Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,6,Mod(195,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("196.195");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.d (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: | \(31.4352286833\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 195.11 | ||
Character | \(\chi\) | \(=\) | 196.195 |
Dual form | 196.6.d.b.195.9 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.23262 | + | 4.64222i | −0.571452 | + | 0.820636i | ||||
\(3\) | −8.56469 | −0.549425 | −0.274713 | − | 0.961526i | \(-0.588583\pi\) | ||||
−0.274713 | + | 0.961526i | \(0.588583\pi\) | |||||||
\(4\) | −11.1004 | − | 30.0130i | −0.346886 | − | 0.937907i | ||||
\(5\) | − | 54.9613i | − | 0.983178i | −0.870827 | − | 0.491589i | \(-0.836416\pi\) | ||
0.870827 | − | 0.491589i | \(-0.163584\pi\) | |||||||
\(6\) | 27.6864 | − | 39.7592i | 0.313970 | − | 0.450878i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 175.210 | + | 45.4904i | 0.967909 | + | 0.251302i | ||||
\(9\) | −169.646 | −0.698132 | ||||||||
\(10\) | 255.142 | + | 177.669i | 0.806831 | + | 0.561839i | ||||
\(11\) | 525.582i | 1.30966i | 0.755775 | + | 0.654831i | \(0.227260\pi\) | ||||
−0.755775 | + | 0.654831i | \(0.772740\pi\) | |||||||
\(12\) | 95.0711 | + | 257.052i | 0.190588 | + | 0.515310i | ||||
\(13\) | 1005.77i | 1.65060i | 0.564696 | + | 0.825299i | \(0.308993\pi\) | ||||
−0.564696 | + | 0.825299i | \(0.691007\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 470.727i | 0.540183i | ||||||||
\(16\) | −777.564 | + | 666.311i | −0.759340 | + | 0.650694i | ||||
\(17\) | − | 1342.87i | − | 1.12697i | −0.826127 | − | 0.563484i | \(-0.809461\pi\) | ||
0.826127 | − | 0.563484i | \(-0.190539\pi\) | |||||||
\(18\) | 548.401 | − | 787.534i | 0.398949 | − | 0.572912i | ||||
\(19\) | −47.0786 | −0.0299185 | −0.0149592 | − | 0.999888i | \(-0.504762\pi\) | ||||
−0.0149592 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(20\) | −1649.56 | + | 610.090i | −0.922130 | + | 0.341051i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2439.87 | − | 1699.01i | −1.07476 | − | 0.748408i | ||||
\(23\) | − | 798.379i | − | 0.314695i | −0.987543 | − | 0.157347i | \(-0.949706\pi\) | ||
0.987543 | − | 0.157347i | \(-0.0502943\pi\) | |||||||
\(24\) | −1500.62 | − | 389.612i | −0.531794 | − | 0.138071i | ||||
\(25\) | 104.255 | 0.0333615 | ||||||||
\(26\) | −4669.01 | − | 3251.28i | −1.35454 | − | 0.943237i | ||||
\(27\) | 3534.19 | 0.932996 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −600.350 | −0.132559 | −0.0662795 | − | 0.997801i | \(-0.521113\pi\) | ||||
−0.0662795 | + | 0.997801i | \(0.521113\pi\) | |||||||
\(30\) | −2185.22 | − | 1521.68i | −0.443293 | − | 0.308688i | ||||
\(31\) | 5238.56 | 0.979057 | 0.489529 | − | 0.871987i | \(-0.337169\pi\) | ||||
0.489529 | + | 0.871987i | \(0.337169\pi\) | |||||||
\(32\) | −579.589 | − | 5763.55i | −0.100056 | − | 0.994982i | ||||
\(33\) | − | 4501.45i | − | 0.719561i | ||||||
\(34\) | 6233.89 | + | 4340.99i | 0.924831 | + | 0.644008i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1883.13 | + | 5091.59i | 0.242172 | + | 0.654783i | ||||
\(37\) | −13219.8 | −1.58752 | −0.793760 | − | 0.608231i | \(-0.791879\pi\) | ||||
−0.793760 | + | 0.608231i | \(0.791879\pi\) | |||||||
\(38\) | 152.187 | − | 218.549i | 0.0170970 | − | 0.0245522i | ||||
\(39\) | − | 8614.13i | − | 0.906880i | ||||||
\(40\) | 2500.21 | − | 9629.78i | 0.247074 | − | 0.951626i | ||||
\(41\) | − | 3464.72i | − | 0.321891i | −0.986963 | − | 0.160946i | \(-0.948546\pi\) | ||
0.986963 | − | 0.160946i | \(-0.0514543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11552.1i | − | 0.952773i | −0.879236 | − | 0.476387i | \(-0.841946\pi\) | ||
0.879236 | − | 0.476387i | \(-0.158054\pi\) | |||||||
\(44\) | 15774.3 | − | 5834.15i | 1.22834 | − | 0.454303i | ||||
\(45\) | 9323.97i | 0.686388i | ||||||||
\(46\) | 3706.25 | + | 2580.86i | 0.258250 | + | 0.179833i | ||||
\(47\) | 3589.67 | 0.237033 | 0.118517 | − | 0.992952i | \(-0.462186\pi\) | ||||
0.118517 | + | 0.992952i | \(0.462186\pi\) | |||||||
\(48\) | 6659.60 | − | 5706.74i | 0.417201 | − | 0.357508i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −337.016 | + | 483.973i | −0.0190645 | + | 0.0273777i | ||||
\(51\) | 11501.3i | 0.619185i | ||||||||
\(52\) | 30186.3 | − | 11164.4i | 1.54811 | − | 0.572569i | ||||
\(53\) | −2690.17 | −0.131550 | −0.0657748 | − | 0.997834i | \(-0.520952\pi\) | ||||
−0.0657748 | + | 0.997834i | \(0.520952\pi\) | |||||||
\(54\) | −11424.7 | + | 16406.5i | −0.533162 | + | 0.765650i | ||||
\(55\) | 28886.7 | 1.28763 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 403.214 | 0.0164380 | ||||||||
\(58\) | 1940.70 | − | 2786.95i | 0.0757510 | − | 0.108783i | ||||
\(59\) | 8262.55 | 0.309018 | 0.154509 | − | 0.987991i | \(-0.450620\pi\) | ||||
0.154509 | + | 0.987991i | \(0.450620\pi\) | |||||||
\(60\) | 14127.9 | − | 5225.23i | 0.506641 | − | 0.187382i | ||||
\(61\) | 12997.7i | 0.447240i | 0.974676 | + | 0.223620i | \(0.0717875\pi\) | ||||
−0.974676 | + | 0.223620i | \(0.928213\pi\) | |||||||
\(62\) | −16934.3 | + | 24318.6i | −0.559484 | + | 0.803449i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 28629.2 | + | 15940.8i | 0.873695 | + | 0.486474i | ||||
\(65\) | 55278.6 | 1.62283 | ||||||||
\(66\) | 20896.7 | + | 14551.5i | 0.590498 | + | 0.411194i | ||||
\(67\) | − | 55772.7i | − | 1.51787i | −0.651166 | − | 0.758936i | \(-0.725720\pi\) | ||
0.651166 | − | 0.758936i | \(-0.274280\pi\) | |||||||
\(68\) | −40303.6 | + | 14906.3i | −1.05699 | + | 0.390930i | ||||
\(69\) | 6837.87i | 0.172901i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 37357.0i | − | 0.879480i | −0.898125 | − | 0.439740i | \(-0.855071\pi\) | ||
0.898125 | − | 0.439740i | \(-0.144929\pi\) | |||||||
\(72\) | −29723.7 | − | 7717.27i | −0.675728 | − | 0.175442i | ||||
\(73\) | 49193.1i | 1.08043i | 0.841527 | + | 0.540216i | \(0.181657\pi\) | ||||
−0.841527 | + | 0.540216i | \(0.818343\pi\) | |||||||
\(74\) | 42734.4 | − | 61369.0i | 0.907191 | − | 1.30278i | ||||
\(75\) | −892.910 | −0.0183297 | ||||||||
\(76\) | 522.589 | + | 1412.97i | 0.0103783 | + | 0.0280608i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 39988.7 | + | 27846.2i | 0.744218 | + | 0.518238i | ||||
\(79\) | − | 108641.i | − | 1.95850i | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||
0.202645 | − | 0.979252i | \(-0.435046\pi\) | |||||||
\(80\) | 36621.3 | + | 42736.0i | 0.639748 | + | 0.746566i | ||||
\(81\) | 10954.8 | 0.185520 | ||||||||
\(82\) | 16084.0 | + | 11200.1i | 0.264155 | + | 0.183945i | ||||
\(83\) | 71003.7 | 1.13132 | 0.565661 | − | 0.824638i | \(-0.308621\pi\) | ||||
0.565661 | + | 0.824638i | \(0.308621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −73805.9 | −1.10801 | ||||||||
\(86\) | 53627.3 | + | 37343.5i | 0.781880 | + | 0.544464i | ||||
\(87\) | 5141.81 | 0.0728312 | ||||||||
\(88\) | −23909.0 | + | 92087.4i | −0.329120 | + | 1.26763i | ||||
\(89\) | − | 69993.0i | − | 0.936655i | −0.883555 | − | 0.468328i | \(-0.844857\pi\) | ||
0.883555 | − | 0.468328i | \(-0.155143\pi\) | |||||||
\(90\) | −43283.9 | − | 30140.8i | −0.563274 | − | 0.392237i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −23961.8 | + | 8862.29i | −0.295155 | + | 0.109163i | ||||
\(93\) | −44866.7 | −0.537919 | ||||||||
\(94\) | −11604.0 | + | 16664.0i | −0.135453 | + | 0.194518i | ||||
\(95\) | 2587.50i | 0.0294152i | ||||||||
\(96\) | 4964.00 | + | 49363.0i | 0.0549736 | + | 0.546668i | ||||
\(97\) | − | 110504.i | − | 1.19247i | −0.802809 | − | 0.596236i | \(-0.796662\pi\) | ||
0.802809 | − | 0.596236i | \(-0.203338\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 89163.0i | − | 0.914317i | ||||||
\(100\) | −1157.26 | − | 3129.00i | −0.0115726 | − | 0.0312900i | ||||
\(101\) | − | 55545.6i | − | 0.541809i | −0.962606 | − | 0.270904i | \(-0.912677\pi\) | ||
0.962606 | − | 0.270904i | \(-0.0873227\pi\) | |||||||
\(102\) | −53391.4 | − | 37179.2i | −0.508125 | − | 0.353834i | ||||
\(103\) | 117652. | 1.09271 | 0.546355 | − | 0.837554i | \(-0.316015\pi\) | ||||
0.546355 | + | 0.837554i | \(0.316015\pi\) | |||||||
\(104\) | −45753.0 | + | 176222.i | −0.414798 | + | 1.59763i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8696.29 | − | 12488.3i | 0.0751743 | − | 0.107954i | ||||
\(107\) | 150598.i | 1.27163i | 0.771843 | + | 0.635813i | \(0.219335\pi\) | ||||
−0.771843 | + | 0.635813i | \(0.780665\pi\) | |||||||
\(108\) | −39230.7 | − | 106072.i | −0.323643 | − | 0.875064i | ||||
\(109\) | 58261.5 | 0.469695 | 0.234847 | − | 0.972032i | \(-0.424541\pi\) | ||||
0.234847 | + | 0.972032i | \(0.424541\pi\) | |||||||
\(110\) | −93379.7 | + | 134098.i | −0.735818 | + | 1.05668i | ||||
\(111\) | 113223. | 0.872223 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −60945.6 | −0.449000 | −0.224500 | − | 0.974474i | \(-0.572075\pi\) | ||||
−0.224500 | + | 0.974474i | \(0.572075\pi\) | |||||||
\(114\) | −1303.44 | + | 1871.81i | −0.00939351 | + | 0.0134896i | ||||
\(115\) | −43880.0 | −0.309401 | ||||||||
\(116\) | 6664.09 | + | 18018.3i | 0.0459829 | + | 0.124328i | ||||
\(117\) | − | 170625.i | − | 1.15234i | ||||||
\(118\) | −26709.7 | + | 38356.5i | −0.176589 | + | 0.253591i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −21413.6 | + | 82476.1i | −0.135749 | + | 0.522848i | ||||
\(121\) | −115186. | −0.715214 | ||||||||
\(122\) | −60338.0 | − | 42016.5i | −0.367021 | − | 0.255576i | ||||
\(123\) | 29674.3i | 0.176855i | ||||||||
\(124\) | −58149.9 | − | 157225.i | −0.339621 | − | 0.918265i | ||||
\(125\) | − | 177484.i | − | 1.01598i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 49258.1i | − | 0.270999i | −0.990777 | − | 0.135500i | \(-0.956736\pi\) | ||
0.990777 | − | 0.135500i | \(-0.0432639\pi\) | |||||||
\(128\) | −166548. | + | 81372.7i | −0.898492 | + | 0.438989i | ||||
\(129\) | 98940.1i | 0.523478i | ||||||||
\(130\) | −178695. | + | 256615.i | −0.927370 | + | 1.33175i | ||||
\(131\) | 148451. | 0.755799 | 0.377899 | − | 0.925847i | \(-0.376646\pi\) | ||||
0.377899 | + | 0.925847i | \(0.376646\pi\) | |||||||
\(132\) | −135102. | + | 49967.7i | −0.674882 | + | 0.249606i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 258909. | + | 180292.i | 1.24562 | + | 0.867390i | ||||
\(135\) | − | 194243.i | − | 0.917301i | ||||||
\(136\) | 61087.8 | − | 235285.i | 0.283209 | − | 1.09080i | ||||
\(137\) | −267905. | −1.21949 | −0.609747 | − | 0.792596i | \(-0.708729\pi\) | ||||
−0.609747 | + | 0.792596i | \(0.708729\pi\) | |||||||
\(138\) | −31742.9 | − | 22104.2i | −0.141889 | − | 0.0988047i | ||||
\(139\) | −181033. | −0.794732 | −0.397366 | − | 0.917660i | \(-0.630076\pi\) | ||||
−0.397366 | + | 0.917660i | \(0.630076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30744.4 | −0.130232 | ||||||||
\(142\) | 173419. | + | 120761.i | 0.721733 | + | 0.502580i | ||||
\(143\) | −528616. | −2.16173 | ||||||||
\(144\) | 131911. | − | 113037.i | 0.530120 | − | 0.454270i | ||||
\(145\) | 32996.0i | 0.130329i | ||||||||
\(146\) | −228365. | − | 159023.i | −0.886640 | − | 0.617414i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 146744. | + | 396765.i | 0.550688 | + | 1.48895i | ||||
\(149\) | 66115.0 | 0.243969 | 0.121984 | − | 0.992532i | \(-0.461074\pi\) | ||||
0.121984 | + | 0.992532i | \(0.461074\pi\) | |||||||
\(150\) | 2886.44 | − | 4145.08i | 0.0104745 | − | 0.0150420i | ||||
\(151\) | 167175.i | 0.596664i | 0.954462 | + | 0.298332i | \(0.0964303\pi\) | ||||
−0.954462 | + | 0.298332i | \(0.903570\pi\) | |||||||
\(152\) | −8248.66 | − | 2141.63i | −0.0289584 | − | 0.00751857i | ||||
\(153\) | 227813.i | 0.786773i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 287918.i | − | 0.962587i | ||||||
\(156\) | −258536. | + | 95619.9i | −0.850569 | + | 0.314584i | ||||
\(157\) | − | 388142.i | − | 1.25673i | −0.777919 | − | 0.628365i | \(-0.783725\pi\) | ||
0.777919 | − | 0.628365i | \(-0.216275\pi\) | |||||||
\(158\) | 504333. | + | 351194.i | 1.60722 | + | 1.11919i | ||||
\(159\) | 23040.5 | 0.0722767 | ||||||||
\(160\) | −316772. | + | 31855.0i | −0.978244 | + | 0.0983733i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −35412.6 | + | 50854.5i | −0.106016 | + | 0.152244i | ||||
\(163\) | 290546.i | 0.856538i | 0.903651 | + | 0.428269i | \(0.140876\pi\) | ||||
−0.903651 | + | 0.428269i | \(0.859124\pi\) | |||||||
\(164\) | −103987. | + | 38459.7i | −0.301904 | + | 0.111660i | ||||
\(165\) | −247406. | −0.707457 | ||||||||
\(166\) | −229528. | + | 329615.i | −0.646495 | + | 0.928402i | ||||
\(167\) | 556102. | 1.54299 | 0.771496 | − | 0.636234i | \(-0.219509\pi\) | ||||
0.771496 | + | 0.636234i | \(0.219509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −640285. | −1.72447 | ||||||||
\(170\) | 238586. | − | 342623.i | 0.633174 | − | 0.909273i | ||||
\(171\) | 7986.70 | 0.0208871 | ||||||||
\(172\) | −346713. | + | 128232.i | −0.893613 | + | 0.330504i | ||||
\(173\) | 46934.5i | 0.119228i | 0.998222 | + | 0.0596139i | \(0.0189869\pi\) | ||||
−0.998222 | + | 0.0596139i | \(0.981013\pi\) | |||||||
\(174\) | −16621.5 | + | 23869.4i | −0.0416195 | + | 0.0597679i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −350201. | − | 408674.i | −0.852189 | − | 0.994479i | ||||
\(177\) | −70766.2 | −0.169782 | ||||||||
\(178\) | 324923. | + | 226261.i | 0.768653 | + | 0.535253i | ||||
\(179\) | − | 32119.9i | − | 0.0749276i | −0.999298 | − | 0.0374638i | \(-0.988072\pi\) | ||
0.999298 | − | 0.0374638i | \(-0.0119279\pi\) | |||||||
\(180\) | 279841. | − | 103499.i | 0.643768 | − | 0.238098i | ||||
\(181\) | − | 512222.i | − | 1.16215i | −0.813851 | − | 0.581074i | \(-0.802633\pi\) | ||
0.813851 | − | 0.581074i | \(-0.197367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 111321.i | − | 0.245725i | ||||||
\(184\) | 36318.6 | − | 139884.i | 0.0790833 | − | 0.304596i | ||||
\(185\) | 726575.i | 1.56081i | ||||||||
\(186\) | 145037. | − | 208281.i | 0.307395 | − | 0.441435i | ||||
\(187\) | 705789. | 1.47595 | ||||||||
\(188\) | −39846.6 | − | 107737.i | −0.0822236 | − | 0.222315i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12011.7 | − | 8364.41i | −0.0241392 | − | 0.0168094i | ||||
\(191\) | 4220.21i | 0.00837049i | 0.999991 | + | 0.00418524i | \(0.00133221\pi\) | ||||
−0.999991 | + | 0.00418524i | \(0.998668\pi\) | |||||||
\(192\) | −245201. | − | 136528.i | −0.480030 | − | 0.267281i | ||||
\(193\) | 17136.0 | 0.0331143 | 0.0165571 | − | 0.999863i | \(-0.494729\pi\) | ||||
0.0165571 | + | 0.999863i | \(0.494729\pi\) | |||||||
\(194\) | 512983. | + | 357217.i | 0.978586 | + | 0.681440i | ||||
\(195\) | −473444. | −0.891624 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 958831. | 1.76026 | 0.880129 | − | 0.474734i | \(-0.157456\pi\) | ||||
0.880129 | + | 0.474734i | \(0.157456\pi\) | |||||||
\(198\) | 413914. | + | 288230.i | 0.750321 | + | 0.522488i | ||||
\(199\) | 57018.5 | 0.102066 | 0.0510332 | − | 0.998697i | \(-0.483749\pi\) | ||||
0.0510332 | + | 0.998697i | \(0.483749\pi\) | |||||||
\(200\) | 18266.5 | + | 4742.60i | 0.0322909 | + | 0.00838380i | ||||
\(201\) | 477676.i | 0.833957i | ||||||||
\(202\) | 257855. | + | 179558.i | 0.444628 | + | 0.309617i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 345188. | − | 127668.i | 0.580738 | − | 0.214787i | ||||
\(205\) | −190426. | −0.316476 | ||||||||
\(206\) | −380323. | + | 546164.i | −0.624431 | + | 0.896717i | ||||
\(207\) | 135442.i | 0.219699i | ||||||||
\(208\) | −670157. | − | 782053.i | −1.07403 | − | 1.25337i | ||||
\(209\) | − | 24743.7i | − | 0.0391831i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 96012.1i | 0.148464i | 0.997241 | + | 0.0742318i | \(0.0236505\pi\) | ||||
−0.997241 | + | 0.0742318i | \(0.976350\pi\) | |||||||
\(212\) | 29861.8 | + | 80740.1i | 0.0456327 | + | 0.123381i | ||||
\(213\) | 319951.i | 0.483208i | ||||||||
\(214\) | −699108. | − | 486826.i | −1.04354 | − | 0.726673i | ||||
\(215\) | −634918. | −0.936745 | ||||||||
\(216\) | 619226. | + | 160772.i | 0.903056 | + | 0.234463i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −188337. | + | 270463.i | −0.268408 | + | 0.385448i | ||||
\(219\) | − | 421324.i | − | 0.593616i | ||||||
\(220\) | −320653. | − | 866977.i | −0.446661 | − | 1.20768i | ||||
\(221\) | 1.35062e6 | 1.86017 | ||||||||
\(222\) | −366007. | + | 525606.i | −0.498433 | + | 0.715778i | ||||
\(223\) | −618991. | −0.833532 | −0.416766 | − | 0.909014i | \(-0.636837\pi\) | ||||
−0.416766 | + | 0.909014i | \(0.636837\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17686.4 | −0.0232907 | ||||||||
\(226\) | 197014. | − | 282923.i | 0.256582 | − | 0.368465i | ||||
\(227\) | 1.31750e6 | 1.69702 | 0.848508 | − | 0.529182i | \(-0.177501\pi\) | ||||
0.848508 | + | 0.529182i | \(0.177501\pi\) | |||||||
\(228\) | −4475.82 | − | 12101.7i | −0.00570210 | − | 0.0154173i | ||||
\(229\) | 33059.7i | 0.0416591i | 0.999783 | + | 0.0208296i | \(0.00663073\pi\) | ||||
−0.999783 | + | 0.0208296i | \(0.993369\pi\) | |||||||
\(230\) | 141847. | − | 203700.i | 0.176808 | − | 0.253906i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −105187. | − | 27310.2i | −0.128305 | − | 0.0333123i | ||||
\(233\) | 762869. | 0.920578 | 0.460289 | − | 0.887769i | \(-0.347746\pi\) | ||||
0.460289 | + | 0.887769i | \(0.347746\pi\) | |||||||
\(234\) | 792080. | + | 551567.i | 0.945647 | + | 0.658504i | ||||
\(235\) | − | 197293.i | − | 0.233046i | ||||||
\(236\) | −91717.2 | − | 247984.i | −0.107194 | − | 0.289830i | ||||
\(237\) | 930473.i | 1.07605i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.17736e6i | 1.33326i | 0.745387 | + | 0.666632i | \(0.232265\pi\) | ||||
−0.745387 | + | 0.666632i | \(0.767735\pi\) | |||||||
\(240\) | −313650. | − | 366020.i | −0.351494 | − | 0.410182i | ||||
\(241\) | − | 1.28491e6i | − | 1.42504i | −0.701649 | − | 0.712522i | \(-0.747553\pi\) | ||
0.701649 | − | 0.712522i | \(-0.252447\pi\) | |||||||
\(242\) | 372352. | − | 534718.i | 0.408710 | − | 0.586930i | ||||
\(243\) | −952632. | −1.03493 | ||||||||
\(244\) | 390099. | − | 144279.i | 0.419470 | − | 0.155141i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −137754. | − | 95925.6i | −0.145134 | − | 0.101064i | ||||
\(247\) | − | 47350.4i | − | 0.0493834i | ||||||
\(248\) | 917850. | + | 238305.i | 0.947638 | + | 0.246039i | ||||
\(249\) | −608125. | −0.621576 | ||||||||
\(250\) | 823919. | + | 573738.i | 0.833748 | + | 0.580582i | ||||
\(251\) | 1.48159e6 | 1.48437 | 0.742186 | − | 0.670194i | \(-0.233789\pi\) | ||||
0.742186 | + | 0.670194i | \(0.233789\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 419614. | 0.412144 | ||||||||
\(254\) | 228667. | + | 159233.i | 0.222392 | + | 0.154863i | ||||
\(255\) | 632125. | 0.608769 | ||||||||
\(256\) | 160637. | − | 1.03620e6i | 0.153195 | − | 0.988196i | ||||
\(257\) | − | 1.11479e6i | − | 1.05283i | −0.850227 | − | 0.526415i | \(-0.823536\pi\) | ||
0.850227 | − | 0.526415i | \(-0.176464\pi\) | |||||||
\(258\) | −459301. | − | 319836.i | −0.429584 | − | 0.299142i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −613612. | − | 1.65908e6i | −0.562937 | − | 1.52207i | ||||
\(261\) | 101847. | 0.0925437 | ||||||||
\(262\) | −479887. | + | 689144.i | −0.431903 | + | 0.620236i | ||||
\(263\) | − | 1.60568e6i | − | 1.43143i | −0.698395 | − | 0.715713i | \(-0.746102\pi\) | ||
0.698395 | − | 0.715713i | \(-0.253898\pi\) | |||||||
\(264\) | 204773. | − | 788700.i | 0.180827 | − | 0.696470i | ||||
\(265\) | 147855.i | 0.129337i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 599469.i | 0.514622i | ||||||||
\(268\) | −1.67391e6 | + | 619097.i | −1.42362 | + | 0.526528i | ||||
\(269\) | − | 812107.i | − | 0.684278i | −0.939649 | − | 0.342139i | \(-0.888849\pi\) | ||
0.939649 | − | 0.342139i | \(-0.111151\pi\) | |||||||
\(270\) | 901720. | + | 627915.i | 0.752770 | + | 0.524193i | ||||
\(271\) | −1.84581e6 | −1.52673 | −0.763366 | − | 0.645966i | \(-0.776455\pi\) | ||||
−0.763366 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(272\) | 894769. | + | 1.04417e6i | 0.733311 | + | 0.855752i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 866035. | − | 1.24367e6i | 0.696882 | − | 1.00076i | ||||
\(275\) | 54794.5i | 0.0436923i | ||||||||
\(276\) | 205225. | − | 75902.8i | 0.162165 | − | 0.0599770i | ||||
\(277\) | −470388. | −0.368347 | −0.184173 | − | 0.982894i | \(-0.558961\pi\) | ||||
−0.184173 | + | 0.982894i | \(0.558961\pi\) | |||||||
\(278\) | 585211. | − | 840394.i | 0.454151 | − | 0.652185i | ||||
\(279\) | −888702. | −0.683511 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 115672. | 0.0873901 | 0.0436950 | − | 0.999045i | \(-0.486087\pi\) | ||||
0.0436950 | + | 0.999045i | \(0.486087\pi\) | |||||||
\(282\) | 99384.9 | − | 142722.i | 0.0744213 | − | 0.106873i | ||||
\(283\) | −1.19333e6 | −0.885717 | −0.442859 | − | 0.896591i | \(-0.646036\pi\) | ||||
−0.442859 | + | 0.896591i | \(0.646036\pi\) | |||||||
\(284\) | −1.12120e6 | + | 414676.i | −0.824871 | + | 0.305079i | ||||
\(285\) | − | 22161.2i | − | 0.0161615i | ||||||
\(286\) | 1.70881e6 | − | 2.45395e6i | 1.23532 | − | 1.77399i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 98325.0 | + | 977764.i | 0.0698526 | + | 0.694629i | ||||
\(289\) | −383443. | −0.270058 | ||||||||
\(290\) | −153175. | − | 106663.i | −0.106953 | − | 0.0744767i | ||||
\(291\) | 946432.i | 0.655174i | ||||||||
\(292\) | 1.47643e6 | − | 546061.i | 1.01334 | − | 0.374786i | ||||
\(293\) | 2.48950e6i | 1.69411i | 0.531503 | + | 0.847056i | \(0.321627\pi\) | ||||
−0.531503 | + | 0.847056i | \(0.678373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 454120.i | − | 0.303820i | ||||||
\(296\) | −2.31624e6 | − | 601373.i | −1.53657 | − | 0.398946i | ||||
\(297\) | 1.85751e6i | 1.22191i | ||||||||
\(298\) | −213724. | + | 306920.i | −0.139416 | + | 0.200209i | ||||
\(299\) | 802988. | 0.519435 | ||||||||
\(300\) | 9911.62 | + | 26798.9i | 0.00635830 | + | 0.0171915i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −776065. | − | 540414.i | −0.489644 | − | 0.340965i | ||||
\(303\) | 475731.i | 0.297683i | ||||||||
\(304\) | 36606.7 | − | 31369.0i | 0.0227183 | − | 0.0194678i | ||||
\(305\) | 714369. | 0.439717 | ||||||||
\(306\) | −1.05756e6 | − | 736431.i | −0.645654 | − | 0.449603i | ||||
\(307\) | −1.47151e6 | −0.891079 | −0.445540 | − | 0.895262i | \(-0.646988\pi\) | ||||
−0.445540 | + | 0.895262i | \(0.646988\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00765e6 | −0.600362 | ||||||||
\(310\) | 1.33658e6 | + | 930730.i | 0.789933 | + | 0.550072i | ||||
\(311\) | 1.15068e6 | 0.674613 | 0.337307 | − | 0.941395i | \(-0.390484\pi\) | ||||
0.337307 | + | 0.941395i | \(0.390484\pi\) | |||||||
\(312\) | 391861. | − | 1.50928e6i | 0.227900 | − | 0.877777i | ||||
\(313\) | 1.28904e6i | 0.743713i | 0.928290 | + | 0.371856i | \(0.121279\pi\) | ||||
−0.928290 | + | 0.371856i | \(0.878721\pi\) | |||||||
\(314\) | 1.80184e6 | + | 1.25472e6i | 1.03132 | + | 0.718160i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.26063e6 | + | 1.20595e6i | −1.83690 | + | 0.679378i | ||||
\(317\) | −266679. | −0.149053 | −0.0745265 | − | 0.997219i | \(-0.523745\pi\) | ||||
−0.0745265 | + | 0.997219i | \(0.523745\pi\) | |||||||
\(318\) | −74481.0 | + | 106959.i | −0.0413026 | + | 0.0593128i | ||||
\(319\) | − | 315533.i | − | 0.173607i | ||||||
\(320\) | 876126. | − | 1.57350e6i | 0.478290 | − | 0.858998i | ||||
\(321\) | − | 1.28982e6i | − | 0.698663i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 63220.5i | 0.0337172i | ||||||||
\(324\) | −121602. | − | 328786.i | −0.0643544 | − | 0.174001i | ||||
\(325\) | 104857.i | 0.0550665i | ||||||||
\(326\) | −1.34878e6 | − | 939226.i | −0.702905 | − | 0.489470i | ||||
\(327\) | −498992. | −0.258062 | ||||||||
\(328\) | 157612. | − | 607055.i | 0.0808917 | − | 0.311561i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 799768. | − | 1.14851e6i | 0.404277 | − | 0.580564i | ||||
\(331\) | 88764.5i | 0.0445317i | 0.999752 | + | 0.0222659i | \(0.00708803\pi\) | ||||
−0.999752 | + | 0.0222659i | \(0.992912\pi\) | |||||||
\(332\) | −788166. | − | 2.13104e6i | −0.392439 | − | 1.06107i | ||||
\(333\) | 2.24268e6 | 1.10830 | ||||||||
\(334\) | −1.79767e6 | + | 2.58155e6i | −0.881745 | + | 1.26623i | ||||
\(335\) | −3.06534e6 | −1.49234 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.73985e6 | 1.31417 | 0.657086 | − | 0.753816i | \(-0.271789\pi\) | ||||
0.657086 | + | 0.753816i | \(0.271789\pi\) | |||||||
\(338\) | 2.06980e6 | − | 2.97234e6i | 0.985453 | − | 1.41516i | ||||
\(339\) | 521980. | 0.246692 | ||||||||
\(340\) | 819272. | + | 2.21514e6i | 0.384353 | + | 1.03921i | ||||
\(341\) | 2.75330e6i | 1.28223i | ||||||||
\(342\) | −25818.0 | + | 37076.0i | −0.0119359 | + | 0.0171407i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 525510. | − | 2.02404e6i | 0.239433 | − | 0.922198i | ||||
\(345\) | 375818. | 0.169993 | ||||||||
\(346\) | −217880. | − | 151721.i | −0.0978425 | − | 0.0681329i | ||||
\(347\) | 1.96156e6i | 0.874536i | 0.899331 | + | 0.437268i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437268i | \(0.855946\pi\) | |||||||
\(348\) | −57075.9 | − | 154321.i | −0.0252641 | − | 0.0683090i | ||||
\(349\) | − | 16825.6i | − | 0.00739446i | −0.999993 | − | 0.00369723i | \(-0.998823\pi\) | ||
0.999993 | − | 0.00369723i | \(-0.00117687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.55459e6i | 1.54000i | ||||||||
\(352\) | 3.02922e6 | − | 304622.i | 1.30309 | − | 0.131040i | ||||
\(353\) | − | 2.01608e6i | − | 0.861134i | −0.902559 | − | 0.430567i | \(-0.858314\pi\) | ||
0.902559 | − | 0.430567i | \(-0.141686\pi\) | |||||||
\(354\) | 228760. | − | 328512.i | 0.0970224 | − | 0.139329i | ||||
\(355\) | −2.05319e6 | −0.864685 | ||||||||
\(356\) | −2.10070e6 | + | 776948.i | −0.878496 | + | 0.324913i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 149108. | + | 103831.i | 0.0614882 | + | 0.0428175i | ||||
\(359\) | 880940.i | 0.360753i | 0.983598 | + | 0.180377i | \(0.0577317\pi\) | ||||
−0.983598 | + | 0.180377i | \(0.942268\pi\) | |||||||
\(360\) | −424152. | + | 1.63365e6i | −0.172490 | + | 0.664361i | ||||
\(361\) | −2.47388e6 | −0.999105 | ||||||||
\(362\) | 2.37784e6 | + | 1.65582e6i | 0.953700 | + | 0.664111i | ||||
\(363\) | 986532. | 0.392957 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.70372e6 | 1.06226 | ||||||||
\(366\) | 516776. | + | 359858.i | 0.201651 | + | 0.140420i | ||||
\(367\) | 1.67655e6 | 0.649758 | 0.324879 | − | 0.945756i | \(-0.394676\pi\) | ||||
0.324879 | + | 0.945756i | \(0.394676\pi\) | |||||||
\(368\) | 531969. | + | 620791.i | 0.204770 | + | 0.238960i | ||||
\(369\) | 587777.i | 0.224722i | ||||||||
\(370\) | −3.37292e6 | − | 2.34874e6i | −1.28086 | − | 0.891930i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 498036. | + | 1.34659e6i | 0.186596 | + | 0.504518i | ||||
\(373\) | −166508. | −0.0619675 | −0.0309837 | − | 0.999520i | \(-0.509864\pi\) | ||||
−0.0309837 | + | 0.999520i | \(0.509864\pi\) | |||||||
\(374\) | −2.28155e6 | + | 3.27643e6i | −0.843433 | + | 1.21122i | ||||
\(375\) | 1.52010e6i | 0.558204i | ||||||||
\(376\) | 628946. | + | 163296.i | 0.229427 | + | 0.0595668i | ||||
\(377\) | − | 603815.i | − | 0.218802i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.67656e6i | 0.957147i | 0.878047 | + | 0.478574i | \(0.158846\pi\) | ||||
−0.878047 | + | 0.478574i | \(0.841154\pi\) | |||||||
\(380\) | 77658.8 | − | 28722.2i | 0.0275887 | − | 0.0102037i | ||||
\(381\) | 421880.i | 0.148894i | ||||||||
\(382\) | −19591.1 | − | 13642.3i | −0.00686912 | − | 0.00478333i | ||||
\(383\) | 4.48421e6 | 1.56203 | 0.781015 | − | 0.624512i | \(-0.214702\pi\) | ||||
0.781015 | + | 0.624512i | \(0.214702\pi\) | |||||||
\(384\) | 1.42643e6 | − | 696932.i | 0.493654 | − | 0.241192i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −55394.0 | + | 79548.8i | −0.0189232 | + | 0.0271747i | ||||
\(387\) | 1.95977e6i | 0.665161i | ||||||||
\(388\) | −3.31656e6 | + | 1.22663e6i | −1.11843 | + | 0.413652i | ||||
\(389\) | −2.27740e6 | −0.763073 | −0.381536 | − | 0.924354i | \(-0.624605\pi\) | ||||
−0.381536 | + | 0.924354i | \(0.624605\pi\) | |||||||
\(390\) | 1.53046e6 | − | 2.19783e6i | 0.509520 | − | 0.731699i | ||||
\(391\) | −1.07212e6 | −0.354651 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.27144e6 | −0.415255 | ||||||||
\(394\) | −3.09954e6 | + | 4.45110e6i | −1.00590 | + | 1.44453i | ||||
\(395\) | −5.97103e6 | −1.92556 | ||||||||
\(396\) | −2.67605e6 | + | 989741.i | −0.857544 | + | 0.317164i | ||||
\(397\) | − | 652519.i | − | 0.207786i | −0.994588 | − | 0.103893i | \(-0.966870\pi\) | ||
0.994588 | − | 0.103893i | \(-0.0331300\pi\) | |||||||
\(398\) | −184319. | + | 264692.i | −0.0583261 | + | 0.0837594i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −81064.8 | + | 69466.1i | −0.0253327 | + | 0.0217081i | ||||
\(401\) | −299794. | −0.0931026 | −0.0465513 | − | 0.998916i | \(-0.514823\pi\) | ||||
−0.0465513 | + | 0.998916i | \(0.514823\pi\) | |||||||
\(402\) | −2.21748e6 | − | 1.54415e6i | −0.684375 | − | 0.476566i | ||||
\(403\) | 5.26880e6i | 1.61603i | ||||||||
\(404\) | −1.66709e6 | + | 616575.i | −0.508166 | + | 0.187946i | ||||
\(405\) | − | 602089.i | − | 0.182399i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.94807e6i | − | 2.07911i | ||||||
\(408\) | −523198. | + | 2.01514e6i | −0.155602 | + | 0.599314i | ||||
\(409\) | − | 1.40471e6i | − | 0.415220i | −0.978212 | − | 0.207610i | \(-0.933432\pi\) | ||
0.978212 | − | 0.207610i | \(-0.0665684\pi\) | |||||||
\(410\) | 615574. | − | 883997.i | 0.180851 | − | 0.259712i | ||||
\(411\) | 2.29452e6 | 0.670021 | ||||||||
\(412\) | −1.30597e6 | − | 3.53108e6i | −0.379046 | − | 1.02486i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −628751. | − | 437832.i | −0.180292 | − | 0.125547i | ||||
\(415\) | − | 3.90246e6i | − | 1.11229i | ||||||
\(416\) | 5.79682e6 | − | 582935.i | 1.64231 | − | 0.165153i | ||||
\(417\) | 1.55049e6 | 0.436646 | ||||||||
\(418\) | 114866. | + | 79986.9i | 0.0321551 | + | 0.0223913i | ||||
\(419\) | 2.63281e6 | 0.732630 | 0.366315 | − | 0.930491i | \(-0.380619\pi\) | ||||
0.366315 | + | 0.930491i | \(0.380619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.29645e6 | −0.631469 | −0.315735 | − | 0.948848i | \(-0.602251\pi\) | ||||
−0.315735 | + | 0.948848i | \(0.602251\pi\) | |||||||
\(422\) | −445709. | − | 310371.i | −0.121835 | − | 0.0848398i | ||||
\(423\) | −608973. | −0.165481 | ||||||||
\(424\) | −471345. | − | 122377.i | −0.127328 | − | 0.0330586i | ||||
\(425\) | − | 140001.i | − | 0.0375974i | ||||||
\(426\) | −1.48528e6 | − | 1.03428e6i | −0.396538 | − | 0.276130i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.51990e6 | − | 1.67169e6i | 1.19267 | − | 0.441109i | ||||
\(429\) | 4.52744e6 | 1.18771 | ||||||||
\(430\) | 2.05245e6 | − | 2.94743e6i | 0.535305 | − | 0.768727i | ||||
\(431\) | − | 2.52971e6i | − | 0.655961i | −0.944684 | − | 0.327981i | \(-0.893632\pi\) | ||
0.944684 | − | 0.327981i | \(-0.106368\pi\) | |||||||
\(432\) | −2.74806e6 | + | 2.35487e6i | −0.708462 | + | 0.607095i | ||||
\(433\) | 506501.i | 0.129826i | 0.997891 | + | 0.0649128i | \(0.0206769\pi\) | ||||
−0.997891 | + | 0.0649128i | \(0.979323\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 282600.i | − | 0.0716061i | ||||||
\(436\) | −646724. | − | 1.74861e6i | −0.162931 | − | 0.440530i | ||||
\(437\) | 37586.6i | 0.00941520i | ||||||||
\(438\) | 1.95588e6 | + | 1.36198e6i | 0.487143 | + | 0.339223i | ||||
\(439\) | −495283. | −0.122657 | −0.0613285 | − | 0.998118i | \(-0.519534\pi\) | ||||
−0.0613285 | + | 0.998118i | \(0.519534\pi\) | |||||||
\(440\) | 5.06124e6 | + | 1.31407e6i | 1.24631 | + | 0.323584i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.36605e6 | + | 6.26988e6i | −1.06300 | + | 1.52652i | ||||
\(443\) | − | 250211.i | − | 0.0605755i | −0.999541 | − | 0.0302877i | \(-0.990358\pi\) | ||
0.999541 | − | 0.0302877i | \(-0.00964236\pi\) | |||||||
\(444\) | −1.25682e6 | − | 3.39817e6i | −0.302562 | − | 0.818065i | ||||
\(445\) | −3.84691e6 | −0.920899 | ||||||||
\(446\) | 2.00096e6 | − | 2.87349e6i | 0.476323 | − | 0.684026i | ||||
\(447\) | −566254. | −0.134043 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.81736e6 | −1.36179 | −0.680894 | − | 0.732382i | \(-0.738409\pi\) | ||||
−0.680894 | + | 0.732382i | \(0.738409\pi\) | |||||||
\(450\) | 57173.4 | − | 82104.2i | 0.0133095 | − | 0.0191132i | ||||
\(451\) | 1.82100e6 | 0.421568 | ||||||||
\(452\) | 676517. | + | 1.82916e6i | 0.155752 | + | 0.421120i | ||||
\(453\) | − | 1.43181e6i | − | 0.327822i | ||||||
\(454\) | −4.25898e6 | + | 6.11612e6i | −0.969763 | + | 1.39263i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 70647.2 | + | 18342.4i | 0.0159105 | + | 0.00413089i | ||||
\(457\) | −5.24207e6 | −1.17412 | −0.587059 | − | 0.809544i | \(-0.699714\pi\) | ||||
−0.587059 | + | 0.809544i | \(0.699714\pi\) | |||||||
\(458\) | −153470. | − | 106869.i | −0.0341870 | − | 0.0238062i | ||||
\(459\) | − | 4.74595e6i | − | 1.05146i | ||||||
\(460\) | 487083. | + | 1.31697e6i | 0.107327 | + | 0.290189i | ||||
\(461\) | − | 2.57206e6i | − | 0.563674i | −0.959462 | − | 0.281837i | \(-0.909056\pi\) | ||
0.959462 | − | 0.281837i | \(-0.0909438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.72459e6i | 0.373881i | 0.982371 | + | 0.186940i | \(0.0598571\pi\) | ||||
−0.982371 | + | 0.186940i | \(0.940143\pi\) | |||||||
\(464\) | 466810. | − | 400019.i | 0.100657 | − | 0.0862553i | ||||
\(465\) | 2.46593e6i | 0.528870i | ||||||||
\(466\) | −2.46607e6 | + | 3.54141e6i | −0.526066 | + | 0.755459i | ||||
\(467\) | −958306. | −0.203335 | −0.101667 | − | 0.994818i | \(-0.532418\pi\) | ||||
−0.101667 | + | 0.994818i | \(0.532418\pi\) | |||||||
\(468\) | −5.12098e6 | + | 1.89400e6i | −1.08078 | + | 0.399729i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 915876. | + | 637772.i | 0.191246 | + | 0.133174i | ||||
\(471\) | 3.32432e6i | 0.690479i | ||||||||
\(472\) | 1.44768e6 | + | 375867.i | 0.299101 | + | 0.0776567i | ||||
\(473\) | 6.07158e6 | 1.24781 | ||||||||
\(474\) | −4.31946e6 | − | 3.00787e6i | −0.883046 | − | 0.614911i | ||||
\(475\) | −4908.17 | −0.000998127 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 456376. | 0.0918390 | ||||||||
\(478\) | −5.46558e6 | − | 3.80597e6i | −1.09412 | − | 0.761896i | ||||
\(479\) | −9.16761e6 | −1.82565 | −0.912825 | − | 0.408351i | \(-0.866104\pi\) | ||||
−0.912825 | + | 0.408351i | \(0.866104\pi\) | |||||||
\(480\) | 2.71306e6 | − | 272828.i | 0.537472 | − | 0.0540488i | ||||
\(481\) | − | 1.32961e7i | − | 2.62036i | ||||||
\(482\) | 5.96481e6 | + | 4.15361e6i | 1.16944 | + | 0.814344i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.27860e6 | + | 3.45708e6i | 0.248098 | + | 0.670804i | ||||
\(485\) | −6.07344e6 | −1.17241 | ||||||||
\(486\) | 3.07949e6 | − | 4.42232e6i | 0.591410 | − | 0.849297i | ||||
\(487\) | − | 3.84357e6i | − | 0.734365i | −0.930149 | − | 0.367183i | \(-0.880322\pi\) | ||
0.930149 | − | 0.367183i | \(-0.119678\pi\) | |||||||
\(488\) | −591270. | + | 2.27732e6i | −0.112392 | + | 0.432888i | ||||
\(489\) | − | 2.48844e6i | − | 0.470603i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.08747e6i | − | 1.51394i | −0.653449 | − | 0.756971i | \(-0.726678\pi\) | ||
0.653449 | − | 0.756971i | \(-0.273322\pi\) | |||||||
\(492\) | 890615. | − | 329395.i | 0.165874 | − | 0.0613485i | ||||
\(493\) | 806191.i | 0.149390i | ||||||||
\(494\) | 219811. | + | 153066.i | 0.0405258 | + | 0.0282202i | ||||
\(495\) | −4.90051e6 | −0.898936 | ||||||||
\(496\) | −4.07332e6 | + | 3.49051e6i | −0.743437 | + | 0.637067i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.96584e6 | − | 2.82305e6i | 0.355201 | − | 0.510088i | ||||
\(499\) | 1.60743e6i | 0.288988i | 0.989506 | + | 0.144494i | \(0.0461554\pi\) | ||||
−0.989506 | + | 0.144494i | \(0.953845\pi\) | |||||||
\(500\) | −5.32684e6 | + | 1.97014e6i | −0.952893 | + | 0.352429i | ||||
\(501\) | −4.76285e6 | −0.847759 | ||||||||
\(502\) | −4.78940e6 | + | 6.87784e6i | −0.848247 | + | 1.21813i | ||||
\(503\) | 9.86993e6 | 1.73938 | 0.869689 | − | 0.493600i | \(-0.164319\pi\) | ||||
0.869689 | + | 0.493600i | \(0.164319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.05286e6 | −0.532694 | ||||||||
\(506\) | −1.35645e6 | + | 1.94794e6i | −0.235520 | + | 0.338220i | ||||
\(507\) | 5.48384e6 | 0.947469 | ||||||||
\(508\) | −1.47838e6 | + | 546782.i | −0.254172 | + | 0.0940058i | ||||
\(509\) | 5.18693e6i | 0.887394i | 0.896177 | + | 0.443697i | \(0.146333\pi\) | ||||
−0.896177 | + | 0.443697i | \(0.853667\pi\) | |||||||
\(510\) | −2.04342e6 | + | 2.93446e6i | −0.347882 | + | 0.499577i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.29098e6 | + | 4.09534e6i | 0.723405 | + | 0.690423i | ||||
\(513\) | −166385. | −0.0279139 | ||||||||
\(514\) | 5.17508e6 | + | 3.60368e6i | 0.863991 | + | 0.601642i | ||||
\(515\) | − | 6.46629e6i | − | 1.07433i | ||||||
\(516\) | 2.96949e6 | − | 1.09827e6i | 0.490973 | − | 0.181587i | ||||
\(517\) | 1.88667e6i | 0.310433i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 401980.i | − | 0.0655067i | ||||||
\(520\) | 9.68537e6 | + | 2.51465e6i | 1.57075 | + | 0.407820i | ||||
\(521\) | 3.11549e6i | 0.502843i | 0.967878 | + | 0.251422i | \(0.0808980\pi\) | ||||
−0.967878 | + | 0.251422i | \(0.919102\pi\) | |||||||
\(522\) | −329232. | + | 472796.i | −0.0528842 | + | 0.0759446i | ||||
\(523\) | 9.96967e6 | 1.59377 | 0.796887 | − | 0.604128i | \(-0.206479\pi\) | ||||
0.796887 | + | 0.604128i | \(0.206479\pi\) | |||||||
\(524\) | −1.64786e6 | − | 4.45548e6i | −0.262176 | − | 0.708869i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.45390e6 | + | 5.19054e6i | 1.17468 | + | 0.817990i | ||||
\(527\) | − | 7.03471e6i | − | 1.10337i | ||||||
\(528\) | 2.99936e6 | + | 3.50017e6i | 0.468214 | + | 0.546392i | ||||
\(529\) | 5.79893e6 | 0.900967 | ||||||||
\(530\) | −686376. | − | 477959.i | −0.106138 | − | 0.0739097i | ||||
\(531\) | −1.40171e6 | −0.215735 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.48472e6 | 0.531313 | ||||||||
\(534\) | −2.78286e6 | − | 1.93785e6i | −0.422317 | − | 0.294082i | ||||
\(535\) | 8.27706e6 | 1.25023 | ||||||||
\(536\) | 2.53713e6 | − | 9.77195e6i | 0.381443 | − | 1.46916i | ||||
\(537\) | 275097.i | 0.0411671i | ||||||||
\(538\) | 3.76998e6 | + | 2.62523e6i | 0.561543 | + | 0.391032i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.82984e6 | + | 2.15617e6i | −0.860344 | + | 0.318199i | ||||
\(541\) | 9.11479e6 | 1.33892 | 0.669458 | − | 0.742850i | \(-0.266526\pi\) | ||||
0.669458 | + | 0.742850i | \(0.266526\pi\) | |||||||
\(542\) | 5.96679e6 | − | 8.56863e6i | 0.872453 | − | 1.25289i | ||||
\(543\) | 4.38702e6i | 0.638514i | ||||||||
\(544\) | −7.73970e6 | + | 778313.i | −1.12131 | + | 0.112761i | ||||
\(545\) | − | 3.20213e6i | − | 0.461793i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.96828e6i | − | 1.13867i | −0.822107 | − | 0.569333i | \(-0.807201\pi\) | ||
0.822107 | − | 0.569333i | \(-0.192799\pi\) | |||||||
\(548\) | 2.97384e6 | + | 8.04064e6i | 0.423025 | + | 1.14377i | ||||
\(549\) | − | 2.20500e6i | − | 0.312233i | ||||||
\(550\) | −254368. | − | 177130.i | −0.0358555 | − | 0.0249680i | ||||
\(551\) | 28263.6 | 0.00396597 | ||||||||
\(552\) | −311058. | + | 1.19807e6i | −0.0434504 | + | 0.167353i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.52058e6 | − | 2.18364e6i | 0.210492 | − | 0.302278i | ||||
\(555\) | − | 6.22289e6i | − | 0.857551i | ||||||
\(556\) | 2.00953e6 | + | 5.43335e6i | 0.275681 | + | 0.745385i | ||||
\(557\) | 754870. | 0.103094 | 0.0515471 | − | 0.998671i | \(-0.483585\pi\) | ||||
0.0515471 | + | 0.998671i | \(0.483585\pi\) | |||||||
\(558\) | 2.87283e6 | − | 4.12555e6i | 0.390594 | − | 0.560914i | ||||
\(559\) | 1.16188e7 | 1.57265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.04487e6 | −0.810923 | ||||||||
\(562\) | −373923. | + | 536974.i | −0.0499392 | + | 0.0717154i | ||||
\(563\) | 5.83089e6 | 0.775289 | 0.387645 | − | 0.921809i | \(-0.373289\pi\) | ||||
0.387645 | + | 0.921809i | \(0.373289\pi\) | |||||||
\(564\) | 341273. | + | 922732.i | 0.0451757 | + | 0.122146i | ||||
\(565\) | 3.34965e6i | 0.441446i | ||||||||
\(566\) | 3.85759e6 | − | 5.53971e6i | 0.506145 | − | 0.726851i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.69939e6 | − | 6.54533e6i | 0.221015 | − | 0.851256i | ||||
\(569\) | 7.32494e6 | 0.948470 | 0.474235 | − | 0.880398i | \(-0.342725\pi\) | ||||
0.474235 | + | 0.880398i | \(0.342725\pi\) | |||||||
\(570\) | 102877. | + | 71638.6i | 0.0132627 | + | 0.00923549i | ||||
\(571\) | − | 6.48463e6i | − | 0.832329i | −0.909289 | − | 0.416164i | \(-0.863374\pi\) | ||
0.909289 | − | 0.416164i | \(-0.136626\pi\) | |||||||
\(572\) | 5.86783e6 | + | 1.58654e7i | 0.749872 | + | 2.02750i | ||||
\(573\) | − | 36144.8i | − | 0.00459896i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 83234.9i | − | 0.0104987i | ||||||
\(576\) | −4.85684e6 | − | 2.70429e6i | −0.609954 | − | 0.339623i | ||||
\(577\) | 2.08701e6i | 0.260966i | 0.991451 | + | 0.130483i | \(0.0416529\pi\) | ||||
−0.991451 | + | 0.130483i | \(0.958347\pi\) | |||||||
\(578\) | 1.23953e6 | − | 1.78003e6i | 0.154325 | − | 0.221619i | ||||
\(579\) | −146764. | −0.0181938 | ||||||||
\(580\) | 990310. | − | 366267.i | 0.122237 | − | 0.0452093i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.39354e6 | − | 3.05945e6i | −0.537660 | − | 0.374400i | ||||
\(583\) | − | 1.41390e6i | − | 0.172286i | ||||||
\(584\) | −2.23782e6 | + | 8.61913e6i | −0.271514 | + | 1.04576i | ||||
\(585\) | −9.37779e6 | −1.13295 | ||||||||
\(586\) | −1.15568e7 | − | 8.04759e6i | −1.39025 | − | 0.968104i | ||||
\(587\) | 8.74889e6 | 1.04799 | 0.523996 | − | 0.851721i | \(-0.324441\pi\) | ||||
0.523996 | + | 0.851721i | \(0.324441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −246624. | −0.0292919 | ||||||||
\(590\) | 2.10813e6 | + | 1.46800e6i | 0.249325 | + | 0.173618i | ||||
\(591\) | −8.21209e6 | −0.967131 | ||||||||
\(592\) | 1.02792e7 | − | 8.80846e6i | 1.20547 | − | 1.03299i | ||||
\(593\) | − | 3.65382e6i | − | 0.426689i | −0.976977 | − | 0.213344i | \(-0.931564\pi\) | ||
0.976977 | − | 0.213344i | \(-0.0684356\pi\) | |||||||
\(594\) | −8.62295e6 | − | 6.00461e6i | −1.00274 | − | 0.698262i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −733899. | − | 1.98431e6i | −0.0846293 | − | 0.228820i | ||||
\(597\) | −488346. | −0.0560779 | ||||||||
\(598\) | −2.59575e6 | + | 3.72764e6i | −0.296832 | + | 0.426267i | ||||
\(599\) | 7.00652e6i | 0.797876i | 0.916978 | + | 0.398938i | \(0.130621\pi\) | ||||
−0.916978 | + | 0.398938i | \(0.869379\pi\) | |||||||
\(600\) | −156447. | − | 40618.9i | −0.0177414 | − | 0.00460627i | ||||
\(601\) | − | 1.24584e7i | − | 1.40694i | −0.710723 | − | 0.703472i | \(-0.751632\pi\) | ||
0.710723 | − | 0.703472i | \(-0.248368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.46162e6i | 1.05967i | ||||||||
\(604\) | 5.01744e6 | − | 1.85571e6i | 0.559616 | − | 0.206975i | ||||
\(605\) | 6.33077e6i | 0.703182i | ||||||||
\(606\) | −2.20844e6 | − | 1.53786e6i | −0.244290 | − | 0.170112i | ||||
\(607\) | 8.20968e6 | 0.904387 | 0.452194 | − | 0.891920i | \(-0.350642\pi\) | ||||
0.452194 | + | 0.891920i | \(0.350642\pi\) | |||||||
\(608\) | 27286.3 | + | 271340.i | 0.00299354 | + | 0.0297684i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.30928e6 | + | 3.31625e6i | −0.251277 | + | 0.360847i | ||||
\(611\) | 3.61039e6i | 0.391247i | ||||||||
\(612\) | 6.83735e6 | − | 2.52880e6i | 0.737920 | − | 0.272920i | ||||
\(613\) | 1.13043e7 | 1.21504 | 0.607520 | − | 0.794304i | \(-0.292164\pi\) | ||||
0.607520 | + | 0.794304i | \(0.292164\pi\) | |||||||
\(614\) | 4.75682e6 | − | 6.83105e6i | 0.509209 | − | 0.731252i | ||||
\(615\) | 1.63094e6 | 0.173880 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.66997e6 | 0.916864 | 0.458432 | − | 0.888729i | \(-0.348411\pi\) | ||||
0.458432 | + | 0.888729i | \(0.348411\pi\) | |||||||
\(618\) | 3.25735e6 | − | 4.67773e6i | 0.343078 | − | 0.492679i | ||||
\(619\) | 1.19172e6 | 0.125011 | 0.0625056 | − | 0.998045i | \(-0.480091\pi\) | ||||
0.0625056 | + | 0.998045i | \(0.480091\pi\) | |||||||
\(620\) | −8.64130e6 | + | 3.19600e6i | −0.902818 | + | 0.333908i | ||||
\(621\) | − | 2.82162e6i | − | 0.293609i | ||||||
\(622\) | −3.71972e6 | + | 5.34172e6i | −0.385509 | + | 0.553612i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.73969e6 | + | 6.69804e6i | 0.590101 | + | 0.688630i | ||||
\(625\) | −9.42896e6 | −0.965525 | ||||||||
\(626\) | −5.98400e6 | − | 4.16697e6i | −0.610317 | − | 0.424996i | ||||
\(627\) | 211922.i | 0.0215282i | ||||||||
\(628\) | −1.16493e7 | + | 4.30852e6i | −1.17870 | + | 0.435942i | ||||
\(629\) | 1.77524e7i | 1.78908i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 351151.i | 0.0351092i | 0.999846 | + | 0.0175546i | \(0.00558809\pi\) | ||||
−0.999846 | + | 0.0175546i | \(0.994412\pi\) | |||||||
\(632\) | 4.94211e6 | − | 1.90349e7i | 0.492175 | − | 1.89565i | ||||
\(633\) | − | 822314.i | − | 0.0815696i | ||||||
\(634\) | 862071. | − | 1.23798e6i | 0.0851766 | − | 0.122318i | ||||
\(635\) | −2.70729e6 | −0.266440 | ||||||||
\(636\) | −255757. | − | 691514.i | −0.0250718 | − | 0.0677888i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.46477e6 | + | 1.02000e6i | 0.142468 | + | 0.0992083i | ||||
\(639\) | 6.33747e6i | 0.613993i | ||||||||
\(640\) | 4.47235e6 | + | 9.15369e6i | 0.431604 | + | 0.883378i | ||||
\(641\) | −1.04424e7 | −1.00382 | −0.501908 | − | 0.864921i | \(-0.667368\pi\) | ||||
−0.501908 | + | 0.864921i | \(0.667368\pi\) | |||||||
\(642\) | 5.98764e6 | + | 4.16951e6i | 0.573348 | + | 0.399252i | ||||
\(643\) | −2.01326e7 | −1.92032 | −0.960159 | − | 0.279456i | \(-0.909846\pi\) | ||||
−0.960159 | + | 0.279456i | \(0.909846\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.43788e6 | 0.514671 | ||||||||
\(646\) | −293483. | − | 204368.i | −0.0276695 | − | 0.0192678i | ||||
\(647\) | −2.91740e6 | −0.273991 | −0.136995 | − | 0.990572i | \(-0.543745\pi\) | ||||
−0.136995 | + | 0.990572i | \(0.543745\pi\) | |||||||
\(648\) | 1.91939e6 | + | 498338.i | 0.179567 | + | 0.0466215i | ||||
\(649\) | 4.34265e6i | 0.404709i | ||||||||
\(650\) | −486767. | − | 338961.i | −0.0451895 | − | 0.0314678i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.72018e6 | − | 3.22517e6i | 0.803353 | − | 0.297121i | ||||
\(653\) | −1.80660e6 | −0.165797 | −0.0828987 | − | 0.996558i | \(-0.526418\pi\) | ||||
−0.0828987 | + | 0.996558i | \(0.526418\pi\) | |||||||
\(654\) | 1.61305e6 | − | 2.31643e6i | 0.147470 | − | 0.211775i | ||||
\(655\) | − | 8.15909e6i | − | 0.743085i | ||||||
\(656\) | 2.30858e6 | + | 2.69405e6i | 0.209453 | + | 0.244425i | ||||
\(657\) | − | 8.34542e6i | − | 0.754283i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.63666e7i | − | 1.46807i | −0.679113 | − | 0.734034i | \(-0.737635\pi\) | ||
0.679113 | − | 0.734034i | \(-0.262365\pi\) | |||||||
\(660\) | 2.74629e6 | + | 7.42539e6i | 0.245407 | + | 0.663529i | ||||
\(661\) | − | 1.17490e6i | − | 0.104591i | −0.998632 | − | 0.0522957i | \(-0.983346\pi\) | ||
0.998632 | − | 0.0522957i | \(-0.0166538\pi\) | |||||||
\(662\) | −412064. | − | 286942.i | −0.0365443 | − | 0.0254477i | ||||
\(663\) | −1.15677e7 | −1.02203 | ||||||||
\(664\) | 1.24406e7 | + | 3.22999e6i | 1.09502 | + | 0.284303i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.24973e6 | + | 1.04110e7i | −0.633339 | + | 0.909509i | ||||
\(667\) | 479307.i | 0.0417156i | ||||||||
\(668\) | −6.17293e6 | − | 1.66903e7i | −0.535242 | − | 1.44718i | ||||
\(669\) | 5.30147e6 | 0.457963 | ||||||||
\(670\) | 9.90908e6 | − | 1.42300e7i | 0.852799 | − | 1.22467i | ||||
\(671\) | −6.83135e6 | −0.585733 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.58661e7 | −1.35031 | −0.675154 | − | 0.737677i | \(-0.735923\pi\) | ||||
−0.675154 | + | 0.737677i | \(0.735923\pi\) | |||||||
\(674\) | −8.85689e6 | + | 1.27190e7i | −0.750985 | + | 1.07846i | ||||
\(675\) | 368456. | 0.0311262 | ||||||||
\(676\) | 7.10739e6 | + | 1.92169e7i | 0.598196 | + | 1.61740i | ||||
\(677\) | 1.76918e7i | 1.48355i | 0.670651 | + | 0.741773i | \(0.266015\pi\) | ||||
−0.670651 | + | 0.741773i | \(0.733985\pi\) | |||||||
\(678\) | −1.68736e6 | + | 2.42314e6i | −0.140972 | + | 0.202444i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.29315e7 | − | 3.35746e6i | −1.07245 | − | 0.278445i | ||||
\(681\) | −1.12840e7 | −0.932384 | ||||||||
\(682\) | −1.27814e7 | − | 8.90036e6i | −1.05225 | − | 0.732735i | ||||
\(683\) | 3.18958e6i | 0.261627i | 0.991407 | + | 0.130813i | \(0.0417589\pi\) | ||||
−0.991407 | + | 0.130813i | \(0.958241\pi\) | |||||||
\(684\) | −88655.2 | − | 239705.i | −0.00724543 | − | 0.0195901i | ||||
\(685\) | 1.47244e7i | 1.19898i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 283146.i | − | 0.0228886i | ||||||
\(688\) | 7.69728e6 | + | 8.98249e6i | 0.619964 | + | 0.723479i | ||||
\(689\) | − | 2.70570e6i | − | 0.217136i | ||||||
\(690\) | −1.21488e6 | + | 1.74463e6i | −0.0971426 | + | 0.139502i | ||||
\(691\) | −2.37212e6 | −0.188991 | −0.0944954 | − | 0.995525i | \(-0.530124\pi\) | ||||
−0.0944954 | + | 0.995525i | \(0.530124\pi\) | |||||||
\(692\) | 1.40865e6 | − | 520990.i | 0.111825 | − | 0.0413584i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.10598e6 | − | 6.34097e6i | −0.717675 | − | 0.499755i | ||||
\(695\) | 9.94981e6i | 0.781363i | ||||||||
\(696\) | 900897. | + | 233903.i | 0.0704940 | + | 0.0183026i | ||||
\(697\) | −4.65267e6 | −0.362761 | ||||||||
\(698\) | 78108.0 | + | 54390.7i | 0.00606816 | + | 0.00422558i | ||||
\(699\) | −6.53374e6 | −0.505789 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.76418e6 | 0.135597 | 0.0677983 | − | 0.997699i | \(-0.478403\pi\) | ||||
0.0677983 | + | 0.997699i | \(0.478403\pi\) | |||||||
\(702\) | −1.65012e7 | − | 1.14906e7i | −1.26378 | − | 0.880037i | ||||
\(703\) | 622368. | 0.0474962 | ||||||||
\(704\) | −8.37819e6 | + | 1.50470e7i | −0.637116 | + | 1.14424i | ||||
\(705\) | 1.68975e6i | 0.128041i | ||||||||
\(706\) | 9.35907e6 | + | 6.51721e6i | 0.706677 | + | 0.492096i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 785529. | + | 2.12391e6i | 0.0588951 | + | 0.159240i | ||||
\(709\) | −1.26071e7 | −0.941888 | −0.470944 | − | 0.882163i | \(-0.656087\pi\) | ||||
−0.470944 | + | 0.882163i | \(0.656087\pi\) | |||||||
\(710\) | 6.63718e6 | − | 9.53135e6i | 0.494126 | − | 0.709592i | ||||
\(711\) | 1.84305e7i | 1.36729i | ||||||||
\(712\) | 3.18401e6 | − | 1.22635e7i | 0.235383 | − | 0.906597i | ||||
\(713\) | − | 4.18236e6i | − | 0.308104i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.90534e7i | 2.12536i | ||||||||
\(716\) | −964016. | + | 356542.i | −0.0702751 | + | 0.0259913i | ||||
\(717\) | − | 1.00838e7i | − | 0.732529i | ||||||
\(718\) | −4.08952e6 | − | 2.84774e6i | −0.296047 | − | 0.206153i | ||||
\(719\) | 1.04868e7 | 0.756520 | 0.378260 | − | 0.925699i | \(-0.376523\pi\) | ||||
0.378260 | + | 0.925699i | \(0.376523\pi\) | |||||||
\(720\) | −6.21266e6 | − | 7.24999e6i | −0.446628 | − | 0.521202i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.99712e6 | − | 1.14843e7i | 0.570940 | − | 0.819901i | ||||
\(723\) | 1.10048e7i | 0.782955i | ||||||||
\(724\) | −1.53733e7 | + | 5.68584e6i | −1.08999 | + | 0.403133i | ||||
\(725\) | −62589.3 | −0.00442237 | ||||||||
\(726\) | −3.18908e6 | + | 4.57969e6i | −0.224556 | + | 0.322474i | ||||
\(727\) | −1.88450e7 | −1.32239 | −0.661196 | − | 0.750213i | \(-0.729951\pi\) | ||||
−0.661196 | + | 0.750213i | \(0.729951\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.49698e6 | 0.383094 | ||||||||
\(730\) | −8.74009e6 | + | 1.25512e7i | −0.607028 | + | 0.871725i | ||||
\(731\) | −1.55130e7 | −1.07375 | ||||||||
\(732\) | −3.34108e6 | + | 1.23570e6i | −0.230467 | + | 0.0852386i | ||||
\(733\) | − | 1.38347e7i | − | 0.951066i | −0.879698 | − | 0.475533i | \(-0.842255\pi\) | ||
0.879698 | − | 0.475533i | \(-0.157745\pi\) | |||||||
\(734\) | −5.41965e6 | + | 7.78292e6i | −0.371305 | + | 0.533215i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.60150e6 | + | 462732.i | −0.313116 | + | 0.0314873i | ||||
\(737\) | 2.93132e7 | 1.98790 | ||||||||
\(738\) | −2.72859e6 | − | 1.90006e6i | −0.184415 | − | 0.128418i | ||||
\(739\) | 8.84502e6i | 0.595782i | 0.954600 | + | 0.297891i | \(0.0962832\pi\) | ||||
−0.954600 | + | 0.297891i | \(0.903717\pi\) | |||||||
\(740\) | 2.18067e7 | − | 8.06524e6i | 1.46390 | − | 0.541425i | ||||
\(741\) | 405541.i | 0.0271325i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.25478e7i | 0.833865i | 0.908937 | + | 0.416933i | \(0.136895\pi\) | ||||
−0.908937 | + | 0.416933i | \(0.863105\pi\) | |||||||
\(744\) | −7.86110e6 | − | 2.04101e6i | −0.520656 | − | 0.135180i | ||||
\(745\) | − | 3.63376e6i | − | 0.239865i | ||||||
\(746\) | 538258. | − | 772967.i | 0.0354114 | − | 0.0508527i | ||||
\(747\) | −1.20455e7 | −0.789811 | ||||||||
\(748\) | −7.83451e6 | − | 2.11829e7i | −0.511986 | − | 1.38430i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.05662e6 | − | 4.91389e6i | −0.458082 | − | 0.318987i | ||||
\(751\) | − | 1.98408e7i | − | 1.28369i | −0.766834 | − | 0.641845i | \(-0.778169\pi\) | ||
0.766834 | − | 0.641845i | \(-0.221831\pi\) | |||||||
\(752\) | −2.79120e6 | + | 2.39183e6i | −0.179989 | + | 0.154236i | ||||
\(753\) | −1.26893e7 | −0.815551 | ||||||||
\(754\) | 2.80304e6 | + | 1.95190e6i | 0.179556 | + | 0.125035i | ||||
\(755\) | 9.18818e6 | 0.586627 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.81038e7 | 1.78248 | 0.891241 | − | 0.453530i | \(-0.149835\pi\) | ||||
0.891241 | + | 0.453530i | \(0.149835\pi\) | |||||||
\(758\) | −1.24252e7 | − | 8.65229e6i | −0.785469 | − | 0.546963i | ||||
\(759\) | −3.59387e6 | −0.226442 | ||||||||
\(760\) | −117707. | + | 453357.i | −0.00739209 | + | 0.0284712i | ||||
\(761\) | − | 1.88493e7i | − | 1.17987i | −0.807452 | − | 0.589934i | \(-0.799154\pi\) | ||
0.807452 | − | 0.589934i | \(-0.200846\pi\) | |||||||
\(762\) | −1.95846e6 | − | 1.36378e6i | −0.122188 | − | 0.0850856i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 126661. | − | 46845.8i | 0.00785074 | − | 0.00290361i | ||||
\(765\) | 1.25209e7 | 0.773537 | ||||||||
\(766\) | −1.44958e7 | + | 2.08167e7i | −0.892625 | + | 1.28186i | ||||
\(767\) | 8.31024e6i | 0.510065i | ||||||||
\(768\) | −1.37580e6 | + | 8.87472e6i | −0.0841692 | + | 0.542940i | ||||
\(769\) | 1.42553e6i | 0.0869279i | 0.999055 | + | 0.0434639i | \(0.0138394\pi\) | ||||
−0.999055 | + | 0.0434639i | \(0.986161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.54780e6i | 0.578452i | ||||||||
\(772\) | −190215. | − | 514302.i | −0.0114869 | − | 0.0310581i | ||||
\(773\) | − | 2.42045e7i | − | 1.45696i | −0.685067 | − | 0.728480i | \(-0.740227\pi\) | ||
0.685067 | − | 0.728480i | \(-0.259773\pi\) | |||||||
\(774\) | −9.09766e6 | − | 6.33518e6i | −0.545855 | − | 0.380108i | ||||
\(775\) | 546145. | 0.0326628 | ||||||||
\(776\) | 5.02687e6 | − | 1.93614e7i | 0.299670 | − | 1.15420i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.36198e6 | − | 1.05722e7i | 0.436059 | − | 0.626205i | ||||
\(779\) | 163114.i | 0.00963050i | ||||||||
\(780\) | 5.25539e6 | + | 1.42095e7i | 0.309292 | + | 0.836261i | ||||
\(781\) | 1.96342e7 | 1.15182 | ||||||||
\(782\) | 3.46575e6 | − | 4.97701e6i | 0.202666 | − | 0.291039i | ||||
\(783\) | −2.12175e6 | −0.123677 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.13328e7 | −1.23559 | ||||||||
\(786\) | 4.11008e6 | − | 5.90230e6i | 0.237298 | − | 0.340773i | ||||
\(787\) | −41394.8 | −0.00238237 | −0.00119118 | − | 0.999999i | \(-0.500379\pi\) | ||||
−0.00119118 | + | 0.999999i | \(0.500379\pi\) | |||||||
\(788\) | −1.06434e7 | − | 2.87774e7i | −0.610609 | − | 1.65096i | ||||
\(789\) | 1.37521e7i | 0.786461i | ||||||||
\(790\) | 1.93021e7 | − | 2.77188e7i | 1.10036 | − | 1.58018i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.05606e6 | − | 1.56223e7i | 0.229769 | − | 0.884975i | ||||
\(793\) | −1.30727e7 | −0.738214 | ||||||||
\(794\) | 3.02914e6 | + | 2.10935e6i | 0.170517 | + | 0.118740i | ||||
\(795\) | − | 1.26633e6i | − | 0.0710608i | ||||||
\(796\) | −632926. | − | 1.71130e6i | −0.0354054 | − | 0.0957289i | ||||
\(797\) | 1.28311e7i | 0.715512i | 0.933815 | + | 0.357756i | \(0.116458\pi\) | ||||
−0.933815 | + | 0.357756i | \(0.883542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.82046e6i | − | 0.267129i | ||||||
\(800\) | −60424.9 | − | 600878.i | −0.00333804 | − | 0.0331941i | ||||
\(801\) | 1.18740e7i | 0.653909i | ||||||||
\(802\) | 969119. | − | 1.39171e6i | 0.0532036 | − | 0.0764033i | ||||
\(803\) | −2.58550e7 | −1.41500 | ||||||||
\(804\) | 1.43365e7 | − | 5.30237e6i | 0.782174 | − | 0.289288i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.44589e7 | − | 1.70320e7i | −1.32617 | − | 0.923483i | ||||
\(807\) | 6.95545e6i | 0.375960i | ||||||||
\(808\) | 2.52679e6 | − | 9.73215e6i | 0.136157 | − | 0.524421i | ||||
\(809\) | −3.03498e6 | −0.163036 | −0.0815182 | − | 0.996672i | \(-0.525977\pi\) | ||||
−0.0815182 | + | 0.996672i | \(0.525977\pi\) | |||||||
\(810\) | 2.79503e6 | + | 1.94632e6i | 0.149683 | + | 0.104232i | ||||
\(811\) | −2.07140e7 | −1.10589 | −0.552945 | − | 0.833218i | \(-0.686496\pi\) | ||||
−0.552945 | + | 0.833218i | \(0.686496\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.58088e7 | 0.838825 | ||||||||
\(814\) | 3.22545e7 | + | 2.24605e7i | 1.70620 | + | 1.18811i | ||||
\(815\) | 1.59688e7 | 0.842129 | ||||||||
\(816\) | −7.66342e6 | − | 8.94298e6i | −0.402900 | − | 0.470172i | ||||
\(817\) | 543857.i | 0.0285055i | ||||||||
\(818\) | 6.52096e6 | + | 4.54089e6i | 0.340744 | + | 0.237278i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.11379e6 | + | 5.71525e6i | 0.109781 | + | 0.296825i | ||||
\(821\) | 3.27252e6 | 0.169443 | 0.0847217 | − | 0.996405i | \(-0.473000\pi\) | ||||
0.0847217 | + | 0.996405i | \(0.473000\pi\) | |||||||
\(822\) | −7.41732e6 | + | 1.06517e7i | −0.382884 | + | 0.549843i | ||||
\(823\) | − | 1.71790e6i | − | 0.0884095i | −0.999022 | − | 0.0442047i | \(-0.985925\pi\) | ||
0.999022 | − | 0.0442047i | \(-0.0140754\pi\) | |||||||
\(824\) | 2.06138e7 | + | 5.35203e6i | 1.05764 | + | 0.274600i | ||||
\(825\) | − | 469298.i | − | 0.0240057i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.41034e7i | 1.22550i | 0.790275 | + | 0.612752i | \(0.209937\pi\) | ||||
−0.790275 | + | 0.612752i | \(0.790063\pi\) | |||||||
\(828\) | 4.06502e6 | − | 1.50345e6i | 0.206057 | − | 0.0762104i | ||||
\(829\) | − | 1.15482e7i | − | 0.583618i | −0.956477 | − | 0.291809i | \(-0.905743\pi\) | ||
0.956477 | − | 0.291809i | \(-0.0942572\pi\) | |||||||
\(830\) | 1.81161e7 | + | 1.26152e7i | 0.912785 | + | 0.635620i | ||||
\(831\) | 4.02873e6 | 0.202379 | ||||||||
\(832\) | −1.60328e7 | + | 2.87945e7i | −0.802973 | + | 1.44212i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.01215e6 | + | 7.19772e6i | −0.249522 | + | 0.358327i | ||||
\(835\) | − | 3.05641e7i | − | 1.51704i | ||||||
\(836\) | −742633. | + | 274664.i | −0.0367501 | + | 0.0135921i | ||||
\(837\) | 1.85141e7 | 0.913457 | ||||||||
\(838\) | −8.51088e6 | + | 1.22221e7i | −0.418663 | + | 0.601223i | ||||
\(839\) | −1.35657e7 | −0.665332 | −0.332666 | − | 0.943045i | \(-0.607948\pi\) | ||||
−0.332666 | + | 0.943045i | \(0.607948\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.01507e7 | −0.982428 | ||||||||
\(842\) | 7.42355e6 | − | 1.06606e7i | 0.360854 | − | 0.518206i | ||||
\(843\) | −990694. | −0.0480143 | ||||||||
\(844\) | 2.88161e6 | − | 1.06577e6i | 0.139245 | − | 0.0514999i | ||||
\(845\) | 3.51909e7i | 1.69546i | ||||||||
\(846\) | 1.96858e6 | − | 2.82698e6i | 0.0945641 | − | 0.135799i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.09178e6 | − | 1.79249e6i | 0.0998909 | − | 0.0855986i | ||||
\(849\) | 1.02205e7 | 0.486635 | ||||||||
\(850\) | 649913. | + | 452569.i | 0.0308538 | + | 0.0214851i | ||||
\(851\) | 1.05544e7i | 0.499584i | ||||||||
\(852\) | 9.60270e6 | − | 3.55157e6i | 0.453205 | − | 0.167618i | ||||
\(853\) | 1.43938e7i | 0.677335i | 0.940906 | + | 0.338668i | \(0.109976\pi\) | ||||
−0.940906 | + | 0.338668i | \(0.890024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 438960.i | − | 0.0205357i | ||||||
\(856\) | −6.85076e6 | + | 2.63863e7i | −0.319562 | + | 1.23082i | ||||
\(857\) | 2.48025e7i | 1.15357i | 0.816897 | + | 0.576784i | \(0.195692\pi\) | ||||
−0.816897 | + | 0.576784i | \(0.804308\pi\) | |||||||
\(858\) | −1.46355e7 | + | 2.10173e7i | −0.678717 | + | 0.974674i | ||||
\(859\) | −9.36134e6 | −0.432868 | −0.216434 | − | 0.976297i | \(-0.569443\pi\) | ||||
−0.216434 | + | 0.976297i | \(0.569443\pi\) | |||||||
\(860\) | 7.04782e6 | + | 1.90558e7i | 0.324944 | + | 0.878580i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.17435e7 | + | 8.17760e6i | 0.538305 | + | 0.374850i | ||||
\(863\) | 3.34039e7i | 1.52676i | 0.645950 | + | 0.763380i | \(0.276461\pi\) | ||||
−0.645950 | + | 0.763380i | \(0.723539\pi\) | |||||||
\(864\) | −2.04838e6 | − | 2.03695e7i | −0.0933523 | − | 0.928314i | ||||
\(865\) | 2.57958e6 | 0.117222 | ||||||||
\(866\) | −2.35129e6 | − | 1.63732e6i | −0.106540 | − | 0.0741890i | ||||
\(867\) | 3.28408e6 | 0.148377 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.70996e7 | 2.56498 | ||||||||
\(870\) | 1.31189e6 | + | 913540.i | 0.0587625 | + | 0.0409194i | ||||
\(871\) | 5.60947e7 | 2.50540 | ||||||||
\(872\) | 1.02080e7 | + | 2.65034e6i | 0.454622 | + | 0.118035i | ||||
\(873\) | 1.87466e7i | 0.832503i | ||||||||
\(874\) | −174485. | − | 121503.i | −0.00772645 | − | 0.00538033i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.26452e7 | + | 4.67684e6i | −0.556757 | + | 0.205917i | ||||
\(877\) | 1.74511e7 | 0.766167 | 0.383084 | − | 0.923714i | \(-0.374862\pi\) | ||||
0.383084 | + | 0.923714i | \(0.374862\pi\) | |||||||
\(878\) | 1.60106e6 | − | 2.29921e6i | 0.0700925 | − | 0.100657i | ||||
\(879\) | − | 2.13218e7i | − | 0.930788i | ||||||
\(880\) | −2.24613e7 | + | 1.92475e7i | −0.977749 | + | 0.837853i | ||||
\(881\) | − | 3.98953e7i | − | 1.73174i | −0.500271 | − | 0.865869i | \(-0.666766\pi\) | ||
0.500271 | − | 0.865869i | \(-0.333234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.52150e7i | − | 0.656706i | −0.944555 | − | 0.328353i | \(-0.893506\pi\) | ||
0.944555 | − | 0.328353i | \(-0.106494\pi\) | |||||||
\(884\) | −1.49924e7 | − | 4.05363e7i | −0.645268 | − | 1.74467i | ||||
\(885\) | 3.88940e6i | 0.166926i | ||||||||
\(886\) | 1.16153e6 | + | 808836.i | 0.0497104 | + | 0.0346160i | ||||
\(887\) | 2.46799e7 | 1.05325 | 0.526627 | − | 0.850096i | \(-0.323456\pi\) | ||||
0.526627 | + | 0.850096i | \(0.323456\pi\) | |||||||
\(888\) | 1.98378e7 | + | 5.15057e6i | 0.844233 | + | 0.219191i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.24356e7 | − | 1.78582e7i | 0.526249 | − | 0.755722i | ||||
\(891\) | 5.75764e6i | 0.242969i | ||||||||
\(892\) | 6.87102e6 | + | 1.85778e7i | 0.289141 | + | 0.781776i | ||||
\(893\) | −168997. | −0.00709168 | ||||||||
\(894\) | 1.83048e6 | − | 2.62867e6i | 0.0765988 | − | 0.110000i | ||||
\(895\) | −1.76535e6 | −0.0736671 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.87734e6 | −0.285391 | ||||||||
\(898\) | 1.88053e7 | − | 2.70054e7i | 0.778196 | − | 1.11753i | ||||
\(899\) | −3.14497e6 | −0.129783 | ||||||||
\(900\) | 196325. | + | 530823.i | 0.00807924 | + | 0.0218446i | ||||
\(901\) | 3.61255e6i | 0.148252i | ||||||||
\(902\) | −5.88659e6 | + | 8.45347e6i | −0.240906 | + | 0.345954i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.06783e7 | − | 2.77244e6i | −0.434591 | − | 0.112834i | ||||
\(905\) | −2.81524e7 | −1.14260 | ||||||||
\(906\) | 6.64675e6 | + | 4.62848e6i | 0.269023 | + | 0.187335i | ||||
\(907\) | − | 6.32324e6i | − | 0.255224i | −0.991824 | − | 0.127612i | \(-0.959269\pi\) | ||
0.991824 | − | 0.127612i | \(-0.0407312\pi\) | |||||||
\(908\) | −1.46247e7 | − | 3.95422e7i | −0.588671 | − | 1.59164i | ||||
\(909\) | 9.42309e6i | 0.378254i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.11360e6i | − | 0.0843774i | −0.999110 | − | 0.0421887i | \(-0.986567\pi\) | ||
0.999110 | − | 0.0421887i | \(-0.0134331\pi\) | |||||||
\(912\) | −313525. | + | 268666.i | −0.0124820 | + | 0.0106961i | ||||
\(913\) | 3.73183e7i | 1.48165i | ||||||||
\(914\) | 1.69456e7 | − | 2.43348e7i | 0.670952 | − | 0.963524i | ||||
\(915\) | −6.11835e6 | −0.241591 | ||||||||
\(916\) | 992221. | − | 366974.i | 0.0390724 | − | 0.0144510i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.20317e7 | + | 1.53419e7i | 0.862864 | + | 0.600857i | ||||
\(919\) | 1.15307e7i | 0.450368i | 0.974316 | + | 0.225184i | \(0.0722983\pi\) | ||||
−0.974316 | + | 0.225184i | \(0.927702\pi\) | |||||||
\(920\) | −7.68822e6 | − | 1.99612e6i | −0.299472 | − | 0.0777530i | ||||
\(921\) | 1.26030e7 | 0.489581 | ||||||||
\(922\) | 1.19400e7 | + | 8.31448e6i | 0.462571 | + | 0.322113i | ||||
\(923\) | 3.75726e7 | 1.45167 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.37822e6 | −0.0529621 | ||||||||
\(926\) | −8.00592e6 | − | 5.57494e6i | −0.306820 | − | 0.213655i | ||||
\(927\) | −1.99591e7 | −0.762856 | ||||||||
\(928\) | 347956. | + | 3.46014e6i | 0.0132634 | + | 0.131894i | ||||
\(929\) | − | 3.28513e7i | − | 1.24886i | −0.781082 | − | 0.624429i | \(-0.785332\pi\) | ||
0.781082 | − | 0.624429i | \(-0.214668\pi\) | |||||||
\(930\) | −1.14474e7 | − | 7.97142e6i | −0.434009 | − | 0.302223i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.46812e6 | − | 2.28960e7i | −0.319336 | − | 0.863416i | ||||
\(933\) | −9.85525e6 | −0.370650 | ||||||||
\(934\) | 3.09784e6 | − | 4.44867e6i | 0.116196 | − | 0.166864i | ||||
\(935\) | − | 3.87911e7i | − | 1.45112i | ||||||
\(936\) | 7.76182e6 | − | 2.98953e7i | 0.289584 | − | 1.11536i | ||||
\(937\) | 4.13580e7i | 1.53890i | 0.638707 | + | 0.769450i | \(0.279469\pi\) | ||||
−0.638707 | + | 0.769450i | \(0.720531\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.10402e7i | − | 0.408615i | ||||||
\(940\) | −5.92135e6 | + | 2.19002e6i | −0.218575 | + | 0.0808404i | ||||
\(941\) | − | 8.21905e6i | − | 0.302585i | −0.988489 | − | 0.151293i | \(-0.951656\pi\) | ||
0.988489 | − | 0.151293i | \(-0.0483436\pi\) | |||||||
\(942\) | −1.54322e7 | − | 1.07463e7i | −0.566631 | − | 0.394575i | ||||
\(943\) | −2.76616e6 | −0.101297 | ||||||||
\(944\) | −6.42466e6 | + | 5.50542e6i | −0.234650 | + | 0.201076i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.96271e7 | + | 2.81856e7i | −0.713063 | + | 1.02400i | ||||
\(947\) | − | 3.56997e7i | − | 1.29357i | −0.762672 | − | 0.646785i | \(-0.776113\pi\) | ||
0.762672 | − | 0.646785i | \(-0.223887\pi\) | |||||||
\(948\) | 2.79263e7 | − | 1.03286e7i | 1.00924 | − | 0.373267i | ||||
\(949\) | −4.94771e7 | −1.78336 | ||||||||
\(950\) | 15866.2 | − | 22784.8i | 0.000570381 | − | 0.000819098i | ||||
\(951\) | 2.28402e6 | 0.0818935 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.96767e7 | −1.77182 | −0.885912 | − | 0.463853i | \(-0.846466\pi\) | ||||
−0.885912 | + | 0.463853i | \(0.846466\pi\) | |||||||
\(954\) | −1.47529e6 | + | 2.11860e6i | −0.0524816 | + | 0.0753664i | ||||
\(955\) | 231948. | 0.00822968 | ||||||||
\(956\) | 3.53363e7 | − | 1.30692e7i | 1.25048 | − | 0.462491i | ||||
\(957\) | 2.70244e6i | 0.0953843i | ||||||||
\(958\) | 2.96354e7 | − | 4.25581e7i | 1.04327 | − | 1.49819i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7.50375e6 | + | 1.34765e7i | −0.262785 | + | 0.471955i | ||||
\(961\) | −1.18660e6 | −0.0414471 | ||||||||
\(962\) | 6.17232e7 | + | 4.29811e7i | 2.15036 | + | 1.49741i | ||||
\(963\) | − | 2.55483e7i | − | 0.887763i | ||||||
\(964\) | −3.85639e7 | + | 1.42629e7i | −1.33656 | + | 0.494328i | ||||
\(965\) | − | 941814.i | − | 0.0325572i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.53358e7i | − | 0.871303i | −0.900115 | − | 0.435651i | \(-0.856518\pi\) | ||
0.900115 | − | 0.435651i | \(-0.143482\pi\) | |||||||
\(968\) | −2.01817e7 | − | 5.23986e6i | −0.692262 | − | 0.179734i | ||||
\(969\) | − | 541464.i | − | 0.0185251i | ||||||
\(970\) | 1.96331e7 | − | 2.81942e7i | 0.669977 | − | 0.962123i | ||||
\(971\) | −1.86858e7 | −0.636008 | −0.318004 | − | 0.948089i | \(-0.603013\pi\) | ||||
−0.318004 | + | 0.948089i | \(0.603013\pi\) | |||||||
\(972\) | 1.05745e7 | + | 2.85914e7i | 0.359001 | + | 0.970665i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.78427e7 | + | 1.24248e7i | 0.602646 | + | 0.419654i | ||||
\(975\) | − | 898064.i | − | 0.0302549i | ||||||
\(976\) | −8.66048e6 | − | 1.01065e7i | −0.291016 | − | 0.339607i | ||||
\(977\) | 5.81534e6 | 0.194912 | 0.0974561 | − | 0.995240i | \(-0.468929\pi\) | ||||
0.0974561 | + | 0.995240i | \(0.468929\pi\) | |||||||
\(978\) | 1.15519e7 | + | 8.04418e6i | 0.386194 | + | 0.268927i | ||||
\(979\) | 3.67871e7 | 1.22670 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.88384e6 | −0.327909 | ||||||||
\(982\) | 3.75438e7 | + | 2.61437e7i | 1.24239 | + | 0.865145i | ||||
\(983\) | −2.91262e7 | −0.961392 | −0.480696 | − | 0.876887i | \(-0.659616\pi\) | ||||
−0.480696 | + | 0.876887i | \(0.659616\pi\) | |||||||
\(984\) | −1.34990e6 | + | 5.19924e6i | −0.0444440 | + | 0.171180i | ||||
\(985\) | − | 5.26986e7i | − | 1.73065i | ||||||
\(986\) | −3.74252e6 | − | 2.60611e6i | −0.122595 | − | 0.0853690i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.42113e6 | + | 525606.i | −0.0463171 | + | 0.0171304i | ||||
\(989\) | −9.22295e6 | −0.299833 | ||||||||
\(990\) | 1.58415e7 | − | 2.27493e7i | 0.513698 | − | 0.737699i | ||||
\(991\) | 3.72612e7i | 1.20524i | 0.798029 | + | 0.602619i | \(0.205876\pi\) | ||||
−0.798029 | + | 0.602619i | \(0.794124\pi\) | |||||||
\(992\) | −3.03621e6 | − | 3.01927e7i | −0.0979610 | − | 0.974144i | ||||
\(993\) | − | 760241.i | − | 0.0244668i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.13381e6i | − | 0.100350i | ||||||
\(996\) | 6.75040e6 | + | 1.82517e7i | 0.215616 | + | 0.582981i | ||||
\(997\) | − | 4.74646e7i | − | 1.51228i | −0.654411 | − | 0.756139i | \(-0.727083\pi\) | ||
0.654411 | − | 0.756139i | \(-0.272917\pi\) | |||||||
\(998\) | −7.46202e6 | − | 5.19620e6i | −0.237154 | − | 0.165143i | ||||
\(999\) | −4.67211e7 | −1.48115 |
(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 | 196.6.d.b.195.11 | 36 | ||
4.3 | odd | 2 | inner | 196.6.d.b.195.10 | 36 | ||
7.4 | even | 3 | 28.6.f.a.19.7 | yes | 36 | ||
7.5 | odd | 6 | 28.6.f.a.3.17 | yes | 36 | ||
7.6 | odd | 2 | inner | 196.6.d.b.195.12 | 36 | ||
28.11 | odd | 6 | 28.6.f.a.19.17 | yes | 36 | ||
28.19 | even | 6 | 28.6.f.a.3.7 | ✓ | 36 | ||
28.27 | even | 2 | inner | 196.6.d.b.195.9 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.6.f.a.3.7 | ✓ | 36 | 28.19 | even | 6 | ||
28.6.f.a.3.17 | yes | 36 | 7.5 | odd | 6 | ||
28.6.f.a.19.7 | yes | 36 | 7.4 | even | 3 | ||
28.6.f.a.19.17 | yes | 36 | 28.11 | odd | 6 | ||
196.6.d.b.195.9 | 36 | 28.27 | even | 2 | inner | ||
196.6.d.b.195.10 | 36 | 4.3 | odd | 2 | inner | ||
196.6.d.b.195.11 | 36 | 1.1 | even | 1 | trivial | ||
196.6.d.b.195.12 | 36 | 7.6 | odd | 2 | inner |