Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(19,60)]
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, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (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: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.8 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.43144 | + | 4.75779i | −0.803931 | + | 0.594723i | ||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | 18.7270 | − | 61.1989i | 0.292609 | − | 0.956232i | ||||
\(5\) | −121.123 | − | 30.8887i | −0.968988 | − | 0.247109i | ||||
\(6\) | 100.256 | − | 74.1665i | 0.464150 | − | 0.343364i | ||||
\(7\) | −549.446 | −1.60188 | −0.800941 | − | 0.598743i | \(-0.795667\pi\) | ||||
−0.800941 | + | 0.598743i | \(0.795667\pi\) | |||||||
\(8\) | 170.730 | + | 482.696i | 0.333456 | + | 0.942766i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 925.960 | − | 377.621i | 0.925960 | − | 0.377621i | ||||
\(11\) | − | 2553.45i | − | 1.91844i | −0.282653 | − | 0.959222i | \(-0.591214\pi\) | ||
0.282653 | − | 0.959222i | \(-0.408786\pi\) | |||||||
\(12\) | −291.924 | + | 953.996i | −0.168938 | + | 0.552081i | ||||
\(13\) | 1094.42i | 0.498142i | 0.968485 | + | 0.249071i | \(0.0801252\pi\) | ||||
−0.968485 | + | 0.249071i | \(0.919875\pi\) | |||||||
\(14\) | 3533.73 | − | 2614.14i | 1.28780 | − | 0.952676i | ||||
\(15\) | 1888.13 | + | 481.507i | 0.559445 | + | 0.142669i | ||||
\(16\) | −3394.60 | − | 2292.14i | −0.828760 | − | 0.559604i | ||||
\(17\) | 1497.06i | 0.304715i | 0.988325 | + | 0.152357i | \(0.0486864\pi\) | ||||
−0.988325 | + | 0.152357i | \(0.951314\pi\) | |||||||
\(18\) | −1562.84 | + | 1156.14i | −0.267977 | + | 0.198241i | ||||
\(19\) | 9519.26i | 1.38785i | 0.720048 | + | 0.693925i | \(0.244120\pi\) | ||||
−0.720048 | + | 0.693925i | \(0.755880\pi\) | |||||||
\(20\) | −4158.63 | + | 6834.17i | −0.519828 | + | 0.854271i | ||||
\(21\) | 8565.01 | 0.924847 | ||||||||
\(22\) | 12148.8 | + | 16422.4i | 1.14094 | + | 1.54230i | ||||
\(23\) | 67.4831 | 0.00554640 | 0.00277320 | − | 0.999996i | \(-0.499117\pi\) | ||||
0.00277320 | + | 0.999996i | \(0.499117\pi\) | |||||||
\(24\) | −2661.41 | − | 7524.49i | −0.192521 | − | 0.544306i | ||||
\(25\) | 13716.8 | + | 7482.69i | 0.877874 | + | 0.478892i | ||||
\(26\) | −5207.00 | − | 7038.68i | −0.296256 | − | 0.400471i | ||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | −10289.4 | + | 33625.4i | −0.468725 | + | 1.53177i | ||||
\(29\) | −6173.49 | −0.253126 | −0.126563 | − | 0.991959i | \(-0.540395\pi\) | ||||
−0.126563 | + | 0.991959i | \(0.540395\pi\) | |||||||
\(30\) | −14434.3 | + | 5886.52i | −0.534604 | + | 0.218019i | ||||
\(31\) | 20870.0i | 0.700547i | 0.936647 | + | 0.350273i | \(0.113911\pi\) | ||||
−0.936647 | + | 0.350273i | \(0.886089\pi\) | |||||||
\(32\) | 32737.7 | − | 1409.04i | 0.999075 | − | 0.0430004i | ||||
\(33\) | 39804.3i | 1.10761i | ||||||||
\(34\) | −7122.70 | − | 9628.28i | −0.181221 | − | 0.244969i | ||||
\(35\) | 66550.7 | + | 16971.6i | 1.55220 | + | 0.395840i | ||||
\(36\) | 4550.65 | − | 14871.3i | 0.0975362 | − | 0.318744i | ||||
\(37\) | − | 26680.6i | − | 0.526732i | −0.964696 | − | 0.263366i | \(-0.915167\pi\) | ||
0.964696 | − | 0.263366i | \(-0.0848327\pi\) | |||||||
\(38\) | −45290.6 | − | 61222.6i | −0.825386 | − | 1.11573i | ||||
\(39\) | − | 17060.3i | − | 0.287602i | ||||||
\(40\) | −5769.53 | − | 63739.4i | −0.0901489 | − | 0.995928i | ||||
\(41\) | 102914. | 1.49322 | 0.746610 | − | 0.665262i | \(-0.231680\pi\) | ||||
0.746610 | + | 0.665262i | \(0.231680\pi\) | |||||||
\(42\) | −55085.4 | + | 40750.5i | −0.743513 | + | 0.550028i | ||||
\(43\) | −8841.12 | −0.111199 | −0.0555996 | − | 0.998453i | \(-0.517707\pi\) | ||||
−0.0555996 | + | 0.998453i | \(0.517707\pi\) | |||||||
\(44\) | −156268. | − | 47818.3i | −1.83448 | − | 0.561354i | ||||
\(45\) | −29433.0 | − | 7505.95i | −0.322996 | − | 0.0823698i | ||||
\(46\) | −434.014 | + | 321.070i | −0.00445892 | + | 0.00329857i | ||||
\(47\) | −49099.5 | −0.472916 | −0.236458 | − | 0.971642i | \(-0.575987\pi\) | ||||
−0.236458 | + | 0.971642i | \(0.575987\pi\) | |||||||
\(48\) | 52916.6 | + | 35730.9i | 0.478485 | + | 0.323087i | ||||
\(49\) | 184241. | 1.56603 | ||||||||
\(50\) | −123820. | + | 17137.0i | −0.990558 | + | 0.137096i | ||||
\(51\) | − | 23336.9i | − | 0.175927i | ||||||
\(52\) | 66977.1 | + | 20495.1i | 0.476339 | + | 0.145761i | ||||
\(53\) | − | 246920.i | − | 1.65855i | −0.558842 | − | 0.829274i | \(-0.688754\pi\) | ||
0.558842 | − | 0.829274i | \(-0.311246\pi\) | |||||||
\(54\) | 24362.3 | − | 18022.5i | 0.154717 | − | 0.114455i | ||||
\(55\) | −78872.7 | + | 309283.i | −0.474066 | + | 1.85895i | ||||
\(56\) | −93806.7 | − | 265215.i | −0.534158 | − | 1.51020i | ||||
\(57\) | − | 148391.i | − | 0.801275i | ||||||
\(58\) | 39704.4 | − | 29372.1i | 0.203496 | − | 0.150540i | ||||
\(59\) | 114674.i | 0.558351i | 0.960240 | + | 0.279175i | \(0.0900611\pi\) | ||||
−0.960240 | + | 0.279175i | \(0.909939\pi\) | |||||||
\(60\) | 64826.6 | − | 106534.i | 0.300123 | − | 0.493213i | ||||
\(61\) | −15188.1 | −0.0669136 | −0.0334568 | − | 0.999440i | \(-0.510652\pi\) | ||||
−0.0334568 | + | 0.999440i | \(0.510652\pi\) | |||||||
\(62\) | −99295.0 | − | 134224.i | −0.416631 | − | 0.563191i | ||||
\(63\) | −133515. | −0.533961 | ||||||||
\(64\) | −203847. | + | 164821.i | −0.777614 | + | 0.628742i | ||||
\(65\) | 33805.1 | − | 132560.i | 0.123095 | − | 0.482693i | ||||
\(66\) | −189381. | − | 255999.i | −0.658724 | − | 0.890445i | ||||
\(67\) | 380903. | 1.26646 | 0.633228 | − | 0.773965i | \(-0.281729\pi\) | ||||
0.633228 | + | 0.773965i | \(0.281729\pi\) | |||||||
\(68\) | 91618.5 | + | 28035.4i | 0.291378 | + | 0.0891621i | ||||
\(69\) | −1051.96 | −0.00320222 | ||||||||
\(70\) | −508765. | + | 207482.i | −1.48328 | + | 0.604904i | ||||
\(71\) | − | 323615.i | − | 0.904177i | −0.891973 | − | 0.452088i | \(-0.850679\pi\) | ||
0.891973 | − | 0.452088i | \(-0.149321\pi\) | |||||||
\(72\) | 41487.3 | + | 117295.i | 0.111152 | + | 0.314255i | ||||
\(73\) | − | 361842.i | − | 0.930145i | −0.885273 | − | 0.465072i | \(-0.846028\pi\) | ||
0.885273 | − | 0.465072i | \(-0.153972\pi\) | |||||||
\(74\) | 126940. | + | 171595.i | 0.313260 | + | 0.423456i | ||||
\(75\) | −213823. | − | 116644.i | −0.506841 | − | 0.276488i | ||||
\(76\) | 582568. | + | 178267.i | 1.32711 | + | 0.406097i | ||||
\(77\) | 1.40298e6i | 3.07312i | ||||||||
\(78\) | 81169.1 | + | 109722.i | 0.171044 | + | 0.231212i | ||||
\(79\) | 753970.i | 1.52923i | 0.644488 | + | 0.764615i | \(0.277071\pi\) | ||||
−0.644488 | + | 0.764615i | \(0.722929\pi\) | |||||||
\(80\) | 340365. | + | 382486.i | 0.664775 | + | 0.747044i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −661887. | + | 489644.i | −1.20045 | + | 0.888053i | ||||
\(83\) | 23678.7 | 0.0414117 | 0.0207059 | − | 0.999786i | \(-0.493409\pi\) | ||||
0.0207059 | + | 0.999786i | \(0.493409\pi\) | |||||||
\(84\) | 160397. | − | 524169.i | 0.270618 | − | 0.884369i | ||||
\(85\) | 46242.3 | − | 181329.i | 0.0752979 | − | 0.295265i | ||||
\(86\) | 56861.2 | − | 42064.1i | 0.0893965 | − | 0.0661328i | ||||
\(87\) | 96235.2 | 0.146142 | ||||||||
\(88\) | 1.23254e6 | − | 435950.i | 1.80864 | − | 0.639718i | ||||
\(89\) | −559777. | −0.794045 | −0.397023 | − | 0.917809i | \(-0.629957\pi\) | ||||
−0.397023 | + | 0.917809i | \(0.629957\pi\) | |||||||
\(90\) | 225008. | − | 91761.8i | 0.308653 | − | 0.125874i | ||||
\(91\) | − | 601322.i | − | 0.797964i | ||||||
\(92\) | 1263.75 | − | 4129.89i | 0.00162293 | − | 0.00530365i | ||||
\(93\) | − | 325331.i | − | 0.404461i | ||||||
\(94\) | 315781. | − | 233605.i | 0.380191 | − | 0.281254i | ||||
\(95\) | 294037. | − | 1.15301e6i | 0.342951 | − | 1.34481i | ||||
\(96\) | −510330. | + | 21964.7i | −0.576816 | + | 0.0248263i | ||||
\(97\) | 843786.i | 0.924522i | 0.886744 | + | 0.462261i | \(0.152962\pi\) | ||||
−0.886744 | + | 0.462261i | \(0.847038\pi\) | |||||||
\(98\) | −1.18494e6 | + | 876581.i | −1.25898 | + | 0.931352i | ||||
\(99\) | − | 620488.i | − | 0.639481i | ||||||
\(100\) | 714805. | − | 699323.i | 0.714805 | − | 0.699323i | ||||
\(101\) | 490739. | 0.476307 | 0.238153 | − | 0.971228i | \(-0.423458\pi\) | ||||
0.238153 | + | 0.971228i | \(0.423458\pi\) | |||||||
\(102\) | 111032. | + | 150090.i | 0.104628 | + | 0.141433i | ||||
\(103\) | −1.06879e6 | −0.978095 | −0.489047 | − | 0.872257i | \(-0.662656\pi\) | ||||
−0.489047 | + | 0.872257i | \(0.662656\pi\) | |||||||
\(104\) | −528271. | + | 186849.i | −0.469631 | + | 0.166108i | ||||
\(105\) | −1.03742e6 | − | 264562.i | −0.896165 | − | 0.228538i | ||||
\(106\) | 1.17479e6 | + | 1.58805e6i | 0.986377 | + | 1.33336i | ||||
\(107\) | 1.83486e6 | 1.49779 | 0.748896 | − | 0.662688i | \(-0.230584\pi\) | ||||
0.748896 | + | 0.662688i | \(0.230584\pi\) | |||||||
\(108\) | −70937.6 | + | 231821.i | −0.0563126 | + | 0.184027i | ||||
\(109\) | 930756. | 0.718714 | 0.359357 | − | 0.933200i | \(-0.382996\pi\) | ||||
0.359357 | + | 0.933200i | \(0.382996\pi\) | |||||||
\(110\) | −964235. | − | 2.36439e6i | −0.724444 | − | 1.77640i | ||||
\(111\) | 415909.i | 0.304109i | ||||||||
\(112\) | 1.86515e6 | + | 1.25940e6i | 1.32758 | + | 0.896419i | ||||
\(113\) | 2.29606e6i | 1.59128i | 0.605767 | + | 0.795642i | \(0.292866\pi\) | ||||
−0.605767 | + | 0.795642i | \(0.707134\pi\) | |||||||
\(114\) | 706010. | + | 954366.i | 0.476537 | + | 0.644170i | ||||
\(115\) | −8173.78 | − | 2084.46i | −0.00537439 | − | 0.00137057i | ||||
\(116\) | −115611. | + | 377811.i | −0.0740669 | + | 0.242047i | ||||
\(117\) | 265943.i | 0.166047i | ||||||||
\(118\) | −545592. | − | 737517.i | −0.332064 | − | 0.448875i | ||||
\(119\) | − | 822554.i | − | 0.488117i | ||||||
\(120\) | 89938.0 | + | 993599.i | 0.0520475 | + | 0.574999i | ||||
\(121\) | −4.74854e6 | −2.68043 | ||||||||
\(122\) | 97681.6 | − | 72261.8i | 0.0537939 | − | 0.0397951i | ||||
\(123\) | −1.60427e6 | −0.862111 | ||||||||
\(124\) | 1.27722e6 | + | 390831.i | 0.669886 | + | 0.204986i | ||||
\(125\) | −1.43029e6 | − | 1.33002e6i | −0.732310 | − | 0.680971i | ||||
\(126\) | 858696. | − | 635237.i | 0.429267 | − | 0.317559i | ||||
\(127\) | −2.86745e6 | −1.39986 | −0.699931 | − | 0.714210i | \(-0.746786\pi\) | ||||
−0.699931 | + | 0.714210i | \(0.746786\pi\) | |||||||
\(128\) | 526846. | − | 2.02990e6i | 0.251220 | − | 0.967930i | ||||
\(129\) | 137819. | 0.0642009 | ||||||||
\(130\) | 413274. | + | 1.01339e6i | 0.188108 | + | 0.461259i | ||||
\(131\) | 1.61676e6i | 0.719170i | 0.933112 | + | 0.359585i | \(0.117082\pi\) | ||||
−0.933112 | + | 0.359585i | \(0.882918\pi\) | |||||||
\(132\) | 2.43598e6 | + | 745414.i | 1.05914 | + | 0.324098i | ||||
\(133\) | − | 5.23031e6i | − | 2.22317i | ||||||
\(134\) | −2.44976e6 | + | 1.81226e6i | −1.01814 | + | 0.753191i | ||||
\(135\) | 458815. | + | 117006.i | 0.186482 | + | 0.0475562i | ||||
\(136\) | −722626. | + | 255593.i | −0.287274 | + | 0.101609i | ||||
\(137\) | − | 1.21351e6i | − | 0.471934i | −0.971761 | − | 0.235967i | \(-0.924174\pi\) | ||
0.971761 | − | 0.235967i | \(-0.0758258\pi\) | |||||||
\(138\) | 6765.60 | − | 5004.99i | 0.00257436 | − | 0.00190443i | ||||
\(139\) | − | 745684.i | − | 0.277658i | −0.990316 | − | 0.138829i | \(-0.955666\pi\) | ||
0.990316 | − | 0.138829i | \(-0.0443339\pi\) | |||||||
\(140\) | 2.28494e6 | − | 3.75500e6i | 0.832703 | − | 1.36844i | ||||
\(141\) | 765386. | 0.273038 | ||||||||
\(142\) | 1.53969e6 | + | 2.08131e6i | 0.537735 | + | 0.726895i | ||||
\(143\) | 2.79454e6 | 0.955657 | ||||||||
\(144\) | −824888. | − | 556989.i | −0.276253 | − | 0.186535i | ||||
\(145\) | 747754. | + | 190691.i | 0.245276 | + | 0.0625498i | ||||
\(146\) | 1.72157e6 | + | 2.32717e6i | 0.553179 | + | 0.747772i | ||||
\(147\) | −2.87204e6 | −0.904145 | ||||||||
\(148\) | −1.63282e6 | − | 499646.i | −0.503678 | − | 0.154126i | ||||
\(149\) | 2.87355e6 | 0.868679 | 0.434340 | − | 0.900749i | \(-0.356982\pi\) | ||||
0.434340 | + | 0.900749i | \(0.356982\pi\) | |||||||
\(150\) | 1.93016e6 | − | 267139.i | 0.571899 | − | 0.0791524i | ||||
\(151\) | − | 1.70934e6i | − | 0.496476i | −0.968699 | − | 0.248238i | \(-0.920149\pi\) | ||
0.968699 | − | 0.248238i | \(-0.0798515\pi\) | |||||||
\(152\) | −4.59491e6 | + | 1.62522e6i | −1.30842 | + | 0.462787i | ||||
\(153\) | 363786.i | 0.101572i | ||||||||
\(154\) | −6.67508e6 | − | 9.02320e6i | −1.82766 | − | 2.47058i | ||||
\(155\) | 644647. | − | 2.52785e6i | 0.173112 | − | 0.678821i | ||||
\(156\) | −1.04407e6 | − | 319487.i | −0.275014 | − | 0.0841549i | ||||
\(157\) | 5.99085e6i | 1.54807i | 0.633145 | + | 0.774033i | \(0.281764\pi\) | ||||
−0.633145 | + | 0.774033i | \(0.718236\pi\) | |||||||
\(158\) | −3.58723e6 | − | 4.84911e6i | −0.909468 | − | 1.22939i | ||||
\(159\) | 3.84910e6i | 0.957563i | ||||||||
\(160\) | −4.00883e6 | − | 840557.i | −0.978717 | − | 0.205214i | ||||
\(161\) | −37078.3 | −0.00888468 | ||||||||
\(162\) | −379770. | + | 280942.i | −0.0893256 | + | 0.0660804i | ||||
\(163\) | 3.10350e6 | 0.716619 | 0.358310 | − | 0.933603i | \(-0.383353\pi\) | ||||
0.358310 | + | 0.933603i | \(0.383353\pi\) | |||||||
\(164\) | 1.92727e6 | − | 6.29823e6i | 0.436929 | − | 1.42787i | ||||
\(165\) | 1.22950e6 | − | 4.82124e6i | 0.273702 | − | 1.07326i | ||||
\(166\) | −152288. | + | 112658.i | −0.0332921 | + | 0.0246285i | ||||
\(167\) | 6.24357e6 | 1.34055 | 0.670276 | − | 0.742112i | \(-0.266176\pi\) | ||||
0.670276 | + | 0.742112i | \(0.266176\pi\) | |||||||
\(168\) | 1.46230e6 | + | 4.13429e6i | 0.308396 | + | 0.871914i | ||||
\(169\) | 3.62906e6 | 0.751855 | ||||||||
\(170\) | 565322. | + | 1.38622e6i | 0.115066 | + | 0.282154i | ||||
\(171\) | 2.31318e6i | 0.462616i | ||||||||
\(172\) | −165567. | + | 541066.i | −0.0325379 | + | 0.106332i | ||||
\(173\) | 4.02510e6i | 0.777389i | 0.921367 | + | 0.388695i | \(0.127074\pi\) | ||||
−0.921367 | + | 0.388695i | \(0.872926\pi\) | |||||||
\(174\) | −618931. | + | 457866.i | −0.117488 | + | 0.0869142i | ||||
\(175\) | −7.53662e6 | − | 4.11133e6i | −1.40625 | − | 0.767128i | ||||
\(176\) | −5.85286e6 | + | 8.66795e6i | −1.07357 | + | 1.58993i | ||||
\(177\) | − | 1.78758e6i | − | 0.322364i | ||||||
\(178\) | 3.60018e6 | − | 2.66330e6i | 0.638357 | − | 0.472237i | ||||
\(179\) | 5.02425e6i | 0.876015i | 0.898971 | + | 0.438008i | \(0.144316\pi\) | ||||
−0.898971 | + | 0.438008i | \(0.855684\pi\) | |||||||
\(180\) | −1.01055e6 | + | 1.66070e6i | −0.173276 | + | 0.284757i | ||||
\(181\) | 7.58820e6 | 1.27969 | 0.639843 | − | 0.768506i | \(-0.279000\pi\) | ||||
0.639843 | + | 0.768506i | \(0.279000\pi\) | |||||||
\(182\) | 2.86096e6 | + | 3.86737e6i | 0.474568 | + | 0.641508i | ||||
\(183\) | 236759. | 0.0386326 | ||||||||
\(184\) | 11521.4 | + | 32573.8i | 0.00184948 | + | 0.00522896i | ||||
\(185\) | −824127. | + | 3.23164e6i | −0.130160 | + | 0.510397i | ||||
\(186\) | 1.54786e6 | + | 2.09235e6i | 0.240542 | + | 0.325159i | ||||
\(187\) | 3.82267e6 | 0.584578 | ||||||||
\(188\) | −919485. | + | 3.00483e6i | −0.138379 | + | 0.452217i | ||||
\(189\) | 2.08130e6 | 0.308282 | ||||||||
\(190\) | 3.59467e6 | + | 8.81446e6i | 0.524080 | + | 1.28509i | ||||
\(191\) | 5.02660e6i | 0.721397i | 0.932682 | + | 0.360699i | \(0.117462\pi\) | ||||
−0.932682 | + | 0.360699i | \(0.882538\pi\) | |||||||
\(192\) | 3.17766e6 | − | 2.56931e6i | 0.448955 | − | 0.363005i | ||||
\(193\) | − | 2.70300e6i | − | 0.375988i | −0.982170 | − | 0.187994i | \(-0.939801\pi\) | ||
0.982170 | − | 0.187994i | \(-0.0601986\pi\) | |||||||
\(194\) | −4.01455e6 | − | 5.42676e6i | −0.549834 | − | 0.743251i | ||||
\(195\) | −526969. | + | 2.06640e6i | −0.0710692 | + | 0.278683i | ||||
\(196\) | 3.45028e6 | − | 1.12754e7i | 0.458233 | − | 1.49748i | ||||
\(197\) | 8.87040e6i | 1.16023i | 0.814534 | + | 0.580115i | \(0.196993\pi\) | ||||
−0.814534 | + | 0.580115i | \(0.803007\pi\) | |||||||
\(198\) | 2.95215e6 | + | 3.99064e6i | 0.380314 | + | 0.514099i | ||||
\(199\) | 1.00354e7i | 1.27343i | 0.771101 | + | 0.636713i | \(0.219706\pi\) | ||||
−0.771101 | + | 0.636713i | \(0.780294\pi\) | |||||||
\(200\) | −1.27000e6 | + | 7.89855e6i | −0.158750 | + | 0.987319i | ||||
\(201\) | −5.93769e6 | −0.731189 | ||||||||
\(202\) | −3.15616e6 | + | 2.33483e6i | −0.382918 | + | 0.283271i | ||||
\(203\) | 3.39200e6 | 0.405478 | ||||||||
\(204\) | −1.42819e6 | − | 437029.i | −0.168227 | − | 0.0514778i | ||||
\(205\) | −1.24653e7 | − | 3.17888e6i | −1.44691 | − | 0.368989i | ||||
\(206\) | 6.87387e6 | − | 5.08508e6i | 0.786320 | − | 0.581696i | ||||
\(207\) | 16398.4 | 0.00184880 | ||||||||
\(208\) | 2.50855e6 | − | 3.71511e6i | 0.278762 | − | 0.412840i | ||||
\(209\) | 2.43069e7 | 2.66251 | ||||||||
\(210\) | 7.93086e6 | − | 3.23432e6i | 0.856372 | − | 0.349241i | ||||
\(211\) | − | 6.66623e6i | − | 0.709631i | −0.934936 | − | 0.354816i | \(-0.884544\pi\) | ||
0.934936 | − | 0.354816i | \(-0.115456\pi\) | |||||||
\(212\) | −1.51112e7 | − | 4.62406e6i | −1.58596 | − | 0.485306i | ||||
\(213\) | 5.04466e6i | 0.522027i | ||||||||
\(214\) | −1.18008e7 | + | 8.72987e6i | −1.20412 | + | 0.890771i | ||||
\(215\) | 1.07087e6 | + | 273090.i | 0.107751 | + | 0.0274784i | ||||
\(216\) | −646723. | − | 1.82845e6i | −0.0641737 | − | 0.181435i | ||||
\(217\) | − | 1.14669e7i | − | 1.12219i | ||||||
\(218\) | −5.98610e6 | + | 4.42834e6i | −0.577796 | + | 0.427436i | ||||
\(219\) | 5.64056e6i | 0.537019i | ||||||||
\(220\) | 1.74507e7 | + | 1.06188e7i | 1.63887 | + | 0.997262i | ||||
\(221\) | −1.63841e6 | −0.151791 | ||||||||
\(222\) | −1.97880e6 | − | 2.67489e6i | −0.180861 | − | 0.244482i | ||||
\(223\) | −6.53736e6 | −0.589506 | −0.294753 | − | 0.955574i | \(-0.595237\pi\) | ||||
−0.294753 | + | 0.955574i | \(0.595237\pi\) | |||||||
\(224\) | −1.79876e7 | + | 774189.i | −1.60040 | + | 0.0688816i | ||||
\(225\) | 3.33318e6 | + | 1.81829e6i | 0.292625 | + | 0.159631i | ||||
\(226\) | −1.09242e7 | − | 1.47670e7i | −0.946373 | − | 1.27928i | ||||
\(227\) | −4.37830e6 | −0.374307 | −0.187154 | − | 0.982331i | \(-0.559926\pi\) | ||||
−0.187154 | + | 0.982331i | \(0.559926\pi\) | |||||||
\(228\) | −9.08133e6 | − | 2.77890e6i | −0.766205 | − | 0.234460i | ||||
\(229\) | 5.31579e6 | 0.442651 | 0.221325 | − | 0.975200i | \(-0.428962\pi\) | ||||
0.221325 | + | 0.975200i | \(0.428962\pi\) | |||||||
\(230\) | 62486.7 | − | 25483.0i | 0.00513575 | − | 0.00209444i | ||||
\(231\) | − | 2.18703e7i | − | 1.77427i | ||||||
\(232\) | −1.05400e6 | − | 2.97992e6i | −0.0844065 | − | 0.238638i | ||||
\(233\) | 604948.i | 0.0478245i | 0.999714 | + | 0.0239122i | \(0.00761223\pi\) | ||||
−0.999714 | + | 0.0239122i | \(0.992388\pi\) | |||||||
\(234\) | −1.26530e6 | − | 1.71040e6i | −0.0987521 | − | 0.133490i | ||||
\(235\) | 5.94710e6 | + | 1.51662e6i | 0.458249 | + | 0.116862i | ||||
\(236\) | 7.01789e6 | + | 2.14749e6i | 0.533913 | + | 0.163378i | ||||
\(237\) | − | 1.17532e7i | − | 0.882901i | ||||||
\(238\) | 3.91354e6 | + | 5.29021e6i | 0.290294 | + | 0.392412i | ||||
\(239\) | 1.45792e6i | 0.106792i | 0.998573 | + | 0.0533962i | \(0.0170046\pi\) | ||||
−0.998573 | + | 0.0533962i | \(0.982995\pi\) | |||||||
\(240\) | −5.30576e6 | − | 5.96237e6i | −0.383808 | − | 0.431306i | ||||
\(241\) | −7.04006e6 | −0.502951 | −0.251475 | − | 0.967864i | \(-0.580916\pi\) | ||||
−0.251475 | + | 0.967864i | \(0.580916\pi\) | |||||||
\(242\) | 3.05400e7 | − | 2.25926e7i | 2.15488 | − | 1.59411i | ||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | −284427. | + | 929496.i | −0.0195795 | + | 0.0639850i | ||||
\(245\) | −2.23160e7 | − | 5.69097e6i | −1.51746 | − | 0.386980i | ||||
\(246\) | 1.03178e7 | − | 7.63279e6i | 0.693077 | − | 0.512717i | ||||
\(247\) | −1.04180e7 | −0.691345 | ||||||||
\(248\) | −1.00739e7 | + | 3.56313e6i | −0.660451 | + | 0.233602i | ||||
\(249\) | −369114. | −0.0239091 | ||||||||
\(250\) | 1.55268e7 | + | 1.74893e6i | 0.993716 | + | 0.111932i | ||||
\(251\) | − | 1.58945e7i | − | 1.00514i | −0.864537 | − | 0.502569i | \(-0.832388\pi\) | ||
0.864537 | − | 0.502569i | \(-0.167612\pi\) | |||||||
\(252\) | −2.50033e6 | + | 8.17098e6i | −0.156242 | + | 0.510590i | ||||
\(253\) | − | 172315.i | − | 0.0106405i | ||||||
\(254\) | 1.84419e7 | − | 1.36427e7i | 1.12539 | − | 0.832531i | ||||
\(255\) | −720846. | + | 2.82665e6i | −0.0434732 | + | 0.170471i | ||||
\(256\) | 6.26943e6 | + | 1.55618e7i | 0.373687 | + | 0.927555i | ||||
\(257\) | − | 2.27306e7i | − | 1.33910i | −0.742768 | − | 0.669549i | \(-0.766487\pi\) | ||
0.742768 | − | 0.669549i | \(-0.233513\pi\) | |||||||
\(258\) | −886378. | + | 655715.i | −0.0516131 | + | 0.0381818i | ||||
\(259\) | 1.46595e7i | 0.843762i | ||||||||
\(260\) | −7.47943e6 | − | 4.55127e6i | −0.425548 | − | 0.258948i | ||||
\(261\) | −1.50016e6 | −0.0843753 | ||||||||
\(262\) | −7.69220e6 | − | 1.03981e7i | −0.427707 | − | 0.578163i | ||||
\(263\) | −8.61581e6 | −0.473619 | −0.236809 | − | 0.971556i | \(-0.576102\pi\) | ||||
−0.236809 | + | 0.971556i | \(0.576102\pi\) | |||||||
\(264\) | −1.92134e7 | + | 6.79578e6i | −1.04422 | + | 0.369341i | ||||
\(265\) | −7.62702e6 | + | 2.99078e7i | −0.409843 | + | 1.60711i | ||||
\(266\) | 2.48847e7 | + | 3.36385e7i | 1.32217 | + | 1.78727i | ||||
\(267\) | 8.72607e6 | 0.458442 | ||||||||
\(268\) | 7.13316e6 | − | 2.33108e7i | 0.370576 | − | 1.21103i | ||||
\(269\) | −2.00001e7 | −1.02748 | −0.513742 | − | 0.857944i | \(-0.671741\pi\) | ||||
−0.513742 | + | 0.857944i | \(0.671741\pi\) | |||||||
\(270\) | −3.50753e6 | + | 1.43042e6i | −0.178201 | + | 0.0726731i | ||||
\(271\) | 7.07623e6i | 0.355545i | 0.984072 | + | 0.177772i | \(0.0568891\pi\) | ||||
−0.984072 | + | 0.177772i | \(0.943111\pi\) | |||||||
\(272\) | 3.43147e6 | − | 5.08193e6i | 0.170519 | − | 0.252535i | ||||
\(273\) | 9.37369e6i | 0.460705i | ||||||||
\(274\) | 5.77362e6 | + | 7.80462e6i | 0.280670 | + | 0.379402i | ||||
\(275\) | 1.91067e7 | − | 3.50251e7i | 0.918728 | − | 1.68415i | ||||
\(276\) | −19700.0 | + | 64378.6i | −0.000936996 | + | 0.00306206i | ||||
\(277\) | − | 5.31398e6i | − | 0.250023i | −0.992155 | − | 0.125012i | \(-0.960103\pi\) | ||
0.992155 | − | 0.125012i | \(-0.0398968\pi\) | |||||||
\(278\) | 3.54781e6 | + | 4.79583e6i | 0.165130 | + | 0.223218i | ||||
\(279\) | 5.07141e6i | 0.233516i | ||||||||
\(280\) | 3.17004e6 | + | 3.50213e7i | 0.144408 | + | 1.59536i | ||||
\(281\) | −3.15126e7 | −1.42025 | −0.710126 | − | 0.704075i | \(-0.751362\pi\) | ||||
−0.710126 | + | 0.704075i | \(0.751362\pi\) | |||||||
\(282\) | −4.92254e6 | + | 3.64154e6i | −0.219504 | + | 0.162382i | ||||
\(283\) | 2.50051e7 | 1.10324 | 0.551620 | − | 0.834096i | \(-0.314010\pi\) | ||||
0.551620 | + | 0.834096i | \(0.314010\pi\) | |||||||
\(284\) | −1.98049e7 | − | 6.06032e6i | −0.864603 | − | 0.264570i | ||||
\(285\) | −4.58359e6 | + | 1.79736e7i | −0.198003 | + | 0.776426i | ||||
\(286\) | −1.79729e7 | + | 1.32958e7i | −0.768282 | + | 0.568351i | ||||
\(287\) | −5.65458e7 | −2.39196 | ||||||||
\(288\) | 7.95526e6 | − | 342396.i | 0.333025 | − | 0.0143335i | ||||
\(289\) | 2.18964e7 | 0.907149 | ||||||||
\(290\) | −5.71641e6 | + | 2.33124e6i | −0.234385 | + | 0.0955856i | ||||
\(291\) | − | 1.31533e7i | − | 0.533773i | ||||||
\(292\) | −2.21443e7 | − | 6.77620e6i | −0.889434 | − | 0.272168i | ||||
\(293\) | 7.88892e6i | 0.313628i | 0.987628 | + | 0.156814i | \(0.0501223\pi\) | ||||
−0.987628 | + | 0.156814i | \(0.949878\pi\) | |||||||
\(294\) | 1.84714e7 | − | 1.36645e7i | 0.726870 | − | 0.537716i | ||||
\(295\) | 3.54211e6 | − | 1.38897e7i | 0.137974 | − | 0.541035i | ||||
\(296\) | 1.28786e7 | − | 4.55516e6i | 0.496585 | − | 0.175642i | ||||
\(297\) | 9.67245e6i | 0.369205i | ||||||||
\(298\) | −1.84811e7 | + | 1.36717e7i | −0.698358 | + | 0.516624i | ||||
\(299\) | 73854.6i | 0.00276289i | ||||||||
\(300\) | −1.11427e7 | + | 1.09014e7i | −0.412693 | + | 0.403755i | ||||
\(301\) | 4.85771e6 | 0.178128 | ||||||||
\(302\) | 8.13268e6 | + | 1.09935e7i | 0.295266 | + | 0.399132i | ||||
\(303\) | −7.64987e6 | −0.274996 | ||||||||
\(304\) | 2.18194e7 | − | 3.23141e7i | 0.776646 | − | 1.15019i | ||||
\(305\) | 1.83964e6 | + | 469141.i | 0.0648385 | + | 0.0165350i | ||||
\(306\) | −1.73082e6 | − | 2.33967e6i | −0.0604069 | − | 0.0816565i | ||||
\(307\) | 3.83562e7 | 1.32562 | 0.662812 | − | 0.748786i | \(-0.269363\pi\) | ||||
0.662812 | + | 0.748786i | \(0.269363\pi\) | |||||||
\(308\) | 8.58609e7 | + | 2.62736e7i | 2.93862 | + | 0.899222i | ||||
\(309\) | 1.66608e7 | 0.564703 | ||||||||
\(310\) | 7.88094e6 | + | 1.93248e7i | 0.264541 | + | 0.648679i | ||||
\(311\) | 4.40873e7i | 1.46566i | 0.680413 | + | 0.732829i | \(0.261800\pi\) | ||||
−0.680413 | + | 0.732829i | \(0.738200\pi\) | |||||||
\(312\) | 8.23492e6 | − | 2.91269e6i | 0.271141 | − | 0.0959028i | ||||
\(313\) | 2.98649e6i | 0.0973931i | 0.998814 | + | 0.0486965i | \(0.0155067\pi\) | ||||
−0.998814 | + | 0.0486965i | \(0.984493\pi\) | |||||||
\(314\) | −2.85032e7 | − | 3.85298e7i | −0.920671 | − | 1.24454i | ||||
\(315\) | 1.61718e7 | + | 4.12411e6i | 0.517401 | + | 0.131947i | ||||
\(316\) | 4.61421e7 | + | 1.41196e7i | 1.46230 | + | 0.447466i | ||||
\(317\) | − | 3.90061e7i | − | 1.22449i | −0.790668 | − | 0.612245i | \(-0.790267\pi\) | ||
0.790668 | − | 0.612245i | \(-0.209733\pi\) | |||||||
\(318\) | −1.83132e7 | − | 2.47553e7i | −0.569485 | − | 0.769815i | ||||
\(319\) | 1.57637e7i | 0.485608i | ||||||||
\(320\) | 2.97817e7 | − | 1.36671e7i | 0.908866 | − | 0.417088i | ||||
\(321\) | −2.86026e7 | −0.864750 | ||||||||
\(322\) | 238467. | − | 176410.i | 0.00714267 | − | 0.00528393i | ||||
\(323\) | −1.42509e7 | −0.422898 | ||||||||
\(324\) | 1.10581e6 | − | 3.61373e6i | 0.0325121 | − | 0.106248i | ||||
\(325\) | −8.18918e6 | + | 1.50119e7i | −0.238556 | + | 0.437305i | ||||
\(326\) | −1.99600e7 | + | 1.47658e7i | −0.576112 | + | 0.426190i | ||||
\(327\) | −1.45090e7 | −0.414950 | ||||||||
\(328\) | 1.75705e7 | + | 4.96763e7i | 0.497924 | + | 1.40776i | ||||
\(329\) | 2.69775e7 | 0.757555 | ||||||||
\(330\) | 1.50309e7 | + | 3.68572e7i | 0.418258 | + | 1.02561i | ||||
\(331\) | − | 4.24129e7i | − | 1.16954i | −0.811200 | − | 0.584768i | \(-0.801185\pi\) | ||
0.811200 | − | 0.584768i | \(-0.198815\pi\) | |||||||
\(332\) | 443430. | − | 1.44911e6i | 0.0121174 | − | 0.0395992i | ||||
\(333\) | − | 6.48337e6i | − | 0.175577i | ||||||
\(334\) | −4.01552e7 | + | 2.97056e7i | −1.07771 | + | 0.797257i | ||||
\(335\) | −4.61363e7 | − | 1.17656e7i | −1.22718 | − | 0.312953i | ||||
\(336\) | −2.90748e7 | − | 1.96322e7i | −0.766476 | − | 0.517548i | ||||
\(337\) | 4.59359e7i | 1.20022i | 0.799916 | + | 0.600112i | \(0.204877\pi\) | ||||
−0.799916 | + | 0.600112i | \(0.795123\pi\) | |||||||
\(338\) | −2.33401e7 | + | 1.72663e7i | −0.604439 | + | 0.447146i | ||||
\(339\) | − | 3.57920e7i | − | 0.918728i | ||||||
\(340\) | −1.02312e7 | − | 6.22572e6i | −0.260309 | − | 0.158399i | ||||
\(341\) | 5.32905e7 | 1.34396 | ||||||||
\(342\) | −1.10056e7 | − | 1.48771e7i | −0.275129 | − | 0.371911i | ||||
\(343\) | −3.65889e7 | −0.906707 | ||||||||
\(344\) | −1.50944e6 | − | 4.26757e6i | −0.0370801 | − | 0.104835i | ||||
\(345\) | 127417. | + | 32493.6i | 0.00310291 | + | 0.000791298i | ||||
\(346\) | −1.91506e7 | − | 2.58872e7i | −0.462331 | − | 0.624967i | ||||
\(347\) | 4.68864e7 | 1.12217 | 0.561085 | − | 0.827758i | \(-0.310384\pi\) | ||||
0.561085 | + | 0.827758i | \(0.310384\pi\) | |||||||
\(348\) | 1.80219e6 | − | 5.88948e6i | 0.0427625 | − | 0.139746i | ||||
\(349\) | 1.85236e7 | 0.435762 | 0.217881 | − | 0.975975i | \(-0.430086\pi\) | ||||
0.217881 | + | 0.975975i | \(0.430086\pi\) | |||||||
\(350\) | 6.80322e7 | − | 9.41585e6i | 1.58676 | − | 0.219612i | ||||
\(351\) | − | 4.14565e6i | − | 0.0958674i | ||||||
\(352\) | −3.59790e6 | − | 8.35940e7i | −0.0824939 | − | 1.91667i | ||||
\(353\) | − | 3.87474e7i | − | 0.880884i | −0.897781 | − | 0.440442i | \(-0.854822\pi\) | ||
0.897781 | − | 0.440442i | \(-0.145178\pi\) | |||||||
\(354\) | 8.50494e6 | + | 1.14967e7i | 0.191717 | + | 0.259158i | ||||
\(355\) | −9.99603e6 | + | 3.91973e7i | −0.223431 | + | 0.876136i | ||||
\(356\) | −1.04829e7 | + | 3.42577e7i | −0.232345 | + | 0.759292i | ||||
\(357\) | 1.28224e7i | 0.281814i | ||||||||
\(358\) | −2.39043e7 | − | 3.23132e7i | −0.520987 | − | 0.704256i | ||||
\(359\) | − | 7.81969e6i | − | 0.169008i | −0.996423 | − | 0.0845038i | \(-0.973069\pi\) | ||
0.996423 | − | 0.0845038i | \(-0.0269305\pi\) | |||||||
\(360\) | −1.40200e6 | − | 1.54887e7i | −0.0300496 | − | 0.331976i | ||||
\(361\) | −4.35704e7 | −0.926126 | ||||||||
\(362\) | −4.88031e7 | + | 3.61030e7i | −1.02878 | + | 0.761058i | ||||
\(363\) | 7.40225e7 | 1.54755 | ||||||||
\(364\) | −3.68003e7 | − | 1.12609e7i | −0.763039 | − | 0.233491i | ||||
\(365\) | −1.11768e7 | + | 4.38276e7i | −0.229848 | + | 0.901299i | ||||
\(366\) | −1.52270e6 | + | 1.12645e6i | −0.0310579 | + | 0.0229757i | ||||
\(367\) | 5.10078e7 | 1.03190 | 0.515951 | − | 0.856618i | \(-0.327439\pi\) | ||||
0.515951 | + | 0.856618i | \(0.327439\pi\) | |||||||
\(368\) | −229078. | − | 154680.i | −0.00459664 | − | 0.00310379i | ||||
\(369\) | 2.50082e7 | 0.497740 | ||||||||
\(370\) | −1.00751e7 | − | 2.47051e7i | −0.198905 | − | 0.487733i | ||||
\(371\) | 1.35669e8i | 2.65680i | ||||||||
\(372\) | −1.99099e7 | − | 6.09246e6i | −0.386759 | − | 0.118349i | ||||
\(373\) | 2.10254e7i | 0.405152i | 0.979267 | + | 0.202576i | \(0.0649313\pi\) | ||||
−0.979267 | + | 0.202576i | \(0.935069\pi\) | |||||||
\(374\) | −2.45853e7 | + | 1.81875e7i | −0.469960 | + | 0.347662i | ||||
\(375\) | 2.22961e7 | + | 2.07330e7i | 0.422799 | + | 0.393159i | ||||
\(376\) | −8.38274e6 | − | 2.37001e7i | −0.157697 | − | 0.445849i | ||||
\(377\) | − | 6.75637e6i | − | 0.126093i | ||||||
\(378\) | −1.33857e7 | + | 9.90236e6i | −0.247838 | + | 0.183343i | ||||
\(379\) | 5.39833e6i | 0.0991613i | 0.998770 | + | 0.0495806i | \(0.0157885\pi\) | ||||
−0.998770 | + | 0.0495806i | \(0.984212\pi\) | |||||||
\(380\) | −6.50562e7 | − | 3.95870e7i | −1.18560 | − | 0.721443i | ||||
\(381\) | 4.46992e7 | 0.808211 | ||||||||
\(382\) | −2.39155e7 | − | 3.23283e7i | −0.429032 | − | 0.579953i | ||||
\(383\) | −6.21222e7 | −1.10573 | −0.552867 | − | 0.833270i | \(-0.686466\pi\) | ||||
−0.552867 | + | 0.833270i | \(0.686466\pi\) | |||||||
\(384\) | −8.21271e6 | + | 3.16430e7i | −0.145042 | + | 0.558835i | ||||
\(385\) | 4.33362e7 | − | 1.69934e8i | 0.759397 | − | 2.97782i | ||||
\(386\) | 1.28603e7 | + | 1.73842e7i | 0.223609 | + | 0.302269i | ||||
\(387\) | −2.14839e6 | −0.0370664 | ||||||||
\(388\) | 5.16387e7 | + | 1.58015e7i | 0.884057 | + | 0.270523i | ||||
\(389\) | −2.55535e7 | −0.434113 | −0.217056 | − | 0.976159i | \(-0.569646\pi\) | ||||
−0.217056 | + | 0.976159i | \(0.569646\pi\) | |||||||
\(390\) | −6.44231e6 | − | 1.57971e7i | −0.108604 | − | 0.266308i | ||||
\(391\) | 101026.i | 0.00169007i | ||||||||
\(392\) | 3.14555e7 | + | 8.89326e7i | 0.522201 | + | 1.47640i | ||||
\(393\) | − | 2.52028e7i | − | 0.415213i | ||||||
\(394\) | −4.22034e7 | − | 5.70495e7i | −0.690016 | − | 0.932745i | ||||
\(395\) | 2.32891e7 | − | 9.13234e7i | 0.377887 | − | 1.48180i | ||||
\(396\) | −3.79732e7 | − | 1.16199e7i | −0.611493 | − | 0.187118i | ||||
\(397\) | − | 1.95610e7i | − | 0.312622i | −0.987708 | − | 0.156311i | \(-0.950040\pi\) | ||
0.987708 | − | 0.156311i | \(-0.0499602\pi\) | |||||||
\(398\) | −4.77461e7 | − | 6.45419e7i | −0.757336 | − | 1.02375i | ||||
\(399\) | 8.15325e7i | 1.28355i | ||||||||
\(400\) | −2.94117e7 | − | 5.68415e7i | −0.459557 | − | 0.888148i | ||||
\(401\) | 4.67869e7 | 0.725589 | 0.362795 | − | 0.931869i | \(-0.381823\pi\) | ||||
0.362795 | + | 0.931869i | \(0.381823\pi\) | |||||||
\(402\) | 3.81880e7 | − | 2.82503e7i | 0.587825 | − | 0.434855i | ||||
\(403\) | −2.28405e7 | −0.348972 | ||||||||
\(404\) | 9.19006e6 | − | 3.00327e7i | 0.139372 | − | 0.455460i | ||||
\(405\) | −7.15222e6 | − | 1.82395e6i | −0.107665 | − | 0.0274566i | ||||
\(406\) | −2.18154e7 | + | 1.61384e7i | −0.325976 | + | 0.241147i | ||||
\(407\) | −6.81275e7 | −1.01051 | ||||||||
\(408\) | 1.12646e7 | − | 3.98430e6i | 0.165858 | − | 0.0586640i | ||||
\(409\) | 8.50968e7 | 1.24378 | 0.621889 | − | 0.783105i | \(-0.286365\pi\) | ||||
0.621889 | + | 0.783105i | \(0.286365\pi\) | |||||||
\(410\) | 9.52945e7 | − | 3.88625e7i | 1.38266 | − | 0.563871i | ||||
\(411\) | 1.89167e7i | 0.272471i | ||||||||
\(412\) | −2.00152e7 | + | 6.54088e7i | −0.286199 | + | 0.935286i | ||||
\(413\) | − | 6.30069e7i | − | 0.894412i | ||||||
\(414\) | −105465. | + | 78020.0i | −0.00148631 | + | 0.00109952i | ||||
\(415\) | −2.86804e6 | − | 731403.i | −0.0401274 | − | 0.0102332i | ||||
\(416\) | 1.54207e6 | + | 3.58287e7i | 0.0214203 | + | 0.497681i | ||||
\(417\) | 1.16241e7i | 0.160306i | ||||||||
\(418\) | −1.56329e8 | + | 1.15647e8i | −2.14047 | + | 1.58346i | ||||
\(419\) | 6.10478e7i | 0.829904i | 0.909843 | + | 0.414952i | \(0.136202\pi\) | ||||
−0.909843 | + | 0.414952i | \(0.863798\pi\) | |||||||
\(420\) | −3.56187e7 | + | 5.85347e7i | −0.480762 | + | 0.790070i | ||||
\(421\) | −7.67905e7 | −1.02911 | −0.514555 | − | 0.857458i | \(-0.672043\pi\) | ||||
−0.514555 | + | 0.857458i | \(0.672043\pi\) | |||||||
\(422\) | 3.17165e7 | + | 4.28735e7i | 0.422034 | + | 0.570494i | ||||
\(423\) | −1.19312e7 | −0.157639 | ||||||||
\(424\) | 1.19187e8 | − | 4.21565e7i | 1.56362 | − | 0.553054i | ||||
\(425\) | −1.12021e7 | + | 2.05349e7i | −0.145925 | + | 0.267501i | ||||
\(426\) | −2.40014e7 | − | 3.24444e7i | −0.310461 | − | 0.419673i | ||||
\(427\) | 8.34504e6 | 0.107188 | ||||||||
\(428\) | 3.43613e7 | − | 1.12291e8i | 0.438267 | − | 1.43224i | ||||
\(429\) | −4.35625e7 | −0.551749 | ||||||||
\(430\) | −8.18652e6 | + | 3.33859e6i | −0.102966 | + | 0.0419911i | ||||
\(431\) | − | 1.61877e7i | − | 0.202188i | −0.994877 | − | 0.101094i | \(-0.967766\pi\) | ||
0.994877 | − | 0.101094i | \(-0.0322342\pi\) | |||||||
\(432\) | 1.28587e7 | + | 8.68260e6i | 0.159495 | + | 0.107696i | ||||
\(433\) | 9.44401e7i | 1.16330i | 0.813438 | + | 0.581651i | \(0.197593\pi\) | ||||
−0.813438 | + | 0.581651i | \(0.802407\pi\) | |||||||
\(434\) | 5.45572e7 | + | 7.37489e7i | 0.667394 | + | 0.902166i | ||||
\(435\) | −1.16563e7 | − | 2.97258e6i | −0.141610 | − | 0.0361131i | ||||
\(436\) | 1.74302e7 | − | 5.69612e7i | 0.210302 | − | 0.687258i | ||||
\(437\) | 642389.i | 0.00769757i | ||||||||
\(438\) | −2.68366e7 | − | 3.62769e7i | −0.319378 | − | 0.431726i | ||||
\(439\) | − | 5.43621e7i | − | 0.642543i | −0.946987 | − | 0.321272i | \(-0.895890\pi\) | ||
0.946987 | − | 0.321272i | \(-0.104110\pi\) | |||||||
\(440\) | −1.62755e8 | + | 1.47322e7i | −1.91063 | + | 0.172946i | ||||
\(441\) | 4.47707e7 | 0.522009 | ||||||||
\(442\) | 1.05373e7 | − | 7.79521e6i | 0.122029 | − | 0.0902736i | ||||
\(443\) | 1.25008e8 | 1.43789 | 0.718945 | − | 0.695067i | \(-0.244625\pi\) | ||||
0.718945 | + | 0.695067i | \(0.244625\pi\) | |||||||
\(444\) | 2.54531e7 | + | 7.78870e6i | 0.290799 | + | 0.0889849i | ||||
\(445\) | 6.78022e7 | + | 1.72908e7i | 0.769420 | + | 0.196216i | ||||
\(446\) | 4.20447e7 | − | 3.11034e7i | 0.473922 | − | 0.350593i | ||||
\(447\) | −4.47942e7 | −0.501532 | ||||||||
\(448\) | 1.12003e8 | − | 9.05602e7i | 1.24565 | − | 1.00717i | ||||
\(449\) | −1.08925e8 | −1.20334 | −0.601672 | − | 0.798743i | \(-0.705499\pi\) | ||||
−0.601672 | + | 0.798743i | \(0.705499\pi\) | |||||||
\(450\) | −3.00882e7 | + | 4.16429e6i | −0.330186 | + | 0.0456987i | ||||
\(451\) | − | 2.62786e8i | − | 2.86466i | ||||||
\(452\) | 1.40516e8 | + | 4.29982e7i | 1.52164 | + | 0.465623i | ||||
\(453\) | 2.66460e7i | 0.286640i | ||||||||
\(454\) | 2.81588e7 | − | 2.08310e7i | 0.300917 | − | 0.222609i | ||||
\(455\) | −1.85741e7 | + | 7.28343e7i | −0.197184 | + | 0.773217i | ||||
\(456\) | 7.16275e7 | − | 2.53347e7i | 0.755415 | − | 0.267190i | ||||
\(457\) | 1.25491e8i | 1.31482i | 0.753534 | + | 0.657408i | \(0.228347\pi\) | ||||
−0.753534 | + | 0.657408i | \(0.771653\pi\) | |||||||
\(458\) | −3.41882e7 | + | 2.52914e7i | −0.355860 | + | 0.263255i | ||||
\(459\) | − | 5.67087e6i | − | 0.0586424i | ||||||
\(460\) | −280637. | + | 461191.i | −0.00288318 | + | 0.00473813i | ||||
\(461\) | 6.26253e7 | 0.639215 | 0.319608 | − | 0.947550i | \(-0.396449\pi\) | ||||
0.319608 | + | 0.947550i | \(0.396449\pi\) | |||||||
\(462\) | 1.04054e8 | + | 1.40658e8i | 1.05520 | + | 1.42639i | ||||
\(463\) | −1.61927e7 | −0.163146 | −0.0815731 | − | 0.996667i | \(-0.525994\pi\) | ||||
−0.0815731 | + | 0.996667i | \(0.525994\pi\) | |||||||
\(464\) | 2.09565e7 | + | 1.41505e7i | 0.209781 | + | 0.141650i | ||||
\(465\) | −1.00490e7 | + | 3.94052e7i | −0.0999461 | + | 0.391918i | ||||
\(466\) | −2.87821e6 | − | 3.89069e6i | −0.0284423 | − | 0.0384475i | ||||
\(467\) | 2.19434e6 | 0.0215453 | 0.0107727 | − | 0.999942i | \(-0.496571\pi\) | ||||
0.0107727 | + | 0.999942i | \(0.496571\pi\) | |||||||
\(468\) | 1.62754e7 | + | 4.98031e6i | 0.158780 | + | 0.0485868i | ||||
\(469\) | −2.09286e8 | −2.02871 | ||||||||
\(470\) | −4.54642e7 | + | 1.85410e7i | −0.437901 | + | 0.178583i | ||||
\(471\) | − | 9.33881e7i | − | 0.893777i | ||||||
\(472\) | −5.53525e7 | + | 1.95782e7i | −0.526394 | + | 0.186186i | ||||
\(473\) | 2.25753e7i | 0.213330i | ||||||||
\(474\) | 5.59193e7 | + | 7.55902e7i | 0.525082 | + | 0.709791i | ||||
\(475\) | −7.12296e7 | + | 1.30574e8i | −0.664630 | + | 1.21836i | ||||
\(476\) | −5.03394e7 | − | 1.54039e7i | −0.466753 | − | 0.142827i | ||||
\(477\) | − | 6.00015e7i | − | 0.552850i | ||||||
\(478\) | −6.93647e6 | − | 9.37653e6i | −0.0635119 | − | 0.0858536i | ||||
\(479\) | − | 1.52962e8i | − | 1.39180i | −0.718140 | − | 0.695899i | \(-0.755006\pi\) | ||
0.718140 | − | 0.695899i | \(-0.244994\pi\) | |||||||
\(480\) | 6.24914e7 | + | 1.31030e7i | 0.565063 | + | 0.118480i | ||||
\(481\) | 2.91997e7 | 0.262387 | ||||||||
\(482\) | 4.52778e7 | − | 3.34951e7i | 0.404337 | − | 0.299116i | ||||
\(483\) | 577993. | 0.00512957 | ||||||||
\(484\) | −8.89258e7 | + | 2.90606e8i | −0.784317 | + | 2.56311i | ||||
\(485\) | 2.60634e7 | − | 1.02202e8i | 0.228458 | − | 0.895850i | ||||
\(486\) | 5.92003e6 | − | 4.37946e6i | 0.0515722 | − | 0.0381515i | ||||
\(487\) | 3.34301e7 | 0.289435 | 0.144717 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144717 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(488\) | −2.59306e6 | − | 7.33124e6i | −0.0223128 | − | 0.0630839i | ||||
\(489\) | −4.83787e7 | −0.413740 | ||||||||
\(490\) | 1.70600e8 | − | 6.95733e7i | 1.45008 | − | 0.591364i | ||||
\(491\) | 7.03915e7i | 0.594670i | 0.954773 | + | 0.297335i | \(0.0960978\pi\) | ||||
−0.954773 | + | 0.297335i | \(0.903902\pi\) | |||||||
\(492\) | −3.00432e7 | + | 9.81797e7i | −0.252261 | + | 0.824378i | ||||
\(493\) | − | 9.24210e6i | − | 0.0771312i | ||||||
\(494\) | 6.70030e7 | − | 4.95668e7i | 0.555794 | − | 0.411159i | ||||
\(495\) | −1.91661e7 | + | 7.51557e7i | −0.158022 | + | 0.619650i | ||||
\(496\) | 4.78369e7 | − | 7.08453e7i | 0.392029 | − | 0.580585i | ||||
\(497\) | 1.77809e8i | 1.44838i | ||||||||
\(498\) | 2.37394e6 | − | 1.75617e6i | 0.0192212 | − | 0.0142193i | ||||
\(499\) | − | 1.54457e7i | − | 0.124310i | −0.998067 | − | 0.0621548i | \(-0.980203\pi\) | ||
0.998067 | − | 0.0621548i | \(-0.0197972\pi\) | |||||||
\(500\) | −1.08181e8 | + | 6.26251e7i | −0.865447 | + | 0.501000i | ||||
\(501\) | −9.73276e7 | −0.773968 | ||||||||
\(502\) | 7.56226e7 | + | 1.02225e8i | 0.597779 | + | 0.808061i | ||||
\(503\) | 1.32839e8 | 1.04381 | 0.521905 | − | 0.853004i | \(-0.325222\pi\) | ||||
0.521905 | + | 0.853004i | \(0.325222\pi\) | |||||||
\(504\) | −2.27950e7 | − | 6.44473e7i | −0.178053 | − | 0.503400i | ||||
\(505\) | −5.94400e7 | − | 1.51583e7i | −0.461535 | − | 0.117700i | ||||
\(506\) | 819836. | + | 1.10823e6i | 0.00632813 | + | 0.00855419i | ||||
\(507\) | −5.65715e7 | −0.434084 | ||||||||
\(508\) | −5.36987e7 | + | 1.75485e8i | −0.409612 | + | 1.33859i | ||||
\(509\) | 7.26222e7 | 0.550701 | 0.275351 | − | 0.961344i | \(-0.411206\pi\) | ||||
0.275351 | + | 0.961344i | \(0.411206\pi\) | |||||||
\(510\) | −8.81249e6 | − | 2.16090e7i | −0.0664337 | − | 0.162901i | ||||
\(511\) | 1.98813e8i | 1.48998i | ||||||||
\(512\) | −1.14361e8 | − | 7.02562e7i | −0.852057 | − | 0.523449i | ||||
\(513\) | − | 3.60589e7i | − | 0.267092i | ||||||
\(514\) | 1.08148e8 | + | 1.46191e8i | 0.796393 | + | 1.07654i | ||||
\(515\) | 1.29456e8 | + | 3.30135e7i | 0.947762 | + | 0.241696i | ||||
\(516\) | 2.58094e6 | − | 8.43439e6i | 0.0187857 | − | 0.0613910i | ||||
\(517\) | 1.25373e8i | 0.907262i | ||||||||
\(518\) | −6.97468e7 | − | 9.42818e7i | −0.501805 | − | 0.678326i | ||||
\(519\) | − | 6.27451e7i | − | 0.448826i | ||||||
\(520\) | 6.97575e7 | − | 6.31427e6i | 0.496113 | − | 0.0449069i | ||||
\(521\) | −1.05596e8 | −0.746682 | −0.373341 | − | 0.927694i | \(-0.621788\pi\) | ||||
−0.373341 | + | 0.927694i | \(0.621788\pi\) | |||||||
\(522\) | 9.64818e6 | − | 7.13743e6i | 0.0678319 | − | 0.0501800i | ||||
\(523\) | 4.78413e7 | 0.334425 | 0.167212 | − | 0.985921i | \(-0.446523\pi\) | ||||
0.167212 | + | 0.985921i | \(0.446523\pi\) | |||||||
\(524\) | 9.89439e7 | + | 3.02770e7i | 0.687694 | + | 0.210435i | ||||
\(525\) | 1.17484e8 | + | 6.40893e7i | 0.811899 | + | 0.442902i | ||||
\(526\) | 5.54121e7 | − | 4.09922e7i | 0.380756 | − | 0.281672i | ||||
\(527\) | −3.12437e7 | −0.213467 | ||||||||
\(528\) | 9.12370e7 | − | 1.35120e8i | 0.619825 | − | 0.917947i | ||||
\(529\) | −1.48031e8 | −0.999969 | ||||||||
\(530\) | −9.32420e7 | − | 2.28638e8i | −0.626302 | − | 1.53575i | ||||
\(531\) | 2.78657e7i | 0.186117i | ||||||||
\(532\) | −3.20089e8 | − | 9.79479e7i | −2.12587 | − | 0.650519i | ||||
\(533\) | 1.12631e8i | 0.743835i | ||||||||
\(534\) | −5.61212e7 | + | 4.15167e7i | −0.368556 | + | 0.272646i | ||||
\(535\) | −2.22244e8 | − | 5.66764e7i | −1.45134 | − | 0.370118i | ||||
\(536\) | 6.50315e7 | + | 1.83860e8i | 0.422308 | + | 1.19397i | ||||
\(537\) | − | 7.83202e7i | − | 0.505768i | ||||||
\(538\) | 1.28630e8 | − | 9.51562e7i | 0.826027 | − | 0.611069i | ||||
\(539\) | − | 4.70451e8i | − | 3.00433i | ||||||
\(540\) | 1.57529e7 | − | 2.58878e7i | 0.100041 | − | 0.164404i | ||||
\(541\) | 2.07113e8 | 1.30802 | 0.654012 | − | 0.756484i | \(-0.273085\pi\) | ||||
0.654012 | + | 0.756484i | \(0.273085\pi\) | |||||||
\(542\) | −3.36672e7 | − | 4.55104e7i | −0.211451 | − | 0.285833i | ||||
\(543\) | −1.18288e8 | −0.738827 | ||||||||
\(544\) | 2.10942e6 | + | 4.90104e7i | 0.0131028 | + | 0.304433i | ||||
\(545\) | −1.12736e8 | − | 2.87498e7i | −0.696425 | − | 0.177601i | ||||
\(546\) | −4.45980e7 | − | 6.02864e7i | −0.273992 | − | 0.370375i | ||||
\(547\) | 2.69963e8 | 1.64946 | 0.824731 | − | 0.565525i | \(-0.191326\pi\) | ||||
0.824731 | + | 0.565525i | \(0.191326\pi\) | |||||||
\(548\) | −7.42654e7 | − | 2.27253e7i | −0.451279 | − | 0.138092i | ||||
\(549\) | −3.69071e6 | −0.0223045 | ||||||||
\(550\) | 4.37585e7 | + | 3.16167e8i | 0.263011 | + | 1.90033i | ||||
\(551\) | − | 5.87670e7i | − | 0.351301i | ||||||
\(552\) | −179600. | − | 507775.i | −0.00106780 | − | 0.00301894i | ||||
\(553\) | − | 4.14265e8i | − | 2.44964i | ||||||
\(554\) | 2.52828e7 | + | 3.41766e7i | 0.148695 | + | 0.201001i | ||||
\(555\) | 1.28469e7 | − | 5.03763e7i | 0.0751482 | − | 0.294678i | ||||
\(556\) | −4.56350e7 | − | 1.39644e7i | −0.265506 | − | 0.0812452i | ||||
\(557\) | 1.22257e8i | 0.707468i | 0.935346 | + | 0.353734i | \(0.115088\pi\) | ||||
−0.935346 | + | 0.353734i | \(0.884912\pi\) | |||||||
\(558\) | −2.41287e7 | − | 3.26165e7i | −0.138877 | − | 0.187730i | ||||
\(559\) | − | 9.67587e6i | − | 0.0553930i | ||||||
\(560\) | −1.87012e8 | − | 2.10155e8i | −1.06489 | − | 1.19668i | ||||
\(561\) | −5.95896e7 | −0.337506 | ||||||||
\(562\) | 2.02672e8 | − | 1.49930e8i | 1.14178 | − | 0.844656i | ||||
\(563\) | −6.05594e7 | −0.339357 | −0.169678 | − | 0.985500i | \(-0.554273\pi\) | ||||
−0.169678 | + | 0.985500i | \(0.554273\pi\) | |||||||
\(564\) | 1.43333e7 | − | 4.68407e7i | 0.0798933 | − | 0.261088i | ||||
\(565\) | 7.09222e7 | − | 2.78107e8i | 0.393221 | − | 1.54193i | ||||
\(566\) | −1.60819e8 | + | 1.18969e8i | −0.886928 | + | 0.656122i | ||||
\(567\) | −3.24442e7 | −0.177987 | ||||||||
\(568\) | 1.56208e8 | − | 5.52507e7i | 0.852427 | − | 0.301504i | ||||
\(569\) | −1.97749e8 | −1.07344 | −0.536719 | − | 0.843761i | \(-0.680336\pi\) | ||||
−0.536719 | + | 0.843761i | \(0.680336\pi\) | |||||||
\(570\) | −5.60353e7 | − | 1.37404e8i | −0.302578 | − | 0.741949i | ||||
\(571\) | 2.35693e8i | 1.26601i | 0.774146 | + | 0.633007i | \(0.218179\pi\) | ||||
−0.774146 | + | 0.633007i | \(0.781821\pi\) | |||||||
\(572\) | 5.23332e7 | − | 1.71023e8i | 0.279634 | − | 0.913830i | ||||
\(573\) | − | 7.83570e7i | − | 0.416499i | ||||||
\(574\) | 3.63671e8 | − | 2.69033e8i | 1.92297 | − | 1.42256i | ||||
\(575\) | 925650. | + | 504955.i | 0.00486904 | + | 0.00265613i | ||||
\(576\) | −4.95348e7 | + | 4.00515e7i | −0.259205 | + | 0.209581i | ||||
\(577\) | − | 1.18751e8i | − | 0.618171i | −0.951034 | − | 0.309085i | \(-0.899977\pi\) | ||
0.951034 | − | 0.309085i | \(-0.100023\pi\) | |||||||
\(578\) | −1.40825e8 | + | 1.04178e8i | −0.729285 | + | 0.539503i | ||||
\(579\) | 4.21356e7i | 0.217077i | ||||||||
\(580\) | 2.56732e7 | − | 4.21907e7i | 0.131582 | − | 0.216238i | ||||
\(581\) | −1.30101e7 | −0.0663367 | ||||||||
\(582\) | 6.25807e7 | + | 8.45948e7i | 0.317447 | + | 0.429116i | ||||
\(583\) | −6.30497e8 | −3.18183 | ||||||||
\(584\) | 1.74660e8 | − | 6.17772e7i | 0.876908 | − | 0.310163i | ||||
\(585\) | 8.21464e6 | − | 3.22120e7i | 0.0410318 | − | 0.160898i | ||||
\(586\) | −3.75338e7 | − | 5.07372e7i | −0.186522 | − | 0.252135i | ||||
\(587\) | 3.48828e7 | 0.172464 | 0.0862318 | − | 0.996275i | \(-0.472517\pi\) | ||||
0.0862318 | + | 0.996275i | \(0.472517\pi\) | |||||||
\(588\) | −5.37845e7 | + | 1.75766e8i | −0.264561 | + | 0.864573i | ||||
\(589\) | −1.98667e8 | −0.972254 | ||||||||
\(590\) | 4.33031e7 | + | 1.06183e8i | 0.210845 | + | 0.517011i | ||||
\(591\) | − | 1.38276e8i | − | 0.669859i | ||||||
\(592\) | −6.11555e7 | + | 9.05699e7i | −0.294761 | + | 0.436535i | ||||
\(593\) | 2.91576e8i | 1.39826i | 0.714994 | + | 0.699130i | \(0.246429\pi\) | ||||
−0.714994 | + | 0.699130i | \(0.753571\pi\) | |||||||
\(594\) | −4.60195e7 | − | 6.22079e7i | −0.219575 | − | 0.296815i | ||||
\(595\) | −2.54076e7 | + | 9.96306e7i | −0.120618 | + | 0.472979i | ||||
\(596\) | 5.38128e7 | − | 1.75858e8i | 0.254183 | − | 0.830659i | ||||
\(597\) | − | 1.56436e8i | − | 0.735213i | ||||||
\(598\) | −351384. | − | 474992.i | −0.00164316 | − | 0.00222117i | ||||
\(599\) | 4.20347e8i | 1.95582i | 0.209036 | + | 0.977908i | \(0.432967\pi\) | ||||
−0.209036 | + | 0.977908i | \(0.567033\pi\) | |||||||
\(600\) | 1.97974e7 | − | 1.23126e8i | 0.0916544 | − | 0.570029i | ||||
\(601\) | 3.31489e8 | 1.52702 | 0.763511 | − | 0.645794i | \(-0.223474\pi\) | ||||
0.763511 | + | 0.645794i | \(0.223474\pi\) | |||||||
\(602\) | −3.12421e7 | + | 2.31120e7i | −0.143203 | + | 0.105937i | ||||
\(603\) | 9.25595e7 | 0.422152 | ||||||||
\(604\) | −1.04610e8 | − | 3.20108e7i | −0.474746 | − | 0.145273i | ||||
\(605\) | 5.75160e8 | + | 1.46676e8i | 2.59730 | + | 0.662359i | ||||
\(606\) | 4.91997e7 | − | 3.63964e7i | 0.221078 | − | 0.163546i | ||||
\(607\) | 2.17689e8 | 0.973355 | 0.486677 | − | 0.873582i | \(-0.338209\pi\) | ||||
0.486677 | + | 0.873582i | \(0.338209\pi\) | |||||||
\(608\) | 1.34130e7 | + | 3.11639e8i | 0.0596781 | + | 1.38657i | ||||
\(609\) | −5.28760e7 | −0.234103 | ||||||||
\(610\) | −1.40636e7 | + | 5.73535e6i | −0.0619594 | + | 0.0252680i | ||||
\(611\) | − | 5.37353e7i | − | 0.235579i | ||||||
\(612\) | 2.22633e7 | + | 6.81261e6i | 0.0971260 | + | 0.0297207i | ||||
\(613\) | 7.52134e7i | 0.326523i | 0.986583 | + | 0.163261i | \(0.0522014\pi\) | ||||
−0.986583 | + | 0.163261i | \(0.947799\pi\) | |||||||
\(614\) | −2.46686e8 | + | 1.82490e8i | −1.06571 | + | 0.788379i | ||||
\(615\) | 1.94315e8 | + | 4.95539e7i | 0.835375 | + | 0.213036i | ||||
\(616\) | −6.77213e8 | + | 2.39531e8i | −2.89723 | + | 1.02475i | ||||
\(617\) | − | 3.12798e8i | − | 1.33171i | −0.746083 | − | 0.665853i | \(-0.768068\pi\) | ||
0.746083 | − | 0.665853i | \(-0.231932\pi\) | |||||||
\(618\) | −1.07153e8 | + | 7.92685e7i | −0.453982 | + | 0.335842i | ||||
\(619\) | 8.50021e7i | 0.358392i | 0.983813 | + | 0.179196i | \(0.0573495\pi\) | ||||
−0.983813 | + | 0.179196i | \(0.942650\pi\) | |||||||
\(620\) | −1.42629e8 | − | 8.67905e7i | −0.598457 | − | 0.364164i | ||||
\(621\) | −255626. | −0.00106741 | ||||||||
\(622\) | −2.09758e8 | − | 2.83545e8i | −0.871660 | − | 1.17829i | ||||
\(623\) | 3.07567e8 | 1.27197 | ||||||||
\(624\) | −3.91045e7 | + | 5.79128e7i | −0.160943 | + | 0.238353i | ||||
\(625\) | 1.32159e8 | + | 2.05277e8i | 0.541325 | + | 0.840813i | ||||
\(626\) | −1.42091e7 | − | 1.92074e7i | −0.0579219 | − | 0.0782973i | ||||
\(627\) | −3.78908e8 | −1.53720 | ||||||||
\(628\) | 3.66633e8 | + | 1.12190e8i | 1.48031 | + | 0.452978i | ||||
\(629\) | 3.99425e7 | 0.160503 | ||||||||
\(630\) | −1.23630e8 | + | 5.04181e7i | −0.494426 | + | 0.201635i | ||||
\(631\) | 4.70789e8i | 1.87386i | 0.349513 | + | 0.936932i | \(0.386347\pi\) | ||||
−0.349513 | + | 0.936932i | \(0.613653\pi\) | |||||||
\(632\) | −3.63938e8 | + | 1.28725e8i | −1.44170 | + | 0.509931i | ||||
\(633\) | 1.03916e8i | 0.409706i | ||||||||
\(634\) | 1.85583e8 | + | 2.50866e8i | 0.728232 | + | 0.984404i | ||||
\(635\) | 3.47316e8 | + | 8.85719e7i | 1.35645 | + | 0.345919i | ||||
\(636\) | 2.35560e8 | + | 7.20819e7i | 0.915653 | + | 0.280191i | ||||
\(637\) | 2.01637e8i | 0.780103i | ||||||||
\(638\) | −7.50003e7 | − | 1.01383e8i | −0.288802 | − | 0.390395i | ||||
\(639\) | − | 7.86384e7i | − | 0.301392i | ||||||
\(640\) | −1.26514e8 | + | 2.29594e8i | −0.482613 | + | 0.875833i | ||||
\(641\) | 2.62768e8 | 0.997698 | 0.498849 | − | 0.866689i | \(-0.333756\pi\) | ||||
0.498849 | + | 0.866689i | \(0.333756\pi\) | |||||||
\(642\) | 1.83956e8 | − | 1.36085e8i | 0.695199 | − | 0.514287i | ||||
\(643\) | 4.31165e8 | 1.62185 | 0.810926 | − | 0.585149i | \(-0.198964\pi\) | ||||
0.810926 | + | 0.585149i | \(0.198964\pi\) | |||||||
\(644\) | −694363. | + | 2.26915e6i | −0.00259974 | + | 0.00849582i | ||||
\(645\) | −1.66932e7 | − | 4.25706e6i | −0.0622099 | − | 0.0158646i | ||||
\(646\) | 9.16541e7 | − | 6.78029e7i | 0.339981 | − | 0.251507i | ||||
\(647\) | −2.35225e7 | −0.0868501 | −0.0434250 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434250 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(648\) | 1.00814e7 | + | 2.85027e7i | 0.0370507 | + | 0.104752i | ||||
\(649\) | 2.92813e8 | 1.07117 | ||||||||
\(650\) | −1.87550e7 | − | 1.35510e8i | −0.0682932 | − | 0.493438i | ||||
\(651\) | 1.78752e8i | 0.647899i | ||||||||
\(652\) | 5.81190e7 | − | 1.89930e8i | 0.209689 | − | 0.685254i | ||||
\(653\) | − | 1.76583e8i | − | 0.634174i | −0.948396 | − | 0.317087i | \(-0.897295\pi\) | ||
0.948396 | − | 0.317087i | \(-0.102705\pi\) | |||||||
\(654\) | 9.33141e7 | − | 6.90309e7i | 0.333591 | − | 0.246780i | ||||
\(655\) | 4.99396e7 | − | 1.95828e8i | 0.177714 | − | 0.696867i | ||||
\(656\) | −3.49353e8 | − | 2.35894e8i | −1.23752 | − | 0.835612i | ||||
\(657\) | − | 8.79276e7i | − | 0.310048i | ||||||
\(658\) | −1.73504e8 | + | 1.28353e8i | −0.609022 | + | 0.450536i | ||||
\(659\) | − | 8.34343e7i | − | 0.291533i | −0.989319 | − | 0.145767i | \(-0.953435\pi\) | ||
0.989319 | − | 0.145767i | \(-0.0465649\pi\) | |||||||
\(660\) | −2.72029e8 | − | 1.65531e8i | −0.946203 | − | 0.575769i | ||||
\(661\) | −4.88849e8 | −1.69266 | −0.846332 | − | 0.532656i | \(-0.821194\pi\) | ||||
−0.846332 | + | 0.532656i | \(0.821194\pi\) | |||||||
\(662\) | 2.01791e8 | + | 2.72776e8i | 0.695550 | + | 0.940226i | ||||
\(663\) | 2.55403e7 | 0.0876366 | ||||||||
\(664\) | 4.04265e6 | + | 1.14296e7i | 0.0138090 | + | 0.0390415i | ||||
\(665\) | −1.61557e8 | + | 6.33514e8i | −0.549366 | + | 2.15422i | ||||
\(666\) | 3.08465e7 | + | 4.16975e7i | 0.104420 | + | 0.141152i | ||||
\(667\) | −416606. | −0.00140394 | ||||||||
\(668\) | 1.16923e8 | − | 3.82099e8i | 0.392257 | − | 1.28188i | ||||
\(669\) | 1.01907e8 | 0.340351 | ||||||||
\(670\) | 3.52701e8 | − | 1.43837e8i | 1.17269 | − | 0.478240i | ||||
\(671\) | 3.87821e7i | 0.128370i | ||||||||
\(672\) | 2.80399e8 | − | 1.20684e7i | 0.923992 | − | 0.0397688i | ||||
\(673\) | 8.80898e7i | 0.288988i | 0.989506 | + | 0.144494i | \(0.0461555\pi\) | ||||
−0.989506 | + | 0.144494i | \(0.953844\pi\) | |||||||
\(674\) | −2.18553e8 | − | 2.95434e8i | −0.713801 | − | 0.964896i | ||||
\(675\) | −5.19591e7 | − | 2.83444e7i | −0.168947 | − | 0.0921628i | ||||
\(676\) | 6.79613e7 | − | 2.22094e8i | 0.219999 | − | 0.718948i | ||||
\(677\) | − | 4.30417e8i | − | 1.38715i | −0.720384 | − | 0.693575i | \(-0.756035\pi\) | ||
0.720384 | − | 0.693575i | \(-0.243965\pi\) | |||||||
\(678\) | 1.70291e8 | + | 2.30194e8i | 0.546389 | + | 0.738594i | ||||
\(679\) | − | 4.63614e8i | − | 1.48097i | ||||||
\(680\) | 9.54219e7 | − | 8.63734e6i | 0.303474 | − | 0.0274697i | ||||
\(681\) | 6.82510e7 | 0.216106 | ||||||||
\(682\) | −3.42735e8 | + | 2.53545e8i | −1.08045 | + | 0.799284i | ||||
\(683\) | −5.22431e8 | −1.63971 | −0.819854 | − | 0.572572i | \(-0.805946\pi\) | ||||
−0.819854 | + | 0.572572i | \(0.805946\pi\) | |||||||
\(684\) | 1.41564e8 | + | 4.33188e7i | 0.442369 | + | 0.135366i | ||||
\(685\) | −3.74837e7 | + | 1.46984e8i | −0.116619 | + | 0.457298i | ||||
\(686\) | 2.35319e8 | − | 1.74082e8i | 0.728929 | − | 0.539239i | ||||
\(687\) | −8.28649e7 | −0.255564 | ||||||||
\(688\) | 3.00121e7 | + | 2.02651e7i | 0.0921575 | + | 0.0622275i | ||||
\(689\) | 2.70233e8 | 0.826192 | ||||||||
\(690\) | −974071. | + | 397241.i | −0.00296513 | + | 0.00120922i | ||||
\(691\) | − | 2.74162e8i | − | 0.830947i | −0.909605 | − | 0.415473i | \(-0.863616\pi\) | ||
0.909605 | − | 0.415473i | \(-0.136384\pi\) | |||||||
\(692\) | 2.46332e8 | + | 7.53779e7i | 0.743365 | + | 0.227471i | ||||
\(693\) | 3.40924e8i | 1.02437i | ||||||||
\(694\) | −3.01547e8 | + | 2.23076e8i | −0.902147 | + | 0.667380i | ||||
\(695\) | −2.30332e7 | + | 9.03198e7i | −0.0686120 | + | 0.269047i | ||||
\(696\) | 1.64302e7 | + | 4.64523e7i | 0.0487321 | + | 0.137778i | ||||
\(697\) | 1.54069e8i | 0.455006i | ||||||||
\(698\) | −1.19134e8 | + | 8.81314e7i | −0.350322 | + | 0.259158i | ||||
\(699\) | − | 9.43020e6i | − | 0.0276115i | ||||||
\(700\) | −3.92747e8 | + | 3.84240e8i | −1.14503 | + | 1.12023i | ||||
\(701\) | −1.41906e8 | −0.411952 | −0.205976 | − | 0.978557i | \(-0.566037\pi\) | ||||
−0.205976 | + | 0.978557i | \(0.566037\pi\) | |||||||
\(702\) | 1.97241e7 | + | 2.66625e7i | 0.0570146 | + | 0.0770707i | ||||
\(703\) | 2.53979e8 | 0.731025 | ||||||||
\(704\) | 4.20862e8 | + | 5.20512e8i | 1.20621 | + | 1.49181i | ||||
\(705\) | −9.27062e7 | − | 2.36418e7i | −0.264570 | − | 0.0674703i | ||||
\(706\) | 1.84352e8 | + | 2.49202e8i | 0.523882 | + | 0.708169i | ||||
\(707\) | −2.69635e8 | −0.762987 | ||||||||
\(708\) | −1.09398e8 | − | 3.34760e7i | −0.308255 | − | 0.0943265i | ||||
\(709\) | −1.21569e8 | −0.341102 | −0.170551 | − | 0.985349i | \(-0.554555\pi\) | ||||
−0.170551 | + | 0.985349i | \(0.554555\pi\) | |||||||
\(710\) | −1.22204e8 | − | 2.99655e8i | −0.341436 | − | 0.837232i | ||||
\(711\) | 1.83215e8i | 0.509743i | ||||||||
\(712\) | −9.55706e7 | − | 2.70202e8i | −0.264780 | − | 0.748599i | ||||
\(713\) | 1.40837e6i | 0.00388551i | ||||||||
\(714\) | −6.10060e7 | − | 8.24663e7i | −0.167602 | − | 0.226559i | ||||
\(715\) | −3.38484e8 | − | 8.63196e7i | −0.926020 | − | 0.236152i | ||||
\(716\) | 3.07478e8 | + | 9.40888e7i | 0.837674 | + | 0.256330i | ||||
\(717\) | − | 2.27267e7i | − | 0.0616566i | ||||||
\(718\) | 3.72044e7 | + | 5.02919e7i | 0.100513 | + | 0.135870i | ||||
\(719\) | − | 6.64252e7i | − | 0.178709i | −0.996000 | − | 0.0893545i | \(-0.971520\pi\) | ||
0.996000 | − | 0.0893545i | \(-0.0284804\pi\) | |||||||
\(720\) | 8.27087e7 | + | 9.29442e7i | 0.221592 | + | 0.249015i | ||||
\(721\) | 5.87242e8 | 1.56679 | ||||||||
\(722\) | 2.80221e8 | − | 2.07299e8i | 0.744541 | − | 0.550788i | ||||
\(723\) | 1.09744e8 | 0.290379 | ||||||||
\(724\) | 1.42104e8 | − | 4.64389e8i | 0.374447 | − | 1.22368i | ||||
\(725\) | −8.46804e7 | − | 4.61943e7i | −0.222213 | − | 0.121220i | ||||
\(726\) | −4.76071e8 | + | 3.52183e8i | −1.24412 | + | 0.920362i | ||||
\(727\) | −9.71701e7 | −0.252889 | −0.126444 | − | 0.991974i | \(-0.540357\pi\) | ||||
−0.126444 | + | 0.991974i | \(0.540357\pi\) | |||||||
\(728\) | 2.90256e8 | − | 1.02664e8i | 0.752293 | − | 0.266086i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −1.36639e8 | − | 3.35051e8i | −0.351242 | − | 0.861277i | ||||
\(731\) | − | 1.32357e7i | − | 0.0338840i | ||||||
\(732\) | 4.43378e6 | − | 1.44894e7i | 0.0113042 | − | 0.0369417i | ||||
\(733\) | − | 7.38776e8i | − | 1.87586i | −0.346821 | − | 0.937931i | \(-0.612739\pi\) | ||
0.346821 | − | 0.937931i | \(-0.387261\pi\) | |||||||
\(734\) | −3.28054e8 | + | 2.42684e8i | −0.829577 | + | 0.613696i | ||||
\(735\) | 3.47871e8 | + | 8.87135e7i | 0.876106 | + | 0.223423i | ||||
\(736\) | 2.20924e6 | − | 95086.1i | 0.00554127 | − | 0.000238497i | ||||
\(737\) | − | 9.72617e8i | − | 2.42963i | ||||||
\(738\) | −1.60839e8 | + | 1.18983e8i | −0.400148 | + | 0.296018i | ||||
\(739\) | − | 9.03695e7i | − | 0.223918i | −0.993713 | − | 0.111959i | \(-0.964288\pi\) | ||
0.993713 | − | 0.111959i | \(-0.0357125\pi\) | |||||||
\(740\) | 1.82339e8 | + | 1.10954e8i | 0.449972 | + | 0.273810i | ||||
\(741\) | 1.62401e8 | 0.399148 | ||||||||
\(742\) | −6.45484e8 | − | 8.72547e8i | −1.58006 | − | 2.13588i | ||||
\(743\) | 5.29875e8 | 1.29183 | 0.645917 | − | 0.763408i | \(-0.276475\pi\) | ||||
0.645917 | + | 0.763408i | \(0.276475\pi\) | |||||||
\(744\) | 1.57036e8 | − | 5.55437e7i | 0.381312 | − | 0.134870i | ||||
\(745\) | −3.48054e8 | − | 8.87600e7i | −0.841739 | − | 0.214659i | ||||
\(746\) | −1.00034e8 | − | 1.35224e8i | −0.240953 | − | 0.325714i | ||||
\(747\) | 5.75392e6 | 0.0138039 | ||||||||
\(748\) | 7.15871e7 | − | 2.33943e8i | 0.171053 | − | 0.558992i | ||||
\(749\) | −1.00816e9 | −2.39929 | ||||||||
\(750\) | −2.42039e8 | − | 2.72632e7i | −0.573722 | − | 0.0646239i | ||||
\(751\) | − | 4.01846e8i | − | 0.948723i | −0.880330 | − | 0.474362i | \(-0.842679\pi\) | ||
0.880330 | − | 0.474362i | \(-0.157321\pi\) | |||||||
\(752\) | 1.66673e8 | + | 1.12543e8i | 0.391934 | + | 0.264645i | ||||
\(753\) | 2.47771e8i | 0.580317i | ||||||||
\(754\) | 3.21454e7 | + | 4.34532e7i | 0.0749902 | + | 0.101370i | ||||
\(755\) | −5.27993e7 | + | 2.07041e8i | −0.122684 | + | 0.481079i | ||||
\(756\) | 3.89764e7 | − | 1.27373e8i | 0.0902061 | − | 0.294790i | ||||
\(757\) | 6.84418e8i | 1.57773i | 0.614564 | + | 0.788867i | \(0.289332\pi\) | ||||
−0.614564 | + | 0.788867i | \(0.710668\pi\) | |||||||
\(758\) | −2.56841e7 | − | 3.47191e7i | −0.0589735 | − | 0.0797188i | ||||
\(759\) | 2.68612e6i | 0.00614327i | ||||||||
\(760\) | 6.06752e8 | − | 5.49216e7i | 1.38220 | − | 0.125113i | ||||
\(761\) | −3.75375e8 | −0.851748 | −0.425874 | − | 0.904782i | \(-0.640033\pi\) | ||||
−0.425874 | + | 0.904782i | \(0.640033\pi\) | |||||||
\(762\) | −2.87480e8 | + | 2.12669e8i | −0.649746 | + | 0.480662i | ||||
\(763\) | −5.11400e8 | −1.15130 | ||||||||
\(764\) | 3.07622e8 | + | 9.41330e7i | 0.689823 | + | 0.211087i | ||||
\(765\) | 1.12369e7 | − | 4.40630e7i | 0.0250993 | − | 0.0984216i | ||||
\(766\) | 3.99536e8 | − | 2.95564e8i | 0.888933 | − | 0.657606i | ||||
\(767\) | −1.25501e8 | −0.278138 | ||||||||
\(768\) | −9.77308e7 | − | 2.42584e8i | −0.215748 | − | 0.535524i | ||||
\(769\) | 4.59463e7 | 0.101035 | 0.0505175 | − | 0.998723i | \(-0.483913\pi\) | ||||
0.0505175 | + | 0.998723i | \(0.483913\pi\) | |||||||
\(770\) | 5.29795e8 | + | 1.29911e9i | 1.16047 | + | 2.84559i | ||||
\(771\) | 3.54336e8i | 0.773129i | ||||||||
\(772\) | −1.65421e8 | − | 5.06190e7i | −0.359532 | − | 0.110017i | ||||
\(773\) | 3.78255e8i | 0.818930i | 0.912326 | + | 0.409465i | \(0.134285\pi\) | ||||
−0.912326 | + | 0.409465i | \(0.865715\pi\) | |||||||
\(774\) | 1.38173e7 | − | 1.02216e7i | 0.0297988 | − | 0.0220443i | ||||
\(775\) | −1.56164e8 | + | 2.86269e8i | −0.335486 | + | 0.614992i | ||||
\(776\) | −4.07292e8 | + | 1.44059e8i | −0.871607 | + | 0.308288i | ||||
\(777\) | − | 2.28519e8i | − | 0.487146i | ||||||
\(778\) | 1.64346e8 | − | 1.21578e8i | 0.348996 | − | 0.258177i | ||||
\(779\) | 9.79667e8i | 2.07236i | ||||||||
\(780\) | 1.16593e8 | + | 7.09473e7i | 0.245690 | + | 0.149504i | ||||
\(781\) | −8.26334e8 | −1.73461 | ||||||||
\(782\) | −480662. | − | 649746.i | −0.00100512 | − | 0.00135870i | ||||
\(783\) | 2.33851e7 | 0.0487141 | ||||||||
\(784\) | −6.25426e8 | − | 4.22306e8i | −1.29786 | − | 0.876354i | ||||
\(785\) | 1.85050e8 | − | 7.25633e8i | 0.382542 | − | 1.50006i | ||||
\(786\) | 1.19909e8 | + | 1.62090e8i | 0.246937 | + | 0.333802i | ||||
\(787\) | 1.56045e8 | 0.320129 | 0.160065 | − | 0.987107i | \(-0.448830\pi\) | ||||
0.160065 | + | 0.987107i | \(0.448830\pi\) | |||||||
\(788\) | 5.42858e8 | + | 1.66116e8i | 1.10945 | + | 0.339494i | ||||
\(789\) | 1.34307e8 | 0.273444 | ||||||||
\(790\) | 2.84714e8 | + | 6.98146e8i | 0.577468 | + | 1.41601i | ||||
\(791\) | − | 1.26156e9i | − | 2.54905i | ||||||
\(792\) | 2.99507e8 | − | 1.05936e8i | 0.602881 | − | 0.213239i | ||||
\(793\) | − | 1.66221e7i | − | 0.0333325i | ||||||
\(794\) | 9.30670e7 | + | 1.25805e8i | 0.185923 | + | 0.251326i | ||||
\(795\) | 1.18894e8 | − | 4.66216e8i | 0.236623 | − | 0.927867i | ||||
\(796\) | 6.14153e8 | + | 1.87932e8i | 1.21769 | + | 0.372616i | ||||
\(797\) | 3.23272e8i | 0.638548i | 0.947662 | + | 0.319274i | \(0.103439\pi\) | ||||
−0.947662 | + | 0.319274i | \(0.896561\pi\) | |||||||
\(798\) | −3.87914e8 | − | 5.24372e8i | −0.763356 | − | 1.03188i | ||||
\(799\) | − | 7.35051e7i | − | 0.144104i | ||||||
\(800\) | 4.59599e8 | + | 2.25638e8i | 0.897654 | + | 0.440700i | ||||
\(801\) | −1.36026e8 | −0.264682 | ||||||||
\(802\) | −3.00907e8 | + | 2.22602e8i | −0.583323 | + | 0.431525i | ||||
\(803\) | −9.23946e8 | −1.78443 | ||||||||
\(804\) | −1.11195e8 | + | 3.63380e8i | −0.213952 | + | 0.699187i | ||||
\(805\) | 4.49105e6 | + | 1.14530e6i | 0.00860915 | + | 0.00219549i | ||||
\(806\) | 1.46897e8 | − | 1.08670e8i | 0.280549 | − | 0.207541i | ||||
\(807\) | 3.11771e8 | 0.593219 | ||||||||
\(808\) | 8.37838e7 | + | 2.36878e8i | 0.158828 | + | 0.449046i | ||||
\(809\) | 1.51271e8 | 0.285700 | 0.142850 | − | 0.989744i | \(-0.454373\pi\) | ||||
0.142850 | + | 0.989744i | \(0.454373\pi\) | |||||||
\(810\) | 5.46770e7 | − | 2.22981e7i | 0.102884 | − | 0.0419578i | ||||
\(811\) | − | 7.39372e8i | − | 1.38612i | −0.720880 | − | 0.693060i | \(-0.756262\pi\) | ||
0.720880 | − | 0.693060i | \(-0.243738\pi\) | |||||||
\(812\) | 6.35218e7 | − | 2.07586e8i | 0.118646 | − | 0.387731i | ||||
\(813\) | − | 1.10308e8i | − | 0.205274i | ||||||
\(814\) | 4.38158e8 | − | 3.24136e8i | 0.812377 | − | 0.600971i | ||||
\(815\) | −3.75906e8 | − | 9.58629e7i | −0.694395 | − | 0.177083i | ||||
\(816\) | −5.34914e7 | + | 7.92195e7i | −0.0984494 | + | 0.145801i | ||||
\(817\) | − | 8.41609e7i | − | 0.154328i | ||||||
\(818\) | −5.47295e8 | + | 4.04872e8i | −0.999912 | + | 0.739704i | ||||
\(819\) | − | 1.46121e8i | − | 0.265988i | ||||||
\(820\) | −4.27982e8 | + | 7.03333e8i | −0.776218 | + | 1.27561i | ||||
\(821\) | 2.62161e8 | 0.473739 | 0.236870 | − | 0.971541i | \(-0.423879\pi\) | ||||
0.236870 | + | 0.971541i | \(0.423879\pi\) | |||||||
\(822\) | −9.00018e7 | − | 1.21662e8i | −0.162045 | − | 0.219048i | ||||
\(823\) | 1.57030e8 | 0.281698 | 0.140849 | − | 0.990031i | \(-0.455017\pi\) | ||||
0.140849 | + | 0.990031i | \(0.455017\pi\) | |||||||
\(824\) | −1.82474e8 | − | 5.15901e8i | −0.326152 | − | 0.922114i | ||||
\(825\) | −2.97843e8 | + | 5.45987e8i | −0.530428 | + | 0.972346i | ||||
\(826\) | 2.99773e8 | + | 4.05225e8i | 0.531928 | + | 0.719045i | ||||
\(827\) | −7.49865e8 | −1.32576 | −0.662882 | − | 0.748724i | \(-0.730667\pi\) | ||||
−0.662882 | + | 0.748724i | \(0.730667\pi\) | |||||||
\(828\) | 307092. | − | 1.00356e6i | 0.000540975 | − | 0.00176788i | ||||
\(829\) | −2.21793e8 | −0.389299 | −0.194650 | − | 0.980873i | \(-0.562357\pi\) | ||||
−0.194650 | + | 0.980873i | \(0.562357\pi\) | |||||||
\(830\) | 2.19255e7 | − | 8.94155e6i | 0.0383456 | − | 0.0156379i | ||||
\(831\) | 8.28367e7i | 0.144351i | ||||||||
\(832\) | −1.80383e8 | − | 2.23093e8i | −0.313203 | − | 0.387362i | ||||
\(833\) | 2.75821e8i | 0.477191i | ||||||||
\(834\) | −5.53048e7 | − | 7.47595e7i | −0.0953377 | − | 0.128875i | ||||
\(835\) | −7.56243e8 | − | 1.92856e8i | −1.29898 | − | 0.331263i | ||||
\(836\) | 4.55195e8 | − | 1.48756e9i | 0.779074 | − | 2.54598i | ||||
\(837\) | − | 7.90554e7i | − | 0.134820i | ||||||
\(838\) | −2.90452e8 | − | 3.92625e8i | −0.493563 | − | 0.667185i | ||||
\(839\) | 3.85183e7i | 0.0652201i | 0.999468 | + | 0.0326101i | \(0.0103819\pi\) | ||||
−0.999468 | + | 0.0326101i | \(0.989618\pi\) | |||||||
\(840\) | −4.94160e7 | − | 5.45929e8i | −0.0833739 | − | 0.921081i | ||||
\(841\) | −5.56711e8 | −0.935927 | ||||||||
\(842\) | 4.93874e8 | − | 3.65353e8i | 0.827332 | − | 0.612035i | ||||
\(843\) | 4.91233e8 | 0.819983 | ||||||||
\(844\) | −4.07965e8 | − | 1.24838e8i | −0.678572 | − | 0.207644i | ||||
\(845\) | −4.39564e8 | − | 1.12097e8i | −0.728538 | − | 0.185790i | ||||
\(846\) | 7.67347e7 | − | 5.67660e7i | 0.126730 | − | 0.0937513i | ||||
\(847\) | 2.60907e9 | 4.29373 | ||||||||
\(848\) | −5.65974e8 | + | 8.38194e8i | −0.928130 | + | 1.37454i | ||||
\(849\) | −3.89791e8 | −0.636956 | ||||||||
\(850\) | −2.56552e7 | − | 1.85366e8i | −0.0417752 | − | 0.301837i | ||||
\(851\) | − | 1.80049e6i | − | 0.00292147i | ||||||
\(852\) | 3.08727e8 | + | 9.44711e7i | 0.499179 | + | 0.152750i | ||||
\(853\) | 6.04161e8i | 0.973433i | 0.873560 | + | 0.486716i | \(0.161805\pi\) | ||||
−0.873560 | + | 0.486716i | \(0.838195\pi\) | |||||||
\(854\) | −5.36707e7 | + | 3.97039e7i | −0.0861715 | + | 0.0637470i | ||||
\(855\) | 7.14511e7 | − | 2.80180e8i | 0.114317 | − | 0.448270i | ||||
\(856\) | 3.13265e8 | + | 8.85679e8i | 0.499448 | + | 1.41207i | ||||
\(857\) | 1.07405e9i | 1.70641i | 0.521576 | + | 0.853205i | \(0.325344\pi\) | ||||
−0.521576 | + | 0.853205i | \(0.674656\pi\) | |||||||
\(858\) | 2.80170e8 | − | 2.07261e8i | 0.443568 | − | 0.328138i | ||||
\(859\) | 4.18661e8i | 0.660516i | 0.943891 | + | 0.330258i | \(0.107136\pi\) | ||||
−0.943891 | + | 0.330258i | \(0.892864\pi\) | |||||||
\(860\) | 3.67669e7 | − | 6.04217e7i | 0.0578045 | − | 0.0949943i | ||||
\(861\) | 8.81461e8 | 1.38100 | ||||||||
\(862\) | 7.70178e7 | + | 1.04111e8i | 0.120246 | + | 0.162545i | ||||
\(863\) | 6.54898e8 | 1.01892 | 0.509461 | − | 0.860493i | \(-0.329845\pi\) | ||||
0.509461 | + | 0.860493i | \(0.329845\pi\) | |||||||
\(864\) | −1.24010e8 | + | 5.33742e6i | −0.192272 | + | 0.00827543i | ||||
\(865\) | 1.24330e8 | − | 4.87534e8i | 0.192100 | − | 0.753281i | ||||
\(866\) | −4.49326e8 | − | 6.07386e8i | −0.691843 | − | 0.935214i | ||||
\(867\) | −3.41331e8 | −0.523743 | ||||||||
\(868\) | −7.01763e8 | − | 2.14741e8i | −1.07308 | − | 0.328364i | ||||
\(869\) | 1.92522e9 | 2.93374 | ||||||||
\(870\) | 8.91100e7 | − | 3.63404e7i | 0.135322 | − | 0.0551863i | ||||
\(871\) | 4.16867e8i | 0.630875i | ||||||||
\(872\) | 1.58908e8 | + | 4.49272e8i | 0.239660 | + | 0.677579i | ||||
\(873\) | 2.05040e8i | 0.308174i | ||||||||
\(874\) | −3.05635e6 | − | 4.13149e6i | −0.00457792 | − | 0.00618831i | ||||
\(875\) | 7.85868e8 | + | 7.30775e8i | 1.17307 | + | 1.09084i | ||||
\(876\) | 3.45196e8 | + | 1.05631e8i | 0.513515 | + | 0.157137i | ||||
\(877\) | 3.34585e8i | 0.496030i | 0.968756 | + | 0.248015i | \(0.0797783\pi\) | ||||
−0.968756 | + | 0.248015i | \(0.920222\pi\) | |||||||
\(878\) | 2.58643e8 | + | 3.49627e8i | 0.382135 | + | 0.516560i | ||||
\(879\) | − | 1.22976e8i | − | 0.181073i | ||||||
\(880\) | 9.76660e8 | − | 8.69104e8i | 1.43316 | − | 1.27533i | ||||
\(881\) | −2.23304e8 | −0.326564 | −0.163282 | − | 0.986579i | \(-0.552208\pi\) | ||||
−0.163282 | + | 0.986579i | \(0.552208\pi\) | |||||||
\(882\) | −2.87940e8 | + | 2.13009e8i | −0.419659 | + | 0.310451i | ||||
\(883\) | −2.19587e8 | −0.318952 | −0.159476 | − | 0.987202i | \(-0.550980\pi\) | ||||
−0.159476 | + | 0.987202i | \(0.550980\pi\) | |||||||
\(884\) | −3.06824e7 | + | 1.00269e8i | −0.0444154 | + | 0.145147i | ||||
\(885\) | −5.52161e7 | + | 2.16518e8i | −0.0796592 | + | 0.312367i | ||||
\(886\) | −8.03981e8 | + | 5.94760e8i | −1.15596 | + | 0.855147i | ||||
\(887\) | −1.05645e9 | −1.51383 | −0.756915 | − | 0.653514i | \(-0.773294\pi\) | ||||
−0.756915 | + | 0.653514i | \(0.773294\pi\) | |||||||
\(888\) | −2.00757e8 | + | 7.10080e7i | −0.286703 | + | 0.101407i | ||||
\(889\) | 1.57551e9 | 2.24241 | ||||||||
\(890\) | −5.18332e8 | + | 2.11383e8i | −0.735255 | + | 0.299848i | ||||
\(891\) | − | 1.50779e8i | − | 0.213160i | ||||||
\(892\) | −1.22425e8 | + | 4.00079e8i | −0.172495 | + | 0.563705i | ||||
\(893\) | − | 4.67391e8i | − | 0.656336i | ||||||
\(894\) | 2.88091e8 | − | 2.13121e8i | 0.403197 | − | 0.298273i | ||||
\(895\) | 1.55192e8 | − | 6.08554e8i | 0.216472 | − | 0.848848i | ||||
\(896\) | −2.89473e8 | + | 1.11532e9i | −0.402424 | + | 1.55051i | ||||
\(897\) | − | 1.15128e6i | − | 0.00159516i | ||||||
\(898\) | 7.00548e8 | − | 5.18244e8i | 0.967406 | − | 0.715657i | ||||
\(899\) | − | 1.28841e8i | − | 0.177327i | ||||||
\(900\) | 1.73698e8 | − | 1.69936e8i | 0.238268 | − | 0.233108i | ||||
\(901\) | 3.69654e8 | 0.505384 | ||||||||
\(902\) | 1.25028e9 | + | 1.69010e9i | 1.70368 | + | 2.30299i | ||||
\(903\) | −7.57242e7 | −0.102842 | ||||||||
\(904\) | −1.10830e9 | + | 3.92005e8i | −1.50021 | + | 0.530624i | ||||
\(905\) | −9.19109e8 | − | 2.34390e8i | −1.24000 | − | 0.316222i | ||||
\(906\) | −1.26776e8 | − | 1.71372e8i | −0.170472 | − | 0.230439i | ||||
\(907\) | −7.33082e8 | −0.982495 | −0.491248 | − | 0.871020i | \(-0.663459\pi\) | ||||
−0.491248 | + | 0.871020i | \(0.663459\pi\) | |||||||
\(908\) | −8.19923e7 | + | 2.67947e8i | −0.109526 | + | 0.357925i | ||||
\(909\) | 1.19250e8 | 0.158769 | ||||||||
\(910\) | −2.27072e8 | − | 5.56801e8i | −0.301328 | − | 0.738883i | ||||
\(911\) | 4.35193e8i | 0.575608i | 0.957689 | + | 0.287804i | \(0.0929252\pi\) | ||||
−0.957689 | + | 0.287804i | \(0.907075\pi\) | |||||||
\(912\) | −3.40131e8 | + | 5.03727e8i | −0.448397 | + | 0.664065i | ||||
\(913\) | − | 6.04623e7i | − | 0.0794461i | ||||||
\(914\) | −5.97061e8 | − | 8.07091e8i | −0.781952 | − | 1.05702i | ||||
\(915\) | −2.86771e7 | − | 7.31318e6i | −0.0374345 | − | 0.00954648i | ||||
\(916\) | 9.95485e7 | − | 3.25320e8i | 0.129523 | − | 0.423277i | ||||
\(917\) | − | 8.88321e8i | − | 1.15203i | ||||||
\(918\) | 2.69808e7 | + | 3.64719e7i | 0.0348760 | + | 0.0471444i | ||||
\(919\) | 9.37380e8i | 1.20773i | 0.797087 | + | 0.603864i | \(0.206373\pi\) | ||||
−0.797087 | + | 0.603864i | \(0.793627\pi\) | |||||||
\(920\) | −389345. | − | 4.30133e6i | −0.000500002 | − | 0.00552382i | ||||
\(921\) | −5.97913e8 | −0.765349 | ||||||||
\(922\) | −4.02771e8 | + | 2.97958e8i | −0.513885 | + | 0.380156i | ||||
\(923\) | 3.54170e8 | 0.450408 | ||||||||
\(924\) | −1.33844e9 | − | 4.09564e8i | −1.69661 | − | 0.519166i | ||||
\(925\) | 1.99642e8 | − | 3.65971e8i | 0.252248 | − | 0.462404i | ||||
\(926\) | 1.04143e8 | − | 7.70415e7i | 0.131158 | − | 0.0970268i | ||||
\(927\) | −2.59716e8 | −0.326032 | ||||||||
\(928\) | −2.02106e8 | + | 8.69867e6i | −0.252892 | + | 0.0108845i | ||||
\(929\) | 1.90323e8 | 0.237380 | 0.118690 | − | 0.992931i | \(-0.462131\pi\) | ||||
0.118690 | + | 0.992931i | \(0.462131\pi\) | |||||||
\(930\) | −1.22852e8 | − | 3.01244e8i | −0.152733 | − | 0.374515i | ||||
\(931\) | 1.75384e9i | 2.17341i | ||||||||
\(932\) | 3.70221e7 | + | 1.13288e7i | 0.0457313 | + | 0.0139939i | ||||
\(933\) | − | 6.87253e8i | − | 0.846198i | ||||||
\(934\) | −1.41128e7 | + | 1.04402e7i | −0.0173209 | + | 0.0128135i | ||||
\(935\) | −4.63016e8 | − | 1.18077e8i | −0.566449 | − | 0.144455i | ||||
\(936\) | −1.28370e8 | + | 4.54044e7i | −0.156544 | + | 0.0553695i | ||||
\(937\) | 1.56976e9i | 1.90816i | 0.299558 | + | 0.954078i | \(0.403161\pi\) | ||||
−0.299558 | + | 0.954078i | \(0.596839\pi\) | |||||||
\(938\) | 1.34601e9 | − | 9.95736e8i | 1.63095 | − | 1.20652i | ||||
\(939\) | − | 4.65548e7i | − | 0.0562299i | ||||||
\(940\) | 2.04187e8 | − | 3.35554e8i | 0.245835 | − | 0.403998i | ||||
\(941\) | −3.37518e8 | −0.405069 | −0.202534 | − | 0.979275i | \(-0.564918\pi\) | ||||
−0.202534 | + | 0.979275i | \(0.564918\pi\) | |||||||
\(942\) | 4.44321e8 | + | 6.00621e8i | 0.531550 | + | 0.718534i | ||||
\(943\) | 6.94497e6 | 0.00828200 | ||||||||
\(944\) | 2.62848e8 | − | 3.89271e8i | 0.312455 | − | 0.462739i | ||||
\(945\) | −2.52094e8 | − | 6.42885e7i | −0.298722 | − | 0.0761795i | ||||
\(946\) | −1.07409e8 | − | 1.45192e8i | −0.126872 | − | 0.171502i | ||||
\(947\) | −9.84991e8 | −1.15980 | −0.579899 | − | 0.814689i | \(-0.696908\pi\) | ||||
−0.579899 | + | 0.814689i | \(0.696908\pi\) | |||||||
\(948\) | −7.19284e8 | − | 2.20102e8i | −0.844258 | − | 0.258344i | ||||
\(949\) | 3.96006e8 | 0.463344 | ||||||||
\(950\) | −1.63132e8 | − | 1.17867e9i | −0.190269 | − | 1.37474i | ||||
\(951\) | 6.08045e8i | 0.706959i | ||||||||
\(952\) | 3.97044e8 | − | 1.40434e8i | 0.460180 | − | 0.162766i | ||||
\(953\) | − | 1.46230e9i | − | 1.68950i | −0.535165 | − | 0.844748i | \(-0.679751\pi\) | ||
0.535165 | − | 0.844748i | \(-0.320249\pi\) | |||||||
\(954\) | 2.85474e8 | + | 3.85896e8i | 0.328792 | + | 0.444453i | ||||
\(955\) | 1.55265e8 | − | 6.08840e8i | 0.178264 | − | 0.699025i | ||||
\(956\) | 8.92231e7 | + | 2.73024e7i | 0.102118 | + | 0.0312484i | ||||
\(957\) | − | 2.45732e8i | − | 0.280366i | ||||||
\(958\) | 7.27759e8 | + | 9.83764e8i | 0.827734 | + | 1.11891i | ||||
\(959\) | 6.66757e8i | 0.755983i | ||||||||
\(960\) | −4.64251e8 | + | 2.13050e8i | −0.524734 | + | 0.240806i | ||||
\(961\) | 4.51947e8 | 0.509234 | ||||||||
\(962\) | −1.87796e8 | + | 1.38926e8i | −0.210941 | + | 0.156048i | ||||
\(963\) | 4.45871e8 | 0.499264 | ||||||||
\(964\) | −1.31839e8 | + | 4.30844e8i | −0.147168 | + | 0.480938i | ||||
\(965\) | −8.34922e7 | + | 3.27397e8i | −0.0929103 | + | 0.364328i | ||||
\(966\) | −3.71733e6 | + | 2.74997e6i | −0.00412382 | + | 0.00305068i | ||||
\(967\) | 1.00253e9 | 1.10871 | 0.554355 | − | 0.832280i | \(-0.312965\pi\) | ||||
0.554355 | + | 0.832280i | \(0.312965\pi\) | |||||||
\(968\) | −8.10717e8 | − | 2.29210e9i | −0.893806 | − | 2.52702i | ||||
\(969\) | 2.22150e8 | 0.244160 | ||||||||
\(970\) | 3.18631e8 | + | 7.81312e8i | 0.349118 | + | 0.856070i | ||||
\(971\) | − | 8.17160e8i | − | 0.892585i | −0.894887 | − | 0.446293i | \(-0.852744\pi\) | ||
0.894887 | − | 0.446293i | \(-0.147256\pi\) | |||||||
\(972\) | −1.72378e7 | + | 5.63325e7i | −0.0187709 | + | 0.0613423i | ||||
\(973\) | 4.09713e8i | 0.444776i | ||||||||
\(974\) | −2.15004e8 | + | 1.59053e8i | −0.232685 | + | 0.172134i | ||||
\(975\) | 1.27657e8 | − | 2.34012e8i | 0.137730 | − | 0.252478i | ||||
\(976\) | 5.15576e7 | + | 3.48133e7i | 0.0554554 | + | 0.0374451i | ||||
\(977\) | 2.61374e8i | 0.280272i | 0.990132 | + | 0.140136i | \(0.0447539\pi\) | ||||
−0.990132 | + | 0.140136i | \(0.955246\pi\) | |||||||
\(978\) | 3.11145e8 | − | 2.30176e8i | 0.332618 | − | 0.246061i | ||||
\(979\) | 1.42936e9i | 1.52333i | ||||||||
\(980\) | −7.66191e8 | + | 1.25914e9i | −0.814064 | + | 1.33781i | ||||
\(981\) | 2.26174e8 | 0.239571 | ||||||||
\(982\) | −3.34908e8 | − | 4.52719e8i | −0.353664 | − | 0.478073i | ||||
\(983\) | 8.00824e7 | 0.0843095 | 0.0421548 | − | 0.999111i | \(-0.486578\pi\) | ||||
0.0421548 | + | 0.999111i | \(0.486578\pi\) | |||||||
\(984\) | −2.73897e8 | − | 7.74377e8i | −0.287476 | − | 0.812769i | ||||
\(985\) | 2.73995e8 | − | 1.07441e9i | 0.286704 | − | 1.12425i | ||||
\(986\) | 4.39719e7 | + | 5.94401e7i | 0.0458717 | + | 0.0620081i | ||||
\(987\) | −4.20538e8 | −0.437375 | ||||||||
\(988\) | −1.95098e8 | + | 6.37572e8i | −0.202294 | + | 0.661087i | ||||
\(989\) | −596626. | −0.000616756 | ||||||||
\(990\) | −2.34309e8 | − | 5.74548e8i | −0.241481 | − | 0.592135i | ||||
\(991\) | − | 6.18860e8i | − | 0.635874i | −0.948112 | − | 0.317937i | \(-0.897010\pi\) | ||
0.948112 | − | 0.317937i | \(-0.102990\pi\) | |||||||
\(992\) | 2.94066e7 | + | 6.83235e8i | 0.0301238 | + | 0.699899i | ||||
\(993\) | 6.61151e8i | 0.675232i | ||||||||
\(994\) | −8.45976e8 | − | 1.14357e9i | −0.861388 | − | 1.16440i | ||||
\(995\) | 3.09979e8 | − | 1.21552e9i | 0.314676 | − | 1.23393i | ||||
\(996\) | −6.91238e6 | + | 2.25894e7i | −0.00699600 | + | 0.0228626i | ||||
\(997\) | − | 1.35069e9i | − | 1.36292i | −0.731854 | − | 0.681461i | \(-0.761345\pi\) | ||
0.731854 | − | 0.681461i | \(-0.238655\pi\) | |||||||
\(998\) | 7.34871e7 | + | 9.93378e7i | 0.0739298 | + | 0.0999363i | ||||
\(999\) | 1.01066e8i | 0.101370i |
(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.f.a.19.8 | yes | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.29 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.30 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.29 | yes | 36 | |
12.11 | even | 2 | 180.7.f.g.19.7 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.8 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.7 | ✓ | 36 | |
60.59 | even | 2 | 180.7.f.g.19.30 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.7 | ✓ | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.8 | yes | 36 | 1.1 | even | 1 | trivial | |
60.7.f.a.19.29 | yes | 36 | 5.4 | even | 2 | inner | |
60.7.f.a.19.30 | yes | 36 | 4.3 | odd | 2 | inner | |
180.7.f.g.19.7 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.8 | 36 | 15.14 | odd | 2 | |||
180.7.f.g.19.29 | 36 | 3.2 | odd | 2 | |||
180.7.f.g.19.30 | 36 | 60.59 | even | 2 |