Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,7,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.30054083620\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.3 |
Dual form | 10.7.c.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | + | 4.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | −23.0000 | − | 23.0000i | −0.851852 | − | 0.851852i | 0.138509 | − | 0.990361i | \(-0.455769\pi\) |
−0.990361 | + | 0.138509i | \(0.955769\pi\) | |||||||
\(4\) | − | 32.0000i | − | 0.500000i | ||||||
\(5\) | −75.0000 | − | 100.000i | −0.600000 | − | 0.800000i | ||||
\(6\) | 184.000 | 0.851852 | ||||||||
\(7\) | −247.000 | + | 247.000i | −0.720117 | + | 0.720117i | −0.968629 | − | 0.248512i | \(-0.920058\pi\) |
0.248512 | + | 0.968629i | \(0.420058\pi\) | |||||||
\(8\) | 128.000 | + | 128.000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 329.000i | 0.451303i | ||||||||
\(10\) | 700.000 | + | 100.000i | 0.700000 | + | 0.100000i | ||||
\(11\) | 1402.00 | 1.05334 | 0.526672 | − | 0.850069i | \(-0.323440\pi\) | ||||
0.526672 | + | 0.850069i | \(0.323440\pi\) | |||||||
\(12\) | −736.000 | + | 736.000i | −0.425926 | + | 0.425926i | ||||
\(13\) | −2703.00 | − | 2703.00i | −1.23031 | − | 1.23031i | −0.963843 | − | 0.266471i | \(-0.914142\pi\) |
−0.266471 | − | 0.963843i | \(-0.585858\pi\) | |||||||
\(14\) | − | 1976.00i | − | 0.720117i | ||||||
\(15\) | −575.000 | + | 4025.00i | −0.170370 | + | 1.19259i | ||||
\(16\) | −1024.00 | −0.250000 | ||||||||
\(17\) | 2593.00 | − | 2593.00i | 0.527783 | − | 0.527783i | −0.392127 | − | 0.919911i | \(-0.628261\pi\) |
0.919911 | + | 0.392127i | \(0.128261\pi\) | |||||||
\(18\) | −1316.00 | − | 1316.00i | −0.225652 | − | 0.225652i | ||||
\(19\) | − | 1720.00i | − | 0.250765i | −0.992108 | − | 0.125383i | \(-0.959984\pi\) | ||
0.992108 | − | 0.125383i | \(-0.0400159\pi\) | |||||||
\(20\) | −3200.00 | + | 2400.00i | −0.400000 | + | 0.300000i | ||||
\(21\) | 11362.0 | 1.22687 | ||||||||
\(22\) | −5608.00 | + | 5608.00i | −0.526672 | + | 0.526672i | ||||
\(23\) | 2137.00 | + | 2137.00i | 0.175639 | + | 0.175639i | 0.789452 | − | 0.613813i | \(-0.210365\pi\) |
−0.613813 | + | 0.789452i | \(0.710365\pi\) | |||||||
\(24\) | − | 5888.00i | − | 0.425926i | ||||||
\(25\) | −4375.00 | + | 15000.0i | −0.280000 | + | 0.960000i | ||||
\(26\) | 21624.0 | 1.23031 | ||||||||
\(27\) | −9200.00 | + | 9200.00i | −0.467408 | + | 0.467408i | ||||
\(28\) | 7904.00 | + | 7904.00i | 0.360058 | + | 0.360058i | ||||
\(29\) | − | 30520.0i | − | 1.25138i | −0.780070 | − | 0.625692i | \(-0.784817\pi\) | ||
0.780070 | − | 0.625692i | \(-0.215183\pi\) | |||||||
\(30\) | −13800.0 | − | 18400.0i | −0.511111 | − | 0.681481i | ||||
\(31\) | −37838.0 | −1.27012 | −0.635058 | − | 0.772465i | \(-0.719024\pi\) | ||||
−0.635058 | + | 0.772465i | \(0.719024\pi\) | |||||||
\(32\) | 4096.00 | − | 4096.00i | 0.125000 | − | 0.125000i | ||||
\(33\) | −32246.0 | − | 32246.0i | −0.897292 | − | 0.897292i | ||||
\(34\) | 20744.0i | 0.527783i | ||||||||
\(35\) | 43225.0 | + | 6175.00i | 1.00816 | + | 0.144023i | ||||
\(36\) | 10528.0 | 0.225652 | ||||||||
\(37\) | 37113.0 | − | 37113.0i | 0.732691 | − | 0.732691i | −0.238461 | − | 0.971152i | \(-0.576643\pi\) |
0.971152 | + | 0.238461i | \(0.0766429\pi\) | |||||||
\(38\) | 6880.00 | + | 6880.00i | 0.125383 | + | 0.125383i | ||||
\(39\) | 124338.i | 2.09609i | ||||||||
\(40\) | 3200.00 | − | 22400.0i | 0.0500000 | − | 0.350000i | ||||
\(41\) | −35438.0 | −0.514183 | −0.257091 | − | 0.966387i | \(-0.582764\pi\) | ||||
−0.257091 | + | 0.966387i | \(0.582764\pi\) | |||||||
\(42\) | −45448.0 | + | 45448.0i | −0.613433 | + | 0.613433i | ||||
\(43\) | 39177.0 | + | 39177.0i | 0.492749 | + | 0.492749i | 0.909171 | − | 0.416422i | \(-0.136716\pi\) |
−0.416422 | + | 0.909171i | \(0.636716\pi\) | |||||||
\(44\) | − | 44864.0i | − | 0.526672i | ||||||
\(45\) | 32900.0 | − | 24675.0i | 0.361043 | − | 0.270782i | ||||
\(46\) | −17096.0 | −0.175639 | ||||||||
\(47\) | 95193.0 | − | 95193.0i | 0.916878 | − | 0.916878i | −0.0799233 | − | 0.996801i | \(-0.525468\pi\) |
0.996801 | + | 0.0799233i | \(0.0254675\pi\) | |||||||
\(48\) | 23552.0 | + | 23552.0i | 0.212963 | + | 0.212963i | ||||
\(49\) | − | 4369.00i | − | 0.0371359i | ||||||
\(50\) | −42500.0 | − | 77500.0i | −0.340000 | − | 0.620000i | ||||
\(51\) | −119278. | −0.899187 | ||||||||
\(52\) | −86496.0 | + | 86496.0i | −0.615157 | + | 0.615157i | ||||
\(53\) | 36017.0 | + | 36017.0i | 0.241925 | + | 0.241925i | 0.817646 | − | 0.575721i | \(-0.195279\pi\) |
−0.575721 | + | 0.817646i | \(0.695279\pi\) | |||||||
\(54\) | − | 73600.0i | − | 0.467408i | ||||||
\(55\) | −105150. | − | 140200.i | −0.632006 | − | 0.842675i | ||||
\(56\) | −63232.0 | −0.360058 | ||||||||
\(57\) | −39560.0 | + | 39560.0i | −0.213615 | + | 0.213615i | ||||
\(58\) | 122080. | + | 122080.i | 0.625692 | + | 0.625692i | ||||
\(59\) | 35960.0i | 0.175091i | 0.996161 | + | 0.0875455i | \(0.0279023\pi\) | ||||
−0.996161 | + | 0.0875455i | \(0.972098\pi\) | |||||||
\(60\) | 128800. | + | 18400.0i | 0.596296 | + | 0.0851852i | ||||
\(61\) | 83322.0 | 0.367088 | 0.183544 | − | 0.983011i | \(-0.441243\pi\) | ||||
0.183544 | + | 0.983011i | \(0.441243\pi\) | |||||||
\(62\) | 151352. | − | 151352.i | 0.635058 | − | 0.635058i | ||||
\(63\) | −81263.0 | − | 81263.0i | −0.324991 | − | 0.324991i | ||||
\(64\) | 32768.0i | 0.125000i | ||||||||
\(65\) | −67575.0 | + | 473025.i | −0.246063 | + | 1.72244i | ||||
\(66\) | 257968. | 0.897292 | ||||||||
\(67\) | 60833.0 | − | 60833.0i | 0.202262 | − | 0.202262i | −0.598706 | − | 0.800969i | \(-0.704318\pi\) |
0.800969 | + | 0.598706i | \(0.204318\pi\) | |||||||
\(68\) | −82976.0 | − | 82976.0i | −0.263892 | − | 0.263892i | ||||
\(69\) | − | 98302.0i | − | 0.299237i | ||||||
\(70\) | −197600. | + | 148200.i | −0.576093 | + | 0.432070i | ||||
\(71\) | −40318.0 | −0.112648 | −0.0563241 | − | 0.998413i | \(-0.517938\pi\) | ||||
−0.0563241 | + | 0.998413i | \(0.517938\pi\) | |||||||
\(72\) | −42112.0 | + | 42112.0i | −0.112826 | + | 0.112826i | ||||
\(73\) | −129023. | − | 129023.i | −0.331664 | − | 0.331664i | 0.521554 | − | 0.853218i | \(-0.325352\pi\) |
−0.853218 | + | 0.521554i | \(0.825352\pi\) | |||||||
\(74\) | 296904.i | 0.732691i | ||||||||
\(75\) | 445625. | − | 244375.i | 1.05630 | − | 0.579259i | ||||
\(76\) | −55040.0 | −0.125383 | ||||||||
\(77\) | −346294. | + | 346294.i | −0.758530 | + | 0.758530i | ||||
\(78\) | −497352. | − | 497352.i | −1.04805 | − | 1.04805i | ||||
\(79\) | − | 524640.i | − | 1.06409i | −0.846715 | − | 0.532047i | \(-0.821423\pi\) | ||
0.846715 | − | 0.532047i | \(-0.178577\pi\) | |||||||
\(80\) | 76800.0 | + | 102400.i | 0.150000 | + | 0.200000i | ||||
\(81\) | 663041. | 1.24763 | ||||||||
\(82\) | 141752. | − | 141752.i | 0.257091 | − | 0.257091i | ||||
\(83\) | −114423. | − | 114423.i | −0.200115 | − | 0.200115i | 0.599934 | − | 0.800049i | \(-0.295193\pi\) |
−0.800049 | + | 0.599934i | \(0.795193\pi\) | |||||||
\(84\) | − | 363584.i | − | 0.613433i | ||||||
\(85\) | −453775. | − | 64825.0i | −0.738897 | − | 0.105557i | ||||
\(86\) | −313416. | −0.492749 | ||||||||
\(87\) | −701960. | + | 701960.i | −1.06599 | + | 1.06599i | ||||
\(88\) | 179456. | + | 179456.i | 0.263336 | + | 0.263336i | ||||
\(89\) | − | 187280.i | − | 0.265657i | −0.991139 | − | 0.132829i | \(-0.957594\pi\) | ||
0.991139 | − | 0.132829i | \(-0.0424060\pi\) | |||||||
\(90\) | −32900.0 | + | 230300.i | −0.0451303 | + | 0.315912i | ||||
\(91\) | 1.33528e6 | 1.77194 | ||||||||
\(92\) | 68384.0 | − | 68384.0i | 0.0878195 | − | 0.0878195i | ||||
\(93\) | 870274. | + | 870274.i | 1.08195 | + | 1.08195i | ||||
\(94\) | 761544.i | 0.916878i | ||||||||
\(95\) | −172000. | + | 129000.i | −0.200612 | + | 0.150459i | ||||
\(96\) | −188416. | −0.212963 | ||||||||
\(97\) | 532833. | − | 532833.i | 0.583816 | − | 0.583816i | −0.352134 | − | 0.935950i | \(-0.614544\pi\) |
0.935950 | + | 0.352134i | \(0.114544\pi\) | |||||||
\(98\) | 17476.0 | + | 17476.0i | 0.0185679 | + | 0.0185679i | ||||
\(99\) | 461258.i | 0.475377i | ||||||||
\(100\) | 480000. | + | 140000.i | 0.480000 | + | 0.140000i | ||||
\(101\) | −1.70508e6 | −1.65493 | −0.827466 | − | 0.561516i | \(-0.810218\pi\) | ||||
−0.827466 | + | 0.561516i | \(0.810218\pi\) | |||||||
\(102\) | 477112. | − | 477112.i | 0.449593 | − | 0.449593i | ||||
\(103\) | −665063. | − | 665063.i | −0.608627 | − | 0.608627i | 0.333960 | − | 0.942587i | \(-0.391615\pi\) |
−0.942587 | + | 0.333960i | \(0.891615\pi\) | |||||||
\(104\) | − | 691968.i | − | 0.615157i | ||||||
\(105\) | −852150. | − | 1.13620e6i | −0.736119 | − | 0.981492i | ||||
\(106\) | −288136. | −0.241925 | ||||||||
\(107\) | 309073. | − | 309073.i | 0.252296 | − | 0.252296i | −0.569616 | − | 0.821911i | \(-0.692908\pi\) |
0.821911 | + | 0.569616i | \(0.192908\pi\) | |||||||
\(108\) | 294400. | + | 294400.i | 0.233704 | + | 0.233704i | ||||
\(109\) | 362440.i | 0.279870i | 0.990161 | + | 0.139935i | \(0.0446894\pi\) | ||||
−0.990161 | + | 0.139935i | \(0.955311\pi\) | |||||||
\(110\) | 981400. | + | 140200.i | 0.737340 | + | 0.105334i | ||||
\(111\) | −1.70720e6 | −1.24829 | ||||||||
\(112\) | 252928. | − | 252928.i | 0.180029 | − | 0.180029i | ||||
\(113\) | 722657. | + | 722657.i | 0.500838 | + | 0.500838i | 0.911698 | − | 0.410861i | \(-0.134772\pi\) |
−0.410861 | + | 0.911698i | \(0.634772\pi\) | |||||||
\(114\) | − | 316480.i | − | 0.213615i | ||||||
\(115\) | 53425.0 | − | 373975.i | 0.0351278 | − | 0.245895i | ||||
\(116\) | −976640. | −0.625692 | ||||||||
\(117\) | 889287. | − | 889287.i | 0.555245 | − | 0.555245i | ||||
\(118\) | −143840. | − | 143840.i | −0.0875455 | − | 0.0875455i | ||||
\(119\) | 1.28094e6i | 0.760131i | ||||||||
\(120\) | −588800. | + | 441600.i | −0.340741 | + | 0.255556i | ||||
\(121\) | 194043. | 0.109532 | ||||||||
\(122\) | −333288. | + | 333288.i | −0.183544 | + | 0.183544i | ||||
\(123\) | 815074. | + | 815074.i | 0.438008 | + | 0.438008i | ||||
\(124\) | 1.21082e6i | 0.635058i | ||||||||
\(125\) | 1.82812e6 | − | 687500.i | 0.936000 | − | 0.352000i | ||||
\(126\) | 650104. | 0.324991 | ||||||||
\(127\) | −1.94641e6 | + | 1.94641e6i | −0.950216 | + | 0.950216i | −0.998818 | − | 0.0486019i | \(-0.984523\pi\) |
0.0486019 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(128\) | −131072. | − | 131072.i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 1.80214e6i | − | 0.839498i | ||||||
\(130\) | −1.62180e6 | − | 2.16240e6i | −0.738188 | − | 0.984251i | ||||
\(131\) | 3.75620e6 | 1.67084 | 0.835420 | − | 0.549612i | \(-0.185224\pi\) | ||||
0.835420 | + | 0.549612i | \(0.185224\pi\) | |||||||
\(132\) | −1.03187e6 | + | 1.03187e6i | −0.448646 | + | 0.448646i | ||||
\(133\) | 424840. | + | 424840.i | 0.180580 | + | 0.180580i | ||||
\(134\) | 486664.i | 0.202262i | ||||||||
\(135\) | 1.61000e6 | + | 230000.i | 0.654372 | + | 0.0934817i | ||||
\(136\) | 663808. | 0.263892 | ||||||||
\(137\) | 1.04283e6 | − | 1.04283e6i | 0.405558 | − | 0.405558i | −0.474628 | − | 0.880186i | \(-0.657417\pi\) |
0.880186 | + | 0.474628i | \(0.157417\pi\) | |||||||
\(138\) | 393208. | + | 393208.i | 0.149618 | + | 0.149618i | ||||
\(139\) | 3.24700e6i | 1.20903i | 0.796593 | + | 0.604516i | \(0.206634\pi\) | ||||
−0.796593 | + | 0.604516i | \(0.793366\pi\) | |||||||
\(140\) | 197600. | − | 1.38320e6i | 0.0720117 | − | 0.504082i | ||||
\(141\) | −4.37888e6 | −1.56209 | ||||||||
\(142\) | 161272. | − | 161272.i | 0.0563241 | − | 0.0563241i | ||||
\(143\) | −3.78961e6 | − | 3.78961e6i | −1.29594 | − | 1.29594i | ||||
\(144\) | − | 336896.i | − | 0.112826i | ||||||
\(145\) | −3.05200e6 | + | 2.28900e6i | −1.00111 | + | 0.750830i | ||||
\(146\) | 1.03218e6 | 0.331664 | ||||||||
\(147\) | −100487. | + | 100487.i | −0.0316343 | + | 0.0316343i | ||||
\(148\) | −1.18762e6 | − | 1.18762e6i | −0.366346 | − | 0.366346i | ||||
\(149\) | − | 5.76420e6i | − | 1.74253i | −0.490813 | − | 0.871265i | \(-0.663300\pi\) | ||
0.490813 | − | 0.871265i | \(-0.336700\pi\) | |||||||
\(150\) | −805000. | + | 2.76000e6i | −0.238519 | + | 0.817778i | ||||
\(151\) | 1.03280e6 | 0.299976 | 0.149988 | − | 0.988688i | \(-0.452077\pi\) | ||||
0.149988 | + | 0.988688i | \(0.452077\pi\) | |||||||
\(152\) | 220160. | − | 220160.i | 0.0626914 | − | 0.0626914i | ||||
\(153\) | 853097. | + | 853097.i | 0.238190 | + | 0.238190i | ||||
\(154\) | − | 2.77035e6i | − | 0.758530i | ||||||
\(155\) | 2.83785e6 | + | 3.78380e6i | 0.762069 | + | 1.01609i | ||||
\(156\) | 3.97882e6 | 1.04805 | ||||||||
\(157\) | 2.30055e6 | − | 2.30055e6i | 0.594475 | − | 0.594475i | −0.344362 | − | 0.938837i | \(-0.611905\pi\) |
0.938837 | + | 0.344362i | \(0.111905\pi\) | |||||||
\(158\) | 2.09856e6 | + | 2.09856e6i | 0.532047 | + | 0.532047i | ||||
\(159\) | − | 1.65678e6i | − | 0.412168i | ||||||
\(160\) | −716800. | − | 102400.i | −0.175000 | − | 0.0250000i | ||||
\(161\) | −1.05568e6 | −0.252961 | ||||||||
\(162\) | −2.65216e6 | + | 2.65216e6i | −0.623814 | + | 0.623814i | ||||
\(163\) | −4.02178e6 | − | 4.02178e6i | −0.928658 | − | 0.928658i | 0.0689613 | − | 0.997619i | \(-0.478032\pi\) |
−0.997619 | + | 0.0689613i | \(0.978032\pi\) | |||||||
\(164\) | 1.13402e6i | 0.257091i | ||||||||
\(165\) | −806150. | + | 5.64305e6i | −0.179458 | + | 1.25621i | ||||
\(166\) | 915384. | 0.200115 | ||||||||
\(167\) | −710167. | + | 710167.i | −0.152479 | + | 0.152479i | −0.779224 | − | 0.626745i | \(-0.784387\pi\) |
0.626745 | + | 0.779224i | \(0.284387\pi\) | |||||||
\(168\) | 1.45434e6 | + | 1.45434e6i | 0.306716 | + | 0.306716i | ||||
\(169\) | 9.78561e6i | 2.02735i | ||||||||
\(170\) | 2.07440e6 | − | 1.55580e6i | 0.422227 | − | 0.316670i | ||||
\(171\) | 565880. | 0.113171 | ||||||||
\(172\) | 1.25366e6 | − | 1.25366e6i | 0.246375 | − | 0.246375i | ||||
\(173\) | 3.77650e6 | + | 3.77650e6i | 0.729375 | + | 0.729375i | 0.970495 | − | 0.241120i | \(-0.0775148\pi\) |
−0.241120 | + | 0.970495i | \(0.577515\pi\) | |||||||
\(174\) | − | 5.61568e6i | − | 1.06599i | ||||||
\(175\) | −2.62438e6 | − | 4.78562e6i | −0.489679 | − | 0.892945i | ||||
\(176\) | −1.43565e6 | −0.263336 | ||||||||
\(177\) | 827080. | − | 827080.i | 0.149152 | − | 0.149152i | ||||
\(178\) | 749120. | + | 749120.i | 0.132829 | + | 0.132829i | ||||
\(179\) | − | 5.46380e6i | − | 0.952655i | −0.879268 | − | 0.476328i | \(-0.841968\pi\) | ||
0.879268 | − | 0.476328i | \(-0.158032\pi\) | |||||||
\(180\) | −789600. | − | 1.05280e6i | −0.135391 | − | 0.180521i | ||||
\(181\) | 9.02436e6 | 1.52188 | 0.760941 | − | 0.648821i | \(-0.224738\pi\) | ||||
0.760941 | + | 0.648821i | \(0.224738\pi\) | |||||||
\(182\) | −5.34113e6 | + | 5.34113e6i | −0.885970 | + | 0.885970i | ||||
\(183\) | −1.91641e6 | − | 1.91641e6i | −0.312705 | − | 0.312705i | ||||
\(184\) | 547072.i | 0.0878195i | ||||||||
\(185\) | −6.49478e6 | − | 927825.i | −1.02577 | − | 0.146538i | ||||
\(186\) | −6.96219e6 | −1.08195 | ||||||||
\(187\) | 3.63539e6 | − | 3.63539e6i | 0.555937 | − | 0.555937i | ||||
\(188\) | −3.04618e6 | − | 3.04618e6i | −0.458439 | − | 0.458439i | ||||
\(189\) | − | 4.54480e6i | − | 0.673177i | ||||||
\(190\) | 172000. | − | 1.20400e6i | 0.0250765 | − | 0.175536i | ||||
\(191\) | −4.02120e6 | −0.577106 | −0.288553 | − | 0.957464i | \(-0.593174\pi\) | ||||
−0.288553 | + | 0.957464i | \(0.593174\pi\) | |||||||
\(192\) | 753664. | − | 753664.i | 0.106481 | − | 0.106481i | ||||
\(193\) | −1.05414e6 | − | 1.05414e6i | −0.146632 | − | 0.146632i | 0.629980 | − | 0.776611i | \(-0.283063\pi\) |
−0.776611 | + | 0.629980i | \(0.783063\pi\) | |||||||
\(194\) | 4.26266e6i | 0.583816i | ||||||||
\(195\) | 1.24338e7 | − | 9.32535e6i | 1.67687 | − | 1.25765i | ||||
\(196\) | −139808. | −0.0185679 | ||||||||
\(197\) | −7.29489e6 | + | 7.29489e6i | −0.954157 | + | 0.954157i | −0.998994 | − | 0.0448372i | \(-0.985723\pi\) |
0.0448372 | + | 0.998994i | \(0.485723\pi\) | |||||||
\(198\) | −1.84503e6 | − | 1.84503e6i | −0.237689 | − | 0.237689i | ||||
\(199\) | 1.41170e7i | 1.79137i | 0.444693 | + | 0.895683i | \(0.353313\pi\) | ||||
−0.444693 | + | 0.895683i | \(0.646687\pi\) | |||||||
\(200\) | −2.48000e6 | + | 1.36000e6i | −0.310000 | + | 0.170000i | ||||
\(201\) | −2.79832e6 | −0.344595 | ||||||||
\(202\) | 6.82031e6 | − | 6.82031e6i | 0.827466 | − | 0.827466i | ||||
\(203\) | 7.53844e6 | + | 7.53844e6i | 0.901142 | + | 0.901142i | ||||
\(204\) | 3.81690e6i | 0.449593i | ||||||||
\(205\) | 2.65785e6 | + | 3.54380e6i | 0.308510 | + | 0.411346i | ||||
\(206\) | 5.32050e6 | 0.608627 | ||||||||
\(207\) | −703073. | + | 703073.i | −0.0792664 | + | 0.0792664i | ||||
\(208\) | 2.76787e6 | + | 2.76787e6i | 0.307579 | + | 0.307579i | ||||
\(209\) | − | 2.41144e6i | − | 0.264142i | ||||||
\(210\) | 7.95340e6 | + | 1.13620e6i | 0.858806 | + | 0.122687i | ||||
\(211\) | −1.23188e7 | −1.31136 | −0.655681 | − | 0.755038i | \(-0.727618\pi\) | ||||
−0.655681 | + | 0.755038i | \(0.727618\pi\) | |||||||
\(212\) | 1.15254e6 | − | 1.15254e6i | 0.120962 | − | 0.120962i | ||||
\(213\) | 927314. | + | 927314.i | 0.0959595 | + | 0.0959595i | ||||
\(214\) | 2.47258e6i | 0.252296i | ||||||||
\(215\) | 979425. | − | 6.85598e6i | 0.0985498 | − | 0.689849i | ||||
\(216\) | −2.35520e6 | −0.233704 | ||||||||
\(217\) | 9.34599e6 | − | 9.34599e6i | 0.914631 | − | 0.914631i | ||||
\(218\) | −1.44976e6 | − | 1.44976e6i | −0.139935 | − | 0.139935i | ||||
\(219\) | 5.93506e6i | 0.565057i | ||||||||
\(220\) | −4.48640e6 | + | 3.36480e6i | −0.421337 | + | 0.316003i | ||||
\(221\) | −1.40178e7 | −1.29868 | ||||||||
\(222\) | 6.82879e6 | − | 6.82879e6i | 0.624144 | − | 0.624144i | ||||
\(223\) | 328857. | + | 328857.i | 0.0296546 | + | 0.0296546i | 0.721779 | − | 0.692124i | \(-0.243325\pi\) |
−0.692124 | + | 0.721779i | \(0.743325\pi\) | |||||||
\(224\) | 2.02342e6i | 0.180029i | ||||||||
\(225\) | −4.93500e6 | − | 1.43938e6i | −0.433251 | − | 0.126365i | ||||
\(226\) | −5.78126e6 | −0.500838 | ||||||||
\(227\) | −7.95085e6 | + | 7.95085e6i | −0.679729 | + | 0.679729i | −0.959939 | − | 0.280210i | \(-0.909596\pi\) |
0.280210 | + | 0.959939i | \(0.409596\pi\) | |||||||
\(228\) | 1.26592e6 | + | 1.26592e6i | 0.106807 | + | 0.106807i | ||||
\(229\) | − | 2.28695e7i | − | 1.90436i | −0.305532 | − | 0.952182i | \(-0.598834\pi\) | ||
0.305532 | − | 0.952182i | \(-0.401166\pi\) | |||||||
\(230\) | 1.28220e6 | + | 1.70960e6i | 0.105383 | + | 0.140511i | ||||
\(231\) | 1.59295e7 | 1.29231 | ||||||||
\(232\) | 3.90656e6 | − | 3.90656e6i | 0.312846 | − | 0.312846i | ||||
\(233\) | 8.59050e6 | + | 8.59050e6i | 0.679126 | + | 0.679126i | 0.959803 | − | 0.280676i | \(-0.0905587\pi\) |
−0.280676 | + | 0.959803i | \(0.590559\pi\) | |||||||
\(234\) | 7.11430e6i | 0.555245i | ||||||||
\(235\) | −1.66588e7 | − | 2.37982e6i | −1.28363 | − | 0.183376i | ||||
\(236\) | 1.15072e6 | 0.0875455 | ||||||||
\(237\) | −1.20667e7 | + | 1.20667e7i | −0.906451 | + | 0.906451i | ||||
\(238\) | −5.12377e6 | − | 5.12377e6i | −0.380066 | − | 0.380066i | ||||
\(239\) | − | 9.66576e6i | − | 0.708015i | −0.935243 | − | 0.354007i | \(-0.884819\pi\) | ||
0.935243 | − | 0.354007i | \(-0.115181\pi\) | |||||||
\(240\) | 588800. | − | 4.12160e6i | 0.0425926 | − | 0.298148i | ||||
\(241\) | 1.85926e7 | 1.32828 | 0.664141 | − | 0.747608i | \(-0.268798\pi\) | ||||
0.664141 | + | 0.747608i | \(0.268798\pi\) | |||||||
\(242\) | −776172. | + | 776172.i | −0.0547661 | + | 0.0547661i | ||||
\(243\) | −8.54314e6 | − | 8.54314e6i | −0.595386 | − | 0.595386i | ||||
\(244\) | − | 2.66630e6i | − | 0.183544i | ||||||
\(245\) | −436900. | + | 327675.i | −0.0297087 | + | 0.0222815i | ||||
\(246\) | −6.52059e6 | −0.438008 | ||||||||
\(247\) | −4.64916e6 | + | 4.64916e6i | −0.308520 | + | 0.308520i | ||||
\(248\) | −4.84326e6 | − | 4.84326e6i | −0.317529 | − | 0.317529i | ||||
\(249\) | 5.26346e6i | 0.340936i | ||||||||
\(250\) | −4.56250e6 | + | 1.00625e7i | −0.292000 | + | 0.644000i | ||||
\(251\) | 1.19350e7 | 0.754747 | 0.377373 | − | 0.926061i | \(-0.376827\pi\) | ||||
0.377373 | + | 0.926061i | \(0.376827\pi\) | |||||||
\(252\) | −2.60042e6 | + | 2.60042e6i | −0.162495 | + | 0.162495i | ||||
\(253\) | 2.99607e6 | + | 2.99607e6i | 0.185008 | + | 0.185008i | ||||
\(254\) | − | 1.55713e7i | − | 0.950216i | ||||||
\(255\) | 8.94585e6 | + | 1.19278e7i | 0.539512 | + | 0.719349i | ||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 1.54304e7 | − | 1.54304e7i | 0.909031 | − | 0.909031i | −0.0871630 | − | 0.996194i | \(-0.527780\pi\) |
0.996194 | + | 0.0871630i | \(0.0277801\pi\) | |||||||
\(258\) | 7.20857e6 | + | 7.20857e6i | 0.419749 | + | 0.419749i | ||||
\(259\) | 1.83338e7i | 1.05525i | ||||||||
\(260\) | 1.51368e7 | + | 2.16240e6i | 0.861220 | + | 0.123031i | ||||
\(261\) | 1.00411e7 | 0.564753 | ||||||||
\(262\) | −1.50248e7 | + | 1.50248e7i | −0.835420 | + | 0.835420i | ||||
\(263\) | 1.27108e7 | + | 1.27108e7i | 0.698723 | + | 0.698723i | 0.964135 | − | 0.265412i | \(-0.0855081\pi\) |
−0.265412 | + | 0.964135i | \(0.585508\pi\) | |||||||
\(264\) | − | 8.25498e6i | − | 0.448646i | ||||||
\(265\) | 900425. | − | 6.30298e6i | 0.0483849 | − | 0.338694i | ||||
\(266\) | −3.39872e6 | −0.180580 | ||||||||
\(267\) | −4.30744e6 | + | 4.30744e6i | −0.226300 | + | 0.226300i | ||||
\(268\) | −1.94666e6 | − | 1.94666e6i | −0.101131 | − | 0.101131i | ||||
\(269\) | − | 2.54188e6i | − | 0.130586i | −0.997866 | − | 0.0652932i | \(-0.979202\pi\) | ||
0.997866 | − | 0.0652932i | \(-0.0207983\pi\) | |||||||
\(270\) | −7.36000e6 | + | 5.52000e6i | −0.373927 | + | 0.280445i | ||||
\(271\) | 6.13384e6 | 0.308194 | 0.154097 | − | 0.988056i | \(-0.450753\pi\) | ||||
0.154097 | + | 0.988056i | \(0.450753\pi\) | |||||||
\(272\) | −2.65523e6 | + | 2.65523e6i | −0.131946 | + | 0.131946i | ||||
\(273\) | −3.07115e7 | − | 3.07115e7i | −1.50943 | − | 1.50943i | ||||
\(274\) | 8.34266e6i | 0.405558i | ||||||||
\(275\) | −6.13375e6 | + | 2.10300e7i | −0.294936 | + | 1.01121i | ||||
\(276\) | −3.14566e6 | −0.149618 | ||||||||
\(277\) | −3.00513e6 | + | 3.00513e6i | −0.141392 | + | 0.141392i | −0.774260 | − | 0.632868i | \(-0.781878\pi\) |
0.632868 | + | 0.774260i | \(0.281878\pi\) | |||||||
\(278\) | −1.29880e7 | − | 1.29880e7i | −0.604516 | − | 0.604516i | ||||
\(279\) | − | 1.24487e7i | − | 0.573207i | ||||||
\(280\) | 4.74240e6 | + | 6.32320e6i | 0.216035 | + | 0.288047i | ||||
\(281\) | −6.49352e6 | −0.292658 | −0.146329 | − | 0.989236i | \(-0.546746\pi\) | ||||
−0.146329 | + | 0.989236i | \(0.546746\pi\) | |||||||
\(282\) | 1.75155e7 | − | 1.75155e7i | 0.781044 | − | 0.781044i | ||||
\(283\) | −2.71607e7 | − | 2.71607e7i | −1.19834 | − | 1.19834i | −0.974663 | − | 0.223680i | \(-0.928193\pi\) |
−0.223680 | − | 0.974663i | \(-0.571807\pi\) | |||||||
\(284\) | 1.29018e6i | 0.0563241i | ||||||||
\(285\) | 6.92300e6 | + | 989000.i | 0.299061 | + | 0.0427230i | ||||
\(286\) | 3.03168e7 | 1.29594 | ||||||||
\(287\) | 8.75319e6 | − | 8.75319e6i | 0.370272 | − | 0.370272i | ||||
\(288\) | 1.34758e6 | + | 1.34758e6i | 0.0564129 | + | 0.0564129i | ||||
\(289\) | 1.06903e7i | 0.442889i | ||||||||
\(290\) | 3.05200e6 | − | 2.13640e7i | 0.125138 | − | 0.875969i | ||||
\(291\) | −2.45103e7 | −0.994649 | ||||||||
\(292\) | −4.12874e6 | + | 4.12874e6i | −0.165832 | + | 0.165832i | ||||
\(293\) | −4.78734e6 | − | 4.78734e6i | −0.190323 | − | 0.190323i | 0.605513 | − | 0.795836i | \(-0.292968\pi\) |
−0.795836 | + | 0.605513i | \(0.792968\pi\) | |||||||
\(294\) | − | 803896.i | − | 0.0316343i | ||||||
\(295\) | 3.59600e6 | − | 2.69700e6i | 0.140073 | − | 0.105055i | ||||
\(296\) | 9.50093e6 | 0.366346 | ||||||||
\(297\) | −1.28984e7 | + | 1.28984e7i | −0.492342 | + | 0.492342i | ||||
\(298\) | 2.30568e7 | + | 2.30568e7i | 0.871265 | + | 0.871265i | ||||
\(299\) | − | 1.15526e7i | − | 0.432182i | ||||||
\(300\) | −7.82000e6 | − | 1.42600e7i | −0.289630 | − | 0.528148i | ||||
\(301\) | −1.93534e7 | −0.709674 | ||||||||
\(302\) | −4.13121e6 | + | 4.13121e6i | −0.149988 | + | 0.149988i | ||||
\(303\) | 3.92168e7 | + | 3.92168e7i | 1.40976 | + | 1.40976i | ||||
\(304\) | 1.76128e6i | 0.0626914i | ||||||||
\(305\) | −6.24915e6 | − | 8.33220e6i | −0.220253 | − | 0.293670i | ||||
\(306\) | −6.82478e6 | −0.238190 | ||||||||
\(307\) | 9.72339e6 | − | 9.72339e6i | 0.336049 | − | 0.336049i | −0.518829 | − | 0.854878i | \(-0.673632\pi\) |
0.854878 | + | 0.518829i | \(0.173632\pi\) | |||||||
\(308\) | 1.10814e7 | + | 1.10814e7i | 0.379265 | + | 0.379265i | ||||
\(309\) | 3.05929e7i | 1.03692i | ||||||||
\(310\) | −2.64866e7 | − | 3.78380e6i | −0.889081 | − | 0.127012i | ||||
\(311\) | 7.03344e6 | 0.233823 | 0.116911 | − | 0.993142i | \(-0.462701\pi\) | ||||
0.116911 | + | 0.993142i | \(0.462701\pi\) | |||||||
\(312\) | −1.59153e7 | + | 1.59153e7i | −0.524023 | + | 0.524023i | ||||
\(313\) | 2.98895e7 | + | 2.98895e7i | 0.974734 | + | 0.974734i | 0.999689 | − | 0.0249545i | \(-0.00794407\pi\) |
−0.0249545 | + | 0.999689i | \(0.507944\pi\) | |||||||
\(314\) | 1.84044e7i | 0.594475i | ||||||||
\(315\) | −2.03158e6 | + | 1.42210e7i | −0.0649982 | + | 0.454987i | ||||
\(316\) | −1.67885e7 | −0.532047 | ||||||||
\(317\) | 2.11266e7 | − | 2.11266e7i | 0.663212 | − | 0.663212i | −0.292924 | − | 0.956136i | \(-0.594628\pi\) |
0.956136 | + | 0.292924i | \(0.0946282\pi\) | |||||||
\(318\) | 6.62713e6 | + | 6.62713e6i | 0.206084 | + | 0.206084i | ||||
\(319\) | − | 4.27890e7i | − | 1.31814i | ||||||
\(320\) | 3.27680e6 | − | 2.45760e6i | 0.100000 | − | 0.0750000i | ||||
\(321\) | −1.42174e7 | −0.429837 | ||||||||
\(322\) | 4.22271e6 | − | 4.22271e6i | 0.126481 | − | 0.126481i | ||||
\(323\) | −4.45996e6 | − | 4.45996e6i | −0.132350 | − | 0.132350i | ||||
\(324\) | − | 2.12173e7i | − | 0.623814i | ||||||
\(325\) | 5.23706e7 | − | 2.87194e7i | 1.52559 | − | 0.836614i | ||||
\(326\) | 3.21743e7 | 0.928658 | ||||||||
\(327\) | 8.33612e6 | − | 8.33612e6i | 0.238408 | − | 0.238408i | ||||
\(328\) | −4.53606e6 | − | 4.53606e6i | −0.128546 | − | 0.128546i | ||||
\(329\) | 4.70253e7i | 1.32052i | ||||||||
\(330\) | −1.93476e7 | − | 2.57968e7i | −0.538375 | − | 0.717834i | ||||
\(331\) | −4.23279e7 | −1.16719 | −0.583596 | − | 0.812044i | \(-0.698355\pi\) | ||||
−0.583596 | + | 0.812044i | \(0.698355\pi\) | |||||||
\(332\) | −3.66154e6 | + | 3.66154e6i | −0.100057 | + | 0.100057i | ||||
\(333\) | 1.22102e7 | + | 1.22102e7i | 0.330666 | + | 0.330666i | ||||
\(334\) | − | 5.68134e6i | − | 0.152479i | ||||||
\(335\) | −1.06458e7 | − | 1.52082e6i | −0.283167 | − | 0.0404524i | ||||
\(336\) | −1.16347e7 | −0.306716 | ||||||||
\(337\) | −1.46217e7 | + | 1.46217e7i | −0.382040 | + | 0.382040i | −0.871837 | − | 0.489797i | \(-0.837071\pi\) |
0.489797 | + | 0.871837i | \(0.337071\pi\) | |||||||
\(338\) | −3.91424e7 | − | 3.91424e7i | −1.01367 | − | 1.01367i | ||||
\(339\) | − | 3.32422e7i | − | 0.853279i | ||||||
\(340\) | −2.07440e6 | + | 1.45208e7i | −0.0527783 | + | 0.369448i | ||||
\(341\) | −5.30489e7 | −1.33787 | ||||||||
\(342\) | −2.26352e6 | + | 2.26352e6i | −0.0565856 | + | 0.0565856i | ||||
\(343\) | −2.79802e7 | − | 2.79802e7i | −0.693374 | − | 0.693374i | ||||
\(344\) | 1.00293e7i | 0.246375i | ||||||||
\(345\) | −9.83020e6 | + | 7.37265e6i | −0.239389 | + | 0.179542i | ||||
\(346\) | −3.02120e7 | −0.729375 | ||||||||
\(347\) | 4.59792e7 | − | 4.59792e7i | 1.10046 | − | 1.10046i | 0.106100 | − | 0.994355i | \(-0.466164\pi\) |
0.994355 | − | 0.106100i | \(-0.0338364\pi\) | |||||||
\(348\) | 2.24627e7 | + | 2.24627e7i | 0.532997 | + | 0.532997i | ||||
\(349\) | 5.03359e7i | 1.18414i | 0.805888 | + | 0.592068i | \(0.201688\pi\) | ||||
−0.805888 | + | 0.592068i | \(0.798312\pi\) | |||||||
\(350\) | 2.96400e7 | + | 8.64500e6i | 0.691312 | + | 0.201633i | ||||
\(351\) | 4.97352e7 | 1.15012 | ||||||||
\(352\) | 5.74259e6 | − | 5.74259e6i | 0.131668 | − | 0.131668i | ||||
\(353\) | −1.59140e7 | − | 1.59140e7i | −0.361789 | − | 0.361789i | 0.502683 | − | 0.864471i | \(-0.332346\pi\) |
−0.864471 | + | 0.502683i | \(0.832346\pi\) | |||||||
\(354\) | 6.61664e6i | 0.149152i | ||||||||
\(355\) | 3.02385e6 | + | 4.03180e6i | 0.0675889 | + | 0.0901185i | ||||
\(356\) | −5.99296e6 | −0.132829 | ||||||||
\(357\) | 2.94617e7 | − | 2.94617e7i | 0.647519 | − | 0.647519i | ||||
\(358\) | 2.18552e7 | + | 2.18552e7i | 0.476328 | + | 0.476328i | ||||
\(359\) | 4.47023e7i | 0.966155i | 0.875578 | + | 0.483077i | \(0.160481\pi\) | ||||
−0.875578 | + | 0.483077i | \(0.839519\pi\) | |||||||
\(360\) | 7.36960e6 | + | 1.05280e6i | 0.157956 | + | 0.0225652i | ||||
\(361\) | 4.40875e7 | 0.937117 | ||||||||
\(362\) | −3.60974e7 | + | 3.60974e7i | −0.760941 | + | 0.760941i | ||||
\(363\) | −4.46299e6 | − | 4.46299e6i | −0.0933052 | − | 0.0933052i | ||||
\(364\) | − | 4.27290e7i | − | 0.885970i | ||||||
\(365\) | −3.22558e6 | + | 2.25790e7i | −0.0663328 | + | 0.464330i | ||||
\(366\) | 1.53312e7 | 0.312705 | ||||||||
\(367\) | −2.70624e7 | + | 2.70624e7i | −0.547480 | + | 0.547480i | −0.925711 | − | 0.378231i | \(-0.876532\pi\) |
0.378231 | + | 0.925711i | \(0.376532\pi\) | |||||||
\(368\) | −2.18829e6 | − | 2.18829e6i | −0.0439098 | − | 0.0439098i | ||||
\(369\) | − | 1.16591e7i | − | 0.232052i | ||||||
\(370\) | 2.96904e7 | − | 2.22678e7i | 0.586153 | − | 0.439615i | ||||
\(371\) | −1.77924e7 | −0.348428 | ||||||||
\(372\) | 2.78488e7 | − | 2.78488e7i | 0.540975 | − | 0.540975i | ||||
\(373\) | −3.82355e7 | − | 3.82355e7i | −0.736784 | − | 0.736784i | 0.235170 | − | 0.971954i | \(-0.424435\pi\) |
−0.971954 | + | 0.235170i | \(0.924435\pi\) | |||||||
\(374\) | 2.90831e7i | 0.555937i | ||||||||
\(375\) | −5.78594e7 | − | 2.62344e7i | −1.09719 | − | 0.497481i | ||||
\(376\) | 2.43694e7 | 0.458439 | ||||||||
\(377\) | −8.24956e7 | + | 8.24956e7i | −1.53960 | + | 1.53960i | ||||
\(378\) | 1.81792e7 | + | 1.81792e7i | 0.336589 | + | 0.336589i | ||||
\(379\) | − | 2.50612e6i | − | 0.0460346i | −0.999735 | − | 0.0230173i | \(-0.992673\pi\) | ||
0.999735 | − | 0.0230173i | \(-0.00732728\pi\) | |||||||
\(380\) | 4.12800e6 | + | 5.50400e6i | 0.0752296 | + | 0.100306i | ||||
\(381\) | 8.95347e7 | 1.61889 | ||||||||
\(382\) | 1.60848e7 | − | 1.60848e7i | 0.288553 | − | 0.288553i | ||||
\(383\) | 4.72095e7 | + | 4.72095e7i | 0.840297 | + | 0.840297i | 0.988897 | − | 0.148600i | \(-0.0474767\pi\) |
−0.148600 | + | 0.988897i | \(0.547477\pi\) | |||||||
\(384\) | 6.02931e6i | 0.106481i | ||||||||
\(385\) | 6.06014e7 | + | 8.65735e6i | 1.06194 | + | 0.151706i | ||||
\(386\) | 8.43314e6 | 0.146632 | ||||||||
\(387\) | −1.28892e7 | + | 1.28892e7i | −0.222379 | + | 0.222379i | ||||
\(388\) | −1.70507e7 | − | 1.70507e7i | −0.291908 | − | 0.291908i | ||||
\(389\) | − | 1.00159e8i | − | 1.70153i | −0.525547 | − | 0.850765i | \(-0.676139\pi\) | ||
0.525547 | − | 0.850765i | \(-0.323861\pi\) | |||||||
\(390\) | −1.24338e7 | + | 8.70366e7i | −0.209609 | + | 1.46726i | ||||
\(391\) | 1.10825e7 | 0.185399 | ||||||||
\(392\) | 559232. | − | 559232.i | 0.00928397 | − | 0.00928397i | ||||
\(393\) | −8.63926e7 | − | 8.63926e7i | −1.42331 | − | 1.42331i | ||||
\(394\) | − | 5.83591e7i | − | 0.954157i | ||||||
\(395\) | −5.24640e7 | + | 3.93480e7i | −0.851275 | + | 0.638457i | ||||
\(396\) | 1.47603e7 | 0.237689 | ||||||||
\(397\) | −7.26282e7 | + | 7.26282e7i | −1.16074 | + | 1.16074i | −0.176423 | + | 0.984314i | \(0.556453\pi\) |
−0.984314 | + | 0.176423i | \(0.943547\pi\) | |||||||
\(398\) | −5.64682e7 | − | 5.64682e7i | −0.895683 | − | 0.895683i | ||||
\(399\) | − | 1.95426e7i | − | 0.307655i | ||||||
\(400\) | 4.48000e6 | − | 1.53600e7i | 0.0700000 | − | 0.240000i | ||||
\(401\) | 5.26293e7 | 0.816196 | 0.408098 | − | 0.912938i | \(-0.366192\pi\) | ||||
0.408098 | + | 0.912938i | \(0.366192\pi\) | |||||||
\(402\) | 1.11933e7 | − | 1.11933e7i | 0.172297 | − | 0.172297i | ||||
\(403\) | 1.02276e8 | + | 1.02276e8i | 1.56264 | + | 1.56264i | ||||
\(404\) | 5.45625e7i | 0.827466i | ||||||||
\(405\) | −4.97281e7 | − | 6.63041e7i | −0.748577 | − | 0.998103i | ||||
\(406\) | −6.03075e7 | −0.901142 | ||||||||
\(407\) | 5.20324e7 | − | 5.20324e7i | 0.771775 | − | 0.771775i | ||||
\(408\) | −1.52676e7 | − | 1.52676e7i | −0.224797 | − | 0.224797i | ||||
\(409\) | − | 1.10687e8i | − | 1.61781i | −0.587939 | − | 0.808906i | \(-0.700060\pi\) | ||
0.587939 | − | 0.808906i | \(-0.299940\pi\) | |||||||
\(410\) | −2.48066e7 | − | 3.54380e6i | −0.359928 | − | 0.0514183i | ||||
\(411\) | −4.79703e7 | −0.690951 | ||||||||
\(412\) | −2.12820e7 | + | 2.12820e7i | −0.304313 | + | 0.304313i | ||||
\(413\) | −8.88212e6 | − | 8.88212e6i | −0.126086 | − | 0.126086i | ||||
\(414\) | − | 5.62458e6i | − | 0.0792664i | ||||||
\(415\) | −2.86058e6 | + | 2.00240e7i | −0.0400229 | + | 0.280161i | ||||
\(416\) | −2.21430e7 | −0.307579 | ||||||||
\(417\) | 7.46810e7 | − | 7.46810e7i | 1.02992 | − | 1.02992i | ||||
\(418\) | 9.64576e6 | + | 9.64576e6i | 0.132071 | + | 0.132071i | ||||
\(419\) | 9.92484e6i | 0.134922i | 0.997722 | + | 0.0674608i | \(0.0214898\pi\) | ||||
−0.997722 | + | 0.0674608i | \(0.978510\pi\) | |||||||
\(420\) | −3.63584e7 | + | 2.72688e7i | −0.490746 | + | 0.368060i | ||||
\(421\) | 3.46957e7 | 0.464975 | 0.232488 | − | 0.972599i | \(-0.425314\pi\) | ||||
0.232488 | + | 0.972599i | \(0.425314\pi\) | |||||||
\(422\) | 4.92754e7 | − | 4.92754e7i | 0.655681 | − | 0.655681i | ||||
\(423\) | 3.13185e7 | + | 3.13185e7i | 0.413790 | + | 0.413790i | ||||
\(424\) | 9.22035e6i | 0.120962i | ||||||||
\(425\) | 2.75506e7 | + | 5.02394e7i | 0.358893 | + | 0.654451i | ||||
\(426\) | −7.41851e6 | −0.0959595 | ||||||||
\(427\) | −2.05805e7 | + | 2.05805e7i | −0.264346 | + | 0.264346i | ||||
\(428\) | −9.89034e6 | − | 9.89034e6i | −0.126148 | − | 0.126148i | ||||
\(429\) | 1.74322e8i | 2.20790i | ||||||||
\(430\) | 2.35062e7 | + | 3.13416e7i | 0.295649 | + | 0.394199i | ||||
\(431\) | −2.72975e7 | −0.340951 | −0.170475 | − | 0.985362i | \(-0.554530\pi\) | ||||
−0.170475 | + | 0.985362i | \(0.554530\pi\) | |||||||
\(432\) | 9.42080e6 | − | 9.42080e6i | 0.116852 | − | 0.116852i | ||||
\(433\) | 4.50017e7 | + | 4.50017e7i | 0.554326 | + | 0.554326i | 0.927686 | − | 0.373360i | \(-0.121795\pi\) |
−0.373360 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(434\) | 7.47679e7i | 0.914631i | ||||||||
\(435\) | 1.22843e8 | + | 1.75490e7i | 1.49239 | + | 0.213199i | ||||
\(436\) | 1.15981e7 | 0.139935 | ||||||||
\(437\) | 3.67564e6 | − | 3.67564e6i | 0.0440442 | − | 0.0440442i | ||||
\(438\) | −2.37402e7 | − | 2.37402e7i | −0.282529 | − | 0.282529i | ||||
\(439\) | − | 4.79986e7i | − | 0.567330i | −0.958924 | − | 0.283665i | \(-0.908450\pi\) | ||
0.958924 | − | 0.283665i | \(-0.0915503\pi\) | |||||||
\(440\) | 4.48640e6 | − | 3.14048e7i | 0.0526672 | − | 0.368670i | ||||
\(441\) | 1.43740e6 | 0.0167595 | ||||||||
\(442\) | 5.60710e7 | − | 5.60710e7i | 0.649339 | − | 0.649339i | ||||
\(443\) | −3.36631e7 | − | 3.36631e7i | −0.387206 | − | 0.387206i | 0.486483 | − | 0.873690i | \(-0.338279\pi\) |
−0.873690 | + | 0.486483i | \(0.838279\pi\) | |||||||
\(444\) | 5.46303e7i | 0.624144i | ||||||||
\(445\) | −1.87280e7 | + | 1.40460e7i | −0.212526 | + | 0.159394i | ||||
\(446\) | −2.63086e6 | −0.0296546 | ||||||||
\(447\) | −1.32577e8 | + | 1.32577e8i | −1.48438 | + | 1.48438i | ||||
\(448\) | −8.09370e6 | − | 8.09370e6i | −0.0900146 | − | 0.0900146i | ||||
\(449\) | − | 8.64789e7i | − | 0.955369i | −0.878532 | − | 0.477684i | \(-0.841476\pi\) | ||
0.878532 | − | 0.477684i | \(-0.158524\pi\) | |||||||
\(450\) | 2.54975e7 | − | 1.39825e7i | 0.279808 | − | 0.153443i | ||||
\(451\) | −4.96841e7 | −0.541611 | ||||||||
\(452\) | 2.31250e7 | − | 2.31250e7i | 0.250419 | − | 0.250419i | ||||
\(453\) | −2.37544e7 | − | 2.37544e7i | −0.255535 | − | 0.255535i | ||||
\(454\) | − | 6.36068e7i | − | 0.679729i | ||||||
\(455\) | −1.00146e8 | − | 1.33528e8i | −1.06316 | − | 1.41755i | ||||
\(456\) | −1.01274e7 | −0.106807 | ||||||||
\(457\) | −3.72501e6 | + | 3.72501e6i | −0.0390282 | + | 0.0390282i | −0.726352 | − | 0.687323i | \(-0.758786\pi\) |
0.687323 | + | 0.726352i | \(0.258786\pi\) | |||||||
\(458\) | 9.14779e7 | + | 9.14779e7i | 0.952182 | + | 0.952182i | ||||
\(459\) | 4.77112e7i | 0.493381i | ||||||||
\(460\) | −1.19672e7 | − | 1.70960e6i | −0.122947 | − | 0.0175639i | ||||
\(461\) | 4.07112e7 | 0.415538 | 0.207769 | − | 0.978178i | \(-0.433380\pi\) | ||||
0.207769 | + | 0.978178i | \(0.433380\pi\) | |||||||
\(462\) | −6.37181e7 | + | 6.37181e7i | −0.646155 | + | 0.646155i | ||||
\(463\) | −2.69113e7 | − | 2.69113e7i | −0.271139 | − | 0.271139i | 0.558420 | − | 0.829559i | \(-0.311408\pi\) |
−0.829559 | + | 0.558420i | \(0.811408\pi\) | |||||||
\(464\) | 3.12525e7i | 0.312846i | ||||||||
\(465\) | 2.17568e7 | − | 1.52298e8i | 0.216390 | − | 1.51473i | ||||
\(466\) | −6.87240e7 | −0.679126 | ||||||||
\(467\) | 1.38966e8 | − | 1.38966e8i | 1.36446 | − | 1.36446i | 0.496310 | − | 0.868146i | \(-0.334688\pi\) |
0.868146 | − | 0.496310i | \(-0.165312\pi\) | |||||||
\(468\) | −2.84572e7 | − | 2.84572e7i | −0.277622 | − | 0.277622i | ||||
\(469\) | 3.00515e7i | 0.291305i | ||||||||
\(470\) | 7.61544e7 | − | 5.71158e7i | 0.733502 | − | 0.550127i | ||||
\(471\) | −1.05825e8 | −1.01281 | ||||||||
\(472\) | −4.60288e6 | + | 4.60288e6i | −0.0437727 | + | 0.0437727i | ||||
\(473\) | 5.49262e7 | + | 5.49262e7i | 0.519034 | + | 0.519034i | ||||
\(474\) | − | 9.65338e7i | − | 0.906451i | ||||||
\(475\) | 2.58000e7 | + | 7.52500e6i | 0.240735 | + | 0.0702143i | ||||
\(476\) | 4.09901e7 | 0.380066 | ||||||||
\(477\) | −1.18496e7 | + | 1.18496e7i | −0.109181 | + | 0.109181i | ||||
\(478\) | 3.86630e7 | + | 3.86630e7i | 0.354007 | + | 0.354007i | ||||
\(479\) | 3.19942e7i | 0.291115i | 0.989350 | + | 0.145558i | \(0.0464977\pi\) | ||||
−0.989350 | + | 0.145558i | \(0.953502\pi\) | |||||||
\(480\) | 1.41312e7 | + | 1.88416e7i | 0.127778 | + | 0.170370i | ||||
\(481\) | −2.00633e8 | −1.80288 | ||||||||
\(482\) | −7.43706e7 | + | 7.43706e7i | −0.664141 | + | 0.664141i | ||||
\(483\) | 2.42806e7 | + | 2.42806e7i | 0.215485 | + | 0.215485i | ||||
\(484\) | − | 6.20938e6i | − | 0.0547661i | ||||||
\(485\) | −9.32458e7 | − | 1.33208e7i | −0.817342 | − | 0.116763i | ||||
\(486\) | 6.83451e7 | 0.595386 | ||||||||
\(487\) | −7.96441e7 | + | 7.96441e7i | −0.689551 | + | 0.689551i | −0.962133 | − | 0.272581i | \(-0.912123\pi\) |
0.272581 | + | 0.962133i | \(0.412123\pi\) | |||||||
\(488\) | 1.06652e7 | + | 1.06652e7i | 0.0917720 | + | 0.0917720i | ||||
\(489\) | 1.85002e8i | 1.58216i | ||||||||
\(490\) | 436900. | − | 3.05830e6i | 0.00371359 | − | 0.0259951i | ||||
\(491\) | 1.53965e8 | 1.30070 | 0.650350 | − | 0.759634i | \(-0.274622\pi\) | ||||
0.650350 | + | 0.759634i | \(0.274622\pi\) | |||||||
\(492\) | 2.60824e7 | − | 2.60824e7i | 0.219004 | − | 0.219004i | ||||
\(493\) | −7.91384e7 | − | 7.91384e7i | −0.660460 | − | 0.660460i | ||||
\(494\) | − | 3.71933e7i | − | 0.308520i | ||||||
\(495\) | 4.61258e7 | − | 3.45944e7i | 0.380302 | − | 0.285226i | ||||
\(496\) | 3.87461e7 | 0.317529 | ||||||||
\(497\) | 9.95855e6 | − | 9.95855e6i | 0.0811198 | − | 0.0811198i | ||||
\(498\) | −2.10538e7 | − | 2.10538e7i | −0.170468 | − | 0.170468i | ||||
\(499\) | 1.02698e8i | 0.826537i | 0.910609 | + | 0.413268i | \(0.135613\pi\) | ||||
−0.910609 | + | 0.413268i | \(0.864387\pi\) | |||||||
\(500\) | −2.20000e7 | − | 5.85000e7i | −0.176000 | − | 0.468000i | ||||
\(501\) | 3.26677e7 | 0.259780 | ||||||||
\(502\) | −4.77400e7 | + | 4.77400e7i | −0.377373 | + | 0.377373i | ||||
\(503\) | 8.43625e7 | + | 8.43625e7i | 0.662896 | + | 0.662896i | 0.956062 | − | 0.293166i | \(-0.0947088\pi\) |
−0.293166 | + | 0.956062i | \(0.594709\pi\) | |||||||
\(504\) | − | 2.08033e7i | − | 0.162495i | ||||||
\(505\) | 1.27881e8 | + | 1.70508e8i | 0.992959 | + | 1.32395i | ||||
\(506\) | −2.39686e7 | −0.185008 | ||||||||
\(507\) | 2.25069e8 | − | 2.25069e8i | 1.72700 | − | 1.72700i | ||||
\(508\) | 6.22850e7 | + | 6.22850e7i | 0.475108 | + | 0.475108i | ||||
\(509\) | − | 4.03774e7i | − | 0.306186i | −0.988212 | − | 0.153093i | \(-0.951077\pi\) | ||
0.988212 | − | 0.153093i | \(-0.0489234\pi\) | |||||||
\(510\) | −8.34946e7 | − | 1.19278e7i | −0.629431 | − | 0.0899187i | ||||
\(511\) | 6.37374e7 | 0.477674 | ||||||||
\(512\) | −4.19430e6 | + | 4.19430e6i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 1.58240e7 | + | 1.58240e7i | 0.117210 | + | 0.117210i | ||||
\(514\) | 1.23443e8i | 0.909031i | ||||||||
\(515\) | −1.66266e7 | + | 1.16386e8i | −0.121725 | + | 0.852078i | ||||
\(516\) | −5.76685e7 | −0.419749 | ||||||||
\(517\) | 1.33461e8 | − | 1.33461e8i | 0.965787 | − | 0.965787i | ||||
\(518\) | −7.33353e7 | − | 7.33353e7i | −0.527623 | − | 0.527623i | ||||
\(519\) | − | 1.73719e8i | − | 1.24264i | ||||||
\(520\) | −6.91968e7 | + | 5.18976e7i | −0.492126 | + | 0.369094i | ||||
\(521\) | −3.68161e7 | −0.260330 | −0.130165 | − | 0.991492i | \(-0.541551\pi\) | ||||
−0.130165 | + | 0.991492i | \(0.541551\pi\) | |||||||
\(522\) | −4.01643e7 | + | 4.01643e7i | −0.282377 | + | 0.282377i | ||||
\(523\) | −1.60054e8 | − | 1.60054e8i | −1.11882 | − | 1.11882i | −0.991915 | − | 0.126907i | \(-0.959495\pi\) |
−0.126907 | − | 0.991915i | \(-0.540505\pi\) | |||||||
\(524\) | − | 1.20198e8i | − | 0.835420i | ||||||
\(525\) | −4.97088e7 | + | 1.70430e8i | −0.343522 | + | 1.17779i | ||||
\(526\) | −1.01686e8 | −0.698723 | ||||||||
\(527\) | −9.81139e7 | + | 9.81139e7i | −0.670346 | + | 0.670346i | ||||
\(528\) | 3.30199e7 | + | 3.30199e7i | 0.224323 | + | 0.224323i | ||||
\(529\) | − | 1.38902e8i | − | 0.938302i | ||||||
\(530\) | 2.16102e7 | + | 2.88136e7i | 0.145155 | + | 0.193540i | ||||
\(531\) | −1.18308e7 | −0.0790191 | ||||||||
\(532\) | 1.35949e7 | − | 1.35949e7i | 0.0902902 | − | 0.0902902i | ||||
\(533\) | 9.57889e7 | + | 9.57889e7i | 0.632606 | + | 0.632606i | ||||
\(534\) | − | 3.44595e7i | − | 0.226300i | ||||||
\(535\) | −5.40878e7 | − | 7.72682e6i | −0.353214 | − | 0.0504591i | ||||
\(536\) | 1.55732e7 | 0.101131 | ||||||||
\(537\) | −1.25667e8 | + | 1.25667e8i | −0.811521 | + | 0.811521i | ||||
\(538\) | 1.01675e7 | + | 1.01675e7i | 0.0652932 | + | 0.0652932i | ||||
\(539\) | − | 6.12534e6i | − | 0.0391168i | ||||||
\(540\) | 7.36000e6 | − | 5.15200e7i | 0.0467408 | − | 0.327186i | ||||
\(541\) | 1.30022e7 | 0.0821155 | 0.0410577 | − | 0.999157i | \(-0.486927\pi\) | ||||
0.0410577 | + | 0.999157i | \(0.486927\pi\) | |||||||
\(542\) | −2.45354e7 | + | 2.45354e7i | −0.154097 | + | 0.154097i | ||||
\(543\) | −2.07560e8 | − | 2.07560e8i | −1.29642 | − | 1.29642i | ||||
\(544\) | − | 2.12419e7i | − | 0.131946i | ||||||
\(545\) | 3.62440e7 | − | 2.71830e7i | 0.223896 | − | 0.167922i | ||||
\(546\) | 2.45692e8 | 1.50943 | ||||||||
\(547\) | 7.28319e7 | − | 7.28319e7i | 0.444999 | − | 0.444999i | −0.448689 | − | 0.893688i | \(-0.648109\pi\) |
0.893688 | + | 0.448689i | \(0.148109\pi\) | |||||||
\(548\) | −3.33707e7 | − | 3.33707e7i | −0.202779 | − | 0.202779i | ||||
\(549\) | 2.74129e7i | 0.165668i | ||||||||
\(550\) | −5.95850e7 | − | 1.08655e8i | −0.358137 | − | 0.653073i | ||||
\(551\) | −5.24944e7 | −0.313804 | ||||||||
\(552\) | 1.25827e7 | − | 1.25827e7i | 0.0748092 | − | 0.0748092i | ||||
\(553\) | 1.29586e8 | + | 1.29586e8i | 0.766272 | + | 0.766272i | ||||
\(554\) | − | 2.40410e7i | − | 0.141392i | ||||||
\(555\) | 1.28040e8 | + | 1.70720e8i | 0.748973 | + | 0.998631i | ||||
\(556\) | 1.03904e8 | 0.604516 | ||||||||
\(557\) | −4.55401e7 | + | 4.55401e7i | −0.263529 | + | 0.263529i | −0.826486 | − | 0.562957i | \(-0.809664\pi\) |
0.562957 | + | 0.826486i | \(0.309664\pi\) | |||||||
\(558\) | 4.97948e7 | + | 4.97948e7i | 0.286603 | + | 0.286603i | ||||
\(559\) | − | 2.11791e8i | − | 1.21247i | ||||||
\(560\) | −4.42624e7 | − | 6.32320e6i | −0.252041 | − | 0.0360058i | ||||
\(561\) | −1.67228e8 | −0.947152 | ||||||||
\(562\) | 2.59741e7 | − | 2.59741e7i | 0.146329 | − | 0.146329i | ||||
\(563\) | −1.85012e8 | − | 1.85012e8i | −1.03675 | − | 1.03675i | −0.999298 | − | 0.0374524i | \(-0.988076\pi\) |
−0.0374524 | − | 0.999298i | \(-0.511924\pi\) | |||||||
\(564\) | 1.40124e8i | 0.781044i | ||||||||
\(565\) | 1.80664e7 | − | 1.26465e8i | 0.100168 | − | 0.701173i | ||||
\(566\) | 2.17285e8 | 1.19834 | ||||||||
\(567\) | −1.63771e8 | + | 1.63771e8i | −0.898438 | + | 0.898438i | ||||
\(568\) | −5.16070e6 | − | 5.16070e6i | −0.0281620 | − | 0.0281620i | ||||
\(569\) | 7.17210e7i | 0.389323i | 0.980871 | + | 0.194661i | \(0.0623608\pi\) | ||||
−0.980871 | + | 0.194661i | \(0.937639\pi\) | |||||||
\(570\) | −3.16480e7 | + | 2.37360e7i | −0.170892 | + | 0.128169i | ||||
\(571\) | 3.09478e8 | 1.66234 | 0.831172 | − | 0.556015i | \(-0.187670\pi\) | ||||
0.831172 | + | 0.556015i | \(0.187670\pi\) | |||||||
\(572\) | −1.21267e8 | + | 1.21267e8i | −0.647972 | + | 0.647972i | ||||
\(573\) | 9.24876e7 | + | 9.24876e7i | 0.491609 | + | 0.491609i | ||||
\(574\) | 7.00255e7i | 0.370272i | ||||||||
\(575\) | −4.14044e7 | + | 2.27056e7i | −0.217792 | + | 0.119435i | ||||
\(576\) | −1.07807e7 | −0.0564129 | ||||||||
\(577\) | −2.15868e7 | + | 2.15868e7i | −0.112373 | + | 0.112373i | −0.761057 | − | 0.648684i | \(-0.775319\pi\) |
0.648684 | + | 0.761057i | \(0.275319\pi\) | |||||||
\(578\) | −4.27611e7 | − | 4.27611e7i | −0.221445 | − | 0.221445i | ||||
\(579\) | 4.84906e7i | 0.249817i | ||||||||
\(580\) | 7.32480e7 | + | 9.76640e7i | 0.375415 | + | 0.500554i | ||||
\(581\) | 5.65250e7 | 0.288212 | ||||||||
\(582\) | 9.80413e7 | − | 9.80413e7i | 0.497325 | − | 0.497325i | ||||
\(583\) | 5.04958e7 | + | 5.04958e7i | 0.254830 | + | 0.254830i | ||||
\(584\) | − | 3.30299e7i | − | 0.165832i | ||||||
\(585\) | −1.55625e8 | − | 2.22322e7i | −0.777342 | − | 0.111049i | ||||
\(586\) | 3.82987e7 | 0.190323 | ||||||||
\(587\) | −2.30927e8 | + | 2.30927e8i | −1.14172 | + | 1.14172i | −0.153588 | + | 0.988135i | \(0.549083\pi\) |
−0.988135 | + | 0.153588i | \(0.950917\pi\) | |||||||
\(588\) | 3.21558e6 | + | 3.21558e6i | 0.0158171 | + | 0.0158171i | ||||
\(589\) | 6.50814e7i | 0.318501i | ||||||||
\(590\) | −3.59600e6 | + | 2.51720e7i | −0.0175091 | + | 0.122564i | ||||
\(591\) | 3.35565e8 | 1.62560 | ||||||||
\(592\) | −3.80037e7 | + | 3.80037e7i | −0.183173 | + | 0.183173i | ||||
\(593\) | −2.66433e7 | − | 2.66433e7i | −0.127768 | − | 0.127768i | 0.640331 | − | 0.768099i | \(-0.278797\pi\) |
−0.768099 | + | 0.640331i | \(0.778797\pi\) | |||||||
\(594\) | − | 1.03187e8i | − | 0.492342i | ||||||
\(595\) | 1.28094e8 | − | 9.60706e7i | 0.608105 | − | 0.456079i | ||||
\(596\) | −1.84454e8 | −0.871265 | ||||||||
\(597\) | 3.24692e8 | − | 3.24692e8i | 1.52598 | − | 1.52598i | ||||
\(598\) | 4.62105e7 | + | 4.62105e7i | 0.216091 | + | 0.216091i | ||||
\(599\) | 3.14489e8i | 1.46327i | 0.681695 | + | 0.731637i | \(0.261243\pi\) | ||||
−0.681695 | + | 0.731637i | \(0.738757\pi\) | |||||||
\(600\) | 8.83200e7 | + | 2.57600e7i | 0.408889 | + | 0.119259i | ||||
\(601\) | −2.50382e8 | −1.15340 | −0.576700 | − | 0.816956i | \(-0.695660\pi\) | ||||
−0.576700 | + | 0.816956i | \(0.695660\pi\) | |||||||
\(602\) | 7.74138e7 | − | 7.74138e7i | 0.354837 | − | 0.354837i | ||||
\(603\) | 2.00141e7 | + | 2.00141e7i | 0.0912816 | + | 0.0912816i | ||||
\(604\) | − | 3.30497e7i | − | 0.149988i | ||||||
\(605\) | −1.45532e7 | − | 1.94043e7i | −0.0657193 | − | 0.0876258i | ||||
\(606\) | −3.13734e8 | −1.40976 | ||||||||
\(607\) | 9.40326e7 | − | 9.40326e7i | 0.420448 | − | 0.420448i | −0.464910 | − | 0.885358i | \(-0.653913\pi\) |
0.885358 | + | 0.464910i | \(0.153913\pi\) | |||||||
\(608\) | −7.04512e6 | − | 7.04512e6i | −0.0313457 | − | 0.0313457i | ||||
\(609\) | − | 3.46768e8i | − | 1.53528i | ||||||
\(610\) | 5.83254e7 | + | 8.33220e6i | 0.256962 | + | 0.0367088i | ||||
\(611\) | −5.14613e8 | −2.25610 | ||||||||
\(612\) | 2.72991e7 | − | 2.72991e7i | 0.119095 | − | 0.119095i | ||||
\(613\) | −1.72963e8 | − | 1.72963e8i | −0.750880 | − | 0.750880i | 0.223763 | − | 0.974644i | \(-0.428166\pi\) |
−0.974644 | + | 0.223763i | \(0.928166\pi\) | |||||||
\(614\) | 7.77871e7i | 0.336049i | ||||||||
\(615\) | 2.03768e7 | − | 1.42638e8i | 0.0876015 | − | 0.613211i | ||||
\(616\) | −8.86513e7 | −0.379265 | ||||||||
\(617\) | 1.31974e8 | − | 1.31974e8i | 0.561868 | − | 0.561868i | −0.367970 | − | 0.929838i | \(-0.619947\pi\) |
0.929838 | + | 0.367970i | \(0.119947\pi\) | |||||||
\(618\) | −1.22372e8 | − | 1.22372e8i | −0.518460 | − | 0.518460i | ||||
\(619\) | 4.22584e8i | 1.78173i | 0.454271 | + | 0.890863i | \(0.349900\pi\) | ||||
−0.454271 | + | 0.890863i | \(0.650100\pi\) | |||||||
\(620\) | 1.21082e8 | − | 9.08112e7i | 0.508046 | − | 0.381035i | ||||
\(621\) | −3.93208e7 | −0.164190 | ||||||||
\(622\) | −2.81338e7 | + | 2.81338e7i | −0.116911 | + | 0.116911i | ||||
\(623\) | 4.62582e7 | + | 4.62582e7i | 0.191304 | + | 0.191304i | ||||
\(624\) | − | 1.27322e8i | − | 0.524023i | ||||||
\(625\) | −2.05859e8 | − | 1.31250e8i | −0.843200 | − | 0.537600i | ||||
\(626\) | −2.39116e8 | −0.974734 | ||||||||
\(627\) | −5.54631e7 | + | 5.54631e7i | −0.225010 | + | 0.225010i | ||||
\(628\) | −7.36177e7 | − | 7.36177e7i | −0.297237 | − | 0.297237i | ||||
\(629\) | − | 1.92468e8i | − | 0.773404i | ||||||
\(630\) | −4.87578e7 | − | 6.50104e7i | −0.194995 | − | 0.259993i | ||||
\(631\) | 2.95144e8 | 1.17475 | 0.587376 | − | 0.809314i | \(-0.300161\pi\) | ||||
0.587376 | + | 0.809314i | \(0.300161\pi\) | |||||||
\(632\) | 6.71539e7 | − | 6.71539e7i | 0.266024 | − | 0.266024i | ||||
\(633\) | 2.83333e8 | + | 2.83333e8i | 1.11709 | + | 1.11709i | ||||
\(634\) | 1.69013e8i | 0.663212i | ||||||||
\(635\) | 3.40621e8 | + | 4.86602e7i | 1.33030 | + | 0.190043i | ||||
\(636\) | −5.30170e7 | −0.206084 | ||||||||
\(637\) | −1.18094e7 | + | 1.18094e7i | −0.0456888 | + | 0.0456888i | ||||
\(638\) | 1.71156e8 | + | 1.71156e8i | 0.659068 | + | 0.659068i | ||||
\(639\) | − | 1.32646e7i | − | 0.0508385i | ||||||
\(640\) | −3.27680e6 | + | 2.29376e7i | −0.0125000 | + | 0.0875000i | ||||
\(641\) | 3.85293e8 | 1.46291 | 0.731453 | − | 0.681891i | \(-0.238842\pi\) | ||||
0.731453 | + | 0.681891i | \(0.238842\pi\) | |||||||
\(642\) | 5.68694e7 | − | 5.68694e7i | 0.214919 | − | 0.214919i | ||||
\(643\) | 1.75998e8 | + | 1.75998e8i | 0.662024 | + | 0.662024i | 0.955857 | − | 0.293833i | \(-0.0949309\pi\) |
−0.293833 | + | 0.955857i | \(0.594931\pi\) | |||||||
\(644\) | 3.37817e7i | 0.126481i | ||||||||
\(645\) | −1.80214e8 | + | 1.35161e8i | −0.671599 | + | 0.503699i | ||||
\(646\) | 3.56797e7 | 0.132350 | ||||||||
\(647\) | −1.00835e8 | + | 1.00835e8i | −0.372304 | + | 0.372304i | −0.868316 | − | 0.496012i | \(-0.834797\pi\) |
0.496012 | + | 0.868316i | \(0.334797\pi\) | |||||||
\(648\) | 8.48692e7 | + | 8.48692e7i | 0.311907 | + | 0.311907i | ||||
\(649\) | 5.04159e7i | 0.184431i | ||||||||
\(650\) | −9.46050e7 | + | 3.24360e8i | −0.344488 | + | 1.18110i | ||||
\(651\) | −4.29915e8 | −1.55826 | ||||||||
\(652\) | −1.28697e8 | + | 1.28697e8i | −0.464329 | + | 0.464329i | ||||
\(653\) | 1.92563e8 | + | 1.92563e8i | 0.691566 | + | 0.691566i | 0.962576 | − | 0.271010i | \(-0.0873577\pi\) |
−0.271010 | + | 0.962576i | \(0.587358\pi\) | |||||||
\(654\) | 6.66890e7i | 0.238408i | ||||||||
\(655\) | −2.81715e8 | − | 3.75620e8i | −1.00250 | − | 1.33667i | ||||
\(656\) | 3.62885e7 | 0.128546 | ||||||||
\(657\) | 4.24486e7 | − | 4.24486e7i | 0.149681 | − | 0.149681i | ||||
\(658\) | −1.88101e8 | − | 1.88101e8i | −0.660259 | − | 0.660259i | ||||
\(659\) | − | 1.31172e8i | − | 0.458337i | −0.973387 | − | 0.229168i | \(-0.926399\pi\) | ||
0.973387 | − | 0.229168i | \(-0.0736007\pi\) | |||||||
\(660\) | 1.80578e8 | + | 2.57968e7i | 0.628105 | + | 0.0897292i | ||||
\(661\) | −1.97154e8 | −0.682656 | −0.341328 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341328 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(662\) | 1.69312e8 | − | 1.69312e8i | 0.583596 | − | 0.583596i | ||||
\(663\) | 3.22408e8 | + | 3.22408e8i | 1.10628 | + | 1.10628i | ||||
\(664\) | − | 2.92923e7i | − | 0.100057i | ||||||
\(665\) | 1.06210e7 | − | 7.43470e7i | 0.0361161 | − | 0.252812i | ||||
\(666\) | −9.76814e7 | −0.330666 | ||||||||
\(667\) | 6.52212e7 | − | 6.52212e7i | 0.219792 | − | 0.219792i | ||||
\(668\) | 2.27253e7 | + | 2.27253e7i | 0.0762397 | + | 0.0762397i | ||||
\(669\) | − | 1.51274e7i | − | 0.0505227i | ||||||
\(670\) | 4.86664e7 | − | 3.64998e7i | 0.161810 | − | 0.121357i | ||||
\(671\) | 1.16817e8 | 0.386670 | ||||||||
\(672\) | 4.65388e7 | − | 4.65388e7i | 0.153358 | − | 0.153358i | ||||
\(673\) | −1.93253e8 | − | 1.93253e8i | −0.633987 | − | 0.633987i | 0.315079 | − | 0.949066i | \(-0.397969\pi\) |
−0.949066 | + | 0.315079i | \(0.897969\pi\) | |||||||
\(674\) | − | 1.16974e8i | − | 0.382040i | ||||||
\(675\) | −9.77500e7 | − | 1.78250e8i | −0.317838 | − | 0.579586i | ||||
\(676\) | 3.13139e8 | 1.01367 | ||||||||
\(677\) | −2.07906e8 | + | 2.07906e8i | −0.670042 | + | 0.670042i | −0.957725 | − | 0.287684i | \(-0.907115\pi\) |
0.287684 | + | 0.957725i | \(0.407115\pi\) | |||||||
\(678\) | 1.32969e8 | + | 1.32969e8i | 0.426639 | + | 0.426639i | ||||
\(679\) | 2.63220e8i | 0.840831i | ||||||||
\(680\) | −4.97856e7 | − | 6.63808e7i | −0.158335 | − | 0.211113i | ||||
\(681\) | 3.65739e8 | 1.15806 | ||||||||
\(682\) | 2.12196e8 | − | 2.12196e8i | 0.668934 | − | 0.668934i | ||||
\(683\) | −3.57632e8 | − | 3.57632e8i | −1.12247 | − | 1.12247i | −0.991369 | − | 0.131099i | \(-0.958149\pi\) |
−0.131099 | − | 0.991369i | \(-0.541851\pi\) | |||||||
\(684\) | − | 1.81082e7i | − | 0.0565856i | ||||||
\(685\) | −1.82496e8 | − | 2.60708e7i | −0.567781 | − | 0.0811116i | ||||
\(686\) | 2.23841e8 | 0.693374 | ||||||||
\(687\) | −5.25998e8 | + | 5.25998e8i | −1.62224 | + | 1.62224i | ||||
\(688\) | −4.01172e7 | − | 4.01172e7i | −0.123187 | − | 0.123187i | ||||
\(689\) | − | 1.94708e8i | − | 0.595286i | ||||||
\(690\) | 9.83020e6 | − | 6.88114e7i | 0.0299237 | − | 0.209466i | ||||
\(691\) | −1.76748e8 | −0.535698 | −0.267849 | − | 0.963461i | \(-0.586313\pi\) | ||||
−0.267849 | + | 0.963461i | \(0.586313\pi\) | |||||||
\(692\) | 1.20848e8 | − | 1.20848e8i | 0.364687 | − | 0.364687i | ||||
\(693\) | −1.13931e8 | − | 1.13931e8i | −0.342327 | − | 0.342327i | ||||
\(694\) | 3.67833e8i | 1.10046i | ||||||||
\(695\) | 3.24700e8 | − | 2.43525e8i | 0.967226 | − | 0.725419i | ||||
\(696\) | −1.79702e8 | −0.532997 | ||||||||
\(697\) | −9.18907e7 | + | 9.18907e7i | −0.271377 | + | 0.271377i | ||||
\(698\) | −2.01344e8 | − | 2.01344e8i | −0.592068 | − | 0.592068i | ||||
\(699\) | − | 3.95163e8i | − | 1.15703i | ||||||
\(700\) | −1.53140e8 | + | 8.39800e7i | −0.446472 | + | 0.244840i | ||||
\(701\) | −3.12897e8 | −0.908338 | −0.454169 | − | 0.890916i | \(-0.650064\pi\) | ||||
−0.454169 | + | 0.890916i | \(0.650064\pi\) | |||||||
\(702\) | −1.98941e8 | + | 1.98941e8i | −0.575059 | + | 0.575059i | ||||
\(703\) | −6.38344e7 | − | 6.38344e7i | −0.183734 | − | 0.183734i | ||||
\(704\) | 4.59407e7i | 0.131668i | ||||||||
\(705\) | 3.28416e8 | + | 4.37888e8i | 0.937253 | + | 1.24967i | ||||
\(706\) | 1.27312e8 | 0.361789 | ||||||||
\(707\) | 4.21154e8 | − | 4.21154e8i | 1.19174 | − | 1.19174i | ||||
\(708\) | −2.64666e7 | − | 2.64666e7i | −0.0745758 | − | 0.0745758i | ||||
\(709\) | − | 1.07924e8i | − | 0.302817i | −0.988471 | − | 0.151408i | \(-0.951619\pi\) | ||
0.988471 | − | 0.151408i | \(-0.0483809\pi\) | |||||||
\(710\) | −2.82226e7 | − | 4.03180e6i | −0.0788537 | − | 0.0112648i | ||||
\(711\) | 1.72607e8 | 0.480229 | ||||||||
\(712\) | 2.39718e7 | − | 2.39718e7i | 0.0664143 | − | 0.0664143i | ||||
\(713\) | −8.08598e7 | − | 8.08598e7i | −0.223082 | − | 0.223082i | ||||
\(714\) | 2.35693e8i | 0.647519i | ||||||||
\(715\) | −9.47402e7 | + | 6.63181e8i | −0.259189 | + | 1.81432i | ||||
\(716\) | −1.74842e8 | −0.476328 | ||||||||
\(717\) | −2.22312e8 | + | 2.22312e8i | −0.603124 | + | 0.603124i | ||||
\(718\) | −1.78809e8 | − | 1.78809e8i | −0.483077 | − | 0.483077i | ||||
\(719\) | − | 1.83233e8i | − | 0.492967i | −0.969147 | − | 0.246484i | \(-0.920725\pi\) | ||
0.969147 | − | 0.246484i | \(-0.0792752\pi\) | |||||||
\(720\) | −3.36896e7 | + | 2.52672e7i | −0.0902606 | + | 0.0676955i | ||||
\(721\) | 3.28541e8 | 0.876565 | ||||||||
\(722\) | −1.76350e8 | + | 1.76350e8i | −0.468558 | + | 0.468558i | ||||
\(723\) | −4.27631e8 | − | 4.27631e8i | −1.13150 | − | 1.13150i | ||||
\(724\) | − | 2.88780e8i | − | 0.760941i | ||||||
\(725\) | 4.57800e8 | + | 1.33525e8i | 1.20133 | + | 0.350387i | ||||
\(726\) | 3.57039e7 | 0.0933052 | ||||||||
\(727\) | 2.98719e8 | − | 2.98719e8i | 0.777428 | − | 0.777428i | −0.201965 | − | 0.979393i | \(-0.564733\pi\) |
0.979393 | + | 0.201965i | \(0.0647327\pi\) | |||||||
\(728\) | 1.70916e8 | + | 1.70916e8i | 0.442985 | + | 0.442985i | ||||
\(729\) | − | 9.03723e7i | − | 0.233267i | ||||||
\(730\) | −7.74138e7 | − | 1.03218e8i | −0.198999 | − | 0.265331i | ||||
\(731\) | 2.03172e8 | 0.520130 | ||||||||
\(732\) | −6.13250e7 | + | 6.13250e7i | −0.156352 | + | 0.156352i | ||||
\(733\) | 4.34598e8 | + | 4.34598e8i | 1.10351 | + | 1.10351i | 0.993984 | + | 0.109524i | \(0.0349325\pi\) |
0.109524 | + | 0.993984i | \(0.465067\pi\) | |||||||
\(734\) | − | 2.16499e8i | − | 0.547480i | ||||||
\(735\) | 1.75852e7 | + | 2.51218e6i | 0.0442880 | + | 0.00632685i | ||||
\(736\) | 1.75063e7 | 0.0439098 | ||||||||
\(737\) | 8.52879e7 | − | 8.52879e7i | 0.213052 | − | 0.213052i | ||||
\(738\) | 4.66364e7 | + | 4.66364e7i | 0.116026 | + | 0.116026i | ||||
\(739\) | 5.77645e8i | 1.43129i | 0.698463 | + | 0.715646i | \(0.253867\pi\) | ||||
−0.698463 | + | 0.715646i | \(0.746133\pi\) | |||||||
\(740\) | −2.96904e7 | + | 2.07833e8i | −0.0732691 | + | 0.512884i | ||||
\(741\) | 2.13861e8 | 0.525627 | ||||||||
\(742\) | 7.11696e7 | − | 7.11696e7i | 0.174214 | − | 0.174214i | ||||
\(743\) | 9.71697e7 | + | 9.71697e7i | 0.236900 | + | 0.236900i | 0.815565 | − | 0.578665i | \(-0.196426\pi\) |
−0.578665 | + | 0.815565i | \(0.696426\pi\) | |||||||
\(744\) | 2.22790e8i | 0.540975i | ||||||||
\(745\) | −5.76420e8 | + | 4.32315e8i | −1.39402 | + | 1.04552i | ||||
\(746\) | 3.05884e8 | 0.736784 | ||||||||
\(747\) | 3.76452e7 | − | 3.76452e7i | 0.0903124 | − | 0.0903124i | ||||
\(748\) | −1.16332e8 | − | 1.16332e8i | −0.277969 | − | 0.277969i | ||||
\(749\) | 1.52682e8i | 0.363365i | ||||||||
\(750\) | 3.36375e8 | − | 1.26500e8i | 0.797333 | − | 0.299852i | ||||
\(751\) | 6.96310e8 | 1.64393 | 0.821963 | − | 0.569540i | \(-0.192879\pi\) | ||||
0.821963 | + | 0.569540i | \(0.192879\pi\) | |||||||
\(752\) | −9.74776e7 | + | 9.74776e7i | −0.229219 | + | 0.229219i | ||||
\(753\) | −2.74505e8 | − | 2.74505e8i | −0.642933 | − | 0.642933i | ||||
\(754\) | − | 6.59964e8i | − | 1.53960i | ||||||
\(755\) | −7.74602e7 | − | 1.03280e8i | −0.179985 | − | 0.239981i | ||||
\(756\) | −1.45434e8 | −0.336589 | ||||||||
\(757\) | −2.26996e8 | + | 2.26996e8i | −0.523276 | + | 0.523276i | −0.918559 | − | 0.395283i | \(-0.870646\pi\) |
0.395283 | + | 0.918559i | \(0.370646\pi\) | |||||||
\(758\) | 1.00245e7 | + | 1.00245e7i | 0.0230173 | + | 0.0230173i | ||||
\(759\) | − | 1.37819e8i | − | 0.315199i | ||||||
\(760\) | −3.85280e7 | − | 5.50400e6i | −0.0877679 | − | 0.0125383i | ||||
\(761\) | −3.36900e8 | −0.764447 | −0.382224 | − | 0.924070i | \(-0.624842\pi\) | ||||
−0.382224 | + | 0.924070i | \(0.624842\pi\) | |||||||
\(762\) | −3.58139e8 | + | 3.58139e8i | −0.809444 | + | 0.809444i |