320 | − | 0.499993i | ||||
\(309\) | −275317. | −0.00933163 | ||||||||
\(310\) | 3.14039e7 | − | 2.62329e7i | 1.05414 | − | 0.880564i | ||||
\(311\) | 1.74437e7i | 0.579907i | 0.957041 | + | 0.289954i | \(0.0936399\pi\) | ||||
−0.957041 | + | 0.289954i | \(0.906360\pi\) | |||||||
\(312\) | −1.27650e7 | + | 4.70026e6i | −0.420299 | + | 0.154760i | ||||
\(313\) | 5.31470e7i | 1.73319i | 0.499013 | + | 0.866594i | \(0.333696\pi\) | ||||
−0.499013 | + | 0.866594i | \(0.666304\pi\) | |||||||
\(314\) | 6.70963e6 | − | 1.56082e7i | 0.216725 | − | 0.504154i | ||||
\(315\) | −6.27688e6 | − | 3.17960e6i | −0.200822 | − | 0.101728i | ||||
\(316\) | −3.01497e7 | + | 2.85872e7i | −0.955479 | + | 0.905963i | ||||
\(317\) | 1.84064e7i | 0.577819i | 0.957356 | + | 0.288909i | \(0.0932927\pi\) | ||||
−0.957356 | + | 0.288909i | \(0.906707\pi\) | |||||||
\(318\) | −4.03177e6 | + | 9.37883e6i | −0.125376 | + | 0.291654i | ||||
\(319\) | 3.68182e7i | 1.13420i | ||||||||
\(320\) | −3.18541e7 | + | 7.68508e6i | −0.972109 | + | 0.234530i | ||||
\(321\) | −3.25098e7 | −0.982877 | ||||||||
\(322\) | 2.46338e7 | + | 1.05896e7i | 0.737842 | + | 0.317183i | ||||
\(323\) | −4.21144e7 | −1.24975 | ||||||||
\(324\) | 2.60025e6 | + | 2.74237e6i | 0.0764504 | + | 0.0806289i | ||||
\(325\) | 2.14704e7 | − | 1.57545e7i | 0.625445 | − | 0.458938i | ||||
\(326\) | −3.55494e7 | − | 1.52820e7i | −1.02608 | − | 0.441089i | ||||
\(327\) | 2.46807e7 | 0.705853 | ||||||||
\(328\) | 1.88000e7 | + | 5.10575e7i | 0.532767 | + | 1.44690i | ||||
\(329\) | −1.73766e7 | −0.487952 | ||||||||
\(330\) | 1.71336e7 | − | 1.43124e7i | 0.476767 | − | 0.398262i | ||||
\(331\) | 3.85547e7i | 1.06315i | 0.847012 | + | 0.531574i | \(0.178399\pi\) | ||||
−0.847012 | + | 0.531574i | \(0.821601\pi\) | |||||||
\(332\) | 1.99374e7 | + | 2.10270e7i | 0.544820 | + | 0.574598i | ||||
\(333\) | − | 1.60491e7i | − | 0.434629i | ||||||
\(334\) | 4.78003e7 | + | 2.05484e7i | 1.28290 | + | 0.551490i | ||||
\(335\) | −4.10968e6 | − | 2.08178e6i | −0.109313 | − | 0.0553734i | ||||
\(336\) | −786335. | + | 1.47698e7i | −0.0207296 | + | 0.389365i | ||||
\(337\) | − | 2.31156e7i | − | 0.603970i | −0.953313 | − | 0.301985i | \(-0.902351\pi\) | ||
0.953313 | − | 0.301985i | \(-0.0976492\pi\) | |||||||
\(338\) | 1.41261e7 | + | 6.07253e6i | 0.365824 | + | 0.157260i | ||||
\(339\) | − | 3.62925e6i | − | 0.0931576i | ||||||
\(340\) | −5.80166e7 | + | 1.73081e7i | −1.47610 | + | 0.440366i | ||||
\(341\) | 5.86020e7 | 1.47792 | ||||||||
\(342\) | −4.27243e6 | + | 9.93867e6i | −0.106806 | + | 0.248456i | ||||
\(343\) | 4.20758e7 | 1.04268 | ||||||||
\(344\) | 1.03219e7 | + | 2.80325e7i | 0.253563 | + | 0.688631i | ||||
\(345\) | 2.51508e7 | + | 1.27403e7i | 0.612483 | + | 0.310257i | ||||
\(346\) | −1.62256e7 | + | 3.77444e7i | −0.391716 | + | 0.911223i | ||||
\(347\) | −4.88908e7 | −1.17014 | −0.585072 | − | 0.810982i | \(-0.698934\pi\) | ||||
−0.585072 | + | 0.810982i | \(0.698934\pi\) | |||||||
\(348\) | −1.76474e7 | − | 1.86119e7i | −0.418738 | − | 0.441625i | ||||
\(349\) | 2.05125e7 | 0.482551 | 0.241275 | − | 0.970457i | \(-0.422434\pi\) | ||||
0.241275 | + | 0.970457i | \(0.422434\pi\) | |||||||
\(350\) | −6.51785e6 | − | 2.82127e7i | −0.152020 | − | 0.658023i | ||||
\(351\) | 6.45606e6i | 0.149295i | ||||||||
\(352\) | −4.20674e7 | − | 2.07996e7i | −0.964534 | − | 0.476899i | ||||
\(353\) | − | 5.06784e7i | − | 1.15212i | −0.817407 | − | 0.576061i | \(-0.804589\pi\) | ||
0.817407 | − | 0.576061i | \(-0.195411\pi\) | |||||||
\(354\) | −9.83170e6 | + | 2.28708e7i | −0.221625 | + | 0.515551i | ||||
\(355\) | 2.53970e7 | − | 5.01365e7i | 0.567671 | − | 1.12065i | ||||
\(356\) | −1.26321e7 | − | 1.33225e7i | −0.279980 | − | 0.295282i | ||||
\(357\) | 2.73279e7i | 0.600622i | ||||||||
\(358\) | −2.24277e7 | + | 5.21720e7i | −0.488805 | + | 1.13707i | ||||
\(359\) | − | 6.09356e7i | − | 1.31701i | −0.752578 | − | 0.658503i | \(-0.771190\pi\) | ||
0.752578 | − | 0.658503i | \(-0.228810\pi\) | |||||||
\(360\) | −1.80110e6 | + | 1.54474e7i | −0.0386038 | + | 0.331090i | ||||
\(361\) | 1.60783e7 | 0.341757 | ||||||||
\(362\) | 6.95546e7 | + | 2.99001e7i | 1.46622 | + | 0.630300i | ||||
\(363\) | 4.35668e6 | 0.0910826 | ||||||||
\(364\) | −1.83357e7 | + | 1.73855e7i | −0.380184 | + | 0.360481i | ||||
\(365\) | −3.30506e6 | + | 6.52456e6i | −0.0679674 | + | 0.134175i | ||||
\(366\) | −1.92527e7 | − | 8.27634e6i | −0.392689 | − | 0.168809i | ||||
\(367\) | 1.49766e7 | 0.302981 | 0.151491 | − | 0.988459i | \(-0.451593\pi\) | ||||
0.151491 | + | 0.988459i | \(0.451593\pi\) | |||||||
\(368\) | 3.15076e6 | − | 5.91810e7i | 0.0632225 | − | 1.18751i | ||||
\(369\) | 2.58229e7 | 0.513956 | ||||||||
\(370\) | 5.06878e7 | − | 4.23415e7i | 1.00069 | − | 0.835913i | ||||
\(371\) | 1.89628e7i | 0.371349i | ||||||||
\(372\) | −2.96239e7 | + | 2.80887e7i | −0.575457 | + | 0.545635i | ||||
\(373\) | − | 8.87162e7i | − | 1.70953i | −0.519016 | − | 0.854764i | \(-0.673702\pi\) | ||
0.519016 | − | 0.854764i | \(-0.326298\pi\) | |||||||
\(374\) | −7.96585e7 | − | 3.42435e7i | −1.52271 | − | 0.654582i | ||||
\(375\) | −4.97559e6 | − | 3.00369e7i | −0.0943520 | − | 0.569588i | ||||
\(376\) | 1.32709e7 | + | 3.60412e7i | 0.249652 | + | 0.678010i | ||||
\(377\) | − | 4.38161e7i | − | 0.817729i | ||||||
\(378\) | 6.44917e6 | + | 2.77237e6i | 0.119407 | + | 0.0513305i | ||||
\(379\) | − | 9.17094e7i | − | 1.68460i | −0.539011 | − | 0.842299i | \(-0.681202\pi\) | ||
0.539011 | − | 0.842299i | \(-0.318798\pi\) | |||||||
\(380\) | −4.26609e7 | + | 1.27270e7i | −0.777462 | + | 0.231941i | ||||
\(381\) | −2.18980e7 | −0.395940 | ||||||||
\(382\) | 3.74854e7 | − | 8.71997e7i | 0.672468 | − | 1.56432i | ||||
\(383\) | 2.76561e7 | 0.492260 | 0.246130 | − | 0.969237i | \(-0.420841\pi\) | ||||
0.246130 | + | 0.969237i | \(0.420841\pi\) | |||||||
\(384\) | 3.12349e7 | − | 9.64903e6i | 0.551629 | − | 0.170408i | ||||
\(385\) | 1.87393e7 | − | 3.69935e7i | 0.328376 | − | 0.648250i | ||||
\(386\) | 1.67258e7 | − | 3.89082e7i | 0.290821 | − | 0.676518i | ||||
\(387\) | 1.41778e7 | 0.244610 | ||||||||
\(388\) | −1.79450e7 | + | 1.70150e7i | −0.307219 | + | 0.291298i | ||||
\(389\) | 2.95064e6 | 0.0501265 | 0.0250632 | − | 0.999686i | \(-0.492021\pi\) | ||||
0.0250632 | + | 0.999686i | \(0.492021\pi\) | |||||||
\(390\) | −2.03901e7 | + | 1.70326e7i | −0.343736 | + | 0.287136i | ||||
\(391\) | − | 1.09500e8i | − | 1.83182i | ||||||
\(392\) | −1.13205e7 | − | 3.07443e7i | −0.187934 | − | 0.510395i | ||||
\(393\) | − | 1.90389e7i | − | 0.313664i | ||||||
\(394\) | 1.75941e7 | − | 4.09279e7i | 0.287659 | − | 0.669161i | ||||
\(395\) | −3.66699e7 | + | 7.23904e7i | −0.595001 | + | 1.17460i | ||||
\(396\) | −1.61624e7 | + | 1.53248e7i | −0.260268 | + | 0.246780i | ||||
\(397\) | 1.13663e7i | 0.181655i | 0.995867 | + | 0.0908273i | \(0.0289511\pi\) | ||||
−0.995867 | + | 0.0908273i | \(0.971049\pi\) | |||||||
\(398\) | 2.09769e7 | − | 4.87972e7i | 0.332731 | − | 0.774009i | ||||
\(399\) | 2.00948e7i | 0.316348i | ||||||||
\(400\) | −5.35389e7 | + | 3.50654e7i | −0.836546 | + | 0.547897i | ||||
\(401\) | −1.00443e7 | −0.155771 | −0.0778854 | − | 0.996962i | \(-0.524817\pi\) | ||||
−0.0778854 | + | 0.996962i | \(0.524817\pi\) | |||||||
\(402\) | 4.22248e6 | + | 1.81516e6i | 0.0649964 | + | 0.0279406i | ||||
\(403\) | −6.97403e7 | −1.06554 | ||||||||
\(404\) | −3.88165e7 | − | 4.09380e7i | −0.588670 | − | 0.620844i | ||||
\(405\) | 6.58452e6 | + | 3.33543e6i | 0.0991195 | + | 0.0502096i | ||||
\(406\) | −4.37693e7 | − | 1.88155e7i | −0.654020 | − | 0.281150i | ||||
\(407\) | 9.45873e7 | 1.40297 | ||||||||
\(408\) | 5.66814e7 | − | 2.08708e7i | 0.834565 | − | 0.307298i | ||||
\(409\) | 6.13215e7 | 0.896279 | 0.448139 | − | 0.893964i | \(-0.352087\pi\) | ||||
0.448139 | + | 0.893964i | \(0.352087\pi\) | |||||||
\(410\) | 6.81270e7 | + | 8.15561e7i | 0.988479 | + | 1.18333i | ||||
\(411\) | 6.34855e7i | 0.914427i | ||||||||
\(412\) | 777735. | + | 820243.i | 0.0111209 | + | 0.0117287i | ||||
\(413\) | 4.62420e7i | 0.656427i | ||||||||
\(414\) | −2.58411e7 | − | 1.11086e7i | −0.364175 | − | 0.156551i | ||||
\(415\) | 5.04867e7 | + | 2.55744e7i | 0.706370 | + | 0.357817i | ||||
\(416\) | 5.00630e7 | + | 2.47529e7i | 0.695403 | + | 0.343832i | ||||
\(417\) | − | 2.83755e7i | − | 0.391323i | ||||||
\(418\) | −5.85746e7 | − | 2.51800e7i | −0.802011 | − | 0.344768i | ||||
\(419\) | 1.15447e8i | 1.56942i | 0.619862 | + | 0.784711i | \(0.287189\pi\) | ||||
−0.619862 | + | 0.784711i | \(0.712811\pi\) | |||||||
\(420\) | 8.25853e6 | + | 2.76825e7i | 0.111469 | + | 0.373643i | ||||
\(421\) | 5.29282e7 | 0.709317 | 0.354659 | − | 0.934996i | \(-0.384597\pi\) | ||||
0.354659 | + | 0.934996i | \(0.384597\pi\) | |||||||
\(422\) | −8.44535e6 | + | 1.96459e7i | −0.112378 | + | 0.261417i | ||||
\(423\) | 1.82283e7 | 0.240837 | ||||||||
\(424\) | 3.93313e7 | − | 1.44823e7i | 0.515989 | − | 0.189994i | ||||
\(425\) | −9.53362e7 | + | 6.99556e7i | −1.24191 | + | 0.911288i | ||||
\(426\) | −2.21442e7 | + | 5.15126e7i | −0.286439 | + | 0.666323i | ||||
\(427\) | −3.89266e7 | −0.499992 | ||||||||
\(428\) | 9.18361e7 | + | 9.68555e7i | 1.17134 | + | 1.23536i | ||||
\(429\) | −3.80495e7 | −0.481922 | ||||||||
\(430\) | 3.74043e7 | + | 4.47774e7i | 0.470453 | + | 0.563188i | ||||
\(431\) | − | 1.28493e8i | − | 1.60490i | −0.596722 | − | 0.802448i | \(-0.703531\pi\) | ||
0.596722 | − | 0.802448i | \(-0.296469\pi\) | |||||||
\(432\) | 824874. | − | 1.54937e7i | 0.0102314 | − | 0.192178i | ||||
\(433\) | 1.05589e8i | 1.30063i | 0.759665 | + | 0.650315i | \(0.225363\pi\) | ||||
−0.759665 | + | 0.650315i | \(0.774637\pi\) | |||||||
\(434\) | −2.99479e7 | + | 6.96658e7i | −0.366351 | + | 0.852218i | ||||
\(435\) | −4.46879e7 | − | 2.26369e7i | −0.542903 | − | 0.275011i | ||||
\(436\) | −6.97199e7 | − | 7.35305e7i | −0.841196 | − | 0.887172i | ||||
\(437\) | − | 8.05176e7i | − | 0.964820i | ||||||
\(438\) | 2.88176e6 | − | 6.70365e6i | 0.0342954 | − | 0.0797790i | ||||
\(439\) | − | 3.96198e7i | − | 0.468294i | −0.972201 | − | 0.234147i | \(-0.924770\pi\) | ||
0.972201 | − | 0.234147i | \(-0.0752297\pi\) | |||||||
\(440\) | −9.10406e7 | − | 1.06150e7i | −1.06875 | − | 0.124612i | ||||
\(441\) | −1.55493e7 | −0.181299 | ||||||||
\(442\) | 9.47989e7 | + | 4.07521e7i | 1.09783 | + | 0.471936i | ||||
\(443\) | −1.10250e8 | −1.26814 | −0.634070 | − | 0.773276i | \(-0.718617\pi\) | ||||
−0.634070 | + | 0.773276i | \(0.718617\pi\) | |||||||
\(444\) | −4.78147e7 | + | 4.53368e7i | −0.546277 | + | 0.517967i | ||||
\(445\) | −3.19879e7 | − | 1.62037e7i | −0.362999 | − | 0.183880i | ||||
\(446\) | 6.45958e7 | + | 2.77684e7i | 0.728114 | + | 0.313001i | ||||
\(447\) | 8.34624e7 | 0.934476 | ||||||||
\(448\) | 4.62245e7 | − | 3.93801e7i | 0.514089 | − | 0.437969i | ||||
\(449\) | 1.05887e8 | 1.16977 | 0.584887 | − | 0.811115i | \(-0.301139\pi\) | ||||
0.584887 | + | 0.811115i | \(0.301139\pi\) | |||||||
\(450\) | 6.83729e6 | + | 2.95955e7i | 0.0750320 | + | 0.324779i | ||||
\(451\) | 1.52190e8i | 1.65904i | ||||||||
\(452\) | −1.08125e7 | + | 1.02522e7i | −0.117088 | + | 0.111020i | ||||
\(453\) | 1.11096e7i | 0.119510i | ||||||||
\(454\) | −1.41322e7 | − | 6.07513e6i | −0.151022 | − | 0.0649214i | ||||
\(455\) | −2.23010e7 | + | 4.40247e7i | −0.236750 | + | 0.467371i | ||||
\(456\) | 4.16791e7 | − | 1.53468e7i | 0.439565 | − | 0.161854i | ||||
\(457\) | − | 9.85857e7i | − | 1.03292i | −0.856312 | − | 0.516459i | \(-0.827250\pi\) | ||
0.856312 | − | 0.516459i | \(-0.172750\pi\) | |||||||
\(458\) | −1.38356e8 | − | 5.94765e7i | −1.44013 | − | 0.619083i | ||||
\(459\) | − | 2.86673e7i | − | 0.296448i | ||||||
\(460\) | −3.30910e7 | − | 1.10921e8i | −0.339967 | − | 1.13957i | ||||
\(461\) | −2.20074e6 | −0.0224629 | −0.0112315 | − | 0.999937i | \(-0.503575\pi\) | ||||
−0.0112315 | + | 0.999937i | \(0.503575\pi\) | |||||||
\(462\) | −1.63392e7 | + | 3.80088e7i | −0.165694 | + | 0.385442i | ||||
\(463\) | −5.10823e7 | −0.514668 | −0.257334 | − | 0.966323i | \(-0.582844\pi\) | ||||
−0.257334 | + | 0.966323i | \(0.582844\pi\) | |||||||
\(464\) | −5.59826e6 | + | 1.05153e8i | −0.0560402 | + | 1.05261i | ||||
\(465\) | −3.60303e7 | + | 7.11279e7i | −0.358352 | + | 0.707427i | ||||
\(466\) | 3.04730e7 | − | 7.08873e7i | 0.301132 | − | 0.700504i | ||||
\(467\) | 7.31478e7 | 0.718209 | 0.359105 | − | 0.933297i | \(-0.383082\pi\) | ||||
0.359105 | + | 0.933297i | \(0.383082\pi\) | |||||||
\(468\) | 1.92344e7 | − | 1.82376e7i | 0.187646 | − | 0.177922i | ||||
\(469\) | 8.53733e6 | 0.0827568 | ||||||||
\(470\) | 4.80905e7 | + | 5.75701e7i | 0.463197 | + | 0.554502i | ||||
\(471\) | 3.31045e7i | 0.316828i | ||||||||
\(472\) | 9.59117e7 | − | 3.53159e7i | 0.912106 | − | 0.335849i | ||||
\(473\) | 8.35581e7i | 0.789596i | ||||||||
\(474\) | 3.19733e7 | − | 7.43774e7i | 0.300229 | − | 0.698403i | ||||
\(475\) | −7.01028e7 | + | 5.14399e7i | −0.654115 | + | 0.479975i | ||||
\(476\) | 8.14171e7 | − | 7.71978e7i | 0.754910 | − | 0.715788i | ||||
\(477\) | − | 1.98922e7i | − | 0.183286i | ||||||
\(478\) | −4.90715e7 | + | 1.14152e8i | −0.449310 | + | 1.04520i | ||||
\(479\) | 1.47715e7i | 0.134406i | 0.997739 | + | 0.0672029i | \(0.0214075\pi\) | ||||
−0.997739 | + | 0.0672029i | \(0.978593\pi\) | |||||||
\(480\) | 5.11097e7 | − | 3.82709e7i | 0.462147 | − | 0.346055i | ||||
\(481\) | −1.12565e8 | −1.01151 | ||||||||
\(482\) | −1.42000e8 | − | 6.10428e7i | −1.26808 | − | 0.545122i | ||||
\(483\) | −5.22476e7 | −0.463687 | ||||||||
\(484\) | −1.23071e7 | − | 1.29797e7i | −0.108547 | − | 0.114480i | ||||
\(485\) | −2.18258e7 | + | 4.30866e7i | −0.191313 | + | 0.377674i | ||||
\(486\) | −6.76525e6 | − | 2.90824e6i | −0.0589352 | − | 0.0253350i | ||||
\(487\) | −8.05091e6 | −0.0697041 | −0.0348521 | − | 0.999392i | \(-0.511096\pi\) | ||||
−0.0348521 | + | 0.999392i | \(0.511096\pi\) | |||||||
\(488\) | 2.97290e7 | + | 8.07386e7i | 0.255812 | + | 0.694739i | ||||
\(489\) | 7.53993e7 | 0.644823 | ||||||||
\(490\) | −4.10227e7 | − | 4.91091e7i | −0.348687 | − | 0.417420i | ||||
\(491\) | − | 1.32710e8i | − | 1.12114i | −0.828108 | − | 0.560568i | \(-0.810583\pi\) | ||
0.828108 | − | 0.560568i | \(-0.189417\pi\) | |||||||
\(492\) | −7.29464e7 | − | 7.69334e7i | −0.612504 | − | 0.645980i | ||||
\(493\) | 1.94559e8i | 1.62372i | ||||||||
\(494\) | 6.97076e7 | + | 2.99659e7i | 0.578229 | + | 0.248569i | ||||
\(495\) | −1.96577e7 | + | 3.88066e7i | −0.162076 | + | 0.319955i | ||||
\(496\) | 1.67367e8 | + | 8.91054e6i | 1.37159 | + | 0.0730229i | ||||
\(497\) | 1.04152e8i | 0.848397i | ||||||||
\(498\) | −5.18724e7 | − | 2.22989e7i | −0.419999 | − | 0.180549i | ||||
\(499\) | 7.22099e7i | 0.581159i | 0.956851 | + | 0.290579i | \(0.0938480\pi\) | ||||
−0.956851 | + | 0.290579i | \(0.906152\pi\) | |||||||
\(500\) | −7.54326e7 | + | 9.96741e7i | −0.603461 | + | 0.797393i | ||||
\(501\) | −1.01383e8 | −0.806218 | ||||||||
\(502\) | 8.41351e7 | − | 1.95718e8i | 0.665068 | − | 1.54710i | ||||
\(503\) | 6.05721e7 | 0.475958 | 0.237979 | − | 0.971270i | \(-0.423515\pi\) | ||||
0.237979 | + | 0.971270i | \(0.423515\pi\) | |||||||
\(504\) | −9.95847e6 | − | 2.70454e7i | −0.0777859 | − | 0.211252i | ||||
\(505\) | −9.82936e7 | − | 4.97913e7i | −0.763222 | − | 0.386615i | ||||
\(506\) | 6.54695e7 | − | 1.52297e8i | 0.505344 | − | 1.17555i | ||||
\(507\) | −2.99611e7 | −0.229897 | ||||||||
\(508\) | 6.18591e7 | + | 6.52401e7i | 0.471859 | + | 0.497649i | ||||
\(509\) | −1.58756e8 | −1.20386 | −0.601931 | − | 0.798548i | \(-0.705602\pi\) | ||||
−0.601931 | + | 0.798548i | \(0.705602\pi\) | |||||||
\(510\) | 9.05394e7 | − | 7.56311e7i | 0.682538 | − | 0.570151i | ||||
\(511\) | − | 1.35540e7i | − | 0.101579i | ||||||
\(512\) | −1.16982e8 | − | 6.58000e7i | −0.871583 | − | 0.490248i | ||||
\(513\) | − | 2.10796e7i | − | 0.156139i | ||||||
\(514\) | −8.43139e7 | + | 1.96134e8i | −0.620883 | + | 1.44432i | ||||
\(515\) | 1.96943e6 | + | 997629.i | 0.0144185 | + | 0.00730378i | ||||
\(516\) | −4.00504e7 | − | 4.22394e7i | −0.291513 | − | 0.307446i | ||||
\(517\) | 1.07430e8i | 0.777418i | ||||||||
\(518\) | −4.83378e7 | + | 1.12445e8i | −0.347774 | + | 0.809004i | ||||
\(519\) | − | 8.00549e7i | − | 0.572646i | ||||||
\(520\) | 1.08344e8 | + | 1.26325e7i | 0.770542 | + | 0.0898421i | ||||
\(521\) | 3.43271e7 | 0.242730 | 0.121365 | − | 0.992608i | \(-0.461273\pi\) | ||||
0.121365 | + | 0.992608i | \(0.461273\pi\) | |||||||
\(522\) | 4.59145e7 | + | 1.97377e7i | 0.322803 | + | 0.138767i | ||||
\(523\) | 7.73418e7 | 0.540641 | 0.270321 | − | 0.962770i | \(-0.412870\pi\) | ||||
0.270321 | + | 0.962770i | \(0.412870\pi\) | |||||||
\(524\) | −5.67220e7 | + | 5.37825e7i | −0.394237 | + | 0.373807i | ||||
\(525\) | 3.33791e7 | + | 4.54894e7i | 0.230673 | + | 0.314364i | ||||
\(526\) | 8.04528e7 | + | 3.45850e7i | 0.552820 | + | 0.237646i | ||||
\(527\) | 3.09672e8 | 2.11578 | ||||||||
\(528\) | 9.13137e7 | + | 4.86148e6i | 0.620346 | + | 0.0330268i | ||||
\(529\) | 6.13144e7 | 0.414186 | ||||||||
\(530\) | 6.28254e7 | − | 5.24805e7i | 0.421995 | − | 0.352509i | ||||
\(531\) | − | 4.85084e7i | − | 0.323991i | ||||||
\(532\) | 5.98678e7 | − | 5.67652e7i | 0.397611 | − | 0.377005i | ||||
\(533\) | − | 1.81116e8i | − | 1.19612i | ||||||
\(534\) | 3.28659e7 | + | 1.41284e7i | 0.215835 | + | 0.0927830i | ||||
\(535\) | 2.32553e8 | + | 1.17802e8i | 1.51866 | + | 0.769289i | ||||
\(536\) | −6.52013e6 | − | 1.77075e7i | −0.0423411 | − | 0.114991i | ||||
\(537\) | − | 1.10655e8i | − | 0.714578i | ||||||
\(538\) | −2.25475e8 | − | 9.69270e7i | −1.44794 | − | 0.622441i | ||||
\(539\) | − | 9.16413e7i | − | 0.585228i | ||||||
\(540\) | −8.66329e6 | − | 2.90392e7i | −0.0550176 | − | 0.184418i | ||||
\(541\) | −1.75419e8 | −1.10786 | −0.553931 | − | 0.832562i | \(-0.686873\pi\) | ||||
−0.553931 | + | 0.832562i | \(0.686873\pi\) | |||||||
\(542\) | −1.73963e7 | + | 4.04678e7i | −0.109259 | + | 0.254163i | ||||
\(543\) | −1.47523e8 | −0.921428 | ||||||||
\(544\) | −2.22298e8 | − | 1.09912e8i | −1.38082 | − | 0.682728i | ||||
\(545\) | −1.76549e8 | − | 8.94322e7i | −1.09063 | − | 0.552464i | ||||
\(546\) | 1.94448e7 | − | 4.52330e7i | 0.119461 | − | 0.277893i | ||||
\(547\) | −2.50778e8 | −1.53224 | −0.766121 | − | 0.642696i | \(-0.777816\pi\) | ||||
−0.766121 | + | 0.642696i | \(0.777816\pi\) | |||||||
\(548\) | 1.89141e8 | − | 1.79339e8i | 1.14933 | − | 1.08976i | ||||
\(549\) | 4.08344e7 | 0.246780 | ||||||||
\(550\) | −1.74424e8 | + | 4.02963e7i | −1.04838 | + | 0.242202i | ||||
\(551\) | 1.43064e8i | 0.855213i | ||||||||
\(552\) | 3.99025e7 | + | 1.08368e8i | 0.237237 | + | 0.644293i | ||||
\(553\) | − | 1.50382e8i | − | 0.889243i | ||||||
\(554\) | −7.33079e7 | + | 1.70531e8i | −0.431143 | + | 1.00294i | ||||
\(555\) | −5.81552e7 | + | 1.14805e8i | −0.340180 | + | 0.671555i | ||||
\(556\) | −8.45382e7 | + | 8.01572e7i | −0.491846 | + | 0.466357i | ||||
\(557\) | − | 1.88247e8i | − | 1.08934i | −0.838652 | − | 0.544668i | \(-0.816656\pi\) | ||
0.838652 | − | 0.544668i | \(-0.183344\pi\) | |||||||
\(558\) | 3.14157e7 | − | 7.30802e7i | 0.180819 | − | 0.420627i | ||||
\(559\) | − | 9.94396e7i | − | 0.569278i | ||||||
\(560\) | 5.91443e7 | − | 1.02804e8i | 0.336782 | − | 0.585391i | ||||
\(561\) | 1.68953e8 | 0.956926 | ||||||||
\(562\) | 1.65988e8 | + | 7.13549e7i | 0.935121 | + | 0.401989i | ||||
\(563\) | 1.77571e8 | 0.995054 | 0.497527 | − | 0.867448i | \(-0.334241\pi\) | ||||
0.497527 | + | 0.867448i | \(0.334241\pi\) | |||||||
\(564\) | −5.14925e7 | − | 5.43069e7i | −0.287017 | − | 0.302704i | ||||
\(565\) | −1.31509e7 | + | 2.59613e7i | −0.0729136 | + | 0.143940i | ||||
\(566\) | 1.36568e8 | + | 5.87079e7i | 0.753183 | + | 0.323778i | ||||
\(567\) | −1.36785e7 | −0.0750394 | ||||||||
\(568\) | 2.16025e8 | − | 7.95431e7i | 1.17885 | − | 0.434067i | ||||
\(569\) | 2.12669e8 | 1.15443 | 0.577216 | − | 0.816592i | \(-0.304139\pi\) | ||||
0.577216 | + | 0.816592i | \(0.304139\pi\) | |||||||
\(570\) | 6.65756e7 | − | 5.56132e7i | 0.359493 | − | 0.300298i | ||||
\(571\) | 1.13543e8i | 0.609889i | 0.952370 | + | 0.304944i | \(0.0986378\pi\) | ||||
−0.952370 | + | 0.304944i | \(0.901362\pi\) | |||||||
\(572\) | 1.07485e8 | + | 1.13360e8i | 0.574328 | + | 0.605718i | ||||
\(573\) | 1.84948e8i | 0.983074i | ||||||||
\(574\) | −1.80923e8 | − | 7.77749e7i | −0.956659 | − | 0.411248i | ||||
\(575\) | −1.33747e8 | − | 1.82271e8i | −0.703524 | − | 0.958770i | ||||
\(576\) | −4.84900e7 | + | 4.13102e7i | −0.253738 | + | 0.216167i | ||||
\(577\) | 1.64538e8i | 0.856524i | 0.903655 | + | 0.428262i | \(0.140874\pi\) | ||||
−0.903655 | + | 0.428262i | \(0.859126\pi\) | |||||||
\(578\) | −2.43538e8 | − | 1.04692e8i | −1.26120 | − | 0.542163i | ||||
\(579\) | 8.25233e7i | 0.425148i | ||||||||
\(580\) | 5.87961e7 | + | 1.97084e8i | 0.301345 | + | 1.01011i | ||||
\(581\) | −1.04880e8 | −0.534765 | ||||||||
\(582\) | 1.90304e7 | − | 4.42692e7i | 0.0965338 | − | 0.224560i | ||||
\(583\) | 1.17237e8 | 0.591642 | ||||||||
\(584\) | −2.81126e7 | + | 1.03514e7i | −0.141144 | + | 0.0519710i | ||||
\(585\) | 2.33940e7 | − | 4.61824e7i | 0.116852 | − | 0.230679i | ||||
\(586\) | −7.62915e7 | + | 1.77472e8i | −0.379126 | + | 0.881935i | ||||
\(587\) | 7.68393e6 | 0.0379900 | 0.0189950 | − | 0.999820i | \(-0.493953\pi\) | ||||
0.0189950 | + | 0.999820i | \(0.493953\pi\) | |||||||
\(588\) | 4.39248e7 | + | 4.63255e7i | 0.216062 | + | 0.227870i | ||||
\(589\) | 2.27709e8 | 1.11438 | ||||||||
\(590\) | 1.53203e8 | − | 1.27977e8i | 0.745954 | − | 0.623125i | ||||
\(591\) | 8.68070e7i | 0.420525i | ||||||||
\(592\) | 2.70141e8 | + | 1.43822e7i | 1.30204 | + | 0.0693200i | ||||
\(593\) | − | 1.75657e8i | − | 0.842366i | −0.906976 | − | 0.421183i | \(-0.861615\pi\) | ||
0.906976 | − | 0.421183i | \(-0.138385\pi\) | |||||||
\(594\) | 1.71400e7 | − | 3.98717e7i | 0.0817810 | − | 0.190242i | ||||
\(595\) | 9.90244e7 | − | 1.95485e8i | 0.470101 | − | 0.928033i | ||||
\(596\) | −2.35771e8 | − | 2.48657e8i | −1.11366 | − | 1.17452i | ||||
\(597\) | 1.03498e8i | 0.486415i | ||||||||
\(598\) | −7.79130e7 | + | 1.81244e8i | −0.364340 | + | 0.847539i | ||||
\(599\) | − | 1.74222e8i | − | 0.810628i | −0.914177 | − | 0.405314i | \(-0.867162\pi\) | ||
0.914177 | − | 0.405314i | \(-0.132838\pi\) | |||||||
\(600\) | 6.88584e7 | − | 1.03974e8i | 0.318789 | − | 0.481359i | ||||
\(601\) | −1.24560e8 | −0.573792 | −0.286896 | − | 0.957962i | \(-0.592623\pi\) | ||||
−0.286896 | + | 0.957962i | \(0.592623\pi\) | |||||||
\(602\) | −9.93334e7 | − | 4.27014e7i | −0.455309 | − | 0.195728i | ||||
\(603\) | −8.95576e6 | −0.0408461 | ||||||||
\(604\) | 3.30985e7 | − | 3.13832e7i | 0.150209 | − | 0.142425i | ||||
\(605\) | −3.11648e7 | − | 1.57867e7i | −0.140734 | − | 0.0712895i | ||||
\(606\) | 1.00991e8 | + | 4.34142e7i | 0.453803 | + | 0.195080i | ||||
\(607\) | −3.95496e8 | −1.76838 | −0.884190 | − | 0.467127i | \(-0.845289\pi\) | ||||
−0.884190 | + | 0.467127i | \(0.845289\pi\) | |||||||
\(608\) | −1.63460e8 | − | 8.08205e7i | −0.727280 | − | 0.359593i | ||||
\(609\) | 9.28334e7 | 0.411010 | ||||||||
\(610\) | 1.07731e8 | + | 1.28967e8i | 0.474626 | + | 0.568183i | ||||
\(611\) | − | 1.27849e8i | − | 0.560497i | ||||||
\(612\) | −8.54075e7 | + | 8.09814e7i | −0.372599 | + | 0.353290i | ||||
\(613\) | − | 2.24663e8i | − | 0.975326i | −0.873032 | − | 0.487663i | \(-0.837850\pi\) | ||
0.873032 | − | 0.487663i | \(-0.162150\pi\) | |||||||
\(614\) | −3.03341e8 | − | 1.30400e8i | −1.31047 | − | 0.563342i | ||||
\(615\) | −1.84720e8 | − | 9.35710e7i | −0.794123 | − | 0.402268i | ||||
\(616\) | 1.59395e8 | − | 5.86913e7i | 0.681918 | − | 0.251091i | ||||
\(617\) | − | 7.20680e7i | − | 0.306822i | −0.988162 | − | 0.153411i | \(-0.950974\pi\) | ||
0.988162 | − | 0.153411i | \(-0.0490259\pi\) | |||||||
\(618\) | −2.02349e6 | − | 869856.i | −0.00857305 | − | 0.00368538i | ||||
\(619\) | 7.72367e7i | 0.325651i | 0.986655 | + | 0.162825i | \(0.0520607\pi\) | ||||
−0.986655 | + | 0.162825i | \(0.947939\pi\) | |||||||
\(620\) | 3.13690e8 | − | 9.35834e7i | 1.31621 | − | 0.392667i | ||||
\(621\) | 5.48083e7 | 0.228861 | ||||||||
\(622\) | −5.51131e7 | + | 1.28206e8i | −0.229025 | + | 0.532766i | ||||
\(623\) | 6.64508e7 | 0.274812 | ||||||||
\(624\) | −1.08669e8 | − | 5.78549e6i | −0.447253 | − | 0.0238115i | ||||
\(625\) | −7.32486e7 | + | 2.32893e8i | −0.300026 | + | 0.953931i | ||||
\(626\) | −1.67917e8 | + | 3.90613e8i | −0.684496 | + | 1.59230i | ||||
\(627\) | 1.24235e8 | 0.504013 | ||||||||
\(628\) | 9.86272e7 | − | 9.35160e7i | 0.398215 | − | 0.377578i | ||||
\(629\) | 4.99830e8 | 2.00849 | ||||||||
\(630\) | −3.60872e7 | − | 4.32007e7i | −0.144322 | − | 0.172770i | ||||
\(631\) | 2.14473e8i | 0.853661i | 0.904332 | + | 0.426831i | \(0.140370\pi\) | ||||
−0.904332 | + | 0.426831i | \(0.859630\pi\) | |||||||
\(632\) | −3.11911e8 | + | 1.14850e8i | −1.23560 | + | 0.454965i | ||||
\(633\) | − | 4.16683e7i | − | 0.164284i | ||||||
\(634\) | −5.81546e7 | + | 1.35281e8i | −0.228201 | + | 0.530848i | ||||
\(635\) | 1.56644e8 | + | 7.93489e7i | 0.611775 | + | 0.309899i | ||||
\(636\) | −5.92643e7 | + | 5.61931e7i | −0.230368 | + | 0.218430i | ||||
\(637\) | 1.09059e8i | 0.421933i | ||||||||
\(638\) | −1.16326e8 | + | 2.70602e8i | −0.447935 | + | 1.04200i | ||||
\(639\) | − | 1.09257e8i | − | 0.418741i | ||||||
\(640\) | −2.58398e8 | − | 4.41592e7i | −0.985709 | − | 0.168454i | ||||
\(641\) | 2.43161e7 | 0.0923250 | 0.0461625 | − | 0.998934i | \(-0.485301\pi\) | ||||
0.0461625 | + | 0.998934i | \(0.485301\pi\) | |||||||
\(642\) | −2.38937e8 | − | 1.02714e8i | −0.902979 | − | 0.388172i | ||||
\(643\) | 1.27297e8 | 0.478834 | 0.239417 | − | 0.970917i | \(-0.423044\pi\) | ||||
0.239417 | + | 0.970917i | \(0.423044\pi\) | |||||||
\(644\) | 1.47593e8 | + | 1.55660e8i | 0.552596 | + | 0.582798i | ||||
\(645\) | −1.01418e8 | − | 5.13741e7i | −0.377952 | − | 0.191454i | ||||
\(646\) | −3.09527e8 | − | 1.33059e8i | −1.14816 | − | 0.493569i | ||||
\(647\) | −6.33889e7 | −0.234046 | −0.117023 | − | 0.993129i | \(-0.537335\pi\) | ||||
−0.117023 | + | 0.993129i | \(0.537335\pi\) | |||||||
\(648\) | 1.04465e7 | + | 2.83709e7i | 0.0383926 | + | 0.104267i | ||||
\(649\) | 2.85889e8 | 1.04584 | ||||||||
\(650\) | 2.07576e8 | − | 4.79553e7i | 0.755853 | − | 0.174621i | ||||
\(651\) | − | 1.47759e8i | − | 0.535565i | ||||||
\(652\) | −2.12993e8 | − | 2.24635e8i | −0.768464 | − | 0.810465i | ||||
\(653\) | 2.20721e8i | 0.792693i | 0.918101 | + | 0.396346i | \(0.129722\pi\) | ||||
−0.918101 | + | 0.396346i | \(0.870278\pi\) | |||||||
\(654\) | 1.81395e8 | + | 7.79780e7i | 0.648474 | + | 0.278766i | ||||
\(655\) | −6.89888e7 | + | 1.36192e8i | −0.245502 | + | 0.484648i | ||||
\(656\) | −2.31407e7 | + | 4.34654e8i | −0.0819720 | + | 1.53969i | ||||
\(657\) | 1.42182e7i | 0.0501360i | ||||||||
\(658\) | −1.27712e8 | − | 5.49009e7i | −0.448286 | − | 0.192709i | ||||
\(659\) | − | 4.58676e8i | − | 1.60269i | −0.598202 | − | 0.801345i | \(-0.704118\pi\) | ||
0.598202 | − | 0.801345i | \(-0.295882\pi\) | |||||||
\(660\) | 1.71146e8 | − | 5.10580e7i | 0.595298 | − | 0.177596i | ||||
\(661\) | 2.41009e8 | 0.834504 | 0.417252 | − | 0.908791i | \(-0.362993\pi\) | ||||
0.417252 | + | 0.908791i | \(0.362993\pi\) | |||||||
\(662\) | −1.21813e8 | + | 2.83365e8i | −0.419874 | + | 0.976724i | ||||
\(663\) | −2.01066e8 | −0.689918 | ||||||||
\(664\) | 8.00987e7 | + | 2.17534e8i | 0.273603 | + | 0.743057i | ||||
\(665\) | 7.28148e7 | − | 1.43745e8i | 0.247602 | − | 0.488795i | ||||
\(666\) | 5.07069e7 | − | 1.17956e8i | 0.171650 | − | 0.399298i | ||||
\(667\) | −3.71973e8 | −1.25353 | ||||||||
\(668\) | 2.86395e8 | + | 3.02048e8i | 0.960805 | + | 1.01332i | ||||
\(669\) | −1.37006e8 | −0.457573 | ||||||||
\(670\) | −2.36274e7 | − | 2.82848e7i | −0.0785583 | − | 0.0940436i | ||||
\(671\) | 2.40662e8i | 0.796599i | ||||||||
\(672\) | −5.24441e7 | + | 1.06069e8i | −0.172818 | + | 0.349526i | ||||
\(673\) | − | 3.13830e8i | − | 1.02955i | −0.857324 | − | 0.514777i | \(-0.827875\pi\) | ||
0.857324 | − | 0.514777i | \(-0.172125\pi\) | |||||||
\(674\) | 7.30331e7 | − | 1.69892e8i | 0.238528 | − | 0.554873i | ||||
\(675\) | −3.50151e7 | − | 4.77189e7i | −0.113853 | − | 0.155160i | ||||
\(676\) | 8.46364e7 | + | 8.92622e7i | 0.273979 | + | 0.288953i | ||||
\(677\) | − | 5.80130e7i | − | 0.186965i | −0.995621 | − | 0.0934824i | \(-0.970200\pi\) | ||
0.995621 | − | 0.0934824i | \(-0.0297999\pi\) | |||||||
\(678\) | 1.14665e7 | − | 2.66738e7i | 0.0367911 | − | 0.0855848i | ||||
\(679\) | − | 8.95069e7i | − | 0.285922i | ||||||
\(680\) | −4.81088e8 | − | 5.60930e7i | −1.53002 | − | 0.178395i | ||||
\(681\) | 2.99739e7 | 0.0949079 | ||||||||
\(682\) | 4.30706e8 | + | 1.85152e8i | 1.35777 | + | 0.583680i | ||||
\(683\) | −3.03960e8 | −0.954014 | −0.477007 | − | 0.878899i | \(-0.658278\pi\) | ||||
−0.477007 | + | 0.878899i | \(0.658278\pi\) | |||||||
\(684\) | −6.28020e7 | + | 5.95474e7i | −0.196248 | + | 0.186078i | ||||
\(685\) | 2.30044e8 | − | 4.54133e8i | 0.715714 | − | 1.41290i | ||||
\(686\) | 3.09243e8 | + | 1.32937e8i | 0.957918 | + | 0.411789i | ||||
\(687\) | 2.93450e8 | 0.905031 | ||||||||
\(688\) | −1.27051e7 | + | 2.38642e8i | −0.0390134 | + | 0.732793i | ||||
\(689\) | −1.39520e8 | −0.426558 | ||||||||
\(690\) | 1.44597e8 | + | 1.73100e8i | 0.440163 | + | 0.526927i | ||||
\(691\) | − | 1.34182e8i | − | 0.406688i | −0.979107 | − | 0.203344i | \(-0.934819\pi\) | ||
0.979107 | − | 0.203344i | \(-0.0651810\pi\) | |||||||
\(692\) | −2.38505e8 | + | 2.26145e8i | −0.719746 | + | 0.682447i | ||||
\(693\) | − | 8.06157e7i | − | 0.242226i | ||||||
\(694\) | −3.59332e8 | − | 1.54469e8i | −1.07502 | − | 0.462130i | ||||
\(695\) | −1.02820e8 | + | 2.02979e8i | −0.306285 | + | 0.604640i | ||||
\(696\) | −7.08987e7 | − | 1.92548e8i | −0.210286 | − | 0.571099i | ||||
\(697\) | 8.04221e8i | 2.37507i | ||||||||
\(698\) | 1.50760e8 | + | 6.48088e7i | 0.443324 | + | 0.190576i | ||||
\(699\) | 1.50350e8i | 0.440222i | ||||||||
\(700\) | 4.12334e7 | − | 2.27947e8i | 0.120214 | − | 0.664570i | ||||
\(701\) | −1.96406e8 | −0.570164 | −0.285082 | − | 0.958503i | \(-0.592021\pi\) | ||||
−0.285082 | + | 0.958503i | \(0.592021\pi\) | |||||||
\(702\) | −2.03978e7 | + | 4.74500e7i | −0.0589619 | + | 0.137159i | ||||
\(703\) | 3.67536e8 | 1.05787 | ||||||||
\(704\) | −2.43466e8 | − | 2.85781e8i | −0.697783 | − | 0.819060i | ||||
\(705\) | −1.30393e8 | − | 6.60513e7i | −0.372123 | − | 0.188501i | ||||
\(706\) | 1.60117e8 | − | 3.72470e8i | 0.455013 | − | 1.05847i | ||||
\(707\) | 2.04192e8 | 0.577805 | ||||||||
\(708\) | −1.44520e8 | + | 1.37030e8i | −0.407218 | + | 0.386115i | ||||
\(709\) | −3.33485e7 | −0.0935701 | −0.0467851 | − | 0.998905i | \(-0.514898\pi\) | ||||
−0.0467851 | + | 0.998905i | \(0.514898\pi\) | |||||||
\(710\) | 3.45064e8 | − | 2.88246e8i | 0.964107 | − | 0.805356i | ||||
\(711\) | 1.57752e8i | 0.438901i | ||||||||
\(712\) | −5.07498e7 | − | 1.37827e8i | −0.140603 | − | 0.381852i | ||||
\(713\) | 5.92055e8i | 1.63340i | ||||||||
\(714\) | −8.63417e7 | + | 2.00851e8i | −0.237206 | + | 0.551797i | ||||
\(715\) | 2.72181e8 | + | 1.37875e8i | 0.744627 | + | 0.377196i | ||||
\(716\) | −3.29672e8 | + | 3.12588e8i | −0.898139 | + | 0.851594i | ||||
\(717\) | − | 2.42113e8i | − | 0.656841i | ||||||
\(718\) | 1.92525e8 | − | 4.47857e8i | 0.520131 | − | 1.20995i | ||||
\(719\) | 2.33498e8i | 0.628197i | 0.949390 | + | 0.314098i | \(0.101702\pi\) | ||||
−0.949390 | + | 0.314098i | \(0.898298\pi\) | |||||||
\(720\) | −6.20430e7 | + | 1.07842e8i | −0.166225 | + | 0.288930i | ||||
\(721\) | −4.09125e6 | −0.0109157 | ||||||||
\(722\) | 1.18170e8 | + | 5.07988e7i | 0.313975 | + | 0.134972i | ||||
\(723\) | 3.01178e8 | 0.796908 | ||||||||
\(724\) | 4.16735e8 | + | 4.39512e8i | 1.09811 | + | 1.15812i | ||||
\(725\) | 2.37641e8 | + | 3.23859e8i | 0.623601 | + | 0.849850i | ||||
\(726\) | 3.20202e7 | + | 1.37648e7i | 0.0836784 | + | 0.0359716i | ||||
\(727\) | −5.57692e8 | −1.45141 | −0.725707 | − | 0.688004i | \(-0.758487\pi\) | ||||
−0.725707 | + | 0.688004i | \(0.758487\pi\) | |||||||
\(728\) | −1.89690e8 | + | 6.98465e7i | −0.491645 | + | 0.181030i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −4.49053e7 | + | 3.75112e7i | −0.115433 | + | 0.0964255i | ||||
\(731\) | 4.41548e8i | 1.13038i | ||||||||
\(732\) | −1.15352e8 | − | 1.21657e8i | −0.294098 | − | 0.310172i | ||||
\(733\) | − | 3.53347e8i | − | 0.897199i | −0.893733 | − | 0.448600i | \(-0.851923\pi\) | ||
0.893733 | − | 0.448600i | \(-0.148077\pi\) | |||||||
\(734\) | 1.10073e8 | + | 4.73183e7i | 0.278352 | + | 0.119658i | ||||
\(735\) | 1.11229e8 | + | 5.63439e7i | 0.280128 | + | 0.141901i | ||||
\(736\) | 2.10138e8 | − | 4.25006e8i | 0.527073 | − | 1.06601i | ||||
\(737\) | − | 5.27817e7i | − | 0.131850i | ||||||
\(738\) | 1.89790e8 | + | 8.15868e7i | 0.472176 | + | 0.202979i | ||||
\(739\) | − | 2.91298e8i | − | 0.721778i | −0.932609 | − | 0.360889i | \(-0.882473\pi\) | ||
0.932609 | − | 0.360889i | \(-0.117527\pi\) | |||||||
\(740\) | 5.06316e8 | − | 1.51049e8i | 1.24947 | − | 0.372755i | ||||
\(741\) | −1.47848e8 | −0.363380 | ||||||||
\(742\) | −5.99126e7 | + | 1.39371e8i | −0.146658 | + | 0.341161i | ||||
\(743\) | −1.31685e8 | −0.321048 | −0.160524 | − | 0.987032i | \(-0.551318\pi\) | ||||
−0.160524 | + | 0.987032i | \(0.551318\pi\) | |||||||
\(744\) | −3.06471e8 | + | 1.12847e8i | −0.744168 | + | 0.274012i | ||||
\(745\) | −5.97034e8 | − | 3.02432e8i | −1.44388 | − | 0.731406i | ||||
\(746\) | 2.80297e8 | − | 6.52035e8i | 0.675152 | − | 1.57056i | ||||
\(747\) | 1.10020e8 | 0.263943 | ||||||||
\(748\) | −4.77272e8 | − | 5.03358e8i | −1.14041 | − | 1.20274i | ||||
\(749\) | −4.83100e8 | −1.14972 | ||||||||
\(750\) | 5.83318e7 | − | 2.36482e8i | 0.138268 | − | 0.560549i | ||||
\(751\) | − | 6.94467e8i | − | 1.63958i | −0.572666 | − | 0.819789i | \(-0.694091\pi\) | ||
0.572666 | − | 0.819789i | \(-0.305909\pi\) | |||||||
\(752\) | −1.63349e7 | + | 3.06820e8i | −0.0384117 | + | 0.721490i | ||||
\(753\) | 4.15112e8i | 0.972255i | ||||||||
\(754\) | 1.38436e8 | − | 3.22034e8i | 0.322949 | − | 0.751255i | ||||
\(755\) | 4.02564e7 | − | 7.94706e7i | 0.0935392 | − | 0.184657i | ||||
\(756\) | 3.86401e7 | + | 4.07520e7i | 0.0894278 | + | 0.0943155i | ||||
\(757\) | − | 2.08147e8i | − | 0.479824i | −0.970795 | − | 0.239912i | \(-0.922881\pi\) | ||
0.970795 | − | 0.239912i | \(-0.0771186\pi\) | |||||||
\(758\) | 2.89754e8 | − | 6.74034e8i | 0.665305 | − | 1.54766i | ||||
\(759\) | 3.23018e8i | 0.738757i | ||||||||
\(760\) | −3.53754e8 | − | 4.12464e7i | −0.805863 | − | 0.0939604i | ||||
\(761\) | −4.53163e8 | −1.02825 | −0.514127 | − | 0.857714i | \(-0.671884\pi\) | ||||
−0.514127 | + | 0.857714i | \(0.671884\pi\) | |||||||
\(762\) | −1.60943e8 | − | 6.91862e7i | −0.363754 | − | 0.156370i | ||||
\(763\) | 3.66759e8 | 0.825671 | ||||||||
\(764\) | 5.51011e8 | − | 5.22456e8i | 1.23561 | − | 1.17157i | ||||
\(765\) | −1.03878e8 | + | 2.05066e8i | −0.232027 | + | 0.458047i | ||||
\(766\) | 2.03263e8 | + | 8.73788e7i | 0.452244 | + | 0.194411i | ||||
\(767\) | −3.40227e8 | −0.754020 | ||||||||
\(768\) | 2.60053e8 | + | 2.77688e7i | 0.574087 | + | 0.0613018i | ||||
\(769\) | −7.62334e8 | −1.67636 | −0.838178 | − | 0.545396i | \(-0.816379\pi\) | ||||
−0.838178 | + | 0.545396i | \(0.816379\pi\) | |||||||
\(770\) | 2.54608e8 | − | 2.12684e8i | 0.557698 | − | 0.465867i | ||||
\(771\) | − | 4.15994e8i | − | 0.907662i | ||||||
\(772\) | 2.45859e8 | − | 2.33118e8i | 0.534360 | − | 0.506668i | ||||
\(773\) | − | 1.52713e7i | − | 0.0330625i | −0.999863 | − | 0.0165313i | \(-0.994738\pi\) | ||
0.999863 | − | 0.0165313i | \(-0.00526231\pi\) | |||||||
\(774\) | 1.04202e8 | + | 4.47943e7i | 0.224726 | + | 0.0966050i | ||||
\(775\) | 5.15474e8 | − | 3.78243e8i | 1.10739 | − | 0.812580i | ||||
\(776\) | −1.85648e8 | + | 6.83582e7i | −0.397289 | + | 0.146287i | ||||
\(777\) | − | 2.38493e8i | − | 0.508407i | ||||||
\(778\) | 2.16862e7 | + | 9.32247e6i | 0.0460517 | + | 0.0197967i | ||||
\(779\) | 5.91361e8i | 1.25095i | ||||||||
\(780\) | −2.03675e8 | + | 6.07624e7i | −0.429194 | + | 0.128042i | ||||
\(781\) | 6.43916e8 | 1.35169 | ||||||||
\(782\) | 3.45962e8 | − | 8.04788e8i | 0.723449 | − | 1.68291i | ||||
\(783\) | −9.73833e7 | −0.202861 | ||||||||
\(784\) | 1.39342e7 | − | 2.61727e8i | 0.0289157 | − | 0.543127i | ||||
\(785\) | 1.19956e8 | − | 2.36807e8i | 0.247979 | − | 0.489538i | ||||
\(786\) | 6.01529e7 | − | 1.39930e8i | 0.123877 | − | 0.288166i | ||||
\(787\) | −8.30033e7 | −0.170283 | −0.0851414 | − | 0.996369i | \(-0.527134\pi\) | ||||
−0.0851414 | + | 0.996369i | \(0.527134\pi\) | |||||||
\(788\) | 2.58621e8 | − | 2.45219e8i | 0.528550 | − | 0.501158i | ||||
\(789\) | −1.70638e8 | −0.347412 | ||||||||
\(790\) | −4.98227e8 | + | 4.16189e8i | −1.01052 | + | 0.844129i | ||||
\(791\) | − | 5.39312e7i | − | 0.108971i | ||||||
\(792\) | −1.67207e8 | + | 6.15678e7i | −0.336573 | + | 0.123930i | ||||
\(793\) | − | 2.86404e8i | − | 0.574327i | ||||||
\(794\) | −3.59114e7 | + | 8.35384e7i | −0.0717416 | + | 0.166888i | ||||
\(795\) | −7.20809e7 | + | 1.42296e8i | −0.143456 | + | 0.283198i | ||||
\(796\) | 3.08347e8 | − | 2.92368e8i | 0.611365 | − | 0.579682i | ||||
\(797\) | 6.35860e8i | 1.25599i | 0.778217 | + | 0.627996i | \(0.216125\pi\) | ||||
−0.778217 | + | 0.627996i | \(0.783875\pi\) | |||||||
\(798\) | −6.34890e7 | + | 1.47690e8i | −0.124937 | + | 0.290632i | ||||
\(799\) | 5.67695e8i | 1.11295i | ||||||||
\(800\) | −5.04282e8 | + | 8.85647e7i | −0.984926 | + | 0.172978i | ||||
\(801\) | −6.97076e7 | −0.135638 | ||||||||
\(802\) | −7.38222e7 | − | 3.17347e7i | −0.143108 | − | 0.0615192i | ||||
\(803\) | −8.37967e7 | −0.161838 | ||||||||
\(804\) | 2.52989e7 | + | 2.66816e7i | 0.0486781 | + | 0.0513386i | ||||
\(805\) | 3.73744e8 | + | 1.89323e8i | 0.716452 | + | 0.362923i | ||||
\(806\) | −5.12569e8 | − | 2.20343e8i | −0.978919 | − | 0.420817i | ||||
\(807\) | 4.78226e8 | 0.909939 | ||||||||
\(808\) | −1.55946e8 | − | 4.23521e8i | −0.295624 | − | 0.802861i | ||||
\(809\) | 2.91205e8 | 0.549989 | 0.274994 | − | 0.961446i | \(-0.411324\pi\) | ||||
0.274994 | + | 0.961446i | \(0.411324\pi\) | |||||||
\(810\) | 3.78559e7 | + | 4.53180e7i | 0.0712325 | + | 0.0852737i | ||||
\(811\) | − | 5.36148e8i | − | 1.00513i | −0.864540 | − | 0.502565i | \(-0.832390\pi\) | ||
0.864540 | − | 0.502565i | \(-0.167610\pi\) | |||||||
\(812\) | −2.62243e8 | − | 2.76576e8i | −0.489819 | − | 0.516590i | ||||
\(813\) | − | 8.58312e7i | − | 0.159725i | ||||||
\(814\) | 6.95186e8 | + | 2.98846e8i | 1.28893 | + | 0.554083i | ||||
\(815\) | −5.39356e8 | − | 2.73214e8i | −0.996329 | − | 0.504697i | ||||
\(816\) | 4.82531e8 | + | 2.56896e7i | 0.888085 | + | 0.0472811i | ||||
\(817\) | 3.24680e8i | 0.595373i | ||||||||
\(818\) | 4.50693e8 | + | 1.93744e8i | 0.823420 | + | 0.353971i | ||||
\(819\) | 9.59380e7i | 0.174638i | ||||||||
\(820\) | 2.43037e8 | + | 8.14656e8i | 0.440789 | + | 1.47752i | ||||
\(821\) | −4.22022e8 | −0.762616 | −0.381308 | − | 0.924448i | \(-0.624526\pi\) | ||||
−0.381308 | + | 0.924448i | \(0.624526\pi\) | |||||||
\(822\) | −2.00581e8 | + | 4.66598e8i | −0.361139 | + | 0.840093i | ||||
\(823\) | −3.66692e8 | −0.657813 | −0.328906 | − | 0.944363i | \(-0.606680\pi\) | ||||
−0.328906 | + | 0.944363i | \(0.606680\pi\) | |||||||
\(824\) | 3.12457e6 | + | 8.48576e6i | 0.00558481 | + | 0.0151673i | ||||
\(825\) | 2.81236e8 | − | 2.06365e8i | 0.500852 | − | 0.367514i | ||||
\(826\) | −1.46100e8 | + | 3.39864e8i | −0.259246 | + | 0.603066i | ||||
\(827\) | 3.86327e8 | 0.683029 | 0.341514 | − | 0.939877i | \(-0.389060\pi\) | ||||
0.341514 | + | 0.939877i | \(0.389060\pi\) | |||||||
\(828\) | −1.54827e8 | − | 1.63289e8i | −0.272743 | − | 0.287650i | ||||
\(829\) | −4.10484e8 | −0.720499 | −0.360249 | − | 0.932856i | \(-0.617308\pi\) | ||||
−0.360249 | + | 0.932856i | \(0.617308\pi\) | |||||||
\(830\) | 2.90259e8 | + | 3.47475e8i | 0.507635 | + | 0.607699i | ||||
\(831\) | − | 3.61692e8i | − | 0.630284i | ||||||
\(832\) | 2.89741e8 | + | 3.40098e8i | 0.503083 | + | 0.590520i | ||||
\(833\) | − | 4.84262e8i | − | 0.837810i | ||||||
\(834\) | 8.96516e7 | − | 2.08551e8i | 0.154547 | − | 0.359512i | ||||
\(835\) | 7.25227e8 | + | 3.67369e8i | 1.24570 | + | 0.631019i | ||||
\(836\) | −3.50949e8 | − | 3.70130e8i | −0.600654 | − | 0.633484i | ||||
\(837\) | 1.55001e8i | 0.264337i | ||||||||
\(838\) | −3.64751e8 | + | 8.48496e8i | −0.619819 | + | 1.44184i | ||||
\(839\) | 2.36009e8i | 0.399615i | 0.979835 | + | 0.199808i | \(0.0640317\pi\) | ||||
−0.979835 | + | 0.199808i | \(0.935968\pi\) | |||||||
\(840\) | −2.67646e7 | + | 2.29550e8i | −0.0451568 | + | 0.387293i | ||||
\(841\) | 6.60984e7 | 0.111123 | ||||||||
\(842\) | 3.89005e8 | + | 1.67225e8i | 0.651656 | + | 0.280134i | ||||
\(843\) | −3.52056e8 | −0.587664 | ||||||||
\(844\) | −1.24141e8 | + | 1.17708e8i | −0.206485 | + | 0.195784i | ||||
\(845\) | 2.14322e8 | + | 1.08566e8i | 0.355219 | + | 0.179939i | ||||
\(846\) | 1.33972e8 | + | 5.75917e7i | 0.221260 | + | 0.0951150i | ||||
\(847\) | 6.47408e7 | 0.106544 | ||||||||
\(848\) | 3.34829e8 | + | 1.78261e7i | 0.549079 | + | 0.0292327i | ||||
\(849\) | −2.89658e8 | −0.473328 | ||||||||
\(850\) | −9.21713e8 | + | 2.12939e8i | −1.50086 | + | 0.346735i | ||||
\(851\) | 9.55614e8i | 1.55058i | ||||||||
\(852\) | −3.25506e8 | + | 3.08637e8i | −0.526307 | + | 0.499033i | ||||
\(853\) | 5.07471e8i | 0.817643i | 0.912614 | + | 0.408822i | \(0.134060\pi\) | ||||
−0.912614 | + | 0.408822i | \(0.865940\pi\) | |||||||
\(854\) | −2.86098e8 | − | 1.22988e8i | −0.459347 | − | 0.197464i | ||||
\(855\) | −7.63835e7 | + | 1.50790e8i | −0.122209 | + | 0.241253i | ||||
\(856\) | 3.68953e8 | + | 1.00201e9i | 0.588234 | + | 1.59754i | ||||
\(857\) | − | 2.68589e8i | − | 0.426723i | −0.976973 | − | 0.213362i | \(-0.931559\pi\) | ||
0.976973 | − | 0.213362i | \(-0.0684412\pi\) | |||||||
\(858\) | −2.79651e8 | − | 1.20216e8i | −0.442746 | − | 0.190328i | ||||
\(859\) | 2.24279e8i | 0.353841i | 0.984225 | + | 0.176921i | \(0.0566136\pi\) | ||||
−0.984225 | + | 0.176921i | \(0.943386\pi\) | |||||||
\(860\) | 1.33436e8 | + | 4.47277e8i | 0.209787 | + | 0.703204i | ||||
\(861\) | 3.83732e8 | 0.601199 | ||||||||
\(862\) | 4.05970e8 | − | 9.44380e8i | 0.633828 | − | 1.47443i | ||||
\(863\) | −9.56622e8 | −1.48836 | −0.744180 | − | 0.667979i | \(-0.767160\pi\) | ||||
−0.744180 | + | 0.667979i | \(0.767160\pi\) | |||||||
\(864\) | 5.50145e7 | − | 1.11267e8i | 0.0852974 | − | 0.172515i | ||||
\(865\) | −2.90084e8 | + | 5.72659e8i | −0.448204 | + | 0.884806i | ||||
\(866\) | −3.33605e8 | + | 7.76043e8i | −0.513664 | + | 1.19490i | ||||
\(867\) | 5.16537e8 | 0.792582 | ||||||||
\(868\) | −4.40215e8 | + | 4.17402e8i | −0.673140 | + | 0.638256i | ||||
\(869\) | −9.29730e8 | −1.41676 | ||||||||
\(870\) | −2.56920e8 | − | 3.07564e8i | −0.390158 | − | 0.467066i | ||||
\(871\) | 6.28137e7i | 0.0950604i | ||||||||
\(872\) | −2.80101e8 | − | 7.60703e8i | −0.422440 | − | 1.14727i | ||||
\(873\) | 9.38937e7i | 0.141122i | ||||||||
\(874\) | 2.54393e8 | − | 5.91778e8i | 0.381041 | − | 0.886389i | ||||
\(875\) | −7.39381e7 | − | 4.46353e8i | −0.110368 | − | 0.666276i | ||||
\(876\) | 4.23600e7 | − | 4.01648e7i | 0.0630150 | − | 0.0597493i | ||||
\(877\) | − | 5.67108e8i | − | 0.840750i | −0.907350 | − | 0.420375i | \(-0.861899\pi\) | ||
0.907350 | − | 0.420375i | \(-0.138101\pi\) | |||||||
\(878\) | 1.25178e8 | − | 2.91193e8i | 0.184945 | − | 0.430226i | ||||
\(879\) | − | 3.76413e8i | − | 0.554240i | ||||||
\(880\) | −6.35581e8 | − | 3.65657e8i | −0.932659 | − | 0.536569i | ||||
\(881\) | 8.13435e8 | 1.18958 | 0.594792 | − | 0.803880i | \(-0.297234\pi\) | ||||
0.594792 | + | 0.803880i | \(0.297234\pi\) | |||||||
\(882\) | −1.14282e8 | − | 4.91275e7i | −0.166561 | − | 0.0716010i | ||||
\(883\) | 1.02540e9 | 1.48940 | 0.744701 | − | 0.667399i | \(-0.232592\pi\) | ||||
0.744701 | + | 0.667399i | \(0.232592\pi\) | |||||||
\(884\) | 5.67986e8 | + | 5.99029e8i | 0.822206 | + | 0.867144i | ||||
\(885\) | −1.75773e8 | + | 3.46997e8i | −0.253585 | + | 0.500605i | ||||
\(886\) | −8.10301e8 | − | 3.48332e8i | −1.16505 | − | 0.500832i | ||||
\(887\) | 1.83308e8 | 0.262670 | 0.131335 | − | 0.991338i | \(-0.458074\pi\) | ||||
0.131335 | + | 0.991338i | \(0.458074\pi\) | |||||||
\(888\) | −4.94663e8 | + | 1.82141e8i | −0.706433 | + | 0.260118i | ||||
\(889\) | −3.25408e8 | −0.463151 | ||||||||
\(890\) | −1.83905e8 | − | 2.20157e8i | −0.260870 | − | 0.312293i | ||||
\(891\) | 8.45668e7i | 0.119555i | ||||||||
\(892\) | 3.87024e8 | + | 4.08177e8i | 0.545310 | + | 0.575114i | ||||
\(893\) | 4.17439e8i | 0.586190i | ||||||||
\(894\) | 6.13421e8 | + | 2.63697e8i | 0.858512 | + | 0.369057i | ||||
\(895\) | −4.00967e8 | + | 7.91555e8i | −0.559294 | + | 1.10411i | ||||
\(896\) | 4.64156e8 | − | 1.43386e8i | 0.645267 | − | 0.199335i | ||||
\(897\) | − | 3.84413e8i | − | 0.532624i | ||||||
\(898\) | 7.78232e8 | + | 3.34546e8i | 1.07468 | + | 0.461984i | ||||
\(899\) | − | 1.05196e9i | − | 1.44784i | ||||||
\(900\) | −4.32543e7 | + | 2.39119e8i | −0.0593337 | + | 0.328010i | ||||
\(901\) | 6.19518e8 | 0.846993 | ||||||||
\(902\) | −4.80840e8 | + | 1.11855e9i | −0.655211 | + | 1.52417i | ||||
\(903\) | 2.10683e8 | 0.286132 | ||||||||
\(904\) | −1.11860e8 | + | 4.11883e7i | −0.151415 | + | 0.0557531i | ||||
\(905\) | 1.05528e9 | + | 5.34561e8i | 1.42372 | + | 0.721193i | ||||
\(906\) | −3.51005e7 | + | 8.16519e7i | −0.0471985 | + | 0.109795i | ||||
\(907\) | −1.14784e9 | −1.53836 | −0.769182 | − | 0.639030i | \(-0.779336\pi\) | ||||
−0.769182 | + | 0.639030i | \(0.779336\pi\) | |||||||
\(908\) | −8.46726e7 | − | 8.93004e7i | −0.113106 | − | 0.119288i | ||||
\(909\) | −2.14200e8 | −0.285186 | ||||||||
\(910\) | −3.03000e8 | + | 2.53108e8i | −0.402085 | + | 0.335878i | ||||
\(911\) | 2.52530e8i | 0.334009i | 0.985956 | + | 0.167004i | \(0.0534094\pi\) | ||||
−0.985956 | + | 0.167004i | \(0.946591\pi\) | |||||||
\(912\) | 3.54815e8 | + | 1.88902e7i | 0.467754 | + | 0.0249030i | ||||
\(913\) | 6.48414e8i | 0.852001i | ||||||||
\(914\) | 3.11479e8 | − | 7.24573e8i | 0.407934 | − | 0.948951i | ||||
\(915\) | −2.92102e8 | − | 1.47966e8i | −0.381304 | − | 0.193152i | ||||
\(916\) | −8.28959e8 | − | 8.74266e8i | −1.07857 | − | 1.13752i | ||||
\(917\) | − | 2.82921e8i | − | 0.366908i | ||||||
\(918\) | 9.05735e7 | − | 2.10695e8i | 0.117077 | − | 0.272349i | ||||
\(919\) | 5.45123e8i | 0.702341i | 0.936312 | + | 0.351170i | \(0.114216\pi\) | ||||
−0.936312 | + | 0.351170i | \(0.885784\pi\) | |||||||
\(920\) | 1.07243e8 | − | 9.19781e8i | 0.137723 | − | 1.18119i | ||||
\(921\) | 6.43377e8 | 0.823544 | ||||||||
\(922\) | −1.61747e7 | − | 6.95318e6i | −0.0206369 | − | 0.00887137i | ||||
\(923\) | −7.66303e8 | −0.974531 | ||||||||
\(924\) | −2.40176e8 | + | 2.27729e8i | −0.304448 | + | 0.288671i | ||||
\(925\) | 8.32006e8 | − | 6.10508e8i | 1.05124 | − | 0.771376i | ||||
\(926\) | −3.75438e8 | − | 1.61393e8i | −0.472830 | − | 0.203260i | ||||
\(927\) | 4.29176e6 | 0.00538762 | ||||||||
\(928\) | −3.73373e8 | + | 7.55150e8i | −0.467195 | + | 0.944908i | ||||
\(929\) | 1.22712e9 | 1.53052 | 0.765260 | − | 0.643721i | \(-0.222610\pi\) | ||||
0.765260 | + | 0.643721i | \(0.222610\pi\) | |||||||
\(930\) | −4.89538e8 | + | 4.08930e8i | −0.608608 | + | 0.508394i | ||||
\(931\) | − | 3.56088e8i | − | 0.441274i | ||||||
\(932\) | 4.47933e8 | − | 4.24720e8i | 0.553306 | − | 0.524632i | ||||
\(933\) | − | 2.71921e8i | − | 0.334810i | ||||||
\(934\) | 5.37613e8 | + | 2.31109e8i | 0.659825 | + | 0.283645i | ||||
\(935\) | −1.20858e9 | − | 6.12214e8i | −1.47857 | − | 0.748977i | ||||
\(936\) | 1.98987e8 | − | 7.32697e7i | 0.242660 | − | 0.0893505i | ||||
\(937\) | − | 4.83356e8i | − | 0.587555i | −0.955874 | − | 0.293777i | \(-0.905088\pi\) | ||
0.955874 | − | 0.293777i | \(-0.0949124\pi\) | |||||||
\(938\) | 6.27466e7 | + | 2.69735e7i | 0.0760294 | + | 0.0326835i | ||||
\(939\) | − | 8.28480e8i | − | 1.00066i | ||||||
\(940\) | 1.71558e8 | + | 5.75062e8i | 0.206552 | + | 0.692359i | ||||
\(941\) | 1.12016e8 | 0.134434 | 0.0672171 | − | 0.997738i | \(-0.478588\pi\) | ||||
0.0672171 | + | 0.997738i | \(0.478588\pi\) | |||||||
\(942\) | −1.04593e8 | + | 2.43307e8i | −0.125126 | + | 0.291073i | ||||
\(943\) | −1.53757e9 | −1.83358 | ||||||||
\(944\) | 8.16499e8 | + | 4.34699e7i | 0.970599 | + | 0.0516741i | ||||
\(945\) | 9.78469e7 | + | 4.95650e7i | 0.115945 | + | 0.0587327i | ||||
\(946\) | −2.64000e8 | + | 6.14125e8i | −0.311839 | + | 0.725409i | ||||
\(947\) | 7.57557e8 | 0.892002 | 0.446001 | − | 0.895033i | \(-0.352848\pi\) | ||||
0.446001 | + | 0.895033i | \(0.352848\pi\) | |||||||
\(948\) | 4.69987e8 | − | 4.45631e8i | 0.551646 | − | 0.523058i | ||||
\(949\) | 9.97237e7 | 0.116681 | ||||||||
\(950\) | −6.77755e8 | + | 1.56578e8i | −0.790501 | + | 0.182625i | ||||
\(951\) | − | 2.86928e8i | − | 0.333604i | ||||||
\(952\) | 8.42294e8 | − | 3.10144e8i | 0.976232 | − | 0.359461i | ||||
\(953\) | 2.90721e8i | 0.335890i | 0.985796 | + | 0.167945i | \(0.0537132\pi\) | ||||
−0.985796 | + | 0.167945i | \(0.946287\pi\) | |||||||
\(954\) | 6.28490e7 | − | 1.46201e8i | 0.0723858 | − | 0.168386i | ||||
\(955\) | 6.70172e8 | − | 1.32300e9i | 0.769443 | − | 1.51897i | ||||
\(956\) | −7.21319e8 | + | 6.83938e8i | −0.825570 | + | 0.782786i | ||||
\(957\) | − | 5.73939e8i | − | 0.654832i | ||||||
\(958\) | −4.66702e7 | + | 1.08566e8i | −0.0530815 | + | 0.123480i | ||||
\(959\) | 9.43404e8i | 1.06965i | ||||||||
\(960\) | 4.96556e8 | − | 1.19799e8i | 0.561247 | − | 0.135406i | ||||
\(961\) | −7.86865e8 | −0.886605 | ||||||||
\(962\) | −8.27317e8 | − | 3.55647e8i | −0.929281 | − | 0.399479i | ||||
\(963\) | 5.06778e8 | 0.567464 | ||||||||
\(964\) | −8.50790e8 | − | 8.97290e8i | −0.949710 | − | 1.00162i | ||||
\(965\) | 2.99029e8 | − | 5.90316e8i | 0.332760 | − | 0.656905i | ||||
\(966\) | −3.84003e8 | − | 1.65075e8i | −0.425993 | − | 0.183126i | ||||
\(967\) | 9.09459e8 | 1.00578 | 0.502891 | − | 0.864350i | \(-0.332270\pi\) | ||||
0.502891 | + | 0.864350i | \(0.332270\pi\) | |||||||
\(968\) | −4.94438e7 | − | 1.34281e8i | −0.0545112 | − | 0.148043i | ||||
\(969\) | 6.56498e8 | 0.721543 | ||||||||
\(970\) | −2.96543e8 | + | 2.47714e8i | −0.324917 | + | 0.271416i | ||||
\(971\) | − | 7.89210e8i | − | 0.862054i | −0.902339 | − | 0.431027i | \(-0.858151\pi\) | ||
0.902339 | − | 0.431027i | \(-0.141849\pi\) | |||||||
\(972\) | −4.05339e7 | − | 4.27493e7i | −0.0441387 | − | 0.0465511i | ||||
\(973\) | − | 4.21664e8i | − | 0.457749i | ||||||
\(974\) | −5.91716e7 | − | 2.54367e7i | −0.0640378 | − | 0.0275285i | ||||
\(975\) | −3.34690e8 | + | 2.45588e8i | −0.361101 | + | 0.264968i | ||||
\(976\) | −3.65930e7 | + | 6.87330e8i | −0.0393595 | + | 0.739292i | ||||
\(977\) | − | 1.59895e9i | − | 1.71455i | −0.514860 | − | 0.857274i | \(-0.672156\pi\) | ||
0.514860 | − | 0.857274i | \(-0.327844\pi\) | |||||||
\(978\) | 5.54160e8 | + | 2.38222e8i | 0.592405 | + | 0.254663i | ||||
\(979\) | − | 4.10829e8i | − | 0.437838i | ||||||
\(980\) | −1.46345e8 | − | 4.90546e8i | −0.155489 | − | 0.521197i | ||||
\(981\) | −3.84734e8 | −0.407524 | ||||||||
\(982\) | 4.19293e8 | − | 9.75373e8i | 0.442775 | − | 1.03000i | ||||
\(983\) | 7.59315e8 | 0.799395 | 0.399697 | − | 0.916647i | \(-0.369115\pi\) | ||||
0.399697 | + | 0.916647i | \(0.369115\pi\) | |||||||
\(984\) | −2.93064e8 | − | 7.95908e8i | −0.307593 | − | 0.835367i | ||||
\(985\) | 3.14551e8 | − | 6.20959e8i | 0.329141 | − | 0.649762i | ||||
\(986\) | −6.14705e8 | + | 1.42995e9i | −0.641262 | + | 1.49173i | ||||
\(987\) | 2.70874e8 | 0.281719 | ||||||||
\(988\) | 4.17652e8 | + | 4.40479e8i | 0.433056 | + | 0.456725i | ||||
\(989\) | −8.44186e8 | −0.872668 | ||||||||
\(990\) | −2.67086e8 | + | 2.23107e8i | −0.275262 | + | 0.229937i | ||||
\(991\) | 1.41221e9i | 1.45104i | 0.688203 | + | 0.725518i | \(0.258400\pi\) | ||||
−0.688203 | + | 0.725518i | \(0.741600\pi\) | |||||||
\(992\) | 1.20194e9 | + | 5.94283e8i | 1.23126 | + | 0.608777i | ||||
\(993\) | − | 6.01009e8i | − | 0.613809i | ||||||
\(994\) | −3.29066e8 | + | 7.65485e8i | −0.335061 | + | 0.779430i | ||||
\(995\) | 3.75031e8 | − | 7.40353e8i | 0.380713 | − | 0.751570i | ||||
\(996\) | −3.10793e8 | − | 3.27779e8i | −0.314552 | − | 0.331744i | ||||
\(997\) | 1.62418e8i | 0.163889i | 0.996637 | + | 0.0819443i | \(0.0261130\pi\) | ||||
−0.996637 | + | 0.0819443i | \(0.973887\pi\) | |||||||
\(998\) | −2.28145e8 | + | 5.30719e8i | −0.229520 | + | 0.533916i | ||||
\(999\) | 2.50181e8i | 0.250933i |
(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 | 60.7.f.a.19.32 | yes | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.5 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.6 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.5 | ✓ | 36 | |
12.11 | even | 2 | 180.7.f.g.19.31 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.32 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.31 | yes | 36 | |
60.59 | even | 2 | 180.7.f.g.19.6 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.5 | ✓ | 36 | 5.4 | even | 2 | inner | |
60.7.f.a.19.6 | yes | 36 | 4.3 | odd | 2 | inner | |
60.7.f.a.19.31 | yes | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.32 | yes | 36 | 1.1 | even | 1 | trivial | |
180.7.f.g.19.5 | 36 | 3.2 | odd | 2 | |||
180.7.f.g.19.6 | 36 | 60.59 | even | 2 | |||
180.7.f.g.19.31 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.32 | 36 | 15.14 | odd | 2 |