Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 6.2 | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.6.c.a.36.2 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.23558 | −1.63263 | −0.816317 | − | 0.577603i | \(-0.803988\pi\) | ||||
−0.816317 | + | 0.577603i | \(0.803988\pi\) | |||||||
\(3\) | −13.7527 | + | 23.8204i | −0.882239 | + | 1.52808i | −0.0333926 | + | 0.999442i | \(0.510631\pi\) |
−0.848846 | + | 0.528640i | \(0.822702\pi\) | |||||||
\(4\) | 53.2959 | 1.66550 | ||||||||
\(5\) | 45.8176 | − | 79.3585i | 0.819611 | − | 1.41961i | −0.0863585 | − | 0.996264i | \(-0.527523\pi\) |
0.905969 | − | 0.423343i | \(-0.139144\pi\) | |||||||
\(6\) | 127.015 | − | 219.996i | 1.44037 | − | 2.49480i | ||||
\(7\) | 101.216 | + | 175.312i | 0.780739 | + | 1.35228i | 0.931512 | + | 0.363712i | \(0.118491\pi\) |
−0.150772 | + | 0.988569i | \(0.548176\pi\) | |||||||
\(8\) | −196.680 | −1.08651 | ||||||||
\(9\) | −256.776 | − | 444.749i | −1.05669 | − | 1.83024i | ||||
\(10\) | −423.152 | + | 732.921i | −1.33813 | + | 2.31770i | ||||
\(11\) | 347.169 | 0.865086 | 0.432543 | − | 0.901613i | \(-0.357616\pi\) | ||||
0.432543 | + | 0.901613i | \(0.357616\pi\) | |||||||
\(12\) | −732.965 | + | 1269.53i | −1.46937 | + | 2.54502i | ||||
\(13\) | 76.3181 | + | 132.187i | 0.125247 | + | 0.216935i | 0.921830 | − | 0.387595i | \(-0.126694\pi\) |
−0.796582 | + | 0.604530i | \(0.793361\pi\) | |||||||
\(14\) | −934.793 | − | 1619.11i | −1.27466 | − | 2.20778i | ||||
\(15\) | 1260.24 | + | 2182.79i | 1.44618 | + | 2.50487i | ||||
\(16\) | 110.984 | 0.108383 | ||||||||
\(17\) | 402.815 | + | 697.696i | 0.338052 | + | 0.585523i | 0.984066 | − | 0.177802i | \(-0.0568988\pi\) |
−0.646014 | + | 0.763325i | \(0.723565\pi\) | |||||||
\(18\) | 2371.47 | + | 4107.51i | 1.72519 | + | 2.98812i | ||||
\(19\) | 243.857 | − | 422.373i | 0.154971 | − | 0.268418i | −0.778077 | − | 0.628169i | \(-0.783805\pi\) |
0.933049 | + | 0.359750i | \(0.117138\pi\) | |||||||
\(20\) | 2441.89 | − | 4229.48i | 1.36506 | − | 2.36435i | ||||
\(21\) | −5568.02 | −2.75519 | ||||||||
\(22\) | −3206.31 | −1.41237 | ||||||||
\(23\) | −423.851 | + | 734.131i | −0.167068 | + | 0.289370i | −0.937388 | − | 0.348288i | \(-0.886763\pi\) |
0.770320 | + | 0.637658i | \(0.220097\pi\) | |||||||
\(24\) | 2704.89 | − | 4685.00i | 0.958564 | − | 1.66028i | ||||
\(25\) | −2636.01 | − | 4565.71i | −0.843524 | − | 1.46103i | ||||
\(26\) | −704.841 | − | 1220.82i | −0.204483 | − | 0.354176i | ||||
\(27\) | 7441.65 | 1.96454 | ||||||||
\(28\) | 5394.42 | + | 9343.42i | 1.30032 | + | 2.25222i | ||||
\(29\) | 2694.73 | + | 4667.41i | 0.595005 | + | 1.03058i | 0.993546 | + | 0.113428i | \(0.0361833\pi\) |
−0.398541 | + | 0.917150i | \(0.630483\pi\) | |||||||
\(30\) | −11639.0 | − | 20159.4i | −2.36109 | − | 4.08953i | ||||
\(31\) | −3286.24 | + | 5691.93i | −0.614179 | + | 1.06379i | 0.376349 | + | 0.926478i | \(0.377179\pi\) |
−0.990528 | + | 0.137311i | \(0.956154\pi\) | |||||||
\(32\) | 5268.75 | 0.909564 | ||||||||
\(33\) | −4774.53 | + | 8269.72i | −0.763213 | + | 1.32192i | ||||
\(34\) | −3720.23 | − | 6443.63i | −0.551915 | − | 0.955945i | ||||
\(35\) | 18550.0 | 2.55961 | ||||||||
\(36\) | −13685.1 | − | 23703.3i | −1.75991 | − | 3.04826i | ||||
\(37\) | 475.250 | − | 823.157i | 0.0570713 | − | 0.0988504i | −0.836078 | − | 0.548610i | \(-0.815157\pi\) |
0.893150 | + | 0.449760i | \(0.148490\pi\) | |||||||
\(38\) | −2252.16 | + | 3900.86i | −0.253012 | + | 0.438229i | ||||
\(39\) | −4198.33 | −0.441993 | ||||||||
\(40\) | −9011.41 | + | 15608.2i | −0.890518 | + | 1.54242i | ||||
\(41\) | 1744.19 | 0.162045 | 0.0810223 | − | 0.996712i | \(-0.474181\pi\) | ||||
0.0810223 | + | 0.996712i | \(0.474181\pi\) | |||||||
\(42\) | 51423.8 | 4.49823 | ||||||||
\(43\) | 9971.46 | + | 6897.72i | 0.822408 | + | 0.568898i | ||||
\(44\) | 18502.7 | 1.44080 | ||||||||
\(45\) | −47059.4 | −3.46430 | ||||||||
\(46\) | 3914.51 | − | 6780.12i | 0.272761 | − | 0.472436i | ||||
\(47\) | −17088.8 | −1.12841 | −0.564205 | − | 0.825635i | \(-0.690817\pi\) | ||||
−0.564205 | + | 0.825635i | \(0.690817\pi\) | |||||||
\(48\) | −1526.34 | + | 2643.70i | −0.0956198 | + | 0.165618i | ||||
\(49\) | −12086.1 | + | 20933.7i | −0.719108 | + | 1.24553i | ||||
\(50\) | 24345.1 | + | 42166.9i | 1.37717 | + | 2.38532i | ||||
\(51\) | −22159.2 | −1.19297 | ||||||||
\(52\) | 4067.44 | + | 7045.01i | 0.208599 | + | 0.361305i | ||||
\(53\) | −4576.75 | + | 7927.17i | −0.223804 | + | 0.387640i | −0.955960 | − | 0.293497i | \(-0.905181\pi\) |
0.732156 | + | 0.681137i | \(0.238514\pi\) | |||||||
\(54\) | −68727.9 | −3.20737 | ||||||||
\(55\) | 15906.5 | − | 27550.8i | 0.709034 | − | 1.22808i | ||||
\(56\) | −19907.3 | − | 34480.4i | −0.848284 | − | 1.46927i | ||||
\(57\) | 6707.41 | + | 11617.6i | 0.273444 | + | 0.473618i | ||||
\(58\) | −24887.4 | − | 43106.3i | −0.971426 | − | 1.68256i | ||||
\(59\) | 25046.0 | 0.936718 | 0.468359 | − | 0.883538i | \(-0.344845\pi\) | ||||
0.468359 | + | 0.883538i | \(0.344845\pi\) | |||||||
\(60\) | 67165.4 | + | 116334.i | 2.40862 | + | 4.17185i | ||||
\(61\) | 14625.9 | + | 25332.7i | 0.503265 | + | 0.871681i | 0.999993 | + | 0.00377430i | \(0.00120140\pi\) |
−0.496728 | + | 0.867906i | \(0.665465\pi\) | |||||||
\(62\) | 30350.3 | − | 52568.3i | 1.00273 | − | 1.73678i | ||||
\(63\) | 51979.9 | − | 90031.8i | 1.65000 | − | 2.85788i | ||||
\(64\) | −52211.5 | −1.59337 | ||||||||
\(65\) | 13986.9 | 0.410617 | ||||||||
\(66\) | 44095.5 | − | 76375.7i | 1.24605 | − | 2.15822i | ||||
\(67\) | −32809.4 | + | 56827.6i | −0.892919 | + | 1.54658i | −0.0565589 | + | 0.998399i | \(0.518013\pi\) |
−0.836360 | + | 0.548181i | \(0.815320\pi\) | |||||||
\(68\) | 21468.4 | + | 37184.3i | 0.563024 | + | 0.975187i | ||||
\(69\) | −11658.2 | − | 20192.6i | −0.294788 | − | 0.510587i | ||||
\(70\) | −171320. | −4.17891 | ||||||||
\(71\) | −22456.3 | − | 38895.5i | −0.528680 | − | 0.915700i | −0.999441 | − | 0.0334395i | \(-0.989354\pi\) |
0.470761 | − | 0.882261i | \(-0.343979\pi\) | |||||||
\(72\) | 50502.6 | + | 87473.2i | 1.14811 | + | 1.98858i | ||||
\(73\) | −21527.7 | − | 37287.0i | −0.472813 | − | 0.818937i | 0.526703 | − | 0.850050i | \(-0.323428\pi\) |
−0.999516 | + | 0.0311130i | \(0.990095\pi\) | |||||||
\(74\) | −4389.21 | + | 7602.33i | −0.0931766 | + | 0.161387i | ||||
\(75\) | 145010. | 2.97676 | ||||||||
\(76\) | 12996.6 | − | 22510.8i | 0.258105 | − | 0.447050i | ||||
\(77\) | 35139.2 | + | 60862.9i | 0.675407 | + | 1.16984i | ||||
\(78\) | 38774.0 | 0.721613 | ||||||||
\(79\) | 29093.3 | + | 50391.1i | 0.524475 | + | 0.908418i | 0.999594 | + | 0.0284961i | \(0.00907183\pi\) |
−0.475119 | + | 0.879922i | \(0.657595\pi\) | |||||||
\(80\) | 5085.04 | − | 8807.55i | 0.0888320 | − | 0.153861i | ||||
\(81\) | −39946.6 | + | 69189.5i | −0.676499 | + | 1.17173i | ||||
\(82\) | −16108.6 | −0.264560 | ||||||||
\(83\) | 14985.1 | − | 25955.0i | 0.238762 | − | 0.413548i | −0.721597 | − | 0.692313i | \(-0.756592\pi\) |
0.960359 | + | 0.278765i | \(0.0899250\pi\) | |||||||
\(84\) | −296752. | −4.58877 | ||||||||
\(85\) | 73824.1 | 1.10828 | ||||||||
\(86\) | −92092.2 | − | 63704.4i | −1.34269 | − | 0.928802i | ||||
\(87\) | −148240. | −2.09975 | ||||||||
\(88\) | −68281.2 | −0.939928 | ||||||||
\(89\) | 25478.4 | − | 44129.9i | 0.340956 | − | 0.590552i | −0.643655 | − | 0.765316i | \(-0.722583\pi\) |
0.984610 | + | 0.174764i | \(0.0559161\pi\) | |||||||
\(90\) | 434621. | 5.65594 | ||||||||
\(91\) | −15449.3 | + | 26759.0i | −0.195571 | + | 0.338739i | ||||
\(92\) | −22589.5 | + | 39126.2i | −0.278251 | + | 0.481945i | ||||
\(93\) | −90389.6 | − | 156559.i | −1.08370 | − | 1.87703i | ||||
\(94\) | 157825. | 1.84228 | ||||||||
\(95\) | −22345.9 | − | 38704.3i | −0.254033 | − | 0.439997i | ||||
\(96\) | −72459.8 | + | 125504.i | −0.802452 | + | 1.38989i | ||||
\(97\) | 64261.3 | 0.693458 | 0.346729 | − | 0.937965i | \(-0.387292\pi\) | ||||
0.346729 | + | 0.937965i | \(0.387292\pi\) | |||||||
\(98\) | 111622. | − | 193334.i | 1.17404 | − | 2.03350i | ||||
\(99\) | −89144.6 | − | 154403.i | −0.914128 | − | 1.58332i | ||||
\(100\) | −140489. | − | 243333.i | −1.40489 | − | 2.43333i | ||||
\(101\) | −58529.0 | − | 101375.i | −0.570910 | − | 0.988846i | −0.996473 | − | 0.0839166i | \(-0.973257\pi\) |
0.425563 | − | 0.904929i | \(-0.360076\pi\) | |||||||
\(102\) | 204653. | 1.94768 | ||||||||
\(103\) | 73244.1 | + | 126863.i | 0.680267 | + | 1.17826i | 0.974899 | + | 0.222647i | \(0.0714697\pi\) |
−0.294632 | + | 0.955611i | \(0.595197\pi\) | |||||||
\(104\) | −15010.2 | − | 25998.5i | −0.136083 | − | 0.235703i | ||||
\(105\) | −255113. | + | 441869.i | −2.25819 | + | 3.91129i | ||||
\(106\) | 42269.0 | − | 73212.0i | 0.365390 | − | 0.632874i | ||||
\(107\) | −31253.7 | −0.263901 | −0.131951 | − | 0.991256i | \(-0.542124\pi\) | ||||
−0.131951 | + | 0.991256i | \(0.542124\pi\) | |||||||
\(108\) | 396609. | 3.27193 | ||||||||
\(109\) | 27884.2 | − | 48296.9i | 0.224798 | − | 0.389361i | −0.731461 | − | 0.681883i | \(-0.761161\pi\) |
0.956259 | + | 0.292522i | \(0.0944945\pi\) | |||||||
\(110\) | −146905. | + | 254448.i | −1.15759 | + | 2.00501i | ||||
\(111\) | 13072.0 | + | 22641.3i | 0.100701 | + | 0.174419i | ||||
\(112\) | 11233.4 | + | 19456.9i | 0.0846190 | + | 0.146564i | ||||
\(113\) | 247692. | 1.82480 | 0.912400 | − | 0.409300i | \(-0.134227\pi\) | ||||
0.912400 | + | 0.409300i | \(0.134227\pi\) | |||||||
\(114\) | −61946.8 | − | 107295.i | −0.446434 | − | 0.773246i | ||||
\(115\) | 38839.7 | + | 67272.3i | 0.273861 | + | 0.474342i | ||||
\(116\) | 143618. | + | 248754.i | 0.990979 | + | 1.71643i | ||||
\(117\) | 39193.3 | − | 67884.7i | 0.264696 | − | 0.458466i | ||||
\(118\) | −231314. | −1.52932 | ||||||||
\(119\) | −81543.0 | + | 141237.i | −0.527861 | + | 0.914282i | ||||
\(120\) | −247863. | − | 429312.i | −1.57130 | − | 2.72157i | ||||
\(121\) | −40524.6 | −0.251626 | ||||||||
\(122\) | −135078. | − | 233962.i | −0.821648 | − | 1.42314i | ||||
\(123\) | −23987.4 | + | 41547.4i | −0.142962 | + | 0.247618i | ||||
\(124\) | −175143. | + | 303357.i | −1.02291 | + | 1.77174i | ||||
\(125\) | −196743. | −1.12622 | ||||||||
\(126\) | −480064. | + | 831496.i | −2.69385 | + | 4.66588i | ||||
\(127\) | 186698. | 1.02714 | 0.513571 | − | 0.858047i | \(-0.328322\pi\) | ||||
0.513571 | + | 0.858047i | \(0.328322\pi\) | |||||||
\(128\) | 313603. | 1.69183 | ||||||||
\(129\) | −301442. | + | 142662.i | −1.59488 | + | 0.754804i | ||||
\(130\) | −129177. | −0.670387 | ||||||||
\(131\) | 66197.8 | 0.337028 | 0.168514 | − | 0.985699i | \(-0.446103\pi\) | ||||
0.168514 | + | 0.985699i | \(0.446103\pi\) | |||||||
\(132\) | −254463. | + | 440742.i | −1.27113 | + | 2.20166i | ||||
\(133\) | 98729.5 | 0.483969 | ||||||||
\(134\) | 303014. | − | 524836.i | 1.45781 | − | 2.52500i | ||||
\(135\) | 340959. | − | 590558.i | 1.61015 | − | 2.78887i | ||||
\(136\) | −79225.6 | − | 137223.i | −0.367298 | − | 0.636179i | ||||
\(137\) | −108271. | −0.492847 | −0.246424 | − | 0.969162i | \(-0.579255\pi\) | ||||
−0.246424 | + | 0.969162i | \(0.579255\pi\) | |||||||
\(138\) | 107670. | + | 186491.i | 0.481281 | + | 0.833603i | ||||
\(139\) | −104370. | + | 180775.i | −0.458184 | + | 0.793598i | −0.998865 | − | 0.0476294i | \(-0.984833\pi\) |
0.540681 | + | 0.841228i | \(0.318167\pi\) | |||||||
\(140\) | 988639. | 4.26302 | ||||||||
\(141\) | 235018. | − | 407063.i | 0.995527 | − | 1.72430i | ||||
\(142\) | 207397. | + | 359222.i | 0.863141 | + | 1.49500i | ||||
\(143\) | 26495.3 | + | 45891.2i | 0.108350 | + | 0.187667i | ||||
\(144\) | −28498.1 | − | 49360.1i | −0.114527 | − | 0.198367i | ||||
\(145\) | 493865. | 1.95069 | ||||||||
\(146\) | 198820. | + | 344367.i | 0.771931 | + | 1.33702i | ||||
\(147\) | −332433. | − | 575790.i | −1.26885 | − | 2.19771i | ||||
\(148\) | 25328.9 | − | 43870.9i | 0.0950521 | − | 0.164635i | ||||
\(149\) | −8200.14 | + | 14203.1i | −0.0302591 | + | 0.0524103i | −0.880758 | − | 0.473566i | \(-0.842967\pi\) |
0.850499 | + | 0.525976i | \(0.176300\pi\) | |||||||
\(150\) | −1.33925e6 | −4.85996 | ||||||||
\(151\) | −168879. | −0.602745 | −0.301372 | − | 0.953506i | \(-0.597445\pi\) | ||||
−0.301372 | + | 0.953506i | \(0.597445\pi\) | |||||||
\(152\) | −47961.8 | + | 83072.4i | −0.168379 | + | 0.291640i | ||||
\(153\) | 206866. | − | 358303.i | 0.714432 | − | 1.23743i | ||||
\(154\) | −324531. | − | 562104.i | −1.10269 | − | 1.90992i | ||||
\(155\) | 301135. | + | 521582.i | 1.00678 | + | 1.74379i | ||||
\(156\) | −223754. | −0.736137 | ||||||||
\(157\) | 97192.4 | + | 168342.i | 0.314690 | + | 0.545059i | 0.979372 | − | 0.202068i | \(-0.0647661\pi\) |
−0.664682 | + | 0.747127i | \(0.731433\pi\) | |||||||
\(158\) | −268693. | − | 465390.i | −0.856277 | − | 1.48311i | ||||
\(159\) | −125886. | − | 218041.i | −0.394897 | − | 0.683982i | ||||
\(160\) | 241402. | − | 418120.i | 0.745488 | − | 1.29122i | ||||
\(161\) | −171603. | −0.521746 | ||||||||
\(162\) | 368930. | − | 639005.i | 1.10448 | − | 1.91301i | ||||
\(163\) | −324963. | − | 562853.i | −0.958000 | − | 1.65930i | −0.727348 | − | 0.686268i | \(-0.759248\pi\) |
−0.230652 | − | 0.973036i | \(-0.574086\pi\) | |||||||
\(164\) | 92958.3 | 0.269885 | ||||||||
\(165\) | 437515. | + | 757798.i | 1.25107 | + | 2.16692i | ||||
\(166\) | −138396. | + | 239710.i | −0.389811 | + | 0.675173i | ||||
\(167\) | −174486. | + | 302218.i | −0.484138 | + | 0.838551i | −0.999834 | − | 0.0182202i | \(-0.994200\pi\) |
0.515696 | + | 0.856772i | \(0.327533\pi\) | |||||||
\(168\) | 1.09512e6 | 2.99356 | ||||||||
\(169\) | 173998. | − | 301373.i | 0.468626 | − | 0.811684i | ||||
\(170\) | −681808. | −1.80942 | ||||||||
\(171\) | −250467. | −0.655027 | ||||||||
\(172\) | 531438. | + | 367620.i | 1.36972 | + | 0.947497i | ||||
\(173\) | −185844. | −0.472098 | −0.236049 | − | 0.971741i | \(-0.575853\pi\) | ||||
−0.236049 | + | 0.971741i | \(0.575853\pi\) | |||||||
\(174\) | 1.36908e6 | 3.42812 | ||||||||
\(175\) | 533616. | − | 924249.i | 1.31714 | − | 2.28136i | ||||
\(176\) | 38530.3 | 0.0937607 | ||||||||
\(177\) | −344451. | + | 596607.i | −0.826409 | + | 1.43138i | ||||
\(178\) | −235308. | + | 407566.i | −0.556656 | + | 0.964156i | ||||
\(179\) | −242542. | − | 420095.i | −0.565789 | − | 0.979975i | −0.996976 | − | 0.0777127i | \(-0.975238\pi\) |
0.431187 | − | 0.902263i | \(-0.358095\pi\) | |||||||
\(180\) | −2.50807e6 | −5.76978 | ||||||||
\(181\) | 22231.3 | + | 38505.8i | 0.0504393 | + | 0.0873635i | 0.890143 | − | 0.455682i | \(-0.150605\pi\) |
−0.839703 | + | 0.543045i | \(0.817271\pi\) | |||||||
\(182\) | 142683. | − | 247134.i | 0.319296 | − | 0.553038i | ||||
\(183\) | −804583. | −1.77600 | ||||||||
\(184\) | 83362.9 | − | 144389.i | 0.181522 | − | 0.314405i | ||||
\(185\) | −43549.7 | − | 75430.3i | −0.0935525 | − | 0.162038i | ||||
\(186\) | 834800. | + | 1.44592e6i | 1.76929 | + | 3.06451i | ||||
\(187\) | 139845. | + | 242218.i | 0.292444 | + | 0.506528i | ||||
\(188\) | −910763. | −1.87936 | ||||||||
\(189\) | 753218. | + | 1.30461e6i | 1.53379 | + | 2.65660i | ||||
\(190\) | 206378. | + | 357456.i | 0.414742 | + | 0.718355i | ||||
\(191\) | 247387. | − | 428488.i | 0.490675 | − | 0.849875i | −0.509267 | − | 0.860609i | \(-0.670083\pi\) |
0.999942 | + | 0.0107338i | \(0.00341674\pi\) | |||||||
\(192\) | 718051. | − | 1.24370e6i | 1.40573 | − | 2.43480i | ||||
\(193\) | −167788. | −0.324241 | −0.162121 | − | 0.986771i | \(-0.551833\pi\) | ||||
−0.162121 | + | 0.986771i | \(0.551833\pi\) | |||||||
\(194\) | −593490. | −1.13216 | ||||||||
\(195\) | −192358. | + | 333173.i | −0.362262 | + | 0.627456i | ||||
\(196\) | −644137. | + | 1.11568e6i | −1.19767 | + | 2.07443i | ||||
\(197\) | 97017.3 | + | 168039.i | 0.178108 | + | 0.308492i | 0.941233 | − | 0.337759i | \(-0.109669\pi\) |
−0.763124 | + | 0.646252i | \(0.776336\pi\) | |||||||
\(198\) | 823302. | + | 1.42600e6i | 1.49244 | + | 2.58498i | ||||
\(199\) | 991853. | 1.77547 | 0.887737 | − | 0.460350i | \(-0.152276\pi\) | ||||
0.887737 | + | 0.460350i | \(0.152276\pi\) | |||||||
\(200\) | 518451. | + | 897983.i | 0.916500 | + | 1.58742i | ||||
\(201\) | −902440. | − | 1.56307e6i | −1.57553 | − | 2.72891i | ||||
\(202\) | 540549. | + | 936259.i | 0.932088 | + | 1.61442i | ||||
\(203\) | −545503. | + | 944838.i | −0.929088 | + | 1.60923i | ||||
\(204\) | −1.18100e6 | −1.98689 | ||||||||
\(205\) | 79914.8 | − | 138416.i | 0.132814 | − | 0.230040i | ||||
\(206\) | −676452. | − | 1.17165e6i | −1.11063 | − | 1.92366i | ||||
\(207\) | 435338. | 0.706157 | ||||||||
\(208\) | 8470.11 | + | 14670.7i | 0.0135747 | + | 0.0235121i | ||||
\(209\) | 84659.7 | − | 146635.i | 0.134064 | − | 0.232205i | ||||
\(210\) | 2.35612e6 | − | 4.08092e6i | 3.68680 | − | 6.38572i | ||||
\(211\) | −686656. | −1.06178 | −0.530888 | − | 0.847442i | \(-0.678142\pi\) | ||||
−0.530888 | + | 0.847442i | \(0.678142\pi\) | |||||||
\(212\) | −243922. | + | 422486.i | −0.372745 | + | 0.645613i | ||||
\(213\) | 1.23534e6 | 1.86569 | ||||||||
\(214\) | 288646. | 0.430855 | ||||||||
\(215\) | 1.00426e6 | − | 475283.i | 1.48167 | − | 0.701222i | ||||
\(216\) | −1.46362e6 | −2.13449 | ||||||||
\(217\) | −1.33049e6 | −1.91806 | ||||||||
\(218\) | −257527. | + | 446050.i | −0.367013 | + | 0.635685i | ||||
\(219\) | 1.18426e6 | 1.66854 | ||||||||
\(220\) | 847750. | − | 1.46835e6i | 1.18089 | − | 2.04537i | ||||
\(221\) | −61484.1 | + | 106494.i | −0.0846803 | + | 0.146671i | ||||
\(222\) | −120727. | − | 209106.i | −0.164408 | − | 0.284763i | ||||
\(223\) | 624678. | 0.841190 | 0.420595 | − | 0.907249i | \(-0.361821\pi\) | ||||
0.420595 | + | 0.907249i | \(0.361821\pi\) | |||||||
\(224\) | 533285. | + | 923676.i | 0.710132 | + | 1.22998i | ||||
\(225\) | −1.35373e6 | + | 2.34473e6i | −1.78269 | + | 3.08770i | ||||
\(226\) | −2.28758e6 | −2.97923 | ||||||||
\(227\) | 134293. | − | 232602.i | 0.172977 | − | 0.299605i | −0.766482 | − | 0.642266i | \(-0.777995\pi\) |
0.939459 | + | 0.342660i | \(0.111328\pi\) | |||||||
\(228\) | 357478. | + | 619169.i | 0.455420 | + | 0.788810i | ||||
\(229\) | −172993. | − | 299632.i | −0.217991 | − | 0.377572i | 0.736202 | − | 0.676761i | \(-0.236617\pi\) |
−0.954194 | + | 0.299189i | \(0.903284\pi\) | |||||||
\(230\) | −358707. | − | 621298.i | −0.447116 | − | 0.774427i | ||||
\(231\) | −1.93304e6 | −2.38348 | ||||||||
\(232\) | −530000. | − | 917987.i | −0.646481 | − | 1.11974i | ||||
\(233\) | 195925. | + | 339353.i | 0.236429 | + | 0.409507i | 0.959687 | − | 0.281071i | \(-0.0906896\pi\) |
−0.723258 | + | 0.690578i | \(0.757356\pi\) | |||||||
\(234\) | −361972. | + | 626955.i | −0.432151 | + | 0.748508i | ||||
\(235\) | −782968. | + | 1.35614e6i | −0.924857 | + | 1.60190i | ||||
\(236\) | 1.33485e6 | 1.56010 | ||||||||
\(237\) | −1.60045e6 | −1.85085 | ||||||||
\(238\) | 753097. | − | 1.30440e6i | 0.861804 | − | 1.49269i | ||||
\(239\) | 118905. | − | 205949.i | 0.134650 | − | 0.233220i | −0.790814 | − | 0.612057i | \(-0.790342\pi\) |
0.925464 | + | 0.378837i | \(0.123676\pi\) | |||||||
\(240\) | 139866. | + | 242256.i | 0.156742 | + | 0.271485i | ||||
\(241\) | 76851.6 | + | 133111.i | 0.0852335 | + | 0.147629i | 0.905491 | − | 0.424366i | \(-0.139503\pi\) |
−0.820257 | + | 0.571995i | \(0.806170\pi\) | |||||||
\(242\) | 374268. | 0.410813 | ||||||||
\(243\) | −194589. | − | 337038.i | −0.211399 | − | 0.366154i | ||||
\(244\) | 779498. | + | 1.35013e6i | 0.838186 | + | 1.45178i | ||||
\(245\) | 1.10751e6 | + | 1.91826e6i | 1.17878 | + | 2.04170i | ||||
\(246\) | 221538. | − | 383715.i | 0.233405 | − | 0.404269i | ||||
\(247\) | 74442.9 | 0.0776391 | ||||||||
\(248\) | 646337. | − | 1.11949e6i | 0.667314 | − | 1.15582i | ||||
\(249\) | 412173. | + | 713905.i | 0.421290 | + | 0.729696i | ||||
\(250\) | 1.81704e6 | 1.83871 | ||||||||
\(251\) | −265646. | − | 460112.i | −0.266145 | − | 0.460977i | 0.701718 | − | 0.712455i | \(-0.252417\pi\) |
−0.967863 | + | 0.251478i | \(0.919083\pi\) | |||||||
\(252\) | 2.77031e6 | − | 4.79833e6i | 2.74807 | − | 4.75980i | ||||
\(253\) | −147148. | + | 254868.i | −0.144528 | + | 0.250330i | ||||
\(254\) | −1.72426e6 | −1.67695 | ||||||||
\(255\) | −1.01528e6 | + | 1.75852e6i | −0.977771 | + | 1.69355i | ||||
\(256\) | −1.22554e6 | −1.16876 | ||||||||
\(257\) | −1.22108e6 | −1.15322 | −0.576609 | − | 0.817020i | \(-0.695624\pi\) | ||||
−0.576609 | + | 0.817020i | \(0.695624\pi\) | |||||||
\(258\) | 2.78399e6 | − | 1.31757e6i | 2.60386 | − | 1.23232i | ||||
\(259\) | 192413. | 0.178231 | ||||||||
\(260\) | 745442. | 0.683881 | ||||||||
\(261\) | 1.38388e6 | − | 2.39696e6i | 1.25747 | − | 2.17801i | ||||
\(262\) | −611375. | −0.550243 | ||||||||
\(263\) | 549628. | − | 951984.i | 0.489982 | − | 0.848673i | −0.509952 | − | 0.860203i | \(-0.670337\pi\) |
0.999934 | + | 0.0115298i | \(0.00367013\pi\) | |||||||
\(264\) | 939054. | − | 1.62649e6i | 0.829241 | − | 1.43629i | ||||
\(265\) | 419392. | + | 726408.i | 0.366864 | + | 0.635428i | ||||
\(266\) | −911824. | −0.790145 | ||||||||
\(267\) | 700797. | + | 1.21382e6i | 0.601608 | + | 1.04202i | ||||
\(268\) | −1.74861e6 | + | 3.02868e6i | −1.48715 | + | 2.57582i | ||||
\(269\) | 1.55580e6 | 1.31091 | 0.655456 | − | 0.755233i | \(-0.272476\pi\) | ||||
0.655456 | + | 0.755233i | \(0.272476\pi\) | |||||||
\(270\) | −3.14895e6 | + | 5.45414e6i | −2.62879 | + | 4.55320i | ||||
\(271\) | −679050. | − | 1.17615e6i | −0.561666 | − | 0.972834i | −0.997351 | − | 0.0727353i | \(-0.976827\pi\) |
0.435685 | − | 0.900099i | \(-0.356506\pi\) | |||||||
\(272\) | 44706.1 | + | 77433.3i | 0.0366391 | + | 0.0634608i | ||||
\(273\) | −424940. | − | 736018.i | −0.345081 | − | 0.597698i | ||||
\(274\) | 999949. | 0.804639 | ||||||||
\(275\) | −915142. | − | 1.58507e6i | −0.729721 | − | 1.26391i | ||||
\(276\) | −621335. | − | 1.07618e6i | −0.490968 | − | 0.850382i | ||||
\(277\) | −368676. | + | 638565.i | −0.288699 | + | 0.500041i | −0.973499 | − | 0.228689i | \(-0.926556\pi\) |
0.684801 | + | 0.728731i | \(0.259889\pi\) | |||||||
\(278\) | 963920. | − | 1.66956e6i | 0.748048 | − | 1.29566i | ||||
\(279\) | 3.37531e6 | 2.59599 | ||||||||
\(280\) | −3.64841e6 | −2.78105 | ||||||||
\(281\) | −252939. | + | 438104.i | −0.191096 | + | 0.330987i | −0.945614 | − | 0.325292i | \(-0.894537\pi\) |
0.754518 | + | 0.656279i | \(0.227871\pi\) | |||||||
\(282\) | −2.17053e6 | + | 3.75946e6i | −1.62533 | + | 2.81516i | ||||
\(283\) | −848680. | − | 1.46996e6i | −0.629909 | − | 1.09103i | −0.987570 | − | 0.157183i | \(-0.949759\pi\) |
0.357661 | − | 0.933852i | \(-0.383574\pi\) | |||||||
\(284\) | −1.19683e6 | − | 2.07297e6i | −0.880515 | − | 1.52510i | ||||
\(285\) | 1.22927e6 | 0.896470 | ||||||||
\(286\) | −244699. | − | 423831.i | −0.176896 | − | 0.306392i | ||||
\(287\) | 176541. | + | 305778.i | 0.126515 | + | 0.219130i | ||||
\(288\) | −1.35289e6 | − | 2.34327e6i | −0.961127 | − | 1.66472i | ||||
\(289\) | 385409. | − | 667548.i | 0.271442 | − | 0.470151i | ||||
\(290\) | −4.56113e6 | −3.18476 | ||||||||
\(291\) | −883769. | + | 1.53073e6i | −0.611795 | + | 1.05966i | ||||
\(292\) | −1.14734e6 | − | 1.98724e6i | −0.787469 | − | 1.36394i | ||||
\(293\) | −1.98407e6 | −1.35017 | −0.675085 | − | 0.737740i | \(-0.735893\pi\) | ||||
−0.675085 | + | 0.737740i | \(0.735893\pi\) | |||||||
\(294\) | 3.07021e6 | + | 5.31776e6i | 2.07157 | + | 3.58806i | ||||
\(295\) | 1.14755e6 | − | 1.98761e6i | 0.767744 | − | 1.32977i | ||||
\(296\) | −93472.2 | + | 161899.i | −0.0620088 | + | 0.107402i | ||||
\(297\) | 2.58351e6 | 1.69949 | ||||||||
\(298\) | 75733.1 | − | 131174.i | 0.0494020 | − | 0.0855668i | ||||
\(299\) | −129390. | −0.0836994 | ||||||||
\(300\) | 7.72841e6 | 4.95778 | ||||||||
\(301\) | −199977. | + | 2.44628e6i | −0.127222 | + | 1.55629i | ||||
\(302\) | 1.55970e6 | 0.984063 | ||||||||
\(303\) | 3.21974e6 | 2.01472 | ||||||||
\(304\) | 27064.3 | − | 46876.8i | 0.0167963 | − | 0.0290920i | ||||
\(305\) | 2.68049e6 | 1.64993 | ||||||||
\(306\) | −1.91053e6 | + | 3.30913e6i | −1.16641 | + | 2.02028i | ||||
\(307\) | 789561. | − | 1.36756e6i | 0.478123 | − | 0.828134i | −0.521562 | − | 0.853213i | \(-0.674651\pi\) |
0.999685 | + | 0.0250797i | \(0.00798394\pi\) | |||||||
\(308\) | 1.87278e6 | + | 3.24375e6i | 1.12489 | + | 1.94836i | ||||
\(309\) | −4.02923e6 | −2.40063 | ||||||||
\(310\) | −2.78116e6 | − | 4.81711e6i | −1.64370 | − | 2.84697i | ||||
\(311\) | 1.26308e6 | − | 2.18773e6i | 0.740511 | − | 1.28260i | −0.211752 | − | 0.977323i | \(-0.567917\pi\) |
0.952263 | − | 0.305279i | \(-0.0987498\pi\) | |||||||
\(312\) | 825727. | 0.480231 | ||||||||
\(313\) | 191140. | − | 331064.i | 0.110278 | − | 0.191008i | −0.805604 | − | 0.592454i | \(-0.798159\pi\) |
0.915883 | + | 0.401446i | \(0.131492\pi\) | |||||||
\(314\) | −897628. | − | 1.55474e6i | −0.513774 | − | 0.889883i | ||||
\(315\) | −4.76319e6 | − | 8.25009e6i | −2.70472 | − | 4.68470i | ||||
\(316\) | 1.55055e6 | + | 2.68564e6i | 0.873512 | + | 1.51297i | ||||
\(317\) | −3.39213e6 | −1.89594 | −0.947968 | − | 0.318365i | \(-0.896866\pi\) | ||||
−0.947968 | + | 0.318365i | \(0.896866\pi\) | |||||||
\(318\) | 1.16263e6 | + | 2.01373e6i | 0.644723 | + | 1.11669i | ||||
\(319\) | 935528. | + | 1.62038e6i | 0.514731 | + | 0.891540i | ||||
\(320\) | −2.39221e6 | + | 4.14342e6i | −1.30594 | + | 2.26196i | ||||
\(321\) | 429824. | − | 744477.i | 0.232824 | − | 0.403263i | ||||
\(322\) | 1.58485e6 | 0.851821 | ||||||||
\(323\) | 392917. | 0.209554 | ||||||||
\(324\) | −2.12899e6 | + | 3.68752e6i | −1.12671 | + | 1.95151i | ||||
\(325\) | 402351. | − | 696892.i | 0.211298 | − | 0.365980i | ||||
\(326\) | 3.00123e6 | + | 5.19828e6i | 1.56406 | + | 2.70904i | ||||
\(327\) | 766969. | + | 1.32843e6i | 0.396651 | + | 0.687020i | ||||
\(328\) | −343048. | −0.176064 | ||||||||
\(329\) | −1.72967e6 | − | 2.99587e6i | −0.880994 | − | 1.52593i | ||||
\(330\) | −4.04070e6 | − | 6.99871e6i | −2.04255 | − | 3.53780i | ||||
\(331\) | 1.88917e6 | + | 3.27213e6i | 0.947765 | + | 1.64158i | 0.750119 | + | 0.661303i | \(0.229996\pi\) |
0.197646 | + | 0.980274i | \(0.436670\pi\) | |||||||
\(332\) | 798646. | − | 1.38330e6i | 0.397658 | − | 0.688763i | ||||
\(333\) | −488131. | −0.241227 | ||||||||
\(334\) | 1.61148e6 | − | 2.79116e6i | 0.790420 | − | 1.36905i | ||||
\(335\) | 3.00650e6 | + | 5.20741e6i | 1.46369 | + | 2.53519i | ||||
\(336\) | −617962. | −0.298617 | ||||||||
\(337\) | 14662.1 | + | 25395.5i | 0.00703269 | + | 0.0121810i | 0.869520 | − | 0.493897i | \(-0.164428\pi\) |
−0.862488 | + | 0.506078i | \(0.831095\pi\) | |||||||
\(338\) | −1.60697e6 | + | 2.78335e6i | −0.765095 | + | 1.32518i | ||||
\(339\) | −3.40644e6 | + | 5.90013e6i | −1.60991 | + | 2.78844i | ||||
\(340\) | 3.93452e6 | 1.84584 | ||||||||
\(341\) | −1.14088e6 | + | 1.97606e6i | −0.531318 | + | 0.920269i | ||||
\(342\) | 2.31320e6 | 1.06942 | ||||||||
\(343\) | −1.49094e6 | −0.684266 | ||||||||
\(344\) | −1.96119e6 | − | 1.35664e6i | −0.893558 | − | 0.618115i | ||||
\(345\) | −2.13661e6 | −0.966445 | ||||||||
\(346\) | 1.71637e6 | 0.770764 | ||||||||
\(347\) | 1.94984e6 | − | 3.37723e6i | 0.869312 | − | 1.50569i | 0.00661202 | − | 0.999978i | \(-0.497895\pi\) |
0.862700 | − | 0.505715i | \(-0.168771\pi\) | |||||||
\(348\) | −7.90057e6 | −3.49712 | ||||||||
\(349\) | 2.21991e6 | − | 3.84499e6i | 0.975599 | − | 1.68979i | 0.297653 | − | 0.954674i | \(-0.403796\pi\) |
0.677946 | − | 0.735112i | \(-0.262871\pi\) | |||||||
\(350\) | −4.92825e6 | + | 8.53598e6i | −2.15042 | + | 3.72463i | ||||
\(351\) | 567932. | + | 983688.i | 0.246053 | + | 0.426176i | ||||
\(352\) | 1.82915e6 | 0.786851 | ||||||||
\(353\) | −430050. | − | 744868.i | −0.183689 | − | 0.318158i | 0.759445 | − | 0.650571i | \(-0.225470\pi\) |
−0.943134 | + | 0.332413i | \(0.892137\pi\) | |||||||
\(354\) | 3.18121e6 | − | 5.51001e6i | 1.34922 | − | 2.33692i | ||||
\(355\) | −4.11558e6 | −1.73325 | ||||||||
\(356\) | 1.35790e6 | − | 2.35195e6i | 0.567860 | − | 0.983563i | ||||
\(357\) | −2.24288e6 | − | 3.88478e6i | −0.931398 | − | 1.61323i | ||||
\(358\) | 2.24002e6 | + | 3.87982e6i | 0.923727 | + | 1.59994i | ||||
\(359\) | −1.05032e6 | − | 1.81921e6i | −0.430116 | − | 0.744983i | 0.566767 | − | 0.823878i | \(-0.308194\pi\) |
−0.996883 | + | 0.0788951i | \(0.974861\pi\) | |||||||
\(360\) | 9.25565e6 | 3.76401 | ||||||||
\(361\) | 1.11912e6 | + | 1.93837e6i | 0.451968 | + | 0.782831i | ||||
\(362\) | −205319. | − | 355623.i | −0.0823490 | − | 0.142633i | ||||
\(363\) | 557324. | − | 965314.i | 0.221994 | − | 0.384505i | ||||
\(364\) | −823384. | + | 1.42614e6i | −0.325723 | + | 0.564169i | ||||
\(365\) | −3.94539e6 | −1.55009 | ||||||||
\(366\) | 7.43079e6 | 2.89956 | ||||||||
\(367\) | 131750. | − | 228198.i | 0.0510605 | − | 0.0884394i | −0.839365 | − | 0.543567i | \(-0.817073\pi\) |
0.890426 | + | 0.455128i | \(0.150407\pi\) | |||||||
\(368\) | −47040.8 | + | 81477.0i | −0.0181074 | + | 0.0313629i | ||||
\(369\) | −447866. | − | 775727.i | −0.171231 | − | 0.296581i | ||||
\(370\) | 402206. | + | 696642.i | 0.152737 | + | 0.264549i | ||||
\(371\) | −1.85297e6 | −0.698930 | ||||||||
\(372\) | −4.81739e6 | − | 8.34397e6i | −1.80491 | − | 3.12619i | ||||
\(373\) | 1.30613e6 | + | 2.26228e6i | 0.486088 | + | 0.841928i | 0.999872 | − | 0.0159908i | \(-0.00509024\pi\) |
−0.513784 | + | 0.857919i | \(0.671757\pi\) | |||||||
\(374\) | −1.29155e6 | − | 2.23703e6i | −0.477454 | − | 0.826975i | ||||
\(375\) | 2.70576e6 | − | 4.68651e6i | 0.993598 | − | 1.72096i | ||||
\(376\) | 3.36102e6 | 1.22603 | ||||||||
\(377\) | −411313. | + | 712416.i | −0.149046 | + | 0.258155i | ||||
\(378\) | −6.95640e6 | − | 1.20488e7i | −2.50412 | − | 4.33726i | ||||
\(379\) | 1.09438e6 | 0.391355 | 0.195677 | − | 0.980668i | \(-0.437309\pi\) | ||||
0.195677 | + | 0.980668i | \(0.437309\pi\) | |||||||
\(380\) | −1.19095e6 | − | 2.06278e6i | −0.423090 | − | 0.732814i | ||||
\(381\) | −2.56761e6 | + | 4.44723e6i | −0.906185 | + | 1.56956i | ||||
\(382\) | −2.28477e6 | + | 3.95733e6i | −0.801094 | + | 1.38754i | ||||
\(383\) | 4.50623e6 | 1.56970 | 0.784849 | − | 0.619687i | \(-0.212740\pi\) | ||||
0.784849 | + | 0.619687i | \(0.212740\pi\) | |||||||
\(384\) | −4.31290e6 | + | 7.47017e6i | −1.49259 | + | 2.58525i | ||||
\(385\) | 6.43999e6 | 2.21428 | ||||||||
\(386\) | 1.54962e6 | 0.529368 | ||||||||
\(387\) | 507321. | − | 6.20596e6i | 0.172189 | − | 2.10635i | ||||
\(388\) | 3.42486e6 | 1.15495 | ||||||||
\(389\) | 734765. | 0.246192 | 0.123096 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123096 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(390\) | 1.77653e6 | − | 3.07705e6i | 0.591442 | − | 1.02441i | ||||
\(391\) | −682933. | −0.225911 | ||||||||
\(392\) | 2.37708e6 | − | 4.11723e6i | 0.781321 | − | 1.35329i | ||||
\(393\) | −910401. | + | 1.57686e6i | −0.297339 | + | 0.515006i | ||||
\(394\) | −896011. | − | 1.55194e6i | −0.290785 | − | 0.503655i | ||||
\(395\) | 5.33194e6 | 1.71946 | ||||||||
\(396\) | −4.75104e6 | − | 8.22905e6i | −1.52248 | − | 2.63701i | ||||
\(397\) | −390667. | + | 676655.i | −0.124403 | + | 0.215472i | −0.921499 | − | 0.388380i | \(-0.873035\pi\) |
0.797097 | + | 0.603852i | \(0.206368\pi\) | |||||||
\(398\) | −9.16033e6 | −2.89870 | ||||||||
\(399\) | −1.35780e6 | + | 2.35178e6i | −0.426977 | + | 0.739545i | ||||
\(400\) | −292556. | − | 506722.i | −0.0914237 | − | 0.158351i | ||||
\(401\) | −504694. | − | 874156.i | −0.156736 | − | 0.271474i | 0.776954 | − | 0.629557i | \(-0.216764\pi\) |
−0.933690 | + | 0.358083i | \(0.883430\pi\) | |||||||
\(402\) | 8.33455e6 | + | 1.44359e7i | 2.57227 | + | 4.45531i | ||||
\(403\) | −1.00320e6 | −0.307697 | ||||||||
\(404\) | −3.11936e6 | − | 5.40289e6i | −0.950849 | − | 1.64692i | ||||
\(405\) | 3.66051e6 | + | 6.34020e6i | 1.10893 | + | 1.92073i | ||||
\(406\) | 5.03803e6 | − | 8.72613e6i | 1.51686 | − | 2.62728i | ||||
\(407\) | 164992. | − | 285775.i | 0.0493716 | − | 0.0855141i | ||||
\(408\) | 4.35828e6 | 1.29618 | ||||||||
\(409\) | 5.85172e6 | 1.72972 | 0.864859 | − | 0.502015i | \(-0.167408\pi\) | ||||
0.864859 | + | 0.502015i | \(0.167408\pi\) | |||||||
\(410\) | −738059. | + | 1.27836e6i | −0.216836 | + | 0.375571i | ||||
\(411\) | 1.48903e6 | − | 2.57907e6i | 0.434809 | − | 0.753111i | ||||
\(412\) | 3.90361e6 | + | 6.76125e6i | 1.13298 | + | 1.96238i | ||||
\(413\) | 2.53507e6 | + | 4.39087e6i | 0.731332 | + | 1.26670i | ||||
\(414\) | −4.02060e6 | −1.15290 | ||||||||
\(415\) | −1.37317e6 | − | 2.37840e6i | −0.391384 | − | 0.677897i | ||||
\(416\) | 402101. | + | 696460.i | 0.113921 | + | 0.197316i | ||||
\(417\) | −2.87076e6 | − | 4.97230e6i | −0.808456 | − | 1.40029i | ||||
\(418\) | −781881. | + | 1.35426e6i | −0.218877 | + | 0.379106i | ||||
\(419\) | −6.53392e6 | −1.81819 | −0.909094 | − | 0.416591i | \(-0.863225\pi\) | ||||
−0.909094 | + | 0.416591i | \(0.863225\pi\) | |||||||
\(420\) | −1.35965e7 | + | 2.35498e7i | −3.76100 | + | 6.51425i | ||||
\(421\) | −1.40920e6 | − | 2.44080e6i | −0.387495 | − | 0.671162i | 0.604617 | − | 0.796517i | \(-0.293326\pi\) |
−0.992112 | + | 0.125355i | \(0.959993\pi\) | |||||||
\(422\) | 6.34167e6 | 1.73349 | ||||||||
\(423\) | 4.38799e6 | + | 7.60022e6i | 1.19238 | + | 2.06526i | ||||
\(424\) | 900155. | − | 1.55912e6i | 0.243166 | − | 0.421176i | ||||
\(425\) | 2.12365e6 | − | 3.67827e6i | 0.570309 | − | 0.987805i | ||||
\(426\) | −1.14091e7 | −3.04599 | ||||||||
\(427\) | −2.96076e6 | + | 5.12818e6i | −0.785838 | + | 1.36111i | ||||
\(428\) | −1.66569e6 | −0.439527 | ||||||||
\(429\) | −1.45753e6 | −0.382362 | ||||||||
\(430\) | −9.27493e6 | + | 4.38951e6i | −2.41902 | + | 1.14484i | ||||
\(431\) | −5.78451e6 | −1.49994 | −0.749970 | − | 0.661472i | \(-0.769932\pi\) | ||||
−0.749970 | + | 0.661472i | \(0.769932\pi\) | |||||||
\(432\) | 825906. | 0.212922 | ||||||||
\(433\) | −45365.5 | + | 78575.4i | −0.0116280 | + | 0.0201403i | −0.871781 | − | 0.489896i | \(-0.837035\pi\) |
0.860153 | + | 0.510036i | \(0.170368\pi\) | |||||||
\(434\) | 1.22878e7 | 3.13148 | ||||||||
\(435\) | −6.79200e6 | + | 1.17641e7i | −1.72097 | + | 2.98081i | ||||
\(436\) | 1.48611e6 | − | 2.57403e6i | 0.374400 | − | 0.648480i | ||||
\(437\) | 206718. | + | 358046.i | 0.0517815 | + | 0.0896883i | ||||
\(438\) | −1.09373e7 | −2.72411 | ||||||||
\(439\) | −2.52784e6 | − | 4.37835e6i | −0.626020 | − | 1.08430i | −0.988343 | − | 0.152246i | \(-0.951349\pi\) |
0.362322 | − | 0.932053i | \(-0.381984\pi\) | |||||||
\(440\) | −3.12848e6 | + | 5.41869e6i | −0.770375 | + | 1.33433i | ||||
\(441\) | 1.24136e7 | 3.03950 | ||||||||
\(442\) | 567841. | − | 983530.i | 0.138252 | − | 0.239459i | ||||
\(443\) | 3.07968e6 | + | 5.33416e6i | 0.745583 | + | 1.29139i | 0.949922 | + | 0.312487i | \(0.101162\pi\) |
−0.204339 | + | 0.978900i | \(0.565505\pi\) | |||||||
\(444\) | 696683. | + | 1.20669e6i | 0.167717 | + | 0.290495i | ||||
\(445\) | −2.33472e6 | − | 4.04386e6i | −0.558902 | − | 0.968046i | ||||
\(446\) | −5.76926e6 | −1.37336 | ||||||||
\(447\) | −225549. | − | 390662.i | −0.0533915 | − | 0.0924767i | ||||
\(448\) | −5.28466e6 | − | 9.15331e6i | −1.24401 | − | 2.15468i | ||||
\(449\) | 1.01066e6 | − | 1.75051e6i | 0.236585 | − | 0.409778i | −0.723147 | − | 0.690694i | \(-0.757305\pi\) |
0.959732 | + | 0.280916i | \(0.0906384\pi\) | |||||||
\(450\) | 1.25025e7 | − | 2.16549e7i | 2.91048 | − | 5.04109i | ||||
\(451\) | 605530. | 0.140183 | ||||||||
\(452\) | 1.32009e7 | 3.03920 | ||||||||
\(453\) | 2.32255e6 | − | 4.02278e6i | 0.531765 | − | 0.921044i | ||||
\(454\) | −1.24027e6 | + | 2.14822e6i | −0.282409 | + | 0.489146i | ||||
\(455\) | 1.41570e6 | + | 2.45206e6i | 0.320585 | + | 0.555269i | ||||
\(456\) | −1.31921e6 | − | 2.28494e6i | −0.297100 | − | 0.514593i | ||||
\(457\) | 1.21074e6 | 0.271181 | 0.135590 | − | 0.990765i | \(-0.456707\pi\) | ||||
0.135590 | + | 0.990765i | \(0.456707\pi\) | |||||||
\(458\) | 1.59769e6 | + | 2.76728e6i | 0.355900 | + | 0.616437i | ||||
\(459\) | 2.99761e6 | + | 5.19201e6i | 0.664115 | + | 1.15028i | ||||
\(460\) | 2.07000e6 | + | 3.58534e6i | 0.456115 | + | 0.790015i | ||||
\(461\) | 2.08491e6 | − | 3.61116e6i | 0.456914 | − | 0.791398i | −0.541882 | − | 0.840454i | \(-0.682288\pi\) |
0.998796 | + | 0.0490565i | \(0.0156214\pi\) | |||||||
\(462\) | 1.78528e7 | 3.89135 | ||||||||
\(463\) | −3.57135e6 | + | 6.18577e6i | −0.774248 | + | 1.34104i | 0.160967 | + | 0.986960i | \(0.448539\pi\) |
−0.935216 | + | 0.354078i | \(0.884795\pi\) | |||||||
\(464\) | 299073. | + | 518010.i | 0.0644885 | + | 0.111697i | ||||
\(465\) | −1.65657e7 | −3.55287 | ||||||||
\(466\) | −1.80948e6 | − | 3.13412e6i | −0.386002 | − | 0.668576i | ||||
\(467\) | −699438. | + | 1.21146e6i | −0.148408 | + | 0.257050i | −0.930639 | − | 0.365938i | \(-0.880748\pi\) |
0.782231 | + | 0.622988i | \(0.214082\pi\) | |||||||
\(468\) | 2.08884e6 | − | 3.61798e6i | 0.440850 | − | 0.763574i | ||||
\(469\) | −1.32834e7 | −2.78855 | ||||||||
\(470\) | 7.23117e6 | − | 1.25247e7i | 1.50995 | − | 2.61532i | ||||
\(471\) | −5.34665e6 | −1.11053 | ||||||||
\(472\) | −4.92605e6 | −1.01776 | ||||||||
\(473\) | 3.46178e6 | + | 2.39467e6i | 0.711454 | + | 0.492145i | ||||
\(474\) | 1.47811e7 | 3.02176 | ||||||||
\(475\) | −2.57124e6 | −0.522888 | ||||||||
\(476\) | −4.34591e6 | + | 7.52733e6i | −0.879151 | + | 1.52273i | ||||
\(477\) | 4.70080e6 | 0.945966 | ||||||||
\(478\) | −1.09816e6 | + | 1.90206e6i | −0.219834 | + | 0.380763i | ||||
\(479\) | −1.07764e6 | + | 1.86653e6i | −0.214602 | + | 0.371702i | −0.953149 | − | 0.302500i | \(-0.902179\pi\) |
0.738547 | + | 0.674202i | \(0.235512\pi\) | |||||||
\(480\) | 6.63988e6 | + | 1.15006e7i | 1.31540 | + | 2.27833i | ||||
\(481\) | 145081. | 0.0285922 | ||||||||
\(482\) | −709769. | − | 1.22936e6i | −0.139155 | − | 0.241024i | ||||
\(483\) | 2.36001e6 | − | 4.08765e6i | 0.460305 | − | 0.797271i | ||||
\(484\) | −2.15980e6 | −0.419082 | ||||||||
\(485\) | 2.94430e6 | − | 5.09968e6i | 0.568366 | − | 0.984438i | ||||
\(486\) | 1.79714e6 | + | 3.11274e6i | 0.345137 | + | 0.597796i | ||||
\(487\) | −1.92960e6 | − | 3.34217e6i | −0.368676 | − | 0.638566i | 0.620682 | − | 0.784062i | \(-0.286856\pi\) |
−0.989359 | + | 0.145496i | \(0.953522\pi\) | |||||||
\(488\) | −2.87661e6 | − | 4.98244e6i | −0.546804 | − | 0.947093i | ||||
\(489\) | 1.78766e7 | 3.38074 | ||||||||
\(490\) | −1.02285e7 | − | 1.77163e7i | −1.92451 | − | 3.33336i | ||||
\(491\) | 3.68314e6 | + | 6.37938e6i | 0.689468 | + | 1.19419i | 0.972010 | + | 0.234939i | \(0.0754891\pi\) |
−0.282542 | + | 0.959255i | \(0.591178\pi\) | |||||||
\(492\) | −1.27843e6 | + | 2.21431e6i | −0.238103 | + | 0.412406i | ||||
\(493\) | −2.17096e6 | + | 3.76021e6i | −0.402285 | + | 0.696778i | ||||
\(494\) | −687523. | −0.126756 | ||||||||
\(495\) | −1.63376e7 | −2.99692 | ||||||||
\(496\) | −364721. | + | 631715.i | −0.0665666 | + | 0.115297i | ||||
\(497\) | 4.54590e6 | − | 7.87373e6i | 0.825522 | − | 1.42985i | ||||
\(498\) | −3.80666e6 | − | 6.59333e6i | −0.687814 | − | 1.19133i | ||||
\(499\) | 141295. | + | 244730.i | 0.0254024 | + | 0.0439983i | 0.878447 | − | 0.477840i | \(-0.158580\pi\) |
−0.853045 | + | 0.521838i | \(0.825247\pi\) | |||||||
\(500\) | −1.04856e7 | −1.87572 | ||||||||
\(501\) | −4.79932e6 | − | 8.31266e6i | −0.854250 | − | 1.47961i | ||||
\(502\) | 2.45339e6 | + | 4.24940e6i | 0.434518 | + | 0.752606i | ||||
\(503\) | −909570. | − | 1.57542e6i | −0.160294 | − | 0.277637i | 0.774680 | − | 0.632353i | \(-0.217911\pi\) |
−0.934974 | + | 0.354716i | \(0.884577\pi\) | |||||||
\(504\) | −1.02234e7 | + | 1.77074e7i | −1.79275 | + | 3.10513i | ||||
\(505\) | −1.07266e7 | −1.87170 | ||||||||
\(506\) | 1.35900e6 | − | 2.35385e6i | 0.235962 | − | 0.408698i | ||||
\(507\) | 4.78589e6 | + | 8.28940e6i | 0.826880 | + | 1.43220i | ||||
\(508\) | 9.95024e6 | 1.71070 | ||||||||
\(509\) | −3.86992e6 | − | 6.70290e6i | −0.662076 | − | 1.14675i | −0.980069 | − | 0.198656i | \(-0.936342\pi\) |
0.317993 | − | 0.948093i | \(-0.396991\pi\) | |||||||
\(510\) | 9.37673e6 | − | 1.62410e7i | 1.59634 | − | 2.76495i | ||||
\(511\) | 4.35791e6 | − | 7.54812e6i | 0.738288 | − | 1.27875i | ||||
\(512\) | 1.28326e6 | 0.216341 | ||||||||
\(513\) | 1.81470e6 | − | 3.14315e6i | 0.304447 | − | 0.527317i | ||||
\(514\) | 1.12774e7 | 1.88278 | ||||||||
\(515\) | 1.34235e7 | 2.23022 | ||||||||
\(516\) | −1.60656e7 | + | 7.60330e6i | −2.65627 | + | 1.25712i | ||||
\(517\) | −5.93270e6 | −0.976172 | ||||||||
\(518\) | −1.77704e6 | −0.290987 | ||||||||
\(519\) | 2.55586e6 | − | 4.42688e6i | 0.416503 | − | 0.721405i | ||||
\(520\) | −2.75093e6 | −0.446141 | ||||||||
\(521\) | 3.01404e6 | − | 5.22047e6i | 0.486468 | − | 0.842588i | −0.513411 | − | 0.858143i | \(-0.671618\pi\) |
0.999879 | + | 0.0155553i | \(0.00495162\pi\) | |||||||
\(522\) | −1.27810e7 | + | 2.21373e7i | −2.05299 | + | 3.55589i | ||||
\(523\) | −832996. | − | 1.44279e6i | −0.133165 | − | 0.230648i | 0.791730 | − | 0.610871i | \(-0.209181\pi\) |
−0.924895 | + | 0.380223i | \(0.875847\pi\) | |||||||
\(524\) | 3.52807e6 | 0.561318 | ||||||||
\(525\) | 1.46774e7 | + | 2.54219e7i | 2.32407 | + | 4.02541i | ||||
\(526\) | −5.07614e6 | + | 8.79213e6i | −0.799961 | + | 1.38557i | ||||
\(527\) | −5.29499e6 | −0.830497 | ||||||||
\(528\) | −529898. | + | 917810.i | −0.0827194 | + | 0.143274i | ||||
\(529\) | 2.85887e6 | + | 4.95171e6i | 0.444177 | + | 0.769336i | ||||
\(530\) | −3.87333e6 | − | 6.70880e6i | −0.598955 | − | 1.03742i | ||||
\(531\) | −6.43121e6 | − | 1.11392e7i | −0.989820 | − | 1.71442i | ||||
\(532\) | 5.26188e6 | 0.806049 | ||||||||
\(533\) | 133113. | + | 230559.i | 0.0202957 | + | 0.0351531i | ||||
\(534\) | −6.47226e6 | − | 1.12103e7i | −0.982207 | − | 1.70123i | ||||
\(535\) | −1.43197e6 | + | 2.48024e6i | −0.216296 | + | 0.374637i | ||||
\(536\) | 6.45296e6 | − | 1.11769e7i | 0.970168 | − | 1.68038i | ||||
\(537\) | 1.33425e7 | 1.99664 | ||||||||
\(538\) | −1.43687e7 | −2.14024 | ||||||||
\(539\) | −4.19590e6 | + | 7.26752e6i | −0.622091 | + | 1.07749i | ||||
\(540\) | 1.81717e7 | − | 3.14743e7i | 2.68171 | − | 4.64485i | ||||
\(541\) | 2.57621e6 | + | 4.46212e6i | 0.378432 | + | 0.655463i | 0.990834 | − | 0.135083i | \(-0.0431301\pi\) |
−0.612402 | + | 0.790546i | \(0.709797\pi\) | |||||||
\(542\) | 6.27142e6 | + | 1.08624e7i | 0.916996 | + | 1.58828i | ||||
\(543\) | −1.22297e6 | −0.177998 | ||||||||
\(544\) | 2.12233e6 | + | 3.67599e6i | 0.307480 | + | 0.532570i | ||||
\(545\) | −2.55518e6 | − | 4.42570e6i | −0.368494 | − | 0.638250i | ||||
\(546\) | 3.92457e6 | + | 6.79755e6i | 0.563391 | + | 0.975823i | ||||
\(547\) | −4.54011e6 | + | 7.86371e6i | −0.648781 | + | 1.12372i | 0.334633 | + | 0.942349i | \(0.391388\pi\) |
−0.983414 | + | 0.181374i | \(0.941946\pi\) | |||||||
\(548\) | −5.77042e6 | −0.820835 | ||||||||
\(549\) | 7.51113e6 | − | 1.30097e7i | 1.06359 | − | 1.84219i | ||||
\(550\) | 8.45186e6 | + | 1.46391e7i | 1.19137 | + | 2.06351i | ||||
\(551\) | 2.62852e6 | 0.368835 | ||||||||
\(552\) | 2.29294e6 | + | 3.97148e6i | 0.320291 | + | 0.554760i | ||||
\(553\) | −5.88944e6 | + | 1.02008e7i | −0.818957 | + | 1.41848i | ||||
\(554\) | 3.40493e6 | − | 5.89752e6i | 0.471340 | − | 0.816385i | ||||
\(555\) | 2.39571e6 | 0.330143 | ||||||||
\(556\) | −5.56251e6 | + | 9.63455e6i | −0.763104 | + | 1.32174i | ||||
\(557\) | −7.26413e6 | −0.992077 | −0.496039 | − | 0.868301i | \(-0.665213\pi\) | ||||
−0.496039 | + | 0.868301i | \(0.665213\pi\) | |||||||
\(558\) | −3.11729e7 | −4.23830 | ||||||||
\(559\) | −150784. | + | 1.84451e6i | −0.0204092 | + | 0.249662i | ||||
\(560\) | 2.05876e6 | 0.277419 | ||||||||
\(561\) | −7.69300e6 | −1.03202 | ||||||||
\(562\) | 2.33604e6 | − | 4.04614e6i | 0.311989 | − | 0.540381i | ||||
\(563\) | −2.03394e6 | −0.270437 | −0.135219 | − | 0.990816i | \(-0.543174\pi\) | ||||
−0.135219 | + | 0.990816i | \(0.543174\pi\) | |||||||
\(564\) | 1.25255e7 | − | 2.16948e7i | 1.65805 | − | 2.87182i | ||||
\(565\) | 1.13486e7 | − | 1.96564e7i | 1.49563 | − | 2.59050i | ||||
\(566\) | 7.83805e6 | + | 1.35759e7i | 1.02841 | + | 1.78126i | ||||
\(567\) | −1.61730e7 | −2.11268 | ||||||||
\(568\) | 4.41671e6 | + | 7.64996e6i | 0.574418 | + | 0.994921i | ||||
\(569\) | 1.86061e6 | − | 3.22266e6i | 0.240921 | − | 0.417287i | −0.720056 | − | 0.693916i | \(-0.755884\pi\) |
0.960977 | + | 0.276629i | \(0.0892174\pi\) | |||||||
\(570\) | −1.13530e7 | −1.46361 | ||||||||
\(571\) | −45318.4 | + | 78493.8i | −0.00581680 | + | 0.0100750i | −0.868919 | − | 0.494954i | \(-0.835185\pi\) |
0.863102 | + | 0.505029i | \(0.168518\pi\) | |||||||
\(572\) | 1.41209e6 | + | 2.44581e6i | 0.180456 | + | 0.312560i | ||||
\(573\) | 6.80451e6 | + | 1.17858e7i | 0.865786 | + | 1.49958i | ||||
\(574\) | −1.63046e6 | − | 2.82404e6i | −0.206552 | − | 0.357759i | ||||
\(575\) | 4.46910e6 | 0.563703 | ||||||||
\(576\) | 1.34066e7 | + | 2.32210e7i | 1.68370 | + | 2.91625i | ||||
\(577\) | −7.12981e6 | − | 1.23492e7i | −0.891535 | − | 1.54418i | −0.838035 | − | 0.545616i | \(-0.816296\pi\) |
−0.0535001 | − | 0.998568i | \(-0.517038\pi\) | |||||||
\(578\) | −3.55947e6 | + | 6.16519e6i | −0.443166 | + | 0.767585i | ||||
\(579\) | 2.30755e6 | − | 3.99679e6i | 0.286058 | − | 0.495467i | ||||
\(580\) | 2.63210e7 | 3.24887 | ||||||||
\(581\) | 6.06697e6 | 0.745644 | ||||||||
\(582\) | 8.16212e6 | − | 1.41372e7i | 0.998838 | − | 1.73004i | ||||
\(583\) | −1.58891e6 | + | 2.75207e6i | −0.193610 | + | 0.335342i | ||||
\(584\) | 4.23406e6 | + | 7.33361e6i | 0.513718 | + | 0.889786i | ||||
\(585\) | −3.59148e6 | − | 6.22063e6i | −0.433895 | − | 0.751528i | ||||
\(586\) | 1.83240e7 | 2.20433 | ||||||||
\(587\) | 2.94718e6 | + | 5.10466e6i | 0.353030 | + | 0.611465i | 0.986779 | − | 0.162073i | \(-0.0518181\pi\) |
−0.633749 | + | 0.773539i | \(0.718485\pi\) | |||||||
\(588\) | −1.77173e7 | − | 3.06873e7i | −2.11327 | − | 3.66028i | ||||
\(589\) | 1.60275e6 | + | 2.77604e6i | 0.190360 | + | 0.329714i | ||||
\(590\) | −1.05983e7 | + | 1.83568e7i | −1.25345 | + | 2.17103i | ||||
\(591\) | −5.33702e6 | −0.628535 | ||||||||
\(592\) | 52745.3 | − | 91357.6i | 0.00618557 | − | 0.0107137i | ||||
\(593\) | 1.52732e6 | + | 2.64540e6i | 0.178358 | + | 0.308926i | 0.941318 | − | 0.337520i | \(-0.109588\pi\) |
−0.762960 | + | 0.646446i | \(0.776255\pi\) | |||||||
\(594\) | −2.38602e7 | −2.77465 | ||||||||
\(595\) | 7.47222e6 | + | 1.29423e7i | 0.865281 | + | 1.49871i | ||||
\(596\) | −437034. | + | 756965.i | −0.0503964 | + | 0.0872891i | ||||
\(597\) | −1.36407e7 | + | 2.36264e7i | −1.56639 | + | 2.71307i | ||||
\(598\) | 1.19499e6 | 0.136651 | ||||||||
\(599\) | 5.87761e6 | − | 1.01803e7i | 0.669320 | − | 1.15930i | −0.308774 | − | 0.951135i | \(-0.599919\pi\) |
0.978095 | − | 0.208161i | \(-0.0667479\pi\) | |||||||
\(600\) | −2.85205e7 | −3.23429 | ||||||||
\(601\) | −1.39098e7 | −1.57085 | −0.785425 | − | 0.618957i | \(-0.787556\pi\) | ||||
−0.785425 | + | 0.618957i | \(0.787556\pi\) | |||||||
\(602\) | 1.84690e6 | − | 2.25928e7i | 0.207708 | − | 2.54085i | ||||
\(603\) | 3.36987e7 | 3.77415 | ||||||||
\(604\) | −9.00057e6 | −1.00387 | ||||||||
\(605\) | −1.85674e6 | + | 3.21597e6i | −0.206235 | + | 0.357210i | ||||
\(606\) | −2.97361e7 | −3.28930 | ||||||||
\(607\) | 1.73786e6 | − | 3.01006e6i | 0.191444 | − | 0.331591i | −0.754285 | − | 0.656547i | \(-0.772016\pi\) |
0.945729 | + | 0.324956i | \(0.105349\pi\) | |||||||
\(608\) | 1.28482e6 | − | 2.22538e6i | 0.140956 | − | 0.244144i | ||||
\(609\) | −1.50043e7 | − | 2.59882e7i | −1.63935 | − | 2.83944i | ||||
\(610\) | −2.47559e7 | −2.69373 | ||||||||
\(611\) | −1.30418e6 | − | 2.25891e6i | −0.141330 | − | 0.244792i | ||||
\(612\) | 1.10251e7 | − | 1.90961e7i | 1.18988 | − | 2.06094i | ||||
\(613\) | 1.29598e6 | 0.139299 | 0.0696493 | − | 0.997572i | \(-0.477812\pi\) | ||||
0.0696493 | + | 0.997572i | \(0.477812\pi\) | |||||||
\(614\) | −7.29205e6 | + | 1.26302e7i | −0.780600 | + | 1.35204i | ||||
\(615\) | 2.19809e6 | + | 3.80721e6i | 0.234346 | + | 0.405900i | ||||
\(616\) | −6.91118e6 | − | 1.19705e7i | −0.733839 | − | 1.27105i | ||||
\(617\) | −4.60498e6 | − | 7.97606e6i | −0.486984 | − | 0.843481i | 0.512904 | − | 0.858446i | \(-0.328570\pi\) |
−0.999888 | + | 0.0149647i | \(0.995236\pi\) | |||||||
\(618\) | 3.72123e7 | 3.91936 | ||||||||
\(619\) | −4.10084e6 | − | 7.10287e6i | −0.430176 | − | 0.745087i | 0.566712 | − | 0.823916i | \(-0.308215\pi\) |
−0.996888 | + | 0.0788287i | \(0.974882\pi\) | |||||||
\(620\) | 1.60493e7 | + | 2.77982e7i | 1.67678 | + | 2.90427i | ||||
\(621\) | −3.15415e6 | + | 5.46314e6i | −0.328211 | + | 0.568478i | ||||
\(622\) | −1.16653e7 | + | 2.02049e7i | −1.20898 | + | 2.09402i | ||||
\(623\) | 1.03153e7 | 1.06479 | ||||||||
\(624\) | −465949. | −0.0479045 | ||||||||
\(625\) | −776766. | + | 1.34540e6i | −0.0795408 | + | 0.137769i | ||||
\(626\) | −1.76529e6 | + | 3.05757e6i | −0.180045 | + | 0.311846i | ||||
\(627\) | 2.32861e6 | + | 4.03326e6i | 0.236552 | + | 0.409721i | ||||
\(628\) | 5.17995e6 | + | 8.97195e6i | 0.524115 | + | 0.907794i | ||||
\(629\) | 765751. | 0.0771723 | ||||||||
\(630\) | 4.39908e7 | + | 7.61943e7i | 4.41581 | + | 7.64841i | ||||
\(631\) | 4.47109e6 | + | 7.74415e6i | 0.447033 | + | 0.774284i | 0.998191 | − | 0.0601168i | \(-0.0191473\pi\) |
−0.551158 | + | 0.834401i | \(0.685814\pi\) | |||||||
\(632\) | −5.72207e6 | − | 9.91091e6i | −0.569850 | − | 0.987008i | ||||
\(633\) | 9.44341e6 | − | 1.63565e7i | 0.936741 | − | 1.62248i | ||||
\(634\) | 3.13282e7 | 3.09537 | ||||||||
\(635\) | 8.55407e6 | − | 1.48161e7i | 0.841857 | − | 1.45814i | ||||
\(636\) | −6.70920e6 | − | 1.16207e7i | −0.657700 | − | 1.13917i | ||||
\(637\) | −3.68954e6 | −0.360266 | ||||||||
\(638\) | −8.64014e6 | − | 1.49652e7i | −0.840367 | − | 1.45556i | ||||
\(639\) | −1.15325e7 | + | 1.99748e7i | −1.11730 | + | 1.93522i | ||||
\(640\) | 1.43686e7 | − | 2.48871e7i | 1.38664 | − | 2.40173i | ||||
\(641\) | −5.87305e6 | −0.564571 | −0.282285 | − | 0.959330i | \(-0.591092\pi\) | ||||
−0.282285 | + | 0.959330i | \(0.591092\pi\) | |||||||
\(642\) | −3.96967e6 | + | 6.87567e6i | −0.380117 | + | 0.658382i | ||||
\(643\) | −1.02881e7 | −0.981316 | −0.490658 | − | 0.871352i | \(-0.663244\pi\) | ||||
−0.490658 | + | 0.871352i | \(0.663244\pi\) | |||||||
\(644\) | −9.14572e6 | −0.868967 | ||||||||
\(645\) | −2.48989e6 | + | 3.04584e7i | −0.235658 | + | 2.88275i | ||||
\(646\) | −3.62882e6 | −0.342124 | ||||||||
\(647\) | −1.21099e7 | −1.13731 | −0.568657 | − | 0.822575i | \(-0.692537\pi\) | ||||
−0.568657 | + | 0.822575i | \(0.692537\pi\) | |||||||
\(648\) | 7.85669e6 | − | 1.36082e7i | 0.735025 | − | 1.27310i | ||||
\(649\) | 8.69520e6 | 0.810341 | ||||||||
\(650\) | −3.71594e6 | + | 6.43620e6i | −0.344973 | + | 0.597511i | ||||
\(651\) | 1.82978e7 | − | 3.16928e7i | 1.69218 | − | 2.93095i | ||||
\(652\) | −1.73192e7 | − | 2.99978e7i | −1.59555 | − | 2.76357i | ||||
\(653\) | 5.54353e6 | 0.508749 | 0.254374 | − | 0.967106i | \(-0.418130\pi\) | ||||
0.254374 | + | 0.967106i | \(0.418130\pi\) | |||||||
\(654\) | −7.08340e6 | − | 1.22688e7i | −0.647586 | − | 1.12165i | ||||
\(655\) | 3.03303e6 | − | 5.25336e6i | 0.276231 | − | 0.478447i | ||||
\(656\) | 193578. | 0.0175629 | ||||||||
\(657\) | −1.10556e7 | + | 1.91488e7i | −0.999234 | + | 1.73072i | ||||
\(658\) | 1.59745e7 | + | 2.76686e7i | 1.43834 | + | 2.49128i | ||||
\(659\) | 9.04906e6 | + | 1.56734e7i | 0.811690 | + | 1.40589i | 0.911681 | + | 0.410899i | \(0.134785\pi\) |
−0.0999912 | + | 0.994988i | \(0.531881\pi\) | |||||||
\(660\) | 2.33178e7 | + | 4.03875e7i | 2.08366 | + | 3.60901i | ||||
\(661\) | −5.39770e6 | −0.480513 | −0.240256 | − | 0.970709i | \(-0.577232\pi\) | ||||
−0.240256 | + | 0.970709i | \(0.577232\pi\) | |||||||
\(662\) | −1.74476e7 | − | 3.02201e7i | −1.54735 | − | 2.68010i | ||||
\(663\) | −1.69115e6 | − | 2.92916e6i | −0.149416 | − | 0.258797i | ||||
\(664\) | −2.94728e6 | + | 5.10483e6i | −0.259418 | + | 0.449326i | ||||
\(665\) | 4.52355e6 | − | 7.83502e6i | 0.396667 | − | 0.687047i | ||||
\(666\) | 4.50817e6 | 0.393835 | ||||||||
\(667\) | −4.56866e6 | −0.397625 | ||||||||
\(668\) | −9.29938e6 | + | 1.61070e7i | −0.806330 | + | 1.39660i | ||||
\(669\) | −8.59103e6 | + | 1.48801e7i | −0.742130 | + | 1.28541i | ||||
\(670\) | −2.77668e7 | − | 4.80935e7i | −2.38967 | − | 4.13904i | ||||
\(671\) | 5.07765e6 | + | 8.79474e6i | 0.435368 | + | 0.754079i | ||||
\(672\) | −2.93365e7 | −2.50602 | ||||||||
\(673\) | −2.68346e6 | − | 4.64789e6i | −0.228380 | − | 0.395566i | 0.728948 | − | 0.684569i | \(-0.240009\pi\) |
−0.957328 | + | 0.289003i | \(0.906676\pi\) | |||||||
\(674\) | −135413. | − | 234542.i | −0.0114818 | − | 0.0198871i | ||||
\(675\) | −1.96163e7 | − | 3.39764e7i | −1.65713 | − | 2.87024i | ||||
\(676\) | 9.27336e6 | − | 1.60619e7i | 0.780495 | − | 1.35186i | ||||
\(677\) | 4.06734e6 | 0.341066 | 0.170533 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170533 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(678\) | 3.14604e7 | − | 5.44911e7i | 2.62839 | − | 4.55251i | ||||
\(679\) | 6.50430e6 | + | 1.12658e7i | 0.541410 | + | 0.937749i | ||||
\(680\) | −1.45197e7 | −1.20417 | ||||||||
\(681\) | 3.69379e6 | + | 6.39784e6i | 0.305214 | + | 0.528647i | ||||
\(682\) | 1.05367e7 | − | 1.82501e7i | 0.867448 | − | 1.50246i | ||||
\(683\) | −2.54345e6 | + | 4.40538e6i | −0.208627 | + | 0.361353i | −0.951282 | − | 0.308321i | \(-0.900233\pi\) |
0.742655 | + | 0.669674i | \(0.233566\pi\) | |||||||
\(684\) | −1.33488e7 | −1.09095 | ||||||||
\(685\) | −4.96074e6 | + | 8.59225e6i | −0.403943 | + | 0.699649i | ||||
\(686\) | 1.37697e7 | 1.11716 | ||||||||
\(687\) | 9.51650e6 | 0.769281 | ||||||||
\(688\) | 1.10668e6 | + | 765538.i | 0.0891352 | + | 0.0616589i | ||||
\(689\) | −1.39716e6 | −0.112124 | ||||||||
\(690\) | 1.97328e7 | 1.57785 | ||||||||
\(691\) | −930178. | + | 1.61112e6i | −0.0741090 | + | 0.128361i | −0.900698 | − | 0.434445i | \(-0.856945\pi\) |
0.826589 | + | 0.562805i | \(0.190278\pi\) | |||||||
\(692\) | −9.90470e6 | −0.786278 | ||||||||
\(693\) | 1.80458e7 | − | 3.12563e7i | 1.42739 | − | 2.47232i | ||||
\(694\) | −1.80079e7 | + | 3.11906e7i | −1.41927 | + | 2.45825i | ||||
\(695\) | 9.56401e6 | + | 1.65653e7i | 0.751065 | + | 1.30088i | ||||
\(696\) | 2.91558e7 | 2.28140 | ||||||||
\(697\) | 702587. | + | 1.21692e6i | 0.0547795 | + | 0.0948808i | ||||
\(698\) | −2.05021e7 | + | 3.55107e7i | −1.59280 | + | 2.75880i | ||||
\(699\) | −1.07780e7 | −0.834348 | ||||||||
\(700\) | 2.84395e7 | − | 4.92587e7i | 2.19370 | − | 3.79960i | ||||
\(701\) | 7.18233e6 | + | 1.24402e7i | 0.552040 | + | 0.956161i | 0.998127 | + | 0.0611715i | \(0.0194837\pi\) |
−0.446088 | + | 0.894989i | \(0.647183\pi\) | |||||||
\(702\) | −5.24518e6 | − | 9.08492e6i | −0.401715 | − | 0.695790i | ||||
\(703\) | −231786. | − | 401466.i | −0.0176889 | − | 0.0306380i | ||||
\(704\) | −1.81262e7 | −1.37840 | ||||||||
\(705\) | −2.15359e7 | − | 3.73013e7i | −1.63189 | − | 2.82652i | ||||
\(706\) | 3.97176e6 | + | 6.87929e6i | 0.299896 | + | 0.519436i | ||||
\(707\) | 1.18482e7 | − | 2.05217e7i | 0.891464 | − | 1.54406i | ||||
\(708\) | −1.83578e7 | + | 3.17967e7i | −1.37638 | + | 2.38396i | ||||
\(709\) | −2.47174e7 | −1.84666 | −0.923331 | − | 0.384005i | \(-0.874544\pi\) | ||||
−0.923331 | + | 0.384005i | \(0.874544\pi\) | |||||||
\(710\) | 3.80098e7 | 2.82976 | ||||||||
\(711\) | 1.49409e7 | − | 2.58784e7i | 1.10842 | − | 1.91983i | ||||
\(712\) | −5.01110e6 | + | 8.67948e6i | −0.370453 | + | 0.641643i | ||||
\(713\) | −2.78575e6 | − | 4.82506e6i | −0.205219 | − | 0.355450i | ||||
\(714\) | 2.07143e7 | + | 3.58782e7i | 1.52063 | + | 2.63381i | ||||
\(715\) | 4.85580e6 | 0.355219 | ||||||||
\(716\) | −1.29265e7 | − | 2.23894e7i | −0.942320 | − | 1.63215i | ||||
\(717\) | 3.27054e6 | + | 5.66473e6i | 0.237586 | + | 0.411511i | ||||
\(718\) | 9.70032e6 | + | 1.68014e7i | 0.702223 | + | 1.21629i | ||||
\(719\) | −5.30481e6 | + | 9.18820e6i | −0.382691 | + | 0.662840i | −0.991446 | − | 0.130519i | \(-0.958336\pi\) |
0.608755 | + | 0.793358i | \(0.291669\pi\) | |||||||
\(720\) | −5.22286e6 | −0.375472 | ||||||||
\(721\) | −1.48270e7 | + | 2.56812e7i | −1.06222 | + | 1.83982i | ||||
\(722\) | −1.03357e7 | − | 1.79019e7i | −0.737898 | − | 1.27808i | ||||
\(723\) | −4.22768e6 | −0.300785 | ||||||||
\(724\) | 1.18484e6 | + | 2.05220e6i | 0.0840065 | + | 0.145504i | ||||
\(725\) | 1.42067e7 | − | 2.46067e7i | 1.00380 | − | 1.73864i | ||||
\(726\) | −5.14721e6 | + | 8.91523e6i | −0.362435 | + | 0.627756i | ||||
\(727\) | 4.45535e6 | 0.312641 | 0.156320 | − | 0.987706i | \(-0.450037\pi\) | ||||
0.156320 | + | 0.987706i | \(0.450037\pi\) | |||||||
\(728\) | 3.03857e6 | − | 5.26295e6i | 0.212491 | − | 0.368045i | ||||
\(729\) | −8.70949e6 | −0.606980 | ||||||||
\(730\) | 3.64379e7 | 2.53073 | ||||||||
\(731\) | −795856. | + | 9.73555e6i | −0.0550860 | + | 0.673856i | ||||
\(732\) | −4.28810e7 | −2.95792 | ||||||||
\(733\) | 1.47058e7 | 1.01095 | 0.505473 | − | 0.862843i | \(-0.331318\pi\) | ||||
0.505473 | + | 0.862843i | \(0.331318\pi\) | |||||||
\(734\) | −1.21679e6 | + | 2.10754e6i | −0.0833632 | + | 0.144389i | ||||
\(735\) | −6.09251e7 | −4.15985 | ||||||||
\(736\) | −2.23317e6 | + | 3.86796e6i | −0.151959 | + | 0.263201i | ||||
\(737\) | −1.13904e7 | + | 1.97288e7i | −0.772452 | + | 1.33793i | ||||
\(738\) | 4.13630e6 | + | 7.16429e6i | 0.279558 | + | 0.484208i | ||||
\(739\) | 2.37725e7 | 1.60127 | 0.800634 | − | 0.599154i | \(-0.204496\pi\) | ||||
0.800634 | + | 0.599154i | \(0.204496\pi\) | |||||||
\(740\) | −2.32102e6 | − | 4.02012e6i | −0.155811 | − | 0.269873i | ||||
\(741\) | −1.02379e6 | + | 1.77326e6i | −0.0684962 | + | 0.118639i | ||||
\(742\) | 1.71133e7 | 1.14110 | ||||||||
\(743\) | 2.95731e6 | − | 5.12221e6i | 0.196528 | − | 0.340397i | −0.750872 | − | 0.660447i | \(-0.770367\pi\) |
0.947400 | + | 0.320051i | \(0.103700\pi\) | |||||||
\(744\) | 1.77778e7 | + | 3.07921e7i | 1.17746 | + | 2.03942i | ||||
\(745\) | 751422. | + | 1.30150e6i | 0.0496013 | + | 0.0859120i | ||||
\(746\) | −1.20629e7 | − | 2.08935e7i | −0.793604 | − | 1.37456i | ||||
\(747\) | −1.53913e7 | −1.00919 | ||||||||
\(748\) | 7.45316e6 | + | 1.29093e7i | 0.487065 | + | 0.843620i | ||||
\(749\) | −3.16339e6 | − | 5.47915e6i | −0.206038 | − | 0.356869i | ||||
\(750\) | −2.49892e7 | + | 4.32826e7i | −1.62218 | + | 2.80970i | ||||
\(751\) | 5.04468e6 | − | 8.73765e6i | 0.326388 | − | 0.565320i | −0.655404 | − | 0.755278i | \(-0.727502\pi\) |
0.981792 | + | 0.189958i | \(0.0608351\pi\) | |||||||
\(752\) | −1.89659e6 | −0.122301 | ||||||||
\(753\) | 1.46134e7 | 0.939214 | ||||||||
\(754\) | 3.79872e6 | − | 6.57957e6i | 0.243337 | − | 0.421472i | ||||
\(755\) | −7.73764e6 | + | 1.34020e7i | −0.494016 | + | 0.855661i | ||||
\(756\) | 4.01434e7 | + | 6.95304e7i | 2.55452 | + | 4.42456i | ||||
\(757\) | 6.50284e6 | + | 1.12633e7i | 0.412443 | + | 0.714372i | 0.995156 | − | 0.0983059i | \(-0.0313424\pi\) |
−0.582714 | + | 0.812678i | \(0.698009\pi\) | |||||||
\(758\) | −1.01072e7 | −0.638939 | ||||||||
\(759\) | −4.04737e6 | − | 7.01026e6i | −0.255017 | − | 0.441702i | ||||
\(760\) | 4.39500e6 | + | 7.61236e6i | 0.276010 | + | 0.478063i | ||||
\(761\) | 1.33010e7 | + | 2.30379e7i | 0.832571 | + | 1.44206i | 0.895993 | + | 0.444069i | \(0.146465\pi\) |
−0.0634215 | + | 0.997987i | \(0.520201\pi\) | |||||||
\(762\) | 2.37134e7 | − | 4.10728e7i | 1.47947 | − | 2.56252i | ||||
\(763\) | 1.12894e7 | 0.702035 | ||||||||
\(764\) | 1.31847e7 | − | 2.28366e7i | 0.817218 | − | 1.41546i | ||||
\(765\) | −1.89562e7 | − | 3.28332e7i | −1.17111 | − | 2.02843i | ||||
\(766\) | −4.16176e7 | −2.56274 | ||||||||
\(767\) | 1.91146e6 | + | 3.31075e6i | 0.117321 | + | 0.203207i | ||||
\(768\) | 1.68545e7 | − | 2.91929e7i | 1.03113 | − | 1.78597i | ||||
\(769\) | 1.51622e7 | − | 2.62617e7i | 0.924583 | − | 1.60143i | 0.132353 | − | 0.991203i | \(-0.457747\pi\) |
0.792230 | − | 0.610223i | \(-0.208920\pi\) | |||||||
\(770\) | −5.94770e7 | −3.61512 | ||||||||
\(771\) | 1.67932e7 | − | 2.90867e7i | 1.01741 | − | 1.76221i | ||||
\(772\) | −8.94243e6 | −0.540023 | ||||||||
\(773\) | 60405.9 | 0.00363606 | 0.00181803 | − | 0.999998i | \(-0.499421\pi\) | ||||
0.00181803 | + | 0.999998i | \(0.499421\pi\) | |||||||
\(774\) | −4.68540e6 | + | 5.73156e7i | −0.281122 | + | 3.43891i | ||||
\(775\) | 3.46503e7 | 2.07230 | ||||||||
\(776\) | −1.26389e7 | −0.753451 | ||||||||
\(777\) | −2.64620e6 | + | 4.58335e6i | −0.157243 | + | 0.272352i | ||||
\(778\) | −6.78598e6 | −0.401942 | ||||||||
\(779\) | 425334. | − | 736700.i | 0.0251123 | − | 0.0434958i | ||||
\(780\) | −1.02519e7 | + | 1.77568e7i | −0.603346 | + | 1.04503i | ||||
\(781\) | −7.79614e6 | − | 1.35033e7i | −0.457354 | − | 0.792160i | ||||
\(782\) | 6.30729e6 | 0.368829 | ||||||||
\(783\) | 2.00533e7 | + | 3.47332e7i | 1.16891 | + | 2.02461i | ||||
\(784\) | −1.34136e6 | + | 2.32331e6i | −0.0779392 | + | 0.134995i | ||||
\(785\) | 1.78125e7 | 1.03169 | ||||||||
\(786\) | 8.40808e6 | − | 1.45632e7i | 0.485446 | − | 0.840817i | ||||
\(787\) | −6.49731e6 | − | 1.12537e7i | −0.373935 | − | 0.647675i | 0.616232 | − | 0.787565i | \(-0.288658\pi\) |
−0.990167 | + | 0.139890i | \(0.955325\pi\) | |||||||
\(788\) | 5.17062e6 | + | 8.95578e6i | 0.296638 | + | 0.513793i | ||||
\(789\) | 1.51178e7 | + | 2.61848e7i | 0.864562 | + | 1.49746i | ||||
\(790\) | −4.92436e7 | −2.80725 | ||||||||
\(791\) | 2.50705e7 | + | 4.34233e7i | 1.42469 | + | 2.46764i | ||||
\(792\) | 1.75330e7 | + | 3.03680e7i | 0.993213 | + | 1.72029i | ||||
\(793\) | −2.23243e6 | + | 3.86669e6i | −0.126065 | + | 0.218352i | ||||
\(794\) | 3.60803e6 | − | 6.24930e6i | 0.203104 | − | 0.351787i | ||||
\(795\) | −2.30712e7 | −1.29465 | ||||||||
\(796\) | 5.28617e7 | 2.95705 | ||||||||
\(797\) | −1.24540e6 | + | 2.15709e6i | −0.0694483 | + | 0.120288i | −0.898659 | − | 0.438649i | \(-0.855457\pi\) |
0.829210 | + | 0.558937i | \(0.188791\pi\) | |||||||
\(798\) | 1.25401e7 | − | 2.17201e7i | 0.697097 | − | 1.20741i | ||||
\(799\) | −6.88362e6 | − | 1.19228e7i | −0.381461 | − | 0.660710i | ||||
\(800\) | −1.38885e7 | − | 2.40556e7i | −0.767238 | − | 1.32890i | ||||
\(801\) | −2.61690e7 | −1.44114 | ||||||||
\(802\) | 4.66114e6 | + | 8.07334e6i | 0.255892 | + | 0.443218i | ||||
\(803\) | −7.47374e6 | − | 1.29449e7i | −0.409024 | − | 0.708451i | ||||
\(804\) | −4.80963e7 | − | 8.33053e7i | −2.62405 | − | 4.54498i | ||||
\(805\) | −7.86243e6 | + | 1.36181e7i | −0.427629 | + | 0.740675i | ||||
\(806\) | 9.26511e6 | 0.502358 | ||||||||
\(807\) | −2.13965e7 | + | 3.70599e7i | −1.15654 | + | 2.00318i | ||||
\(808\) | 1.15115e7 | + | 1.99385e7i | 0.620302 | + | 1.07439i | ||||
\(809\) | 992448. | 0.0533134 | 0.0266567 | − | 0.999645i | \(-0.491514\pi\) | ||||
0.0266567 | + | 0.999645i | \(0.491514\pi\) | |||||||
\(810\) | −3.38070e7 | − | 5.85554e7i | −1.81048 | − | 3.13584i | ||||
\(811\) | 1.47993e6 | − | 2.56331e6i | 0.0790113 | − | 0.136852i | −0.823812 | − | 0.566863i | \(-0.808157\pi\) |
0.902824 | + | 0.430011i | \(0.141490\pi\) | |||||||
\(812\) | −2.90731e7 | + | 5.03560e7i | −1.54739 | + | 2.68016i | ||||
\(813\) | 3.73552e7 | 1.98209 | ||||||||
\(814\) | −1.52380e6 | + | 2.63930e6i | −0.0806058 | + | 0.139613i | ||||
\(815\) | −5.95562e7 | −3.14075 | ||||||||
\(816\) | −2.45933e6 | −0.129298 | ||||||||
\(817\) | 5.34502e6 | − | 2.52962e6i | 0.280152 | − | 0.132587i | ||||
\(818\) | −5.40440e7 | −2.82400 | ||||||||
\(819\) | 1.58680e7 | 0.826633 | ||||||||
\(820\) | 4.25913e6 | − | 7.37703e6i | 0.221201 | − | 0.383131i | ||||
\(821\) | 2.56255e7 | 1.32683 | 0.663413 | − | 0.748254i | \(-0.269107\pi\) | ||||
0.663413 | + | 0.748254i | \(0.269107\pi\) | |||||||
\(822\) | −1.37520e7 | + | 2.38192e7i | −0.709884 | + | 1.22956i | ||||
\(823\) | 1.39762e7 | − | 2.42074e7i | 0.719264 | − | 1.24580i | −0.242028 | − | 0.970269i | \(-0.577813\pi\) |
0.961292 | − | 0.275532i | \(-0.0888541\pi\) | |||||||
\(824\) | −1.44056e7 | − | 2.49513e7i | −0.739120 | − | 1.28019i | ||||
\(825\) | 5.03428e7 | 2.57515 | ||||||||
\(826\) | −2.34128e7 | − | 4.05522e7i | −1.19400 | − | 2.06807i | ||||
\(827\) | 4.83247e6 | − | 8.37008e6i | 0.245700 | − | 0.425565i | −0.716628 | − | 0.697455i | \(-0.754315\pi\) |
0.962328 | + | 0.271890i | \(0.0876488\pi\) | |||||||
\(828\) | 2.32017e7 | 1.17610 | ||||||||
\(829\) | 3.74010e6 | − | 6.47804e6i | 0.189015 | − | 0.327384i | −0.755907 | − | 0.654679i | \(-0.772804\pi\) |
0.944922 | + | 0.327295i | \(0.106137\pi\) | |||||||
\(830\) | 1.26820e7 | + | 2.19659e7i | 0.638987 | + | 1.10676i | ||||
\(831\) | −1.01406e7 | − | 1.75640e7i | −0.509403 | − | 0.882311i | ||||
\(832\) | −3.98468e6 | − | 6.90167e6i | −0.199565 | − | 0.345657i | ||||
\(833\) | −1.94738e7 | −0.972383 | ||||||||
\(834\) | 2.65131e7 | + | 4.59220e7i | 1.31991 | + | 2.28616i | ||||
\(835\) | 1.59891e7 | + | 2.76939e7i | 0.793609 | + | 1.37457i | ||||
\(836\) | 4.51202e6 | − | 7.81504e6i | 0.223283 | − | 0.386737i | ||||
\(837\) | −2.44550e7 | + | 4.23574e7i | −1.20658 | + | 2.08985i | ||||
\(838\) | 6.03445e7 | 2.96844 | ||||||||
\(839\) | −2.92170e7 | −1.43295 | −0.716474 | − | 0.697614i | \(-0.754245\pi\) | ||||
−0.716474 | + | 0.697614i | \(0.754245\pi\) | |||||||
\(840\) | 5.01757e7 | − | 8.69068e7i | 2.45355 | − | 4.24967i | ||||
\(841\) | −4.26759e6 | + | 7.39168e6i | −0.208062 | + | 0.360374i | ||||
\(842\) | 1.30148e7 | + | 2.25422e7i | 0.632639 | + | 1.09576i | ||||
\(843\) | −6.95722e6 | − | 1.20503e7i | −0.337184 | − | 0.584019i | ||||
\(844\) | −3.65960e7 | −1.76839 | ||||||||
\(845\) | −1.59443e7 | − | 2.76164e7i | −0.768182 | − | 1.33053i | ||||
\(846\) | −4.05256e7 | − | 7.01924e7i | −1.94672 | − | 3.37182i | ||||
\(847\) | −4.10176e6 | − | 7.10445e6i | −0.196454 | − | 0.340269i | ||||
\(848\) | −507948. | + | 879791.i | −0.0242566 | + | 0.0420136i | ||||
\(849\) | 4.66867e7 | 2.22292 | ||||||||
\(850\) | −1.96131e7 | + | 3.39709e7i | −0.931107 | + | 1.61272i | ||||
\(851\) | 402870. | + | 697792.i | 0.0190696 | + | 0.0330295i | ||||
\(852\) | 6.58388e7 | 3.10730 | ||||||||
\(853\) | 1.36789e6 | + | 2.36926e6i | 0.0643694 | + | 0.111491i | 0.896414 | − | 0.443218i | \(-0.146163\pi\) |
−0.832045 | + | 0.554709i | \(0.812830\pi\) | |||||||
\(854\) | 2.73443e7 | − | 4.73617e7i | 1.28299 | − | 2.22220i | ||||
\(855\) | −1.14758e7 | + | 1.98766e7i | −0.536868 | + | 0.929882i | ||||
\(856\) | 6.14697e6 | 0.286733 | ||||||||
\(857\) | 7.94500e6 | − | 1.37611e7i | 0.369523 | − | 0.640033i | −0.619968 | − | 0.784627i | \(-0.712854\pi\) |
0.989491 | + | 0.144594i | \(0.0461877\pi\) | |||||||
\(858\) | 1.34611e7 | 0.624257 | ||||||||
\(859\) | 6.91409e6 | 0.319707 | 0.159854 | − | 0.987141i | \(-0.448898\pi\) | ||||
0.159854 | + | 0.987141i | \(0.448898\pi\) | |||||||
\(860\) | 5.35230e7 | − | 2.53306e7i | 2.46771 | − | 1.16788i | ||||
\(861\) | −9.71169e6 | −0.446464 | ||||||||
\(862\) | 5.34233e7 | 2.44885 | ||||||||
\(863\) | −6.33807e6 | + | 1.09779e7i | −0.289688 | + | 0.501754i | −0.973735 | − | 0.227684i | \(-0.926885\pi\) |
0.684047 | + | 0.729438i | \(0.260218\pi\) | |||||||
\(864\) | 3.92082e7 | 1.78687 | ||||||||
\(865\) | −8.51491e6 | + | 1.47483e7i | −0.386937 | + | 0.670194i | ||||
\(866\) | 418977. | − | 725689.i | 0.0189843 | − | 0.0328818i | ||||
\(867\) | 1.06009e7 | + | 1.83612e7i | 0.478953 | + | 0.829571i | ||||
\(868\) | −7.09095e7 | −3.19451 | ||||||||
\(869\) | 1.01003e7 | + | 1.74942e7i | 0.453716 | + | 0.785860i | ||||
\(870\) | 6.27280e7 | − | 1.08648e8i | 2.80972 | − | 4.86658i | ||||
\(871\) | −1.00158e7 | −0.447343 | ||||||||
\(872\) | −5.48427e6 | + | 9.49903e6i | −0.244246 | + | 0.423047i | ||||
\(873\) | −1.65007e7 | − | 2.85801e7i | −0.732770 | − | 1.26920i | ||||
\(874\) | −1.90916e6 | − | 3.30676e6i | −0.0845404 | − | 0.146428i | ||||
\(875\) | −1.99136e7 | − | 3.44914e7i | −0.879287 | − | 1.52297i | ||||
\(876\) | 6.31161e7 | 2.77894 | ||||||||
\(877\) | −1.27013e7 | − | 2.19993e7i | −0.557633 | − | 0.965849i | −0.997693 | − | 0.0678811i | \(-0.978376\pi\) |
0.440060 | − | 0.897968i | \(-0.354957\pi\) | |||||||
\(878\) | 2.33461e7 | + | 4.04366e7i | 1.02206 | + | 1.77026i | ||||
\(879\) | 2.72864e7 | − | 4.72615e7i | 1.19117 | − | 2.06317i | ||||
\(880\) | 1.76537e6 | − | 3.05771e6i | 0.0768473 | − | 0.133103i | ||||
\(881\) | −3.02870e7 | −1.31467 | −0.657334 | − | 0.753600i | \(-0.728316\pi\) | ||||
−0.657334 | + | 0.753600i | \(0.728316\pi\) | |||||||
\(882\) | −1.14647e8 | −4.96239 | ||||||||
\(883\) | −2.13995e7 | + | 3.70651e7i | −0.923640 | + | 1.59979i | −0.129906 | + | 0.991526i | \(0.541468\pi\) |
−0.793734 | + | 0.608265i | \(0.791866\pi\) | |||||||
\(884\) | −3.27685e6 | + | 5.67567e6i | −0.141035 | + | 0.244279i | ||||
\(885\) | 3.15639e7 | + | 5.46703e7i | 1.35467 | + | 2.34635i | ||||
\(886\) | −2.84426e7 | − | 4.92640e7i | −1.21726 | − | 2.10836i | ||||
\(887\) | −2.80596e7 | −1.19749 | −0.598745 | − | 0.800939i | \(-0.704334\pi\) | ||||
−0.598745 | + | 0.800939i | \(0.704334\pi\) | |||||||
\(888\) | −2.57100e6 | − | 4.45310e6i | −0.109413 | − | 0.189509i | ||||
\(889\) | 1.88969e7 | + | 3.27304e7i | 0.801930 | + | 1.38898i | ||||
\(890\) | 2.15625e7 | + | 3.73474e7i | 0.912482 | + | 1.58047i | ||||
\(891\) | −1.38682e7 | + | 2.40205e7i | −0.585230 | + | 1.01365i | ||||
\(892\) | 3.32928e7 | 1.40100 | ||||||||
\(893\) | −4.16723e6 | + | 7.21785e6i | −0.174871 | + | 0.302886i | ||||
\(894\) | 2.08307e6 | + | 3.60799e6i | 0.0871688 | + | 0.150981i | ||||
\(895\) | −4.44508e7 | −1.85491 | ||||||||
\(896\) | 3.17418e7 | + | 5.49784e7i | 1.32087 | + | 2.28782i | ||||
\(897\) | 1.77946e6 | − | 3.08212e6i | 0.0738428 | − | 0.127900i | ||||
\(898\) | −9.33400e6 | + | 1.61670e7i | −0.386257 | + | 0.669017i | ||||
\(899\) | −3.54221e7 | −1.46176 | ||||||||
\(900\) | −7.21481e7 | + | 1.24964e8i | −2.96906 | + | 5.14256i | ||||
\(901\) | −7.37434e6 | −0.302629 | ||||||||
\(902\) | −5.59242e6 | −0.228867 | ||||||||
\(903\) | −5.55212e7 | − | 3.84066e7i | −2.26589 | − | 1.56742i | ||||
\(904\) | −4.87160e7 | −1.98267 | ||||||||
\(905\) | 4.07435e6 | 0.165362 | ||||||||
\(906\) | −2.14501e7 | + | 3.71527e7i | −0.868178 | + | 1.50373i | ||||
\(907\) | 1.76967e7 | 0.714289 | 0.357144 | − | 0.934049i | \(-0.383750\pi\) | ||||
0.357144 | + | 0.934049i | \(0.383750\pi\) | |||||||
\(908\) | 7.15727e6 | − | 1.23967e7i | 0.288093 | − | 0.498992i | ||||
\(909\) | −3.00577e7 | + | 5.20614e7i | −1.20655 | + | 2.08981i | ||||
\(910\) | −1.30748e7 | − | 2.26462e7i | −0.523398 | − | 0.906551i | ||||
\(911\) | −2.20849e7 | −0.881656 | −0.440828 | − | 0.897592i | \(-0.645315\pi\) | ||||
−0.440828 | + | 0.897592i | \(0.645315\pi\) | |||||||
\(912\) | 744418. | + | 1.28937e6i | 0.0296367 | + | 0.0513322i | ||||
\(913\) | 5.20238e6 | − | 9.01078e6i | 0.206550 | − | 0.357755i | ||||
\(914\) | −1.11818e7 | −0.442739 | ||||||||
\(915\) | −3.68641e7 | + | 6.38504e7i | −1.45563 | + | 2.52122i | ||||
\(916\) | −9.21980e6 | − | 1.59692e7i | −0.363064 | − | 0.628845i | ||||
\(917\) | 6.70031e6 | + | 1.16053e7i | 0.263131 | + | 0.455756i | ||||
\(918\) | −2.76846e7 | − | 4.79512e7i | −1.08426 | − | 1.87799i | ||||
\(919\) | 4.64182e7 | 1.81301 | 0.906503 | − | 0.422200i | \(-0.138742\pi\) | ||||
0.906503 | + | 0.422200i | \(0.138742\pi\) | |||||||
\(920\) | −7.63898e6 | − | 1.32311e7i | −0.297554 | − | 0.515379i | ||||
\(921\) | 2.17173e7 | + | 3.76154e7i | 0.843637 | + | 1.46122i | ||||
\(922\) | −1.92553e7 | + | 3.33512e7i | −0.745973 | + | 1.29206i | ||||
\(923\) | 3.42765e6 | − | 5.93686e6i | 0.132432 | − | 0.229378i | ||||
\(924\) | −1.03023e8 | −3.96968 | ||||||||
\(925\) | −5.01106e6 | −0.192564 | ||||||||
\(926\) | 3.29835e7 | − | 5.71291e7i | 1.26407 | − | 2.18943i | ||||
\(927\) | 3.76146e7 | − | 6.51504e7i | 1.43766 | − | 2.49011i | ||||
\(928\) | 1.41979e7 | + | 2.45915e7i | 0.541195 | + | 0.937377i | ||||
\(929\) | 9.67619e6 | + | 1.67597e7i | 0.367845 | + | 0.637127i | 0.989228 | − | 0.146380i | \(-0.0467623\pi\) |
−0.621383 | + | 0.783507i | \(0.713429\pi\) | |||||||
\(930\) | 1.52994e8 | 5.80053 | ||||||||
\(931\) | 5.89454e6 | + | 1.02096e7i | 0.222883 | + | 0.386044i | ||||
\(932\) | 1.04420e7 | + | 1.80861e7i | 0.393772 | + | 0.682033i | ||||
\(933\) | 3.47418e7 | + | 6.01745e7i | 1.30661 | + | 2.26312i | ||||
\(934\) | 6.45972e6 | − | 1.11886e7i | 0.242296 | − | 0.419669i | ||||
\(935\) | 2.56295e7 | 0.958761 | ||||||||
\(936\) | −7.70853e6 | + | 1.33516e7i | −0.287595 | + | 0.498130i | ||||
\(937\) | −2.13659e7 | − | 3.70068e7i | −0.795009 | − | 1.37700i | −0.922834 | − | 0.385198i | \(-0.874133\pi\) |
0.127825 | − | 0.991797i | \(-0.459200\pi\) | |||||||
\(938\) | 1.22680e8 | 4.55268 | ||||||||
\(939\) | 5.25740e6 | + | 9.10608e6i | 0.194584 | + | 0.337029i | ||||
\(940\) | −4.17290e7 | + | 7.22768e7i | −1.54035 | + | 2.66796i | ||||
\(941\) | 1.43638e7 | − | 2.48788e7i | 0.528805 | − | 0.915917i | −0.470631 | − | 0.882330i | \(-0.655974\pi\) |
0.999436 | − | 0.0335869i | \(-0.0106931\pi\) | |||||||
\(942\) | 4.93794e7 | 1.81309 | ||||||||
\(943\) | −739277. | + | 1.28047e6i | −0.0270725 | + | 0.0468909i | ||||
\(944\) | 2.77972e6 | 0.101524 | ||||||||
\(945\) | 1.38043e8 | 5.02844 | ||||||||
\(946\) | −3.19716e7 | − | 2.21162e7i | −1.16154 | − | 0.803494i | ||||
\(947\) | 8.31693e6 | 0.301362 | 0.150681 | − | 0.988582i | \(-0.451853\pi\) | ||||
0.150681 | + | 0.988582i | \(0.451853\pi\) | |||||||
\(948\) | −8.52974e7 | −3.08258 | ||||||||
\(949\) | 3.28590e6 | − | 5.69134e6i | 0.118437 | − | 0.205139i | ||||
\(950\) | 2.37469e7 | 0.853686 | ||||||||
\(951\) | 4.66510e7 | − | 8.08020e7i | 1.67267 | − | 2.89715i | ||||
\(952\) | 1.60379e7 | − | 2.77784e7i | 0.573528 | − | 0.993379i | ||||
\(953\) | −1.72520e7 | − | 2.98813e7i | −0.615329 | − | 1.06578i | −0.990327 | − | 0.138755i | \(-0.955690\pi\) |
0.374998 | − | 0.927026i | \(-0.377643\pi\) | |||||||
\(954\) | −4.34146e7 | −1.54442 | ||||||||
\(955\) | −2.26694e7 | − | 3.92646e7i | −0.804326 | − | 1.39313i | ||||
\(956\) | 6.33714e6 | − | 1.09763e7i | 0.224258 | − | 0.388427i | ||||
\(957\) | −5.14643e7 | −1.81646 | ||||||||
\(958\) | 9.95262e6 | − | 1.72384e7i | 0.350367 | − | 0.606854i | ||||
\(959\) | −1.09588e7 | − | 1.89813e7i | −0.384785 | − | 0.666467i | ||||
\(960\) | −6.57988e7 | − | 1.13967e8i | −2.30430 | − | 3.99117i | ||||
\(961\) | −7.28416e6 | − | 1.26165e7i | −0.254432 | − | 0.440688i | ||||
\(962\) | −1.33990e6 | −0.0466806 | ||||||||
\(963\) | 8.02519e6 | + | 1.39000e7i | 0.278862 | + | 0.483003i | ||||
\(964\) | 4.09587e6 | + | 7.09426e6i | 0.141956 | + | 0.245875i | ||||
\(965\) | −7.68766e6 | + | 1.33154e7i | −0.265752 | + | 0.460295i | ||||
\(966\) | −2.17960e7 | + | 3.77518e7i | −0.751510 | + | 1.30165i | ||||
\(967\) | 2.53555e6 | 0.0871980 | 0.0435990 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435990 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(968\) | 7.97038e6 | 0.273395 | ||||||||
\(969\) | −5.40369e6 | + | 9.35947e6i | −0.184876 | + | 0.320215i | ||||
\(970\) | −2.71923e7 | + | 4.70985e7i | −0.927933 | + | 1.60723i | ||||
\(971\) | 3.85207e6 | + | 6.67199e6i | 0.131113 | + | 0.227095i | 0.924106 | − | 0.382136i | \(-0.124812\pi\) |
−0.792993 | + | 0.609231i | \(0.791478\pi\) | |||||||
\(972\) | −1.03708e7 | − | 1.79628e7i | −0.352084 | − | 0.609828i | ||||
\(973\) | −4.22560e7 | −1.43089 | ||||||||
\(974\) | 1.78210e7 | + | 3.08669e7i | 0.601914 | + | 1.04255i | ||||
\(975\) | 1.10668e7 | + | 1.91683e7i | 0.372831 | + | 0.645763i | ||||
\(976\) | 1.62324e6 | + | 2.81154e6i | 0.0545454 | + | 0.0944755i | ||||
\(977\) | −5.05477e6 | + | 8.75512e6i | −0.169420 | + | 0.293444i | −0.938216 | − | 0.346050i | \(-0.887523\pi\) |
0.768796 | + | 0.639494i | \(0.220856\pi\) | |||||||
\(978\) | −1.65100e8 | −5.51951 | ||||||||
\(979\) | 8.84533e6 | − | 1.53206e7i | 0.294956 | − | 0.510879i | ||||
\(980\) | 5.90257e7 | + | 1.02235e8i | 1.96325 | + | 3.40045i | ||||
\(981\) | −2.86400e7 | −0.950167 | ||||||||
\(982\) | −3.40159e7 | − | 5.89173e7i | −1.12565 | − | 1.94968i | ||||
\(983\) | 1.23407e7 | − | 2.13748e7i | 0.407341 | − | 0.705534i | −0.587250 | − | 0.809405i | \(-0.699790\pi\) |
0.994591 | + | 0.103871i | \(0.0331229\pi\) | |||||||
\(984\) | 4.71785e6 | − | 8.17155e6i | 0.155330 | − | 0.269040i | ||||
\(985\) | 1.77804e7 | 0.583917 | ||||||||
\(986\) | 2.00500e7 | − | 3.47277e7i | 0.656785 | − | 1.13758i | ||||
\(987\) | 9.51507e7 | 3.10899 | ||||||||
\(988\) | 3.96750e6 | 0.129308 | ||||||||
\(989\) | −9.29023e6 | + | 4.39675e6i | −0.302020 | + | 0.142936i | ||||
\(990\) | 1.50887e8 | 4.89287 | ||||||||
\(991\) | 2.35191e7 | 0.760740 | 0.380370 | − | 0.924834i | \(-0.375797\pi\) | ||||
0.380370 | + | 0.924834i | \(0.375797\pi\) | |||||||
\(992\) | −1.73144e7 | + | 2.99894e7i | −0.558635 | + | 0.967584i | ||||
\(993\) | −1.03925e8 | −3.34462 | ||||||||
\(994\) | −4.19840e7 | + | 7.27184e7i | −1.34778 | + | 2.33442i | ||||
\(995\) | 4.54443e7 | − | 7.87119e7i | 1.45520 | − | 2.52048i | ||||
\(996\) | 2.19672e7 | + | 3.80482e7i | 0.701658 | + | 1.21531i | ||||
\(997\) | 3.74659e7 | 1.19371 | 0.596854 | − | 0.802350i | \(-0.296417\pi\) | ||||
0.596854 | + | 0.802350i | \(0.296417\pi\) | |||||||
\(998\) | −1.30494e6 | − | 2.26022e6i | −0.0414729 | − | 0.0718331i | ||||
\(999\) | 3.53665e6 | − | 6.12565e6i | 0.112119 | − | 0.194195i |
(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 | 43.6.c.a.6.2 | ✓ | 34 | |
43.36 | even | 3 | inner | 43.6.c.a.36.2 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.2 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.6.c.a.36.2 | yes | 34 | 43.36 | even | 3 | inner |