Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,6,Mod(75,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.75");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.b (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: | \(24.3783406116\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.3 | ||
Character | \(\chi\) | \(=\) | 152.75 |
Dual form | 152.6.b.b.75.4 |
$q$-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 \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.61333 | − | 0.700358i | −0.992306 | − | 0.123807i | ||||
\(3\) | − | 4.49700i | − | 0.288483i | −0.989543 | − | 0.144241i | \(-0.953926\pi\) | ||
0.989543 | − | 0.144241i | \(-0.0460741\pi\) | |||||||
\(4\) | 31.0190 | + | 7.86269i | 0.969344 | + | 0.245709i | ||||
\(5\) | 93.3850i | 1.67052i | 0.549853 | + | 0.835261i | \(0.314684\pi\) | ||||
−0.549853 | + | 0.835261i | \(0.685316\pi\) | |||||||
\(6\) | −3.14951 | + | 25.2431i | −0.0357162 | + | 0.286263i | ||||
\(7\) | − | 95.0367i | − | 0.733072i | −0.930404 | − | 0.366536i | \(-0.880544\pi\) | ||
0.930404 | − | 0.366536i | \(-0.119456\pi\) | |||||||
\(8\) | −168.613 | − | 65.8603i | −0.931465 | − | 0.363830i | ||||
\(9\) | 222.777 | 0.916778 | ||||||||
\(10\) | 65.4030 | − | 524.201i | 0.206822 | − | 1.65767i | ||||
\(11\) | 300.630 | 0.749118 | 0.374559 | − | 0.927203i | \(-0.377794\pi\) | ||||
0.374559 | + | 0.927203i | \(0.377794\pi\) | |||||||
\(12\) | 35.3585 | − | 139.492i | 0.0708827 | − | 0.279639i | ||||
\(13\) | 276.831 | 0.454315 | 0.227158 | − | 0.973858i | \(-0.427057\pi\) | ||||
0.227158 | + | 0.973858i | \(0.427057\pi\) | |||||||
\(14\) | −66.5598 | + | 533.473i | −0.0907594 | + | 0.727432i | ||||
\(15\) | 419.952 | 0.481917 | ||||||||
\(16\) | 900.356 | + | 487.785i | 0.879254 | + | 0.476353i | ||||
\(17\) | −1297.16 | −1.08860 | −0.544302 | − | 0.838889i | \(-0.683206\pi\) | ||||
−0.544302 | + | 0.838889i | \(0.683206\pi\) | |||||||
\(18\) | −1250.52 | − | 156.024i | −0.909724 | − | 0.113504i | ||||
\(19\) | 654.993 | − | 1430.76i | 0.416248 | − | 0.909251i | ||||
\(20\) | −734.257 | + | 2896.71i | −0.410462 | + | 1.61931i | ||||
\(21\) | −427.380 | −0.211478 | ||||||||
\(22\) | −1687.53 | − | 210.548i | −0.743354 | − | 0.0927460i | ||||
\(23\) | 2226.45i | 0.877592i | 0.898587 | + | 0.438796i | \(0.144595\pi\) | ||||
−0.898587 | + | 0.438796i | \(0.855405\pi\) | |||||||
\(24\) | −296.174 | + | 758.253i | −0.104959 | + | 0.268712i | ||||
\(25\) | −5595.77 | −1.79065 | ||||||||
\(26\) | −1553.95 | − | 193.881i | −0.450820 | − | 0.0562474i | ||||
\(27\) | − | 2094.60i | − | 0.552957i | ||||||
\(28\) | 747.244 | − | 2947.94i | 0.180122 | − | 0.710598i | ||||
\(29\) | 3508.64 | 0.774718 | 0.387359 | − | 0.921929i | \(-0.373387\pi\) | ||||
0.387359 | + | 0.921929i | \(0.373387\pi\) | |||||||
\(30\) | −2357.33 | − | 294.117i | −0.478209 | − | 0.0596647i | ||||
\(31\) | 3472.71 | 0.649028 | 0.324514 | − | 0.945881i | \(-0.394799\pi\) | ||||
0.324514 | + | 0.945881i | \(0.394799\pi\) | |||||||
\(32\) | −4712.37 | − | 3368.67i | −0.813514 | − | 0.581546i | ||||
\(33\) | − | 1351.93i | − | 0.216107i | ||||||
\(34\) | 7281.37 | + | 908.474i | 1.08023 | + | 0.134777i | ||||
\(35\) | 8875.01 | 1.22461 | ||||||||
\(36\) | 6910.32 | + | 1751.63i | 0.888673 | + | 0.225261i | ||||
\(37\) | −5424.58 | −0.651422 | −0.325711 | − | 0.945469i | \(-0.605604\pi\) | ||||
−0.325711 | + | 0.945469i | \(0.605604\pi\) | |||||||
\(38\) | −4678.74 | + | 7572.62i | −0.525618 | + | 0.850721i | ||||
\(39\) | − | 1244.91i | − | 0.131062i | ||||||
\(40\) | 6150.37 | − | 15746.0i | 0.607786 | − | 1.55603i | ||||
\(41\) | 19973.8i | 1.85567i | 0.372992 | + | 0.927834i | \(0.378332\pi\) | ||||
−0.372992 | + | 0.927834i | \(0.621668\pi\) | |||||||
\(42\) | 2399.03 | + | 299.319i | 0.209851 | + | 0.0261825i | ||||
\(43\) | 15101.0 | 1.24548 | 0.622739 | − | 0.782430i | \(-0.286020\pi\) | ||||
0.622739 | + | 0.782430i | \(0.286020\pi\) | |||||||
\(44\) | 9325.23 | + | 2363.76i | 0.726152 | + | 0.184065i | ||||
\(45\) | 20804.0i | 1.53150i | ||||||||
\(46\) | 1559.31 | − | 12497.8i | 0.108652 | − | 0.870840i | ||||
\(47\) | 4008.50i | 0.264690i | 0.991204 | + | 0.132345i | \(0.0422506\pi\) | ||||
−0.991204 | + | 0.132345i | \(0.957749\pi\) | |||||||
\(48\) | 2193.57 | − | 4048.90i | 0.137419 | − | 0.253650i | ||||
\(49\) | 7775.02 | 0.462606 | ||||||||
\(50\) | 31410.9 | + | 3919.04i | 1.77687 | + | 0.221694i | ||||
\(51\) | 5833.31i | 0.314043i | ||||||||
\(52\) | 8587.03 | + | 2176.64i | 0.440387 | + | 0.111629i | ||||
\(53\) | 3492.83 | 0.170800 | 0.0854001 | − | 0.996347i | \(-0.472783\pi\) | ||||
0.0854001 | + | 0.996347i | \(0.472783\pi\) | |||||||
\(54\) | −1466.97 | + | 11757.7i | −0.0684599 | + | 0.548703i | ||||
\(55\) | 28074.3i | 1.25142i | ||||||||
\(56\) | −6259.15 | + | 16024.5i | −0.266713 | + | 0.682831i | ||||
\(57\) | −6434.14 | − | 2945.50i | −0.262303 | − | 0.120080i | ||||
\(58\) | −19695.2 | − | 2457.30i | −0.768758 | − | 0.0959156i | ||||
\(59\) | 5272.90i | 0.197206i | 0.995127 | + | 0.0986028i | \(0.0314373\pi\) | ||||
−0.995127 | + | 0.0986028i | \(0.968563\pi\) | |||||||
\(60\) | 13026.5 | + | 3301.95i | 0.467143 | + | 0.118411i | ||||
\(61\) | 5218.99i | 0.179582i | 0.995961 | + | 0.0897909i | \(0.0286199\pi\) | ||||
−0.995961 | + | 0.0897909i | \(0.971380\pi\) | |||||||
\(62\) | −19493.5 | − | 2432.14i | −0.644035 | − | 0.0803543i | ||||
\(63\) | − | 21172.0i | − | 0.672064i | ||||||
\(64\) | 24092.8 | + | 22209.8i | 0.735255 | + | 0.677790i | ||||
\(65\) | 25851.9i | 0.758943i | ||||||||
\(66\) | −946.836 | + | 7588.84i | −0.0267556 | + | 0.214445i | ||||
\(67\) | 44164.6i | 1.20195i | 0.799267 | + | 0.600976i | \(0.205221\pi\) | ||||
−0.799267 | + | 0.600976i | \(0.794779\pi\) | |||||||
\(68\) | −40236.5 | − | 10199.1i | −1.05523 | − | 0.267480i | ||||
\(69\) | 10012.3 | 0.253170 | ||||||||
\(70\) | −49818.4 | − | 6215.69i | −1.21519 | − | 0.151616i | ||||
\(71\) | 59386.9 | 1.39812 | 0.699061 | − | 0.715062i | \(-0.253602\pi\) | ||||
0.699061 | + | 0.715062i | \(0.253602\pi\) | |||||||
\(72\) | −37563.2 | − | 14672.2i | −0.853947 | − | 0.333551i | ||||
\(73\) | 67977.3 | 1.49299 | 0.746495 | − | 0.665391i | \(-0.231735\pi\) | ||||
0.746495 | + | 0.665391i | \(0.231735\pi\) | |||||||
\(74\) | 30450.0 | + | 3799.15i | 0.646410 | + | 0.0806506i | ||||
\(75\) | 25164.2i | 0.516570i | ||||||||
\(76\) | 31566.9 | − | 39230.8i | 0.626899 | − | 0.779101i | ||||
\(77\) | − | 28570.9i | − | 0.549157i | ||||||
\(78\) | −871.883 | + | 6988.10i | −0.0162264 | + | 0.130054i | ||||
\(79\) | −2688.59 | −0.0484681 | −0.0242341 | − | 0.999706i | \(-0.507715\pi\) | ||||
−0.0242341 | + | 0.999706i | \(0.507715\pi\) | |||||||
\(80\) | −45551.9 | + | 84079.8i | −0.795758 | + | 1.46881i | ||||
\(81\) | 44715.4 | 0.757259 | ||||||||
\(82\) | 13988.8 | − | 112119.i | 0.229745 | − | 1.84139i | ||||
\(83\) | −53937.2 | −0.859395 | −0.429698 | − | 0.902973i | \(-0.641380\pi\) | ||||
−0.429698 | + | 0.902973i | \(0.641380\pi\) | |||||||
\(84\) | −13256.9 | − | 3360.35i | −0.204995 | − | 0.0519621i | ||||
\(85\) | − | 121135.i | − | 1.81854i | ||||||
\(86\) | −84767.2 | − | 10576.1i | −1.23590 | − | 0.154199i | ||||
\(87\) | − | 15778.3i | − | 0.223493i | ||||||
\(88\) | −50690.1 | − | 19799.6i | −0.697777 | − | 0.272552i | ||||
\(89\) | − | 46866.4i | − | 0.627172i | −0.949560 | − | 0.313586i | \(-0.898470\pi\) | ||
0.949560 | − | 0.313586i | \(-0.101530\pi\) | |||||||
\(90\) | 14570.3 | − | 116780.i | 0.189610 | − | 1.51972i | ||||
\(91\) | − | 26309.2i | − | 0.333045i | ||||||
\(92\) | −17505.9 | + | 69062.2i | −0.215632 | + | 0.850689i | ||||
\(93\) | − | 15616.8i | − | 0.187233i | ||||||
\(94\) | 2807.38 | − | 22501.0i | 0.0327704 | − | 0.262653i | ||||
\(95\) | 133612. | + | 61166.6i | 1.51892 | + | 0.695352i | ||||
\(96\) | −15148.9 | + | 21191.5i | −0.167766 | + | 0.234685i | ||||
\(97\) | 81391.3i | 0.878311i | 0.898411 | + | 0.439156i | \(0.144722\pi\) | ||||
−0.898411 | + | 0.439156i | \(0.855278\pi\) | |||||||
\(98\) | −43643.8 | − | 5445.30i | −0.459047 | − | 0.0572739i | ||||
\(99\) | 66973.4 | 0.686774 | ||||||||
\(100\) | −173575. | − | 43997.8i | −1.73575 | − | 0.439978i | ||||
\(101\) | − | 2539.86i | − | 0.0247746i | −0.999923 | − | 0.0123873i | \(-0.996057\pi\) | ||
0.999923 | − | 0.0123873i | \(-0.00394310\pi\) | |||||||
\(102\) | 4085.41 | − | 32744.3i | 0.0388808 | − | 0.311627i | ||||
\(103\) | −92949.2 | −0.863282 | −0.431641 | − | 0.902045i | \(-0.642065\pi\) | ||||
−0.431641 | + | 0.902045i | \(0.642065\pi\) | |||||||
\(104\) | −46677.5 | − | 18232.2i | −0.423179 | − | 0.165293i | ||||
\(105\) | − | 39910.9i | − | 0.353279i | ||||||
\(106\) | −19606.4 | − | 2446.24i | −0.169486 | − | 0.0211463i | ||||
\(107\) | 168149.i | 1.41983i | 0.704288 | + | 0.709914i | \(0.251266\pi\) | ||||
−0.704288 | + | 0.709914i | \(0.748734\pi\) | |||||||
\(108\) | 16469.2 | − | 64972.3i | 0.135866 | − | 0.536005i | ||||
\(109\) | −190552. | −1.53620 | −0.768098 | − | 0.640332i | \(-0.778797\pi\) | ||||
−0.768098 | + | 0.640332i | \(0.778797\pi\) | |||||||
\(110\) | 19662.1 | − | 157590.i | 0.154934 | − | 1.24179i | ||||
\(111\) | 24394.3i | 0.187924i | ||||||||
\(112\) | 46357.5 | − | 85566.9i | 0.349201 | − | 0.644556i | ||||
\(113\) | 200780.i | 1.47919i | 0.673050 | + | 0.739597i | \(0.264984\pi\) | ||||
−0.673050 | + | 0.739597i | \(0.735016\pi\) | |||||||
\(114\) | 34054.1 | + | 21040.3i | 0.245418 | + | 0.151632i | ||||
\(115\) | −207917. | −1.46604 | ||||||||
\(116\) | 108834. | + | 27587.3i | 0.750968 | + | 0.190355i | ||||
\(117\) | 61671.7 | 0.416506 | ||||||||
\(118\) | 3692.92 | − | 29598.5i | 0.0244154 | − | 0.195688i | ||||
\(119\) | 123278.i | 0.798025i | ||||||||
\(120\) | −70809.5 | − | 27658.2i | −0.448889 | − | 0.175336i | ||||
\(121\) | −70672.8 | −0.438823 | ||||||||
\(122\) | 3655.17 | − | 29296.0i | 0.0222335 | − | 0.178200i | ||||
\(123\) | 89822.0 | 0.535328 | ||||||||
\(124\) | 107720. | + | 27304.8i | 0.629132 | + | 0.159472i | ||||
\(125\) | − | 230733.i | − | 1.32079i | ||||||
\(126\) | −14828.0 | + | 118845.i | −0.0832062 | + | 0.666893i | ||||
\(127\) | −360363. | −1.98258 | −0.991292 | − | 0.131684i | \(-0.957962\pi\) | ||||
−0.991292 | + | 0.131684i | \(0.957962\pi\) | |||||||
\(128\) | −119686. | − | 141545.i | −0.645683 | − | 0.763605i | ||||
\(129\) | − | 67909.4i | − | 0.359299i | ||||||
\(130\) | 18105.6 | − | 145115.i | 0.0939625 | − | 0.753104i | ||||
\(131\) | 145926. | 0.742943 | 0.371472 | − | 0.928444i | \(-0.378853\pi\) | ||||
0.371472 | + | 0.928444i | \(0.378853\pi\) | |||||||
\(132\) | 10629.8 | − | 41935.5i | 0.0530995 | − | 0.209482i | ||||
\(133\) | −135975. | − | 62248.4i | −0.666546 | − | 0.305140i | ||||
\(134\) | 30931.0 | − | 247911.i | 0.148810 | − | 1.19270i | ||||
\(135\) | 195604. | 0.923727 | ||||||||
\(136\) | 218718. | + | 85431.1i | 1.01400 | + | 0.396067i | ||||
\(137\) | −65742.5 | −0.299257 | −0.149629 | − | 0.988742i | \(-0.547808\pi\) | ||||
−0.149629 | + | 0.988742i | \(0.547808\pi\) | |||||||
\(138\) | −56202.5 | − | 7012.22i | −0.251222 | − | 0.0313442i | ||||
\(139\) | 220332. | 0.967253 | 0.483627 | − | 0.875274i | \(-0.339319\pi\) | ||||
0.483627 | + | 0.875274i | \(0.339319\pi\) | |||||||
\(140\) | 275294. | + | 69781.4i | 1.18707 | + | 0.300898i | ||||
\(141\) | 18026.2 | 0.0763583 | ||||||||
\(142\) | −333359. | − | 41592.1i | −1.38737 | − | 0.173097i | ||||
\(143\) | 83223.7 | 0.340335 | ||||||||
\(144\) | 200579. | + | 108667.i | 0.806081 | + | 0.436710i | ||||
\(145\) | 327654.i | 1.29418i | ||||||||
\(146\) | −381579. | − | 47608.5i | −1.48150 | − | 0.184843i | ||||
\(147\) | − | 34964.3i | − | 0.133454i | ||||||
\(148\) | −168265. | − | 42651.8i | −0.631451 | − | 0.160060i | ||||
\(149\) | − | 311465.i | − | 1.14933i | −0.818390 | − | 0.574663i | \(-0.805133\pi\) | ||
0.818390 | − | 0.574663i | \(-0.194867\pi\) | |||||||
\(150\) | 17623.9 | − | 141255.i | 0.0639550 | − | 0.512596i | ||||
\(151\) | 171779. | 0.613093 | 0.306547 | − | 0.951856i | \(-0.400826\pi\) | ||||
0.306547 | + | 0.951856i | \(0.400826\pi\) | |||||||
\(152\) | −204671. | + | 198108.i | −0.718534 | + | 0.695492i | ||||
\(153\) | −288977. | −0.998008 | ||||||||
\(154\) | −20009.8 | + | 160378.i | −0.0679895 | + | 0.544932i | ||||
\(155\) | 324299.i | 1.08422i | ||||||||
\(156\) | 9788.34 | − | 38615.9i | 0.0322031 | − | 0.127044i | ||||
\(157\) | 60313.0i | 0.195282i | 0.995222 | + | 0.0976409i | \(0.0311297\pi\) | ||||
−0.995222 | + | 0.0976409i | \(0.968870\pi\) | |||||||
\(158\) | 15091.9 | + | 1882.97i | 0.0480952 | + | 0.00600070i | ||||
\(159\) | − | 15707.3i | − | 0.0492729i | ||||||
\(160\) | 314584. | − | 440065.i | 0.971485 | − | 1.35899i | ||||
\(161\) | 211594. | 0.643338 | ||||||||
\(162\) | −251002. | − | 31316.8i | −0.751433 | − | 0.0937540i | ||||
\(163\) | 134718. | 0.397153 | 0.198576 | − | 0.980085i | \(-0.436368\pi\) | ||||
0.198576 | + | 0.980085i | \(0.436368\pi\) | |||||||
\(164\) | −157048. | + | 619566.i | −0.455954 | + | 1.79878i | ||||
\(165\) | 126250. | 0.361012 | ||||||||
\(166\) | 302767. | + | 37775.4i | 0.852784 | + | 0.106399i | ||||
\(167\) | 459295. | 1.27438 | 0.637192 | − | 0.770705i | \(-0.280096\pi\) | ||||
0.637192 | + | 0.770705i | \(0.280096\pi\) | |||||||
\(168\) | 72061.9 | + | 28147.4i | 0.196985 | + | 0.0769422i | ||||
\(169\) | −294657. | −0.793598 | ||||||||
\(170\) | −84837.9 | + | 679971.i | −0.225148 | + | 1.80455i | ||||
\(171\) | 145917. | − | 318741.i | 0.381607 | − | 0.833581i | ||||
\(172\) | 468419. | + | 118735.i | 1.20730 | + | 0.306025i | ||||
\(173\) | 254781. | 0.647219 | 0.323609 | − | 0.946191i | \(-0.395104\pi\) | ||||
0.323609 | + | 0.946191i | \(0.395104\pi\) | |||||||
\(174\) | −11050.5 | + | 88569.1i | −0.0276700 | + | 0.221773i | ||||
\(175\) | 531803.i | 1.31267i | ||||||||
\(176\) | 270674. | + | 146643.i | 0.658665 | + | 0.356844i | ||||
\(177\) | 23712.2 | 0.0568904 | ||||||||
\(178\) | −32823.3 | + | 263077.i | −0.0776483 | + | 0.622346i | ||||
\(179\) | − | 616670.i | − | 1.43853i | −0.694734 | − | 0.719267i | \(-0.744478\pi\) | ||
0.694734 | − | 0.719267i | \(-0.255522\pi\) | |||||||
\(180\) | −163576. | + | 645320.i | −0.376303 | + | 1.48455i | ||||
\(181\) | 493543. | 1.11977 | 0.559885 | − | 0.828571i | \(-0.310845\pi\) | ||||
0.559885 | + | 0.828571i | \(0.310845\pi\) | |||||||
\(182\) | −18425.8 | + | 147682.i | −0.0412334 | + | 0.330483i | ||||
\(183\) | 23469.8 | 0.0518062 | ||||||||
\(184\) | 146634. | − | 375408.i | 0.319295 | − | 0.817447i | ||||
\(185\) | − | 506575.i | − | 1.08821i | ||||||
\(186\) | −10937.3 | + | 87662.0i | −0.0231808 | + | 0.185793i | ||||
\(187\) | −389964. | −0.815493 | ||||||||
\(188\) | −31517.6 | + | 124340.i | −0.0650366 | + | 0.256575i | ||||
\(189\) | −199064. | −0.405357 | ||||||||
\(190\) | −707169. | − | 436924.i | −1.42115 | − | 0.878056i | ||||
\(191\) | 839278.i | 1.66465i | 0.554290 | + | 0.832324i | \(0.312990\pi\) | ||||
−0.554290 | + | 0.832324i | \(0.687010\pi\) | |||||||
\(192\) | 99877.6 | − | 108345.i | 0.195531 | − | 0.212108i | ||||
\(193\) | − | 85037.8i | − | 0.164331i | −0.996619 | − | 0.0821653i | \(-0.973816\pi\) | ||
0.996619 | − | 0.0821653i | \(-0.0261835\pi\) | |||||||
\(194\) | 57003.0 | − | 456876.i | 0.108741 | − | 0.871554i | ||||
\(195\) | 116256. | 0.218942 | ||||||||
\(196\) | 241173. | + | 61132.5i | 0.448424 | + | 0.113666i | ||||
\(197\) | − | 932798.i | − | 1.71247i | −0.516589 | − | 0.856233i | \(-0.672799\pi\) | ||
0.516589 | − | 0.856233i | \(-0.327201\pi\) | |||||||
\(198\) | −375944. | − | 46905.3i | −0.681491 | − | 0.0850275i | ||||
\(199\) | 158415.i | 0.283573i | 0.989897 | + | 0.141786i | \(0.0452846\pi\) | ||||
−0.989897 | + | 0.141786i | \(0.954715\pi\) | |||||||
\(200\) | 943520. | + | 368539.i | 1.66792 | + | 0.651491i | ||||
\(201\) | 198608. | 0.346742 | ||||||||
\(202\) | −1778.81 | + | 14257.1i | −0.00306727 | + | 0.0245840i | ||||
\(203\) | − | 333450.i | − | 0.567924i | ||||||
\(204\) | −45865.5 | + | 180943.i | −0.0771633 | + | 0.304416i | ||||
\(205\) | −1.86525e6 | −3.09994 | ||||||||
\(206\) | 521755. | + | 65097.8i | 0.856640 | + | 0.106880i | ||||
\(207\) | 496001.i | 0.804557i | ||||||||
\(208\) | 249247. | + | 135034.i | 0.399458 | + | 0.216414i | ||||
\(209\) | 196910. | − | 430130.i | 0.311819 | − | 0.681136i | ||||
\(210\) | −27951.9 | + | 224033.i | −0.0437385 | + | 0.350561i | ||||
\(211\) | − | 140861.i | − | 0.217813i | −0.994052 | − | 0.108907i | \(-0.965265\pi\) | ||
0.994052 | − | 0.108907i | \(-0.0347350\pi\) | |||||||
\(212\) | 108344. | + | 27463.1i | 0.165564 | + | 0.0419671i | ||||
\(213\) | − | 267063.i | − | 0.403334i | ||||||
\(214\) | 117765. | − | 943878.i | 0.175785 | − | 1.40890i | ||||
\(215\) | 1.41021e6i | 2.08060i | ||||||||
\(216\) | −137951. | + | 353177.i | −0.201182 | + | 0.515060i | ||||
\(217\) | − | 330035.i | − | 0.475784i | ||||||
\(218\) | 1.06963e6 | + | 133454.i | 1.52438 | + | 0.190192i | ||||
\(219\) | − | 305694.i | − | 0.430702i | ||||||
\(220\) | −220739. | + | 870837.i | −0.307485 | + | 1.21305i | ||||
\(221\) | −359094. | −0.494569 | ||||||||
\(222\) | 17084.8 | − | 136934.i | 0.0232663 | − | 0.186478i | ||||
\(223\) | −2964.04 | −0.00399137 | −0.00199568 | − | 0.999998i | \(-0.500635\pi\) | ||||
−0.00199568 | + | 0.999998i | \(0.500635\pi\) | |||||||
\(224\) | −320148. | + | 447849.i | −0.426315 | + | 0.596364i | ||||
\(225\) | −1.24661e6 | −1.64162 | ||||||||
\(226\) | 140618. | − | 1.12705e6i | 0.183135 | − | 1.46781i | ||||
\(227\) | 447740.i | 0.576715i | 0.957523 | + | 0.288358i | \(0.0931092\pi\) | ||||
−0.957523 | + | 0.288358i | \(0.906891\pi\) | |||||||
\(228\) | −176421. | − | 141956.i | −0.224757 | − | 0.180849i | ||||
\(229\) | 99233.7i | 0.125046i | 0.998044 | + | 0.0625231i | \(0.0199147\pi\) | ||||
−0.998044 | + | 0.0625231i | \(0.980085\pi\) | |||||||
\(230\) | 1.16711e6 | + | 145616.i | 1.45476 | + | 0.181506i | ||||
\(231\) | −128483. | −0.158422 | ||||||||
\(232\) | −591603. | − | 231080.i | −0.721623 | − | 0.281866i | ||||
\(233\) | 1.17832e6 | 1.42192 | 0.710960 | − | 0.703232i | \(-0.248261\pi\) | ||||
0.710960 | + | 0.703232i | \(0.248261\pi\) | |||||||
\(234\) | −346184. | − | 43192.3i | −0.413301 | − | 0.0515664i | ||||
\(235\) | −374334. | −0.442170 | ||||||||
\(236\) | −41459.1 | + | 163560.i | −0.0484552 | + | 0.191160i | ||||
\(237\) | 12090.6i | 0.0139822i | ||||||||
\(238\) | 86338.4 | − | 691998.i | 0.0988011 | − | 0.791885i | ||||
\(239\) | − | 1.16687e6i | − | 1.32138i | −0.750658 | − | 0.660690i | \(-0.770264\pi\) | ||
0.750658 | − | 0.660690i | \(-0.229736\pi\) | |||||||
\(240\) | 378107. | + | 204847.i | 0.423727 | + | 0.229562i | ||||
\(241\) | − | 1.02176e6i | − | 1.13320i | −0.823994 | − | 0.566599i | \(-0.808259\pi\) | ||
0.823994 | − | 0.566599i | \(-0.191741\pi\) | |||||||
\(242\) | 396710. | + | 49496.3i | 0.435447 | + | 0.0543293i | ||||
\(243\) | − | 710072.i | − | 0.771413i | ||||||
\(244\) | −41035.3 | + | 161888.i | −0.0441249 | + | 0.174076i | ||||
\(245\) | 726071.i | 0.772794i | ||||||||
\(246\) | −504201. | − | 62907.6i | −0.531209 | − | 0.0662774i | ||||
\(247\) | 181323. | − | 396080.i | 0.189108 | − | 0.413086i | ||||
\(248\) | −585544. | − | 228713.i | −0.604548 | − | 0.236136i | ||||
\(249\) | 242555.i | 0.247921i | ||||||||
\(250\) | −161595. | + | 1.29518e6i | −0.163523 | + | 1.31063i | ||||
\(251\) | −786942. | −0.788421 | −0.394211 | − | 0.919020i | \(-0.628982\pi\) | ||||
−0.394211 | + | 0.919020i | \(0.628982\pi\) | |||||||
\(252\) | 166469. | − | 656734.i | 0.165132 | − | 0.651461i | ||||
\(253\) | 669336.i | 0.657420i | ||||||||
\(254\) | 2.02284e6 | + | 252384.i | 1.96733 | + | 0.245458i | ||||
\(255\) | −544744. | −0.524617 | ||||||||
\(256\) | 572707. | + | 878361.i | 0.546176 | + | 0.837670i | ||||
\(257\) | − | 680976.i | − | 0.643130i | −0.946887 | − | 0.321565i | \(-0.895791\pi\) | ||
0.946887 | − | 0.321565i | \(-0.104209\pi\) | |||||||
\(258\) | −47560.9 | + | 381198.i | −0.0444837 | + | 0.356534i | ||||
\(259\) | 515535.i | 0.477539i | ||||||||
\(260\) | −203266. | + | 801901.i | −0.186479 | + | 0.735677i | ||||
\(261\) | 781644. | 0.710245 | ||||||||
\(262\) | −819134. | − | 102201.i | −0.737227 | − | 0.0919816i | ||||
\(263\) | − | 702665.i | − | 0.626411i | −0.949685 | − | 0.313205i | \(-0.898597\pi\) | ||
0.949685 | − | 0.313205i | \(-0.101403\pi\) | |||||||
\(264\) | −89038.5 | + | 227953.i | −0.0786264 | + | 0.201297i | ||||
\(265\) | 326179.i | 0.285326i | ||||||||
\(266\) | 719677. | + | 444652.i | 0.623639 | + | 0.385315i | ||||
\(267\) | −210758. | −0.180928 | ||||||||
\(268\) | −347252. | + | 1.36994e6i | −0.295330 | + | 1.16510i | ||||
\(269\) | −954364. | −0.804144 | −0.402072 | − | 0.915608i | \(-0.631710\pi\) | ||||
−0.402072 | + | 0.915608i | \(0.631710\pi\) | |||||||
\(270\) | −1.09799e6 | − | 136993.i | −0.916620 | − | 0.114364i | ||||
\(271\) | 1.30739e6i | 1.08139i | 0.841219 | + | 0.540695i | \(0.181839\pi\) | ||||
−0.841219 | + | 0.540695i | \(0.818161\pi\) | |||||||
\(272\) | −1.16790e6 | − | 632734.i | −0.957160 | − | 0.518560i | ||||
\(273\) | −118312. | −0.0960778 | ||||||||
\(274\) | 369035. | + | 46043.3i | 0.296955 | + | 0.0370502i | ||||
\(275\) | −1.68225e6 | −1.34140 | ||||||||
\(276\) | 310572. | + | 78723.8i | 0.245409 | + | 0.0622062i | ||||
\(277\) | − | 2.32222e6i | − | 1.81846i | −0.416290 | − | 0.909232i | \(-0.636670\pi\) | ||
0.416290 | − | 0.909232i | \(-0.363330\pi\) | |||||||
\(278\) | −1.23680e6 | − | 154311.i | −0.959812 | − | 0.119753i | ||||
\(279\) | 773639. | 0.595015 | ||||||||
\(280\) | −1.49644e6 | − | 584511.i | −1.14068 | − | 0.445551i | ||||
\(281\) | 1.63016e6i | 1.23158i | 0.787909 | + | 0.615792i | \(0.211164\pi\) | ||||
−0.787909 | + | 0.615792i | \(0.788836\pi\) | |||||||
\(282\) | −101187. | − | 12624.8i | −0.0757708 | − | 0.00945370i | ||||
\(283\) | 821287. | 0.609577 | 0.304789 | − | 0.952420i | \(-0.401414\pi\) | ||||
0.304789 | + | 0.952420i | \(0.401414\pi\) | |||||||
\(284\) | 1.84212e6 | + | 466941.i | 1.35526 | + | 0.343531i | ||||
\(285\) | 275066. | − | 600852.i | 0.200597 | − | 0.438183i | ||||
\(286\) | −467162. | − | 58286.4i | −0.337717 | − | 0.0421359i | ||||
\(287\) | 1.89824e6 | 1.36034 | ||||||||
\(288\) | −1.04981e6 | − | 750463.i | −0.745811 | − | 0.533148i | ||||
\(289\) | 262758. | 0.185060 | ||||||||
\(290\) | 229476. | − | 1.83923e6i | 0.160229 | − | 1.28423i | ||||
\(291\) | 366016. | 0.253378 | ||||||||
\(292\) | 2.10859e6 | + | 534484.i | 1.44722 | + | 0.366841i | ||||
\(293\) | 2.23127e6 | 1.51839 | 0.759194 | − | 0.650864i | \(-0.225593\pi\) | ||||
0.759194 | + | 0.650864i | \(0.225593\pi\) | |||||||
\(294\) | −24487.5 | + | 196266.i | −0.0165225 | + | 0.132427i | ||||
\(295\) | −492410. | −0.329436 | ||||||||
\(296\) | 914657. | + | 357265.i | 0.606777 | + | 0.237007i | ||||
\(297\) | − | 629698.i | − | 0.414230i | ||||||
\(298\) | −218137. | + | 1.74835e6i | −0.142295 | + | 1.14048i | ||||
\(299\) | 616351.i | 0.398703i | ||||||||
\(300\) | −197858. | + | 780567.i | −0.126926 | + | 0.500734i | ||||
\(301\) | − | 1.43515e6i | − | 0.913024i | ||||||
\(302\) | −964250. | − | 120306.i | −0.608376 | − | 0.0759052i | ||||
\(303\) | −11421.8 | −0.00714704 | ||||||||
\(304\) | 1.28763e6 | − | 968701.i | 0.799112 | − | 0.601182i | ||||
\(305\) | −487376. | −0.299995 | ||||||||
\(306\) | 1.62212e6 | + | 202387.i | 0.990330 | + | 0.123560i | ||||
\(307\) | − | 1.82839e6i | − | 1.10719i | −0.832786 | − | 0.553595i | \(-0.813255\pi\) | ||
0.832786 | − | 0.553595i | \(-0.186745\pi\) | |||||||
\(308\) | 224644. | − | 886239.i | 0.134933 | − | 0.532322i | ||||
\(309\) | 417992.i | 0.249042i | ||||||||
\(310\) | 227125. | − | 1.82040e6i | 0.134234 | − | 1.07588i | ||||
\(311\) | − | 1.90568e6i | − | 1.11724i | −0.829422 | − | 0.558622i | \(-0.811330\pi\) | ||
0.829422 | − | 0.558622i | \(-0.188670\pi\) | |||||||
\(312\) | −81990.2 | + | 209908.i | −0.0476843 | + | 0.122080i | ||||
\(313\) | −2.31801e6 | −1.33738 | −0.668688 | − | 0.743543i | \(-0.733144\pi\) | ||||
−0.668688 | + | 0.743543i | \(0.733144\pi\) | |||||||
\(314\) | 42240.7 | − | 338557.i | 0.0241773 | − | 0.193779i | ||||
\(315\) | 1.97715e6 | 1.12270 | ||||||||
\(316\) | −83397.3 | − | 21139.5i | −0.0469823 | − | 0.0119091i | ||||
\(317\) | −2.82404e6 | −1.57842 | −0.789211 | − | 0.614122i | \(-0.789510\pi\) | ||||
−0.789211 | + | 0.614122i | \(0.789510\pi\) | |||||||
\(318\) | −11000.7 | + | 88170.1i | −0.00610033 | + | 0.0488938i | ||||
\(319\) | 1.05480e6 | 0.580355 | ||||||||
\(320\) | −2.07407e6 | + | 2.24991e6i | −1.13226 | + | 1.22826i | ||||
\(321\) | 756167. | 0.409596 | ||||||||
\(322\) | −1.18775e6 | − | 148192.i | −0.638388 | − | 0.0796498i | ||||
\(323\) | −849628. | + | 1.85592e6i | −0.453130 | + | 0.989815i | ||||
\(324\) | 1.38703e6 | + | 351583.i | 0.734045 | + | 0.186065i | ||||
\(325\) | −1.54908e6 | −0.813517 | ||||||||
\(326\) | −756219. | − | 94351.1i | −0.394097 | − | 0.0491703i | ||||
\(327\) | 856911.i | 0.443166i | ||||||||
\(328\) | 1.31548e6 | − | 3.36784e6i | 0.675148 | − | 1.72849i | ||||
\(329\) | 380954. | 0.194036 | ||||||||
\(330\) | −708684. | − | 88420.3i | −0.358235 | − | 0.0446958i | ||||
\(331\) | − | 2.30744e6i | − | 1.15760i | −0.815468 | − | 0.578802i | \(-0.803521\pi\) | ||
0.815468 | − | 0.578802i | \(-0.196479\pi\) | |||||||
\(332\) | −1.67308e6 | − | 424091.i | −0.833050 | − | 0.211161i | ||||
\(333\) | −1.20847e6 | −0.597209 | ||||||||
\(334\) | −2.57818e6 | − | 321671.i | −1.26458 | − | 0.157778i | ||||
\(335\) | −4.12431e6 | −2.00789 | ||||||||
\(336\) | −384794. | − | 208470.i | −0.185943 | − | 0.100738i | ||||
\(337\) | 1.22825e6i | 0.589130i | 0.955631 | + | 0.294565i | \(0.0951748\pi\) | ||||
−0.955631 | + | 0.294565i | \(0.904825\pi\) | |||||||
\(338\) | 1.65401e6 | + | 206366.i | 0.787492 | + | 0.0982530i | ||||
\(339\) | 902909. | 0.426722 | ||||||||
\(340\) | 952447. | − | 3.75749e6i | 0.446831 | − | 1.76279i | ||||
\(341\) | 1.04400e6 | 0.486199 | ||||||||
\(342\) | −1.04232e6 | + | 1.68701e6i | −0.481875 | + | 0.779922i | ||||
\(343\) | − | 2.33619e6i | − | 1.07219i | ||||||
\(344\) | −2.54624e6 | − | 994559.i | −1.16012 | − | 0.453142i | ||||
\(345\) | 935002.i | 0.422926i | ||||||||
\(346\) | −1.43017e6 | − | 178438.i | −0.642239 | − | 0.0801302i | ||||
\(347\) | 884418. | 0.394307 | 0.197153 | − | 0.980373i | \(-0.436830\pi\) | ||||
0.197153 | + | 0.980373i | \(0.436830\pi\) | |||||||
\(348\) | 124060. | − | 489428.i | 0.0549142 | − | 0.216641i | ||||
\(349\) | − | 1.51416e6i | − | 0.665438i | −0.943026 | − | 0.332719i | \(-0.892034\pi\) | ||
0.943026 | − | 0.332719i | \(-0.107966\pi\) | |||||||
\(350\) | 372453. | − | 2.98519e6i | 0.162518 | − | 1.30257i | ||||
\(351\) | − | 579851.i | − | 0.251217i | ||||||
\(352\) | −1.41668e6 | − | 1.01272e6i | −0.609417 | − | 0.435646i | ||||
\(353\) | −924516. | −0.394892 | −0.197446 | − | 0.980314i | \(-0.563265\pi\) | ||||
−0.197446 | + | 0.980314i | \(0.563265\pi\) | |||||||
\(354\) | −133105. | − | 16607.0i | −0.0564527 | − | 0.00704343i | ||||
\(355\) | 5.54585e6i | 2.33559i | ||||||||
\(356\) | 368496. | − | 1.45375e6i | 0.154102 | − | 0.607945i | ||||
\(357\) | 554379. | 0.230216 | ||||||||
\(358\) | −431890. | + | 3.46157e6i | −0.178101 | + | 1.42747i | ||||
\(359\) | 3.57999e6i | 1.46604i | 0.680208 | + | 0.733019i | \(0.261889\pi\) | ||||
−0.680208 | + | 0.733019i | \(0.738111\pi\) | |||||||
\(360\) | 1.37016e6 | − | 3.50784e6i | 0.557205 | − | 1.42654i | ||||
\(361\) | −1.61807e6 | − | 1.87428e6i | −0.653474 | − | 0.756949i | ||||
\(362\) | −2.77042e6 | − | 345657.i | −1.11115 | − | 0.138635i | ||||
\(363\) | 317816.i | 0.126593i | ||||||||
\(364\) | 206861. | − | 816084.i | 0.0818322 | − | 0.322835i | ||||
\(365\) | 6.34807e6i | 2.49407i | ||||||||
\(366\) | −131744. | − | 16437.3i | −0.0514076 | − | 0.00641397i | ||||
\(367\) | − | 1.35151e6i | − | 0.523787i | −0.965097 | − | 0.261893i | \(-0.915653\pi\) | ||
0.965097 | − | 0.261893i | \(-0.0843469\pi\) | |||||||
\(368\) | −1.08603e6 | + | 2.00460e6i | −0.418044 | + | 0.771627i | ||||
\(369\) | 4.44970e6i | 1.70124i | ||||||||
\(370\) | −354784. | + | 2.84357e6i | −0.134729 | + | 1.07984i | ||||
\(371\) | − | 331948.i | − | 0.125209i | ||||||
\(372\) | 122790. | − | 484416.i | 0.0460049 | − | 0.181494i | ||||
\(373\) | 4.87847e6 | 1.81556 | 0.907781 | − | 0.419443i | \(-0.137775\pi\) | ||||
0.907781 | + | 0.419443i | \(0.137775\pi\) | |||||||
\(374\) | 2.18900e6 | + | 273114.i | 0.809219 | + | 0.100964i | ||||
\(375\) | −1.03760e6 | −0.381025 | ||||||||
\(376\) | 264001. | − | 675886.i | 0.0963020 | − | 0.246549i | ||||
\(377\) | 971302. | 0.351966 | ||||||||
\(378\) | 1.11741e6 | + | 139416.i | 0.402238 | + | 0.0501860i | ||||
\(379\) | − | 2.12271e6i | − | 0.759088i | −0.925174 | − | 0.379544i | \(-0.876081\pi\) | ||
0.925174 | − | 0.379544i | \(-0.123919\pi\) | |||||||
\(380\) | 3.66357e6 | + | 2.94787e6i | 1.30151 | + | 1.04725i | ||||
\(381\) | 1.62055e6i | 0.571941i | ||||||||
\(382\) | 587795. | − | 4.71114e6i | 0.206095 | − | 1.65184i | ||||
\(383\) | −506796. | −0.176537 | −0.0882687 | − | 0.996097i | \(-0.528133\pi\) | ||||
−0.0882687 | + | 0.996097i | \(0.528133\pi\) | |||||||
\(384\) | −636527. | + | 538229.i | −0.220287 | + | 0.186268i | ||||
\(385\) | 2.66809e6 | 0.917379 | ||||||||
\(386\) | −59556.9 | + | 477345.i | −0.0203453 | + | 0.163066i | ||||
\(387\) | 3.36417e6 | 1.14183 | ||||||||
\(388\) | −639954. | + | 2.52468e6i | −0.215809 | + | 0.851386i | ||||
\(389\) | − | 1.63640e6i | − | 0.548296i | −0.961688 | − | 0.274148i | \(-0.911604\pi\) | ||
0.961688 | − | 0.274148i | \(-0.0883958\pi\) | |||||||
\(390\) | −652584. | − | 81420.9i | −0.217257 | − | 0.0271065i | ||||
\(391\) | − | 2.88805e6i | − | 0.955351i | ||||||
\(392\) | −1.31097e6 | − | 512065.i | −0.430902 | − | 0.168310i | ||||
\(393\) | − | 656231.i | − | 0.214326i | ||||||
\(394\) | −653293. | + | 5.23611e6i | −0.212015 | + | 1.69929i | ||||
\(395\) | − | 251074.i | − | 0.0809671i | ||||||
\(396\) | 2.07745e6 | + | 526591.i | 0.665720 | + | 0.168747i | ||||
\(397\) | 2.66069e6i | 0.847261i | 0.905835 | + | 0.423631i | \(0.139245\pi\) | ||||
−0.905835 | + | 0.423631i | \(0.860755\pi\) | |||||||
\(398\) | 110947. | − | 889238.i | 0.0351083 | − | 0.281391i | ||||
\(399\) | −279931. | + | 611480.i | −0.0880275 | + | 0.192287i | ||||
\(400\) | −5.03818e6 | − | 2.72953e6i | −1.57443 | − | 0.852979i | ||||
\(401\) | − | 4.45829e6i | − | 1.38454i | −0.721636 | − | 0.692272i | \(-0.756610\pi\) | ||
0.721636 | − | 0.692272i | \(-0.243390\pi\) | |||||||
\(402\) | −1.11485e6 | − | 139097.i | −0.344075 | − | 0.0429291i | ||||
\(403\) | 961354. | 0.294863 | ||||||||
\(404\) | 19970.1 | − | 78784.0i | 0.00608734 | − | 0.0240151i | ||||
\(405\) | 4.17575e6i | 1.26502i | ||||||||
\(406\) | −233534. | + | 1.87176e6i | −0.0703130 | + | 0.563555i | ||||
\(407\) | −1.63079e6 | −0.487991 | ||||||||
\(408\) | 384183. | − | 983573.i | 0.114258 | − | 0.292521i | ||||
\(409\) | 4.62121e6i | 1.36599i | 0.730424 | + | 0.682994i | \(0.239323\pi\) | ||||
−0.730424 | + | 0.682994i | \(0.760677\pi\) | |||||||
\(410\) | 1.04703e7 | + | 1.30634e6i | 3.07609 | + | 0.383794i | ||||
\(411\) | 295644.i | 0.0863306i | ||||||||
\(412\) | −2.88319e6 | − | 730831.i | −0.836817 | − | 0.212116i | ||||
\(413\) | 501119. | 0.144566 | ||||||||
\(414\) | 347379. | − | 2.78422e6i | 0.0996098 | − | 0.798367i | ||||
\(415\) | − | 5.03693e6i | − | 1.43564i | ||||||
\(416\) | −1.30453e6 | − | 932555.i | −0.369591 | − | 0.264205i | ||||
\(417\) | − | 990832.i | − | 0.279036i | ||||||
\(418\) | −1.40657e6 | + | 2.27655e6i | −0.393749 | + | 0.637290i | ||||
\(419\) | −4.42550e6 | −1.23148 | −0.615740 | − | 0.787950i | \(-0.711143\pi\) | ||||
−0.615740 | + | 0.787950i | \(0.711143\pi\) | |||||||
\(420\) | 313807. | − | 1.23800e6i | 0.0868039 | − | 0.342449i | ||||
\(421\) | 2.80313e6 | 0.770793 | 0.385396 | − | 0.922751i | \(-0.374065\pi\) | ||||
0.385396 | + | 0.922751i | \(0.374065\pi\) | |||||||
\(422\) | −98653.1 | + | 790699.i | −0.0269668 | + | 0.216138i | ||||
\(423\) | 893001.i | 0.242662i | ||||||||
\(424\) | −588938. | − | 230039.i | −0.159094 | − | 0.0621422i | ||||
\(425\) | 7.25858e6 | 1.94930 | ||||||||
\(426\) | −187040. | + | 1.49911e6i | −0.0499356 | + | 0.400231i | ||||
\(427\) | 495996. | 0.131646 | ||||||||
\(428\) | −1.32211e6 | + | 5.21583e6i | −0.348865 | + | 1.37630i | ||||
\(429\) | − | 374257.i | − | 0.0981808i | ||||||
\(430\) | 987654. | − | 7.91599e6i | 0.257593 | − | 2.06459i | ||||
\(431\) | 3.60636e6 | 0.935137 | 0.467569 | − | 0.883957i | \(-0.345130\pi\) | ||||
0.467569 | + | 0.883957i | \(0.345130\pi\) | |||||||
\(432\) | 1.02171e6 | − | 1.88588e6i | 0.263403 | − | 0.486190i | ||||
\(433\) | 5.37862e6i | 1.37864i | 0.724457 | + | 0.689320i | \(0.242091\pi\) | ||||
−0.724457 | + | 0.689320i | \(0.757909\pi\) | |||||||
\(434\) | −231142. | + | 1.85259e6i | −0.0589054 | + | 0.472124i | ||||
\(435\) | 1.47346e6 | 0.373350 | ||||||||
\(436\) | −5.91072e6 | − | 1.49825e6i | −1.48910 | − | 0.377457i | ||||
\(437\) | 3.18552e6 | + | 1.45831e6i | 0.797952 | + | 0.365297i | ||||
\(438\) | −214095. | + | 1.71596e6i | −0.0533239 | + | 0.427388i | ||||
\(439\) | 1.29172e6 | 0.319894 | 0.159947 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159947 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(440\) | 1.84898e6 | − | 4.73370e6i | 0.455303 | − | 1.16565i | ||||
\(441\) | 1.73210e6 | 0.424107 | ||||||||
\(442\) | 2.01571e6 | + | 251494.i | 0.490764 | + | 0.0612312i | ||||
\(443\) | 2.33522e6 | 0.565352 | 0.282676 | − | 0.959215i | \(-0.408778\pi\) | ||||
0.282676 | + | 0.959215i | \(0.408778\pi\) | |||||||
\(444\) | −191805. | + | 756688.i | −0.0461746 | + | 0.182163i | ||||
\(445\) | 4.37662e6 | 1.04770 | ||||||||
\(446\) | 16638.1 | + | 2075.89i | 0.00396066 | + | 0.000494159i | ||||
\(447\) | −1.40066e6 | −0.331560 | ||||||||
\(448\) | 2.11075e6 | − | 2.28971e6i | 0.496869 | − | 0.538995i | ||||
\(449\) | − | 2.56046e6i | − | 0.599379i | −0.954037 | − | 0.299690i | \(-0.903117\pi\) | ||
0.954037 | − | 0.299690i | \(-0.0968831\pi\) | |||||||
\(450\) | 6.99763e6 | + | 873072.i | 1.62899 | + | 0.203245i | ||||
\(451\) | 6.00471e6i | 1.39011i | ||||||||
\(452\) | −1.57867e6 | + | 6.22801e6i | −0.363451 | + | 1.43385i | ||||
\(453\) | − | 772488.i | − | 0.176867i | ||||||
\(454\) | 313579. | − | 2.51331e6i | 0.0714014 | − | 0.572278i | ||||
\(455\) | 2.45688e6 | 0.556360 | ||||||||
\(456\) | 890889. | + | 920405.i | 0.200637 | + | 0.207284i | ||||
\(457\) | −2.84015e6 | −0.636138 | −0.318069 | − | 0.948068i | \(-0.603034\pi\) | ||||
−0.318069 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(458\) | 69499.1 | − | 557031.i | 0.0154816 | − | 0.124084i | ||||
\(459\) | 2.71702e6i | 0.601951i | ||||||||
\(460\) | −6.44937e6 | − | 1.63479e6i | −1.42109 | − | 0.360219i | ||||
\(461\) | 3.23395e6i | 0.708730i | 0.935107 | + | 0.354365i | \(0.115303\pi\) | ||||
−0.935107 | + | 0.354365i | \(0.884697\pi\) | |||||||
\(462\) | 721218. | + | 89984.2i | 0.157203 | + | 0.0196138i | ||||
\(463\) | − | 8.68840e6i | − | 1.88360i | −0.336180 | − | 0.941798i | \(-0.609135\pi\) | ||
0.336180 | − | 0.941798i | \(-0.390865\pi\) | |||||||
\(464\) | 3.15903e6 | + | 1.71146e6i | 0.681174 | + | 0.369039i | ||||
\(465\) | 1.45837e6 | 0.312778 | ||||||||
\(466\) | −6.61433e6 | − | 825249.i | −1.41098 | − | 0.176044i | ||||
\(467\) | −7.68880e6 | −1.63142 | −0.815711 | − | 0.578459i | \(-0.803654\pi\) | ||||
−0.815711 | + | 0.578459i | \(0.803654\pi\) | |||||||
\(468\) | 1.91299e6 | + | 484905.i | 0.403737 | + | 0.102339i | ||||
\(469\) | 4.19726e6 | 0.881117 | ||||||||
\(470\) | 2.10126e6 | + | 262168.i | 0.438768 | + | 0.0547437i | ||||
\(471\) | 271227. | 0.0563354 | ||||||||
\(472\) | 347275. | − | 889080.i | 0.0717493 | − | 0.183690i | ||||
\(473\) | 4.53982e6 | 0.933009 | ||||||||
\(474\) | 8467.73 | − | 67868.4i | 0.00173110 | − | 0.0138746i | ||||
\(475\) | −3.66519e6 | + | 8.00622e6i | −0.745353 | + | 1.62815i | ||||
\(476\) | −969292. | + | 3.82394e6i | −0.196082 | + | 0.773560i | ||||
\(477\) | 778123. | 0.156586 | ||||||||
\(478\) | −817228. | + | 6.55003e6i | −0.163596 | + | 1.31121i | ||||
\(479\) | 6.32466e6i | 1.25950i | 0.776797 | + | 0.629751i | \(0.216843\pi\) | ||||
−0.776797 | + | 0.629751i | \(0.783157\pi\) | |||||||
\(480\) | −1.97897e6 | − | 1.41468e6i | −0.392046 | − | 0.280257i | ||||
\(481\) | −1.50170e6 | −0.295951 | ||||||||
\(482\) | −715597. | + | 5.73547e6i | −0.140298 | + | 1.12448i | ||||
\(483\) | − | 951539.i | − | 0.185592i | ||||||
\(484\) | −2.19220e6 | − | 555678.i | −0.425370 | − | 0.107823i | ||||
\(485\) | −7.60073e6 | −1.46724 | ||||||||
\(486\) | −497305. | + | 3.98587e6i | −0.0955063 | + | 0.765478i | ||||
\(487\) | −1.68772e6 | −0.322462 | −0.161231 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161231 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(488\) | 343724. | − | 879992.i | 0.0653373 | − | 0.167274i | ||||
\(489\) | − | 605828.i | − | 0.114572i | ||||||
\(490\) | 508510. | − | 4.07568e6i | 0.0956773 | − | 0.766848i | ||||
\(491\) | −4.39190e6 | −0.822146 | −0.411073 | − | 0.911602i | \(-0.634846\pi\) | ||||
−0.411073 | + | 0.911602i | \(0.634846\pi\) | |||||||
\(492\) | 2.78619e6 | + | 706242.i | 0.518917 | + | 0.131535i | ||||
\(493\) | −4.55126e6 | −0.843362 | ||||||||
\(494\) | −1.29522e6 | + | 2.09634e6i | −0.238796 | + | 0.386495i | ||||
\(495\) | 6.25431e6i | 1.14727i | ||||||||
\(496\) | 3.12667e6 | + | 1.69393e6i | 0.570661 | + | 0.309167i | ||||
\(497\) | − | 5.64394e6i | − | 1.02492i | ||||||
\(498\) | 169876. | − | 1.36154e6i | 0.0306943 | − | 0.246013i | ||||
\(499\) | 5.21260e6 | 0.937137 | 0.468568 | − | 0.883427i | \(-0.344770\pi\) | ||||
0.468568 | + | 0.883427i | \(0.344770\pi\) | |||||||
\(500\) | 1.81418e6 | − | 7.15709e6i | 0.324530 | − | 1.28030i | ||||
\(501\) | − | 2.06545e6i | − | 0.367638i | ||||||
\(502\) | 4.41736e6 | + | 551141.i | 0.782355 | + | 0.0976121i | ||||
\(503\) | − | 1.33359e6i | − | 0.235018i | −0.993072 | − | 0.117509i | \(-0.962509\pi\) | ||
0.993072 | − | 0.117509i | \(-0.0374909\pi\) | |||||||
\(504\) | −1.39439e6 | + | 3.56988e6i | −0.244517 | + | 0.626004i | ||||
\(505\) | 237185. | 0.0413865 | ||||||||
\(506\) | 468775. | − | 3.75721e6i | 0.0813932 | − | 0.652362i | ||||
\(507\) | 1.32507e6i | 0.228939i | ||||||||
\(508\) | −1.11781e7 | − | 2.83343e6i | −1.92180 | − | 0.487139i | ||||
\(509\) | 960938. | 0.164400 | 0.0821998 | − | 0.996616i | \(-0.473805\pi\) | ||||
0.0821998 | + | 0.996616i | \(0.473805\pi\) | |||||||
\(510\) | 3.05783e6 | + | 381516.i | 0.520580 | + | 0.0649512i | ||||
\(511\) | − | 6.46034e6i | − | 1.09447i | ||||||
\(512\) | −2.59963e6 | − | 5.33163e6i | −0.438264 | − | 0.898846i | ||||
\(513\) | −2.99687e6 | − | 1.37195e6i | −0.502777 | − | 0.230167i | ||||
\(514\) | −476927. | + | 3.82254e6i | −0.0796240 | + | 0.638182i | ||||
\(515\) | − | 8.68007e6i | − | 1.44213i | ||||||
\(516\) | 533950. | − | 2.10648e6i | 0.0882829 | − | 0.348284i | ||||
\(517\) | 1.20507e6i | 0.198284i | ||||||||
\(518\) | 361059. | − | 2.89387e6i | 0.0591226 | − | 0.473865i | ||||
\(519\) | − | 1.14575e6i | − | 0.186711i | ||||||
\(520\) | 1.70261e6 | − | 4.35898e6i | 0.276126 | − | 0.706930i | ||||
\(521\) | 1.08312e7i | 1.74816i | 0.485782 | + | 0.874080i | \(0.338535\pi\) | ||||
−0.485782 | + | 0.874080i | \(0.661465\pi\) | |||||||
\(522\) | −4.38763e6 | − | 547431.i | −0.704780 | − | 0.0879333i | ||||
\(523\) | − | 3.86911e6i | − | 0.618524i | −0.950977 | − | 0.309262i | \(-0.899918\pi\) | ||
0.950977 | − | 0.309262i | \(-0.100082\pi\) | |||||||
\(524\) | 4.52649e6 | + | 1.14737e6i | 0.720168 | + | 0.182548i | ||||
\(525\) | 2.39152e6 | 0.378683 | ||||||||
\(526\) | −492117. | + | 3.94429e6i | −0.0775540 | + | 0.621591i | ||||
\(527\) | −4.50464e6 | −0.706535 | ||||||||
\(528\) | 659452. | − | 1.21722e6i | 0.102943 | − | 0.190013i | ||||
\(529\) | 1.47928e6 | 0.229832 | ||||||||
\(530\) | 228442. | − | 1.83095e6i | 0.0353253 | − | 0.283130i | ||||
\(531\) | 1.17468e6i | 0.180794i | ||||||||
\(532\) | −3.72837e6 | − | 3.00001e6i | −0.571136 | − | 0.459562i | ||||
\(533\) | 5.52937e6i | 0.843058i | ||||||||
\(534\) | 1.18305e6 | + | 147606.i | 0.179536 | + | 0.0224002i | ||||
\(535\) | −1.57026e7 | −2.37186 | ||||||||
\(536\) | 2.90869e6 | − | 7.44674e6i | 0.437306 | − | 1.11958i | ||||
\(537\) | −2.77316e6 | −0.414992 | ||||||||
\(538\) | 5.35716e6 | + | 668397.i | 0.797957 | + | 0.0995586i | ||||
\(539\) | 2.33740e6 | 0.346546 | ||||||||
\(540\) | 6.06744e6 | + | 1.53797e6i | 0.895409 | + | 0.226968i | ||||
\(541\) | 9.20084e6i | 1.35156i | 0.737105 | + | 0.675779i | \(0.236193\pi\) | ||||
−0.737105 | + | 0.675779i | \(0.763807\pi\) | |||||||
\(542\) | 915642. | − | 7.33882e6i | 0.133884 | − | 1.07307i | ||||
\(543\) | − | 2.21946e6i | − | 0.323034i | ||||||
\(544\) | 6.11269e6 | + | 4.36970e6i | 0.885595 | + | 0.633073i | ||||
\(545\) | − | 1.77947e7i | − | 2.56625i | ||||||
\(546\) | 664126. | + | 82860.9i | 0.0953386 | + | 0.0118951i | ||||
\(547\) | − | 1.36673e7i | − | 1.95306i | −0.215380 | − | 0.976530i | \(-0.569099\pi\) | ||
0.215380 | − | 0.976530i | \(-0.430901\pi\) | |||||||
\(548\) | −2.03927e6 | − | 516913.i | −0.290083 | − | 0.0735302i | ||||
\(549\) | 1.16267e6i | 0.164637i | ||||||||
\(550\) | 9.44305e6 | + | 1.17818e6i | 1.33108 | + | 0.166075i | ||||
\(551\) | 2.29813e6 | − | 5.02003e6i | 0.322475 | − | 0.704413i | ||||
\(552\) | −1.68821e6 | − | 659415.i | −0.235819 | − | 0.0921109i | ||||
\(553\) | 255515.i | 0.0355306i | ||||||||
\(554\) | −1.62639e6 | + | 1.30354e7i | −0.225139 | + | 1.80447i | ||||
\(555\) | −2.27807e6 | −0.313931 | ||||||||
\(556\) | 6.83447e6 | + | 1.73240e6i | 0.937601 | + | 0.237663i | ||||
\(557\) | − | 4.93456e6i | − | 0.673923i | −0.941518 | − | 0.336962i | \(-0.890601\pi\) | ||
0.941518 | − | 0.336962i | \(-0.109399\pi\) | |||||||
\(558\) | −4.34269e6 | − | 541824.i | −0.590437 | − | 0.0736670i | ||||
\(559\) | 4.18045e6 | 0.565839 | ||||||||
\(560\) | 7.99067e6 | + | 4.32910e6i | 1.07675 | + | 0.583348i | ||||
\(561\) | 1.75367e6i | 0.235255i | ||||||||
\(562\) | 1.14169e6 | − | 9.15062e6i | 0.152479 | − | 1.22211i | ||||
\(563\) | − | 4.87905e6i | − | 0.648730i | −0.945932 | − | 0.324365i | \(-0.894849\pi\) | ||
0.945932 | − | 0.324365i | \(-0.105151\pi\) | |||||||
\(564\) | 559155. | + | 141734.i | 0.0740175 | + | 0.0187619i | ||||
\(565\) | −1.87499e7 | −2.47103 | ||||||||
\(566\) | −4.61016e6 | − | 575195.i | −0.604888 | − | 0.0754700i | ||||
\(567\) | − | 4.24961e6i | − | 0.555125i | ||||||
\(568\) | −1.00134e7 | − | 3.91124e6i | −1.30230 | − | 0.508679i | ||||
\(569\) | − | 3.03918e6i | − | 0.393528i | −0.980451 | − | 0.196764i | \(-0.936957\pi\) | ||
0.980451 | − | 0.196764i | \(-0.0630433\pi\) | |||||||
\(570\) | −1.96485e6 | + | 3.18014e6i | −0.253304 | + | 0.409977i | ||||
\(571\) | 715082. | 0.0917837 | 0.0458919 | − | 0.998946i | \(-0.485387\pi\) | ||||
0.0458919 | + | 0.998946i | \(0.485387\pi\) | |||||||
\(572\) | 2.58152e6 | + | 654362.i | 0.329902 | + | 0.0836235i | ||||
\(573\) | 3.77423e6 | 0.480222 | ||||||||
\(574\) | −1.06555e7 | − | 1.32945e6i | −1.34987 | − | 0.168419i | ||||
\(575\) | − | 1.24587e7i | − | 1.57146i | ||||||
\(576\) | 5.36733e6 | + | 4.94784e6i | 0.674066 | + | 0.621383i | ||||
\(577\) | −7.57765e6 | −0.947534 | −0.473767 | − | 0.880650i | \(-0.657106\pi\) | ||||
−0.473767 | + | 0.880650i | \(0.657106\pi\) | |||||||
\(578\) | −1.47495e6 | − | 184025.i | −0.183636 | − | 0.0229117i | ||||
\(579\) | −382415. | −0.0474065 | ||||||||
\(580\) | −2.57624e6 | + | 1.01635e7i | −0.317993 | + | 1.25451i | ||||
\(581\) | 5.12601e6i | 0.629998i | ||||||||
\(582\) | −2.05457e6 | − | 256343.i | −0.251428 | − | 0.0313699i | ||||
\(583\) | 1.05005e6 | 0.127949 | ||||||||
\(584\) | −1.14619e7 | − | 4.47701e6i | −1.39067 | − | 0.543195i | ||||
\(585\) | 5.75921e6i | 0.695783i | ||||||||
\(586\) | −1.25249e7 | − | 1.56269e6i | −1.50671 | − | 0.187987i | ||||
\(587\) | 7.04413e6 | 0.843785 | 0.421893 | − | 0.906646i | \(-0.361366\pi\) | ||||
0.421893 | + | 0.906646i | \(0.361366\pi\) | |||||||
\(588\) | 274913. | − | 1.08456e6i | 0.0327908 | − | 0.129363i | ||||
\(589\) | 2.27460e6 | − | 4.96862e6i | 0.270157 | − | 0.590130i | ||||
\(590\) | 2.76406e6 | + | 344863.i | 0.326902 | + | 0.0407865i | ||||
\(591\) | −4.19479e6 | −0.494017 | ||||||||
\(592\) | −4.88406e6 | − | 2.64603e6i | −0.572765 | − | 0.310307i | ||||
\(593\) | −1.54904e7 | −1.80895 | −0.904473 | − | 0.426531i | \(-0.859736\pi\) | ||||
−0.904473 | + | 0.426531i | \(0.859736\pi\) | |||||||
\(594\) | −441014. | + | 3.53471e6i | −0.0512846 | + | 0.411043i | ||||
\(595\) | −1.15123e7 | −1.33312 | ||||||||
\(596\) | 2.44895e6 | − | 9.66132e6i | 0.282400 | − | 1.11409i | ||||
\(597\) | 712393. | 0.0818058 | ||||||||
\(598\) | 431666. | − | 3.45978e6i | 0.0493623 | − | 0.395636i | ||||
\(599\) | −8.16729e6 | −0.930059 | −0.465030 | − | 0.885295i | \(-0.653956\pi\) | ||||
−0.465030 | + | 0.885295i | \(0.653956\pi\) | |||||||
\(600\) | 1.65732e6 | − | 4.24301e6i | 0.187944 | − | 0.481167i | ||||
\(601\) | 5.00996e6i | 0.565781i | 0.959152 | + | 0.282891i | \(0.0912933\pi\) | ||||
−0.959152 | + | 0.282891i | \(0.908707\pi\) | |||||||
\(602\) | −1.00512e6 | + | 8.05600e6i | −0.113039 | + | 0.906000i | ||||
\(603\) | 9.83886e6i | 1.10192i | ||||||||
\(604\) | 5.32840e6 | + | 1.35064e6i | 0.594298 | + | 0.150642i | ||||
\(605\) | − | 6.59979e6i | − | 0.733063i | ||||||
\(606\) | 64114.1 | + | 7999.32i | 0.00709205 | + | 0.000884854i | ||||
\(607\) | 1.30779e7 | 1.44068 | 0.720338 | − | 0.693623i | \(-0.243987\pi\) | ||||
0.720338 | + | 0.693623i | \(0.243987\pi\) | |||||||
\(608\) | −7.90635e6 | + | 4.53583e6i | −0.867395 | + | 0.497621i | ||||
\(609\) | −1.49952e6 | −0.163836 | ||||||||
\(610\) | 2.73580e6 | + | 341338.i | 0.297687 | + | 0.0371415i | ||||
\(611\) | 1.10968e6i | 0.120252i | ||||||||
\(612\) | −8.96377e6 | − | 2.27213e6i | −0.967413 | − | 0.245220i | ||||
\(613\) | − | 3.44034e6i | − | 0.369785i | −0.982759 | − | 0.184893i | \(-0.940806\pi\) | ||
0.982759 | − | 0.184893i | \(-0.0591937\pi\) | |||||||
\(614\) | −1.28053e6 | + | 1.02633e7i | −0.137078 | + | 1.09867i | ||||
\(615\) | 8.38803e6i | 0.894278i | ||||||||
\(616\) | −1.88168e6 | + | 4.81742e6i | −0.199800 | + | 0.511521i | ||||
\(617\) | −1.31680e7 | −1.39254 | −0.696269 | − | 0.717781i | \(-0.745158\pi\) | ||||
−0.696269 | + | 0.717781i | \(0.745158\pi\) | |||||||
\(618\) | 292744. | − | 2.34633e6i | 0.0308331 | − | 0.247126i | ||||
\(619\) | 1.10190e7 | 1.15589 | 0.577945 | − | 0.816076i | \(-0.303855\pi\) | ||||
0.577945 | + | 0.816076i | \(0.303855\pi\) | |||||||
\(620\) | −2.54986e6 | + | 1.00594e7i | −0.266402 | + | 1.05098i | ||||
\(621\) | 4.66351e6 | 0.485271 | ||||||||
\(622\) | −1.33466e6 | + | 1.06972e7i | −0.138323 | + | 1.10865i | ||||
\(623\) | −4.45403e6 | −0.459762 | ||||||||
\(624\) | 607249. | − | 1.12086e6i | 0.0624317 | − | 0.115237i | ||||
\(625\) | 4.06021e6 | 0.415765 | ||||||||
\(626\) | 1.30117e7 | + | 1.62343e6i | 1.32709 | + | 0.165577i | ||||
\(627\) | −1.93429e6 | − | 885505.i | −0.196496 | − | 0.0899544i | ||||
\(628\) | −474222. | + | 1.87085e6i | −0.0479825 | + | 0.189295i | ||||
\(629\) | 7.03653e6 | 0.709140 | ||||||||
\(630\) | −1.10984e7 | − | 1.38471e6i | −1.11406 | − | 0.138998i | ||||
\(631\) | − | 6.53113e6i | − | 0.653003i | −0.945197 | − | 0.326501i | \(-0.894130\pi\) | ||
0.945197 | − | 0.326501i | \(-0.105870\pi\) | |||||||
\(632\) | 453331. | + | 177071.i | 0.0451464 | + | 0.0176342i | ||||
\(633\) | −633452. | −0.0628354 | ||||||||
\(634\) | 1.58523e7 | + | 1.97784e6i | 1.56628 | + | 0.195420i | ||||
\(635\) | − | 3.36526e7i | − | 3.31195i | ||||||
\(636\) | 123501. | − | 487224.i | 0.0121068 | − | 0.0477623i | ||||
\(637\) | 2.15237e6 | 0.210169 | ||||||||
\(638\) | −5.92095e6 | − | 738739.i | −0.575890 | − | 0.0718520i | ||||
\(639\) | 1.32300e7 | 1.28177 | ||||||||
\(640\) | 1.32182e7 | − | 1.11769e7i | 1.27562 | − | 1.07863i | ||||
\(641\) | − | 1.26861e7i | − | 1.21950i | −0.792594 | − | 0.609750i | \(-0.791270\pi\) | ||
0.792594 | − | 0.609750i | \(-0.208730\pi\) | |||||||
\(642\) | −4.24462e6 | − | 529588.i | −0.406444 | − | 0.0507108i | ||||
\(643\) | 8.74310e6 | 0.833946 | 0.416973 | − | 0.908919i | \(-0.363091\pi\) | ||||
0.416973 | + | 0.908919i | \(0.363091\pi\) | |||||||
\(644\) | 6.56344e6 | + | 1.66370e6i | 0.623616 | + | 0.158074i | ||||
\(645\) | 6.34172e6 | 0.600216 | ||||||||
\(646\) | 6.06906e6 | − | 9.82287e6i | 0.572190 | − | 0.926099i | ||||
\(647\) | − | 2.39445e6i | − | 0.224877i | −0.993659 | − | 0.112438i | \(-0.964134\pi\) | ||
0.993659 | − | 0.112438i | \(-0.0358661\pi\) | |||||||
\(648\) | −7.53961e6 | − | 2.94497e6i | −0.705361 | − | 0.275514i | ||||
\(649\) | 1.58519e6i | 0.147730i | ||||||||
\(650\) | 8.69552e6 | + | 1.08491e6i | 0.807258 | + | 0.100719i | ||||
\(651\) | −1.48416e6 | −0.137255 | ||||||||
\(652\) | 4.17883e6 | + | 1.05925e6i | 0.384978 | + | 0.0975840i | ||||
\(653\) | 4.14995e6i | 0.380855i | 0.981701 | + | 0.190428i | \(0.0609874\pi\) | ||||
−0.981701 | + | 0.190428i | \(0.939013\pi\) | |||||||
\(654\) | 600145. | − | 4.81013e6i | 0.0548670 | − | 0.439756i | ||||
\(655\) | 1.36273e7i | 1.24110i | ||||||||
\(656\) | −9.74291e6 | + | 1.79835e7i | −0.883953 | + | 1.63160i | ||||
\(657\) | 1.51438e7 | 1.36874 | ||||||||
\(658\) | −2.13842e6 | − | 266805.i | −0.192544 | − | 0.0240231i | ||||
\(659\) | 1.08924e7i | 0.977036i | 0.872554 | + | 0.488518i | \(0.162462\pi\) | ||||
−0.872554 | + | 0.488518i | \(0.837538\pi\) | |||||||
\(660\) | 3.91615e6 | + | 992665.i | 0.349945 | + | 0.0887039i | ||||
\(661\) | −3.44356e6 | −0.306552 | −0.153276 | − | 0.988183i | \(-0.548982\pi\) | ||||
−0.153276 | + | 0.988183i | \(0.548982\pi\) | |||||||
\(662\) | −1.61603e6 | + | 1.29524e7i | −0.143319 | + | 1.14870i | ||||
\(663\) | 1.61484e6i | 0.142675i | ||||||||
\(664\) | 9.09452e6 | + | 3.55232e6i | 0.800497 | + | 0.312674i | ||||
\(665\) | 5.81307e6 | − | 1.26980e7i | 0.509743 | − | 1.11348i | ||||
\(666\) | 6.78356e6 | + | 846364.i | 0.592614 | + | 0.0739386i | ||||
\(667\) | 7.81180e6i | 0.679887i | ||||||||
\(668\) | 1.42469e7 | + | 3.61129e6i | 1.23532 | + | 0.313128i | ||||
\(669\) | 13329.3i | 0.00115144i | ||||||||
\(670\) | 2.31511e7 | + | 2.88850e6i | 1.99244 | + | 0.248591i | ||||
\(671\) | 1.56898e6i | 0.134528i | ||||||||
\(672\) | 2.01397e6 | + | 1.43970e6i | 0.172041 | + | 0.122984i | ||||
\(673\) | 1.24306e7i | 1.05792i | 0.848645 | + | 0.528962i | \(0.177419\pi\) | ||||
−0.848645 | + | 0.528962i | \(0.822581\pi\) | |||||||
\(674\) | 860213. | − | 6.89456e6i | 0.0729384 | − | 0.584597i | ||||
\(675\) | 1.17209e7i | 0.990150i | ||||||||
\(676\) | −9.13997e6 | − | 2.31680e6i | −0.769269 | − | 0.194994i | ||||
\(677\) | −1.41359e7 | −1.18536 | −0.592681 | − | 0.805437i | \(-0.701931\pi\) | ||||
−0.592681 | + | 0.805437i | \(0.701931\pi\) | |||||||
\(678\) | −5.06833e6 | − | 632360.i | −0.423439 | − | 0.0528311i | ||||
\(679\) | 7.73516e6 | 0.643865 | ||||||||
\(680\) | −7.97799e6 | + | 2.04250e7i | −0.661639 | + | 1.69391i | ||||
\(681\) | 2.01349e6 | 0.166372 | ||||||||
\(682\) | −5.86031e6 | − | 731173.i | −0.482458 | − | 0.0601948i | ||||
\(683\) | − | 1.02525e7i | − | 0.840967i | −0.907300 | − | 0.420484i | \(-0.861860\pi\) | ||
0.907300 | − | 0.420484i | \(-0.138140\pi\) | |||||||
\(684\) | 7.03237e6 | − | 8.73973e6i | 0.574727 | − | 0.714262i | ||||
\(685\) | − | 6.13937e6i | − | 0.499916i | ||||||
\(686\) | −1.63617e6 | + | 1.31138e7i | −0.132745 | + | 1.06395i | ||||
\(687\) | 446254. | 0.0360736 | ||||||||
\(688\) | 1.35963e7 | + | 7.36607e6i | 1.09509 | + | 0.593287i | ||||
\(689\) | 966927. | 0.0775971 | ||||||||
\(690\) | 654836. | − | 5.24848e6i | 0.0523612 | − | 0.419672i | ||||
\(691\) | −2.17104e6 | −0.172971 | −0.0864854 | − | 0.996253i | \(-0.527564\pi\) | ||||
−0.0864854 | + | 0.996253i | \(0.527564\pi\) | |||||||
\(692\) | 7.90304e6 | + | 2.00326e6i | 0.627378 | + | 0.159027i | ||||
\(693\) | − | 6.36493e6i | − | 0.503455i | ||||||
\(694\) | −4.96453e6 | − | 619410.i | −0.391273 | − | 0.0488179i | ||||
\(695\) | 2.05757e7i | 1.61582i | ||||||||
\(696\) | −1.03917e6 | + | 2.66044e6i | −0.0813134 | + | 0.208176i | ||||
\(697\) | − | 2.59091e7i | − | 2.02009i | ||||||
\(698\) | −1.06045e6 | + | 8.49948e6i | −0.0823859 | + | 0.660319i | ||||
\(699\) | − | 5.29892e6i | − | 0.410199i | ||||||
\(700\) | −4.18140e6 | + | 1.64960e7i | −0.322535 | + | 1.27243i | ||||
\(701\) | − | 1.47483e7i | − | 1.13357i | −0.823866 | − | 0.566785i | \(-0.808187\pi\) | ||
0.823866 | − | 0.566785i | \(-0.191813\pi\) | |||||||
\(702\) | −406103. | + | 3.25489e6i | −0.0311024 | + | 0.249284i | ||||
\(703\) | −3.55306e6 | + | 7.76130e6i | −0.271153 | + | 0.592306i | ||||
\(704\) | 7.24302e6 | + | 6.67693e6i | 0.550793 | + | 0.507745i | ||||
\(705\) | 1.68338e6i | 0.127558i | ||||||||
\(706\) | 5.18962e6 | + | 647493.i | 0.391853 | + | 0.0488903i | ||||
\(707\) | −241380. | −0.0181616 | ||||||||
\(708\) | 735529. | + | 186442.i | 0.0551463 | + | 0.0139785i | ||||
\(709\) | − | 579292.i | − | 0.0432795i | −0.999766 | − | 0.0216397i | \(-0.993111\pi\) | ||
0.999766 | − | 0.0216397i | \(-0.00688868\pi\) | |||||||
\(710\) | 3.88408e6 | − | 3.11307e7i | 0.289163 | − | 2.31762i | ||||
\(711\) | −598955. | −0.0444345 | ||||||||
\(712\) | −3.08663e6 | + | 7.90229e6i | −0.228184 | + | 0.584189i | ||||
\(713\) | 7.73180e6i | 0.569582i | ||||||||
\(714\) | −3.11191e6 | − | 388264.i | −0.228445 | − | 0.0285024i | ||||
\(715\) | 7.77185e6i | 0.568538i | ||||||||
\(716\) | 4.84868e6 | − | 1.91285e7i | 0.353461 | − | 1.39443i | ||||
\(717\) | −5.24742e6 | −0.381195 | ||||||||
\(718\) | 2.50727e6 | − | 2.00957e7i | 0.181506 | − | 1.45476i | ||||
\(719\) | 2.45890e7i | 1.77386i | 0.461906 | + | 0.886929i | \(0.347166\pi\) | ||||
−0.461906 | + | 0.886929i | \(0.652834\pi\) | |||||||
\(720\) | −1.01479e7 | + | 1.87310e7i | −0.729533 | + | 1.34658i | ||||
\(721\) | 8.83359e6i | 0.632848i | ||||||||
\(722\) | 7.77008e6 | + | 1.16542e7i | 0.554731 | + | 0.832030i | ||||
\(723\) | −4.59485e6 | −0.326908 | ||||||||
\(724\) | 1.53092e7 | + | 3.88057e6i | 1.08544 | + | 0.275137i | ||||
\(725\) | −1.96335e7 | −1.38725 | ||||||||
\(726\) | 222585. | − | 1.78400e6i | 0.0156731 | − | 0.125619i | ||||
\(727\) | 1.45708e7i | 1.02246i | 0.859443 | + | 0.511232i | \(0.170811\pi\) | ||||
−0.859443 | + | 0.511232i | \(0.829189\pi\) | |||||||
\(728\) | −1.73273e6 | + | 4.43607e6i | −0.121172 | + | 0.310220i | ||||
\(729\) | 7.67265e6 | 0.534720 | ||||||||
\(730\) | 4.44592e6 | − | 3.56338e7i | 0.308784 | − | 2.47488i | ||||
\(731\) | −1.95884e7 | −1.35583 | ||||||||
\(732\) | 728010. | + | 184536.i | 0.0502180 | + | 0.0127292i | ||||
\(733\) | 1.87450e6i | 0.128862i | 0.997922 | + | 0.0644311i | \(0.0205233\pi\) | ||||
−0.997922 | + | 0.0644311i | \(0.979477\pi\) | |||||||
\(734\) | −946542. | + | 7.58648e6i | −0.0648485 | + | 0.519757i | ||||
\(735\) | 3.26514e6 | 0.222938 | ||||||||
\(736\) | 7.50017e6 | − | 1.04919e7i | 0.510360 | − | 0.713933i | ||||
\(737\) | 1.32772e7i | 0.900404i | ||||||||
\(738\) | 3.11638e6 | − | 2.49776e7i | 0.210625 | − | 1.68815i | ||||
\(739\) | −1.58113e7 | −1.06502 | −0.532508 | − | 0.846425i | \(-0.678750\pi\) | ||||
−0.532508 | + | 0.846425i | \(0.678750\pi\) | |||||||
\(740\) | 3.98304e6 | − | 1.57134e7i | 0.267384 | − | 1.05485i | ||||
\(741\) | −1.78117e6 | − | 815408.i | −0.119168 | − | 0.0545543i | ||||
\(742\) | −232482. | + | 1.86333e6i | −0.0155017 | + | 0.124245i | ||||
\(743\) | 1.94622e7 | 1.29336 | 0.646680 | − | 0.762761i | \(-0.276157\pi\) | ||||
0.646680 | + | 0.762761i | \(0.276157\pi\) | |||||||
\(744\) | −1.02852e6 | + | 2.63319e6i | −0.0681211 | + | 0.174401i | ||||
\(745\) | 2.90861e7 | 1.91997 | ||||||||
\(746\) | −2.73845e7 | − | 3.41667e6i | −1.80159 | − | 0.224779i | ||||
\(747\) | −1.20160e7 | −0.787875 | ||||||||
\(748\) | −1.20963e7 | − | 3.06616e6i | −0.790493 | − | 0.200374i | ||||
\(749\) | 1.59804e7 | 1.04084 | ||||||||
\(750\) | 5.82442e6 | + | 726695.i | 0.378094 | + | 0.0471736i | ||||
\(751\) | −2.18798e7 | −1.41561 | −0.707804 | − | 0.706409i | \(-0.750314\pi\) | ||||
−0.707804 | + | 0.706409i | \(0.750314\pi\) | |||||||
\(752\) | −1.95529e6 | + | 3.60907e6i | −0.126086 | + | 0.232729i | ||||
\(753\) | 3.53887e6i | 0.227446i | ||||||||
\(754\) | −5.45224e6 | − | 680259.i | −0.349258 | − | 0.0435759i | ||||
\(755\) | 1.60415e7i | 1.02419i | ||||||||
\(756\) | −6.17476e6 | − | 1.56518e6i | −0.392930 | − | 0.0995999i | ||||
\(757\) | 2.59831e7i | 1.64797i | 0.566608 | + | 0.823987i | \(0.308255\pi\) | ||||
−0.566608 | + | 0.823987i | \(0.691745\pi\) | |||||||
\(758\) | −1.48665e6 | + | 1.19155e7i | −0.0939804 | + | 0.753247i | ||||
\(759\) | 3.01000e6 | 0.189654 | ||||||||
\(760\) | −1.85003e7 | − | 1.91132e7i | −1.16183 | − | 1.20033i | ||||
\(761\) | −1.42185e7 | −0.890006 | −0.445003 | − | 0.895529i | \(-0.646797\pi\) | ||||
−0.445003 | + | 0.895529i | \(0.646797\pi\) | |||||||
\(762\) | 1.13497e6 | − | 9.09671e6i | 0.0708103 | − | 0.567540i | ||||
\(763\) | 1.81094e7i | 1.12614i | ||||||||
\(764\) | −6.59898e6 | + | 2.60336e7i | −0.409019 | + | 1.61362i | ||||
\(765\) | − | 2.69861e7i | − | 1.66720i | ||||||
\(766\) | 2.84482e6 | + | 354939.i | 0.175179 | + | 0.0218566i | ||||
\(767\) | 1.45970e6i | 0.0895935i | ||||||||
\(768\) | 3.94999e6 | − | 2.57546e6i | 0.241653 | − | 0.157562i | ||||
\(769\) | 1.06124e7 | 0.647142 | 0.323571 | − | 0.946204i | \(-0.395117\pi\) | ||||
0.323571 | + | 0.946204i | \(0.395117\pi\) | |||||||
\(770\) | −1.49769e7 | − | 1.86862e6i | −0.910321 | − | 0.113578i | ||||
\(771\) | −3.06235e6 | −0.185532 | ||||||||
\(772\) | 668625. | − | 2.63779e6i | 0.0403775 | − | 0.159293i | ||||
\(773\) | −2.24785e7 | −1.35306 | −0.676531 | − | 0.736414i | \(-0.736517\pi\) | ||||
−0.676531 | + | 0.736414i | \(0.736517\pi\) | |||||||
\(774\) | −1.88842e7 | − | 2.35612e6i | −1.13304 | − | 0.141366i | ||||
\(775\) | −1.94325e7 | −1.16218 | ||||||||
\(776\) | 5.36045e6 | − | 1.37236e7i | 0.319556 | − | 0.818117i | ||||
\(777\) | 2.31836e6 | 0.137762 | ||||||||
\(778\) | −1.14606e6 | + | 9.18565e6i | −0.0678829 | + | 0.544078i | ||||
\(779\) | 2.85777e7 | + | 1.30827e7i | 1.68727 | + | 0.772419i | ||||
\(780\) | 3.60615e6 | + | 914085.i | 0.212230 | + | 0.0537960i | ||||
\(781\) | 1.78535e7 | 1.04736 | ||||||||
\(782\) | −2.02267e6 | + | 1.62116e7i | −0.118279 | + | 0.948001i | ||||
\(783\) | − | 7.34919e6i | − | 0.428386i | ||||||
\(784\) | 7.00029e6 | + | 3.79254e6i | 0.406748 | + | 0.220364i | ||||
\(785\) | −5.63233e6 | −0.326223 | ||||||||
\(786\) | −459597. | + | 3.68364e6i | −0.0265351 | + | 0.212677i | ||||
\(787\) | − | 3.06719e7i | − | 1.76524i | −0.470088 | − | 0.882619i | \(-0.655778\pi\) | ||
0.470088 | − | 0.882619i | \(-0.344222\pi\) | |||||||
\(788\) | 7.33430e6 | − | 2.89345e7i | 0.420768 | − | 1.65997i | ||||
\(789\) | −3.15988e6 | −0.180709 | ||||||||
\(790\) | −175842. | + | 1.40936e6i | −0.0100243 | + | 0.0803442i | ||||
\(791\) | 1.90815e7 | 1.08435 | ||||||||
\(792\) | −1.12926e7 | − | 4.41088e6i | −0.639707 | − | 0.249869i | ||||
\(793\) | 1.44478e6i | 0.0815867i | ||||||||
\(794\) | 1.86343e6 | − | 1.49353e7i | 0.104897 | − | 0.840743i | ||||
\(795\) | 1.46682e6 | 0.0823114 | ||||||||
\(796\) | −1.24557e6 | + | 4.91388e6i | −0.0696764 | + | 0.274879i | ||||
\(797\) | 2.18608e7 | 1.21905 | 0.609524 | − | 0.792767i | \(-0.291360\pi\) | ||||
0.609524 | + | 0.792767i | \(0.291360\pi\) | |||||||
\(798\) | 1.99960e6 | − | 3.23639e6i | 0.111157 | − | 0.179909i | ||||
\(799\) | − | 5.19965e6i | − | 0.288142i | ||||||
\(800\) | 2.63693e7 | + | 1.88503e7i | 1.45671 | + | 1.04134i | ||||
\(801\) | − | 1.04408e7i | − | 0.574977i | ||||||
\(802\) | −3.12240e6 | + | 2.50258e7i | −0.171416 | + | 1.37389i | ||||
\(803\) | 2.04360e7 | 1.11843 | ||||||||
\(804\) | 6.16062e6 | + | 1.56159e6i | 0.336112 | + | 0.0851977i | ||||
\(805\) | 1.97597e7i | 1.07471i | ||||||||
\(806\) | −5.39640e6 | − | 673292.i | −0.292595 | − | 0.0365062i | ||||
\(807\) | 4.29178e6i | 0.231981i | ||||||||
\(808\) | −167276. | + | 428254.i | −0.00901375 | + | 0.0230767i | ||||
\(809\) | −2.05190e7 | −1.10226 | −0.551131 | − | 0.834419i | \(-0.685803\pi\) | ||||
−0.551131 | + | 0.834419i | \(0.685803\pi\) | |||||||
\(810\) | 2.92452e6 | − | 2.34399e7i | 0.156618 | − | 1.25529i | ||||
\(811\) | 8.82513e6i | 0.471160i | 0.971855 | + | 0.235580i | \(0.0756990\pi\) | ||||
−0.971855 | + | 0.235580i | \(0.924301\pi\) | |||||||
\(812\) | 2.62181e6 | − | 1.03433e7i | 0.139544 | − | 0.550513i | ||||
\(813\) | 5.87933e6 | 0.311962 | ||||||||
\(814\) | 9.15417e6 | + | 1.14214e6i | 0.484237 | + | 0.0604168i | ||||
\(815\) | 1.25807e7i | 0.663453i | ||||||||
\(816\) | −2.84540e6 | + | 5.25206e6i | −0.149595 | + | 0.276124i | ||||
\(817\) | 9.89108e6 | − | 2.16060e7i | 0.518428 | − | 1.13245i | ||||
\(818\) | 3.23650e6 | − | 2.59404e7i | 0.169119 | − | 1.35548i | ||||
\(819\) | − | 5.86108e6i | − | 0.305329i | ||||||
\(820\) | −5.78582e7 | − | 1.46659e7i | −3.00490 | − | 0.761682i | ||||
\(821\) | − | 2.37349e7i | − | 1.22894i | −0.788942 | − | 0.614468i | \(-0.789371\pi\) | ||
0.788942 | − | 0.614468i | \(-0.210629\pi\) | |||||||
\(822\) | 207057. | − | 1.65955e6i | 0.0106883 | − | 0.0856664i | ||||
\(823\) | − | 2.05277e7i | − | 1.05643i | −0.849110 | − | 0.528215i | \(-0.822861\pi\) | ||
0.849110 | − | 0.528215i | \(-0.177139\pi\) | |||||||
\(824\) | 1.56725e7 | + | 6.12166e6i | 0.804117 | + | 0.314088i | ||||
\(825\) | 7.56509e6i | 0.386972i | ||||||||
\(826\) | −2.81295e6 | − | 350963.i | −0.143454 | − | 0.0178983i | ||||
\(827\) | − | 3.05316e7i | − | 1.55234i | −0.630526 | − | 0.776168i | \(-0.717161\pi\) | ||
0.630526 | − | 0.776168i | \(-0.282839\pi\) | |||||||
\(828\) | −3.89990e6 | + | 1.53855e7i | −0.197687 | + | 0.779892i | ||||
\(829\) | 2.25540e6 | 0.113982 | 0.0569911 | − | 0.998375i | \(-0.481849\pi\) | ||||
0.0569911 | + | 0.998375i | \(0.481849\pi\) | |||||||
\(830\) | −3.52765e6 | + | 2.82739e7i | −0.177742 | + | 1.42459i | ||||
\(831\) | −1.04430e7 | −0.524595 | ||||||||
\(832\) | 6.66966e6 | + | 6.14838e6i | 0.334038 | + | 0.307930i | ||||
\(833\) | −1.00854e7 | −0.503595 | ||||||||
\(834\) | −693937. | + | 5.56187e6i | −0.0345466 | + | 0.276889i | ||||
\(835\) | 4.28913e7i | 2.12889i | ||||||||
\(836\) | 9.48993e6 | − | 1.17939e7i | 0.469621 | − | 0.583638i | ||||
\(837\) | − | 7.27392e6i | − | 0.358885i | ||||||
\(838\) | 2.48418e7 | + | 3.09943e6i | 1.22200 | + | 0.152466i | ||||
\(839\) | 1.74935e7 | 0.857969 | 0.428984 | − | 0.903312i | \(-0.358872\pi\) | ||||
0.428984 | + | 0.903312i | \(0.358872\pi\) | |||||||
\(840\) | −2.62854e6 | + | 6.72951e6i | −0.128534 | + | 0.329067i | ||||
\(841\) | −8.20059e6 | −0.399812 | ||||||||
\(842\) | −1.57349e7 | − | 1.96319e6i | −0.764862 | − | 0.0954295i | ||||
\(843\) | 7.33082e6 | 0.355290 | ||||||||
\(844\) | 1.10755e6 | − | 4.36937e6i | 0.0535187 | − | 0.211136i | ||||
\(845\) | − | 2.75166e7i | − | 1.32572i | ||||||
\(846\) | 625420. | − | 5.01271e6i | 0.0300432 | − | 0.240795i | ||||
\(847\) | 6.71652e6i | 0.321688i | ||||||||
\(848\) | 3.14480e6 | + | 1.70375e6i | 0.150177 | + | 0.0813612i | ||||
\(849\) | − | 3.69333e6i | − | 0.175852i | ||||||
\(850\) | −4.07448e7 | − | 5.08361e6i | −1.93431 | − | 0.241338i | ||||
\(851\) | − | 1.20776e7i | − | 0.571683i | ||||||
\(852\) | 2.09983e6 | − | 8.28402e6i | 0.0991027 | − | 0.390969i | ||||
\(853\) | − | 3.59976e7i | − | 1.69395i | −0.531631 | − | 0.846976i | \(-0.678421\pi\) | ||
0.531631 | − | 0.846976i | \(-0.321579\pi\) | |||||||
\(854\) | −2.78419e6 | − | 347375.i | −0.130633 | − | 0.0162987i | ||||
\(855\) | 2.97657e7 | + | 1.36265e7i | 1.39252 | + | 0.637484i | ||||
\(856\) | 1.10744e7 | − | 2.83522e7i | 0.516576 | − | 1.32252i | ||||
\(857\) | 1.66793e7i | 0.775758i | 0.921710 | + | 0.387879i | \(0.126792\pi\) | ||||
−0.921710 | + | 0.387879i | \(0.873208\pi\) | |||||||
\(858\) | −262114. | + | 2.10083e6i | −0.0121555 | + | 0.0974255i | ||||
\(859\) | 3.05812e7 | 1.41407 | 0.707036 | − | 0.707178i | \(-0.250032\pi\) | ||||
0.707036 | + | 0.707178i | \(0.250032\pi\) | |||||||
\(860\) | −1.10881e7 | + | 4.37434e7i | −0.511222 | + | 2.01681i | ||||
\(861\) | − | 8.53639e6i | − | 0.392434i | ||||||
\(862\) | −2.02437e7 | − | 2.52574e6i | −0.927943 | − | 0.115777i | ||||
\(863\) | 2.23026e7 | 1.01936 | 0.509682 | − | 0.860363i | \(-0.329763\pi\) | ||||
0.509682 | + | 0.860363i | \(0.329763\pi\) | |||||||
\(864\) | −7.05602e6 | + | 9.87053e6i | −0.321570 | + | 0.449838i | ||||
\(865\) | 2.37927e7i | 1.08119i | ||||||||
\(866\) | 3.76696e6 | − | 3.01920e7i | 0.170685 | − | 1.36803i | ||||
\(867\) | − | 1.18162e6i | − | 0.0533864i | ||||||
\(868\) | 2.59496e6 | − | 1.02373e7i | 0.116904 | − | 0.461199i | ||||
\(869\) | −808269. | −0.0363083 | ||||||||
\(870\) | −8.27103e6 | − | 1.03195e6i | −0.370477 | − | 0.0462233i | ||||
\(871\) | 1.22262e7i | 0.546065i | ||||||||
\(872\) | 3.21295e7 | + | 1.25498e7i | 1.43091 | + | 0.558914i | ||||
\(873\) | 1.81321e7i | 0.805216i | ||||||||
\(874\) | −1.68600e7 | − | 1.04170e7i | −0.746586 | − | 0.461278i | ||||
\(875\) | −2.19281e7 | −0.968234 | ||||||||
\(876\) | 2.40358e6 | − | 9.48232e6i | 0.105827 | − | 0.417498i | ||||
\(877\) | −4.16206e7 | −1.82730 | −0.913648 | − | 0.406505i | \(-0.866747\pi\) | ||||
−0.913648 | + | 0.406505i | \(0.866747\pi\) | |||||||
\(878\) | −7.25083e6 | − | 904664.i | −0.317433 | − | 0.0396051i | ||||
\(879\) | − | 1.00340e7i | − | 0.438029i | ||||||
\(880\) | −1.36942e7 | + | 2.52769e7i | −0.596116 | + | 1.10031i | ||||
\(881\) | −7.80431e6 | −0.338762 | −0.169381 | − | 0.985551i | \(-0.554177\pi\) | ||||
−0.169381 | + | 0.985551i | \(0.554177\pi\) | |||||||
\(882\) | −9.72283e6 | − | 1.21309e6i | −0.420844 | − | 0.0525074i | ||||
\(883\) | 2.87613e7 | 1.24139 | 0.620693 | − | 0.784054i | \(-0.286851\pi\) | ||||
0.620693 | + | 0.784054i | \(0.286851\pi\) | |||||||
\(884\) | −1.11387e7 | − | 2.82344e6i | −0.479408 | − | 0.121520i | ||||
\(885\) | 2.21437e6i | 0.0950367i | ||||||||
\(886\) | −1.31084e7 | − | 1.63549e6i | −0.561002 | − | 0.0699945i | ||||
\(887\) | −1.02058e7 | −0.435550 | −0.217775 | − | 0.975999i | \(-0.569880\pi\) | ||||
−0.217775 | + | 0.975999i | \(0.569880\pi\) | |||||||
\(888\) | 1.60662e6 | − | 4.11321e6i | 0.0683723 | − | 0.175044i | ||||
\(889\) | 3.42478e7i | 1.45338i | ||||||||
\(890\) | −2.45674e7 | − | 3.06520e6i | −1.03964 | − | 0.129713i | ||||
\(891\) | 1.34428e7 | 0.567276 | ||||||||
\(892\) | −91941.5 | − | 23305.3i | −0.00386901 | − | 0.000980714i | ||||
\(893\) | 5.73521e6 | + | 2.62554e6i | 0.240669 | + | 0.110177i | ||||
\(894\) | 7.86235e6 | + | 980961.i | 0.329009 | + | 0.0410495i | ||||
\(895\) | 5.75877e7 | 2.40310 | ||||||||
\(896\) | −1.34520e7 | + | 1.13746e7i | −0.559777 | + | 0.473332i | ||||
\(897\) | 2.77173e6 | 0.115019 | ||||||||
\(898\) | −1.79324e6 | + | 1.43727e7i | −0.0742074 | + | 0.594768i | ||||
\(899\) | 1.21845e7 | 0.502814 | ||||||||
\(900\) | −3.86685e7 | − | 9.80169e6i | −1.59130 | − | 0.403362i | ||||
\(901\) | −4.53075e6 | −0.185934 | ||||||||
\(902\) | 4.20545e6 | − | 3.37064e7i | 0.172106 | − | 1.37942i | ||||
\(903\) | −6.45389e6 | −0.263392 | ||||||||
\(904\) | 1.32235e7 | − | 3.38542e7i | 0.538175 | − | 1.37782i | ||||
\(905\) | 4.60895e7i | 1.87060i | ||||||||
\(906\) | −541018. | + | 4.33623e6i | −0.0218973 | + | 0.175506i | ||||
\(907\) | 2.99715e7i | 1.20974i | 0.796325 | + | 0.604868i | \(0.206774\pi\) | ||||
−0.796325 | + | 0.604868i | \(0.793226\pi\) | |||||||
\(908\) | −3.52044e6 | + | 1.38885e7i | −0.141704 | + | 0.559035i | ||||
\(909\) | − | 565823.i | − | 0.0227128i | ||||||
\(910\) | −1.37913e7 | − | 1.72070e6i | −0.552079 | − | 0.0688813i | ||||
\(911\) | −3.93768e7 | −1.57197 | −0.785985 | − | 0.618246i | \(-0.787844\pi\) | ||||
−0.785985 | + | 0.618246i | \(0.787844\pi\) | |||||||
\(912\) | −4.35624e6 | − | 5.79048e6i | −0.173430 | − | 0.230530i | ||||
\(913\) | −1.62151e7 | −0.643788 | ||||||||
\(914\) | 1.59427e7 | + | 1.98912e6i | 0.631244 | + | 0.0787583i | ||||
\(915\) | 2.19173e6i | 0.0865434i | ||||||||
\(916\) | −780243. | + | 3.07813e6i | −0.0307250 | + | 0.121213i | ||||
\(917\) | − | 1.38684e7i | − | 0.544631i | ||||||
\(918\) | 1.90289e6 | − | 1.52515e7i | 0.0745258 | − | 0.597320i | ||||
\(919\) | 1.74439e7i | 0.681326i | 0.940185 | + | 0.340663i | \(0.110652\pi\) | ||||
−0.940185 | + | 0.340663i | \(0.889348\pi\) | |||||||
\(920\) | 3.50575e7 | + | 1.36935e7i | 1.36556 | + | 0.533389i | ||||
\(921\) | −8.22226e6 | −0.319405 | ||||||||
\(922\) | 2.26492e6 | − | 1.81532e7i | 0.0877457 | − | 0.703277i | ||||
\(923\) | 1.64402e7 | 0.635188 | ||||||||
\(924\) | −3.98542e6 | − | 1.01022e6i | −0.153566 | − | 0.0389257i | ||||
\(925\) | 3.03547e7 | 1.16646 | ||||||||
\(926\) | −6.08500e6 | + | 4.87709e7i | −0.233202 | + | 1.86910i | ||||
\(927\) | −2.07069e7 | −0.791438 | ||||||||
\(928\) | −1.65340e7 | − | 1.18195e7i | −0.630244 | − | 0.450534i | ||||
\(929\) | −2.13025e7 | −0.809824 | −0.404912 | − | 0.914356i | \(-0.632698\pi\) | ||||
−0.404912 | + | 0.914356i | \(0.632698\pi\) | |||||||
\(930\) | −8.18632e6 | − | 1.02138e6i | −0.310371 | − | 0.0387241i | ||||
\(931\) | 5.09258e6 | − | 1.11242e7i | 0.192559 | − | 0.420625i | ||||
\(932\) | 3.65504e7 | + | 9.26480e6i | 1.37833 | + | 0.349378i | ||||
\(933\) | −8.56982e6 | −0.322305 | ||||||||
\(934\) | 4.31598e7 | + | 5.38491e6i | 1.61887 | + | 0.201982i | ||||
\(935\) | − | 3.64168e7i | − | 1.36230i | ||||||
\(936\) | −1.03987e7 | − | 4.06171e6i | −0.387961 | − | 0.151537i | ||||
\(937\) | −333669. | −0.0124156 | −0.00620778 | − | 0.999981i | \(-0.501976\pi\) | ||||
−0.00620778 | + | 0.999981i | \(0.501976\pi\) | |||||||
\(938\) | −2.35606e7 | − | 2.93958e6i | −0.874338 | − | 0.109088i | ||||
\(939\) | 1.04241e7i | 0.385810i | ||||||||
\(940\) | −1.16115e7 | − | 2.94327e6i | −0.428615 | − | 0.108645i | ||||
\(941\) | −4.98749e7 | −1.83615 | −0.918076 | − | 0.396405i | \(-0.870257\pi\) | ||||
−0.918076 | + | 0.396405i | \(0.870257\pi\) | |||||||
\(942\) | −1.52249e6 | − | 189956.i | −0.0559020 | − | 0.00697472i | ||||
\(943\) | −4.44706e7 | −1.62852 | ||||||||
\(944\) | −2.57204e6 | + | 4.74749e6i | −0.0939395 | + | 0.173394i | ||||
\(945\) | − | 1.85896e7i | − | 0.677158i | ||||||
\(946\) | −2.54835e7 | − | 3.17950e6i | −0.925831 | − | 0.115513i | ||||
\(947\) | 3.12985e7 | 1.13409 | 0.567047 | − | 0.823685i | \(-0.308086\pi\) | ||||
0.567047 | + | 0.823685i | \(0.308086\pi\) | |||||||
\(948\) | −95064.4 | + | 375037.i | −0.00343556 | + | 0.0135536i | ||||
\(949\) | 1.88183e7 | 0.678288 | ||||||||
\(950\) | 2.61811e7 | − | 4.23746e7i | 0.941195 | − | 1.52334i | ||||
\(951\) | 1.26997e7i | 0.455347i | ||||||||
\(952\) | 8.11909e6 | − | 2.07862e7i | 0.290345 | − | 0.743333i | ||||
\(953\) | 6.44799e6i | 0.229981i | 0.993367 | + | 0.114991i | \(0.0366838\pi\) | ||||
−0.993367 | + | 0.114991i | \(0.963316\pi\) | |||||||
\(954\) | −4.36786e6 | − | 544965.i | −0.155381 | − | 0.0193864i | ||||
\(955\) | −7.83760e7 | −2.78083 | ||||||||
\(956\) | 9.17474e6 | − | 3.61952e7i | 0.324675 | − | 1.28087i | ||||
\(957\) | − | 4.74344e6i | − | 0.167422i | ||||||
\(958\) | 4.42953e6 | − | 3.55024e7i | 0.155935 | − | 1.24981i | ||||
\(959\) | 6.24795e6i | 0.219377i | ||||||||
\(960\) | 1.01178e7 | + | 9.32707e6i | 0.354332 | + | 0.326638i | ||||
\(961\) | −1.65695e7 | −0.578762 | ||||||||
\(962\) | 8.42952e6 | + | 1.05172e6i | 0.293674 | + | 0.0366408i | ||||
\(963\) | 3.74598e7i | 1.30167i | ||||||||
\(964\) | 8.03377e6 | − | 3.16939e7i | 0.278437 | − | 1.09846i | ||||
\(965\) | 7.94125e6 | 0.274518 | ||||||||
\(966\) | −666418. | + | 5.34130e6i | −0.0229776 | + | 0.184164i | ||||
\(967\) | − | 3.65275e7i | − | 1.25619i | −0.778139 | − | 0.628093i | \(-0.783836\pi\) | ||
0.778139 | − | 0.628093i | \(-0.216164\pi\) | |||||||
\(968\) | 1.19164e7 | + | 4.65453e6i | 0.408748 | + | 0.159657i | ||||
\(969\) | 8.34609e6 | + | 3.82078e6i | 0.285544 | + | 0.130720i | ||||
\(970\) | 4.26654e7 | + | 5.32323e6i | 1.45595 | + | 0.181654i | ||||
\(971\) | − | 1.46193e7i | − | 0.497598i | −0.968555 | − | 0.248799i | \(-0.919964\pi\) | ||
0.968555 | − | 0.248799i | \(-0.0800358\pi\) | |||||||
\(972\) | 5.58308e6 | − | 2.20257e7i | 0.189543 | − | 0.747764i | ||||
\(973\) | − | 2.09396e7i | − | 0.709066i | ||||||
\(974\) | 9.47373e6 | + | 1.18201e6i | 0.319981 | + | 0.0399230i | ||||
\(975\) | 6.96623e6i | 0.234685i | ||||||||
\(976\) | −2.54575e6 | + | 4.69895e6i | −0.0855443 | + | 0.157898i | ||||
\(977\) | − | 1.70811e7i | − | 0.572505i | −0.958154 | − | 0.286252i | \(-0.907590\pi\) | ||
0.958154 | − | 0.286252i | \(-0.0924096\pi\) | |||||||
\(978\) | −424297. | + | 3.40071e6i | −0.0141848 | + | 0.113690i | ||||
\(979\) | − | 1.40894e7i | − | 0.469825i | ||||||
\(980\) | −5.70887e6 | + | 2.25220e7i | −0.189882 | + | 0.749103i | ||||
\(981\) | −4.24506e7 | −1.40835 | ||||||||
\(982\) | 2.46532e7 | + | 3.07591e6i | 0.815821 | + | 0.101787i | ||||
\(983\) | −4.08627e7 | −1.34879 | −0.674394 | − | 0.738372i | \(-0.735595\pi\) | ||||
−0.674394 | + | 0.738372i | \(0.735595\pi\) | |||||||
\(984\) | −1.51452e7 | − | 5.91570e6i | −0.498640 | − | 0.194768i | ||||
\(985\) | 8.71094e7 | 2.86071 | ||||||||
\(986\) | 2.55477e7 | + | 3.18751e6i | 0.836873 | + | 0.104414i | ||||
\(987\) | − | 1.71315e6i | − | 0.0559761i | ||||||
\(988\) | 8.73870e6 | − | 1.08603e7i | 0.284810 | − | 0.353957i | ||||
\(989\) | 3.36217e7i | 1.09302i | ||||||||
\(990\) | 4.38026e6 | − | 3.51075e7i | 0.142040 | − | 1.13845i | ||||
\(991\) | 4.47322e7 | 1.44689 | 0.723446 | − | 0.690381i | \(-0.242557\pi\) | ||||
0.723446 | + | 0.690381i | \(0.242557\pi\) | |||||||
\(992\) | −1.63647e7 | − | 1.16984e7i | −0.527994 | − | 0.377440i | ||||
\(993\) | −1.03765e7 | −0.333948 | ||||||||
\(994\) | −3.95278e6 | + | 3.16813e7i | −0.126893 | + | 1.01704i | ||||
\(995\) | −1.47936e7 | −0.473715 | ||||||||
\(996\) | −1.90714e6 | + | 7.52383e6i | −0.0609163 | + | 0.240320i | ||||
\(997\) | 3.59648e7i | 1.14588i | 0.819597 | + | 0.572941i | \(0.194198\pi\) | ||||
−0.819597 | + | 0.572941i | \(0.805802\pi\) | |||||||
\(998\) | −2.92601e7 | − | 3.65069e6i | −0.929927 | − | 0.116024i | ||||
\(999\) | 1.13623e7i | 0.360208i |
(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 | 152.6.b.b.75.3 | ✓ | 96 | |
4.3 | odd | 2 | 608.6.b.b.303.56 | 96 | |||
8.3 | odd | 2 | inner | 152.6.b.b.75.93 | yes | 96 | |
8.5 | even | 2 | 608.6.b.b.303.55 | 96 | |||
19.18 | odd | 2 | inner | 152.6.b.b.75.94 | yes | 96 | |
76.75 | even | 2 | 608.6.b.b.303.42 | 96 | |||
152.37 | odd | 2 | 608.6.b.b.303.41 | 96 | |||
152.75 | even | 2 | inner | 152.6.b.b.75.4 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.6.b.b.75.3 | ✓ | 96 | 1.1 | even | 1 | trivial | |
152.6.b.b.75.4 | yes | 96 | 152.75 | even | 2 | inner | |
152.6.b.b.75.93 | yes | 96 | 8.3 | odd | 2 | inner | |
152.6.b.b.75.94 | yes | 96 | 19.18 | odd | 2 | inner | |
608.6.b.b.303.41 | 96 | 152.37 | odd | 2 | |||
608.6.b.b.303.42 | 96 | 76.75 | even | 2 | |||
608.6.b.b.303.55 | 96 | 8.5 | even | 2 | |||
608.6.b.b.303.56 | 96 | 4.3 | odd | 2 |