Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), 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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 37.8 | ||
Character | \(\chi\) | \(=\) | 43.37 |
Dual form | 43.7.d.a.7.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6.20332i | − | 0.775414i | −0.921783 | − | 0.387707i | \(-0.873267\pi\) | ||
0.921783 | − | 0.387707i | \(-0.126733\pi\) | |||||||
\(3\) | −29.5720 | − | 17.0734i | −1.09526 | − | 0.632349i | −0.160288 | − | 0.987070i | \(-0.551242\pi\) |
−0.934972 | + | 0.354721i | \(0.884576\pi\) | |||||||
\(4\) | 25.5189 | 0.398732 | ||||||||
\(5\) | −46.5574 | − | 26.8799i | −0.372459 | − | 0.215039i | 0.302073 | − | 0.953285i | \(-0.402321\pi\) |
−0.674532 | + | 0.738245i | \(0.735655\pi\) | |||||||
\(6\) | −105.912 | + | 183.445i | −0.490332 | + | 0.849281i | ||||
\(7\) | −448.906 | + | 259.176i | −1.30876 | + | 0.755616i | −0.981890 | − | 0.189452i | \(-0.939329\pi\) |
−0.326875 | + | 0.945068i | \(0.605995\pi\) | |||||||
\(8\) | − | 555.314i | − | 1.08460i | ||||||
\(9\) | 218.503 | + | 378.459i | 0.299730 | + | 0.519148i | ||||
\(10\) | −166.745 | + | 288.810i | −0.166745 | + | 0.288810i | ||||
\(11\) | 668.930 | 0.502577 | 0.251289 | − | 0.967912i | \(-0.419146\pi\) | ||||
0.251289 | + | 0.967912i | \(0.419146\pi\) | |||||||
\(12\) | −754.645 | − | 435.695i | −0.436716 | − | 0.252138i | ||||
\(13\) | 1458.97 | + | 2527.02i | 0.664076 | + | 1.15021i | 0.979535 | + | 0.201274i | \(0.0645081\pi\) |
−0.315459 | + | 0.948939i | \(0.602159\pi\) | |||||||
\(14\) | 1607.75 | + | 2784.71i | 0.585915 | + | 1.01483i | ||||
\(15\) | 917.864 | + | 1589.79i | 0.271960 | + | 0.471048i | ||||
\(16\) | −1811.58 | −0.442280 | ||||||||
\(17\) | 4621.51 | + | 8004.68i | 0.940669 | + | 1.62929i | 0.764199 | + | 0.644980i | \(0.223134\pi\) |
0.176469 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(18\) | 2347.70 | − | 1355.45i | 0.402555 | − | 0.232415i | ||||
\(19\) | −8611.09 | − | 4971.62i | −1.25544 | − | 0.724831i | −0.283259 | − | 0.959044i | \(-0.591416\pi\) |
−0.972185 | + | 0.234212i | \(0.924749\pi\) | |||||||
\(20\) | −1188.09 | − | 685.945i | −0.148511 | − | 0.0857431i | ||||
\(21\) | 17700.1 | 1.91125 | ||||||||
\(22\) | − | 4149.58i | − | 0.389706i | ||||||
\(23\) | 1260.28 | − | 2182.87i | 0.103582 | − | 0.179409i | −0.809576 | − | 0.587015i | \(-0.800303\pi\) |
0.913158 | + | 0.407606i | \(0.133636\pi\) | |||||||
\(24\) | −9481.11 | + | 16421.8i | −0.685844 | + | 1.18792i | ||||
\(25\) | −6367.44 | − | 11028.7i | −0.407516 | − | 0.705839i | ||||
\(26\) | 15675.9 | − | 9050.48i | 0.891892 | − | 0.514934i | ||||
\(27\) | 9970.65i | 0.506561i | ||||||||
\(28\) | −11455.6 | + | 6613.88i | −0.521847 | + | 0.301288i | ||||
\(29\) | −28975.0 | + | 16728.7i | −1.18803 | + | 0.685912i | −0.957859 | − | 0.287237i | \(-0.907263\pi\) |
−0.230175 | + | 0.973149i | \(0.573930\pi\) | |||||||
\(30\) | 9861.95 | − | 5693.80i | 0.365257 | − | 0.210881i | ||||
\(31\) | −12187.6 | + | 21109.5i | −0.409103 | + | 0.708587i | −0.994789 | − | 0.101951i | \(-0.967492\pi\) |
0.585686 | + | 0.810538i | \(0.300825\pi\) | |||||||
\(32\) | − | 24302.3i | − | 0.741647i | ||||||
\(33\) | −19781.6 | − | 11420.9i | −0.550453 | − | 0.317804i | ||||
\(34\) | 49655.6 | − | 28668.7i | 1.26337 | − | 0.729408i | ||||
\(35\) | 27866.5 | 0.649948 | ||||||||
\(36\) | 5575.96 | + | 9657.85i | 0.119512 | + | 0.207001i | ||||
\(37\) | 20245.7 | + | 11688.9i | 0.399694 | + | 0.230763i | 0.686352 | − | 0.727270i | \(-0.259211\pi\) |
−0.286658 | + | 0.958033i | \(0.592544\pi\) | |||||||
\(38\) | −30840.5 | + | 53417.3i | −0.562044 | + | 0.973490i | ||||
\(39\) | − | 99638.7i | − | 1.67971i | ||||||
\(40\) | −14926.8 | + | 25854.0i | −0.233231 | + | 0.403968i | ||||
\(41\) | −115817. | −1.68044 | −0.840219 | − | 0.542248i | \(-0.817573\pi\) | ||||
−0.840219 | + | 0.542248i | \(0.817573\pi\) | |||||||
\(42\) | − | 109799.i | − | 1.48201i | ||||||
\(43\) | −76602.8 | − | 21292.5i | −0.963473 | − | 0.267806i | ||||
\(44\) | 17070.3 | 0.200394 | ||||||||
\(45\) | − | 23493.4i | − | 0.257815i | ||||||
\(46\) | −13541.0 | − | 7817.91i | −0.139116 | − | 0.0803188i | ||||
\(47\) | 61753.5 | 0.594796 | 0.297398 | − | 0.954754i | \(-0.403881\pi\) | ||||
0.297398 | + | 0.954754i | \(0.403881\pi\) | |||||||
\(48\) | 53572.1 | + | 30929.8i | 0.484412 | + | 0.279675i | ||||
\(49\) | 75520.0 | − | 130805.i | 0.641910 | − | 1.11182i | ||||
\(50\) | −68414.7 | + | 39499.2i | −0.547318 | + | 0.315994i | ||||
\(51\) | − | 315620.i | − | 2.37932i | ||||||
\(52\) | 37231.4 | + | 64486.7i | 0.264789 | + | 0.458627i | ||||
\(53\) | −78565.5 | + | 136079.i | −0.527721 | + | 0.914040i | 0.471757 | + | 0.881729i | \(0.343620\pi\) |
−0.999478 | + | 0.0323110i | \(0.989713\pi\) | |||||||
\(54\) | 61851.1 | 0.392795 | ||||||||
\(55\) | −31143.6 | − | 17980.8i | −0.187189 | − | 0.108074i | ||||
\(56\) | 143924. | + | 249284.i | 0.819539 | + | 1.41948i | ||||
\(57\) | 169765. | + | 294042.i | 0.916692 | + | 1.58776i | ||||
\(58\) | 103773. | + | 179741.i | 0.531866 | + | 0.921219i | ||||
\(59\) | −124631. | −0.606836 | −0.303418 | − | 0.952858i | \(-0.598128\pi\) | ||||
−0.303418 | + | 0.952858i | \(0.598128\pi\) | |||||||
\(60\) | 23422.9 | + | 40569.6i | 0.108439 | + | 0.187822i | ||||
\(61\) | 142533. | − | 82291.6i | 0.627952 | − | 0.362548i | −0.152006 | − | 0.988380i | \(-0.548573\pi\) |
0.779959 | + | 0.625831i | \(0.215240\pi\) | |||||||
\(62\) | 130949. | + | 75603.4i | 0.549449 | + | 0.317224i | ||||
\(63\) | −196175. | − | 113262.i | −0.784553 | − | 0.452962i | ||||
\(64\) | −266696. | −1.01736 | ||||||||
\(65\) | − | 156868.i | − | 0.571210i | ||||||
\(66\) | −70847.6 | + | 122712.i | −0.246430 | + | 0.426829i | ||||
\(67\) | −153628. | + | 266092.i | −0.510795 | + | 0.884722i | 0.489127 | + | 0.872213i | \(0.337315\pi\) |
−0.999922 | + | 0.0125099i | \(0.996018\pi\) | |||||||
\(68\) | 117936. | + | 204271.i | 0.375075 | + | 0.649649i | ||||
\(69\) | −74538.0 | + | 43034.6i | −0.226898 | + | 0.131000i | ||||
\(70\) | − | 172865.i | − | 0.503979i | ||||||
\(71\) | 144911. | − | 83664.3i | 0.404879 | − | 0.233757i | −0.283708 | − | 0.958911i | \(-0.591565\pi\) |
0.688587 | + | 0.725154i | \(0.258231\pi\) | |||||||
\(72\) | 210163. | − | 121338.i | 0.563067 | − | 0.325087i | ||||
\(73\) | −92149.8 | + | 53202.7i | −0.236879 | + | 0.136762i | −0.613741 | − | 0.789507i | \(-0.710336\pi\) |
0.376863 | + | 0.926269i | \(0.377003\pi\) | |||||||
\(74\) | 72509.7 | − | 125590.i | 0.178937 | − | 0.309928i | ||||
\(75\) | 434856.i | 1.03077i | ||||||||
\(76\) | −219745. | − | 126870.i | −0.500586 | − | 0.289014i | ||||
\(77\) | −300287. | + | 173371.i | −0.657755 | + | 0.379755i | ||||
\(78\) | −618090. | −1.30247 | ||||||||
\(79\) | −42654.8 | − | 73880.2i | −0.0865140 | − | 0.149847i | 0.819521 | − | 0.573049i | \(-0.194239\pi\) |
−0.906035 | + | 0.423202i | \(0.860906\pi\) | |||||||
\(80\) | 84342.4 | + | 48695.1i | 0.164731 | + | 0.0951076i | ||||
\(81\) | 329522. | − | 570749.i | 0.620054 | − | 1.07396i | ||||
\(82\) | 718452.i | 1.30304i | ||||||||
\(83\) | 215515. | − | 373283.i | 0.376915 | − | 0.652837i | −0.613696 | − | 0.789542i | \(-0.710318\pi\) |
0.990612 | + | 0.136706i | \(0.0436514\pi\) | |||||||
\(84\) | 451686. | 0.762078 | ||||||||
\(85\) | − | 496903.i | − | 0.809123i | ||||||
\(86\) | −132084. | + | 475192.i | −0.207661 | + | 0.747091i | ||||
\(87\) | 1.14247e6 | 1.73494 | ||||||||
\(88\) | − | 371466.i | − | 0.545094i | ||||||
\(89\) | 336288. | + | 194156.i | 0.477026 | + | 0.275411i | 0.719176 | − | 0.694828i | \(-0.244519\pi\) |
−0.242150 | + | 0.970239i | \(0.577853\pi\) | |||||||
\(90\) | −145737. | −0.199914 | ||||||||
\(91\) | −1.30989e6 | − | 756263.i | −1.73824 | − | 1.00357i | ||||
\(92\) | 32160.9 | − | 55704.3i | 0.0413014 | − | 0.0715361i | ||||
\(93\) | 720823. | − | 416168.i | 0.896149 | − | 0.517392i | ||||
\(94\) | − | 383077.i | − | 0.461214i | ||||||
\(95\) | 267273. | + | 462931.i | 0.311734 | + | 0.539940i | ||||
\(96\) | −414923. | + | 718668.i | −0.468980 | + | 0.812297i | ||||
\(97\) | 1.25371e6 | 1.37367 | 0.686834 | − | 0.726814i | \(-0.259000\pi\) | ||||
0.686834 | + | 0.726814i | \(0.259000\pi\) | |||||||
\(98\) | −811422. | − | 468475.i | −0.862121 | − | 0.497746i | ||||
\(99\) | 146163. | + | 253163.i | 0.150638 | + | 0.260912i | ||||
\(100\) | −162490. | − | 281441.i | −0.162490 | − | 0.281441i | ||||
\(101\) | 173483. | + | 300482.i | 0.168381 | + | 0.291645i | 0.937851 | − | 0.347039i | \(-0.112813\pi\) |
−0.769470 | + | 0.638683i | \(0.779479\pi\) | |||||||
\(102\) | −1.95789e6 | −1.84496 | ||||||||
\(103\) | −860379. | − | 1.49022e6i | −0.787369 | − | 1.36376i | −0.927574 | − | 0.373640i | \(-0.878110\pi\) |
0.140205 | − | 0.990122i | \(-0.455224\pi\) | |||||||
\(104\) | 1.40329e6 | − | 810189.i | 1.24752 | − | 0.720255i | ||||
\(105\) | −824070. | − | 475777.i | −0.711862 | − | 0.410994i | ||||
\(106\) | 844144. | + | 487367.i | 0.708760 | + | 0.409203i | ||||
\(107\) | −1.37113e6 | −1.11925 | −0.559624 | − | 0.828746i | \(-0.689055\pi\) | ||||
−0.559624 | + | 0.828746i | \(0.689055\pi\) | |||||||
\(108\) | 254440.i | 0.201983i | ||||||||
\(109\) | 21429.7 | − | 37117.4i | 0.0165477 | − | 0.0286614i | −0.857633 | − | 0.514262i | \(-0.828066\pi\) |
0.874181 | + | 0.485601i | \(0.161399\pi\) | |||||||
\(110\) | −111540. | + | 193194.i | −0.0838020 | + | 0.145149i | ||||
\(111\) | −399138. | − | 691327.i | −0.291846 | − | 0.505492i | ||||
\(112\) | 813229. | − | 469518.i | 0.578840 | − | 0.334194i | ||||
\(113\) | 1.35765e6i | 0.940922i | 0.882421 | + | 0.470461i | \(0.155912\pi\) | ||||
−0.882421 | + | 0.470461i | \(0.844088\pi\) | |||||||
\(114\) | 1.82403e6 | − | 1.05311e6i | 1.23117 | − | 0.710816i | ||||
\(115\) | −117351. | + | 67752.4i | −0.0771599 | + | 0.0445483i | ||||
\(116\) | −739409. | + | 426898.i | −0.473708 | + | 0.273495i | ||||
\(117\) | −637582. | + | 1.10432e6i | −0.398087 | + | 0.689507i | ||||
\(118\) | 773128.i | 0.470549i | ||||||||
\(119\) | −4.14925e6 | − | 2.39557e6i | −2.46223 | − | 1.42157i | ||||
\(120\) | 882831. | − | 509703.i | 0.510897 | − | 0.294967i | ||||
\(121\) | −1.32409e6 | −0.747416 | ||||||||
\(122\) | −510481. | − | 884179.i | −0.281125 | − | 0.486923i | ||||
\(123\) | 3.42496e6 | + | 1.97740e6i | 1.84052 | + | 1.06262i | ||||
\(124\) | −311014. | + | 538691.i | −0.163123 | + | 0.282537i | ||||
\(125\) | 1.52462e6i | 0.780607i | ||||||||
\(126\) | −702598. | + | 1.21694e6i | −0.351233 | + | 0.608353i | ||||
\(127\) | −713613. | −0.348379 | −0.174189 | − | 0.984712i | \(-0.555731\pi\) | ||||
−0.174189 | + | 0.984712i | \(0.555731\pi\) | |||||||
\(128\) | 99051.7i | 0.0472315i | ||||||||
\(129\) | 1.90177e6 | + | 1.93753e6i | 0.885907 | + | 0.902568i | ||||
\(130\) | −973104. | −0.442924 | ||||||||
\(131\) | 2.32324e6i | 1.03343i | 0.856158 | + | 0.516714i | \(0.172845\pi\) | ||||
−0.856158 | + | 0.516714i | \(0.827155\pi\) | |||||||
\(132\) | −504805. | − | 291449.i | −0.219483 | − | 0.126719i | ||||
\(133\) | 5.15410e6 | 2.19077 | ||||||||
\(134\) | 1.65065e6 | + | 953004.i | 0.686027 | + | 0.396078i | ||||
\(135\) | 268010. | − | 464207.i | 0.108931 | − | 0.188673i | ||||
\(136\) | 4.44511e6 | − | 2.56639e6i | 1.76712 | − | 1.02025i | ||||
\(137\) | 2.19066e6i | 0.851947i | 0.904736 | + | 0.425974i | \(0.140068\pi\) | ||||
−0.904736 | + | 0.425974i | \(0.859932\pi\) | |||||||
\(138\) | 266957. | + | 462383.i | 0.101579 | + | 0.175940i | ||||
\(139\) | 856023. | − | 1.48268e6i | 0.318743 | − | 0.552080i | −0.661483 | − | 0.749960i | \(-0.730072\pi\) |
0.980226 | + | 0.197881i | \(0.0634058\pi\) | |||||||
\(140\) | 711123. | 0.259155 | ||||||||
\(141\) | −1.82618e6 | − | 1.05434e6i | −0.651457 | − | 0.376119i | ||||
\(142\) | −518996. | − | 898927.i | −0.181259 | − | 0.313949i | ||||
\(143\) | 975952. | + | 1.69040e6i | 0.333749 | + | 0.578071i | ||||
\(144\) | −395836. | − | 685608.i | −0.132565 | − | 0.229609i | ||||
\(145\) | 1.79866e6 | 0.589992 | ||||||||
\(146\) | 330033. | + | 571634.i | 0.106047 | + | 0.183679i | ||||
\(147\) | −4.46656e6 | + | 2.57877e6i | −1.40612 | + | 0.811822i | ||||
\(148\) | 516648. | + | 298287.i | 0.159371 | + | 0.0920129i | ||||
\(149\) | −3.52607e6 | − | 2.03578e6i | −1.06594 | − | 0.615419i | −0.138869 | − | 0.990311i | \(-0.544347\pi\) |
−0.927069 | + | 0.374891i | \(0.877680\pi\) | |||||||
\(150\) | 2.69755e6 | 0.799274 | ||||||||
\(151\) | − | 5.74517e6i | − | 1.66868i | −0.551253 | − | 0.834338i | \(-0.685850\pi\) | ||
0.551253 | − | 0.834338i | \(-0.314150\pi\) | |||||||
\(152\) | −2.76081e6 | + | 4.78186e6i | −0.786150 | + | 1.36165i | ||||
\(153\) | −2.01963e6 | + | 3.49810e6i | −0.563894 | + | 0.976693i | ||||
\(154\) | 1.07547e6 | + | 1.86277e6i | 0.294468 | + | 0.510033i | ||||
\(155\) | 1.13484e6 | − | 655203.i | 0.304748 | − | 0.175946i | ||||
\(156\) | − | 2.54267e6i | − | 0.669755i | ||||||
\(157\) | −3.59467e6 | + | 2.07538e6i | −0.928880 | + | 0.536289i | −0.886457 | − | 0.462811i | \(-0.846841\pi\) |
−0.0424228 | + | 0.999100i | \(0.513508\pi\) | |||||||
\(158\) | −458302. | + | 264601.i | −0.116193 | + | 0.0670842i | ||||
\(159\) | 4.64668e6 | − | 2.68276e6i | 1.15598 | − | 0.667408i | ||||
\(160\) | −653243. | + | 1.13145e6i | −0.159483 | + | 0.276233i | ||||
\(161\) | 1.30654e6i | 0.313072i | ||||||||
\(162\) | −3.54054e6 | − | 2.04413e6i | −0.832768 | − | 0.480799i | ||||
\(163\) | −1.14929e6 | + | 663544.i | −0.265380 | + | 0.153217i | −0.626786 | − | 0.779191i | \(-0.715630\pi\) |
0.361406 | + | 0.932408i | \(0.382297\pi\) | |||||||
\(164\) | −2.95553e6 | −0.670045 | ||||||||
\(165\) | 613987. | + | 1.06346e6i | 0.136681 | + | 0.236738i | ||||
\(166\) | −2.31559e6 | − | 1.33691e6i | −0.506219 | − | 0.292266i | ||||
\(167\) | 2.30365e6 | − | 3.99003e6i | 0.494614 | − | 0.856696i | −0.505367 | − | 0.862905i | \(-0.668643\pi\) |
0.999981 | + | 0.00620824i | \(0.00197616\pi\) | |||||||
\(168\) | − | 9.82911e6i | − | 2.07294i | ||||||
\(169\) | −1.84381e6 | + | 3.19357e6i | −0.381993 | + | 0.661632i | ||||
\(170\) | −3.08244e6 | −0.627406 | ||||||||
\(171\) | − | 4.34526e6i | − | 0.869015i | ||||||
\(172\) | −1.95482e6 | − | 543360.i | −0.384168 | − | 0.106783i | ||||
\(173\) | 5.40326e6 | 1.04356 | 0.521780 | − | 0.853080i | \(-0.325268\pi\) | ||||
0.521780 | + | 0.853080i | \(0.325268\pi\) | |||||||
\(174\) | − | 7.08707e6i | − | 1.34530i | ||||||
\(175\) | 5.71677e6 | + | 3.30058e6i | 1.06669 | + | 0.615851i | ||||
\(176\) | −1.21182e6 | −0.222280 | ||||||||
\(177\) | 3.68560e6 | + | 2.12788e6i | 0.664644 | + | 0.383732i | ||||
\(178\) | 1.20441e6 | − | 2.08610e6i | 0.213558 | − | 0.369893i | ||||
\(179\) | −4.30512e6 | + | 2.48556e6i | −0.750631 | + | 0.433377i | −0.825922 | − | 0.563785i | \(-0.809345\pi\) |
0.0752909 | + | 0.997162i | \(0.476011\pi\) | |||||||
\(180\) | − | 599525.i | − | 0.102799i | ||||||
\(181\) | 1.85635e6 | + | 3.21528e6i | 0.313057 | + | 0.542230i | 0.979023 | − | 0.203752i | \(-0.0653137\pi\) |
−0.665966 | + | 0.745982i | \(0.731980\pi\) | |||||||
\(182\) | −4.69134e6 | + | 8.12563e6i | −0.778184 | + | 1.34785i | ||||
\(183\) | −5.62000e6 | −0.917029 | ||||||||
\(184\) | −1.21218e6 | − | 699851.i | −0.194586 | − | 0.112345i | ||||
\(185\) | −628391. | − | 1.08841e6i | −0.0992464 | − | 0.171900i | ||||
\(186\) | −2.58162e6 | − | 4.47149e6i | −0.401193 | − | 0.694887i | ||||
\(187\) | 3.09146e6 | + | 5.35457e6i | 0.472759 | + | 0.818842i | ||||
\(188\) | 1.57588e6 | 0.237165 | ||||||||
\(189\) | −2.58415e6 | − | 4.47589e6i | −0.382766 | − | 0.662970i | ||||
\(190\) | 2.87171e6 | − | 1.65798e6i | 0.418677 | − | 0.241723i | ||||
\(191\) | 1.54128e6 | + | 889857.i | 0.221198 | + | 0.127709i | 0.606505 | − | 0.795080i | \(-0.292571\pi\) |
−0.385307 | + | 0.922788i | \(0.625904\pi\) | |||||||
\(192\) | 7.88674e6 | + | 4.55341e6i | 1.11428 | + | 0.643329i | ||||
\(193\) | −903040. | −0.125613 | −0.0628066 | − | 0.998026i | \(-0.520005\pi\) | ||||
−0.0628066 | + | 0.998026i | \(0.520005\pi\) | |||||||
\(194\) | − | 7.77716e6i | − | 1.06516i | ||||||
\(195\) | −2.67828e6 | + | 4.63892e6i | −0.361204 | + | 0.625623i | ||||
\(196\) | 1.92719e6 | − | 3.33799e6i | 0.255950 | − | 0.443319i | ||||
\(197\) | 60217.6 | + | 104300.i | 0.00787634 | + | 0.0136422i | 0.869937 | − | 0.493163i | \(-0.164160\pi\) |
−0.862060 | + | 0.506806i | \(0.830826\pi\) | |||||||
\(198\) | 1.57045e6 | − | 906698.i | 0.202315 | − | 0.116807i | ||||
\(199\) | 6.23092e6i | 0.790666i | 0.918538 | + | 0.395333i | \(0.129371\pi\) | ||||
−0.918538 | + | 0.395333i | \(0.870629\pi\) | |||||||
\(200\) | −6.12441e6 | + | 3.53593e6i | −0.765551 | + | 0.441991i | ||||
\(201\) | 9.08619e6 | − | 5.24592e6i | 1.11891 | − | 0.646001i | ||||
\(202\) | 1.86398e6 | − | 1.07617e6i | 0.226146 | − | 0.130565i | ||||
\(203\) | 8.67136e6 | − | 1.50192e7i | 1.03657 | − | 1.79539i | ||||
\(204\) | − | 8.05426e6i | − | 0.948713i | ||||||
\(205\) | 5.39216e6 | + | 3.11316e6i | 0.625894 | + | 0.361360i | ||||
\(206\) | −9.24430e6 | + | 5.33720e6i | −1.05748 | + | 0.610537i | ||||
\(207\) | 1.10150e6 | 0.124186 | ||||||||
\(208\) | −2.64305e6 | − | 4.57789e6i | −0.293707 | − | 0.508716i | ||||
\(209\) | −5.76022e6 | − | 3.32566e6i | −0.630958 | − | 0.364283i | ||||
\(210\) | −2.95139e6 | + | 5.11197e6i | −0.318691 | + | 0.551988i | ||||
\(211\) | − | 2.45973e6i | − | 0.261842i | −0.991393 | − | 0.130921i | \(-0.958207\pi\) | ||
0.991393 | − | 0.130921i | \(-0.0417934\pi\) | |||||||
\(212\) | −2.00490e6 | + | 3.47260e6i | −0.210420 | + | 0.364457i | ||||
\(213\) | −5.71374e6 | −0.591264 | ||||||||
\(214\) | 8.50554e6i | 0.867882i | ||||||||
\(215\) | 2.99409e6 | + | 3.05040e6i | 0.301265 | + | 0.306931i | ||||
\(216\) | 5.53684e6 | 0.549415 | ||||||||
\(217\) | − | 1.26349e7i | − | 1.23650i | ||||||
\(218\) | −230251. | − | 132935.i | −0.0222245 | − | 0.0128313i | ||||
\(219\) | 3.63341e6 | 0.345925 | ||||||||
\(220\) | −794751. | − | 458849.i | −0.0746385 | − | 0.0430925i | ||||
\(221\) | −1.34853e7 | + | 2.33573e7i | −1.24935 | + | 2.16394i | ||||
\(222\) | −4.28852e6 | + | 2.47598e6i | −0.391966 | + | 0.226302i | ||||
\(223\) | 1.89364e7i | 1.70759i | 0.520612 | + | 0.853793i | \(0.325704\pi\) | ||||
−0.520612 | + | 0.853793i | \(0.674296\pi\) | |||||||
\(224\) | 6.29857e6 | + | 1.09094e7i | 0.560400 | + | 0.970641i | ||||
\(225\) | 2.78261e6 | − | 4.81963e6i | 0.244290 | − | 0.423122i | ||||
\(226\) | 8.42196e6 | 0.729605 | ||||||||
\(227\) | −3.72718e6 | − | 2.15189e6i | −0.318642 | − | 0.183968i | 0.332145 | − | 0.943228i | \(-0.392228\pi\) |
−0.650787 | + | 0.759260i | \(0.725561\pi\) | |||||||
\(228\) | 4.33221e6 | + | 7.50361e6i | 0.365515 | + | 0.633090i | ||||
\(229\) | −1.14094e7 | − | 1.97617e7i | −0.950074 | − | 1.64558i | −0.745259 | − | 0.666776i | \(-0.767674\pi\) |
−0.204815 | − | 0.978801i | \(-0.565659\pi\) | |||||||
\(230\) | 420289. | + | 727963.i | 0.0345434 | + | 0.0598309i | ||||
\(231\) | 1.18401e7 | 0.960551 | ||||||||
\(232\) | 9.28968e6 | + | 1.60902e7i | 0.743938 | + | 1.28854i | ||||
\(233\) | 2.66804e6 | − | 1.54039e6i | 0.210923 | − | 0.121777i | −0.390817 | − | 0.920468i | \(-0.627808\pi\) |
0.601740 | + | 0.798692i | \(0.294474\pi\) | |||||||
\(234\) | 6.85047e6 | + | 3.95512e6i | 0.534654 | + | 0.308683i | ||||
\(235\) | −2.87508e6 | − | 1.65993e6i | −0.221537 | − | 0.127905i | ||||
\(236\) | −3.18045e6 | −0.241965 | ||||||||
\(237\) | 2.91305e6i | 0.218828i | ||||||||
\(238\) | −1.48605e7 | + | 2.57391e7i | −1.10230 | + | 1.90925i | ||||
\(239\) | 2.69489e6 | − | 4.66768e6i | 0.197400 | − | 0.341906i | −0.750285 | − | 0.661115i | \(-0.770084\pi\) |
0.947685 | + | 0.319208i | \(0.103417\pi\) | |||||||
\(240\) | −1.66278e6 | − | 2.88002e6i | −0.120282 | − | 0.208335i | ||||
\(241\) | 1.49349e7 | − | 8.62267e6i | 1.06697 | − | 0.616014i | 0.139616 | − | 0.990206i | \(-0.455413\pi\) |
0.927351 | + | 0.374192i | \(0.122080\pi\) | |||||||
\(242\) | 8.21377e6i | 0.579557i | ||||||||
\(243\) | −1.31945e7 | + | 7.61783e6i | −0.919546 | + | 0.530900i | ||||
\(244\) | 3.63729e6 | − | 2.09999e6i | 0.250385 | − | 0.144560i | ||||
\(245\) | −7.03203e6 | + | 4.05994e6i | −0.478170 | + | 0.276072i | ||||
\(246\) | 1.22664e7 | − | 2.12461e7i | 0.823973 | − | 1.42716i | ||||
\(247\) | − | 2.90138e7i | − | 1.92537i | ||||||
\(248\) | 1.17224e7 | + | 6.76794e6i | 0.768532 | + | 0.443712i | ||||
\(249\) | −1.27464e7 | + | 7.35917e6i | −0.825641 | + | 0.476684i | ||||
\(250\) | 9.45771e6 | 0.605294 | ||||||||
\(251\) | −6.17532e6 | − | 1.06960e7i | −0.390516 | − | 0.676393i | 0.602002 | − | 0.798495i | \(-0.294370\pi\) |
−0.992518 | + | 0.122101i | \(0.961037\pi\) | |||||||
\(252\) | −5.00617e6 | − | 2.89031e6i | −0.312827 | − | 0.180611i | ||||
\(253\) | 843039. | − | 1.46019e6i | 0.0520578 | − | 0.0901668i | ||||
\(254\) | 4.42677e6i | 0.270138i | ||||||||
\(255\) | −8.48383e6 | + | 1.46944e7i | −0.511648 | + | 0.886200i | ||||
\(256\) | −1.64541e7 | −0.980740 | ||||||||
\(257\) | 1.77205e7i | 1.04394i | 0.852963 | + | 0.521972i | \(0.174803\pi\) | ||||
−0.852963 | + | 0.521972i | \(0.825197\pi\) | |||||||
\(258\) | 1.20191e7 | − | 1.17973e7i | 0.699865 | − | 0.686945i | ||||
\(259\) | −1.21179e7 | −0.697474 | ||||||||
\(260\) | − | 4.00311e6i | − | 0.227760i | ||||||
\(261\) | −1.26623e7 | − | 7.31056e6i | −0.712180 | − | 0.411177i | ||||
\(262\) | 1.44118e7 | 0.801336 | ||||||||
\(263\) | 1.22138e7 | + | 7.05165e6i | 0.671405 | + | 0.387636i | 0.796609 | − | 0.604495i | \(-0.206625\pi\) |
−0.125204 | + | 0.992131i | \(0.539959\pi\) | |||||||
\(264\) | −6.34220e6 | + | 1.09850e7i | −0.344689 | + | 0.597020i | ||||
\(265\) | 7.31561e6 | − | 4.22367e6i | 0.393109 | − | 0.226962i | ||||
\(266\) | − | 3.19725e7i | − | 1.69876i | ||||||
\(267\) | −6.62982e6 | − | 1.14832e7i | −0.348312 | − | 0.603294i | ||||
\(268\) | −3.92042e6 | + | 6.79036e6i | −0.203670 | + | 0.352768i | ||||
\(269\) | 2.14683e7 | 1.10291 | 0.551456 | − | 0.834204i | \(-0.314072\pi\) | ||||
0.551456 | + | 0.834204i | \(0.314072\pi\) | |||||||
\(270\) | −2.87962e6 | − | 1.66255e6i | −0.146300 | − | 0.0844664i | ||||
\(271\) | −1.37437e7 | − | 2.38047e7i | −0.690550 | − | 1.19607i | −0.971658 | − | 0.236391i | \(-0.924035\pi\) |
0.281108 | − | 0.959676i | \(-0.409298\pi\) | |||||||
\(272\) | −8.37222e6 | − | 1.45011e7i | −0.416039 | − | 0.720601i | ||||
\(273\) | 2.58240e7 | + | 4.47284e7i | 1.26922 | + | 2.19835i | ||||
\(274\) | 1.35893e7 | 0.660612 | ||||||||
\(275\) | −4.25937e6 | − | 7.37745e6i | −0.204808 | − | 0.354738i | ||||
\(276\) | −1.90213e6 | + | 1.09819e6i | −0.0904716 | + | 0.0522338i | ||||
\(277\) | −3.23105e7 | − | 1.86545e7i | −1.52021 | − | 0.877695i | −0.999716 | − | 0.0238320i | \(-0.992413\pi\) |
−0.520497 | − | 0.853863i | \(-0.674253\pi\) | |||||||
\(278\) | −9.19751e6 | − | 5.31018e6i | −0.428091 | − | 0.247158i | ||||
\(279\) | −1.06521e7 | −0.490482 | ||||||||
\(280\) | − | 1.54747e7i | − | 0.704932i | ||||||
\(281\) | 7.17388e6 | − | 1.24255e7i | 0.323322 | − | 0.560010i | −0.657849 | − | 0.753149i | \(-0.728534\pi\) |
0.981171 | + | 0.193140i | \(0.0618670\pi\) | |||||||
\(282\) | −6.54043e6 | + | 1.13284e7i | −0.291648 | + | 0.505149i | ||||
\(283\) | −1.77367e7 | − | 3.07209e7i | −0.782553 | − | 1.35542i | −0.930450 | − | 0.366418i | \(-0.880584\pi\) |
0.147898 | − | 0.989003i | \(-0.452749\pi\) | |||||||
\(284\) | 3.69796e6 | − | 2.13502e6i | 0.161439 | − | 0.0932066i | ||||
\(285\) | − | 1.82531e7i | − | 0.788499i | ||||||
\(286\) | 1.04861e7 | − | 6.05414e6i | 0.448244 | − | 0.258794i | ||||
\(287\) | 5.19912e7 | − | 3.00171e7i | 2.19930 | − | 1.26976i | ||||
\(288\) | 9.19742e6 | − | 5.31013e6i | 0.385025 | − | 0.222294i | ||||
\(289\) | −3.06478e7 | + | 5.30836e7i | −1.26972 | + | 2.19921i | ||||
\(290\) | − | 1.11577e7i | − | 0.457488i | ||||||
\(291\) | −3.70748e7 | − | 2.14051e7i | −1.50453 | − | 0.868638i | ||||
\(292\) | −2.35156e6 | + | 1.35767e6i | −0.0944512 | + | 0.0545314i | ||||
\(293\) | 3.15473e7 | 1.25418 | 0.627088 | − | 0.778948i | \(-0.284247\pi\) | ||||
0.627088 | + | 0.778948i | \(0.284247\pi\) | |||||||
\(294\) | 1.59969e7 | + | 2.77075e7i | 0.629498 | + | 1.09032i | ||||
\(295\) | 5.80251e6 | + | 3.35008e6i | 0.226022 | + | 0.130494i | ||||
\(296\) | 6.49099e6 | − | 1.12427e7i | 0.250285 | − | 0.433507i | ||||
\(297\) | 6.66967e6i | 0.254586i | ||||||||
\(298\) | −1.26286e7 | + | 2.18733e7i | −0.477205 | + | 0.826543i | ||||
\(299\) | 7.35486e6 | 0.275145 | ||||||||
\(300\) | 1.10970e7i | 0.411001i | ||||||||
\(301\) | 3.99060e7 | − | 1.02953e7i | 1.46332 | − | 0.377520i | ||||
\(302\) | −3.56391e7 | −1.29392 | ||||||||
\(303\) | − | 1.18478e7i | − | 0.425903i | ||||||
\(304\) | 1.55997e7 | + | 9.00647e6i | 0.555258 | + | 0.320578i | ||||
\(305\) | −8.84797e6 | −0.311849 | ||||||||
\(306\) | 2.16998e7 | + | 1.25284e7i | 0.757342 | + | 0.437251i | ||||
\(307\) | −6.04673e6 | + | 1.04732e7i | −0.208980 | + | 0.361964i | −0.951394 | − | 0.307978i | \(-0.900348\pi\) |
0.742413 | + | 0.669942i | \(0.233681\pi\) | |||||||
\(308\) | −7.66298e6 | + | 4.42423e6i | −0.262268 | + | 0.151421i | ||||
\(309\) | 5.87584e7i | 1.99157i | ||||||||
\(310\) | −4.06443e6 | − | 7.03980e6i | −0.136431 | − | 0.236306i | ||||
\(311\) | −2.20469e7 | + | 3.81863e7i | −0.732936 | + | 1.26948i | 0.222687 | + | 0.974890i | \(0.428517\pi\) |
−0.955623 | + | 0.294593i | \(0.904816\pi\) | |||||||
\(312\) | −5.53308e7 | −1.82181 | ||||||||
\(313\) | −2.14728e7 | − | 1.23973e7i | −0.700255 | − | 0.404292i | 0.107188 | − | 0.994239i | \(-0.465815\pi\) |
−0.807442 | + | 0.589947i | \(0.799149\pi\) | |||||||
\(314\) | 1.28742e7 | + | 2.22988e7i | 0.415846 | + | 0.720267i | ||||
\(315\) | 6.08893e6 | + | 1.05463e7i | 0.194809 | + | 0.337419i | ||||
\(316\) | −1.08850e6 | − | 1.88534e6i | −0.0344959 | − | 0.0597487i | ||||
\(317\) | 8.18204e6 | 0.256853 | 0.128426 | − | 0.991719i | \(-0.459007\pi\) | ||||
0.128426 | + | 0.991719i | \(0.459007\pi\) | |||||||
\(318\) | −1.66420e7 | − | 2.88248e7i | −0.517518 | − | 0.896367i | ||||
\(319\) | −1.93822e7 | + | 1.11903e7i | −0.597079 | + | 0.344724i | ||||
\(320\) | 1.24167e7 | + | 7.16876e6i | 0.378926 | + | 0.218773i | ||||
\(321\) | 4.05470e7 | + | 2.34098e7i | 1.22587 | + | 0.707756i | ||||
\(322\) | 8.10486e6 | 0.242761 | ||||||||
\(323\) | − | 9.19054e7i | − | 2.72730i | ||||||
\(324\) | 8.40903e6 | − | 1.45649e7i | 0.247236 | − | 0.428225i | ||||
\(325\) | 1.85799e7 | − | 3.21813e7i | 0.541243 | − | 0.937461i | ||||
\(326\) | 4.11617e6 | + | 7.12942e6i | 0.118807 | + | 0.205779i | ||||
\(327\) | −1.26744e6 | + | 731758.i | −0.0362481 | + | 0.0209278i | ||||
\(328\) | 6.43150e7i | 1.82260i | ||||||||
\(329\) | −2.77215e7 | + | 1.60050e7i | −0.778448 | + | 0.449437i | ||||
\(330\) | 6.59696e6 | − | 3.80875e6i | 0.183570 | − | 0.105984i | ||||
\(331\) | −3.95322e6 | + | 2.28240e6i | −0.109010 | + | 0.0629371i | −0.553514 | − | 0.832840i | \(-0.686713\pi\) |
0.444504 | + | 0.895777i | \(0.353380\pi\) | |||||||
\(332\) | 5.49971e6 | − | 9.52577e6i | 0.150288 | − | 0.260307i | ||||
\(333\) | 1.02162e7i | 0.276667i | ||||||||
\(334\) | −2.47514e7 | − | 1.42902e7i | −0.664295 | − | 0.383531i | ||||
\(335\) | 1.43050e7 | − | 8.25902e6i | 0.380500 | − | 0.219682i | ||||
\(336\) | −3.20651e7 | −0.845308 | ||||||||
\(337\) | 5.02155e6 | + | 8.69758e6i | 0.131204 | + | 0.227252i | 0.924141 | − | 0.382051i | \(-0.124782\pi\) |
−0.792937 | + | 0.609304i | \(0.791449\pi\) | |||||||
\(338\) | 1.98107e7 | + | 1.14377e7i | 0.513039 | + | 0.296203i | ||||
\(339\) | 2.31798e7 | − | 4.01486e7i | 0.594991 | − | 1.03056i | ||||
\(340\) | − | 1.26804e7i | − | 0.322624i | ||||||
\(341\) | −8.15264e6 | + | 1.41208e7i | −0.205606 | + | 0.356120i | ||||
\(342\) | −2.69550e7 | −0.673847 | ||||||||
\(343\) | 1.73083e7i | 0.428917i | ||||||||
\(344\) | −1.18240e7 | + | 4.25386e7i | −0.290462 | + | 1.04498i | ||||
\(345\) | 4.62706e6 | 0.112680 | ||||||||
\(346\) | − | 3.35181e7i | − | 0.809191i | ||||||
\(347\) | −2.84111e6 | − | 1.64031e6i | −0.0679984 | − | 0.0392589i | 0.465615 | − | 0.884987i | \(-0.345833\pi\) |
−0.533614 | + | 0.845728i | \(0.679166\pi\) | |||||||
\(348\) | 2.91544e7 | 0.691778 | ||||||||
\(349\) | −5.13253e6 | − | 2.96327e6i | −0.120741 | − | 0.0697099i | 0.438413 | − | 0.898774i | \(-0.355541\pi\) |
−0.559154 | + | 0.829064i | \(0.688874\pi\) | |||||||
\(350\) | 2.04745e7 | − | 3.54629e7i | 0.477540 | − | 0.827123i | ||||
\(351\) | −2.51960e7 | + | 1.45469e7i | −0.582654 | + | 0.336395i | ||||
\(352\) | − | 1.62565e7i | − | 0.372735i | ||||||
\(353\) | 2.03432e6 | + | 3.52354e6i | 0.0462482 | + | 0.0801042i | 0.888223 | − | 0.459413i | \(-0.151940\pi\) |
−0.841975 | + | 0.539517i | \(0.818607\pi\) | |||||||
\(354\) | 1.31999e7 | − | 2.28630e7i | 0.297551 | − | 0.515374i | ||||
\(355\) | −8.99555e6 | −0.201068 | ||||||||
\(356\) | 8.58170e6 | + | 4.95465e6i | 0.190206 | + | 0.109815i | ||||
\(357\) | 8.18011e7 | + | 1.41684e8i | 1.79785 | + | 3.11397i | ||||
\(358\) | 1.54187e7 | + | 2.67060e7i | 0.336047 | + | 0.582050i | ||||
\(359\) | 1.84451e7 | + | 3.19478e7i | 0.398655 | + | 0.690490i | 0.993560 | − | 0.113306i | \(-0.0361439\pi\) |
−0.594906 | + | 0.803796i | \(0.702811\pi\) | |||||||
\(360\) | −1.30462e7 | −0.279626 | ||||||||
\(361\) | 2.59110e7 | + | 4.48792e7i | 0.550760 | + | 0.953944i | ||||
\(362\) | 1.99454e7 | − | 1.15155e7i | 0.420453 | − | 0.242749i | ||||
\(363\) | 3.91561e7 | + | 2.26068e7i | 0.818615 | + | 0.472628i | ||||
\(364\) | −3.34268e7 | − | 1.92990e7i | −0.693092 | − | 0.400157i | ||||
\(365\) | 5.72034e6 | 0.117637 | ||||||||
\(366\) | 3.48626e7i | 0.711077i | ||||||||
\(367\) | −1.81628e7 | + | 3.14589e7i | −0.367438 | + | 0.636421i | −0.989164 | − | 0.146813i | \(-0.953098\pi\) |
0.621726 | + | 0.783235i | \(0.286432\pi\) | |||||||
\(368\) | −2.28310e6 | + | 3.95444e6i | −0.0458121 | + | 0.0793490i | ||||
\(369\) | −2.53065e7 | − | 4.38321e7i | −0.503678 | − | 0.872396i | ||||
\(370\) | −6.75172e6 | + | 3.89811e6i | −0.133294 | + | 0.0769571i | ||||
\(371\) | − | 8.14492e7i | − | 1.59502i | ||||||
\(372\) | 1.83946e7 | − | 1.06201e7i | 0.357324 | − | 0.206301i | ||||
\(373\) | 2.20476e6 | − | 1.27292e6i | 0.0424848 | − | 0.0245286i | −0.478607 | − | 0.878029i | \(-0.658858\pi\) |
0.521092 | + | 0.853501i | \(0.325525\pi\) | |||||||
\(374\) | 3.32161e7 | − | 1.91773e7i | 0.634942 | − | 0.366584i | ||||
\(375\) | 2.60305e7 | − | 4.50862e7i | 0.493616 | − | 0.854967i | ||||
\(376\) | − | 3.42926e7i | − | 0.645114i | ||||||
\(377\) | −8.45475e7 | − | 4.88135e7i | −1.57789 | − | 0.910995i | ||||
\(378\) | −2.77653e7 | + | 1.60303e7i | −0.514076 | + | 0.296802i | ||||
\(379\) | −2.52059e7 | −0.463004 | −0.231502 | − | 0.972834i | \(-0.574364\pi\) | ||||
−0.231502 | + | 0.972834i | \(0.574364\pi\) | |||||||
\(380\) | 6.82051e6 | + | 1.18135e7i | 0.124299 | + | 0.215291i | ||||
\(381\) | 2.11030e7 | + | 1.21838e7i | 0.381566 | + | 0.220297i | ||||
\(382\) | 5.52006e6 | − | 9.56103e6i | 0.0990271 | − | 0.171520i | ||||
\(383\) | 6.62860e7i | 1.17985i | 0.807460 | + | 0.589923i | \(0.200842\pi\) | ||||
−0.807460 | + | 0.589923i | \(0.799158\pi\) | |||||||
\(384\) | 1.69115e6 | − | 2.92916e6i | 0.0298668 | − | 0.0517308i | ||||
\(385\) | 1.86408e7 | 0.326649 | ||||||||
\(386\) | 5.60184e6i | 0.0974022i | ||||||||
\(387\) | −8.67966e6 | − | 3.36435e7i | −0.149751 | − | 0.580455i | ||||
\(388\) | 3.19933e7 | 0.547726 | ||||||||
\(389\) | − | 4.24593e7i | − | 0.721313i | −0.932699 | − | 0.360656i | \(-0.882553\pi\) | ||
0.932699 | − | 0.360656i | \(-0.117447\pi\) | |||||||
\(390\) | 2.87767e7 | + | 1.66142e7i | 0.485117 | + | 0.280083i | ||||
\(391\) | 2.32976e7 | 0.389745 | ||||||||
\(392\) | −7.26376e7 | − | 4.19373e7i | −1.20588 | − | 0.696214i | ||||
\(393\) | 3.96657e7 | − | 6.87030e7i | 0.653488 | − | 1.13187i | ||||
\(394\) | 647005. | − | 373549.i | 0.0105784 | − | 0.00610743i | ||||
\(395\) | 4.58622e6i | 0.0744156i | ||||||||
\(396\) | 3.72993e6 | + | 6.46042e6i | 0.0600641 | + | 0.104034i | ||||
\(397\) | −3.13517e7 | + | 5.43028e7i | −0.501060 | + | 0.867862i | 0.498939 | + | 0.866637i | \(0.333723\pi\) |
−0.999999 | + | 0.00122482i | \(0.999610\pi\) | |||||||
\(398\) | 3.86524e7 | 0.613094 | ||||||||
\(399\) | −1.52417e8 | − | 8.79981e7i | −2.39947 | − | 1.38533i | ||||
\(400\) | 1.15351e7 | + | 1.99794e7i | 0.180236 | + | 0.312178i | ||||
\(401\) | −575801. | − | 997317.i | −0.00892976 | − | 0.0154668i | 0.861526 | − | 0.507713i | \(-0.169509\pi\) |
−0.870456 | + | 0.492247i | \(0.836176\pi\) | |||||||
\(402\) | −3.25421e7 | − | 5.63645e7i | −0.500918 | − | 0.867616i | ||||
\(403\) | −7.11255e7 | −1.08670 | ||||||||
\(404\) | 4.42710e6 | + | 7.66796e6i | 0.0671391 | + | 0.116288i | ||||
\(405\) | −3.06834e7 | + | 1.77150e7i | −0.461889 | + | 0.266672i | ||||
\(406\) | −9.31691e7 | − | 5.37912e7i | −1.39217 | − | 0.803773i | ||||
\(407\) | 1.35430e7 | + | 7.81903e6i | 0.200877 | + | 0.115976i | ||||
\(408\) | −1.75268e8 | −2.58061 | ||||||||
\(409\) | 1.10392e8i | 1.61350i | 0.590896 | + | 0.806748i | \(0.298774\pi\) | ||||
−0.590896 | + | 0.806748i | \(0.701226\pi\) | |||||||
\(410\) | 1.93119e7 | − | 3.34492e7i | 0.280204 | − | 0.485327i | ||||
\(411\) | 3.74020e7 | − | 6.47822e7i | 0.538728 | − | 0.933104i | ||||
\(412\) | −2.19559e7 | − | 3.80287e7i | −0.313949 | − | 0.543776i | ||||
\(413\) | 5.59478e7 | − | 3.23015e7i | 0.794206 | − | 0.458535i | ||||
\(414\) | − | 6.83296e6i | − | 0.0962959i | ||||||
\(415\) | −2.00677e7 | + | 1.15861e7i | −0.280771 | + | 0.162103i | ||||
\(416\) | 6.14123e7 | − | 3.54564e7i | 0.853052 | − | 0.492510i | ||||
\(417\) | −5.06287e7 | + | 2.92305e7i | −0.698214 | + | 0.403114i | ||||
\(418\) | −2.06301e7 | + | 3.57325e7i | −0.282471 | + | 0.489254i | ||||
\(419\) | 9.30327e7i | 1.26472i | 0.774676 | + | 0.632359i | \(0.217913\pi\) | ||||
−0.774676 | + | 0.632359i | \(0.782087\pi\) | |||||||
\(420\) | −2.10293e7 | − | 1.21413e7i | −0.283843 | − | 0.163877i | ||||
\(421\) | 1.22611e8 | − | 7.07892e7i | 1.64317 | − | 0.948683i | 0.663469 | − | 0.748204i | \(-0.269084\pi\) |
0.979698 | − | 0.200479i | \(-0.0642498\pi\) | |||||||
\(422\) | −1.52585e7 | −0.203036 | ||||||||
\(423\) | 1.34934e7 | + | 2.33712e7i | 0.178278 | + | 0.308787i | ||||
\(424\) | 7.55668e7 | + | 4.36285e7i | 0.991365 | + | 0.572365i | ||||
\(425\) | 5.88543e7 | − | 1.01939e8i | 0.766676 | − | 1.32792i | ||||
\(426\) | 3.54441e7i | 0.458475i | ||||||||
\(427\) | −4.26560e7 | + | 7.38824e7i | −0.547895 | + | 0.948981i | ||||
\(428\) | −3.49896e7 | −0.446281 | ||||||||
\(429\) | − | 6.66514e7i | − | 0.844184i | ||||||
\(430\) | 1.89226e7 | − | 1.85733e7i | 0.237999 | − | 0.233605i | ||||
\(431\) | 1.16660e8 | 1.45710 | 0.728550 | − | 0.684993i | \(-0.240195\pi\) | ||||
0.728550 | + | 0.684993i | \(0.240195\pi\) | |||||||
\(432\) | − | 1.80626e7i | − | 0.224042i | ||||||
\(433\) | −7.64773e6 | − | 4.41542e6i | −0.0942039 | − | 0.0543886i | 0.452158 | − | 0.891938i | \(-0.350654\pi\) |
−0.546362 | + | 0.837549i | \(0.683988\pi\) | |||||||
\(434\) | −7.83784e7 | −0.958799 | ||||||||
\(435\) | −5.31902e7 | − | 3.07094e7i | −0.646195 | − | 0.373081i | ||||
\(436\) | 546863. | − | 947195.i | 0.00659810 | − | 0.0114283i | ||||
\(437\) | −2.17048e7 | + | 1.25312e7i | −0.260082 | + | 0.150159i | ||||
\(438\) | − | 2.25392e7i | − | 0.268235i | ||||||
\(439\) | 3.29147e7 | + | 5.70099e7i | 0.389041 | + | 0.673840i | 0.992321 | − | 0.123690i | \(-0.0394730\pi\) |
−0.603279 | + | 0.797530i | \(0.706140\pi\) | |||||||
\(440\) | −9.98498e6 | + | 1.72945e7i | −0.117217 | + | 0.203025i | ||||
\(441\) | 6.60055e7 | 0.769599 | ||||||||
\(442\) | 1.44892e8 | + | 8.36537e7i | 1.67795 | + | 0.968765i | ||||
\(443\) | −5.61873e7 | − | 9.73193e7i | −0.646290 | − | 1.11941i | −0.984002 | − | 0.178157i | \(-0.942986\pi\) |
0.337712 | − | 0.941249i | \(-0.390347\pi\) | |||||||
\(444\) | −1.01855e7 | − | 1.76419e7i | −0.116368 | − | 0.201556i | ||||
\(445\) | −1.04378e7 | − | 1.80788e7i | −0.118448 | − | 0.205159i | ||||
\(446\) | 1.17468e8 | 1.32409 | ||||||||
\(447\) | 6.95153e7 | + | 1.20404e8i | 0.778320 | + | 1.34809i | ||||
\(448\) | 1.19721e8 | − | 6.91212e7i | 1.33149 | − | 0.768736i | ||||
\(449\) | 1.32726e8 | + | 7.66293e7i | 1.46628 | + | 0.846556i | 0.999289 | − | 0.0377062i | \(-0.0120051\pi\) |
0.466990 | + | 0.884263i | \(0.345338\pi\) | |||||||
\(450\) | −2.98977e7 | − | 1.72614e7i | −0.328095 | − | 0.189426i | ||||
\(451\) | −7.74738e7 | −0.844549 | ||||||||
\(452\) | 3.46458e7i | 0.375176i | ||||||||
\(453\) | −9.80897e7 | + | 1.69896e8i | −1.05519 | + | 1.82763i | ||||
\(454\) | −1.33488e7 | + | 2.31209e7i | −0.142651 | + | 0.247080i | ||||
\(455\) | 4.06566e7 | + | 7.04192e7i | 0.431615 | + | 0.747579i | ||||
\(456\) | 1.63285e8 | − | 9.42728e7i | 1.72208 | − | 0.994242i | ||||
\(457\) | 1.64429e7i | 0.172278i | 0.996283 | + | 0.0861389i | \(0.0274529\pi\) | ||||
−0.996283 | + | 0.0861389i | \(0.972547\pi\) | |||||||
\(458\) | −1.22588e8 | + | 7.07763e7i | −1.27600 | + | 0.736701i | ||||
\(459\) | −7.98119e7 | + | 4.60794e7i | −0.825334 | + | 0.476507i | ||||
\(460\) | −2.99466e6 | + | 1.72897e6i | −0.0307662 | + | 0.0177629i | ||||
\(461\) | −4.19616e7 | + | 7.26796e7i | −0.428301 | + | 0.741840i | −0.996722 | − | 0.0808982i | \(-0.974221\pi\) |
0.568421 | + | 0.822738i | \(0.307554\pi\) | |||||||
\(462\) | − | 7.34480e7i | − | 0.744825i | ||||||
\(463\) | 1.73378e7 | + | 1.00100e7i | 0.174683 | + | 0.100853i | 0.584792 | − | 0.811183i | \(-0.301176\pi\) |
−0.410109 | + | 0.912036i | \(0.634509\pi\) | |||||||
\(464\) | 5.24904e7 | − | 3.03054e7i | 0.525444 | − | 0.303365i | ||||
\(465\) | −4.47462e7 | −0.445038 | ||||||||
\(466\) | −9.55554e6 | − | 1.65507e7i | −0.0944273 | − | 0.163553i | ||||
\(467\) | −1.06776e7 | − | 6.16471e6i | −0.104839 | − | 0.0605287i | 0.446664 | − | 0.894702i | \(-0.352612\pi\) |
−0.551503 | + | 0.834173i | \(0.685945\pi\) | |||||||
\(468\) | −1.62704e7 | + | 2.81811e7i | −0.158730 | + | 0.274929i | ||||
\(469\) | − | 1.59267e8i | − | 1.54386i | ||||||
\(470\) | −1.02971e7 | + | 1.78350e7i | −0.0991790 | + | 0.171783i | ||||
\(471\) | 1.41735e8 | 1.35649 | ||||||||
\(472\) | 6.92095e7i | 0.658173i | ||||||||
\(473\) | −5.12419e7 | − | 1.42432e7i | −0.484219 | − | 0.134593i | ||||
\(474\) | 1.80706e7 | 0.169682 | ||||||||
\(475\) | 1.26626e8i | 1.18152i | ||||||||
\(476\) | −1.05884e8 | − | 6.11322e7i | −0.981770 | − | 0.566825i | ||||
\(477\) | −6.86673e7 | −0.632696 | ||||||||
\(478\) | −2.89551e7 | − | 1.67172e7i | −0.265119 | − | 0.153067i | ||||
\(479\) | −7.48247e6 | + | 1.29600e7i | −0.0680830 | + | 0.117923i | −0.898057 | − | 0.439878i | \(-0.855022\pi\) |
0.829974 | + | 0.557801i | \(0.188355\pi\) | |||||||
\(480\) | 3.86355e7 | − | 2.23062e7i | 0.349351 | − | 0.201698i | ||||
\(481\) | 6.82150e7i | 0.612978i | ||||||||
\(482\) | −5.34891e7 | − | 9.26459e7i | −0.477666 | − | 0.827342i | ||||
\(483\) | 2.23071e7 | − | 3.86370e7i | 0.197971 | − | 0.342895i | ||||
\(484\) | −3.37894e7 | −0.298019 | ||||||||
\(485\) | −5.83695e7 | − | 3.36996e7i | −0.511635 | − | 0.295393i | ||||
\(486\) | 4.72558e7 | + | 8.18495e7i | 0.411667 | + | 0.713029i | ||||
\(487\) | 7.00576e7 | + | 1.21343e8i | 0.606552 | + | 1.05058i | 0.991804 | + | 0.127768i | \(0.0407813\pi\) |
−0.385252 | + | 0.922811i | \(0.625885\pi\) | |||||||
\(488\) | −4.56977e7 | − | 7.91507e7i | −0.393219 | − | 0.681076i | ||||
\(489\) | 4.53159e7 | 0.387546 | ||||||||
\(490\) | 2.51851e7 | + | 4.36219e7i | 0.214070 | + | 0.370780i | ||||
\(491\) | 1.05605e8 | − | 6.09709e7i | 0.892152 | − | 0.515084i | 0.0175060 | − | 0.999847i | \(-0.494427\pi\) |
0.874646 | + | 0.484763i | \(0.161094\pi\) | |||||||
\(492\) | 8.74010e7 | + | 5.04610e7i | 0.733874 | + | 0.423702i | ||||
\(493\) | −2.67816e8 | − | 1.54624e8i | −2.23509 | − | 1.29043i | ||||
\(494\) | −1.79982e8 | −1.49296 | ||||||||
\(495\) | − | 1.57154e7i | − | 0.129572i | ||||||
\(496\) | 2.20788e7 | − | 3.82416e7i | 0.180938 | − | 0.313394i | ||||
\(497\) | −4.33676e7 | + | 7.51148e7i | −0.353261 | + | 0.611866i | ||||
\(498\) | 4.56512e7 | + | 7.90702e7i | 0.369628 | + | 0.640214i | ||||
\(499\) | 1.62527e8 | − | 9.38351e7i | 1.30805 | − | 0.755203i | 0.326279 | − | 0.945273i | \(-0.394205\pi\) |
0.981770 | + | 0.190071i | \(0.0608717\pi\) | |||||||
\(500\) | 3.89066e7i | 0.311253i | ||||||||
\(501\) | −1.36247e8 | + | 7.86622e7i | −1.08346 | + | 0.625537i | ||||
\(502\) | −6.63505e7 | + | 3.83075e7i | −0.524485 | + | 0.302812i | ||||
\(503\) | 1.09233e8 | − | 6.30659e7i | 0.858324 | − | 0.495554i | −0.00512643 | − | 0.999987i | \(-0.501632\pi\) |
0.863451 | + | 0.504433i | \(0.168298\pi\) | |||||||
\(504\) | −6.28958e7 | + | 1.08939e8i | −0.491281 | + | 0.850924i | ||||
\(505\) | − | 1.86529e7i | − | 0.144834i | ||||||
\(506\) | −9.05799e6 | − | 5.22964e6i | −0.0699166 | − | 0.0403664i | ||||
\(507\) | 1.09050e8 | − | 6.29602e7i | 0.836764 | − | 0.483106i | ||||
\(508\) | −1.82106e7 | −0.138910 | ||||||||
\(509\) | 4.23079e7 | + | 7.32794e7i | 0.320825 | + | 0.555685i | 0.980658 | − | 0.195727i | \(-0.0627067\pi\) |
−0.659834 | + | 0.751412i | \(0.729373\pi\) | |||||||
\(510\) | 9.11541e7 | + | 5.26279e7i | 0.687173 | + | 0.396739i | ||||
\(511\) | 2.75777e7 | − | 4.77661e7i | 0.206679 | − | 0.357978i | ||||
\(512\) | 1.08409e8i | 0.807711i | ||||||||
\(513\) | 4.95702e7 | − | 8.58582e7i | 0.367171 | − | 0.635960i | ||||
\(514\) | 1.09926e8 | 0.809489 | ||||||||
\(515\) | 9.25076e7i | 0.677261i | ||||||||
\(516\) | 4.85309e7 | + | 4.94437e7i | 0.353240 | + | 0.359883i | ||||
\(517\) | 4.13088e7 | 0.298931 | ||||||||
\(518\) | 7.51711e7i | 0.540831i | ||||||||
\(519\) | −1.59785e8 | − | 9.22521e7i | −1.14297 | − | 0.659894i | ||||
\(520\) | −8.71112e7 | −0.619532 | ||||||||
\(521\) | −1.29051e8 | − | 7.45079e7i | −0.912535 | − | 0.526852i | −0.0312890 | − | 0.999510i | \(-0.509961\pi\) |
−0.881246 | + | 0.472658i | \(0.843295\pi\) | |||||||
\(522\) | −4.53497e7 | + | 7.85480e7i | −0.318833 | + | 0.552234i | ||||
\(523\) | −6.41649e7 | + | 3.70456e7i | −0.448531 | + | 0.258959i | −0.707210 | − | 0.707004i | \(-0.750046\pi\) |
0.258679 | + | 0.965963i | \(0.416713\pi\) | |||||||
\(524\) | 5.92865e7i | 0.412062i | ||||||||
\(525\) | −1.12704e8 | − | 1.95210e8i | −0.778866 | − | 1.34903i | ||||
\(526\) | 4.37436e7 | − | 7.57662e7i | 0.300578 | − | 0.520617i | ||||
\(527\) | −2.25300e8 | −1.53932 | ||||||||
\(528\) | 3.58360e7 | + | 2.06899e7i | 0.243454 | + | 0.140558i | ||||
\(529\) | 7.08413e7 | + | 1.22701e8i | 0.478542 | + | 0.828858i | ||||
\(530\) | −2.62008e7 | − | 4.53810e7i | −0.175989 | − | 0.304822i | ||||
\(531\) | −2.72324e7 | − | 4.71679e7i | −0.181887 | − | 0.315038i | ||||
\(532\) | 1.31527e8 | 0.873533 | ||||||||
\(533\) | −1.68975e8 | − | 2.92673e8i | −1.11594 | − | 1.93286i | ||||
\(534\) | −7.12338e7 | + | 4.11269e7i | −0.467803 | + | 0.270086i | ||||
\(535\) | 6.38361e7 | + | 3.68558e7i | 0.416874 | + | 0.240683i | ||||
\(536\) | 1.47764e8 | + | 8.53118e7i | 0.959568 | + | 0.554007i | ||||
\(537\) | 1.69748e8 | 1.09618 | ||||||||
\(538\) | − | 1.33175e8i | − | 0.855215i | ||||||
\(539\) | 5.05176e7 | − | 8.74991e7i | 0.322609 | − | 0.558775i | ||||
\(540\) | 6.83932e6 | − | 1.18460e7i | 0.0434342 | − | 0.0752302i | ||||
\(541\) | −1.21099e8 | − | 2.09749e8i | −0.764800 | − | 1.32467i | −0.940352 | − | 0.340202i | \(-0.889505\pi\) |
0.175553 | − | 0.984470i | \(-0.443829\pi\) | |||||||
\(542\) | −1.47668e8 | + | 8.52564e7i | −0.927448 | + | 0.535462i | ||||
\(543\) | − | 1.26777e8i | − | 0.791844i | ||||||
\(544\) | 1.94532e8 | − | 1.12313e8i | 1.20836 | − | 0.697644i | ||||
\(545\) | −1.99543e6 | + | 1.15206e6i | −0.0123267 | + | 0.00711681i | ||||
\(546\) | 2.77465e8 | − | 1.60194e8i | 1.70463 | − | 0.984168i | ||||
\(547\) | −2.17719e7 | + | 3.77101e7i | −0.133025 | + | 0.230407i | −0.924841 | − | 0.380353i | \(-0.875803\pi\) |
0.791816 | + | 0.610760i | \(0.209136\pi\) | |||||||
\(548\) | 5.59031e7i | 0.339699i | ||||||||
\(549\) | 6.22880e7 | + | 3.59620e7i | 0.376433 | + | 0.217333i | ||||
\(550\) | −4.57647e7 | + | 2.64222e7i | −0.275069 | + | 0.158811i | ||||
\(551\) | 3.32675e8 | 1.98868 | ||||||||
\(552\) | 2.38977e7 | + | 4.13920e7i | 0.142082 | + | 0.246093i | ||||
\(553\) | 3.82960e7 | + | 2.21102e7i | 0.226453 | + | 0.130743i | ||||
\(554\) | −1.15720e8 | + | 2.00432e8i | −0.680578 | + | 1.17880i | ||||
\(555\) | 4.29151e7i | 0.251033i | ||||||||
\(556\) | 2.18448e7 | − | 3.78362e7i | 0.127093 | − | 0.220132i | ||||
\(557\) | 5.85664e7 | 0.338909 | 0.169455 | − | 0.985538i | \(-0.445799\pi\) | ||||
0.169455 | + | 0.985538i | \(0.445799\pi\) | |||||||
\(558\) | 6.60784e7i | 0.380327i | ||||||||
\(559\) | −5.79552e7 | − | 2.24642e8i | −0.331785 | − | 1.28604i | ||||
\(560\) | −5.04824e7 | −0.287459 | ||||||||
\(561\) | − | 2.11127e8i | − | 1.19579i | ||||||
\(562\) | −7.70794e7 | − | 4.45018e7i | −0.434240 | − | 0.250708i | ||||
\(563\) | 2.07101e7 | 0.116053 | 0.0580266 | − | 0.998315i | \(-0.481519\pi\) | ||||
0.0580266 | + | 0.998315i | \(0.481519\pi\) | |||||||
\(564\) | −4.66020e7 | − | 2.69057e7i | −0.259757 | − | 0.149971i | ||||
\(565\) | 3.64936e7 | − | 6.32088e7i | 0.202335 | − | 0.350455i | ||||
\(566\) | −1.90571e8 | + | 1.10026e8i | −1.05101 | + | 0.606803i | ||||
\(567\) | 3.41617e8i | 1.87409i | ||||||||
\(568\) | −4.64599e7 | − | 8.04710e7i | −0.253532 | − | 0.439131i | ||||
\(569\) | 1.48797e8 | − | 2.57724e8i | 0.807713 | − | 1.39900i | −0.106732 | − | 0.994288i | \(-0.534039\pi\) |
0.914444 | − | 0.404712i | \(-0.132628\pi\) | |||||||
\(570\) | −1.13230e8 | −0.611414 | ||||||||
\(571\) | −1.96290e8 | − | 1.13328e8i | −1.05436 | − | 0.608737i | −0.130496 | − | 0.991449i | \(-0.541657\pi\) |
−0.923868 | + | 0.382711i | \(0.874990\pi\) | |||||||
\(572\) | 2.49052e7 | + | 4.31371e7i | 0.133077 | + | 0.230496i | ||||
\(573\) | −3.03858e7 | − | 5.26298e7i | −0.161513 | − | 0.279748i | ||||
\(574\) | −1.86206e8 | − | 3.22518e8i | −0.984594 | − | 1.70537i | ||||
\(575\) | −3.20990e7 | −0.168845 | ||||||||
\(576\) | −5.82739e7 | − | 1.00933e8i | −0.304935 | − | 0.528162i | ||||
\(577\) | −2.98289e8 | + | 1.72217e8i | −1.55278 | + | 0.896497i | −0.554863 | + | 0.831941i | \(0.687229\pi\) |
−0.997914 | + | 0.0645551i | \(0.979437\pi\) | |||||||
\(578\) | 3.29295e8 | + | 1.90118e8i | 1.70530 | + | 0.984556i | ||||
\(579\) | 2.67047e7 | + | 1.54180e7i | 0.137579 | + | 0.0794313i | ||||
\(580\) | 4.58999e7 | 0.235249 | ||||||||
\(581\) | 2.23426e8i | 1.13921i | ||||||||
\(582\) | −1.32783e8 | + | 2.29986e8i | −0.673554 | + | 1.16663i | ||||
\(583\) | −5.25549e7 | + | 9.10277e7i | −0.265221 | + | 0.459375i | ||||
\(584\) | 2.95442e7 | + | 5.11721e7i | 0.148332 | + | 0.256918i | ||||
\(585\) | 5.93682e7 | − | 3.42763e7i | 0.296542 | − | 0.171209i | ||||
\(586\) | − | 1.95698e8i | − | 0.972507i | ||||||
\(587\) | −1.96030e8 | + | 1.13178e8i | −0.969191 | + | 0.559562i | −0.898989 | − | 0.437970i | \(-0.855697\pi\) |
−0.0702012 | + | 0.997533i | \(0.522364\pi\) | |||||||
\(588\) | −1.13982e8 | + | 6.58073e7i | −0.560664 | + | 0.323700i | ||||
\(589\) | 2.09897e8 | − | 1.21184e8i | 1.02721 | − | 0.593061i | ||||
\(590\) | 2.07816e7 | − | 3.59948e7i | 0.101187 | − | 0.175260i | ||||
\(591\) | − | 4.11248e6i | − | 0.0199224i | ||||||
\(592\) | −3.66767e7 | − | 2.11753e7i | −0.176777 | − | 0.102062i | ||||
\(593\) | 2.50649e8 | − | 1.44712e8i | 1.20199 | − | 0.693972i | 0.240996 | − | 0.970526i | \(-0.422526\pi\) |
0.960998 | + | 0.276555i | \(0.0891927\pi\) | |||||||
\(594\) | 4.13741e7 | 0.197410 | ||||||||
\(595\) | 1.28785e8 | + | 2.23063e8i | 0.611386 | + | 1.05895i | ||||
\(596\) | −8.99813e7 | − | 5.19507e7i | −0.425024 | − | 0.245388i | ||||
\(597\) | 1.06383e8 | − | 1.84261e8i | 0.499977 | − | 0.865985i | ||||
\(598\) | − | 4.56245e7i | − | 0.213351i | ||||||
\(599\) | −1.35327e7 | + | 2.34393e7i | −0.0629657 | + | 0.109060i | −0.895790 | − | 0.444478i | \(-0.853389\pi\) |
0.832824 | + | 0.553538i | \(0.186723\pi\) | |||||||
\(600\) | 2.41482e8 | 1.11797 | ||||||||
\(601\) | 2.60433e8i | 1.19970i | 0.800112 | + | 0.599850i | \(0.204773\pi\) | ||||
−0.800112 | + | 0.599850i | \(0.795227\pi\) | |||||||
\(602\) | −6.38651e7 | − | 2.47549e8i | −0.292734 | − | 1.13468i | ||||
\(603\) | −1.34273e8 | −0.612403 | ||||||||
\(604\) | − | 1.46610e8i | − | 0.665355i | ||||||
\(605\) | 6.16463e7 | + | 3.55915e7i | 0.278382 | + | 0.160724i | ||||
\(606\) | −7.34957e7 | −0.330251 | ||||||||
\(607\) | −1.24979e8 | − | 7.21569e7i | −0.558820 | − | 0.322635i | 0.193852 | − | 0.981031i | \(-0.437902\pi\) |
−0.752672 | + | 0.658396i | \(0.771235\pi\) | |||||||
\(608\) | −1.20822e8 | + | 2.09269e8i | −0.537569 | + | 0.931096i | ||||
\(609\) | −5.12860e8 | + | 2.96100e8i | −2.27063 | + | 1.31095i | ||||
\(610\) | 5.48867e7i | 0.241812i | ||||||||
\(611\) | 9.00968e7 | + | 1.56052e8i | 0.394990 | + | 0.684142i | ||||
\(612\) | −5.15387e7 | + | 8.92676e7i | −0.224843 | + | 0.389439i | ||||
\(613\) | 2.49331e8 | 1.08242 | 0.541209 | − | 0.840888i | \(-0.317967\pi\) | ||||
0.541209 | + | 0.840888i | \(0.317967\pi\) | |||||||
\(614\) | 6.49688e7 | + | 3.75098e7i | 0.280672 | + | 0.162046i | ||||
\(615\) | −1.06305e8 | − | 1.84125e8i | −0.457011 | − | 0.791567i | ||||
\(616\) | 9.62752e7 | + | 1.66753e8i | 0.411881 | + | 0.713399i | ||||
\(617\) | −9.28316e7 | − | 1.60789e8i | −0.395221 | − | 0.684543i | 0.597908 | − | 0.801565i | \(-0.295999\pi\) |
−0.993129 | + | 0.117021i | \(0.962665\pi\) | |||||||
\(618\) | 3.64497e8 | 1.54429 | ||||||||
\(619\) | 1.43768e8 | + | 2.49014e8i | 0.606166 | + | 1.04991i | 0.991866 | + | 0.127286i | \(0.0406267\pi\) |
−0.385700 | + | 0.922624i | \(0.626040\pi\) | |||||||
\(620\) | 2.89599e7 | − | 1.67200e7i | 0.121513 | − | 0.0701556i | ||||
\(621\) | 2.17646e7 | + | 1.25658e7i | 0.0908816 | + | 0.0524705i | ||||
\(622\) | 2.36882e8 | + | 1.36764e8i | 0.984375 | + | 0.568329i | ||||
\(623\) | −2.01283e8 | −0.832420 | ||||||||
\(624\) | 1.80503e8i | 0.742902i | ||||||||
\(625\) | −5.85095e7 | + | 1.01342e8i | −0.239655 | + | 0.415095i | ||||
\(626\) | −7.69046e7 | + | 1.33203e8i | −0.313494 | + | 0.542988i | ||||
\(627\) | 1.13561e8 | + | 1.96693e8i | 0.460709 | + | 0.797971i | ||||
\(628\) | −9.17318e7 | + | 5.29614e7i | −0.370375 | + | 0.213836i | ||||
\(629\) | 2.16081e8i | 0.868288i | ||||||||
\(630\) | 6.54222e7 | − | 3.77715e7i | 0.261640 | − | 0.151058i | ||||
\(631\) | 1.51379e8 | − | 8.73987e7i | 0.602528 | − | 0.347870i | −0.167507 | − | 0.985871i | \(-0.553572\pi\) |
0.770036 | + | 0.638001i | \(0.220238\pi\) | |||||||
\(632\) | −4.10267e7 | + | 2.36868e7i | −0.162523 | + | 0.0938328i | ||||
\(633\) | −4.19959e7 | + | 7.27391e7i | −0.165576 | + | 0.286785i | ||||
\(634\) | − | 5.07558e7i | − | 0.199167i | ||||||
\(635\) | 3.32240e7 | + | 1.91819e7i | 0.129757 | + | 0.0749152i | ||||
\(636\) | 1.18578e8 | − | 6.84611e7i | 0.460928 | − | 0.266117i | ||||
\(637\) | 4.40727e8 | 1.70511 | ||||||||
\(638\) | 6.94172e7 | + | 1.20234e8i | 0.267304 | + | 0.462984i | ||||
\(639\) | 6.33270e7 | + | 3.65618e7i | 0.242709 | + | 0.140128i | ||||
\(640\) | 2.66250e6 | − | 4.61159e6i | 0.0101566 | − | 0.0175918i | ||||
\(641\) | − | 1.89612e8i | − | 0.719932i | −0.932965 | − | 0.359966i | \(-0.882788\pi\) | ||
0.932965 | − | 0.359966i | \(-0.117212\pi\) | |||||||
\(642\) | 1.45219e8 | − | 2.51526e8i | 0.548804 | − | 0.950557i | ||||
\(643\) | 1.33022e8 | 0.500369 | 0.250184 | − | 0.968198i | \(-0.419509\pi\) | ||||
0.250184 | + | 0.968198i | \(0.419509\pi\) | |||||||
\(644\) | 3.33414e7i | 0.124832i | ||||||||
\(645\) | −3.64605e7 | − | 1.41326e8i | −0.135876 | − | 0.526674i | ||||
\(646\) | −5.70118e8 | −2.11479 | ||||||||
\(647\) | 1.37461e8i | 0.507537i | 0.967265 | + | 0.253769i | \(0.0816702\pi\) | ||||
−0.967265 | + | 0.253769i | \(0.918330\pi\) | |||||||
\(648\) | −3.16945e8 | − | 1.82988e8i | −1.16482 | − | 0.672509i | ||||
\(649\) | −8.33697e7 | −0.304982 | ||||||||
\(650\) | −1.99631e8 | − | 1.15257e8i | −0.726921 | − | 0.419688i | ||||
\(651\) | −2.15721e8 | + | 3.73640e8i | −0.781898 | + | 1.35429i | ||||
\(652\) | −2.93286e7 | + | 1.69329e7i | −0.105815 | + | 0.0610926i | ||||
\(653\) | 1.14931e8i | 0.412758i | 0.978472 | + | 0.206379i | \(0.0661680\pi\) | ||||
−0.978472 | + | 0.206379i | \(0.933832\pi\) | |||||||
\(654\) | 4.53933e6 | + | 7.86234e6i | 0.0162277 | + | 0.0281073i | ||||
\(655\) | 6.24486e7 | − | 1.08164e8i | 0.222228 | − | 0.384910i | ||||
\(656\) | 2.09812e8 | 0.743224 | ||||||||
\(657\) | −4.02701e7 | − | 2.32499e7i | −0.141999 | − | 0.0819834i | ||||
\(658\) | 9.92843e7 | + | 1.71965e8i | 0.348500 | + | 0.603620i | ||||
\(659\) | 1.87292e8 | + | 3.24399e8i | 0.654428 | + | 1.13350i | 0.982037 | + | 0.188690i | \(0.0604240\pi\) |
−0.327608 | + | 0.944814i | \(0.606243\pi\) | |||||||
\(660\) | 1.56683e7 | + | 2.71382e7i | 0.0544990 | + | 0.0943951i | ||||
\(661\) | −4.84528e8 | −1.67770 | −0.838851 | − | 0.544361i | \(-0.816772\pi\) | ||||
−0.838851 | + | 0.544361i | \(0.816772\pi\) | |||||||
\(662\) | 1.41584e7 | + | 2.45231e7i | 0.0488024 | + | 0.0845282i | ||||
\(663\) | 7.97576e8 | − | 4.60481e8i | 2.73673 | − | 1.58005i | ||||
\(664\) | −2.07289e8 | − | 1.19679e8i | −0.708065 | − | 0.408801i | ||||
\(665\) | −2.39961e8 | − | 1.38542e8i | −0.815974 | − | 0.471103i | ||||
\(666\) | 6.33744e7 | 0.214532 | ||||||||
\(667\) | 8.43314e7i | 0.284192i | ||||||||
\(668\) | 5.87865e7 | − | 1.01821e8i | 0.197219 | − | 0.341593i | ||||
\(669\) | 3.23309e8 | − | 5.59988e8i | 1.07979 | − | 1.87025i | ||||
\(670\) | −5.12333e7 | − | 8.87387e7i | −0.170345 | − | 0.295045i | ||||
\(671\) | 9.53448e7 | − | 5.50473e7i | 0.315595 | − | 0.182209i | ||||
\(672\) | − | 4.30153e8i | − | 1.41747i | ||||||
\(673\) | 3.55951e8 | − | 2.05508e8i | 1.16774 | − | 0.674193i | 0.214591 | − | 0.976704i | \(-0.431158\pi\) |
0.953146 | + | 0.302510i | \(0.0978247\pi\) | |||||||
\(674\) | 5.39538e7 | − | 3.11502e7i | 0.176215 | − | 0.101738i | ||||
\(675\) | 1.09964e8 | − | 6.34875e7i | 0.357551 | − | 0.206432i | ||||
\(676\) | −4.70519e7 | + | 8.14963e7i | −0.152313 | + | 0.263814i | ||||
\(677\) | 1.63502e8i | 0.526935i | 0.964668 | + | 0.263467i | \(0.0848662\pi\) | ||||
−0.964668 | + | 0.263467i | \(0.915134\pi\) | |||||||
\(678\) | −2.49054e8 | − | 1.43792e8i | −0.799107 | − | 0.461365i | ||||
\(679\) | −5.62799e8 | + | 3.24932e8i | −1.79781 | + | 1.03797i | ||||
\(680\) | −2.75937e8 | −0.877573 | ||||||||
\(681\) | 7.34802e7 | + | 1.27271e8i | 0.232664 | + | 0.402986i | ||||
\(682\) | 8.75957e7 | + | 5.05734e7i | 0.276140 | + | 0.159430i | ||||
\(683\) | −5.22561e7 | + | 9.05102e7i | −0.164012 | + | 0.284077i | −0.936304 | − | 0.351191i | \(-0.885777\pi\) |
0.772292 | + | 0.635268i | \(0.219110\pi\) | |||||||
\(684\) | − | 1.10886e8i | − | 0.346505i | ||||||
\(685\) | 5.88847e7 | − | 1.01991e8i | 0.183202 | − | 0.317316i | ||||
\(686\) | 1.07369e8 | 0.332588 | ||||||||
\(687\) | 7.79192e8i | 2.40311i | ||||||||
\(688\) | 1.38772e8 | + | 3.85730e7i | 0.426125 | + | 0.118445i | ||||
\(689\) | −4.58500e8 | −1.40179 | ||||||||
\(690\) | − | 2.87031e7i | − | 0.0873739i | ||||||
\(691\) | 3.48853e8 | + | 2.01410e8i | 1.05732 | + | 0.610446i | 0.924691 | − | 0.380719i | \(-0.124323\pi\) |
0.132633 | + | 0.991165i | \(0.457657\pi\) | |||||||
\(692\) | 1.37885e8 | 0.416101 | ||||||||
\(693\) | −1.31227e8 | − | 7.57642e7i | −0.394298 | − | 0.227648i | ||||
\(694\) | −1.01754e7 | + | 1.76243e7i | −0.0304419 | + | 0.0527270i | ||||
\(695\) | −7.97084e7 | + | 4.60197e7i | −0.237438 | + | 0.137085i | ||||
\(696\) | − | 6.34427e8i | − | 1.88171i | ||||||
\(697\) | −5.35251e8 | − | 9.27082e8i | −1.58073 | − | 2.73791i | ||||
\(698\) | −1.83821e7 | + | 3.18387e7i | −0.0540541 | + | 0.0936244i | ||||
\(699\) | −1.05199e8 | −0.308021 | ||||||||
\(700\) | 1.45885e8 | + | 8.42270e7i | 0.425322 | + | 0.245560i | ||||
\(701\) | 6.38983e7 | + | 1.10675e8i | 0.185496 | + | 0.321289i | 0.943744 | − | 0.330678i | \(-0.107277\pi\) |
−0.758247 | + | 0.651967i | \(0.773944\pi\) | |||||||
\(702\) | 9.02391e7 | + | 1.56299e8i | 0.260846 | + | 0.451798i | ||||
\(703\) | −1.16225e8 | − | 2.01308e8i | −0.334529 | − | 0.579421i | ||||
\(704\) | −1.78401e8 | −0.511304 | ||||||||
\(705\) | 5.66813e7 | + | 9.81750e7i | 0.161761 | + | 0.280178i | ||||
\(706\) | 2.18576e7 | − | 1.26195e7i | 0.0621140 | − | 0.0358615i | ||||
\(707\) | −1.55756e8 | − | 8.99255e7i | −0.440743 | − | 0.254463i | ||||
\(708\) | 9.40525e7 | + | 5.43012e7i | 0.265015 | + | 0.153006i | ||||
\(709\) | −4.60321e8 | −1.29158 | −0.645791 | − | 0.763514i | \(-0.723472\pi\) | ||||
−0.645791 | + | 0.763514i | \(0.723472\pi\) | |||||||
\(710\) | 5.58023e7i | 0.155911i | ||||||||
\(711\) | 1.86404e7 | − | 3.22861e7i | 0.0518617 | − | 0.0898271i | ||||
\(712\) | 1.07818e8 | − | 1.86746e8i | 0.298710 | − | 0.517381i | ||||
\(713\) | 3.07195e7 | + | 5.32078e7i | 0.0847512 | + | 0.146793i | ||||
\(714\) | 8.78908e8 | − | 5.07438e8i | 2.41462 | − | 1.39408i | ||||
\(715\) | − | 1.04934e8i | − | 0.287077i | ||||||
\(716\) | −1.09862e8 | + | 6.34288e7i | −0.299301 | + | 0.172801i | ||||
\(717\) | −1.59386e8 | + | 9.20218e7i | −0.432408 | + | 0.249651i | ||||
\(718\) | 1.98182e8 | − | 1.14421e8i | 0.535416 | − | 0.309123i | ||||
\(719\) | −6.61492e7 | + | 1.14574e8i | −0.177966 | + | 0.308247i | −0.941184 | − | 0.337895i | \(-0.890285\pi\) |
0.763217 | + | 0.646142i | \(0.223619\pi\) | |||||||
\(720\) | 4.25601e7i | 0.114026i | ||||||||
\(721\) | 7.72459e8 | + | 4.45979e8i | 2.06096 | + | 1.18990i | ||||
\(722\) | 2.78400e8 | − | 1.60734e8i | 0.739702 | − | 0.427067i | ||||
\(723\) | −5.88874e8 | −1.55814 | ||||||||
\(724\) | 4.73718e7 | + | 8.20504e7i | 0.124826 | + | 0.216205i | ||||
\(725\) | 3.68993e8 | + | 2.13038e8i | 0.968287 | + | 0.559041i | ||||
\(726\) | 1.40237e8 | − | 2.42898e8i | 0.366482 | − | 0.634766i | ||||
\(727\) | − | 8.29080e7i | − | 0.215771i | −0.994163 | − | 0.107885i | \(-0.965592\pi\) | ||
0.994163 | − | 0.107885i | \(-0.0344080\pi\) | |||||||
\(728\) | −4.19963e8 | + | 7.27397e8i | −1.08847 | + | 1.88529i | ||||
\(729\) | 3.98068e7 | 0.102748 | ||||||||
\(730\) | − | 3.54851e7i | − | 0.0912172i | ||||||
\(731\) | −1.83581e8 | − | 7.11585e8i | −0.469976 | − | 1.82169i | ||||
\(732\) | −1.43416e8 | −0.365649 | ||||||||
\(733\) | − | 1.96454e8i | − | 0.498827i | −0.968397 | − | 0.249413i | \(-0.919762\pi\) | ||
0.968397 | − | 0.249413i | \(-0.0802378\pi\) | |||||||
\(734\) | 1.95149e8 | + | 1.12669e8i | 0.493490 | + | 0.284917i | ||||
\(735\) | 2.77269e8 | 0.698294 | ||||||||
\(736\) | −5.30487e7 | − | 3.06277e7i | −0.133058 | − | 0.0768211i | ||||
\(737\) | −1.02767e8 | + | 1.77997e8i | −0.256714 | + | 0.444641i | ||||
\(738\) | −2.71905e8 | + | 1.56984e8i | −0.676468 | + | 0.390559i | ||||
\(739\) | − | 2.13462e8i | − | 0.528916i | −0.964397 | − | 0.264458i | \(-0.914807\pi\) | ||
0.964397 | − | 0.264458i | \(-0.0851931\pi\) | |||||||
\(740\) | −1.60358e7 | − | 2.77749e7i | −0.0395728 | − | 0.0685420i | ||||
\(741\) | −4.95366e8 | + | 8.57998e8i | −1.21751 | + | 2.10878i | ||||
\(742\) | −5.05255e8 | −1.23680 | ||||||||
\(743\) | −6.05847e8 | − | 3.49786e8i | −1.47706 | − | 0.852778i | −0.477391 | − | 0.878691i | \(-0.658418\pi\) |
−0.999664 | + | 0.0259125i | \(0.991751\pi\) | |||||||
\(744\) | −2.31104e8 | − | 4.00283e8i | −0.561162 | − | 0.971960i | ||||
\(745\) | 1.09443e8 | + | 1.89561e8i | 0.264679 | + | 0.458437i | ||||
\(746\) | −7.89630e6 | − | 1.36768e7i | −0.0190199 | − | 0.0329434i | ||||
\(747\) | 1.88363e8 | 0.451892 | ||||||||
\(748\) | 7.88907e7 | + | 1.36643e8i | 0.188504 | + | 0.326499i | ||||
\(749\) | 6.15508e8 | − | 3.55364e8i | 1.46483 | − | 0.845722i | ||||
\(750\) | −2.79684e8 | − | 1.61476e8i | −0.662954 | − | 0.382757i | ||||
\(751\) | −2.45634e8 | − | 1.41817e8i | −0.579920 | − | 0.334817i | 0.181181 | − | 0.983450i | \(-0.442008\pi\) |
−0.761102 | + | 0.648632i | \(0.775341\pi\) | |||||||
\(752\) | −1.11871e8 | −0.263066 | ||||||||
\(753\) | 4.21736e8i | 0.987769i | ||||||||
\(754\) | −3.02806e8 | + | 5.24475e8i | −0.706399 | + | 1.22352i | ||||
\(755\) | −1.54430e8 | + | 2.67480e8i | −0.358831 | + | 0.621513i | ||||
\(756\) | −6.59447e7 | − | 1.14220e8i | −0.152621 | − | 0.264348i | ||||
\(757\) | 7.03780e7 | − | 4.06328e7i | 0.162237 | − | 0.0936675i | −0.416683 | − | 0.909052i | \(-0.636808\pi\) |
0.578920 | + | 0.815384i | \(0.303474\pi\) | |||||||
\(758\) | 1.56360e8i | 0.359020i | ||||||||
\(759\) | −4.98607e7 | + | 2.87871e7i | −0.114034 | + | 0.0658374i | ||||
\(760\) | 2.57072e8 | − | 1.48421e8i | 0.585617 | − | 0.338106i | ||||
\(761\) | −3.43132e8 | + | 1.98107e8i | −0.778587 | + | 0.449518i | −0.835929 | − | 0.548837i | \(-0.815071\pi\) |
0.0573420 | + | 0.998355i | \(0.481737\pi\) | |||||||
\(762\) | 7.55801e7 | − | 1.30909e8i | 0.170821 | − | 0.295872i | ||||
\(763\) | 2.22163e7i | 0.0500148i | ||||||||
\(764\) | 3.93317e7 | + | 2.27082e7i | 0.0881987 | + | 0.0509216i | ||||
\(765\) | 1.88057e8 | − | 1.08575e8i | 0.420055 | − | 0.242519i | ||||
\(766\) | 4.11193e8 | 0.914869 | ||||||||
\(767\) | −1.81834e8 | − | 3.14946e8i | −0.402985 | − | 0.697991i | ||||
\(768\) | 4.86581e8 | + | 2.80927e8i | 1.07417 | + | 0.620170i | ||||
\(769\) | −3.29301e8 | + | 5.70366e8i | −0.724126 | + | 1.25422i | 0.235207 | + | 0.971945i | \(0.424423\pi\) |
−0.959333 | + | 0.282277i | \(0.908910\pi\) | |||||||
\(770\) | − | 1.15635e8i | − | 0.253288i | ||||||
\(771\) | 3.02550e8 | − | 5.24032e8i | 0.660136 | − | 1.14339i | ||||
\(772\) | −2.30446e7 | −0.0500860 | ||||||||
\(773\) | − | 8.12844e8i | − | 1.75982i | −0.475139 | − | 0.879911i | \(-0.657602\pi\) | ||
0.475139 | − | 0.879911i | \(-0.342398\pi\) | |||||||
\(774\) | −2.08701e8 | + | 5.38426e7i | −0.450093 | + | 0.116119i | ||||
\(775\) | 3.10415e8 | 0.666864 | ||||||||
\(776\) | − | 6.96203e8i | − | 1.48988i | ||||||
\(777\) | 3.58351e8 | + | 2.06894e8i | 0.763915 | + | 0.441047i | ||||
\(778\) | −2.63388e8 | −0.559316 | ||||||||
\(779\) | 9.97314e8 | + | 5.75800e8i | 2.10970 | + | 1.21803i | ||||
\(780\) | −6.83467e7 | + | 1.18380e8i | −0.144024 | + | 0.249456i | ||||
\(781\) | 9.69352e7 | − | 5.59656e7i | 0.203483 | − | 0.117481i | ||||
\(782\) | − | 1.44522e8i | − | 0.302214i | ||||||
\(783\) | −1.66796e8 | − | 2.88899e8i | −0.347457 | − | 0.601813i | ||||
\(784\) | −1.36810e8 | + | 2.36963e8i | −0.283904 | + | 0.491736i | ||||
\(785\) | 2.23144e8 | 0.461293 | ||||||||
\(786\) | −4.26186e8 | − | 2.46059e8i | −0.877671 | − | 0.506724i | ||||
\(787\) | 4.21700e8 | + | 7.30406e8i | 0.865127 | + | 1.49844i | 0.866921 | + | 0.498445i | \(0.166095\pi\) |
−0.00179452 | + | 0.999998i | \(0.500571\pi\) | |||||||
\(788\) | 1.53668e6 | + | 2.66162e6i | 0.00314055 | + | 0.00543960i | ||||
\(789\) | −2.40792e8 | − | 4.17063e8i | −0.490242 | − | 0.849124i | ||||
\(790\) | 2.84498e7 | 0.0577029 | ||||||||
\(791\) | −3.51872e8 | − | 6.09459e8i | −0.710976 | − | 1.23145i | ||||
\(792\) | 1.40585e8 | − | 8.11666e7i | 0.282984 | − | 0.163381i | ||||
\(793\) | 4.15905e8 | + | 2.40123e8i | 0.834016 | + | 0.481519i | ||||
\(794\) | 3.36857e8 | + | 1.94485e8i | 0.672953 | + | 0.388529i | ||||
\(795\) | −2.88450e8 | −0.574076 | ||||||||
\(796\) | 1.59006e8i | 0.315264i | ||||||||
\(797\) | 3.66849e8 | − | 6.35400e8i | 0.724623 | − | 1.25508i | −0.234507 | − | 0.972115i | \(-0.575347\pi\) |
0.959129 | − | 0.282969i | \(-0.0913193\pi\) | |||||||
\(798\) | −5.45880e8 | + | 9.45491e8i | −1.07421 | + | 1.86058i | ||||
\(799\) | 2.85394e8 | + | 4.94317e8i | 0.559506 | + | 0.969093i | ||||
\(800\) | −2.68023e8 | + | 1.54743e8i | −0.523483 | + | 0.302233i | ||||
\(801\) | 1.69695e8i | 0.330196i | ||||||||
\(802\) | −6.18667e6 | + | 3.57188e6i | −0.0119932 | + | 0.00692426i | ||||
\(803\) | −6.16418e7 | + | 3.55889e7i | −0.119050 | + | 0.0687334i | ||||
\(804\) | 2.31869e8 | − | 1.33870e8i | 0.446144 | − | 0.257582i | ||||
\(805\) | 3.51196e7 | − | 6.08289e7i | 0.0673228 | − | 0.116606i | ||||
\(806\) | 4.41214e8i | 0.842644i | ||||||||
\(807\) | −6.34862e8 | − | 3.66538e8i | −1.20798 | − | 0.697426i | ||||
\(808\) | 1.66862e8 | − | 9.63377e7i | 0.316317 | − | 0.182626i | ||||
\(809\) | −1.58094e8 | −0.298586 | −0.149293 | − | 0.988793i | \(-0.547700\pi\) | ||||
−0.149293 | + | 0.988793i | \(0.547700\pi\) | |||||||
\(810\) | 1.09892e8 | + | 1.90339e8i | 0.206781 | + | 0.358156i | ||||
\(811\) | 6.64402e8 | + | 3.83593e8i | 1.24557 | + | 0.719131i | 0.970223 | − | 0.242214i | \(-0.0778736\pi\) |
0.275348 | + | 0.961345i | \(0.411207\pi\) | |||||||
\(812\) | 2.21283e8 | − | 3.83274e8i | 0.413315 | − | 0.715882i | ||||
\(813\) | 9.38606e8i | 1.74667i | ||||||||
\(814\) | 4.85039e7 | − | 8.40112e7i | 0.0899298 | − | 0.155763i | ||||
\(815\) | 7.13440e7 | 0.131791 | ||||||||
\(816\) | 5.71770e8i | 1.05233i | ||||||||
\(817\) | 5.53776e8 | + | 5.64191e8i | 1.01547 | + | 1.03457i | ||||
\(818\) | 6.84796e8 | 1.25113 | ||||||||
\(819\) | − | 6.60984e8i | − | 1.20320i | ||||||
\(820\) | 1.37602e8 | + | 7.94444e7i | 0.249564 | + | 0.144086i | ||||
\(821\) | 4.61403e8 | 0.833779 | 0.416890 | − | 0.908957i | \(-0.363120\pi\) | ||||
0.416890 | + | 0.908957i | \(0.363120\pi\) | |||||||
\(822\) | −4.01864e8 | − | 2.32017e8i | −0.723543 | − | 0.417737i | ||||
\(823\) | −3.73048e8 | + | 6.46138e8i | −0.669214 | + | 1.15911i | 0.308910 | + | 0.951091i | \(0.400036\pi\) |
−0.978124 | + | 0.208022i | \(0.933298\pi\) | |||||||
\(824\) | −8.27540e8 | + | 4.77780e8i | −1.47913 | + | 0.853978i | ||||
\(825\) | 2.90888e8i | 0.518041i | ||||||||
\(826\) | −2.00376e8 | − | 3.47062e8i | −0.355555 | − | 0.615838i | ||||
\(827\) | −1.51546e8 | + | 2.62486e8i | −0.267935 | + | 0.464077i | −0.968328 | − | 0.249680i | \(-0.919675\pi\) |
0.700394 | + | 0.713757i | \(0.253008\pi\) | |||||||
\(828\) | 2.81091e7 | 0.0495171 | ||||||||
\(829\) | −8.42804e8 | − | 4.86593e8i | −1.47932 | − | 0.854087i | −0.479596 | − | 0.877489i | \(-0.659217\pi\) |
−0.999726 | + | 0.0234023i | \(0.992550\pi\) | |||||||
\(830\) | 7.18720e7 | + | 1.24486e8i | 0.125697 | + | 0.217714i | ||||
\(831\) | 6.36992e8 | + | 1.10330e9i | 1.11002 | + | 1.92261i | ||||
\(832\) | −3.89102e8 | − | 6.73945e8i | −0.675607 | − | 1.17019i | ||||
\(833\) | 1.39607e9 | 2.41530 | ||||||||
\(834\) | 1.81326e8 | + | 3.14066e8i | 0.312581 | + | 0.541405i | ||||
\(835\) | −2.14503e8 | + | 1.23844e8i | −0.368447 | + | 0.212723i | ||||
\(836\) | −1.46994e8 | − | 8.48672e7i | −0.251583 | − | 0.145252i | ||||
\(837\) | −2.10476e8 | − | 1.21518e8i | −0.358943 | − | 0.207236i | ||||
\(838\) | 5.77111e8 | 0.980680 | ||||||||
\(839\) | − | 5.78345e8i | − | 0.979267i | −0.871928 | − | 0.489634i | \(-0.837130\pi\) | ||
0.871928 | − | 0.489634i | \(-0.162870\pi\) | |||||||
\(840\) | −2.64206e8 | + | 4.57617e8i | −0.445763 | + | 0.772084i | ||||
\(841\) | 2.62288e8 | − | 4.54296e8i | 0.440951 | − | 0.763749i | ||||
\(842\) | −4.39128e8 | − | 7.60592e8i | −0.735622 | − | 1.27414i | ||||
\(843\) | −4.24292e8 | + | 2.44965e8i | −0.708243 | + | 0.408904i | ||||
\(844\) | − | 6.27695e7i | − | 0.104405i | ||||||
\(845\) | 1.71686e8 | − | 9.91228e7i | 0.284554 | − | 0.164287i | ||||
\(846\) | 1.44979e8 | − | 8.37035e7i | 0.239438 | − | 0.138240i | ||||
\(847\) | 5.94394e8 | − | 3.43173e8i | 0.978192 | − | 0.564759i | ||||
\(848\) | 1.42328e8 | − | 2.46519e8i | 0.233400 | − | 0.404261i | ||||
\(849\) | 1.21130e9i | 1.97938i | ||||||||
\(850\) | −6.32358e8 | − | 3.65092e8i | −1.02969 | − | 0.594491i | ||||
\(851\) | 5.10305e7 | − | 2.94625e7i | 0.0828020 | − | 0.0478058i | ||||
\(852\) | −1.45808e8 | −0.235756 | ||||||||
\(853\) | −2.77399e8 | − | 4.80469e8i | −0.446949 | − | 0.774138i | 0.551237 | − | 0.834349i | \(-0.314156\pi\) |
−0.998186 | + | 0.0602105i | \(0.980823\pi\) | |||||||
\(854\) | 4.58316e8 | + | 2.64609e8i | 0.735854 | + | 0.424845i | ||||
\(855\) | −1.16800e8 | + | 2.02304e8i | −0.186872 | + | 0.323672i | ||||
\(856\) | 7.61406e8i | 1.21393i | ||||||||
\(857\) | 2.95137e8 | − | 5.11193e8i | 0.468902 | − | 0.812162i | −0.530466 | − | 0.847706i | \(-0.677983\pi\) |
0.999368 | + | 0.0355443i | \(0.0113165\pi\) | |||||||
\(858\) | −4.13459e8 | −0.654592 | ||||||||
\(859\) | − | 4.31335e8i | − | 0.680512i | −0.940333 | − | 0.340256i | \(-0.889486\pi\) | ||
0.940333 | − | 0.340256i | \(-0.110514\pi\) | |||||||
\(860\) | 7.64058e7 | + | 7.78427e7i | 0.120124 | + | 0.122383i | ||||
\(861\) | −2.04998e9 | −3.21174 | ||||||||
\(862\) | − | 7.23677e8i | − | 1.12986i | ||||||
\(863\) | 3.79589e8 | + | 2.19156e8i | 0.590584 | + | 0.340974i | 0.765328 | − | 0.643640i | \(-0.222577\pi\) |
−0.174744 | + | 0.984614i | \(0.555910\pi\) | |||||||
\(864\) | 2.42310e8 | 0.375690 | ||||||||
\(865\) | −2.51561e8 | − | 1.45239e8i | −0.388683 | − | 0.224406i | ||||
\(866\) | −2.73902e7 | + | 4.74413e7i | −0.0421737 | + | 0.0730471i | ||||
\(867\) | 1.81264e9 | − | 1.04653e9i | 2.78134 | − | 1.60581i | ||||
\(868\) | − | 3.22429e8i | − | 0.493032i | ||||||
\(869\) | −2.85331e7 | − | 4.94207e7i | −0.0434799 | − | 0.0753095i | ||||
\(870\) | −1.90500e8 | + | 3.29955e8i | −0.289292 | + | 0.501069i | ||||
\(871\) | −8.96558e8 | −1.35683 | ||||||||
\(872\) | −2.06118e7 | − | 1.19002e7i | −0.0310861 | − | 0.0179476i | ||||
\(873\) | 2.73940e8 | + | 4.74478e8i | 0.411730 | + | 0.713137i | ||||
\(874\) | 7.77353e7 | + | 1.34641e8i | 0.116435 | + | 0.201672i | ||||
\(875\) | −3.95146e8 | − | 6.84412e8i | −0.589838 | − | 1.02163i | ||||
\(876\) | 9.27205e7 | 0.137932 | ||||||||
\(877\) | −2.96462e8 | − | 5.13487e8i | −0.439511 | − | 0.761256i | 0.558141 | − | 0.829746i | \(-0.311515\pi\) |
−0.997652 | + | 0.0684908i | \(0.978182\pi\) | |||||||
\(878\) | 3.53650e8 | − | 2.04180e8i | 0.522505 | − | 0.301668i | ||||
\(879\) | −9.32916e8 | − | 5.38619e8i | −1.37365 | − | 0.793077i | ||||
\(880\) | 5.64191e7 | + | 3.25736e7i | 0.0827901 | + | 0.0477989i | ||||
\(881\) | −8.21570e8 | −1.20148 | −0.600741 | − | 0.799444i | \(-0.705128\pi\) | ||||
−0.600741 | + | 0.799444i | \(0.705128\pi\) | |||||||
\(882\) | − | 4.09453e8i | − | 0.596758i | ||||||
\(883\) | −5.90051e8 | + | 1.02200e9i | −0.857053 | + | 1.48446i | 0.0176742 | + | 0.999844i | \(0.494374\pi\) |
−0.874727 | + | 0.484616i | \(0.838960\pi\) | |||||||
\(884\) | −3.44130e8 | + | 5.96051e8i | −0.498157 | + | 0.862833i | ||||
\(885\) | −1.14395e8 | − | 1.98137e8i | −0.165035 | − | 0.285849i | ||||
\(886\) | −6.03703e8 | + | 3.48548e8i | −0.868004 | + | 0.501143i | ||||
\(887\) | 2.67958e8i | 0.383968i | 0.981398 | + | 0.191984i | \(0.0614922\pi\) | ||||
−0.981398 | + | 0.191984i | \(0.938508\pi\) | |||||||
\(888\) | −3.83903e8 | + | 2.21647e8i | −0.548255 | + | 0.316535i | ||||
\(889\) | 3.20346e8 | − | 1.84952e8i | 0.455946 | − | 0.263241i | ||||
\(890\) | −1.12149e8 | + | 6.47490e7i | −0.159083 | + | 0.0918466i | ||||
\(891\) | 2.20427e8 | − | 3.81791e8i | 0.311625 | − | 0.539750i | ||||
\(892\) | 4.83236e8i | 0.680870i | ||||||||
\(893\) | −5.31765e8 | − | 3.07015e8i | −0.746733 | − | 0.431127i | ||||
\(894\) | 7.46904e8 | − | 4.31225e8i | 1.04533 | − | 0.603520i | ||||
\(895\) | 2.67247e8 | 0.372772 | ||||||||
\(896\) | −2.56718e7 | − | 4.44649e7i | −0.0356889 | − | 0.0618149i | ||||
\(897\) | −2.17498e8 | − | 1.25573e8i | −0.301355 | − | 0.173987i | ||||
\(898\) | 4.75356e8 | − | 8.23340e8i | 0.656432 | − | 1.13697i | ||||
\(899\) | − | 8.15530e8i | − | 1.12243i | ||||||
\(900\) | 7.10092e7 | − | 1.22992e8i | 0.0974063 | − | 0.168713i | ||||
\(901\) | −1.45236e9 | −1.98564 | ||||||||
\(902\) | 4.80594e8i | 0.654876i | ||||||||
\(903\) | −1.35588e9 | − | 3.76878e8i | −1.84144 | − | 0.511845i | ||||
\(904\) | 7.53924e8 | 1.02052 | ||||||||
\(905\) | − | 1.99594e8i | − | 0.269278i | ||||||
\(906\) | 1.05392e9 | + | 6.08481e8i | 1.41717 | + | 0.818206i | ||||
\(907\) | 6.86645e8 | 0.920260 | 0.460130 | − | 0.887852i | \(-0.347803\pi\) | ||||
0.460130 | + | 0.887852i | \(0.347803\pi\) | |||||||
\(908\) | −9.51135e7 | − | 5.49138e7i | −0.127053 | − | 0.0733540i | ||||
\(909\) | −7.58134e7 | + | 1.31313e8i | −0.100938 | + | 0.174830i | ||||
\(910\) | 4.36833e8 | − | 2.52205e8i | 0.579683 | − | 0.334680i | ||||
\(911\) | 6.73501e8i | 0.890806i | 0.895330 | + | 0.445403i | \(0.146940\pi\) | ||||
−0.895330 | + | 0.445403i | \(0.853060\pi\) | |||||||
\(912\) | −3.07543e8 | − | 5.32679e8i | −0.405435 | − | 0.702233i | ||||
\(913\) | 1.44165e8 | − | 2.49701e8i | 0.189429 | − | 0.328101i | ||||
\(914\) | 1.02000e8 | 0.133587 | ||||||||
\(915\) | 2.61652e8 | + | 1.51065e8i | 0.341556 | + | 0.197197i | ||||
\(916\) | −2.91156e8 | − | 5.04297e8i | −0.378825 | − | 0.656145i | ||||
\(917\) | −6.02129e8 | − | 1.04292e9i | −0.780875 | − | 1.35252i | ||||
\(918\) | 2.85845e8 | + | 4.95098e8i | 0.369490 | + | 0.639976i | ||||
\(919\) | 8.89840e8 | 1.14648 | 0.573239 | − | 0.819388i | \(-0.305687\pi\) | ||||
0.573239 | + | 0.819388i | \(0.305687\pi\) | |||||||
\(920\) | 3.76238e7 | + | 6.51664e7i | 0.0483170 | + | 0.0836874i | ||||
\(921\) | 3.57628e8 | − | 2.06477e8i | 0.457776 | − | 0.264297i | ||||
\(922\) | 4.50855e8 | + | 2.60301e8i | 0.575233 | + | 0.332111i | ||||
\(923\) | 4.22842e8 | + | 2.44128e8i | 0.537741 | + | 0.310465i | ||||
\(924\) | 3.02147e8 | 0.383003 | ||||||||
\(925\) | − | 2.97712e8i | − | 0.376159i | ||||||
\(926\) | 6.20950e7 | − | 1.07552e8i | 0.0782031 | − | 0.135452i | ||||
\(927\) | 3.75991e8 | − | 6.51236e8i | 0.471996 | − | 0.817522i | ||||
\(928\) | 4.06546e8 | + | 7.04158e8i | 0.508705 | + | 0.881102i | ||||
\(929\) | 1.01846e9 | − | 5.88008e8i | 1.27027 | − | 0.733392i | 0.295233 | − | 0.955425i | \(-0.404603\pi\) |
0.975039 | + | 0.222034i | \(0.0712695\pi\) | |||||||
\(930\) | 2.77575e8i | 0.345089i | ||||||||
\(931\) | −1.30062e9 | + | 7.50913e8i | −1.61176 | + | 0.930552i | ||||
\(932\) | 6.80854e7 | − | 3.93091e7i | 0.0841019 | − | 0.0485563i | ||||
\(933\) | 1.30394e9 | − | 7.52832e8i | 1.60551 | − | 0.926943i | ||||
\(934\) | −3.82416e7 | + | 6.62364e7i | −0.0469349 | + | 0.0812936i | ||||
\(935\) | − | 3.32393e8i | − | 0.406647i | ||||||
\(936\) | 6.13246e8 | + | 3.54058e8i | 0.747838 | + | 0.431764i | ||||
\(937\) | 2.17673e8 | − | 1.25674e8i | 0.264598 | − | 0.152766i | −0.361832 | − | 0.932243i | \(-0.617849\pi\) |
0.626430 | + | 0.779478i | \(0.284515\pi\) | |||||||
\(938\) | −9.87984e8 | −1.19713 | ||||||||
\(939\) | 4.23330e8 | + | 7.33229e8i | 0.511307 | + | 0.885611i | ||||
\(940\) | −7.33689e7 | − | 4.23595e7i | −0.0883341 | − | 0.0509997i | ||||
\(941\) | 1.42007e8 | − | 2.45963e8i | 0.170428 | − | 0.295190i | −0.768142 | − | 0.640280i | \(-0.778818\pi\) |
0.938570 | + | 0.345090i | \(0.112152\pi\) | |||||||
\(942\) | − | 8.79230e8i | − | 1.05184i | ||||||
\(943\) | −1.45962e8 | + | 2.52814e8i | −0.174063 | + | 0.301485i | ||||
\(944\) | 2.25780e8 | 0.268391 | ||||||||
\(945\) | 2.77847e8i | 0.329239i | ||||||||
\(946\) | −8.83549e7 | + | 3.17870e8i | −0.104366 | + | 0.375471i | ||||
\(947\) | −8.92411e8 | −1.05079 | −0.525394 | − | 0.850859i | \(-0.676082\pi\) | ||||
−0.525394 | + | 0.850859i | \(0.676082\pi\) | |||||||
\(948\) | 7.43378e7i | 0.0872538i | ||||||||
\(949\) | −2.68888e8 | − | 1.55243e8i | −0.314611 | − | 0.181641i | ||||
\(950\) | 7.85500e8 | 0.916169 | ||||||||
\(951\) | −2.41960e8 | − | 1.39695e8i | −0.281320 | − | 0.162420i | ||||
\(952\) | −1.33029e9 | + | 2.30413e9i | −1.54183 | + | 2.67053i | ||||
\(953\) | 1.15087e9 | − | 6.64455e8i | 1.32968 | − | 0.767691i | 0.344430 | − | 0.938812i | \(-0.388072\pi\) |
0.985250 | + | 0.171121i | \(0.0547388\pi\) | |||||||
\(954\) | 4.25965e8i | 0.490601i | ||||||||
\(955\) | −4.78386e7 | − | 8.28588e7i | −0.0549247 | − | 0.0951324i | ||||
\(956\) | 6.87704e7 | − | 1.19114e8i | 0.0787097 | − | 0.136329i | ||||
\(957\) | 7.64229e8 | 0.871943 | ||||||||
\(958\) | 8.03951e7 | + | 4.64161e7i | 0.0914394 | + | 0.0527925i | ||||
\(959\) | −5.67766e8 | − | 9.83400e8i | −0.643745 | − | 1.11500i | ||||
\(960\) | −2.44791e8 | − | 4.23990e8i | −0.276682 | − | 0.479227i | ||||
\(961\) | 1.46677e8 | + | 2.54053e8i | 0.165270 | + | 0.286255i | ||||
\(962\) | 4.23159e8 | 0.475312 | ||||||||
\(963\) | −2.99596e8 | − | 5.18916e8i | −0.335473 | − | 0.581056i | ||||
\(964\) | 3.81122e8 | − | 2.20041e8i | 0.425435 | − | 0.245625i | ||||
\(965\) | 4.20432e7 | + | 2.42736e7i | 0.0467857 | + | 0.0270118i | ||||
\(966\) | −2.39677e8 | − | 1.38378e8i | −0.265886 | − | 0.153509i | ||||
\(967\) | −5.44142e8 | −0.601773 | −0.300886 | − | 0.953660i | \(-0.597282\pi\) | ||||
−0.300886 | + | 0.953660i | \(0.597282\pi\) | |||||||
\(968\) | 7.35287e8i | 0.810646i | ||||||||
\(969\) | −1.56914e9 | + | 2.71783e9i | −1.72461 | + | 2.98711i | ||||
\(970\) | −2.09049e8 | + | 3.62084e8i | −0.229052 | + | 0.396729i | ||||
\(971\) | 1.69262e8 | + | 2.93171e8i | 0.184886 | + | 0.320231i | 0.943538 | − | 0.331264i | \(-0.107475\pi\) |
−0.758652 | + | 0.651496i | \(0.774142\pi\) | |||||||
\(972\) | −3.36708e8 | + | 1.94399e8i | −0.366653 | + | 0.211687i | ||||
\(973\) | 8.87443e8i | 0.963390i | ||||||||
\(974\) | 7.52731e8 | − | 4.34589e8i | 0.814634 | − | 0.470329i | ||||
\(975\) | −1.09889e9 | + | 6.34444e8i | −1.18560 | + | 0.684509i | ||||
\(976\) | −2.58210e8 | + | 1.49078e8i | −0.277731 | + | 0.160348i | ||||
\(977\) | −3.32161e8 | + | 5.75320e8i | −0.356177 | + | 0.616916i | −0.987319 | − | 0.158751i | \(-0.949253\pi\) |
0.631142 | + | 0.775667i | \(0.282587\pi\) | |||||||
\(978\) | − | 2.81109e8i | − | 0.300509i | ||||||
\(979\) | 2.24954e8 | + | 1.29877e8i | 0.239742 | + | 0.138415i | ||||
\(980\) | −1.79449e8 | + | 1.03605e8i | −0.190662 | + | 0.110079i | ||||
\(981\) | 1.87299e7 | 0.0198394 | ||||||||
\(982\) | −3.78222e8 | − | 6.55099e8i | −0.399404 | − | 0.691787i | ||||
\(983\) | 1.31731e9 | + | 7.60548e8i | 1.38684 | + | 0.800693i | 0.992958 | − | 0.118467i | \(-0.0377981\pi\) |
0.393883 | + | 0.919161i | \(0.371131\pi\) | |||||||
\(984\) | 1.09808e9 | − | 1.90193e9i | 1.15252 | − | 1.99622i | ||||
\(985\) | − | 6.47457e6i | − | 0.00677489i | ||||||
\(986\) | −9.59179e8 | + | 1.66135e9i | −1.00062 | + | 1.73312i | ||||
\(987\) | 1.09304e9 | 1.13680 | ||||||||
\(988\) | − | 7.40401e8i | − | 0.767708i | ||||||
\(989\) | −1.43020e8 | + | 1.40379e8i | −0.147845 | + | 0.145116i | ||||
\(990\) | −9.74879e7 | −0.100472 | ||||||||
\(991\) | − | 5.07385e8i | − | 0.521335i | −0.965429 | − | 0.260667i | \(-0.916057\pi\) | ||
0.965429 | − | 0.260667i | \(-0.0839426\pi\) | |||||||
\(992\) | 5.13010e8 | + | 2.96186e8i | 0.525522 | + | 0.303410i | ||||
\(993\) | 1.55873e8 | 0.159193 | ||||||||
\(994\) | 4.65961e8 | + | 2.69023e8i | 0.474450 | + | 0.273924i | ||||
\(995\) | 1.67487e8 | − | 2.90095e8i | 0.170024 | − | 0.294491i | ||||
\(996\) | −3.25275e8 | + | 1.87798e8i | −0.329210 | + | 0.190069i | ||||
\(997\) | − | 6.58672e7i | − | 0.0664636i | −0.999448 | − | 0.0332318i | \(-0.989420\pi\) | ||
0.999448 | − | 0.0332318i | \(-0.0105800\pi\) | |||||||
\(998\) | −5.82089e8 | − | 1.00821e9i | −0.585595 | − | 1.01428i | ||||
\(999\) | −1.16546e8 | + | 2.01863e8i | −0.116896 | + | 0.202470i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.7.d.a.37.8 | yes | 42 | |
43.7 | odd | 6 | inner | 43.7.d.a.7.14 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.14 | ✓ | 42 | 43.7 | odd | 6 | inner | |
43.7.d.a.37.8 | yes | 42 | 1.1 | even | 1 | trivial |