Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.7.c.a.31.1 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.80071 | + | 1.77450i | −0.975089 | + | 0.221812i | ||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | 57.7023 | − | 27.6847i | 0.901599 | − | 0.432574i | ||||
\(5\) | 55.9017 | 0.447214 | ||||||||
\(6\) | −27.6617 | − | 121.601i | −0.128063 | − | 0.562968i | ||||
\(7\) | − | 264.480i | − | 0.771079i | −0.922691 | − | 0.385539i | \(-0.874015\pi\) | ||
0.922691 | − | 0.385539i | \(-0.125985\pi\) | |||||||
\(8\) | −400.993 | + | 318.353i | −0.783189 | + | 0.621784i | ||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | −436.073 | + | 99.1975i | −0.436073 | + | 0.0991975i | ||||
\(11\) | 29.4629i | 0.0221359i | 0.999939 | + | 0.0110680i | \(0.00352312\pi\) | ||||
−0.999939 | + | 0.0110680i | \(0.996477\pi\) | |||||||
\(12\) | 431.562 | + | 899.490i | 0.249747 | + | 0.520538i | ||||
\(13\) | −2759.92 | −1.25622 | −0.628112 | − | 0.778123i | \(-0.716172\pi\) | ||||
−0.628112 | + | 0.778123i | \(0.716172\pi\) | |||||||
\(14\) | 469.319 | + | 2063.13i | 0.171035 | + | 0.751870i | ||||
\(15\) | 871.421i | 0.258199i | ||||||||
\(16\) | 2563.11 | − | 3194.95i | 0.625760 | − | 0.780016i | ||||
\(17\) | 1562.12 | 0.317955 | 0.158978 | − | 0.987282i | \(-0.449180\pi\) | ||||
0.158978 | + | 0.987282i | \(0.449180\pi\) | |||||||
\(18\) | 1895.57 | − | 431.203i | 0.325030 | − | 0.0739375i | ||||
\(19\) | − | 7299.42i | − | 1.06421i | −0.846678 | − | 0.532105i | \(-0.821401\pi\) | ||
0.846678 | − | 0.532105i | \(-0.178599\pi\) | |||||||
\(20\) | 3225.66 | − | 1547.62i | 0.403207 | − | 0.193453i | ||||
\(21\) | 4122.83 | 0.445182 | ||||||||
\(22\) | −52.2820 | − | 229.832i | −0.00491003 | − | 0.0215845i | ||||
\(23\) | − | 16832.0i | − | 1.38341i | −0.722179 | − | 0.691706i | \(-0.756859\pi\) | ||
0.722179 | − | 0.691706i | \(-0.243141\pi\) | |||||||
\(24\) | −4962.64 | − | 6250.86i | −0.358987 | − | 0.452174i | ||||
\(25\) | 3125.00 | 0.200000 | ||||||||
\(26\) | 21529.4 | − | 4897.48i | 1.22493 | − | 0.278646i | ||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | −7322.05 | − | 15261.1i | −0.333548 | − | 0.695203i | ||||
\(29\) | 36225.1 | 1.48531 | 0.742653 | − | 0.669676i | \(-0.233567\pi\) | ||||
0.742653 | + | 0.669676i | \(0.233567\pi\) | |||||||
\(30\) | −1546.34 | − | 6797.71i | −0.0572717 | − | 0.251767i | ||||
\(31\) | − | 45432.8i | − | 1.52505i | −0.646959 | − | 0.762525i | \(-0.723959\pi\) | ||
0.646959 | − | 0.762525i | \(-0.276041\pi\) | |||||||
\(32\) | −14324.7 | + | 29471.1i | −0.437154 | + | 0.899386i | ||||
\(33\) | −459.282 | −0.0127802 | ||||||||
\(34\) | −12185.6 | + | 2771.97i | −0.310035 | + | 0.0705265i | ||||
\(35\) | − | 14784.9i | − | 0.344837i | ||||||
\(36\) | −14021.7 | + | 6727.39i | −0.300533 | + | 0.144191i | ||||
\(37\) | −40535.5 | −0.800258 | −0.400129 | − | 0.916459i | \(-0.631035\pi\) | ||||
−0.400129 | + | 0.916459i | \(0.631035\pi\) | |||||||
\(38\) | 12952.8 | + | 56940.7i | 0.236055 | + | 1.03770i | ||||
\(39\) | − | 43023.0i | − | 0.725281i | ||||||
\(40\) | −22416.2 | + | 17796.5i | −0.350253 | + | 0.278070i | ||||
\(41\) | 54626.1 | 0.792590 | 0.396295 | − | 0.918123i | \(-0.370296\pi\) | ||||
0.396295 | + | 0.918123i | \(0.370296\pi\) | |||||||
\(42\) | −32161.1 | + | 7315.97i | −0.434093 | + | 0.0987470i | ||||
\(43\) | − | 53952.0i | − | 0.678582i | −0.940681 | − | 0.339291i | \(-0.889813\pi\) | ||
0.940681 | − | 0.339291i | \(-0.110187\pi\) | |||||||
\(44\) | 815.673 | + | 1700.08i | 0.00957543 | + | 0.0199577i | ||||
\(45\) | −13584.1 | −0.149071 | ||||||||
\(46\) | 29868.3 | + | 131301.i | 0.306858 | + | 1.34895i | ||||
\(47\) | 112919.i | 1.08761i | 0.839213 | + | 0.543803i | \(0.183016\pi\) | ||||
−0.839213 | + | 0.543803i | \(0.816984\pi\) | |||||||
\(48\) | 49804.3 | + | 39955.0i | 0.450342 | + | 0.361283i | ||||
\(49\) | 47699.4 | 0.405438 | ||||||||
\(50\) | −24377.2 | + | 5545.31i | −0.195018 | + | 0.0443625i | ||||
\(51\) | 24351.0i | 0.183572i | ||||||||
\(52\) | −159254. | + | 76407.7i | −1.13261 | + | 0.543410i | ||||
\(53\) | −78155.8 | −0.524969 | −0.262484 | − | 0.964936i | \(-0.584542\pi\) | ||||
−0.262484 | + | 0.964936i | \(0.584542\pi\) | |||||||
\(54\) | 6721.79 | + | 29549.1i | 0.0426878 | + | 0.187656i | ||||
\(55\) | 1647.03i | 0.00989949i | ||||||||
\(56\) | 84198.1 | + | 106055.i | 0.479444 | + | 0.603900i | ||||
\(57\) | 113787. | 0.614422 | ||||||||
\(58\) | −282582. | + | 64281.5i | −1.44831 | + | 0.329459i | ||||
\(59\) | − | 267725.i | − | 1.30357i | −0.758406 | − | 0.651783i | \(-0.774021\pi\) | ||
0.758406 | − | 0.651783i | \(-0.225979\pi\) | |||||||
\(60\) | 24125.1 | + | 50283.0i | 0.111690 | + | 0.232792i | ||||
\(61\) | −353443. | −1.55715 | −0.778575 | − | 0.627552i | \(-0.784057\pi\) | ||||
−0.778575 | + | 0.627552i | \(0.784057\pi\) | |||||||
\(62\) | 80620.4 | + | 354408.i | 0.338275 | + | 1.48706i | ||||
\(63\) | 64268.6i | 0.257026i | ||||||||
\(64\) | 59446.3 | − | 255315.i | 0.226770 | − | 0.973948i | ||||
\(65\) | −154284. | −0.561800 | ||||||||
\(66\) | 3582.73 | − | 814.995i | 0.0124618 | − | 0.00283480i | ||||
\(67\) | − | 203409.i | − | 0.676310i | −0.941090 | − | 0.338155i | \(-0.890197\pi\) | ||
0.941090 | − | 0.338155i | \(-0.109803\pi\) | |||||||
\(68\) | 90137.6 | − | 43246.7i | 0.286668 | − | 0.137539i | ||||
\(69\) | 262385. | 0.798713 | ||||||||
\(70\) | 26235.8 | + | 115333.i | 0.0764891 | + | 0.336247i | ||||
\(71\) | 51657.2i | 0.144330i | 0.997393 | + | 0.0721649i | \(0.0229908\pi\) | ||||
−0.997393 | + | 0.0721649i | \(0.977009\pi\) | |||||||
\(72\) | 97441.2 | − | 77359.9i | 0.261063 | − | 0.207261i | ||||
\(73\) | 221763. | 0.570059 | 0.285030 | − | 0.958519i | \(-0.407997\pi\) | ||||
0.285030 | + | 0.958519i | \(0.407997\pi\) | |||||||
\(74\) | 316206. | − | 71930.2i | 0.780323 | − | 0.177507i | ||||
\(75\) | 48713.9i | 0.115470i | ||||||||
\(76\) | −202083. | − | 421193.i | −0.460350 | − | 0.959491i | ||||
\(77\) | 7792.35 | 0.0170685 | ||||||||
\(78\) | 76344.2 | + | 335610.i | 0.160876 | + | 0.707214i | ||||
\(79\) | − | 540997.i | − | 1.09727i | −0.836062 | − | 0.548635i | \(-0.815148\pi\) | ||
0.836062 | − | 0.548635i | \(-0.184852\pi\) | |||||||
\(80\) | 143282. | − | 178603.i | 0.279848 | − | 0.348834i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −426123. | + | 96934.0i | −0.772846 | + | 0.175806i | ||||
\(83\) | − | 264246.i | − | 0.462141i | −0.972937 | − | 0.231070i | \(-0.925777\pi\) | ||
0.972937 | − | 0.231070i | \(-0.0742228\pi\) | |||||||
\(84\) | 237897. | − | 114140.i | 0.401376 | − | 0.192574i | ||||
\(85\) | 87324.9 | 0.142194 | ||||||||
\(86\) | 95737.8 | + | 420864.i | 0.150518 | + | 0.661678i | ||||
\(87\) | 564694.i | 0.857542i | ||||||||
\(88\) | −9379.62 | − | 11814.4i | −0.0137638 | − | 0.0173366i | ||||
\(89\) | 314597. | 0.446257 | 0.223128 | − | 0.974789i | \(-0.428373\pi\) | ||||
0.223128 | + | 0.974789i | \(0.428373\pi\) | |||||||
\(90\) | 105966. | − | 24105.0i | 0.145358 | − | 0.0330658i | ||||
\(91\) | 729945.i | 0.968647i | ||||||||
\(92\) | −465989. | − | 971244.i | −0.598428 | − | 1.24728i | ||||
\(93\) | 708227. | 0.880488 | ||||||||
\(94\) | −200374. | − | 880846.i | −0.241245 | − | 1.06051i | ||||
\(95\) | − | 408050.i | − | 0.475930i | ||||||
\(96\) | −459409. | − | 223300.i | −0.519261 | − | 0.252391i | ||||
\(97\) | −155146. | −0.169990 | −0.0849952 | − | 0.996381i | \(-0.527087\pi\) | ||||
−0.0849952 | + | 0.996381i | \(0.527087\pi\) | |||||||
\(98\) | −372089. | + | 84642.5i | −0.395338 | + | 0.0899312i | ||||
\(99\) | − | 7159.49i | − | 0.00737865i | ||||||
\(100\) | 180320. | − | 86514.8i | 0.180320 | − | 0.0865148i | ||||
\(101\) | −1.55143e6 | −1.50580 | −0.752902 | − | 0.658133i | \(-0.771347\pi\) | ||||
−0.752902 | + | 0.658133i | \(0.771347\pi\) | |||||||
\(102\) | −43210.8 | − | 189955.i | −0.0407185 | − | 0.178999i | ||||
\(103\) | 1.69380e6i | 1.55007i | 0.631920 | + | 0.775033i | \(0.282267\pi\) | ||||
−0.631920 | + | 0.775033i | \(0.717733\pi\) | |||||||
\(104\) | 1.10671e6 | − | 878631.i | 0.983861 | − | 0.781100i | ||||
\(105\) | 230473. | 0.199092 | ||||||||
\(106\) | 609671. | − | 138687.i | 0.511892 | − | 0.116445i | ||||
\(107\) | 1.31304e6i | 1.07183i | 0.844271 | + | 0.535916i | \(0.180034\pi\) | ||||
−0.844271 | + | 0.535916i | \(0.819966\pi\) | |||||||
\(108\) | −104870. | − | 218576.i | −0.0832489 | − | 0.173513i | ||||
\(109\) | −150713. | −0.116378 | −0.0581889 | − | 0.998306i | \(-0.518533\pi\) | ||||
−0.0581889 | + | 0.998306i | \(0.518533\pi\) | |||||||
\(110\) | −2922.65 | − | 12848.0i | −0.00219583 | − | 0.00965289i | ||||
\(111\) | − | 631885.i | − | 0.462029i | ||||||
\(112\) | −844999. | − | 677892.i | −0.601454 | − | 0.482510i | ||||
\(113\) | −1.70784e6 | −1.18362 | −0.591811 | − | 0.806077i | \(-0.701587\pi\) | ||||
−0.591811 | + | 0.806077i | \(0.701587\pi\) | |||||||
\(114\) | −887618. | + | 201914.i | −0.599117 | + | 0.136287i | ||||
\(115\) | − | 940936.i | − | 0.618681i | ||||||
\(116\) | 2.09027e6 | − | 1.00288e6i | 1.33915 | − | 0.642505i | ||||
\(117\) | 670662. | 0.418741 | ||||||||
\(118\) | 475078. | + | 2.08845e6i | 0.289147 | + | 1.27109i | ||||
\(119\) | − | 413148.i | − | 0.245169i | ||||||
\(120\) | −277420. | − | 349434.i | −0.160544 | − | 0.202218i | ||||
\(121\) | 1.77069e6 | 0.999510 | ||||||||
\(122\) | 2.75711e6 | − | 627185.i | 1.51836 | − | 0.345395i | ||||
\(123\) | 851536.i | 0.457602i | ||||||||
\(124\) | −1.25779e6 | − | 2.62158e6i | −0.659697 | − | 1.37498i | ||||
\(125\) | 174693. | 0.0894427 | ||||||||
\(126\) | −114045. | − | 501341.i | −0.0570116 | − | 0.250623i | ||||
\(127\) | − | 471582.i | − | 0.230222i | −0.993353 | − | 0.115111i | \(-0.963278\pi\) | ||
0.993353 | − | 0.115111i | \(-0.0367223\pi\) | |||||||
\(128\) | −10667.6 | + | 2.09712e6i | −0.00508672 | + | 0.999987i | ||||
\(129\) | 841029. | 0.391779 | ||||||||
\(130\) | 1.20353e6 | − | 273778.i | 0.547806 | − | 0.124614i | ||||
\(131\) | 3.66693e6i | 1.63113i | 0.578666 | + | 0.815565i | \(0.303574\pi\) | ||||
−0.578666 | + | 0.815565i | \(0.696426\pi\) | |||||||
\(132\) | −26501.6 | + | 12715.1i | −0.0115226 | + | 0.00552838i | ||||
\(133\) | −1.93055e6 | −0.820590 | ||||||||
\(134\) | 360949. | + | 1.58674e6i | 0.150014 | + | 0.659463i | ||||
\(135\) | − | 211755.i | − | 0.0860663i | ||||||
\(136\) | −626397. | + | 497305.i | −0.249019 | + | 0.197700i | ||||
\(137\) | −1.97967e6 | −0.769893 | −0.384947 | − | 0.922939i | \(-0.625780\pi\) | ||||
−0.384947 | + | 0.922939i | \(0.625780\pi\) | |||||||
\(138\) | −2.04679e6 | + | 465601.i | −0.778817 | + | 0.177165i | ||||
\(139\) | 1.30893e6i | 0.487383i | 0.969853 | + | 0.243692i | \(0.0783585\pi\) | ||||
−0.969853 | + | 0.243692i | \(0.921642\pi\) | |||||||
\(140\) | −409315. | − | 853122.i | −0.149167 | − | 0.310904i | ||||
\(141\) | −1.76023e6 | −0.627930 | ||||||||
\(142\) | −91665.7 | − | 402963.i | −0.0320141 | − | 0.140734i | ||||
\(143\) | − | 81315.5i | − | 0.0278077i | ||||||
\(144\) | −622836. | + | 776372.i | −0.208587 | + | 0.260005i | ||||
\(145\) | 2.02505e6 | 0.664249 | ||||||||
\(146\) | −1.72991e6 | + | 393518.i | −0.555859 | + | 0.126446i | ||||
\(147\) | 743559.i | 0.234080i | ||||||||
\(148\) | −2.33899e6 | + | 1.12221e6i | −0.721511 | + | 0.346171i | ||||
\(149\) | −1.19790e6 | −0.362126 | −0.181063 | − | 0.983471i | \(-0.557954\pi\) | ||||
−0.181063 | + | 0.983471i | \(0.557954\pi\) | |||||||
\(150\) | −86442.8 | − | 380003.i | −0.0256127 | − | 0.112594i | ||||
\(151\) | 5.97408e6i | 1.73516i | 0.497296 | + | 0.867581i | \(0.334326\pi\) | ||||
−0.497296 | + | 0.867581i | \(0.665674\pi\) | |||||||
\(152\) | 2.32380e6 | + | 2.92701e6i | 0.661709 | + | 0.833478i | ||||
\(153\) | −379594. | −0.105985 | ||||||||
\(154\) | −60785.9 | + | 13827.5i | −0.0166434 | + | 0.00378602i | ||||
\(155\) | − | 2.53977e6i | − | 0.682023i | ||||||
\(156\) | −1.19108e6 | − | 2.48252e6i | −0.313738 | − | 0.653912i | ||||
\(157\) | 2.98776e6 | 0.772053 | 0.386026 | − | 0.922488i | \(-0.373847\pi\) | ||||
0.386026 | + | 0.922488i | \(0.373847\pi\) | |||||||
\(158\) | 959998. | + | 4.22016e6i | 0.243388 | + | 1.06994i | ||||
\(159\) | − | 1.21833e6i | − | 0.303091i | ||||||
\(160\) | −800774. | + | 1.64748e6i | −0.195501 | + | 0.402218i | ||||
\(161\) | −4.45172e6 | −1.06672 | ||||||||
\(162\) | −460624. | + | 104782.i | −0.108343 | + | 0.0246458i | ||||
\(163\) | − | 5.21249e6i | − | 1.20360i | −0.798646 | − | 0.601801i | \(-0.794450\pi\) | ||
0.798646 | − | 0.601801i | \(-0.205550\pi\) | |||||||
\(164\) | 3.15205e6 | − | 1.51231e6i | 0.714598 | − | 0.342854i | ||||
\(165\) | −25674.6 | −0.00571547 | ||||||||
\(166\) | 468905. | + | 2.06131e6i | 0.102509 | + | 0.450629i | ||||
\(167\) | − | 4.71791e6i | − | 1.01298i | −0.862246 | − | 0.506490i | \(-0.830943\pi\) | ||
0.862246 | − | 0.506490i | \(-0.169057\pi\) | |||||||
\(168\) | −1.65323e6 | + | 1.31252e6i | −0.348662 | + | 0.276807i | ||||
\(169\) | 2.79037e6 | 0.578099 | ||||||||
\(170\) | −681197. | + | 154958.i | −0.138652 | + | 0.0315404i | ||||
\(171\) | 1.77376e6i | 0.354737i | ||||||||
\(172\) | −1.49365e6 | − | 3.11315e6i | −0.293537 | − | 0.611808i | ||||
\(173\) | −898914. | −0.173612 | −0.0868060 | − | 0.996225i | \(-0.527666\pi\) | ||||
−0.0868060 | + | 0.996225i | \(0.527666\pi\) | |||||||
\(174\) | −1.00205e6 | − | 4.40502e6i | −0.190213 | − | 0.836180i | ||||
\(175\) | − | 826500.i | − | 0.154216i | ||||||
\(176\) | 94132.5 | + | 75516.8i | 0.0172664 | + | 0.0138518i | ||||
\(177\) | 4.17342e6 | 0.752614 | ||||||||
\(178\) | −2.45408e6 | + | 558252.i | −0.435140 | + | 0.0989853i | ||||
\(179\) | − | 3.75535e6i | − | 0.654774i | −0.944890 | − | 0.327387i | \(-0.893832\pi\) | ||
0.944890 | − | 0.327387i | \(-0.106168\pi\) | |||||||
\(180\) | −783835. | + | 376072.i | −0.134402 | + | 0.0644843i | ||||
\(181\) | 1.00688e7 | 1.69802 | 0.849008 | − | 0.528380i | \(-0.177200\pi\) | ||||
0.849008 | + | 0.528380i | \(0.177200\pi\) | |||||||
\(182\) | −1.29529e6 | − | 5.69409e6i | −0.214858 | − | 0.944518i | ||||
\(183\) | − | 5.50964e6i | − | 0.899021i | ||||||
\(184\) | 5.35852e6 | + | 6.74950e6i | 0.860183 | + | 1.08347i | ||||
\(185\) | −2.26600e6 | −0.357886 | ||||||||
\(186\) | −5.52467e6 | + | 1.25675e6i | −0.858554 | + | 0.195303i | ||||
\(187\) | 46024.5i | 0.00703824i | ||||||||
\(188\) | 3.12612e6 | + | 6.51566e6i | 0.470470 | + | 0.980585i | ||||
\(189\) | −1.00185e6 | −0.148394 | ||||||||
\(190\) | 724085. | + | 3.18308e6i | 0.105567 | + | 0.464074i | ||||
\(191\) | − | 9.44334e6i | − | 1.35527i | −0.735399 | − | 0.677634i | \(-0.763005\pi\) | ||
0.735399 | − | 0.677634i | \(-0.236995\pi\) | |||||||
\(192\) | 3.97996e6 | + | 926676.i | 0.562309 | + | 0.130925i | ||||
\(193\) | 1.09450e7 | 1.52246 | 0.761228 | − | 0.648485i | \(-0.224597\pi\) | ||||
0.761228 | + | 0.648485i | \(0.224597\pi\) | |||||||
\(194\) | 1.21025e6 | − | 275306.i | 0.165756 | − | 0.0377060i | ||||
\(195\) | − | 2.40506e6i | − | 0.324356i | ||||||
\(196\) | 2.75236e6 | − | 1.32054e6i | 0.365542 | − | 0.175382i | ||||
\(197\) | −1.05084e7 | −1.37448 | −0.687242 | − | 0.726428i | \(-0.741179\pi\) | ||||
−0.687242 | + | 0.726428i | \(0.741179\pi\) | |||||||
\(198\) | 12704.5 | + | 55849.2i | 0.00163668 | + | 0.00719484i | ||||
\(199\) | − | 1.04841e7i | − | 1.33037i | −0.746679 | − | 0.665184i | \(-0.768353\pi\) | ||
0.746679 | − | 0.665184i | \(-0.231647\pi\) | |||||||
\(200\) | −1.25310e6 | + | 994854.i | −0.156638 | + | 0.124357i | ||||
\(201\) | 3.17083e6 | 0.390468 | ||||||||
\(202\) | 1.21023e7 | − | 2.75301e6i | 1.46829 | − | 0.334006i | ||||
\(203\) | − | 9.58082e6i | − | 1.14529i | ||||||
\(204\) | 674150. | + | 1.40511e6i | 0.0794083 | + | 0.165508i | ||||
\(205\) | 3.05369e6 | 0.354457 | ||||||||
\(206\) | −3.00565e6 | − | 1.32128e7i | −0.343824 | − | 1.51145i | ||||
\(207\) | 4.09017e6i | 0.461137i | ||||||||
\(208\) | −7.07399e6 | + | 8.81781e6i | −0.786094 | + | 0.979875i | ||||
\(209\) | 215062. | 0.0235573 | ||||||||
\(210\) | −1.79786e6 | + | 408975.i | −0.194132 | + | 0.0441610i | ||||
\(211\) | 1.36416e7i | 1.45217i | 0.687602 | + | 0.726087i | \(0.258663\pi\) | ||||
−0.687602 | + | 0.726087i | \(0.741337\pi\) | |||||||
\(212\) | −4.50977e6 | + | 2.16372e6i | −0.473311 | + | 0.227088i | ||||
\(213\) | −805256. | −0.0833288 | ||||||||
\(214\) | −2.32999e6 | − | 1.02427e7i | −0.237746 | − | 1.04513i | ||||
\(215\) | − | 3.01601e6i | − | 0.303471i | ||||||
\(216\) | 1.20592e6 | + | 1.51896e6i | 0.119662 | + | 0.150725i | ||||
\(217\) | −1.20161e7 | −1.17593 | ||||||||
\(218\) | 1.17567e6 | − | 267439.i | 0.113479 | − | 0.0258140i | ||||
\(219\) | 3.45694e6i | 0.329124i | ||||||||
\(220\) | 45597.5 | + | 95037.3i | 0.00428226 | + | 0.00892537i | ||||
\(221\) | −4.31132e6 | −0.399423 | ||||||||
\(222\) | 1.12128e6 | + | 4.92916e6i | 0.102484 | + | 0.450520i | ||||
\(223\) | − | 2.02736e7i | − | 1.82817i | −0.405523 | − | 0.914085i | \(-0.632911\pi\) | ||
0.405523 | − | 0.914085i | \(-0.367089\pi\) | |||||||
\(224\) | 7.79451e6 | + | 3.78859e6i | 0.693498 | + | 0.337080i | ||||
\(225\) | −759375. | −0.0666667 | ||||||||
\(226\) | 1.33224e7 | − | 3.03057e6i | 1.15414 | − | 0.262542i | ||||
\(227\) | 1.36821e7i | 1.16970i | 0.811140 | + | 0.584852i | \(0.198848\pi\) | ||||
−0.811140 | + | 0.584852i | \(0.801152\pi\) | |||||||
\(228\) | 6.56576e6 | − | 3.15015e6i | 0.553962 | − | 0.265783i | ||||
\(229\) | −1.72378e7 | −1.43541 | −0.717705 | − | 0.696347i | \(-0.754808\pi\) | ||||
−0.717705 | + | 0.696347i | \(0.754808\pi\) | |||||||
\(230\) | 1.66969e6 | + | 7.33997e6i | 0.137231 | + | 0.603269i | ||||
\(231\) | 121471.i | 0.00985453i | ||||||||
\(232\) | −1.45260e7 | + | 1.15324e7i | −1.16328 | + | 0.923540i | ||||
\(233\) | 1.24552e7 | 0.984656 | 0.492328 | − | 0.870410i | \(-0.336146\pi\) | ||||
0.492328 | + | 0.870410i | \(0.336146\pi\) | |||||||
\(234\) | −5.23164e6 | + | 1.19009e6i | −0.408310 | + | 0.0928820i | ||||
\(235\) | 6.31234e6i | 0.486393i | ||||||||
\(236\) | −7.41189e6 | − | 1.54484e7i | −0.563888 | − | 1.17529i | ||||
\(237\) | 8.43330e6 | 0.633509 | ||||||||
\(238\) | 733131. | + | 3.22285e6i | 0.0543814 | + | 0.239061i | ||||
\(239\) | 2.17394e7i | 1.59241i | 0.605028 | + | 0.796204i | \(0.293162\pi\) | ||||
−0.605028 | + | 0.796204i | \(0.706838\pi\) | |||||||
\(240\) | 2.78414e6 | + | 2.23355e6i | 0.201399 | + | 0.161570i | ||||
\(241\) | −7.91913e6 | −0.565752 | −0.282876 | − | 0.959156i | \(-0.591289\pi\) | ||||
−0.282876 | + | 0.959156i | \(0.591289\pi\) | |||||||
\(242\) | −1.38127e7 | + | 3.14209e6i | −0.974612 | + | 0.221704i | ||||
\(243\) | 920483.i | 0.0641500i | ||||||||
\(244\) | −2.03945e7 | + | 9.78498e6i | −1.40392 | + | 0.673582i | ||||
\(245\) | 2.66648e6 | 0.181317 | ||||||||
\(246\) | −1.51105e6 | − | 6.64259e6i | −0.101502 | − | 0.446203i | ||||
\(247\) | 2.01458e7i | 1.33689i | ||||||||
\(248\) | 1.44637e7 | + | 1.82182e7i | 0.948252 | + | 1.19440i | ||||
\(249\) | 4.11919e6 | 0.266817 | ||||||||
\(250\) | −1.36273e6 | + | 309992.i | −0.0872146 | + | 0.0198395i | ||||
\(251\) | 2.60051e7i | 1.64451i | 0.569118 | + | 0.822256i | \(0.307285\pi\) | ||||
−0.569118 | + | 0.822256i | \(0.692715\pi\) | |||||||
\(252\) | 1.77926e6 | + | 3.70845e6i | 0.111183 | + | 0.231734i | ||||
\(253\) | 495919. | 0.0306231 | ||||||||
\(254\) | 836822. | + | 3.67868e6i | 0.0510660 | + | 0.224487i | ||||
\(255\) | 1.36126e6i | 0.0820957i | ||||||||
\(256\) | −3.63813e6 | − | 1.63780e7i | −0.216850 | − | 0.976205i | ||||
\(257\) | −1.09623e7 | −0.645807 | −0.322903 | − | 0.946432i | \(-0.604659\pi\) | ||||
−0.322903 | + | 0.946432i | \(0.604659\pi\) | |||||||
\(258\) | −6.56062e6 | + | 1.49240e6i | −0.382020 | + | 0.0869015i | ||||
\(259\) | 1.07208e7i | 0.617062i | ||||||||
\(260\) | −8.90257e6 | + | 4.27132e6i | −0.506518 | + | 0.243020i | ||||
\(261\) | −8.80271e6 | −0.495102 | ||||||||
\(262\) | −6.50696e6 | − | 2.86047e7i | −0.361805 | − | 1.59050i | ||||
\(263\) | − | 1.86567e7i | − | 1.02558i | −0.858515 | − | 0.512788i | \(-0.828613\pi\) | ||
0.858515 | − | 0.512788i | \(-0.171387\pi\) | |||||||
\(264\) | 184169. | − | 146214.i | 0.0100093 | − | 0.00794652i | ||||
\(265\) | −4.36904e6 | −0.234773 | ||||||||
\(266\) | 1.50597e7 | − | 3.42576e6i | 0.800149 | − | 0.182017i | ||||
\(267\) | 4.90408e6i | 0.257646i | ||||||||
\(268\) | −5.63133e6 | − | 1.17372e7i | −0.292554 | − | 0.609760i | ||||
\(269\) | 3.29387e7 | 1.69219 | 0.846095 | − | 0.533033i | \(-0.178948\pi\) | ||||
0.846095 | + | 0.533033i | \(0.178948\pi\) | |||||||
\(270\) | 375760. | + | 1.65184e6i | 0.0190906 | + | 0.0839223i | ||||
\(271\) | 4.83316e6i | 0.242842i | 0.992601 | + | 0.121421i | \(0.0387450\pi\) | ||||
−0.992601 | + | 0.121421i | \(0.961255\pi\) | |||||||
\(272\) | 4.00388e6 | − | 4.99087e6i | 0.198964 | − | 0.248010i | ||||
\(273\) | −1.13787e7 | −0.559249 | ||||||||
\(274\) | 1.54428e7 | − | 3.51292e6i | 0.750714 | − | 0.170772i | ||||
\(275\) | 92071.7i | 0.00442719i | ||||||||
\(276\) | 1.51402e7 | − | 7.26404e6i | 0.720119 | − | 0.345503i | ||||
\(277\) | −951737. | −0.0447793 | −0.0223897 | − | 0.999749i | \(-0.507127\pi\) | ||||
−0.0223897 | + | 0.999749i | \(0.507127\pi\) | |||||||
\(278\) | −2.32269e6 | − | 1.02106e7i | −0.108108 | − | 0.475242i | ||||
\(279\) | 1.10402e7i | 0.508350i | ||||||||
\(280\) | 4.70682e6 | + | 5.92863e6i | 0.214414 | + | 0.270072i | ||||
\(281\) | 1.05420e7 | 0.475121 | 0.237560 | − | 0.971373i | \(-0.423652\pi\) | ||||
0.237560 | + | 0.971373i | \(0.423652\pi\) | |||||||
\(282\) | 1.37310e7 | − | 3.12352e6i | 0.612288 | − | 0.139283i | ||||
\(283\) | − | 2.15466e7i | − | 0.950648i | −0.879811 | − | 0.475324i | \(-0.842331\pi\) | ||
0.879811 | − | 0.475324i | \(-0.157669\pi\) | |||||||
\(284\) | 1.43012e6 | + | 2.98074e6i | 0.0624333 | + | 0.130127i | ||||
\(285\) | 6.36087e6 | 0.274778 | ||||||||
\(286\) | 144294. | + | 634319.i | 0.00616809 | + | 0.0271150i | ||||
\(287\) | − | 1.44475e7i | − | 0.611149i | ||||||
\(288\) | 3.48090e6 | − | 7.16148e6i | 0.145718 | − | 0.299795i | ||||
\(289\) | −2.16974e7 | −0.898904 | ||||||||
\(290\) | −1.57968e7 | + | 3.59344e6i | −0.647702 | + | 0.147339i | ||||
\(291\) | − | 2.41848e6i | − | 0.0981440i | ||||||
\(292\) | 1.27962e7 | − | 6.13944e6i | 0.513965 | − | 0.246593i | ||||
\(293\) | 2.97274e7 | 1.18183 | 0.590915 | − | 0.806734i | \(-0.298767\pi\) | ||||
0.590915 | + | 0.806734i | \(0.298767\pi\) | |||||||
\(294\) | −1.31945e6 | − | 5.80030e6i | −0.0519218 | − | 0.228249i | ||||
\(295\) | − | 1.49663e7i | − | 0.582972i | ||||||
\(296\) | 1.62544e7 | − | 1.29046e7i | 0.626753 | − | 0.497587i | ||||
\(297\) | 111605. | 0.00426006 | ||||||||
\(298\) | 9.34444e6 | − | 2.12566e6i | 0.353105 | − | 0.0803241i | ||||
\(299\) | 4.64550e7i | 1.73788i | ||||||||
\(300\) | 1.34863e6 | + | 2.81091e6i | 0.0499493 | + | 0.104108i | ||||
\(301\) | −1.42692e7 | −0.523240 | ||||||||
\(302\) | −1.06010e7 | − | 4.66021e7i | −0.384880 | − | 1.69194i | ||||
\(303\) | − | 2.41844e7i | − | 0.869376i | ||||||
\(304\) | −2.33213e7 | − | 1.87092e7i | −0.830101 | − | 0.665940i | ||||
\(305\) | −1.97581e7 | −0.696379 | ||||||||
\(306\) | 2.96110e6 | − | 673589.i | 0.103345 | − | 0.0235088i | ||||
\(307\) | 1.66951e7i | 0.576999i | 0.957480 | + | 0.288499i | \(0.0931563\pi\) | ||||
−0.957480 | + | 0.288499i | \(0.906844\pi\) | |||||||
\(308\) | 449637. | − | 215729.i | 0.0153890 | − | 0.00738341i | ||||
\(309\) | −2.64037e7 | −0.894931 | ||||||||
\(310\) | 4.50682e6 | + | 1.98120e7i | 0.151281 | + | 0.665033i | ||||
\(311\) | 2.09869e7i | 0.697699i | 0.937179 | + | 0.348849i | \(0.113428\pi\) | ||||
−0.937179 | + | 0.348849i | \(0.886572\pi\) | |||||||
\(312\) | 1.36965e7 | + | 1.72519e7i | 0.450968 | + | 0.568032i | ||||
\(313\) | −2.69018e7 | −0.877299 | −0.438650 | − | 0.898658i | \(-0.644543\pi\) | ||||
−0.438650 | + | 0.898658i | \(0.644543\pi\) | |||||||
\(314\) | −2.33067e7 | + | 5.30178e6i | −0.752820 | + | 0.171251i | ||||
\(315\) | 3.59273e6i | 0.114946i | ||||||||
\(316\) | −1.49773e7 | − | 3.12168e7i | −0.474650 | − | 0.989297i | ||||
\(317\) | 3.75955e7 | 1.18021 | 0.590104 | − | 0.807327i | \(-0.299087\pi\) | ||||
0.590104 | + | 0.807327i | \(0.299087\pi\) | |||||||
\(318\) | 2.16192e6 | + | 9.50383e6i | 0.0672293 | + | 0.295541i | ||||
\(319\) | 1.06730e6i | 0.0328787i | ||||||||
\(320\) | 3.32315e6 | − | 1.42725e7i | 0.101414 | − | 0.435563i | ||||
\(321\) | −2.04683e7 | −0.618823 | ||||||||
\(322\) | 3.47266e7 | − | 7.89957e6i | 1.04015 | − | 0.236612i | ||||
\(323\) | − | 1.14025e7i | − | 0.338372i | ||||||
\(324\) | 3.40726e6 | − | 1.63476e6i | 0.100178 | − | 0.0480638i | ||||
\(325\) | −8.62476e6 | −0.251245 | ||||||||
\(326\) | 9.24957e6 | + | 4.06612e7i | 0.266974 | + | 1.17362i | ||||
\(327\) | − | 2.34938e6i | − | 0.0671908i | ||||||
\(328\) | −2.19047e7 | + | 1.73904e7i | −0.620748 | + | 0.492820i | ||||
\(329\) | 2.98647e7 | 0.838630 | ||||||||
\(330\) | 200280. | − | 45559.6i | 0.00557310 | − | 0.00126776i | ||||
\(331\) | − | 9.30712e6i | − | 0.256644i | −0.991733 | − | 0.128322i | \(-0.959041\pi\) | ||
0.991733 | − | 0.128322i | \(-0.0409591\pi\) | |||||||
\(332\) | −7.31558e6 | − | 1.52476e7i | −0.199910 | − | 0.416665i | ||||
\(333\) | 9.85012e6 | 0.266753 | ||||||||
\(334\) | 8.37194e6 | + | 3.68031e7i | 0.224691 | + | 0.987745i | ||||
\(335\) | − | 1.13709e7i | − | 0.302455i | ||||||
\(336\) | 1.05673e7 | − | 1.31722e7i | 0.278577 | − | 0.347249i | ||||
\(337\) | 6.20337e7 | 1.62083 | 0.810417 | − | 0.585854i | \(-0.199241\pi\) | ||||
0.810417 | + | 0.585854i | \(0.199241\pi\) | |||||||
\(338\) | −2.17669e7 | + | 4.95151e6i | −0.563698 | + | 0.128229i | ||||
\(339\) | − | 2.66226e7i | − | 0.683364i | ||||||
\(340\) | 5.03885e6 | − | 2.41757e6i | 0.128202 | − | 0.0615094i | ||||
\(341\) | 1.33858e6 | 0.0337584 | ||||||||
\(342\) | −3.14754e6 | − | 1.38366e7i | −0.0786851 | − | 0.345900i | ||||
\(343\) | − | 4.37313e7i | − | 1.08370i | ||||||
\(344\) | 1.71758e7 | + | 2.16344e7i | 0.421931 | + | 0.531458i | ||||
\(345\) | 1.46677e7 | 0.357195 | ||||||||
\(346\) | 7.01217e6 | − | 1.59512e6i | 0.169287 | − | 0.0385093i | ||||
\(347\) | − | 2.00609e7i | − | 0.480132i | −0.970757 | − | 0.240066i | \(-0.922831\pi\) | ||
0.970757 | − | 0.240066i | \(-0.0771692\pi\) | |||||||
\(348\) | 1.56334e7 | + | 3.25841e7i | 0.370950 | + | 0.773159i | ||||
\(349\) | −7.17249e7 | −1.68731 | −0.843653 | − | 0.536889i | \(-0.819599\pi\) | ||||
−0.843653 | + | 0.536889i | \(0.819599\pi\) | |||||||
\(350\) | 1.46662e6 | + | 6.44729e6i | 0.0342070 | + | 0.150374i | ||||
\(351\) | 1.04546e7i | 0.241760i | ||||||||
\(352\) | −868305. | − | 422047.i | −0.0199088 | − | 0.00967682i | ||||
\(353\) | 1.66396e7 | 0.378284 | 0.189142 | − | 0.981950i | \(-0.439429\pi\) | ||||
0.189142 | + | 0.981950i | \(0.439429\pi\) | |||||||
\(354\) | −3.25557e7 | + | 7.40573e6i | −0.733866 | + | 0.166939i | ||||
\(355\) | 2.88773e6i | 0.0645462i | ||||||||
\(356\) | 1.81530e7 | − | 8.70954e6i | 0.402344 | − | 0.193039i | ||||
\(357\) | 6.44034e6 | 0.141548 | ||||||||
\(358\) | 6.66387e6 | + | 2.92944e7i | 0.145237 | + | 0.638463i | ||||
\(359\) | − | 2.91649e7i | − | 0.630344i | −0.949035 | − | 0.315172i | \(-0.897938\pi\) | ||
0.949035 | − | 0.315172i | \(-0.102062\pi\) | |||||||
\(360\) | 5.44713e6 | − | 4.32455e6i | 0.116751 | − | 0.0926901i | ||||
\(361\) | −6.23568e6 | −0.132545 | ||||||||
\(362\) | −7.85438e7 | + | 1.78671e7i | −1.65572 | + | 0.376641i | ||||
\(363\) | 2.76024e7i | 0.577067i | ||||||||
\(364\) | 2.02083e7 | + | 4.21195e7i | 0.419012 | + | 0.873331i | ||||
\(365\) | 1.23969e7 | 0.254938 | ||||||||
\(366\) | 9.77685e6 | + | 4.29791e7i | 0.199414 | + | 0.876626i | ||||
\(367\) | − | 6.15826e7i | − | 1.24583i | −0.782288 | − | 0.622917i | \(-0.785948\pi\) | ||
0.782288 | − | 0.622917i | \(-0.214052\pi\) | |||||||
\(368\) | −5.37772e7 | − | 4.31422e7i | −1.07908 | − | 0.865684i | ||||
\(369\) | −1.32741e7 | −0.264197 | ||||||||
\(370\) | 1.76764e7 | − | 4.02102e6i | 0.348971 | − | 0.0793836i | ||||
\(371\) | 2.06706e7i | 0.404792i | ||||||||
\(372\) | 4.08663e7 | − | 1.96071e7i | 0.793847 | − | 0.380876i | ||||
\(373\) | 6.41180e7 | 1.23553 | 0.617765 | − | 0.786363i | \(-0.288038\pi\) | ||||
0.617765 | + | 0.786363i | \(0.288038\pi\) | |||||||
\(374\) | −81670.4 | − | 359024.i | −0.00156117 | − | 0.00686291i | ||||
\(375\) | 2.72319e6i | 0.0516398i | ||||||||
\(376\) | −3.59480e7 | − | 4.52795e7i | −0.676256 | − | 0.851801i | ||||
\(377\) | −9.99786e7 | −1.86588 | ||||||||
\(378\) | 7.81514e6 | − | 1.77778e6i | 0.144698 | − | 0.0329157i | ||||
\(379\) | 4.31205e7i | 0.792075i | 0.918234 | + | 0.396038i | \(0.129615\pi\) | ||||
−0.918234 | + | 0.396038i | \(0.870385\pi\) | |||||||
\(380\) | −1.12968e7 | − | 2.35454e7i | −0.205875 | − | 0.429097i | ||||
\(381\) | 7.35124e6 | 0.132918 | ||||||||
\(382\) | 1.67572e7 | + | 7.36648e7i | 0.300615 | + | 1.32151i | ||||
\(383\) | − | 4.47938e7i | − | 0.797299i | −0.917103 | − | 0.398650i | \(-0.869479\pi\) | ||
0.917103 | − | 0.398650i | \(-0.130521\pi\) | |||||||
\(384\) | −3.26909e7 | − | 166292.i | −0.577343 | − | 0.00293682i | ||||
\(385\) | 435606. | 0.00763329 | ||||||||
\(386\) | −8.53790e7 | + | 1.94219e7i | −1.48453 | + | 0.337699i | ||||
\(387\) | 1.31103e7i | 0.226194i | ||||||||
\(388\) | −8.95226e6 | + | 4.29516e6i | −0.153263 | + | 0.0735334i | ||||
\(389\) | 6.70778e7 | 1.13954 | 0.569770 | − | 0.821804i | \(-0.307032\pi\) | ||||
0.569770 | + | 0.821804i | \(0.307032\pi\) | |||||||
\(390\) | 4.26777e6 | + | 1.87612e7i | 0.0719461 | + | 0.316276i | ||||
\(391\) | − | 2.62935e7i | − | 0.439863i | ||||||
\(392\) | −1.91271e7 | + | 1.51853e7i | −0.317534 | + | 0.252095i | ||||
\(393\) | −5.71617e7 | −0.941733 | ||||||||
\(394\) | 8.19734e7 | − | 1.86472e7i | 1.34025 | − | 0.304878i | ||||
\(395\) | − | 3.02426e7i | − | 0.490714i | ||||||
\(396\) | −198209. | − | 413119.i | −0.00319181 | − | 0.00665258i | ||||
\(397\) | 3.89648e7 | 0.622731 | 0.311366 | − | 0.950290i | \(-0.399214\pi\) | ||||
0.311366 | + | 0.950290i | \(0.399214\pi\) | |||||||
\(398\) | 1.86040e7 | + | 8.17835e7i | 0.295092 | + | 1.29723i | ||||
\(399\) | − | 3.00943e7i | − | 0.473768i | ||||||
\(400\) | 8.00972e6 | − | 9.98420e6i | 0.125152 | − | 0.156003i | ||||
\(401\) | 9.85306e7 | 1.52805 | 0.764026 | − | 0.645186i | \(-0.223220\pi\) | ||||
0.764026 | + | 0.645186i | \(0.223220\pi\) | |||||||
\(402\) | −2.47348e7 | + | 5.62664e6i | −0.380741 | + | 0.0866107i | ||||
\(403\) | 1.25391e8i | 1.91580i | ||||||||
\(404\) | −8.95212e7 | + | 4.29510e7i | −1.35763 | + | 0.651372i | ||||
\(405\) | 3.30094e6 | 0.0496904 | ||||||||
\(406\) | 1.70012e7 | + | 7.47373e7i | 0.254039 | + | 1.11676i | ||||
\(407\) | − | 1.19429e6i | − | 0.0177145i | ||||||
\(408\) | −7.75221e6 | − | 9.76456e6i | −0.114142 | − | 0.143771i | ||||
\(409\) | 2.55058e7 | 0.372794 | 0.186397 | − | 0.982475i | \(-0.440319\pi\) | ||||
0.186397 | + | 0.982475i | \(0.440319\pi\) | |||||||
\(410\) | −2.38210e7 | + | 5.41877e6i | −0.345627 | + | 0.0786230i | ||||
\(411\) | − | 3.08600e7i | − | 0.444498i | ||||||
\(412\) | 4.68924e7 | + | 9.77361e7i | 0.670518 | + | 1.39754i | ||||
\(413\) | −7.08079e7 | −1.00515 | ||||||||
\(414\) | −7.25800e6 | − | 3.19063e7i | −0.102286 | − | 0.449650i | ||||
\(415\) | − | 1.47718e7i | − | 0.206676i | ||||||
\(416\) | 3.95350e7 | − | 8.13380e7i | 0.549164 | − | 1.12983i | ||||
\(417\) | −2.04041e7 | −0.281391 | ||||||||
\(418\) | −1.67764e6 | + | 381628.i | −0.0229705 | + | 0.00522530i | ||||
\(419\) | 4.64583e6i | 0.0631569i | 0.999501 | + | 0.0315785i | \(0.0100534\pi\) | ||||
−0.999501 | + | 0.0315785i | \(0.989947\pi\) | |||||||
\(420\) | 1.32988e7 | − | 6.38059e6i | 0.179501 | − | 0.0861218i | ||||
\(421\) | −6.21970e7 | −0.833534 | −0.416767 | − | 0.909013i | \(-0.636837\pi\) | ||||
−0.416767 | + | 0.909013i | \(0.636837\pi\) | |||||||
\(422\) | −2.42071e7 | − | 1.06414e8i | −0.322110 | − | 1.41600i | ||||
\(423\) | − | 2.74392e7i | − | 0.362536i | ||||||
\(424\) | 3.13399e7 | − | 2.48812e7i | 0.411150 | − | 0.326417i | ||||
\(425\) | 4.88161e6 | 0.0635911 | ||||||||
\(426\) | 6.28157e6 | − | 1.42893e6i | 0.0812530 | − | 0.0184834i | ||||
\(427\) | 9.34787e7i | 1.20068i | ||||||||
\(428\) | 3.63512e7 | + | 7.57655e7i | 0.463647 | + | 0.966363i | ||||
\(429\) | 1.26758e6 | 0.0160548 | ||||||||
\(430\) | 5.35191e6 | + | 2.35270e7i | 0.0673136 | + | 0.295911i | ||||
\(431\) | − | 8.54691e7i | − | 1.06752i | −0.845635 | − | 0.533761i | \(-0.820778\pi\) | ||
0.845635 | − | 0.533761i | \(-0.179222\pi\) | |||||||
\(432\) | −1.21024e7 | − | 9.70906e6i | −0.150114 | − | 0.120428i | ||||
\(433\) | 4.86765e7 | 0.599591 | 0.299796 | − | 0.954003i | \(-0.403081\pi\) | ||||
0.299796 | + | 0.954003i | \(0.403081\pi\) | |||||||
\(434\) | 9.37338e7 | − | 2.13225e7i | 1.14664 | − | 0.260837i | ||||
\(435\) | 3.15674e7i | 0.383505i | ||||||||
\(436\) | −8.69647e6 | + | 4.17244e6i | −0.104926 | + | 0.0503420i | ||||
\(437\) | −1.22864e8 | −1.47224 | ||||||||
\(438\) | −6.13434e6 | − | 2.69666e7i | −0.0730038 | − | 0.320925i | ||||
\(439\) | − | 1.38585e8i | − | 1.63804i | −0.573768 | − | 0.819018i | \(-0.694519\pi\) | ||
0.573768 | − | 0.819018i | \(-0.305481\pi\) | |||||||
\(440\) | −524337. | − | 660446.i | −0.00615534 | − | 0.00775317i | ||||
\(441\) | −1.15909e7 | −0.135146 | ||||||||
\(442\) | 3.36314e7 | − | 7.65043e6i | 0.389473 | − | 0.0885970i | ||||
\(443\) | 1.24746e8i | 1.43488i | 0.696619 | + | 0.717442i | \(0.254687\pi\) | ||||
−0.696619 | + | 0.717442i | \(0.745313\pi\) | |||||||
\(444\) | −1.74936e7 | − | 3.64612e7i | −0.199862 | − | 0.416565i | ||||
\(445\) | 1.75865e7 | 0.199572 | ||||||||
\(446\) | 3.59755e7 | + | 1.58149e8i | 0.405511 | + | 1.78263i | ||||
\(447\) | − | 1.86733e7i | − | 0.209074i | ||||||
\(448\) | −6.75256e7 | − | 1.57223e7i | −0.750991 | − | 0.174857i | ||||
\(449\) | 4.35883e7 | 0.481539 | 0.240769 | − | 0.970582i | \(-0.422600\pi\) | ||||
0.240769 | + | 0.970582i | \(0.422600\pi\) | |||||||
\(450\) | 5.92367e6 | − | 1.34751e6i | 0.0650060 | − | 0.0147875i | ||||
\(451\) | 1.60944e6i | 0.0175447i | ||||||||
\(452\) | −9.85465e7 | + | 4.72812e7i | −1.06715 | + | 0.512004i | ||||
\(453\) | −9.31266e7 | −1.00180 | ||||||||
\(454\) | −2.42789e7 | − | 1.06730e8i | −0.259455 | − | 1.14057i | ||||
\(455\) | 4.08051e7i | 0.433192i | ||||||||
\(456\) | −4.56276e7 | + | 3.62244e7i | −0.481209 | + | 0.382038i | ||||
\(457\) | 3.43555e7 | 0.359954 | 0.179977 | − | 0.983671i | \(-0.442398\pi\) | ||||
0.179977 | + | 0.983671i | \(0.442398\pi\) | |||||||
\(458\) | 1.34467e8 | − | 3.05885e7i | 1.39965 | − | 0.318392i | ||||
\(459\) | − | 5.91728e6i | − | 0.0611906i | ||||||
\(460\) | −2.60496e7 | − | 5.42942e7i | −0.267625 | − | 0.557802i | ||||
\(461\) | −6.32112e7 | −0.645195 | −0.322598 | − | 0.946536i | \(-0.604556\pi\) | ||||
−0.322598 | + | 0.946536i | \(0.604556\pi\) | |||||||
\(462\) | −215550. | − | 947559.i | −0.00218586 | − | 0.00960905i | ||||
\(463\) | 7.88603e7i | 0.794539i | 0.917702 | + | 0.397270i | \(0.130042\pi\) | ||||
−0.917702 | + | 0.397270i | \(0.869958\pi\) | |||||||
\(464\) | 9.28491e7 | − | 1.15737e8i | 0.929445 | − | 1.15856i | ||||
\(465\) | 3.95911e7 | 0.393766 | ||||||||
\(466\) | −9.71598e7 | + | 2.21018e7i | −0.960128 | + | 0.218409i | ||||
\(467\) | − | 5.22025e7i | − | 0.512556i | −0.966603 | − | 0.256278i | \(-0.917504\pi\) | ||
0.966603 | − | 0.256278i | \(-0.0824962\pi\) | |||||||
\(468\) | 3.86987e7 | − | 1.85671e7i | 0.377537 | − | 0.181137i | ||||
\(469\) | −5.37976e7 | −0.521488 | ||||||||
\(470\) | −1.12012e7 | − | 4.92408e7i | −0.107888 | − | 0.474276i | ||||
\(471\) | 4.65746e7i | 0.445745i | ||||||||
\(472\) | 8.52312e7 | + | 1.07356e8i | 0.810536 | + | 1.02094i | ||||
\(473\) | 1.58958e6 | 0.0150210 | ||||||||
\(474\) | −6.57858e7 | + | 1.49649e7i | −0.617728 | + | 0.140520i | ||||
\(475\) | − | 2.28107e7i | − | 0.212842i | ||||||
\(476\) | −1.14379e7 | − | 2.38396e7i | −0.106054 | − | 0.221044i | ||||
\(477\) | 1.89919e7 | 0.174990 | ||||||||
\(478\) | −3.85766e7 | − | 1.69583e8i | −0.353216 | − | 1.55274i | ||||
\(479\) | − | 8.50400e7i | − | 0.773778i | −0.922126 | − | 0.386889i | \(-0.873550\pi\) | ||
0.922126 | − | 0.386889i | \(-0.126450\pi\) | |||||||
\(480\) | −2.56817e7 | − | 1.24828e7i | −0.232221 | − | 0.112873i | ||||
\(481\) | 1.11875e8 | 1.00530 | ||||||||
\(482\) | 6.17748e7 | − | 1.40525e7i | 0.551659 | − | 0.125491i | ||||
\(483\) | − | 6.93954e7i | − | 0.615871i | ||||||
\(484\) | 1.02173e8 | − | 4.90211e7i | 0.901157 | − | 0.432362i | ||||
\(485\) | −8.67290e6 | −0.0760220 | ||||||||
\(486\) | −1.63340e6 | − | 7.18042e6i | −0.0142293 | − | 0.0625520i | ||||
\(487\) | 6.20201e6i | 0.0536964i | 0.999640 | + | 0.0268482i | \(0.00854708\pi\) | ||||
−0.999640 | + | 0.0268482i | \(0.991453\pi\) | |||||||
\(488\) | 1.41728e8 | − | 1.12520e8i | 1.21954 | − | 0.968211i | ||||
\(489\) | 8.12547e7 | 0.694900 | ||||||||
\(490\) | −2.08004e7 | + | 4.73166e6i | −0.176801 | + | 0.0402184i | ||||
\(491\) | 1.34450e8i | 1.13584i | 0.823083 | + | 0.567921i | \(0.192252\pi\) | ||||
−0.823083 | + | 0.567921i | \(0.807748\pi\) | |||||||
\(492\) | 2.35746e7 | + | 4.91356e7i | 0.197947 | + | 0.412573i | ||||
\(493\) | 5.65878e7 | 0.472261 | ||||||||
\(494\) | −3.57488e7 | − | 1.57152e8i | −0.296538 | − | 1.30358i | ||||
\(495\) | − | 400228.i | − | 0.00329983i | ||||||
\(496\) | −1.45155e8 | − | 1.16449e8i | −1.18956 | − | 0.954315i | ||||
\(497\) | 1.36623e7 | 0.111290 | ||||||||
\(498\) | −3.21326e7 | + | 7.30950e6i | −0.260171 | + | 0.0591833i | ||||
\(499\) | − | 1.21185e8i | − | 0.975321i | −0.873033 | − | 0.487660i | \(-0.837850\pi\) | ||
0.873033 | − | 0.487660i | \(-0.162150\pi\) | |||||||
\(500\) | 1.00802e7 | − | 4.83632e6i | 0.0806414 | − | 0.0386906i | ||||
\(501\) | 7.35450e7 | 0.584844 | ||||||||
\(502\) | −4.61460e7 | − | 2.02858e8i | −0.364773 | − | 1.60355i | ||||
\(503\) | 2.01030e8i | 1.57964i | 0.613342 | + | 0.789818i | \(0.289825\pi\) | ||||
−0.613342 | + | 0.789818i | \(0.710175\pi\) | |||||||
\(504\) | −2.04601e7 | − | 2.57712e7i | −0.159815 | − | 0.201300i | ||||
\(505\) | −8.67277e7 | −0.673416 | ||||||||
\(506\) | −3.86853e6 | + | 880009.i | −0.0298603 | + | 0.00679259i | ||||
\(507\) | 4.34976e7i | 0.333765i | ||||||||
\(508\) | −1.30556e7 | − | 2.72114e7i | −0.0995878 | − | 0.207567i | ||||
\(509\) | 2.09283e8 | 1.58701 | 0.793507 | − | 0.608562i | \(-0.208253\pi\) | ||||
0.793507 | + | 0.608562i | \(0.208253\pi\) | |||||||
\(510\) | −2.41556e6 | − | 1.06188e7i | −0.0182099 | − | 0.0800507i | ||||
\(511\) | − | 5.86518e7i | − | 0.439560i | ||||||
\(512\) | 5.74428e7 | + | 1.21304e8i | 0.427982 | + | 0.903787i | ||||
\(513\) | −2.76502e7 | −0.204807 | ||||||||
\(514\) | 8.55138e7 | − | 1.94526e7i | 0.629719 | − | 0.143248i | ||||
\(515\) | 9.46863e7i | 0.693211i | ||||||||
\(516\) | 4.85293e7 | − | 2.32836e7i | 0.353228 | − | 0.169474i | ||||
\(517\) | −3.32691e6 | −0.0240752 | ||||||||
\(518\) | −1.90241e7 | − | 8.36300e7i | −0.136872 | − | 0.601690i | ||||
\(519\) | − | 1.40127e7i | − | 0.100235i | ||||||
\(520\) | 6.18669e7 | − | 4.91170e7i | 0.439996 | − | 0.349318i | ||||
\(521\) | −1.09676e8 | −0.775531 | −0.387766 | − | 0.921758i | \(-0.626753\pi\) | ||||
−0.387766 | + | 0.921758i | \(0.626753\pi\) | |||||||
\(522\) | 6.86674e7 | − | 1.56204e7i | 0.482769 | − | 0.109820i | ||||
\(523\) | 1.53121e8i | 1.07036i | 0.844738 | + | 0.535180i | \(0.179756\pi\) | ||||
−0.844738 | + | 0.535180i | \(0.820244\pi\) | |||||||
\(524\) | 1.01518e8 | + | 2.11590e8i | 0.705584 | + | 1.47062i | ||||
\(525\) | 1.28839e7 | 0.0890365 | ||||||||
\(526\) | 3.31063e7 | + | 1.45536e8i | 0.227485 | + | 1.00003i | ||||
\(527\) | − | 7.09712e7i | − | 0.484898i | ||||||
\(528\) | −1.17719e6 | + | 1.46738e6i | −0.00799733 | + | 0.00996875i | ||||
\(529\) | −1.35280e8 | −0.913829 | ||||||||
\(530\) | 3.40817e7 | − | 7.75286e6i | 0.228925 | − | 0.0520756i | ||||
\(531\) | 6.50572e7i | 0.434522i | ||||||||
\(532\) | −1.11397e8 | + | 5.34468e7i | −0.739843 | + | 0.354966i | ||||
\(533\) | −1.50764e8 | −0.995670 | ||||||||
\(534\) | −8.70229e6 | − | 3.82554e7i | −0.0571492 | − | 0.251228i | ||||
\(535\) | 7.34013e7i | 0.479338i | ||||||||
\(536\) | 6.47560e7 | + | 8.15656e7i | 0.420519 | + | 0.529679i | ||||
\(537\) | 5.85401e7 | 0.378034 | ||||||||
\(538\) | −2.56945e8 | + | 5.84496e7i | −1.65004 | + | 0.375349i | ||||
\(539\) | 1.40536e6i | 0.00897475i | ||||||||
\(540\) | −5.86239e6 | − | 1.22188e7i | −0.0372300 | − | 0.0775972i | ||||
\(541\) | 1.17596e8 | 0.742676 | 0.371338 | − | 0.928498i | \(-0.378899\pi\) | ||||
0.371338 | + | 0.928498i | \(0.378899\pi\) | |||||||
\(542\) | −8.57643e6 | − | 3.77021e7i | −0.0538653 | − | 0.236792i | ||||
\(543\) | 1.56957e8i | 0.980350i | ||||||||
\(544\) | −2.23768e7 | + | 4.60372e7i | −0.138996 | + | 0.285965i | ||||
\(545\) | −8.42509e6 | −0.0520457 | ||||||||
\(546\) | 8.87621e7 | − | 2.01915e7i | 0.545318 | − | 0.124048i | ||||
\(547\) | 1.63945e8i | 1.00170i | 0.865535 | + | 0.500848i | \(0.166979\pi\) | ||||
−0.865535 | + | 0.500848i | \(0.833021\pi\) | |||||||
\(548\) | −1.14231e8 | + | 5.48065e7i | −0.694134 | + | 0.333036i | ||||
\(549\) | 8.58867e7 | 0.519050 | ||||||||
\(550\) | −163381. | − | 718225.i | −0.000982005 | − | 0.00431690i | ||||
\(551\) | − | 2.64423e8i | − | 1.58068i | ||||||
\(552\) | −1.05214e8 | + | 8.35310e7i | −0.625543 | + | 0.496627i | ||||
\(553\) | −1.43083e8 | −0.846081 | ||||||||
\(554\) | 7.42423e6 | − | 1.68886e6i | 0.0436639 | − | 0.00993262i | ||||
\(555\) | − | 3.53235e7i | − | 0.206626i | ||||||
\(556\) | 3.62373e7 | + | 7.55280e7i | 0.210829 | + | 0.439424i | ||||
\(557\) | −2.93846e8 | −1.70041 | −0.850206 | − | 0.526450i | \(-0.823523\pi\) | ||||
−0.850206 | + | 0.526450i | \(0.823523\pi\) | |||||||
\(558\) | −1.95908e7 | − | 8.61212e7i | −0.112758 | − | 0.495687i | ||||
\(559\) | 1.48903e8i | 0.852451i | ||||||||
\(560\) | −4.72369e7 | − | 3.78953e7i | −0.268978 | − | 0.215785i | ||||
\(561\) | −717451. | −0.00406353 | ||||||||
\(562\) | −8.22352e7 | + | 1.87068e7i | −0.463285 | + | 0.105388i | ||||
\(563\) | 1.32511e8i | 0.742554i | 0.928522 | + | 0.371277i | \(0.121080\pi\) | ||||
−0.928522 | + | 0.371277i | \(0.878920\pi\) | |||||||
\(564\) | −1.01569e8 | + | 4.87314e7i | −0.566141 | + | 0.271626i | ||||
\(565\) | −9.54713e7 | −0.529331 | ||||||||
\(566\) | 3.82344e7 | + | 1.68079e8i | 0.210865 | + | 0.926967i | ||||
\(567\) | − | 1.56173e7i | − | 0.0856754i | ||||||
\(568\) | −1.64452e7 | − | 2.07142e7i | −0.0897419 | − | 0.113037i | ||||
\(569\) | −1.92681e8 | −1.04593 | −0.522964 | − | 0.852354i | \(-0.675174\pi\) | ||||
−0.522964 | + | 0.852354i | \(0.675174\pi\) | |||||||
\(570\) | −4.96193e7 | + | 1.12874e7i | −0.267933 | + | 0.0609492i | ||||
\(571\) | − | 7.65822e7i | − | 0.411357i | −0.978620 | − | 0.205679i | \(-0.934060\pi\) | ||
0.978620 | − | 0.205679i | \(-0.0659402\pi\) | |||||||
\(572\) | −2.25120e6 | − | 4.69209e6i | −0.0120289 | − | 0.0250714i | ||||
\(573\) | 1.47207e8 | 0.782465 | ||||||||
\(574\) | 2.56371e7 | + | 1.12701e8i | 0.135560 | + | 0.595925i | ||||
\(575\) | − | 5.25999e7i | − | 0.276682i | ||||||
\(576\) | −1.44454e7 | + | 6.20415e7i | −0.0755899 | + | 0.324649i | ||||
\(577\) | 1.71942e8 | 0.895066 | 0.447533 | − | 0.894268i | \(-0.352303\pi\) | ||||
0.447533 | + | 0.894268i | \(0.352303\pi\) | |||||||
\(578\) | 1.69255e8 | − | 3.85020e7i | 0.876512 | − | 0.199388i | ||||
\(579\) | 1.70616e8i | 0.878990i | ||||||||
\(580\) | 1.16850e8 | − | 5.60629e7i | 0.598886 | − | 0.287337i | ||||
\(581\) | −6.98878e7 | −0.356347 | ||||||||
\(582\) | 4.29159e6 | + | 1.88659e7i | 0.0217695 | + | 0.0956991i | ||||
\(583\) | − | 2.30270e6i | − | 0.0116207i | ||||||
\(584\) | −8.89252e7 | + | 7.05989e7i | −0.446464 | + | 0.354454i | ||||
\(585\) | 3.74911e7 | 0.187267 | ||||||||
\(586\) | −2.31895e8 | + | 5.27513e7i | −1.15239 | + | 0.262144i | ||||
\(587\) | − | 1.75375e8i | − | 0.867068i | −0.901137 | − | 0.433534i | \(-0.857266\pi\) | ||
0.901137 | − | 0.433534i | \(-0.142734\pi\) | |||||||
\(588\) | 2.05852e7 | + | 4.29051e7i | 0.101257 | + | 0.211046i | ||||
\(589\) | −3.31633e8 | −1.62297 | ||||||||
\(590\) | 2.65577e7 | + | 1.16748e8i | 0.129310 | + | 0.568450i | ||||
\(591\) | − | 1.63810e8i | − | 0.793559i | ||||||
\(592\) | −1.03897e8 | + | 1.29509e8i | −0.500769 | + | 0.624214i | ||||
\(593\) | −1.46804e8 | −0.704003 | −0.352001 | − | 0.935999i | \(-0.614499\pi\) | ||||
−0.352001 | + | 0.935999i | \(0.614499\pi\) | |||||||
\(594\) | −870602. | + | 198044.i | −0.00415394 | + | 0.000944935i | ||||
\(595\) | − | 2.30957e7i | − | 0.109643i | ||||||
\(596\) | −6.91213e7 | + | 3.31634e7i | −0.326492 | + | 0.156646i | ||||
\(597\) | 1.63431e8 | 0.768088 | ||||||||
\(598\) | −8.24343e7 | − | 3.62382e8i | −0.385482 | − | 1.69458i | ||||
\(599\) | 1.52954e8i | 0.711672i | 0.934548 | + | 0.355836i | \(0.115804\pi\) | ||||
−0.934548 | + | 0.355836i | \(0.884196\pi\) | |||||||
\(600\) | −1.55082e7 | − | 1.95339e7i | −0.0717974 | − | 0.0904349i | ||||
\(601\) | 1.98847e8 | 0.916003 | 0.458001 | − | 0.888952i | \(-0.348565\pi\) | ||||
0.458001 | + | 0.888952i | \(0.348565\pi\) | |||||||
\(602\) | 1.11310e8 | − | 2.53207e7i | 0.510206 | − | 0.116061i | ||||
\(603\) | 4.94284e7i | 0.225437i | ||||||||
\(604\) | 1.65391e8 | + | 3.44718e8i | 0.750586 | + | 1.56442i | ||||
\(605\) | 9.89847e7 | 0.446994 | ||||||||
\(606\) | 4.29152e7 | + | 1.88656e8i | 0.192838 | + | 0.847720i | ||||
\(607\) | − | 2.62997e8i | − | 1.17594i | −0.808883 | − | 0.587970i | \(-0.799927\pi\) | ||
0.808883 | − | 0.587970i | \(-0.200073\pi\) | |||||||
\(608\) | 2.15122e8 | + | 1.04562e8i | 0.957137 | + | 0.465224i | ||||
\(609\) | 1.49350e8 | 0.661232 | ||||||||
\(610\) | 1.54127e8 | − | 3.50607e7i | 0.679031 | − | 0.154465i | ||||
\(611\) | − | 3.11647e8i | − | 1.36628i | ||||||
\(612\) | −2.19034e7 | + | 1.05090e7i | −0.0955561 | + | 0.0458464i | ||||
\(613\) | 3.30925e8 | 1.43664 | 0.718321 | − | 0.695712i | \(-0.244911\pi\) | ||||
0.718321 | + | 0.695712i | \(0.244911\pi\) | |||||||
\(614\) | −2.96255e7 | − | 1.30234e8i | −0.127986 | − | 0.562625i | ||||
\(615\) | 4.76023e7i | 0.204646i | ||||||||
\(616\) | −3.12468e6 | + | 2.48072e6i | −0.0133679 | + | 0.0106129i | ||||
\(617\) | 3.38754e8 | 1.44221 | 0.721106 | − | 0.692824i | \(-0.243634\pi\) | ||||
0.721106 | + | 0.692824i | \(0.243634\pi\) | |||||||
\(618\) | 2.05968e8 | − | 4.68534e7i | 0.872638 | − | 0.198507i | ||||
\(619\) | − | 2.66432e8i | − | 1.12335i | −0.827358 | − | 0.561675i | \(-0.810157\pi\) | ||
0.827358 | − | 0.561675i | \(-0.189843\pi\) | |||||||
\(620\) | −7.03128e7 | − | 1.46551e8i | −0.295025 | − | 0.614911i | ||||
\(621\) | −6.37594e7 | −0.266238 | ||||||||
\(622\) | −3.72413e7 | − | 1.63713e8i | −0.154758 | − | 0.680319i | ||||
\(623\) | − | 8.32046e7i | − | 0.344099i | ||||||
\(624\) | −1.37456e8 | − | 1.10273e8i | −0.565731 | − | 0.453852i | ||||
\(625\) | 9.76562e6 | 0.0400000 | ||||||||
\(626\) | 2.09853e8 | − | 4.77372e7i | 0.855445 | − | 0.194596i | ||||
\(627\) | 3.35249e6i | 0.0136008i | ||||||||
\(628\) | 1.72401e8 | − | 8.27153e7i | 0.696081 | − | 0.333970i | ||||
\(629\) | −6.33211e7 | −0.254446 | ||||||||
\(630\) | −6.37529e6 | − | 2.80258e7i | −0.0254964 | − | 0.112082i | ||||
\(631\) | − | 1.51752e8i | − | 0.604013i | −0.953306 | − | 0.302007i | \(-0.902343\pi\) | ||
0.953306 | − | 0.302007i | \(-0.0976565\pi\) | |||||||
\(632\) | 1.72228e8 | + | 2.16936e8i | 0.682265 | + | 0.859369i | ||||
\(633\) | −2.12652e8 | −0.838413 | ||||||||
\(634\) | −2.93272e8 | + | 6.67133e7i | −1.15081 | + | 0.261785i | ||||
\(635\) | − | 2.63622e7i | − | 0.102958i | ||||||
\(636\) | −3.37291e7 | − | 7.03004e7i | −0.131109 | − | 0.273266i | ||||
\(637\) | −1.31647e8 | −0.509321 | ||||||||
\(638\) | −1.89392e6 | − | 8.32569e6i | −0.00729289 | − | 0.0320596i | ||||
\(639\) | − | 1.25527e7i | − | 0.0481099i | ||||||
\(640\) | −596339. | + | 1.17233e8i | −0.00227485 | + | 0.447208i | ||||
\(641\) | −1.47284e8 | −0.559219 | −0.279610 | − | 0.960114i | \(-0.590205\pi\) | ||||
−0.279610 | + | 0.960114i | \(0.590205\pi\) | |||||||
\(642\) | 1.59667e8 | − | 3.63210e7i | 0.603408 | − | 0.137263i | ||||
\(643\) | − | 5.45081e7i | − | 0.205035i | −0.994731 | − | 0.102518i | \(-0.967310\pi\) | ||
0.994731 | − | 0.102518i | \(-0.0326898\pi\) | |||||||
\(644\) | −2.56874e8 | + | 1.23245e8i | −0.961753 | + | 0.461435i | ||||
\(645\) | 4.70149e7 | 0.175209 | ||||||||
\(646\) | 2.02338e7 | + | 8.89479e7i | 0.0750550 | + | 0.329943i | ||||
\(647\) | − | 1.13471e8i | − | 0.418960i | −0.977813 | − | 0.209480i | \(-0.932823\pi\) | ||
0.977813 | − | 0.209480i | \(-0.0671771\pi\) | |||||||
\(648\) | −2.36782e7 | + | 1.87984e7i | −0.0870210 | + | 0.0690871i | ||||
\(649\) | 7.88796e6 | 0.0288556 | ||||||||
\(650\) | 6.72793e7 | − | 1.53046e7i | 0.244986 | − | 0.0557292i | ||||
\(651\) | − | 1.87312e8i | − | 0.678925i | ||||||
\(652\) | −1.44306e8 | − | 3.00773e8i | −0.520647 | − | 1.08517i | ||||
\(653\) | 1.43973e8 | 0.517060 | 0.258530 | − | 0.966003i | \(-0.416762\pi\) | ||||
0.258530 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(654\) | 4.16897e6 | + | 1.83268e7i | 0.0149037 | + | 0.0655170i | ||||
\(655\) | 2.04988e8i | 0.729463i | ||||||||
\(656\) | 1.40013e8 | − | 1.74527e8i | 0.495971 | − | 0.618233i | ||||
\(657\) | −5.38883e7 | −0.190020 | ||||||||
\(658\) | −2.32966e8 | + | 5.29949e7i | −0.817739 | + | 0.186019i | ||||
\(659\) | 8.17629e7i | 0.285693i | 0.989745 | + | 0.142847i | \(0.0456256\pi\) | ||||
−0.989745 | + | 0.142847i | \(0.954374\pi\) | |||||||
\(660\) | −1.48149e6 | + | 710795.i | −0.00515306 | + | 0.00247236i | ||||
\(661\) | −1.06717e7 | −0.0369512 | −0.0184756 | − | 0.999829i | \(-0.505881\pi\) | ||||
−0.0184756 | + | 0.999829i | \(0.505881\pi\) | |||||||
\(662\) | 1.65155e7 | + | 7.26022e7i | 0.0569268 | + | 0.250251i | ||||
\(663\) | − | 6.72068e7i | − | 0.230607i | ||||||
\(664\) | 8.41236e7 | + | 1.05961e8i | 0.287352 | + | 0.361944i | ||||
\(665\) | −1.07921e8 | −0.366979 | ||||||||
\(666\) | −7.68380e7 | + | 1.74790e7i | −0.260108 | + | 0.0591690i | ||||
\(667\) | − | 6.09741e8i | − | 2.05479i | ||||||
\(668\) | −1.30614e8 | − | 2.72235e8i | −0.438188 | − | 0.913301i | ||||
\(669\) | 3.16034e8 | 1.05549 | ||||||||
\(670\) | 2.01777e7 | + | 8.87013e7i | 0.0670883 | + | 0.294921i | ||||
\(671\) | − | 1.04135e7i | − | 0.0344690i | ||||||
\(672\) | −5.90583e7 | + | 1.21504e8i | −0.194613 | + | 0.400391i | ||||
\(673\) | 4.04111e8 | 1.32573 | 0.662865 | − | 0.748739i | \(-0.269340\pi\) | ||||
0.662865 | + | 0.748739i | \(0.269340\pi\) | |||||||
\(674\) | −4.83908e8 | + | 1.10079e8i | −1.58046 | + | 0.359521i | ||||
\(675\) | − | 1.18375e7i | − | 0.0384900i | ||||||
\(676\) | 1.61011e8 | − | 7.72507e7i | 0.521213 | − | 0.250070i | ||||
\(677\) | 4.71145e8 | 1.51841 | 0.759204 | − | 0.650853i | \(-0.225589\pi\) | ||||
0.759204 | + | 0.650853i | \(0.225589\pi\) | |||||||
\(678\) | 4.72419e7 | + | 2.07676e8i | 0.151579 | + | 0.666341i | ||||
\(679\) | 4.10329e7i | 0.131076i | ||||||||
\(680\) | −3.50166e7 | + | 2.78002e7i | −0.111365 | + | 0.0884139i | ||||
\(681\) | −2.13283e8 | −0.675329 | ||||||||
\(682\) | −1.04419e7 | + | 2.37531e6i | −0.0329175 | + | 0.00748803i | ||||
\(683\) | − | 3.10535e8i | − | 0.974649i | −0.873221 | − | 0.487325i | \(-0.837973\pi\) | ||
0.873221 | − | 0.487325i | \(-0.162027\pi\) | |||||||
\(684\) | 4.91060e7 | + | 1.02350e8i | 0.153450 | + | 0.319830i | ||||
\(685\) | −1.10667e8 | −0.344307 | ||||||||
\(686\) | 7.76012e7 | + | 3.41136e8i | 0.240379 | + | 1.05671i | ||||
\(687\) | − | 2.68711e8i | − | 0.828735i | ||||||
\(688\) | −1.72374e8 | − | 1.38285e8i | −0.529305 | − | 0.424629i | ||||
\(689\) | 2.15704e8 | 0.659479 | ||||||||
\(690\) | −1.14419e8 | + | 2.60279e7i | −0.348298 | + | 0.0792304i | ||||
\(691\) | 6.84679e7i | 0.207517i | 0.994603 | + | 0.103758i | \(0.0330869\pi\) | ||||
−0.994603 | + | 0.103758i | \(0.966913\pi\) | |||||||
\(692\) | −5.18694e7 | + | 2.48862e7i | −0.156528 | + | 0.0751000i | ||||
\(693\) | −1.89354e6 | −0.00568952 | ||||||||
\(694\) | 3.55980e7 | + | 1.56489e8i | 0.106499 | + | 0.468172i | ||||
\(695\) | 7.31712e7i | 0.217964i | ||||||||
\(696\) | −1.79772e8 | − | 2.26438e8i | −0.533206 | − | 0.671617i | ||||
\(697\) | 8.53322e7 | 0.252008 | ||||||||
\(698\) | 5.59505e8 | − | 1.27276e8i | 1.64527 | − | 0.374265i | ||||
\(699\) | 1.94158e8i | 0.568492i | ||||||||
\(700\) | −2.28814e7 | − | 4.76909e7i | −0.0667097 | − | 0.139041i | ||||
\(701\) | −1.82766e8 | −0.530569 | −0.265285 | − | 0.964170i | \(-0.585466\pi\) | ||||
−0.265285 | + | 0.964170i | \(0.585466\pi\) | |||||||
\(702\) | −1.85516e7 | − | 8.15532e7i | −0.0536255 | − | 0.235738i | ||||
\(703\) | 2.95885e8i | 0.851643i | ||||||||
\(704\) | 7.52232e6 | + | 1.75146e6i | 0.0215593 | + | 0.00501976i | ||||
\(705\) | −9.83997e7 | −0.280819 | ||||||||
\(706\) | −1.29801e8 | + | 2.95269e7i | −0.368861 | + | 0.0839081i | ||||
\(707\) | 4.10323e8i | 1.16109i | ||||||||
\(708\) | 2.40816e8 | − | 1.15540e8i | 0.678556 | − | 0.325561i | ||||
\(709\) | −4.30437e8 | −1.20773 | −0.603867 | − | 0.797085i | \(-0.706374\pi\) | ||||
−0.603867 | + | 0.797085i | \(0.706374\pi\) | |||||||
\(710\) | −5.12427e6 | − | 2.25263e7i | −0.0143172 | − | 0.0629383i | ||||
\(711\) | 1.31462e8i | 0.365757i | ||||||||
\(712\) | −1.26151e8 | + | 1.00153e8i | −0.349503 | + | 0.277475i | ||||
\(713\) | −7.64723e8 | −2.10977 | ||||||||
\(714\) | −5.02393e7 | + | 1.14284e7i | −0.138022 | + | 0.0313971i | ||||
\(715\) | − | 4.54567e6i | − | 0.0124360i | ||||||
\(716\) | −1.03966e8 | − | 2.16692e8i | −0.283238 | − | 0.590343i | ||||
\(717\) | −3.38884e8 | −0.919378 | ||||||||
\(718\) | 5.17532e7 | + | 2.27507e8i | 0.139818 | + | 0.614642i | ||||
\(719\) | 3.35482e8i | 0.902573i | 0.892379 | + | 0.451287i | \(0.149035\pi\) | ||||
−0.892379 | + | 0.451287i | \(0.850965\pi\) | |||||||
\(720\) | −3.48176e7 | + | 4.34005e7i | −0.0932828 | + | 0.116278i | ||||
\(721\) | 4.47976e8 | 1.19522 | ||||||||
\(722\) | 4.86428e7 | − | 1.10652e7i | 0.129243 | − | 0.0294001i | ||||
\(723\) | − | 1.23447e8i | − | 0.326637i | ||||||
\(724\) | 5.80993e8 | − | 2.78752e8i | 1.53093 | − | 0.734517i | ||||
\(725\) | 1.13204e8 | 0.297061 | ||||||||
\(726\) | −4.89804e7 | − | 2.15318e8i | −0.128001 | − | 0.562692i | ||||
\(727\) | 3.91654e8i | 1.01929i | 0.860383 | + | 0.509647i | \(0.170224\pi\) | ||||
−0.860383 | + | 0.509647i | \(0.829776\pi\) | |||||||
\(728\) | −2.32380e8 | − | 2.92702e8i | −0.602289 | − | 0.758634i | ||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | −9.67048e7 | + | 2.19983e7i | −0.248588 | + | 0.0565485i | ||||
\(731\) | − | 8.42792e7i | − | 0.215759i | ||||||
\(732\) | −1.52533e8 | − | 3.17919e8i | −0.388893 | − | 0.810556i | ||||
\(733\) | 4.73042e8 | 1.20112 | 0.600562 | − | 0.799578i | \(-0.294944\pi\) | ||||
0.600562 | + | 0.799578i | \(0.294944\pi\) | |||||||
\(734\) | 1.09278e8 | + | 4.80389e8i | 0.276341 | + | 1.21480i | ||||
\(735\) | 4.15662e7i | 0.104684i | ||||||||
\(736\) | 4.96057e8 | + | 2.41113e8i | 1.24422 | + | 0.604765i | ||||
\(737\) | 5.99303e6 | 0.0149708 | ||||||||
\(738\) | 1.03548e8 | − | 2.35550e7i | 0.257615 | − | 0.0586021i | ||||
\(739\) | 3.38422e8i | 0.838543i | 0.907861 | + | 0.419272i | \(0.137715\pi\) | ||||
−0.907861 | + | 0.419272i | \(0.862285\pi\) | |||||||
\(740\) | −1.30753e8 | + | 6.27336e7i | −0.322670 | + | 0.154812i | ||||
\(741\) | −3.14043e8 | −0.771852 | ||||||||
\(742\) | −3.66800e7 | − | 1.61246e8i | −0.0897880 | − | 0.394709i | ||||
\(743\) | − | 3.10086e8i | − | 0.755990i | −0.925808 | − | 0.377995i | \(-0.876614\pi\) | ||
0.925808 | − | 0.377995i | \(-0.123386\pi\) | |||||||
\(744\) | −2.83994e8 | + | 2.25466e8i | −0.689588 | + | 0.547473i | ||||
\(745\) | −6.69644e7 | −0.161948 | ||||||||
\(746\) | −5.00166e8 | + | 1.13777e8i | −1.20475 | + | 0.274056i | ||||
\(747\) | 6.42118e7i | 0.154047i | ||||||||
\(748\) | 1.27418e6 | + | 2.65572e6i | 0.00304456 | + | 0.00634567i | ||||
\(749\) | 3.47273e8 | 0.826467 | ||||||||
\(750\) | −4.83230e6 | − | 2.12428e7i | −0.0114543 | − | 0.0503534i | ||||
\(751\) | 3.62391e8i | 0.855575i | 0.903879 | + | 0.427787i | \(0.140707\pi\) | ||||
−0.903879 | + | 0.427787i | \(0.859293\pi\) | |||||||
\(752\) | 3.60769e8 | + | 2.89423e8i | 0.848351 | + | 0.680580i | ||||
\(753\) | −4.05379e8 | −0.949460 | ||||||||
\(754\) | 7.79905e8 | − | 1.77412e8i | 1.81940 | − | 0.413875i | ||||
\(755\) | 3.33961e8i | 0.775988i | ||||||||
\(756\) | −5.78090e7 | + | 2.77359e7i | −0.133792 | + | 0.0641914i | ||||
\(757\) | −6.63275e8 | −1.52900 | −0.764498 | − | 0.644627i | \(-0.777013\pi\) | ||||
−0.764498 | + | 0.644627i | \(0.777013\pi\) | |||||||
\(758\) | −7.65174e7 | − | 3.36371e8i | −0.175692 | − | 0.772344i | ||||
\(759\) | 7.73062e6i | 0.0176803i | ||||||||
\(760\) | 1.29904e8 | + | 1.63625e8i | 0.295925 | + | 0.372743i | ||||
\(761\) | 3.91992e8 | 0.889453 | 0.444726 | − | 0.895666i | \(-0.353301\pi\) | ||||
0.444726 | + | 0.895666i | \(0.353301\pi\) | |||||||
\(762\) | −5.73449e7 | + | 1.30448e7i | −0.129607 | + | 0.0294830i | ||||
\(763\) | 3.98605e7i | 0.0897364i | ||||||||
\(764\) | −2.61436e8 | − | 5.44902e8i | −0.586254 | − | 1.22191i | ||||
\(765\) | −2.12199e7 | −0.0473980 | ||||||||
\(766\) | 7.94865e7 | + | 3.49423e8i | 0.176851 | + | 0.777438i | ||||
\(767\) | 7.38901e8i | 1.63757i | ||||||||
\(768\) | 2.55308e8 | − | 5.67129e7i | 0.563612 | − | 0.125198i | ||||
\(769\) | −8.33190e8 | −1.83217 | −0.916084 | − | 0.400988i | \(-0.868667\pi\) | ||||
−0.916084 | + | 0.400988i | \(0.868667\pi\) | |||||||
\(770\) | −3.39804e6 | + | 772982.i | −0.00744314 | + | 0.00169316i | ||||
\(771\) | − | 1.70885e8i | − | 0.372857i | ||||||
\(772\) | 6.31553e8 | − | 3.03010e8i | 1.37264 | − | 0.658574i | ||||
\(773\) | 1.73029e7 | 0.0374612 | 0.0187306 | − | 0.999825i | \(-0.494038\pi\) | ||||
0.0187306 | + | 0.999825i | \(0.494038\pi\) | |||||||
\(774\) | −2.32643e7 | − | 1.02270e8i | −0.0501726 | − | 0.220559i | ||||
\(775\) | − | 1.41977e8i | − | 0.305010i | ||||||
\(776\) | 6.22122e7 | − | 4.93911e7i | 0.133135 | − | 0.105697i | ||||
\(777\) | −1.67121e8 | −0.356261 | ||||||||
\(778\) | −5.23254e8 | + | 1.19029e8i | −1.11115 | + | 0.252764i | ||||
\(779\) | − | 3.98739e8i | − | 0.843483i | ||||||
\(780\) | −6.65833e7 | − | 1.38777e8i | −0.140308 | − | 0.292439i | ||||
\(781\) | −1.52197e6 | −0.00319487 | ||||||||
\(782\) | 4.66578e7 | + | 2.05108e8i | 0.0975672 | + | 0.428906i | ||||
\(783\) | − | 1.37221e8i | − | 0.285847i | ||||||
\(784\) | 1.22259e8 | − | 1.52397e8i | 0.253707 | − | 0.316248i | ||||
\(785\) | 1.67021e8 | 0.345272 | ||||||||
\(786\) | 4.45903e8 | − | 1.01433e8i | 0.918274 | − | 0.208888i | ||||
\(787\) | 4.60899e8i | 0.945544i | 0.881185 | + | 0.472772i | \(0.156747\pi\) | ||||
−0.881185 | + | 0.472772i | \(0.843253\pi\) | |||||||
\(788\) | −6.06362e8 | + | 2.90924e8i | −1.23923 | + | 0.594566i | ||||
\(789\) | 2.90829e8 | 0.592116 | ||||||||
\(790\) | 5.36655e7 | + | 2.35914e8i | 0.108846 | + | 0.478490i | ||||
\(791\) | 4.51690e8i | 0.912665i | ||||||||
\(792\) | 2.27925e6 | + | 2.87090e6i | 0.00458792 | + | 0.00577887i | ||||
\(793\) | 9.75477e8 | 1.95613 | ||||||||
\(794\) | −3.03953e8 | + | 6.91430e7i | −0.607219 | + | 0.138130i | ||||
\(795\) | − | 6.81066e7i | − | 0.135546i | ||||||
\(796\) | −2.90249e8 | − | 6.04957e8i | −0.575482 | − | 1.19946i | ||||
\(797\) | 3.41609e8 | 0.674768 | 0.337384 | − | 0.941367i | \(-0.390458\pi\) | ||||
0.337384 | + | 0.941367i | \(0.390458\pi\) | |||||||
\(798\) | 5.34023e7 | + | 2.34757e8i | 0.105088 | + | 0.461966i | ||||
\(799\) | 1.76392e8i | 0.345810i | ||||||||
\(800\) | −4.47646e7 | + | 9.20972e7i | −0.0874309 | + | 0.179877i | ||||
\(801\) | −7.64471e7 | −0.148752 | ||||||||
\(802\) | −7.68609e8 | + | 1.74843e8i | −1.48999 | + | 0.338941i | ||||
\(803\) | 6.53378e6i | 0.0126188i | ||||||||
\(804\) | 1.82964e8 | − | 8.77837e7i | 0.352045 | − | 0.168906i | ||||
\(805\) | −2.48859e8 | −0.477051 | ||||||||
\(806\) | −2.22506e8 | − | 9.78139e8i | −0.424949 | − | 1.86808i | ||||
\(807\) | 5.13463e8i | 0.976986i | ||||||||
\(808\) | 6.22113e8 | − | 4.93903e8i | 1.17933 | − | 0.936285i | ||||
\(809\) | −3.89991e8 | −0.736562 | −0.368281 | − | 0.929714i | \(-0.620054\pi\) | ||||
−0.368281 | + | 0.929714i | \(0.620054\pi\) | |||||||
\(810\) | −2.57497e7 | + | 5.85751e6i | −0.0484526 | + | 0.0110219i | ||||
\(811\) | 3.29858e8i | 0.618394i | 0.950998 | + | 0.309197i | \(0.100060\pi\) | ||||
−0.950998 | + | 0.309197i | \(0.899940\pi\) | |||||||
\(812\) | −2.65242e8 | − | 5.52836e8i | −0.495422 | − | 1.03259i | ||||
\(813\) | −7.53414e7 | −0.140205 | ||||||||
\(814\) | 2.11927e6 | + | 9.31634e6i | 0.00392929 | + | 0.0172732i | ||||
\(815\) | − | 2.91387e8i | − | 0.538267i | ||||||
\(816\) | 7.78000e7 | + | 6.24142e7i | 0.143189 | + | 0.114872i | ||||
\(817\) | −3.93818e8 | −0.722154 | ||||||||
\(818\) | −1.98963e8 | + | 4.52600e7i | −0.363507 | + | 0.0826903i | ||||
\(819\) | − | 1.77377e8i | − | 0.322882i | ||||||
\(820\) | 1.76205e8 | − | 8.45406e7i | 0.319578 | − | 0.153329i | ||||
\(821\) | 3.48609e8 | 0.629955 | 0.314978 | − | 0.949099i | \(-0.398003\pi\) | ||||
0.314978 | + | 0.949099i | \(0.398003\pi\) | |||||||
\(822\) | 5.47610e7 | + | 2.40730e8i | 0.0985952 | + | 0.433425i | ||||
\(823\) | − | 2.21129e8i | − | 0.396685i | −0.980133 | − | 0.198343i | \(-0.936444\pi\) | ||
0.980133 | − | 0.198343i | \(-0.0635559\pi\) | |||||||
\(824\) | −5.39227e8 | − | 6.79201e8i | −0.963806 | − | 1.21399i | ||||
\(825\) | −1.43526e6 | −0.00255604 | ||||||||
\(826\) | 5.52352e8 | − | 1.25649e8i | 0.980113 | − | 0.222955i | ||||
\(827\) | − | 2.45088e8i | − | 0.433317i | −0.976247 | − | 0.216659i | \(-0.930484\pi\) | ||
0.976247 | − | 0.216659i | \(-0.0695158\pi\) | |||||||
\(828\) | 1.13235e8 | + | 2.36012e8i | 0.199476 | + | 0.415761i | ||||
\(829\) | 7.32697e7 | 0.128606 | 0.0643029 | − | 0.997930i | \(-0.479518\pi\) | ||||
0.0643029 | + | 0.997930i | \(0.479518\pi\) | |||||||
\(830\) | 2.62126e7 | + | 1.15231e8i | 0.0458432 | + | 0.201527i | ||||
\(831\) | − | 1.48361e7i | − | 0.0258534i | ||||||
\(832\) | −1.64067e8 | + | 7.04649e8i | −0.284873 | + | 1.22350i | ||||
\(833\) | 7.45119e7 | 0.128911 | ||||||||
\(834\) | 1.59167e8 | − | 3.62071e7i | 0.274381 | − | 0.0624160i | ||||
\(835\) | − | 2.63739e8i | − | 0.453018i | ||||||
\(836\) | 1.24096e7 | − | 5.95394e6i | 0.0212392 | − | 0.0101903i | ||||
\(837\) | −1.72099e8 | −0.293496 | ||||||||
\(838\) | −8.24402e6 | − | 3.62408e7i | −0.0140090 | − | 0.0615837i | ||||
\(839\) | 3.17675e8i | 0.537895i | 0.963155 | + | 0.268948i | \(0.0866759\pi\) | ||||
−0.963155 | + | 0.268948i | \(0.913324\pi\) | |||||||
\(840\) | −9.24182e7 | + | 7.33720e7i | −0.155926 | + | 0.123792i | ||||
\(841\) | 7.17438e8 | 1.20614 | ||||||||
\(842\) | 4.85181e8 | − | 1.10369e8i | 0.812770 | − | 0.184888i | ||||
\(843\) | 1.64334e8i | 0.274311i | ||||||||
\(844\) | 3.77665e8 | + | 7.87153e8i | 0.628173 | + | 1.30928i | ||||
\(845\) | 1.55986e8 | 0.258534 | ||||||||
\(846\) | 4.86909e7 | + | 2.14046e8i | 0.0804149 | + | 0.353505i | ||||
\(847\) | − | 4.68313e8i | − | 0.770701i | ||||||
\(848\) | −2.00322e8 | + | 2.49704e8i | −0.328504 | + | 0.409484i | ||||
\(849\) | 3.35878e8 | 0.548857 | ||||||||
\(850\) | −3.80800e7 | + | 8.66241e6i | −0.0620070 | + | 0.0141053i | ||||
\(851\) | 6.82292e8i | 1.10709i | ||||||||
\(852\) | −4.64651e7 | + | 2.22933e7i | −0.0751291 | + | 0.0360459i | ||||
\(853\) | −8.91387e8 | −1.43621 | −0.718107 | − | 0.695933i | \(-0.754991\pi\) | ||||
−0.718107 | + | 0.695933i | \(0.754991\pi\) | |||||||
\(854\) | −1.65878e8 | − | 7.29201e8i | −0.266327 | − | 1.17077i | ||||
\(855\) | 9.91562e7i | 0.158643i | ||||||||
\(856\) | −4.18011e8 | − | 5.26520e8i | −0.666448 | − | 0.839448i | ||||
\(857\) | −1.67921e8 | −0.266786 | −0.133393 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133393 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(858\) | −9.88805e6 | + | 2.24932e6i | −0.0156548 | + | 0.00356115i | ||||
\(859\) | − | 7.27537e8i | − | 1.14782i | −0.818917 | − | 0.573912i | \(-0.805425\pi\) | ||
0.818917 | − | 0.573912i | \(-0.194575\pi\) | |||||||
\(860\) | −8.34974e7 | − | 1.74031e8i | −0.131274 | − | 0.273609i | ||||
\(861\) | 2.25214e8 | 0.352847 | ||||||||
\(862\) | 1.51665e8 | + | 6.66720e8i | 0.236790 | + | 1.04093i | ||||
\(863\) | − | 6.52206e8i | − | 1.01474i | −0.861730 | − | 0.507368i | \(-0.830619\pi\) | ||
0.861730 | − | 0.507368i | \(-0.169381\pi\) | |||||||
\(864\) | 1.11636e8 | + | 5.42618e7i | 0.173087 | + | 0.0841304i | ||||
\(865\) | −5.02508e7 | −0.0776416 | ||||||||
\(866\) | −3.79711e8 | + | 8.63764e7i | −0.584655 | + | 0.132997i | ||||
\(867\) | − | 3.38228e8i | − | 0.518983i | ||||||
\(868\) | −6.93354e8 | + | 3.32661e8i | −1.06022 | + | 0.508678i | ||||
\(869\) | 1.59393e7 | 0.0242891 | ||||||||
\(870\) | −5.60163e7 | − | 2.46248e8i | −0.0850661 | − | 0.373951i | ||||
\(871\) | 5.61394e8i | 0.849597i | ||||||||
\(872\) | 6.04347e7 | − | 4.79799e7i | 0.0911458 | − | 0.0723618i | ||||
\(873\) | 3.77004e7 | 0.0566634 | ||||||||
\(874\) | 9.58425e8 | − | 2.18022e8i | 1.43557 | − | 0.326562i | ||||
\(875\) | − | 4.62027e7i | − | 0.0689674i | ||||||
\(876\) | 9.57044e7 | + | 1.99473e8i | 0.142370 | + | 0.296738i | ||||
\(877\) | 9.00052e7 | 0.133435 | 0.0667174 | − | 0.997772i | \(-0.478747\pi\) | ||||
0.0667174 | + | 0.997772i | \(0.478747\pi\) | |||||||
\(878\) | 2.45919e8 | + | 1.08106e9i | 0.363337 | + | 1.59723i | ||||
\(879\) | 4.63405e8i | 0.682329i | ||||||||
\(880\) | 5.26216e6 | + | 4.22152e6i | 0.00772176 | + | 0.00619470i | ||||
\(881\) | −6.72192e8 | −0.983027 | −0.491514 | − | 0.870870i | \(-0.663556\pi\) | ||||
−0.491514 | + | 0.870870i | \(0.663556\pi\) | |||||||
\(882\) | 9.04177e7 | − | 2.05681e7i | 0.131779 | − | 0.0299771i | ||||
\(883\) | − | 1.80609e8i | − | 0.262336i | −0.991360 | − | 0.131168i | \(-0.958127\pi\) | ||
0.991360 | − | 0.131168i | \(-0.0418727\pi\) | |||||||
\(884\) | −2.48773e8 | + | 1.19358e8i | −0.360119 | + | 0.172780i | ||||
\(885\) | 2.33301e8 | 0.336579 | ||||||||
\(886\) | −2.21362e8 | − | 9.73111e8i | −0.318275 | − | 1.39914i | ||||
\(887\) | 1.00620e9i | 1.44183i | 0.693022 | + | 0.720916i | \(0.256279\pi\) | ||||
−0.693022 | + | 0.720916i | \(0.743721\pi\) | |||||||
\(888\) | 2.01163e8 | + | 2.53381e8i | 0.287282 | + | 0.361856i | ||||
\(889\) | −1.24724e8 | −0.177519 | ||||||||
\(890\) | −1.37187e8 | + | 3.12073e7i | −0.194601 | + | 0.0442676i | ||||
\(891\) | 1.73976e6i | 0.00245955i | ||||||||
\(892\) | −5.61269e8 | − | 1.16983e9i | −0.790818 | − | 1.64828i | ||||
\(893\) | 8.24240e8 | 1.15744 | ||||||||
\(894\) | 3.31358e7 | + | 1.45665e8i | 0.0463751 | + | 0.203866i | ||||
\(895\) | − | 2.09930e8i | − | 0.292824i | ||||||
\(896\) | 5.54647e8 | + | 2.82137e6i | 0.771069 | + | 0.00392226i | ||||
\(897\) | −7.24161e8 | −1.00336 | ||||||||
\(898\) | −3.40020e8 | + | 7.73474e7i | −0.469543 | + | 0.106811i | ||||
\(899\) | − | 1.64581e9i | − | 2.26517i | ||||||
\(900\) | −4.38177e7 | + | 2.10231e7i | −0.0601066 | + | 0.0288383i | ||||
\(901\) | −1.22088e8 | −0.166917 | ||||||||
\(902\) | −2.85596e6 | − | 1.25548e7i | −0.00389164 | − | 0.0171077i | ||||
\(903\) | − | 2.22435e8i | − | 0.302093i | ||||||
\(904\) | 6.84833e8 | − | 5.43698e8i | 0.926999 | − | 0.735957i | ||||
\(905\) | 5.62863e8 | 0.759376 | ||||||||
\(906\) | 7.26454e8 | − | 1.65253e8i | 0.976841 | − | 0.222211i | ||||
\(907\) | − | 8.47891e8i | − | 1.13637i | −0.822903 | − | 0.568183i | \(-0.807647\pi\) | ||
0.822903 | − | 0.568183i | \(-0.192353\pi\) | |||||||
\(908\) | 3.78786e8 | + | 7.89490e8i | 0.505984 | + | 1.05460i | ||||
\(909\) | 3.76998e8 | 0.501935 | ||||||||
\(910\) | −7.24087e7 | − | 3.18309e8i | −0.0960874 | − | 0.422401i | ||||
\(911\) | − | 3.23382e8i | − | 0.427722i | −0.976864 | − | 0.213861i | \(-0.931396\pi\) | ||
0.976864 | − | 0.213861i | \(-0.0686039\pi\) | |||||||
\(912\) | 2.91648e8 | − | 3.63542e8i | 0.384481 | − | 0.479259i | ||||
\(913\) | 7.78547e6 | 0.0102299 | ||||||||
\(914\) | −2.67997e8 | + | 6.09638e7i | −0.350988 | + | 0.0798423i | ||||
\(915\) | − | 3.07998e8i | − | 0.402054i | ||||||
\(916\) | −9.94663e8 | + | 4.77225e8i | −1.29416 | + | 0.620921i | ||||
\(917\) | 9.69829e8 | 1.25773 | ||||||||
\(918\) | 1.05002e7 | + | 4.61590e7i | 0.0135728 | + | 0.0596663i | ||||
\(919\) | 1.03492e8i | 0.133340i | 0.997775 | + | 0.0666699i | \(0.0212374\pi\) | ||||
−0.997775 | + | 0.0666699i | \(0.978763\pi\) | |||||||
\(920\) | 2.99550e8 | + | 3.77308e8i | 0.384686 | + | 0.484544i | ||||
\(921\) | −2.60251e8 | −0.333130 | ||||||||
\(922\) | 4.93092e8 | − | 1.12168e8i | 0.629123 | − | 0.143112i | ||||
\(923\) | − | 1.42570e8i | − | 0.181310i | ||||||
\(924\) | 3.36289e6 | + | 7.00914e6i | 0.00426281 | + | 0.00888483i | ||||
\(925\) | −1.26673e8 | −0.160052 | ||||||||
\(926\) | −1.39938e8 | − | 6.15167e8i | −0.176239 | − | 0.774747i | ||||
\(927\) | − | 4.11593e8i | − | 0.516689i | ||||||
\(928\) | −5.18913e8 | + | 1.06759e9i | −0.649308 | + | 1.33586i | ||||
\(929\) | 1.31287e9 | 1.63747 | 0.818735 | − | 0.574172i | \(-0.194676\pi\) | ||||
0.818735 | + | 0.574172i | \(0.194676\pi\) | |||||||
\(930\) | −3.08839e8 | + | 7.02543e7i | −0.383957 | + | 0.0873422i | ||||
\(931\) | − | 3.48178e8i | − | 0.431471i | ||||||
\(932\) | 7.18697e8 | − | 3.44820e8i | 0.887765 | − | 0.425937i | ||||
\(933\) | −3.27154e8 | −0.402817 | ||||||||
\(934\) | 9.26334e7 | + | 4.07217e8i | 0.113691 | + | 0.499788i | ||||
\(935\) | 2.57285e6i | 0.00314760i | ||||||||
\(936\) | −2.68930e8 | + | 2.13507e8i | −0.327954 | + | 0.260367i | ||||
\(937\) | 4.13735e8 | 0.502926 | 0.251463 | − | 0.967867i | \(-0.419088\pi\) | ||||
0.251463 | + | 0.967867i | \(0.419088\pi\) | |||||||
\(938\) | 4.19660e8 | − | 9.54639e7i | 0.508498 | − | 0.115673i | ||||
\(939\) | − | 4.19357e8i | − | 0.506509i | ||||||
\(940\) | 1.74755e8 | + | 3.64237e8i | 0.210401 | + | 0.438531i | ||||
\(941\) | −7.06411e8 | −0.847791 | −0.423895 | − | 0.905711i | \(-0.639338\pi\) | ||||
−0.423895 | + | 0.905711i | \(0.639338\pi\) | |||||||
\(942\) | −8.26466e7 | − | 3.63315e8i | −0.0988717 | − | 0.434641i | ||||
\(943\) | − | 9.19465e8i | − | 1.09648i | ||||||
\(944\) | −8.55367e8 | − | 6.86209e8i | −1.01680 | − | 0.815719i | ||||
\(945\) | −5.60050e7 | −0.0663639 | ||||||||
\(946\) | −1.23999e7 | + | 2.82072e6i | −0.0146469 | + | 0.00333185i | ||||
\(947\) | − | 1.19548e9i | − | 1.40764i | −0.710377 | − | 0.703822i | \(-0.751475\pi\) | ||
0.710377 | − | 0.703822i | \(-0.248525\pi\) | |||||||
\(948\) | 4.86621e8 | − | 2.33474e8i | 0.571171 | − | 0.274039i | ||||
\(949\) | −6.12048e8 | −0.716122 | ||||||||
\(950\) | 4.04776e7 | + | 1.77940e8i | 0.0472110 | + | 0.207540i | ||||
\(951\) | 5.86056e8i | 0.681393i | ||||||||
\(952\) | 1.31527e8 | + | 1.65669e8i | 0.152442 | + | 0.192013i | ||||
\(953\) | −6.95229e8 | −0.803247 | −0.401623 | − | 0.915805i | \(-0.631554\pi\) | ||||
−0.401623 | + | 0.915805i | \(0.631554\pi\) | |||||||
\(954\) | −1.48150e8 | + | 3.37010e7i | −0.170631 | + | 0.0388149i | ||||
\(955\) | − | 5.27899e8i | − | 0.606094i | ||||||
\(956\) | 6.01850e8 | + | 1.25442e9i | 0.688834 | + | 1.43571i | ||||
\(957\) | −1.66375e7 | −0.0189825 | ||||||||
\(958\) | 1.50903e8 | + | 6.63372e8i | 0.171634 | + | 0.754503i | ||||
\(959\) | 5.23582e8i | 0.593648i | ||||||||
\(960\) | 2.22487e8 | + | 5.18028e7i | 0.251472 | + | 0.0585516i | ||||
\(961\) | −1.17663e9 | −1.32578 | ||||||||
\(962\) | −8.72703e8 | + | 1.98522e8i | −0.980260 | + | 0.222989i | ||||
\(963\) | − | 3.19069e8i | − | 0.357278i | ||||||
\(964\) | −4.56952e8 | + | 2.19239e8i | −0.510081 | + | 0.244730i | ||||
\(965\) | 6.11845e8 | 0.680863 | ||||||||
\(966\) | 1.23142e8 | + | 5.41334e8i | 0.136608 | + | 0.600529i | ||||
\(967\) | 8.16482e8i | 0.902958i | 0.892282 | + | 0.451479i | \(0.149103\pi\) | ||||
−0.892282 | + | 0.451479i | \(0.850897\pi\) | |||||||
\(968\) | −7.10035e8 | + | 5.63706e8i | −0.782805 | + | 0.621479i | ||||
\(969\) | 1.77748e8 | 0.195359 | ||||||||
\(970\) | 6.76548e7 | − | 1.53901e7i | 0.0741282 | − | 0.0168626i | ||||
\(971\) | 3.34681e8i | 0.365572i | 0.983153 | + | 0.182786i | \(0.0585115\pi\) | ||||
−0.983153 | + | 0.182786i | \(0.941488\pi\) | |||||||
\(972\) | 2.54833e7 | + | 5.31140e7i | 0.0277496 | + | 0.0578376i | ||||
\(973\) | 3.46185e8 | 0.375811 | ||||||||
\(974\) | −1.10055e7 | − | 4.83801e7i | −0.0119105 | − | 0.0523588i | ||||
\(975\) | − | 1.34447e8i | − | 0.145056i | ||||||
\(976\) | −9.05915e8 | + | 1.12923e9i | −0.974402 | + | 1.21460i | ||||
\(977\) | 4.91550e8 | 0.527089 | 0.263545 | − | 0.964647i | \(-0.415108\pi\) | ||||
0.263545 | + | 0.964647i | \(0.415108\pi\) | |||||||
\(978\) | −6.33845e8 | + | 1.44186e8i | −0.677589 | + | 0.154137i | ||||
\(979\) | 9.26896e6i | 0.00987831i | ||||||||
\(980\) | 1.53862e8 | − | 7.38206e7i | 0.163475 | − | 0.0784331i | ||||
\(981\) | 3.66232e7 | 0.0387926 | ||||||||
\(982\) | −2.38582e8 | − | 1.04881e9i | −0.251944 | − | 1.10755i | ||||
\(983\) | 8.15838e8i | 0.858902i | 0.903090 | + | 0.429451i | \(0.141293\pi\) | ||||
−0.903090 | + | 0.429451i | \(0.858707\pi\) | |||||||
\(984\) | −2.71089e8 | − | 3.41460e8i | −0.284530 | − | 0.358389i | ||||
\(985\) | −5.87440e8 | −0.614688 | ||||||||
\(986\) | −4.41426e8 | + | 1.00415e8i | −0.460497 | + | 0.104753i | ||||
\(987\) | 4.65545e8i | 0.484183i | ||||||||
\(988\) | 5.57732e8 | + | 1.16246e9i | 0.578302 | + | 1.20534i | ||||
\(989\) | −9.08119e8 | −0.938758 | ||||||||
\(990\) | 710204. | + | 3.12206e6i | 0.000731943 | + | 0.00321763i | ||||
\(991\) | 1.09131e9i | 1.12132i | 0.828047 | + | 0.560659i | \(0.189452\pi\) | ||||
−0.828047 | + | 0.560659i | \(0.810548\pi\) | |||||||
\(992\) | 1.33895e9 | + | 6.50810e8i | 1.37161 | + | 0.666682i | ||||
\(993\) | 1.45084e8 | 0.148173 | ||||||||
\(994\) | −1.06576e8 | + | 2.42437e7i | −0.108517 | + | 0.0246854i | ||||
\(995\) | − | 5.86079e8i | − | 0.594959i | ||||||
\(996\) | 2.37687e8 | − | 1.14039e8i | 0.240562 | − | 0.115418i | ||||
\(997\) | −4.66809e8 | −0.471035 | −0.235518 | − | 0.971870i | \(-0.575679\pi\) | ||||
−0.235518 | + | 0.971870i | \(0.575679\pi\) | |||||||
\(998\) | 2.15043e8 | + | 9.45330e8i | 0.216338 | + | 0.951025i | ||||
\(999\) | 1.53548e8i | 0.154010i |
(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 | 60.7.c.a.31.2 | yes | 24 | |
3.2 | odd | 2 | 180.7.c.b.91.23 | 24 | |||
4.3 | odd | 2 | inner | 60.7.c.a.31.1 | ✓ | 24 | |
12.11 | even | 2 | 180.7.c.b.91.24 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.c.a.31.1 | ✓ | 24 | 4.3 | odd | 2 | inner | |
60.7.c.a.31.2 | yes | 24 | 1.1 | even | 1 | trivial | |
180.7.c.b.91.23 | 24 | 3.2 | odd | 2 | |||
180.7.c.b.91.24 | 24 | 12.11 | even | 2 |