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 | 31.15 | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.7.c.a.31.16 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.43879 | − | 7.22321i | 0.429849 | − | 0.902901i | ||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | −40.3494 | − | 49.6782i | −0.630460 | − | 0.776222i | ||||
\(5\) | 55.9017 | 0.447214 | ||||||||
\(6\) | 112.599 | + | 53.6055i | 0.521290 | + | 0.248173i | ||||
\(7\) | 472.024i | 1.37616i | 0.725634 | + | 0.688081i | \(0.241547\pi\) | ||||
−0.725634 | + | 0.688081i | \(0.758453\pi\) | |||||||
\(8\) | −497.589 | + | 120.619i | −0.971854 | + | 0.235585i | ||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | 192.234 | − | 403.790i | 0.192234 | − | 0.403790i | ||||
\(11\) | 939.392i | 0.705779i | 0.935665 | + | 0.352890i | \(0.114801\pi\) | ||||
−0.935665 | + | 0.352890i | \(0.885199\pi\) | |||||||
\(12\) | 774.407 | − | 628.985i | 0.448152 | − | 0.363996i | ||||
\(13\) | 22.5854 | 0.0102801 | 0.00514005 | − | 0.999987i | \(-0.498364\pi\) | ||||
0.00514005 | + | 0.999987i | \(0.498364\pi\) | |||||||
\(14\) | 3409.52 | + | 1623.19i | 1.24254 | + | 0.591542i | ||||
\(15\) | 871.421i | 0.258199i | ||||||||
\(16\) | −839.847 | + | 4008.97i | −0.205041 | + | 0.978753i | ||||
\(17\) | 6247.86 | 1.27170 | 0.635850 | − | 0.771813i | \(-0.280650\pi\) | ||||
0.635850 | + | 0.771813i | \(0.280650\pi\) | |||||||
\(18\) | −835.626 | + | 1755.24i | −0.143283 | + | 0.300967i | ||||
\(19\) | 11163.0i | 1.62750i | 0.581219 | + | 0.813748i | \(0.302576\pi\) | ||||
−0.581219 | + | 0.813748i | \(0.697424\pi\) | |||||||
\(20\) | −2255.60 | − | 2777.10i | −0.281950 | − | 0.347137i | ||||
\(21\) | −7358.12 | −0.794527 | ||||||||
\(22\) | 6785.42 | + | 3230.37i | 0.637248 | + | 0.303378i | ||||
\(23\) | − | 1168.18i | − | 0.0960125i | −0.998847 | − | 0.0480062i | \(-0.984713\pi\) | ||
0.998847 | − | 0.0480062i | \(-0.0152867\pi\) | |||||||
\(24\) | −1880.27 | − | 7756.65i | −0.136015 | − | 0.561100i | ||||
\(25\) | 3125.00 | 0.200000 | ||||||||
\(26\) | 77.6664 | − | 163.139i | 0.00441889 | − | 0.00928191i | ||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | 23449.3 | − | 19045.9i | 1.06821 | − | 0.867615i | ||||
\(29\) | 25619.9 | 1.05047 | 0.525235 | − | 0.850957i | \(-0.323977\pi\) | ||||
0.525235 | + | 0.850957i | \(0.323977\pi\) | |||||||
\(30\) | 6294.46 | + | 2996.64i | 0.233128 | + | 0.110987i | ||||
\(31\) | 4304.29i | 0.144483i | 0.997387 | + | 0.0722414i | \(0.0230152\pi\) | ||||
−0.997387 | + | 0.0722414i | \(0.976985\pi\) | |||||||
\(32\) | 26069.6 | + | 19852.4i | 0.795581 | + | 0.605848i | ||||
\(33\) | −14643.7 | −0.407482 | ||||||||
\(34\) | 21485.1 | − | 45129.6i | 0.546639 | − | 1.14822i | ||||
\(35\) | 26386.9i | 0.615438i | ||||||||
\(36\) | 9804.91 | + | 12071.8i | 0.210153 | + | 0.258741i | ||||
\(37\) | −50696.3 | −1.00086 | −0.500428 | − | 0.865778i | \(-0.666824\pi\) | ||||
−0.500428 | + | 0.865778i | \(0.666824\pi\) | |||||||
\(38\) | 80632.6 | + | 38387.2i | 1.46947 | + | 0.699577i | ||||
\(39\) | 352.071i | 0.00593522i | ||||||||
\(40\) | −27816.1 | + | 6742.82i | −0.434626 | + | 0.105357i | ||||
\(41\) | −113093. | −1.64090 | −0.820452 | − | 0.571715i | \(-0.806278\pi\) | ||||
−0.820452 | + | 0.571715i | \(0.806278\pi\) | |||||||
\(42\) | −25303.0 | + | 53149.2i | −0.341527 | + | 0.717380i | ||||
\(43\) | − | 113727.i | − | 1.43040i | −0.698920 | − | 0.715200i | \(-0.746336\pi\) | ||
0.698920 | − | 0.715200i | \(-0.253664\pi\) | |||||||
\(44\) | 46667.3 | − | 37903.9i | 0.547841 | − | 0.444965i | ||||
\(45\) | −13584.1 | −0.149071 | ||||||||
\(46\) | −8438.03 | − | 4017.14i | −0.0866898 | − | 0.0412709i | ||||
\(47\) | 184245.i | 1.77460i | 0.461190 | + | 0.887301i | \(0.347422\pi\) | ||||
−0.461190 | + | 0.887301i | \(0.652578\pi\) | |||||||
\(48\) | −62493.7 | − | 13091.9i | −0.565084 | − | 0.118380i | ||||
\(49\) | −105157. | −0.893822 | ||||||||
\(50\) | 10746.2 | − | 22572.5i | 0.0859698 | − | 0.180580i | ||||
\(51\) | 97394.5i | 0.734216i | ||||||||
\(52\) | −911.307 | − | 1122.00i | −0.00648119 | − | 0.00797964i | ||||
\(53\) | −133403. | −0.896063 | −0.448032 | − | 0.894018i | \(-0.647875\pi\) | ||||
−0.448032 | + | 0.894018i | \(0.647875\pi\) | |||||||
\(54\) | −27361.5 | − | 13026.1i | −0.173763 | − | 0.0827245i | ||||
\(55\) | 52513.6i | 0.315634i | ||||||||
\(56\) | −56935.1 | − | 234874.i | −0.324202 | − | 1.33743i | ||||
\(57\) | −174014. | −0.939635 | ||||||||
\(58\) | 88101.5 | − | 185058.i | 0.451543 | − | 0.948470i | ||||
\(59\) | − | 55214.8i | − | 0.268844i | −0.990924 | − | 0.134422i | \(-0.957082\pi\) | ||
0.990924 | − | 0.134422i | \(-0.0429177\pi\) | |||||||
\(60\) | 43290.6 | − | 35161.3i | 0.200420 | − | 0.162784i | ||||
\(61\) | 204814. | 0.902341 | 0.451170 | − | 0.892438i | \(-0.351007\pi\) | ||||
0.451170 | + | 0.892438i | \(0.351007\pi\) | |||||||
\(62\) | 31090.8 | + | 14801.5i | 0.130454 | + | 0.0621058i | ||||
\(63\) | − | 114702.i | − | 0.458721i | ||||||
\(64\) | 233046. | − | 120038.i | 0.889000 | − | 0.457907i | ||||
\(65\) | 1262.56 | 0.00459740 | ||||||||
\(66\) | −50356.5 | + | 105774.i | −0.175156 | + | 0.367916i | ||||
\(67\) | − | 244236.i | − | 0.812056i | −0.913861 | − | 0.406028i | \(-0.866914\pi\) | ||
0.913861 | − | 0.406028i | \(-0.133086\pi\) | |||||||
\(68\) | −252098. | − | 310383.i | −0.801756 | − | 0.987121i | ||||
\(69\) | 18210.2 | 0.0554328 | ||||||||
\(70\) | 190598. | + | 90739.1i | 0.555680 | + | 0.264546i | ||||
\(71\) | − | 14227.6i | − | 0.0397518i | −0.999802 | − | 0.0198759i | \(-0.993673\pi\) | ||
0.999802 | − | 0.0198759i | \(-0.00632711\pi\) | |||||||
\(72\) | 120914. | − | 29310.5i | 0.323951 | − | 0.0785282i | ||||
\(73\) | −278492. | −0.715885 | −0.357943 | − | 0.933744i | \(-0.616522\pi\) | ||||
−0.357943 | + | 0.933744i | \(0.616522\pi\) | |||||||
\(74\) | −174334. | + | 366190.i | −0.430216 | + | 0.903673i | ||||
\(75\) | 48713.9i | 0.115470i | ||||||||
\(76\) | 554557. | − | 450420.i | 1.26330 | − | 1.02607i | ||||
\(77\) | −443415. | −0.971266 | ||||||||
\(78\) | 2543.08 | + | 1210.70i | 0.00535891 | + | 0.00255125i | ||||
\(79\) | − | 358976.i | − | 0.728088i | −0.931382 | − | 0.364044i | \(-0.881396\pi\) | ||
0.931382 | − | 0.364044i | \(-0.118604\pi\) | |||||||
\(80\) | −46948.9 | + | 224108.i | −0.0916971 | + | 0.437712i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −388902. | + | 816892.i | −0.705341 | + | 1.48157i | ||||
\(83\) | 820615.i | 1.43518i | 0.696468 | + | 0.717588i | \(0.254754\pi\) | ||||
−0.696468 | + | 0.717588i | \(0.745246\pi\) | |||||||
\(84\) | 296896. | + | 365538.i | 0.500918 | + | 0.616730i | ||||
\(85\) | 349266. | 0.568722 | ||||||||
\(86\) | −821472. | − | 391083.i | −1.29151 | − | 0.614856i | ||||
\(87\) | 399375.i | 0.606489i | ||||||||
\(88\) | −113309. | − | 467431.i | −0.166271 | − | 0.685914i | ||||
\(89\) | 1.00519e6 | 1.42587 | 0.712935 | − | 0.701230i | \(-0.247365\pi\) | ||||
0.712935 | + | 0.701230i | \(0.247365\pi\) | |||||||
\(90\) | −46712.9 | + | 98120.9i | −0.0640781 | + | 0.134597i | ||||
\(91\) | 10660.8i | 0.0141471i | ||||||||
\(92\) | −58033.3 | + | 47135.6i | −0.0745270 | + | 0.0605320i | ||||
\(93\) | −67097.2 | −0.0834172 | ||||||||
\(94\) | 1.33084e6 | + | 633579.i | 1.60229 | + | 0.762811i | ||||
\(95\) | 624030.i | 0.727838i | ||||||||
\(96\) | −309469. | + | 406385.i | −0.349786 | + | 0.459329i | ||||
\(97\) | 1.44195e6 | 1.57992 | 0.789962 | − | 0.613156i | \(-0.210100\pi\) | ||||
0.789962 | + | 0.613156i | \(0.210100\pi\) | |||||||
\(98\) | −361614. | + | 759572.i | −0.384208 | + | 0.807032i | ||||
\(99\) | − | 228272.i | − | 0.235260i | ||||||
\(100\) | −126092. | − | 155244.i | −0.126092 | − | 0.155244i | ||||
\(101\) | 778264. | 0.755375 | 0.377688 | − | 0.925933i | \(-0.376719\pi\) | ||||
0.377688 | + | 0.925933i | \(0.376719\pi\) | |||||||
\(102\) | 703501. | + | 334919.i | 0.662925 | + | 0.315602i | ||||
\(103\) | − | 1.15772e6i | − | 1.05948i | −0.848161 | − | 0.529739i | \(-0.822290\pi\) | ||
0.848161 | − | 0.529739i | \(-0.177710\pi\) | |||||||
\(104\) | −11238.2 | + | 2724.23i | −0.00999076 | + | 0.00242183i | ||||
\(105\) | −411331. | −0.355323 | ||||||||
\(106\) | −458746. | + | 963599.i | −0.385172 | + | 0.809056i | ||||
\(107\) | − | 1.02649e6i | − | 0.837925i | −0.908004 | − | 0.418962i | \(-0.862394\pi\) | ||
0.908004 | − | 0.418962i | \(-0.137606\pi\) | |||||||
\(108\) | −188181. | + | 152843.i | −0.149384 | + | 0.121332i | ||||
\(109\) | 769438. | 0.594147 | 0.297074 | − | 0.954855i | \(-0.403989\pi\) | ||||
0.297074 | + | 0.954855i | \(0.403989\pi\) | |||||||
\(110\) | 379317. | + | 180583.i | 0.284986 | + | 0.135675i | ||||
\(111\) | − | 790277.i | − | 0.577844i | ||||||
\(112\) | −1.89233e6 | − | 396428.i | −1.34692 | − | 0.282169i | ||||
\(113\) | −337398. | −0.233834 | −0.116917 | − | 0.993142i | \(-0.537301\pi\) | ||||
−0.116917 | + | 0.993142i | \(0.537301\pi\) | |||||||
\(114\) | −598397. | + | 1.25694e6i | −0.403901 | + | 0.848397i | ||||
\(115\) | − | 65303.5i | − | 0.0429381i | ||||||
\(116\) | −1.03375e6 | − | 1.27275e6i | −0.662279 | − | 0.815398i | ||||
\(117\) | −5488.25 | −0.00342670 | ||||||||
\(118\) | −398828. | − | 189872.i | −0.242739 | − | 0.115562i | ||||
\(119\) | 2.94914e6i | 1.75007i | ||||||||
\(120\) | −105110. | − | 433610.i | −0.0608277 | − | 0.250932i | ||||
\(121\) | 889104. | 0.501876 | ||||||||
\(122\) | 704313. | − | 1.47942e6i | 0.387870 | − | 0.814724i | ||||
\(123\) | − | 1.76294e6i | − | 0.947376i | ||||||
\(124\) | 213829. | − | 173676.i | 0.112151 | − | 0.0910906i | ||||
\(125\) | 174693. | 0.0894427 | ||||||||
\(126\) | −828514. | − | 394435.i | −0.414179 | − | 0.197181i | ||||
\(127\) | − | 3.10443e6i | − | 1.51555i | −0.652515 | − | 0.757776i | \(-0.726286\pi\) | ||
0.652515 | − | 0.757776i | \(-0.273714\pi\) | |||||||
\(128\) | −65660.6 | − | 2.09612e6i | −0.0313094 | − | 0.999510i | ||||
\(129\) | 1.77283e6 | 0.825842 | ||||||||
\(130\) | 4341.68 | − | 9119.74i | 0.00197619 | − | 0.00415100i | ||||
\(131\) | 70316.0i | 0.0312781i | 0.999878 | + | 0.0156390i | \(0.00497826\pi\) | ||||
−0.999878 | + | 0.0156390i | \(0.995022\pi\) | |||||||
\(132\) | 590864. | + | 727471.i | 0.256901 | + | 0.316296i | ||||
\(133\) | −5.26919e6 | −2.23970 | ||||||||
\(134\) | −1.76417e6 | − | 839878.i | −0.733206 | − | 0.349061i | ||||
\(135\) | − | 211755.i | − | 0.0860663i | ||||||
\(136\) | −3.10887e6 | + | 753613.i | −1.23591 | + | 0.299593i | ||||
\(137\) | 3.75318e6 | 1.45961 | 0.729807 | − | 0.683654i | \(-0.239610\pi\) | ||||
0.729807 | + | 0.683654i | \(0.239610\pi\) | |||||||
\(138\) | 62621.0 | − | 131536.i | 0.0238277 | − | 0.0500504i | ||||
\(139\) | 4.22525e6i | 1.57329i | 0.617406 | + | 0.786645i | \(0.288184\pi\) | ||||
−0.617406 | + | 0.786645i | \(0.711816\pi\) | |||||||
\(140\) | 1.31085e6 | − | 1.06470e6i | 0.477717 | − | 0.388009i | ||||
\(141\) | −2.87209e6 | −1.02457 | ||||||||
\(142\) | −102769. | − | 48925.7i | −0.0358919 | − | 0.0170873i | ||||
\(143\) | 21216.5i | 0.00725548i | ||||||||
\(144\) | 204083. | − | 974181.i | 0.0683470 | − | 0.326251i | ||||
\(145\) | 1.43220e6 | 0.469784 | ||||||||
\(146\) | −957674. | + | 2.01160e6i | −0.307722 | + | 0.646373i | ||||
\(147\) | − | 1.63924e6i | − | 0.516048i | ||||||
\(148\) | 2.04557e6 | + | 2.51850e6i | 0.630999 | + | 0.776886i | ||||
\(149\) | 3.77574e6 | 1.14141 | 0.570707 | − | 0.821154i | \(-0.306669\pi\) | ||||
0.570707 | + | 0.821154i | \(0.306669\pi\) | |||||||
\(150\) | 351871. | + | 167517.i | 0.104258 | + | 0.0496347i | ||||
\(151\) | − | 3.33342e6i | − | 0.968186i | −0.875017 | − | 0.484093i | \(-0.839150\pi\) | ||
0.875017 | − | 0.484093i | \(-0.160850\pi\) | |||||||
\(152\) | −1.34647e6 | − | 5.55458e6i | −0.383413 | − | 1.58169i | ||||
\(153\) | −1.51823e6 | −0.423900 | ||||||||
\(154\) | −1.52481e6 | + | 3.20288e6i | −0.417498 | + | 0.876957i | ||||
\(155\) | 240617.i | 0.0646147i | ||||||||
\(156\) | 17490.3 | − | 14205.9i | 0.00460705 | − | 0.00374192i | ||||
\(157\) | −7.25721e6 | −1.87530 | −0.937650 | − | 0.347580i | \(-0.887003\pi\) | ||||
−0.937650 | + | 0.347580i | \(0.887003\pi\) | |||||||
\(158\) | −2.59296e6 | − | 1.23444e6i | −0.657392 | − | 0.312968i | ||||
\(159\) | − | 2.07955e6i | − | 0.517342i | ||||||
\(160\) | 1.45733e6 | + | 1.10978e6i | 0.355794 | + | 0.270943i | ||||
\(161\) | 551410. | 0.132129 | ||||||||
\(162\) | 203057. | − | 426523.i | 0.0477610 | − | 0.100322i | ||||
\(163\) | 2.00685e6i | 0.463396i | 0.972788 | + | 0.231698i | \(0.0744281\pi\) | ||||
−0.972788 | + | 0.231698i | \(0.925572\pi\) | |||||||
\(164\) | 4.56323e6 | + | 5.61824e6i | 1.03452 | + | 1.27371i | ||||
\(165\) | −818606. | −0.182231 | ||||||||
\(166\) | 5.92747e6 | + | 2.82192e6i | 1.29582 | + | 0.616909i | ||||
\(167\) | 3.95037e6i | 0.848182i | 0.905620 | + | 0.424091i | \(0.139406\pi\) | ||||
−0.905620 | + | 0.424091i | \(0.860594\pi\) | |||||||
\(168\) | 3.66132e6 | − | 887531.i | 0.772165 | − | 0.187178i | ||||
\(169\) | −4.82630e6 | −0.999894 | ||||||||
\(170\) | 1.20105e6 | − | 2.52282e6i | 0.244464 | − | 0.513499i | ||||
\(171\) | − | 2.71261e6i | − | 0.542498i | ||||||
\(172\) | −5.64974e6 | + | 4.58881e6i | −1.11031 | + | 0.901810i | ||||
\(173\) | −4.23383e6 | −0.817703 | −0.408851 | − | 0.912601i | \(-0.634071\pi\) | ||||
−0.408851 | + | 0.912601i | \(0.634071\pi\) | |||||||
\(174\) | 2.88477e6 | + | 1.37337e6i | 0.547599 | + | 0.260699i | ||||
\(175\) | 1.47507e6i | 0.275232i | ||||||||
\(176\) | −3.76600e6 | − | 788946.i | −0.690784 | − | 0.144714i | ||||
\(177\) | 860714. | 0.155217 | ||||||||
\(178\) | 3.45665e6 | − | 7.26072e6i | 0.612909 | − | 1.28742i | ||||
\(179\) | 5.09011e6i | 0.887499i | 0.896151 | + | 0.443750i | \(0.146352\pi\) | ||||
−0.896151 | + | 0.443750i | \(0.853648\pi\) | |||||||
\(180\) | 548111. | + | 674834.i | 0.0939834 | + | 0.115712i | ||||
\(181\) | 7.69100e6 | 1.29702 | 0.648510 | − | 0.761206i | \(-0.275392\pi\) | ||||
0.648510 | + | 0.761206i | \(0.275392\pi\) | |||||||
\(182\) | 77005.4 | + | 36660.4i | 0.0127734 | + | 0.00608111i | ||||
\(183\) | 3.19274e6i | 0.520967i | ||||||||
\(184\) | 140906. | + | 581276.i | 0.0226191 | + | 0.0933101i | ||||
\(185\) | −2.83401e6 | −0.447596 | ||||||||
\(186\) | −230733. | + | 484657.i | −0.0358568 | + | 0.0753174i | ||||
\(187\) | 5.86919e6i | 0.897539i | ||||||||
\(188\) | 9.15294e6 | − | 7.43416e6i | 1.37749 | − | 1.11882i | ||||
\(189\) | 1.78802e6 | 0.264842 | ||||||||
\(190\) | 4.50750e6 | + | 2.14591e6i | 0.657165 | + | 0.312860i | ||||
\(191\) | − | 472014.i | − | 0.0677415i | −0.999426 | − | 0.0338708i | \(-0.989217\pi\) | ||
0.999426 | − | 0.0338708i | \(-0.0107835\pi\) | |||||||
\(192\) | 1.87120e6 | + | 3.63283e6i | 0.264373 | + | 0.513264i | ||||
\(193\) | −5.76885e6 | −0.802449 | −0.401225 | − | 0.915980i | \(-0.631415\pi\) | ||||
−0.401225 | + | 0.915980i | \(0.631415\pi\) | |||||||
\(194\) | 4.95858e6 | − | 1.04155e7i | 0.679129 | − | 1.42651i | ||||
\(195\) | 19681.4i | 0.00265431i | ||||||||
\(196\) | 4.24303e6 | + | 5.22402e6i | 0.563519 | + | 0.693804i | ||||
\(197\) | 1.01304e7 | 1.32504 | 0.662521 | − | 0.749043i | \(-0.269486\pi\) | ||||
0.662521 | + | 0.749043i | \(0.269486\pi\) | |||||||
\(198\) | −1.64886e6 | − | 784981.i | −0.212416 | − | 0.101126i | ||||
\(199\) | − | 8.69529e6i | − | 1.10338i | −0.834050 | − | 0.551690i | \(-0.813983\pi\) | ||
0.834050 | − | 0.551690i | \(-0.186017\pi\) | |||||||
\(200\) | −1.55497e6 | + | 376935.i | −0.194371 | + | 0.0471169i | ||||
\(201\) | 3.80727e6 | 0.468841 | ||||||||
\(202\) | 2.67629e6 | − | 5.62156e6i | 0.324697 | − | 0.682029i | ||||
\(203\) | 1.20932e7i | 1.44562i | ||||||||
\(204\) | 4.83839e6 | − | 3.92981e6i | 0.569915 | − | 0.462894i | ||||
\(205\) | −6.32208e6 | −0.733835 | ||||||||
\(206\) | −8.36246e6 | − | 3.98116e6i | −0.956604 | − | 0.455416i | ||||
\(207\) | 283869.i | 0.0320042i | ||||||||
\(208\) | −18968.3 | + | 90544.2i | −0.00210784 | + | 0.0100617i | ||||
\(209\) | −1.04864e7 | −1.14865 | ||||||||
\(210\) | −1.41448e6 | + | 2.97113e6i | −0.152735 | + | 0.320822i | ||||
\(211\) | 2.10959e6i | 0.224570i | 0.993676 | + | 0.112285i | \(0.0358169\pi\) | ||||
−0.993676 | + | 0.112285i | \(0.964183\pi\) | |||||||
\(212\) | 5.38274e6 | + | 6.62723e6i | 0.564932 | + | 0.695544i | ||||
\(213\) | 221786. | 0.0229507 | ||||||||
\(214\) | −7.41458e6 | − | 3.52990e6i | −0.756563 | − | 0.360181i | ||||
\(215\) | − | 6.35752e6i | − | 0.639694i | ||||||
\(216\) | 456905. | + | 1.88487e6i | 0.0453383 | + | 0.187033i | ||||
\(217\) | −2.03172e6 | −0.198832 | ||||||||
\(218\) | 2.64594e6 | − | 5.55781e6i | 0.255394 | − | 0.536456i | ||||
\(219\) | − | 4.34125e6i | − | 0.413317i | ||||||
\(220\) | 2.60878e6 | − | 2.11889e6i | 0.245002 | − | 0.198995i | ||||
\(221\) | 141110. | 0.0130732 | ||||||||
\(222\) | −5.70834e6 | − | 2.71760e6i | −0.521736 | − | 0.248386i | ||||
\(223\) | 5.11069e6i | 0.460855i | 0.973089 | + | 0.230428i | \(0.0740125\pi\) | ||||
−0.973089 | + | 0.230428i | \(0.925987\pi\) | |||||||
\(224\) | −9.37081e6 | + | 1.23055e7i | −0.833744 | + | 1.09485i | ||||
\(225\) | −759375. | −0.0666667 | ||||||||
\(226\) | −1.16024e6 | + | 2.43709e6i | −0.100513 | + | 0.211129i | ||||
\(227\) | − | 2.13819e6i | − | 0.182797i | −0.995814 | − | 0.0913983i | \(-0.970866\pi\) | ||
0.995814 | − | 0.0913983i | \(-0.0291336\pi\) | |||||||
\(228\) | 7.02136e6 | + | 8.64469e6i | 0.592402 | + | 0.729365i | ||||
\(229\) | 1.43797e7 | 1.19741 | 0.598706 | − | 0.800969i | \(-0.295682\pi\) | ||||
0.598706 | + | 0.800969i | \(0.295682\pi\) | |||||||
\(230\) | −471700. | − | 224565.i | −0.0387688 | − | 0.0184569i | ||||
\(231\) | − | 6.91216e6i | − | 0.560761i | ||||||
\(232\) | −1.27482e7 | + | 3.09025e6i | −1.02090 | + | 0.247474i | ||||
\(233\) | −2.16907e7 | −1.71477 | −0.857385 | − | 0.514676i | \(-0.827912\pi\) | ||||
−0.857385 | + | 0.514676i | \(0.827912\pi\) | |||||||
\(234\) | −18872.9 | + | 39642.7i | −0.00147296 | + | 0.00309397i | ||||
\(235\) | 1.02996e7i | 0.793626i | ||||||||
\(236\) | −2.74297e6 | + | 2.22789e6i | −0.208682 | + | 0.169495i | ||||
\(237\) | 5.59588e6 | 0.420362 | ||||||||
\(238\) | 2.13022e7 | + | 1.01415e7i | 1.58014 | + | 0.752264i | ||||
\(239\) | − | 4.39731e6i | − | 0.322102i | −0.986946 | − | 0.161051i | \(-0.948512\pi\) | ||
0.986946 | − | 0.161051i | \(-0.0514883\pi\) | |||||||
\(240\) | −3.49351e6 | − | 731861.i | −0.252713 | − | 0.0529413i | ||||
\(241\) | 1.72165e7 | 1.22997 | 0.614985 | − | 0.788539i | \(-0.289162\pi\) | ||||
0.614985 | + | 0.788539i | \(0.289162\pi\) | |||||||
\(242\) | 3.05744e6 | − | 6.42218e6i | 0.215731 | − | 0.453144i | ||||
\(243\) | 920483.i | 0.0641500i | ||||||||
\(244\) | −8.26414e6 | − | 1.01748e7i | −0.568890 | − | 0.700417i | ||||
\(245\) | −5.87847e6 | −0.399729 | ||||||||
\(246\) | −1.27341e7 | − | 6.06239e6i | −0.855387 | − | 0.407229i | ||||
\(247\) | 252120.i | 0.0167308i | ||||||||
\(248\) | −519180. | − | 2.14177e6i | −0.0340379 | − | 0.140416i | ||||
\(249\) | −1.27921e7 | −0.828600 | ||||||||
\(250\) | 600732. | − | 1.26184e6i | 0.0384469 | − | 0.0807579i | ||||
\(251\) | − | 4.94767e6i | − | 0.312881i | −0.987687 | − | 0.156441i | \(-0.949998\pi\) | ||
0.987687 | − | 0.156441i | \(-0.0500020\pi\) | |||||||
\(252\) | −5.69818e6 | + | 4.62815e6i | −0.356069 | + | 0.289205i | ||||
\(253\) | 1.09738e6 | 0.0677636 | ||||||||
\(254\) | −2.24239e7 | − | 1.06755e7i | −1.36839 | − | 0.651458i | ||||
\(255\) | 5.44452e6i | 0.328352i | ||||||||
\(256\) | −1.53665e7 | − | 6.73385e6i | −0.915916 | − | 0.401369i | ||||
\(257\) | 2.51861e7 | 1.48375 | 0.741876 | − | 0.670537i | \(-0.233936\pi\) | ||||
0.741876 | + | 0.670537i | \(0.233936\pi\) | |||||||
\(258\) | 6.09638e6 | − | 1.28055e7i | 0.354987 | − | 0.745653i | ||||
\(259\) | − | 2.39299e7i | − | 1.37734i | ||||||
\(260\) | −50943.6 | − | 62721.8i | −0.00289848 | − | 0.00356860i | ||||
\(261\) | −6.22564e6 | −0.350157 | ||||||||
\(262\) | 507907. | + | 241802.i | 0.0282410 | + | 0.0134448i | ||||
\(263\) | − | 4.00969e6i | − | 0.220416i | −0.993909 | − | 0.110208i | \(-0.964848\pi\) | ||
0.993909 | − | 0.110208i | \(-0.0351518\pi\) | |||||||
\(264\) | 7.28653e6 | − | 1.76631e6i | 0.396013 | − | 0.0959964i | ||||
\(265\) | −7.45747e6 | −0.400732 | ||||||||
\(266\) | −1.81197e7 | + | 3.80605e7i | −0.962731 | + | 2.02222i | ||||
\(267\) | 1.56694e7i | 0.823226i | ||||||||
\(268\) | −1.21332e7 | + | 9.85480e6i | −0.630336 | + | 0.511969i | ||||
\(269\) | 777261. | 0.0399310 | 0.0199655 | − | 0.999801i | \(-0.493644\pi\) | ||||
0.0199655 | + | 0.999801i | \(0.493644\pi\) | |||||||
\(270\) | −1.52955e6 | − | 728183.i | −0.0777093 | − | 0.0369955i | ||||
\(271\) | − | 3.29929e7i | − | 1.65773i | −0.559450 | − | 0.828864i | \(-0.688988\pi\) | ||
0.559450 | − | 0.828864i | \(-0.311012\pi\) | |||||||
\(272\) | −5.24725e6 | + | 2.50475e7i | −0.260750 | + | 1.24468i | ||||
\(273\) | −166186. | −0.00816782 | ||||||||
\(274\) | 1.29064e7 | − | 2.71100e7i | 0.627413 | − | 1.31789i | ||||
\(275\) | 2.93560e6i | 0.141156i | ||||||||
\(276\) | −734771. | − | 904649.i | −0.0349482 | − | 0.0430282i | ||||
\(277\) | −2.00830e7 | −0.944906 | −0.472453 | − | 0.881356i | \(-0.656631\pi\) | ||||
−0.472453 | + | 0.881356i | \(0.656631\pi\) | |||||||
\(278\) | 3.05199e7 | + | 1.45298e7i | 1.42052 | + | 0.676277i | ||||
\(279\) | − | 1.04594e6i | − | 0.0481609i | ||||||
\(280\) | −3.18277e6 | − | 1.31298e7i | −0.144988 | − | 0.598116i | ||||
\(281\) | 3.59969e7 | 1.62235 | 0.811177 | − | 0.584800i | \(-0.198827\pi\) | ||||
0.811177 | + | 0.584800i | \(0.198827\pi\) | |||||||
\(282\) | −9.87651e6 | + | 2.07457e7i | −0.440409 | + | 0.925082i | ||||
\(283\) | − | 8.24433e6i | − | 0.363744i | −0.983322 | − | 0.181872i | \(-0.941784\pi\) | ||
0.983322 | − | 0.181872i | \(-0.0582157\pi\) | |||||||
\(284\) | −706801. | + | 574075.i | −0.0308562 | + | 0.0250619i | ||||
\(285\) | −9.72767e6 | −0.420217 | ||||||||
\(286\) | 153251. | + | 72959.2i | 0.00655098 | + | 0.00311876i | ||||
\(287\) | − | 5.33824e7i | − | 2.25815i | ||||||
\(288\) | −6.33491e6 | − | 4.82414e6i | −0.265194 | − | 0.201949i | ||||
\(289\) | 1.48982e7 | 0.617221 | ||||||||
\(290\) | 4.92502e6 | − | 1.03451e7i | 0.201936 | − | 0.424169i | ||||
\(291\) | 2.24778e7i | 0.912169i | ||||||||
\(292\) | 1.12370e7 | + | 1.38350e7i | 0.451337 | + | 0.555686i | ||||
\(293\) | 1.01669e7 | 0.404191 | 0.202096 | − | 0.979366i | \(-0.435225\pi\) | ||||
0.202096 | + | 0.979366i | \(0.435225\pi\) | |||||||
\(294\) | −1.18406e7 | − | 5.63700e6i | −0.465940 | − | 0.221823i | ||||
\(295\) | − | 3.08660e6i | − | 0.120230i | ||||||
\(296\) | 2.52259e7 | − | 6.11495e6i | 0.972685 | − | 0.235786i | ||||
\(297\) | 3.55841e6 | 0.135827 | ||||||||
\(298\) | 1.29840e7 | − | 2.72729e7i | 0.490635 | − | 1.03058i | ||||
\(299\) | − | 26383.9i | − | 0.000987018i | ||||||
\(300\) | 2.42002e6 | − | 1.96558e6i | 0.0896304 | − | 0.0727992i | ||||
\(301\) | 5.36817e7 | 1.96846 | ||||||||
\(302\) | −2.40780e7 | − | 1.14629e7i | −0.874176 | − | 0.416174i | ||||
\(303\) | 1.21319e7i | 0.436116i | ||||||||
\(304\) | −4.47521e7 | − | 9.37521e6i | −1.59292 | − | 0.333703i | ||||
\(305\) | 1.14495e7 | 0.403539 | ||||||||
\(306\) | −5.22088e6 | + | 1.09665e7i | −0.182213 | + | 0.382740i | ||||
\(307\) | 1.30424e7i | 0.450756i | 0.974271 | + | 0.225378i | \(0.0723617\pi\) | ||||
−0.974271 | + | 0.225378i | \(0.927638\pi\) | |||||||
\(308\) | 1.78915e7 | + | 2.20281e7i | 0.612344 | + | 0.753918i | ||||
\(309\) | 1.80471e7 | 0.611690 | ||||||||
\(310\) | 1.73803e6 | + | 827432.i | 0.0583406 | + | 0.0277745i | ||||
\(311\) | 1.78289e7i | 0.592712i | 0.955077 | + | 0.296356i | \(0.0957716\pi\) | ||||
−0.955077 | + | 0.296356i | \(0.904228\pi\) | |||||||
\(312\) | −42466.6 | − | 175187.i | −0.00139825 | − | 0.00576817i | ||||
\(313\) | 992789. | 0.0323761 | 0.0161880 | − | 0.999869i | \(-0.494847\pi\) | ||||
0.0161880 | + | 0.999869i | \(0.494847\pi\) | |||||||
\(314\) | −2.49560e7 | + | 5.24203e7i | −0.806096 | + | 1.69321i | ||||
\(315\) | − | 6.41202e6i | − | 0.205146i | ||||||
\(316\) | −1.78333e7 | + | 1.44845e7i | −0.565158 | + | 0.459030i | ||||
\(317\) | −4.91937e6 | −0.154430 | −0.0772150 | − | 0.997014i | \(-0.524603\pi\) | ||||
−0.0772150 | + | 0.997014i | \(0.524603\pi\) | |||||||
\(318\) | −1.50210e7 | − | 7.15114e6i | −0.467109 | − | 0.222379i | ||||
\(319\) | 2.40671e7i | 0.741400i | ||||||||
\(320\) | 1.30277e7 | − | 6.71031e6i | 0.397573 | − | 0.204782i | ||||
\(321\) | 1.60015e7 | 0.483776 | ||||||||
\(322\) | 1.89619e6 | − | 3.98295e6i | 0.0567954 | − | 0.119299i | ||||
\(323\) | 6.97448e7i | 2.06969i | ||||||||
\(324\) | −2.38259e6 | − | 2.93345e6i | −0.0700511 | − | 0.0862469i | ||||
\(325\) | 70579.3 | 0.00205602 | ||||||||
\(326\) | 1.44959e7 | + | 6.90114e6i | 0.418400 | + | 0.199190i | ||||
\(327\) | 1.19944e7i | 0.343031i | ||||||||
\(328\) | 5.62737e7 | − | 1.36412e7i | 1.59472 | − | 0.386572i | ||||
\(329\) | −8.69678e7 | −2.44214 | ||||||||
\(330\) | −2.81502e6 | + | 5.91296e6i | −0.0783320 | + | 0.164537i | ||||
\(331\) | 5.36048e7i | 1.47815i | 0.673620 | + | 0.739077i | \(0.264738\pi\) | ||||
−0.673620 | + | 0.739077i | \(0.735262\pi\) | |||||||
\(332\) | 4.07667e7 | − | 3.31114e7i | 1.11402 | − | 0.904821i | ||||
\(333\) | 1.23192e7 | 0.333618 | ||||||||
\(334\) | 2.85344e7 | + | 1.35845e7i | 0.765824 | + | 0.364590i | ||||
\(335\) | − | 1.36532e7i | − | 0.363162i | ||||||
\(336\) | 6.17970e6 | − | 2.94985e7i | 0.162911 | − | 0.777646i | ||||
\(337\) | 6.45496e7 | 1.68657 | 0.843284 | − | 0.537468i | \(-0.180619\pi\) | ||||
0.843284 | + | 0.537468i | \(0.180619\pi\) | |||||||
\(338\) | −1.65966e7 | + | 3.48614e7i | −0.429803 | + | 0.902805i | ||||
\(339\) | − | 5.25951e6i | − | 0.135004i | ||||||
\(340\) | −1.40927e7 | − | 1.73509e7i | −0.358556 | − | 0.441454i | ||||
\(341\) | −4.04341e6 | −0.101973 | ||||||||
\(342\) | −1.95937e7 | − | 9.32809e6i | −0.489822 | − | 0.233192i | ||||
\(343\) | 5.89641e6i | 0.146119i | ||||||||
\(344\) | 1.37176e7 | + | 5.65892e7i | 0.336980 | + | 1.39014i | ||||
\(345\) | 1.01798e6 | 0.0247903 | ||||||||
\(346\) | −1.45593e7 | + | 3.05819e7i | −0.351489 | + | 0.738305i | ||||
\(347\) | − | 4.82937e7i | − | 1.15585i | −0.816089 | − | 0.577926i | \(-0.803862\pi\) | ||
0.816089 | − | 0.577926i | \(-0.196138\pi\) | |||||||
\(348\) | 1.98402e7 | − | 1.61145e7i | 0.470770 | − | 0.382367i | ||||
\(349\) | −3.08221e7 | −0.725081 | −0.362541 | − | 0.931968i | \(-0.618091\pi\) | ||||
−0.362541 | + | 0.931968i | \(0.618091\pi\) | |||||||
\(350\) | 1.06548e7 | + | 5.07247e6i | 0.248508 | + | 0.118308i | ||||
\(351\) | − | 85553.3i | − | 0.00197841i | ||||||
\(352\) | −1.86492e7 | + | 2.44896e7i | −0.427595 | + | 0.561504i | ||||
\(353\) | −6.23969e7 | −1.41853 | −0.709266 | − | 0.704941i | \(-0.750974\pi\) | ||||
−0.709266 | + | 0.704941i | \(0.750974\pi\) | |||||||
\(354\) | 2.95981e6 | − | 6.21711e6i | 0.0667198 | − | 0.140145i | ||||
\(355\) | − | 795347.i | − | 0.0177775i | ||||||
\(356\) | −4.05590e7 | − | 4.99362e7i | −0.898954 | − | 1.10679i | ||||
\(357\) | −4.59725e7 | −1.01040 | ||||||||
\(358\) | 3.67669e7 | + | 1.75038e7i | 0.801324 | + | 0.381491i | ||||
\(359\) | − | 5.26134e7i | − | 1.13714i | −0.822636 | − | 0.568569i | \(-0.807497\pi\) | ||
0.822636 | − | 0.568569i | \(-0.192503\pi\) | |||||||
\(360\) | 6.75931e6 | − | 1.63851e6i | 0.144875 | − | 0.0351189i | ||||
\(361\) | −7.75664e7 | −1.64874 | ||||||||
\(362\) | 2.64477e7 | − | 5.55537e7i | 0.557523 | − | 1.17108i | ||||
\(363\) | 1.38598e7i | 0.289758i | ||||||||
\(364\) | 529611. | − | 430158.i | 0.0109813 | − | 0.00891917i | ||||
\(365\) | −1.55681e7 | −0.320154 | ||||||||
\(366\) | 2.30618e7 | + | 1.09792e7i | 0.470381 | + | 0.223937i | ||||
\(367\) | − | 2.05775e7i | − | 0.416288i | −0.978098 | − | 0.208144i | \(-0.933258\pi\) | ||
0.978098 | − | 0.208144i | \(-0.0667423\pi\) | |||||||
\(368\) | 4.68322e6 | + | 981096.i | 0.0939726 | + | 0.0196865i | ||||
\(369\) | 2.74815e7 | 0.546968 | ||||||||
\(370\) | −9.74557e6 | + | 2.04706e7i | −0.192399 | + | 0.404135i | ||||
\(371\) | − | 6.29695e7i | − | 1.23313i | ||||||
\(372\) | 2.70733e6 | + | 3.33327e6i | 0.0525912 | + | 0.0647502i | ||||
\(373\) | −2.72046e7 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(374\) | 4.23944e7 | + | 2.01829e7i | 0.810389 | + | 0.385806i | ||||
\(375\) | 2.72319e6i | 0.0516398i | ||||||||
\(376\) | −2.22234e7 | − | 9.16781e7i | −0.418069 | − | 1.72465i | ||||
\(377\) | 578635. | 0.0107989 | ||||||||
\(378\) | 6.14864e6 | − | 1.29153e7i | 0.113842 | − | 0.239127i | ||||
\(379\) | 7.15245e7i | 1.31382i | 0.753967 | + | 0.656912i | \(0.228138\pi\) | ||||
−0.753967 | + | 0.656912i | \(0.771862\pi\) | |||||||
\(380\) | 3.10007e7 | − | 2.51793e7i | 0.564964 | − | 0.458873i | ||||
\(381\) | 4.83933e7 | 0.875004 | ||||||||
\(382\) | −3.40946e6 | − | 1.62316e6i | −0.0611639 | − | 0.0291186i | ||||
\(383\) | − | 4.10963e7i | − | 0.731486i | −0.930716 | − | 0.365743i | \(-0.880815\pi\) | ||
0.930716 | − | 0.365743i | \(-0.119185\pi\) | |||||||
\(384\) | 3.26753e7 | − | 1.02355e6i | 0.577067 | − | 0.0180765i | ||||
\(385\) | −2.47877e7 | −0.434363 | ||||||||
\(386\) | −1.98379e7 | + | 4.16696e7i | −0.344932 | + | 0.724532i | ||||
\(387\) | 2.76356e7i | 0.476800i | ||||||||
\(388\) | −5.81820e7 | − | 7.16337e7i | −0.996078 | − | 1.22637i | ||||
\(389\) | −1.73618e7 | −0.294948 | −0.147474 | − | 0.989066i | \(-0.547114\pi\) | ||||
−0.147474 | + | 0.989066i | \(0.547114\pi\) | |||||||
\(390\) | 142163. | + | 67680.2i | 0.00239658 | + | 0.00114095i | ||||
\(391\) | − | 7.29865e6i | − | 0.122099i | ||||||
\(392\) | 5.23251e7 | − | 1.26840e7i | 0.868664 | − | 0.210571i | ||||
\(393\) | −1.09612e6 | −0.0180584 | ||||||||
\(394\) | 3.48365e7 | − | 7.31743e7i | 0.569568 | − | 1.19638i | ||||
\(395\) | − | 2.00674e7i | − | 0.325611i | ||||||
\(396\) | −1.13402e7 | + | 9.21065e6i | −0.182614 | + | 0.148322i | ||||
\(397\) | −1.59499e7 | −0.254909 | −0.127455 | − | 0.991844i | \(-0.540681\pi\) | ||||
−0.127455 | + | 0.991844i | \(0.540681\pi\) | |||||||
\(398\) | −6.28079e7 | − | 2.99013e7i | −0.996242 | − | 0.474286i | ||||
\(399\) | − | 8.21386e7i | − | 1.29309i | ||||||
\(400\) | −2.62452e6 | + | 1.25280e7i | −0.0410082 | + | 0.195751i | ||||
\(401\) | −4.96019e7 | −0.769245 | −0.384623 | − | 0.923074i | \(-0.625668\pi\) | ||||
−0.384623 | + | 0.923074i | \(0.625668\pi\) | |||||||
\(402\) | 1.30924e7 | − | 2.75007e7i | 0.201531 | − | 0.423317i | ||||
\(403\) | 97214.0i | 0.00148530i | ||||||||
\(404\) | −3.14025e7 | − | 3.86628e7i | −0.476234 | − | 0.586339i | ||||
\(405\) | 3.30094e6 | 0.0496904 | ||||||||
\(406\) | 8.73517e7 | + | 4.15860e7i | 1.30525 | + | 0.621397i | ||||
\(407\) | − | 4.76237e7i | − | 0.706383i | ||||||
\(408\) | −1.17477e7 | − | 4.84625e7i | −0.172970 | − | 0.713551i | ||||
\(409\) | 7.38246e7 | 1.07902 | 0.539512 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539512 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(410\) | −2.17403e7 | + | 4.56657e7i | −0.315438 | + | 0.662580i | ||||
\(411\) | 5.85063e7i | 0.842708i | ||||||||
\(412\) | −5.75135e7 | + | 4.67134e7i | −0.822390 | + | 0.667959i | ||||
\(413\) | 2.60627e7 | 0.369972 | ||||||||
\(414\) | 2.05044e6 | + | 976165.i | 0.0288966 | + | 0.0137570i | ||||
\(415\) | 4.58738e7i | 0.641830i | ||||||||
\(416\) | 588792. | + | 448374.i | 0.00817865 | + | 0.00622817i | ||||
\(417\) | −6.58652e7 | −0.908339 | ||||||||
\(418\) | −3.60606e7 | + | 7.57456e7i | −0.493747 | + | 1.03712i | ||||
\(419\) | 1.31477e8i | 1.78735i | 0.448717 | + | 0.893674i | \(0.351881\pi\) | ||||
−0.448717 | + | 0.893674i | \(0.648119\pi\) | |||||||
\(420\) | 1.65970e7 | + | 2.04342e7i | 0.224017 | + | 0.275810i | ||||
\(421\) | −1.33132e8 | −1.78417 | −0.892087 | − | 0.451863i | \(-0.850760\pi\) | ||||
−0.892087 | + | 0.451863i | \(0.850760\pi\) | |||||||
\(422\) | 1.52380e7 | + | 7.25444e6i | 0.202764 | + | 0.0965310i | ||||
\(423\) | − | 4.47714e7i | − | 0.591534i | ||||||
\(424\) | 6.63800e7 | − | 1.60910e7i | 0.870843 | − | 0.211099i | ||||
\(425\) | 1.95246e7 | 0.254340 | ||||||||
\(426\) | 762676. | − | 1.60201e6i | 0.00986533 | − | 0.0207222i | ||||
\(427\) | 9.66771e7i | 1.24177i | ||||||||
\(428\) | −5.09944e7 | + | 4.14184e7i | −0.650416 | + | 0.528278i | ||||
\(429\) | −330733. | −0.00418895 | ||||||||
\(430\) | −4.59217e7 | − | 2.18622e7i | −0.577581 | − | 0.274972i | ||||
\(431\) | − | 4.13997e7i | − | 0.517089i | −0.965999 | − | 0.258544i | \(-0.916757\pi\) | ||
0.965999 | − | 0.258544i | \(-0.0832428\pi\) | |||||||
\(432\) | 1.51860e7 | + | 3.18134e6i | 0.188361 | + | 0.0394601i | ||||
\(433\) | −1.14745e8 | −1.41341 | −0.706706 | − | 0.707507i | \(-0.749820\pi\) | ||||
−0.706706 | + | 0.707507i | \(0.749820\pi\) | |||||||
\(434\) | −6.98668e6 | + | 1.46756e7i | −0.0854676 | + | 0.179525i | ||||
\(435\) | 2.23257e7i | 0.271230i | ||||||||
\(436\) | −3.10464e7 | − | 3.82243e7i | −0.374586 | − | 0.461190i | ||||
\(437\) | 1.30404e7 | 0.156260 | ||||||||
\(438\) | −3.13578e7 | − | 1.49287e7i | −0.373184 | − | 0.177664i | ||||
\(439\) | 6.31007e7i | 0.745832i | 0.927865 | + | 0.372916i | \(0.121642\pi\) | ||||
−0.927865 | + | 0.372916i | \(0.878358\pi\) | |||||||
\(440\) | −6.33415e6 | − | 2.61302e7i | −0.0743585 | − | 0.306750i | ||||
\(441\) | 2.55532e7 | 0.297941 | ||||||||
\(442\) | 485249. | − | 1.01927e6i | 0.00561950 | − | 0.0118038i | ||||
\(443\) | 3.81520e7i | 0.438840i | 0.975630 | + | 0.219420i | \(0.0704165\pi\) | ||||
−0.975630 | + | 0.219420i | \(0.929584\pi\) | |||||||
\(444\) | −3.92596e7 | + | 3.18872e7i | −0.448535 | + | 0.364307i | ||||
\(445\) | 5.61921e7 | 0.637668 | ||||||||
\(446\) | 3.69156e7 | + | 1.75746e7i | 0.416107 | + | 0.198098i | ||||
\(447\) | 5.88579e7i | 0.658996i | ||||||||
\(448\) | 5.66606e7 | + | 1.10003e8i | 0.630155 | + | 1.22341i | ||||
\(449\) | 1.25616e8 | 1.38773 | 0.693867 | − | 0.720103i | \(-0.255905\pi\) | ||||
0.693867 | + | 0.720103i | \(0.255905\pi\) | |||||||
\(450\) | −2.61133e6 | + | 5.48512e6i | −0.0286566 | + | 0.0601934i | ||||
\(451\) | − | 1.06238e8i | − | 1.15812i | ||||||
\(452\) | 1.36138e7 | + | 1.67613e7i | 0.147423 | + | 0.181507i | ||||
\(453\) | 5.19628e7 | 0.558982 | ||||||||
\(454\) | −1.54446e7 | − | 7.35278e6i | −0.165047 | − | 0.0785749i | ||||
\(455\) | 595959.i | 0.00632677i | ||||||||
\(456\) | 8.65874e7 | − | 2.09894e7i | 0.913188 | − | 0.221363i | ||||
\(457\) | 5.74907e7 | 0.602350 | 0.301175 | − | 0.953569i | \(-0.402621\pi\) | ||||
0.301175 | + | 0.953569i | \(0.402621\pi\) | |||||||
\(458\) | 4.94488e7 | − | 1.03868e8i | 0.514707 | − | 1.08114i | ||||
\(459\) | − | 2.36669e7i | − | 0.244739i | ||||||
\(460\) | −3.24416e6 | + | 2.63496e6i | −0.0333295 | + | 0.0270707i | ||||
\(461\) | 2.77042e7 | 0.282776 | 0.141388 | − | 0.989954i | \(-0.454844\pi\) | ||||
0.141388 | + | 0.989954i | \(0.454844\pi\) | |||||||
\(462\) | −4.99279e7 | − | 2.37695e7i | −0.506311 | − | 0.241042i | ||||
\(463\) | − | 1.76037e8i | − | 1.77362i | −0.462137 | − | 0.886809i | \(-0.652917\pi\) | ||
0.462137 | − | 0.886809i | \(-0.347083\pi\) | |||||||
\(464\) | −2.15168e7 | + | 1.02710e8i | −0.215389 | + | 1.02815i | ||||
\(465\) | −3.75085e6 | −0.0373053 | ||||||||
\(466\) | −7.45898e7 | + | 1.56676e8i | −0.737092 | + | 1.54827i | ||||
\(467\) | 7.46722e7i | 0.733176i | 0.930383 | + | 0.366588i | \(0.119474\pi\) | ||||
−0.930383 | + | 0.366588i | \(0.880526\pi\) | |||||||
\(468\) | 221448. | + | 272646.i | 0.00216040 | + | 0.00265988i | ||||
\(469\) | 1.15285e8 | 1.11752 | ||||||||
\(470\) | 7.43960e7 | + | 3.54181e7i | 0.716566 | + | 0.341139i | ||||
\(471\) | − | 1.13129e8i | − | 1.08271i | ||||||
\(472\) | 6.65997e6 | + | 2.74743e7i | 0.0633354 | + | 0.261277i | ||||
\(473\) | 1.06834e8 | 1.00955 | ||||||||
\(474\) | 1.92431e7 | − | 4.04202e7i | 0.180692 | − | 0.379545i | ||||
\(475\) | 3.48843e7i | 0.325499i | ||||||||
\(476\) | 1.46508e8 | − | 1.18996e8i | 1.35844 | − | 1.10335i | ||||
\(477\) | 3.24170e7 | 0.298688 | ||||||||
\(478\) | −3.17627e7 | − | 1.51214e7i | −0.290826 | − | 0.138455i | ||||
\(479\) | 1.32477e7i | 0.120541i | 0.998182 | + | 0.0602705i | \(0.0191963\pi\) | ||||
−0.998182 | + | 0.0602705i | \(0.980804\pi\) | |||||||
\(480\) | −1.72998e7 | + | 2.27176e7i | −0.156429 | + | 0.205418i | ||||
\(481\) | −1.14500e6 | −0.0102889 | ||||||||
\(482\) | 5.92040e7 | − | 1.24359e8i | 0.528701 | − | 1.11054i | ||||
\(483\) | 8.59564e6i | 0.0762846i | ||||||||
\(484\) | −3.58748e7 | − | 4.41691e7i | −0.316413 | − | 0.389567i | ||||
\(485\) | 8.06077e7 | 0.706563 | ||||||||
\(486\) | 6.64884e6 | + | 3.16535e6i | 0.0579211 | + | 0.0275748i | ||||
\(487\) | 4.04387e7i | 0.350114i | 0.984558 | + | 0.175057i | \(0.0560110\pi\) | ||||
−0.984558 | + | 0.175057i | \(0.943989\pi\) | |||||||
\(488\) | −1.01913e8 | + | 2.47045e7i | −0.876943 | + | 0.212578i | ||||
\(489\) | −3.12837e7 | −0.267542 | ||||||||
\(490\) | −2.02148e7 | + | 4.24614e7i | −0.171823 | + | 0.360916i | ||||
\(491\) | 2.04121e8i | 1.72442i | 0.506547 | + | 0.862212i | \(0.330922\pi\) | ||||
−0.506547 | + | 0.862212i | \(0.669078\pi\) | |||||||
\(492\) | −8.75798e7 | + | 7.11337e7i | −0.735374 | + | 0.597283i | ||||
\(493\) | 1.60070e8 | 1.33588 | ||||||||
\(494\) | 1.82112e6 | + | 866989.i | 0.0151063 | + | 0.00719172i | ||||
\(495\) | − | 1.27608e7i | − | 0.105211i | ||||||
\(496\) | −1.72558e7 | − | 3.61494e6i | −0.141413 | − | 0.0296249i | ||||
\(497\) | 6.71576e6 | 0.0547049 | ||||||||
\(498\) | −4.39895e7 | + | 9.24002e7i | −0.356173 | + | 0.748143i | ||||
\(499\) | 6.92447e7i | 0.557294i | 0.960394 | + | 0.278647i | \(0.0898860\pi\) | ||||
−0.960394 | + | 0.278647i | \(0.910114\pi\) | |||||||
\(500\) | −7.04875e6 | − | 8.67842e6i | −0.0563900 | − | 0.0694274i | ||||
\(501\) | −6.15802e7 | −0.489698 | ||||||||
\(502\) | −3.57381e7 | − | 1.70140e7i | −0.282501 | − | 0.134492i | ||||
\(503\) | − | 1.44266e8i | − | 1.13360i | −0.823856 | − | 0.566799i | \(-0.808182\pi\) | ||
0.823856 | − | 0.566799i | \(-0.191818\pi\) | |||||||
\(504\) | 1.38352e7 | + | 5.70743e7i | 0.108067 | + | 0.445809i | ||||
\(505\) | 4.35063e7 | 0.337814 | ||||||||
\(506\) | 3.77367e6 | − | 7.92662e6i | 0.0291281 | − | 0.0611838i | ||||
\(507\) | − | 7.52346e7i | − | 0.577289i | ||||||
\(508\) | −1.54222e8 | + | 1.25262e8i | −1.17640 | + | 0.955494i | ||||
\(509\) | −7.15475e7 | −0.542552 | −0.271276 | − | 0.962502i | \(-0.587446\pi\) | ||||
−0.271276 | + | 0.962502i | \(0.587446\pi\) | |||||||
\(510\) | 3.93269e7 | + | 1.87226e7i | 0.296469 | + | 0.141142i | ||||
\(511\) | − | 1.31455e8i | − | 0.985174i | ||||||
\(512\) | −1.01482e8 | + | 8.78393e7i | −0.756102 | + | 0.654454i | ||||
\(513\) | 4.22853e7 | 0.313212 | ||||||||
\(514\) | 8.66097e7 | − | 1.81924e8i | 0.637789 | − | 1.33968i | ||||
\(515\) | − | 6.47186e7i | − | 0.473813i | ||||||
\(516\) | −7.15325e7 | − | 8.80708e7i | −0.520660 | − | 0.641037i | ||||
\(517\) | −1.73078e8 | −1.25248 | ||||||||
\(518\) | −1.72850e8 | − | 8.22898e7i | −1.24360 | − | 0.592048i | ||||
\(519\) | − | 6.59989e7i | − | 0.472101i | ||||||
\(520\) | −628237. | + | 152289.i | −0.00446800 | + | 0.00108308i | ||||
\(521\) | 8.19625e7 | 0.579565 | 0.289783 | − | 0.957093i | \(-0.406417\pi\) | ||||
0.289783 | + | 0.957093i | \(0.406417\pi\) | |||||||
\(522\) | −2.14087e7 | + | 4.49691e7i | −0.150514 | + | 0.316157i | ||||
\(523\) | − | 2.55778e8i | − | 1.78796i | −0.448107 | − | 0.893980i | \(-0.647902\pi\) | ||
0.448107 | − | 0.893980i | \(-0.352098\pi\) | |||||||
\(524\) | 3.49317e6 | − | 2.83721e6i | 0.0242787 | − | 0.0197196i | ||||
\(525\) | −2.29941e7 | −0.158905 | ||||||||
\(526\) | −2.89628e7 | − | 1.37885e7i | −0.199014 | − | 0.0947457i | ||||
\(527\) | 2.68926e7i | 0.183739i | ||||||||
\(528\) | 1.22984e7 | − | 5.87061e7i | 0.0835504 | − | 0.398824i | ||||
\(529\) | 1.46671e8 | 0.990782 | ||||||||
\(530\) | −2.56447e7 | + | 5.38668e7i | −0.172254 | + | 0.361821i | ||||
\(531\) | 1.34172e7i | 0.0896145i | ||||||||
\(532\) | 2.12609e8 | + | 2.61764e8i | 1.41204 | + | 1.73850i | ||||
\(533\) | −2.55424e6 | −0.0168687 | ||||||||
\(534\) | 1.13183e8 | + | 5.38839e7i | 0.743292 | + | 0.353863i | ||||
\(535\) | − | 5.73827e7i | − | 0.374731i | ||||||
\(536\) | 2.94596e7 | + | 1.21529e8i | 0.191308 | + | 0.789200i | ||||
\(537\) | −7.93469e7 | −0.512398 | ||||||||
\(538\) | 2.67284e6 | − | 5.61432e6i | 0.0171643 | − | 0.0360537i | ||||
\(539\) | − | 9.87838e7i | − | 0.630841i | ||||||
\(540\) | −1.05196e7 | + | 8.54421e6i | −0.0668065 | + | 0.0542613i | ||||
\(541\) | −2.16239e8 | −1.36566 | −0.682831 | − | 0.730577i | \(-0.739251\pi\) | ||||
−0.682831 | + | 0.730577i | \(0.739251\pi\) | |||||||
\(542\) | −2.38315e8 | − | 1.13456e8i | −1.49676 | − | 0.712573i | ||||
\(543\) | 1.19891e8i | 0.748835i | ||||||||
\(544\) | 1.62879e8 | + | 1.24035e8i | 1.01174 | + | 0.770456i | ||||
\(545\) | 4.30129e7 | 0.265711 | ||||||||
\(546\) | −571479. | + | 1.20040e6i | −0.00351093 | + | 0.00737473i | ||||
\(547\) | 1.04526e6i | 0.00638648i | 0.999995 | + | 0.00319324i | \(0.00101644\pi\) | ||||
−0.999995 | + | 0.00319324i | \(0.998984\pi\) | |||||||
\(548\) | −1.51439e8 | − | 1.86451e8i | −0.920227 | − | 1.13298i | ||||
\(549\) | −4.97699e7 | −0.300780 | ||||||||
\(550\) | 2.12044e7 | + | 1.00949e7i | 0.127450 | + | 0.0606757i | ||||
\(551\) | 2.85995e8i | 1.70963i | ||||||||
\(552\) | −9.06119e6 | + | 2.19650e6i | −0.0538726 | + | 0.0130591i | ||||
\(553\) | 1.69445e8 | 1.00197 | ||||||||
\(554\) | −6.90611e7 | + | 1.45063e8i | −0.406167 | + | 0.853157i | ||||
\(555\) | − | 4.41778e7i | − | 0.258420i | ||||||
\(556\) | 2.09903e8 | − | 1.70487e8i | 1.22122 | − | 0.991895i | ||||
\(557\) | 1.12606e8 | 0.651624 | 0.325812 | − | 0.945435i | \(-0.394362\pi\) | ||||
0.325812 | + | 0.945435i | \(0.394362\pi\) | |||||||
\(558\) | −7.55505e6 | − | 3.59678e6i | −0.0434845 | − | 0.0207019i | ||||
\(559\) | − | 2.56856e6i | − | 0.0147047i | ||||||
\(560\) | −1.05784e8 | − | 2.21610e7i | −0.602362 | − | 0.126190i | ||||
\(561\) | −9.14916e7 | −0.518195 | ||||||||
\(562\) | 1.23786e8 | − | 2.60013e8i | 0.697367 | − | 1.46483i | ||||
\(563\) | 1.29568e8i | 0.726060i | 0.931777 | + | 0.363030i | \(0.118258\pi\) | ||||
−0.931777 | + | 0.363030i | \(0.881742\pi\) | |||||||
\(564\) | 1.15887e8 | + | 1.42680e8i | 0.645948 | + | 0.795291i | ||||
\(565\) | −1.88611e7 | −0.104574 | ||||||||
\(566\) | −5.95505e7 | − | 2.83505e7i | −0.328425 | − | 0.156355i | ||||
\(567\) | 2.78725e7i | 0.152907i | ||||||||
\(568\) | 1.71612e6 | + | 7.07950e6i | 0.00936490 | + | 0.0386329i | ||||
\(569\) | −9.50189e7 | −0.515791 | −0.257895 | − | 0.966173i | \(-0.583029\pi\) | ||||
−0.257895 | + | 0.966173i | \(0.583029\pi\) | |||||||
\(570\) | −3.34514e7 | + | 7.02649e7i | −0.180630 | + | 0.379415i | ||||
\(571\) | 2.03875e7i | 0.109510i | 0.998500 | + | 0.0547552i | \(0.0174378\pi\) | ||||
−0.998500 | + | 0.0547552i | \(0.982562\pi\) | |||||||
\(572\) | 1.05400e6 | − | 856075.i | 0.00563186 | − | 0.00457429i | ||||
\(573\) | 7.35797e6 | 0.0391106 | ||||||||
\(574\) | −3.85592e8 | − | 1.83571e8i | −2.03889 | − | 0.970663i | ||||
\(575\) | − | 3.65058e6i | − | 0.0192025i | ||||||
\(576\) | −5.66302e7 | + | 2.91692e7i | −0.296333 | + | 0.152636i | ||||
\(577\) | −1.37188e8 | −0.714149 | −0.357074 | − | 0.934076i | \(-0.616226\pi\) | ||||
−0.357074 | + | 0.934076i | \(0.616226\pi\) | |||||||
\(578\) | 5.12318e7 | − | 1.07613e8i | 0.265312 | − | 0.557289i | ||||
\(579\) | − | 8.99275e7i | − | 0.463294i | ||||||
\(580\) | −5.77883e7 | − | 7.11489e7i | −0.296180 | − | 0.364657i | ||||
\(581\) | −3.87350e8 | −1.97504 | ||||||||
\(582\) | 1.62362e8 | + | 7.72966e7i | 0.823599 | + | 0.392095i | ||||
\(583\) | − | 1.25318e8i | − | 0.632423i | ||||||
\(584\) | 1.38574e8 | − | 3.35914e7i | 0.695736 | − | 0.168651i | ||||
\(585\) | −306802. | −0.00153247 | ||||||||
\(586\) | 3.49619e7 | − | 7.34378e7i | 0.173741 | − | 0.364945i | ||||
\(587\) | 1.85031e8i | 0.914808i | 0.889259 | + | 0.457404i | \(0.151221\pi\) | ||||
−0.889259 | + | 0.457404i | \(0.848779\pi\) | |||||||
\(588\) | −8.14344e7 | + | 6.61424e7i | −0.400568 | + | 0.325348i | ||||
\(589\) | −4.80487e7 | −0.235145 | ||||||||
\(590\) | −2.22952e7 | − | 1.06142e7i | −0.108556 | − | 0.0516809i | ||||
\(591\) | 1.57918e8i | 0.765014i | ||||||||
\(592\) | 4.25772e7 | − | 2.03240e8i | 0.205216 | − | 0.979590i | ||||
\(593\) | 1.40041e8 | 0.671570 | 0.335785 | − | 0.941939i | \(-0.390998\pi\) | ||||
0.335785 | + | 0.941939i | \(0.390998\pi\) | |||||||
\(594\) | 1.22366e7 | − | 2.57031e7i | 0.0583852 | − | 0.122639i | ||||
\(595\) | 1.64862e8i | 0.782653i | ||||||||
\(596\) | −1.52349e8 | − | 1.87572e8i | −0.719616 | − | 0.885990i | ||||
\(597\) | 1.35546e8 | 0.637036 | ||||||||
\(598\) | −190576. | − | 90728.7i | −0.000891179 | − | 0.000424269i | ||||
\(599\) | 3.86610e6i | 0.0179884i | 0.999960 | + | 0.00899421i | \(0.00286298\pi\) | ||||
−0.999960 | + | 0.00899421i | \(0.997137\pi\) | |||||||
\(600\) | −5.87584e6 | − | 2.42395e7i | −0.0272030 | − | 0.112220i | ||||
\(601\) | 1.17489e8 | 0.541220 | 0.270610 | − | 0.962689i | \(-0.412775\pi\) | ||||
0.270610 | + | 0.962689i | \(0.412775\pi\) | |||||||
\(602\) | 1.84600e8 | − | 3.87754e8i | 0.846141 | − | 1.77733i | ||||
\(603\) | 5.93494e7i | 0.270685i | ||||||||
\(604\) | −1.65598e8 | + | 1.34501e8i | −0.751527 | + | 0.610402i | ||||
\(605\) | 4.97024e7 | 0.224446 | ||||||||
\(606\) | 8.76315e7 | + | 4.17192e7i | 0.393770 | + | 0.187464i | ||||
\(607\) | − | 3.82398e8i | − | 1.70982i | −0.518778 | − | 0.854909i | \(-0.673613\pi\) | ||
0.518778 | − | 0.854909i | \(-0.326387\pi\) | |||||||
\(608\) | −2.21612e8 | + | 2.91015e8i | −0.986014 | + | 1.29480i | ||||
\(609\) | −1.88514e8 | −0.834627 | ||||||||
\(610\) | 3.93723e7 | − | 8.27018e7i | 0.173461 | − | 0.364356i | ||||
\(611\) | 4.16123e6i | 0.0182431i | ||||||||
\(612\) | 6.12597e7 | + | 7.54230e7i | 0.267252 | + | 0.329040i | ||||
\(613\) | −91040.9 | −0.000395235 | −0.000197617 | − | 1.00000i | \(-0.500063\pi\) | ||||
−0.000197617 | 1.00000i | \(0.500063\pi\) | ||||||||
\(614\) | 9.42078e7 | + | 4.48500e7i | 0.406988 | + | 0.193757i | ||||
\(615\) | − | 9.85514e7i | − | 0.423680i | ||||||
\(616\) | 2.20639e8 | − | 5.34844e7i | 0.943929 | − | 0.228815i | ||||
\(617\) | −2.18687e8 | −0.931039 | −0.465519 | − | 0.885038i | \(-0.654132\pi\) | ||||
−0.465519 | + | 0.885038i | \(0.654132\pi\) | |||||||
\(618\) | 6.20601e7 | − | 1.30358e8i | 0.262934 | − | 0.552296i | ||||
\(619\) | 1.09965e8i | 0.463641i | 0.972759 | + | 0.231820i | \(0.0744682\pi\) | ||||
−0.972759 | + | 0.231820i | \(0.925532\pi\) | |||||||
\(620\) | 1.19534e7 | − | 9.70876e6i | 0.0501553 | − | 0.0407370i | ||||
\(621\) | −4.42508e6 | −0.0184776 | ||||||||
\(622\) | 1.28782e8 | + | 6.13100e7i | 0.535161 | + | 0.254777i | ||||
\(623\) | 4.74475e8i | 1.96223i | ||||||||
\(624\) | −1.41144e6 | − | 295686.i | −0.00580912 | − | 0.00121696i | ||||
\(625\) | 9.76562e6 | 0.0400000 | ||||||||
\(626\) | 3.41399e6 | − | 7.17112e6i | 0.0139168 | − | 0.0292324i | ||||
\(627\) | − | 1.63467e8i | − | 0.663174i | ||||||
\(628\) | 2.92824e8 | + | 3.60525e8i | 1.18230 | + | 1.45565i | ||||
\(629\) | −3.16744e8 | −1.27279 | ||||||||
\(630\) | −4.63154e7 | − | 2.20496e7i | −0.185227 | − | 0.0881818i | ||||
\(631\) | − | 6.46615e6i | − | 0.0257370i | −0.999917 | − | 0.0128685i | \(-0.995904\pi\) | ||
0.999917 | − | 0.0128685i | \(-0.00409628\pi\) | |||||||
\(632\) | 4.32994e7 | + | 1.78623e8i | 0.171526 | + | 0.707596i | ||||
\(633\) | −3.28853e7 | −0.129655 | ||||||||
\(634\) | −1.69167e7 | + | 3.55336e7i | −0.0663815 | + | 0.139435i | ||||
\(635\) | − | 1.73543e8i | − | 0.677775i | ||||||
\(636\) | −1.03308e8 | + | 8.39087e7i | −0.401572 | + | 0.326164i | ||||
\(637\) | −2.37502e6 | −0.00918858 | ||||||||
\(638\) | 1.73842e8 | + | 8.27619e7i | 0.669410 | + | 0.318690i | ||||
\(639\) | 3.45730e6i | 0.0132506i | ||||||||
\(640\) | −3.67054e6 | − | 1.17177e8i | −0.0140020 | − | 0.446994i | ||||
\(641\) | 1.74561e7 | 0.0662785 | 0.0331393 | − | 0.999451i | \(-0.489450\pi\) | ||||
0.0331393 | + | 0.999451i | \(0.489450\pi\) | |||||||
\(642\) | 5.50257e7 | − | 1.15582e8i | 0.207951 | − | 0.436802i | ||||
\(643\) | − | 5.28201e7i | − | 0.198685i | −0.995053 | − | 0.0993427i | \(-0.968326\pi\) | ||
0.995053 | − | 0.0993427i | \(-0.0316740\pi\) | |||||||
\(644\) | −2.22491e7 | − | 2.73931e7i | −0.0833019 | − | 0.102561i | ||||
\(645\) | 9.91040e7 | 0.369328 | ||||||||
\(646\) | 5.03781e8 | + | 2.39838e8i | 1.86872 | + | 0.889652i | ||||
\(647\) | − | 2.46885e8i | − | 0.911552i | −0.890094 | − | 0.455776i | \(-0.849362\pi\) | ||
0.890094 | − | 0.455776i | \(-0.150638\pi\) | |||||||
\(648\) | −2.93821e7 | + | 7.12245e6i | −0.107984 | + | 0.0261761i | ||||
\(649\) | 5.18683e7 | 0.189744 | ||||||||
\(650\) | 242708. | − | 509809.i | 0.000883778 | − | 0.00185638i | ||||
\(651\) | − | 3.16715e7i | − | 0.114796i | ||||||
\(652\) | 9.96967e7 | − | 8.09752e7i | 0.359698 | − | 0.292152i | ||||
\(653\) | 4.03664e8 | 1.44971 | 0.724854 | − | 0.688903i | \(-0.241907\pi\) | ||||
0.724854 | + | 0.688903i | \(0.241907\pi\) | |||||||
\(654\) | 8.66377e7 | + | 4.12461e7i | 0.309723 | + | 0.147452i | ||||
\(655\) | 3.93078e6i | 0.0139880i | ||||||||
\(656\) | 9.49806e7 | − | 4.53386e8i | 0.336452 | − | 1.60604i | ||||
\(657\) | 6.76734e7 | 0.238628 | ||||||||
\(658\) | −2.99064e8 | + | 6.28186e8i | −1.04975 | + | 2.20501i | ||||
\(659\) | 1.15030e8i | 0.401935i | 0.979598 | + | 0.200968i | \(0.0644086\pi\) | ||||
−0.979598 | + | 0.200968i | \(0.935591\pi\) | |||||||
\(660\) | 3.30303e7 | + | 4.06669e7i | 0.114890 | + | 0.141452i | ||||
\(661\) | −1.28637e8 | −0.445410 | −0.222705 | − | 0.974886i | \(-0.571489\pi\) | ||||
−0.222705 | + | 0.974886i | \(0.571489\pi\) | |||||||
\(662\) | 3.87199e8 | + | 1.84336e8i | 1.33463 | + | 0.635383i | ||||
\(663\) | 2.19969e6i | 0.00754782i | ||||||||
\(664\) | −9.89820e7 | − | 4.08329e8i | −0.338105 | − | 1.39478i | ||||
\(665\) | −2.94557e8 | −1.00162 | ||||||||
\(666\) | 4.23632e7 | − | 8.89842e7i | 0.143405 | − | 0.301224i | ||||
\(667\) | − | 2.99288e7i | − | 0.100858i | ||||||
\(668\) | 1.96248e8 | − | 1.59395e8i | 0.658377 | − | 0.534744i | ||||
\(669\) | −7.96677e7 | −0.266075 | ||||||||
\(670\) | −9.86201e7 | − | 4.69506e7i | −0.327900 | − | 0.156105i | ||||
\(671\) | 1.92401e8i | 0.636853i | ||||||||
\(672\) | −1.91823e8 | − | 1.46076e8i | −0.632111 | − | 0.481363i | ||||
\(673\) | −2.22256e7 | −0.0729137 | −0.0364568 | − | 0.999335i | \(-0.511607\pi\) | ||||
−0.0364568 | + | 0.999335i | \(0.511607\pi\) | |||||||
\(674\) | 2.21973e8 | − | 4.66255e8i | 0.724969 | − | 1.52280i | ||||
\(675\) | − | 1.18375e7i | − | 0.0384900i | ||||||
\(676\) | 1.94738e8 | + | 2.39762e8i | 0.630393 | + | 0.776140i | ||||
\(677\) | 1.43051e8 | 0.461025 | 0.230512 | − | 0.973069i | \(-0.425960\pi\) | ||||
0.230512 | + | 0.973069i | \(0.425960\pi\) | |||||||
\(678\) | −3.79905e7 | − | 1.80864e7i | −0.121895 | − | 0.0580313i | ||||
\(679\) | 6.80636e8i | 2.17423i | ||||||||
\(680\) | −1.73791e8 | + | 4.21282e7i | −0.552714 | + | 0.133982i | ||||
\(681\) | 3.33310e7 | 0.105538 | ||||||||
\(682\) | −1.39045e7 | + | 2.92064e7i | −0.0438330 | + | 0.0920715i | ||||
\(683\) | − | 1.47199e8i | − | 0.461999i | −0.972954 | − | 0.231000i | \(-0.925800\pi\) | ||
0.972954 | − | 0.231000i | \(-0.0741996\pi\) | |||||||
\(684\) | −1.34757e8 | + | 1.09452e8i | −0.421099 | + | 0.342023i | ||||
\(685\) | 2.09809e8 | 0.652759 | ||||||||
\(686\) | 4.25910e7 | + | 2.02765e7i | 0.131931 | + | 0.0628089i | ||||
\(687\) | 2.24158e8i | 0.691327i | ||||||||
\(688\) | 4.55928e8 | + | 9.55132e7i | 1.40001 | + | 0.293290i | ||||
\(689\) | −3.01296e6 | −0.00921162 | ||||||||
\(690\) | 3.50062e6 | − | 7.35308e6i | 0.0106561 | − | 0.0223832i | ||||
\(691\) | 4.86917e8i | 1.47578i | 0.674922 | + | 0.737889i | \(0.264177\pi\) | ||||
−0.674922 | + | 0.737889i | \(0.735823\pi\) | |||||||
\(692\) | 1.70833e8 | + | 2.10329e8i | 0.515529 | + | 0.634719i | ||||
\(693\) | 1.07750e8 | 0.323755 | ||||||||
\(694\) | −3.48835e8 | − | 1.66072e8i | −1.04362 | − | 0.496842i | ||||
\(695\) | 2.36199e8i | 0.703596i | ||||||||
\(696\) | −4.81723e7 | − | 1.98725e8i | −0.142879 | − | 0.589419i | ||||
\(697\) | −7.06588e8 | −2.08674 | ||||||||
\(698\) | −1.05991e8 | + | 2.22635e8i | −0.311675 | + | 0.654676i | ||||
\(699\) | − | 3.38125e8i | − | 0.990023i | ||||||
\(700\) | 7.32790e7 | − | 5.95184e7i | 0.213641 | − | 0.173523i | ||||
\(701\) | 3.70660e8 | 1.07602 | 0.538012 | − | 0.842937i | \(-0.319176\pi\) | ||||
0.538012 | + | 0.842937i | \(0.319176\pi\) | |||||||
\(702\) | −617969. | − | 294200.i | −0.00178630 | − | 0.000850416i | ||||
\(703\) | − | 5.65922e8i | − | 1.62889i | ||||||
\(704\) | 1.12762e8 | + | 2.18922e8i | 0.323182 | + | 0.627437i | ||||
\(705\) | −1.60555e8 | −0.458200 | ||||||||
\(706\) | −2.14570e8 | + | 4.50706e8i | −0.609754 | + | 1.28079i | ||||
\(707\) | 3.67359e8i | 1.03952i | ||||||||
\(708\) | −3.47293e7 | − | 4.27587e7i | −0.0978580 | − | 0.120483i | ||||
\(709\) | −2.70875e8 | −0.760028 | −0.380014 | − | 0.924981i | \(-0.624081\pi\) | ||||
−0.380014 | + | 0.924981i | \(0.624081\pi\) | |||||||
\(710\) | −5.74495e6 | − | 2.73503e6i | −0.0160513 | − | 0.00764165i | ||||
\(711\) | 8.72312e7i | 0.242696i | ||||||||
\(712\) | −5.00174e8 | + | 1.21246e8i | −1.38574 | + | 0.335913i | ||||
\(713\) | 5.02820e6 | 0.0138722 | ||||||||
\(714\) | −1.58090e8 | + | 3.32069e8i | −0.434320 | + | 0.912292i | ||||
\(715\) | 1.18604e6i | 0.00324475i | ||||||||
\(716\) | 2.52867e8 | − | 2.05383e8i | 0.688896 | − | 0.559532i | ||||
\(717\) | 6.85473e7 | 0.185966 | ||||||||
\(718\) | −3.80037e8 | − | 1.80926e8i | −1.02672 | − | 0.488797i | ||||
\(719\) | − | 6.11851e8i | − | 1.64611i | −0.567962 | − | 0.823055i | \(-0.692268\pi\) | ||
0.567962 | − | 0.823055i | \(-0.307732\pi\) | |||||||
\(720\) | 1.14086e7 | − | 5.44584e7i | 0.0305657 | − | 0.145904i | ||||
\(721\) | 5.46471e8 | 1.45801 | ||||||||
\(722\) | −2.66735e8 | + | 5.60278e8i | −0.708709 | + | 1.48865i | ||||
\(723\) | 2.68379e8i | 0.710123i | ||||||||
\(724\) | −3.10327e8 | − | 3.82075e8i | −0.817719 | − | 1.00678i | ||||
\(725\) | 8.00622e7 | 0.210094 | ||||||||
\(726\) | 1.00112e8 | + | 4.76608e7i | 0.261623 | + | 0.124552i | ||||
\(727\) | 4.50232e8i | 1.17175i | 0.810403 | + | 0.585873i | \(0.199248\pi\) | ||||
−0.810403 | + | 0.585873i | \(0.800752\pi\) | |||||||
\(728\) | −1.28590e6 | − | 5.30471e6i | −0.00333283 | − | 0.0137489i | ||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | −5.35356e7 | + | 1.12452e8i | −0.137618 | + | 0.289067i | ||||
\(731\) | − | 7.10550e8i | − | 1.81904i | ||||||
\(732\) | 1.58609e8 | − | 1.28825e8i | 0.404386 | − | 0.328449i | ||||
\(733\) | −6.51431e8 | −1.65408 | −0.827040 | − | 0.562143i | \(-0.809977\pi\) | ||||
−0.827040 | + | 0.562143i | \(0.809977\pi\) | |||||||
\(734\) | −1.48635e8 | − | 7.07617e7i | −0.375867 | − | 0.178941i | ||||
\(735\) | − | 9.16362e7i | − | 0.230784i | ||||||
\(736\) | 2.31913e7 | − | 3.04541e7i | 0.0581689 | − | 0.0763857i | ||||
\(737\) | 2.29434e8 | 0.573132 | ||||||||
\(738\) | 9.45033e7 | − | 1.98505e8i | 0.235114 | − | 0.493858i | ||||
\(739\) | − | 4.11562e8i | − | 1.01977i | −0.860243 | − | 0.509885i | \(-0.829688\pi\) | ||
0.860243 | − | 0.509885i | \(-0.170312\pi\) | |||||||
\(740\) | 1.14351e8 | + | 1.40789e8i | 0.282191 | + | 0.347434i | ||||
\(741\) | −3.93017e6 | −0.00965954 | ||||||||
\(742\) | −4.54841e8 | − | 2.16539e8i | −1.11339 | − | 0.530059i | ||||
\(743\) | 1.79409e8i | 0.437400i | 0.975792 | + | 0.218700i | \(0.0701816\pi\) | ||||
−0.975792 | + | 0.218700i | \(0.929818\pi\) | |||||||
\(744\) | 3.33868e7 | − | 8.09322e6i | 0.0810693 | − | 0.0196518i | ||||
\(745\) | 2.11070e8 | 0.510456 | ||||||||
\(746\) | −9.35508e7 | + | 1.96504e8i | −0.225336 | + | 0.473320i | ||||
\(747\) | − | 1.99410e8i | − | 0.478392i | ||||||
\(748\) | 2.91571e8 | − | 2.36819e8i | 0.696690 | − | 0.565862i | ||||
\(749\) | 4.84529e8 | 1.15312 | ||||||||
\(750\) | 1.96702e7 | + | 9.36449e6i | 0.0466256 | + | 0.0221973i | ||||
\(751\) | − | 3.37918e8i | − | 0.797796i | −0.916995 | − | 0.398898i | \(-0.869393\pi\) | ||
0.916995 | − | 0.398898i | \(-0.130607\pi\) | |||||||
\(752\) | −7.38632e8 | − | 1.54737e8i | −1.73690 | − | 0.363866i | ||||
\(753\) | 7.71266e7 | 0.180642 | ||||||||
\(754\) | 1.98981e6 | − | 4.17960e6i | 0.00464191 | − | 0.00975037i | ||||
\(755\) | − | 1.86344e8i | − | 0.432986i | ||||||
\(756\) | −7.21457e7 | − | 8.88258e7i | −0.166973 | − | 0.205577i | ||||
\(757\) | 4.17269e8 | 0.961896 | 0.480948 | − | 0.876749i | \(-0.340293\pi\) | ||||
0.480948 | + | 0.876749i | \(0.340293\pi\) | |||||||
\(758\) | 5.16636e8 | + | 2.45958e8i | 1.18625 | + | 0.564746i | ||||
\(759\) | 1.71065e7i | 0.0391233i | ||||||||
\(760\) | −7.52701e7 | − | 3.10511e8i | −0.171467 | − | 0.707352i | ||||
\(761\) | −4.73073e8 | −1.07343 | −0.536715 | − | 0.843763i | \(-0.680335\pi\) | ||||
−0.536715 | + | 0.843763i | \(0.680335\pi\) | |||||||
\(762\) | 1.66414e8 | − | 3.49555e8i | 0.376119 | − | 0.790042i | ||||
\(763\) | 3.63193e8i | 0.817643i | ||||||||
\(764\) | −2.34488e7 | + | 1.90455e7i | −0.0525824 | + | 0.0427083i | ||||
\(765\) | −8.48717e7 | −0.189574 | ||||||||
\(766\) | −2.96847e8 | − | 1.41322e8i | −0.660460 | − | 0.314429i | ||||
\(767\) | − | 1.24705e6i | − | 0.00276374i | ||||||
\(768\) | 1.04970e8 | − | 2.39540e8i | 0.231730 | − | 0.528805i | ||||
\(769\) | −1.35864e8 | −0.298763 | −0.149381 | − | 0.988780i | \(-0.547728\pi\) | ||||
−0.149381 | + | 0.988780i | \(0.547728\pi\) | |||||||
\(770\) | −8.52396e7 | + | 1.79046e8i | −0.186711 | + | 0.392187i | ||||
\(771\) | 3.92612e8i | 0.856645i | ||||||||
\(772\) | 2.32770e8 | + | 2.86586e8i | 0.505912 | + | 0.622879i | ||||
\(773\) | 8.97765e8 | 1.94368 | 0.971839 | − | 0.235646i | \(-0.0757207\pi\) | ||||
0.971839 | + | 0.235646i | \(0.0757207\pi\) | |||||||
\(774\) | 1.99618e8 | + | 9.50331e7i | 0.430503 | + | 0.204952i | ||||
\(775\) | 1.34509e7i | 0.0288966i | ||||||||
\(776\) | −7.17501e8 | + | 1.73927e8i | −1.53545 | + | 0.372206i | ||||
\(777\) | 3.73030e8 | 0.795207 | ||||||||
\(778\) | −5.97035e7 | + | 1.25408e8i | −0.126783 | + | 0.266309i | ||||
\(779\) | − | 1.26245e9i | − | 2.67056i | ||||||
\(780\) | 977736. | − | 794132.i | 0.00206033 | − | 0.00167344i | ||||
\(781\) | 1.33653e7 | 0.0280560 | ||||||||
\(782\) | −5.27197e7 | − | 2.50985e7i | −0.110243 | − | 0.0524842i | ||||
\(783\) | − | 9.70481e7i | − | 0.202163i | ||||||
\(784\) | 8.83160e7 | − | 4.21573e8i | 0.183270 | − | 0.874831i | ||||
\(785\) | −4.05690e8 | −0.838660 | ||||||||
\(786\) | −3.76932e6 | + | 7.91748e6i | −0.00776239 | + | 0.0163050i | ||||
\(787\) | − | 5.14017e8i | − | 1.05452i | −0.849705 | − | 0.527258i | \(-0.823220\pi\) | ||
0.849705 | − | 0.527258i | \(-0.176780\pi\) | |||||||
\(788\) | −4.08758e8 | − | 5.03262e8i | −0.835386 | − | 1.02853i | ||||
\(789\) | 6.25049e7 | 0.127257 | ||||||||
\(790\) | −1.44951e8 | − | 6.90075e7i | −0.293994 | − | 0.139964i | ||||
\(791\) | − | 1.59260e8i | − | 0.321793i | ||||||
\(792\) | 2.75340e7 | + | 1.13586e8i | 0.0554235 | + | 0.228638i | ||||
\(793\) | 4.62581e6 | 0.00927615 | ||||||||
\(794\) | −5.48482e7 | + | 1.15209e8i | −0.109572 | + | 0.230158i | ||||
\(795\) | − | 1.16250e8i | − | 0.231363i | ||||||
\(796\) | −4.31966e8 | + | 3.50850e8i | −0.856467 | + | 0.695636i | ||||
\(797\) | −7.71528e8 | −1.52397 | −0.761986 | − | 0.647594i | \(-0.775775\pi\) | ||||
−0.761986 | + | 0.647594i | \(0.775775\pi\) | |||||||
\(798\) | −5.93304e8 | − | 2.82457e8i | −1.16753 | − | 0.555833i | ||||
\(799\) | 1.15113e9i | 2.25676i | ||||||||
\(800\) | 8.14675e7 | + | 6.20388e7i | 0.159116 | + | 0.121170i | ||||
\(801\) | −2.44262e8 | −0.475290 | ||||||||
\(802\) | −1.70570e8 | + | 3.58284e8i | −0.330659 | + | 0.694552i | ||||
\(803\) | − | 2.61613e8i | − | 0.505257i | ||||||
\(804\) | −1.53621e8 | − | 1.89138e8i | −0.295585 | − | 0.363924i | ||||
\(805\) | 3.08248e7 | 0.0590898 | ||||||||
\(806\) | 702197. | + | 334299.i | 0.00134108 | + | 0.000638454i | ||||
\(807\) | 1.21163e7i | 0.0230542i | ||||||||
\(808\) | −3.87256e8 | + | 9.38736e7i | −0.734114 | + | 0.177955i | ||||
\(809\) | −1.84538e8 | −0.348529 | −0.174265 | − | 0.984699i | \(-0.555755\pi\) | ||||
−0.174265 | + | 0.984699i | \(0.555755\pi\) | |||||||
\(810\) | 1.13512e7 | − | 2.38434e7i | 0.0213594 | − | 0.0448655i | ||||
\(811\) | − | 3.93099e8i | − | 0.736952i | −0.929637 | − | 0.368476i | \(-0.879880\pi\) | ||
0.929637 | − | 0.368476i | \(-0.120120\pi\) | |||||||
\(812\) | 6.00768e8 | − | 4.87954e8i | 1.12212 | − | 0.911403i | ||||
\(813\) | 5.14309e8 | 0.957090 | ||||||||
\(814\) | −3.43996e8 | − | 1.63768e8i | −0.637793 | − | 0.303638i | ||||
\(815\) | 1.12186e8i | 0.207237i | ||||||||
\(816\) | −3.90452e8 | − | 8.17965e7i | −0.718617 | − | 0.150544i | ||||
\(817\) | 1.26953e9 | 2.32797 | ||||||||
\(818\) | 2.53867e8 | − | 5.33250e8i | 0.463817 | − | 0.974251i | ||||
\(819\) | − | 2.59058e6i | − | 0.00471569i | ||||||
\(820\) | 2.55092e8 | + | 3.14069e8i | 0.462653 | + | 0.569618i | ||||
\(821\) | 3.12484e8 | 0.564674 | 0.282337 | − | 0.959315i | \(-0.408890\pi\) | ||||
0.282337 | + | 0.959315i | \(0.408890\pi\) | |||||||
\(822\) | 4.22603e8 | + | 2.01191e8i | 0.760882 | + | 0.362237i | ||||
\(823\) | 3.56442e8i | 0.639424i | 0.947515 | + | 0.319712i | \(0.103586\pi\) | ||||
−0.947515 | + | 0.319712i | \(0.896414\pi\) | |||||||
\(824\) | 1.39643e8 | + | 5.76069e8i | 0.249597 | + | 1.02966i | ||||
\(825\) | −4.57615e7 | −0.0814963 | ||||||||
\(826\) | 8.96242e7 | − | 1.88256e8i | 0.159032 | − | 0.334048i | ||||
\(827\) | 3.14494e8i | 0.556027i | 0.960577 | + | 0.278014i | \(0.0896760\pi\) | ||||
−0.960577 | + | 0.278014i | \(0.910324\pi\) | |||||||
\(828\) | 1.41021e7 | − | 1.14539e7i | 0.0248423 | − | 0.0201773i | ||||
\(829\) | −1.01121e8 | −0.177491 | −0.0887457 | − | 0.996054i | \(-0.528286\pi\) | ||||
−0.0887457 | + | 0.996054i | \(0.528286\pi\) | |||||||
\(830\) | 3.31356e8 | + | 1.57750e8i | 0.579509 | + | 0.275890i | ||||
\(831\) | − | 3.13063e8i | − | 0.545542i | ||||||
\(832\) | 5.26343e6 | − | 2.71110e6i | 0.00913901 | − | 0.00470733i | ||||
\(833\) | −6.57008e8 | −1.13667 | ||||||||
\(834\) | −2.26497e8 | + | 4.75758e8i | −0.390448 | + | 0.820140i | ||||
\(835\) | 2.20833e8i | 0.379318i | ||||||||
\(836\) | 4.23121e8 | + | 5.20947e8i | 0.724179 | + | 0.891609i | ||||
\(837\) | 1.63046e7 | 0.0278057 | ||||||||
\(838\) | 9.49688e8 | + | 4.52123e8i | 1.61380 | + | 0.768289i | ||||
\(839\) | − | 1.00055e9i | − | 1.69416i | −0.531469 | − | 0.847078i | \(-0.678360\pi\) | ||
0.531469 | − | 0.847078i | \(-0.321640\pi\) | |||||||
\(840\) | 2.04674e8 | − | 4.96145e7i | 0.345322 | − | 0.0837087i | ||||
\(841\) | 6.15564e7 | 0.103487 | ||||||||
\(842\) | −4.57814e8 | + | 9.61643e8i | −0.766926 | + | 1.61093i | ||||
\(843\) | 5.61136e8i | 0.936667i | ||||||||
\(844\) | 1.04801e8 | − | 8.51208e7i | 0.174316 | − | 0.141582i | ||||
\(845\) | −2.69798e8 | −0.447166 | ||||||||
\(846\) | −3.23393e8 | − | 1.53960e8i | −0.534097 | − | 0.254270i | ||||
\(847\) | 4.19678e8i | 0.690663i | ||||||||
\(848\) | 1.12038e8 | − | 5.34810e8i | 0.183730 | − | 0.877025i | ||||
\(849\) | 1.28516e8 | 0.210008 | ||||||||
\(850\) | 6.71409e7 | − | 1.41030e8i | 0.109328 | − | 0.229644i | ||||
\(851\) | 5.92226e7i | 0.0960946i | ||||||||
\(852\) | −8.94895e6 | − | 1.10179e7i | −0.0144695 | − | 0.0178148i | ||||
\(853\) | −2.13653e8 | −0.344240 | −0.172120 | − | 0.985076i | \(-0.555062\pi\) | ||||
−0.172120 | + | 0.985076i | \(0.555062\pi\) | |||||||
\(854\) | 6.98319e8 | + | 3.32452e8i | 1.12119 | + | 0.533772i | ||||
\(855\) | − | 1.51639e8i | − | 0.242613i | ||||||
\(856\) | 1.23815e8 | + | 5.10772e8i | 0.197402 | + | 0.814340i | ||||
\(857\) | −4.72771e8 | −0.751118 | −0.375559 | − | 0.926799i | \(-0.622549\pi\) | ||||
−0.375559 | + | 0.926799i | \(0.622549\pi\) | |||||||
\(858\) | −1.13732e6 | + | 2.38895e6i | −0.00180062 | + | 0.00378221i | ||||
\(859\) | 9.05036e8i | 1.42786i | 0.700216 | + | 0.713931i | \(0.253087\pi\) | ||||
−0.700216 | + | 0.713931i | \(0.746913\pi\) | |||||||
\(860\) | −3.15830e8 | + | 2.56522e8i | −0.496545 | + | 0.403302i | ||||
\(861\) | 8.32150e8 | 1.30374 | ||||||||
\(862\) | −2.99038e8 | − | 1.42365e8i | −0.466880 | − | 0.222270i | ||||
\(863\) | − | 2.48053e8i | − | 0.385932i | −0.981205 | − | 0.192966i | \(-0.938189\pi\) | ||
0.981205 | − | 0.192966i | \(-0.0618108\pi\) | |||||||
\(864\) | 7.52009e7 | − | 9.87515e7i | 0.116595 | − | 0.153110i | ||||
\(865\) | −2.36679e8 | −0.365688 | ||||||||
\(866\) | −3.94583e8 | + | 8.28824e8i | −0.607554 | + | 1.27617i | ||||
\(867\) | 2.32240e8i | 0.356353i | ||||||||
\(868\) | 8.19789e7 | + | 1.00932e8i | 0.125355 | + | 0.154338i | ||||
\(869\) | 3.37219e8 | 0.513870 | ||||||||
\(870\) | 1.61263e8 | + | 7.67735e7i | 0.244894 | + | 0.116588i | ||||
\(871\) | − | 5.51617e6i | − | 0.00834802i | ||||||
\(872\) | −3.82864e8 | + | 9.28091e7i | −0.577424 | + | 0.139972i | ||||
\(873\) | −3.50395e8 | −0.526641 | ||||||||
\(874\) | 4.48433e7 | − | 9.41937e7i | 0.0671681 | − | 0.141087i | ||||
\(875\) | 8.24591e7i | 0.123088i | ||||||||
\(876\) | −2.15666e8 | + | 1.75167e8i | −0.320825 | + | 0.260579i | ||||
\(877\) | 3.09904e8 | 0.459439 | 0.229720 | − | 0.973257i | \(-0.426219\pi\) | ||||
0.229720 | + | 0.973257i | \(0.426219\pi\) | |||||||
\(878\) | 4.55790e8 | + | 2.16990e8i | 0.673412 | + | 0.320595i | ||||
\(879\) | 1.58487e8i | 0.233360i | ||||||||
\(880\) | −2.10526e8 | − | 4.41034e7i | −0.308928 | − | 0.0647179i | ||||
\(881\) | 7.41617e8 | 1.08456 | 0.542278 | − | 0.840199i | \(-0.317562\pi\) | ||||
0.542278 | + | 0.840199i | \(0.317562\pi\) | |||||||
\(882\) | 8.78721e7 | − | 1.84576e8i | 0.128069 | − | 0.269011i | ||||
\(883\) | − | 1.03000e9i | − | 1.49608i | −0.663656 | − | 0.748038i | \(-0.730996\pi\) | ||
0.663656 | − | 0.748038i | \(-0.269004\pi\) | |||||||
\(884\) | −5.69372e6 | − | 7.01011e6i | −0.00824213 | − | 0.0101477i | ||||
\(885\) | 4.81154e7 | 0.0694151 | ||||||||
\(886\) | 2.75580e8 | + | 1.31197e8i | 0.396229 | + | 0.188635i | ||||
\(887\) | 1.01764e9i | 1.45822i | 0.684395 | + | 0.729112i | \(0.260066\pi\) | ||||
−0.684395 | + | 0.729112i | \(0.739934\pi\) | |||||||
\(888\) | 9.53227e7 | + | 3.93233e8i | 0.136131 | + | 0.561580i | ||||
\(889\) | 1.46536e9 | 2.08564 | ||||||||
\(890\) | 1.93233e8 | − | 4.05887e8i | 0.274101 | − | 0.575751i | ||||
\(891\) | 5.54702e7i | 0.0784199i | ||||||||
\(892\) | 2.53890e8 | − | 2.06213e8i | 0.357726 | − | 0.290551i | ||||
\(893\) | −2.05672e9 | −2.88816 | ||||||||
\(894\) | 4.25143e8 | + | 2.02400e8i | 0.595008 | + | 0.283269i | ||||
\(895\) | 2.84546e8i | 0.396902i | ||||||||
\(896\) | 9.89420e8 | − | 3.09934e7i | 1.37549 | − | 0.0430868i | ||||
\(897\) | 411284. | 0.000569855 | ||||||||
\(898\) | 4.31968e8 | − | 9.07352e8i | 0.596516 | − | 1.25299i | ||||
\(899\) | 1.10275e8i | 0.151775i | ||||||||
\(900\) | 3.06403e7 | + | 3.77244e7i | 0.0420307 | + | 0.0517481i | ||||
\(901\) | −8.33485e8 | −1.13952 | ||||||||
\(902\) | −7.67382e8 | − | 3.65332e8i | −1.04566 | − | 0.497815i | ||||
\(903\) | 8.36816e8i | 1.13649i | ||||||||
\(904\) | 1.67886e8 | − | 4.06967e7i | 0.227252 | − | 0.0550876i | ||||
\(905\) | 4.29940e8 | 0.580045 | ||||||||
\(906\) | 1.78689e8 | − | 3.75338e8i | 0.240278 | − | 0.504706i | ||||
\(907\) | − | 1.33458e9i | − | 1.78864i | −0.447430 | − | 0.894319i | \(-0.647661\pi\) | ||
0.447430 | − | 0.894319i | \(-0.352339\pi\) | |||||||
\(908\) | −1.06221e8 | + | 8.62746e7i | −0.141891 | + | 0.115246i | ||||
\(909\) | −1.89118e8 | −0.251792 | ||||||||
\(910\) | 4.30473e6 | + | 2.04938e6i | 0.00571244 | + | 0.00271955i | ||||
\(911\) | 2.62935e8i | 0.347771i | 0.984766 | + | 0.173886i | \(0.0556323\pi\) | ||||
−0.984766 | + | 0.173886i | \(0.944368\pi\) | |||||||
\(912\) | 1.46145e8 | − | 6.97617e8i | 0.192664 | − | 0.919671i | ||||
\(913\) | −7.70879e8 | −1.01292 | ||||||||
\(914\) | 1.97698e8 | − | 4.15267e8i | 0.258919 | − | 0.543862i | ||||
\(915\) | 1.78479e8i | 0.232983i | ||||||||
\(916\) | −5.80213e8 | − | 7.14358e8i | −0.754921 | − | 0.929458i | ||||
\(917\) | −3.31908e7 | −0.0430437 | ||||||||
\(918\) | −1.70951e8 | − | 8.13854e7i | −0.220975 | − | 0.105201i | ||||
\(919\) | 9.16411e8i | 1.18071i | 0.807143 | + | 0.590356i | \(0.201013\pi\) | ||||
−0.807143 | + | 0.590356i | \(0.798987\pi\) | |||||||
\(920\) | 7.87686e6 | + | 3.24943e7i | 0.0101156 | + | 0.0417296i | ||||
\(921\) | −2.03311e8 | −0.260244 | ||||||||
\(922\) | 9.52689e7 | − | 2.00113e8i | 0.121551 | − | 0.255319i | ||||
\(923\) | − | 321336.i | − | 0.000408652i | ||||||
\(924\) | −3.43384e8 | + | 2.78902e8i | −0.435275 | + | 0.353537i | ||||
\(925\) | −1.58426e8 | −0.200171 | ||||||||
\(926\) | −1.27155e9 | − | 6.05353e8i | −1.60140 | − | 0.762387i | ||||
\(927\) | 2.81326e8i | 0.353159i | ||||||||
\(928\) | 6.67900e8 | + | 5.08617e8i | 0.835733 | + | 0.636425i | ||||
\(929\) | 7.28953e8 | 0.909185 | 0.454592 | − | 0.890700i | \(-0.349785\pi\) | ||||
0.454592 | + | 0.890700i | \(0.349785\pi\) | |||||||
\(930\) | −1.28984e7 | + | 2.70931e7i | −0.0160356 | + | 0.0336830i | ||||
\(931\) | − | 1.17387e9i | − | 1.45469i | ||||||
\(932\) | 8.75207e8 | + | 1.07755e9i | 1.08109 | + | 1.33104i | ||||
\(933\) | −2.77925e8 | −0.342203 | ||||||||
\(934\) | 5.39373e8 | + | 2.56782e8i | 0.661985 | + | 0.315155i | ||||
\(935\) | 3.28098e8i | 0.401392i | ||||||||
\(936\) | 2.73089e6 | − | 661988.i | 0.00333025 | − | 0.000807278i | ||||
\(937\) | 5.03858e8 | 0.612477 | 0.306238 | − | 0.951955i | \(-0.400929\pi\) | ||||
0.306238 | + | 0.951955i | \(0.400929\pi\) | |||||||
\(938\) | 3.96442e8 | − | 8.32730e8i | 0.480365 | − | 1.00901i | ||||
\(939\) | 1.54761e7i | 0.0186923i | ||||||||
\(940\) | 5.11665e8 | − | 4.15582e8i | 0.616030 | − | 0.500349i | ||||
\(941\) | 1.86452e8 | 0.223768 | 0.111884 | − | 0.993721i | \(-0.464311\pi\) | ||||
0.111884 | + | 0.993721i | \(0.464311\pi\) | |||||||
\(942\) | −8.17152e8 | − | 3.89026e8i | −0.977575 | − | 0.465400i | ||||
\(943\) | 1.32113e8i | 0.157547i | ||||||||
\(944\) | 2.21355e8 | + | 4.63720e7i | 0.263131 | + | 0.0551239i | ||||
\(945\) | 9.99535e7 | 0.118441 | ||||||||
\(946\) | 3.67380e8 | − | 7.71685e8i | 0.433953 | − | 0.911520i | ||||
\(947\) | − | 5.29448e8i | − | 0.623409i | −0.950179 | − | 0.311705i | \(-0.899100\pi\) | ||
0.950179 | − | 0.311705i | \(-0.100900\pi\) | |||||||
\(948\) | −2.25791e8 | − | 2.77993e8i | −0.265021 | − | 0.326294i | ||||
\(949\) | −6.28984e6 | −0.00735937 | ||||||||
\(950\) | 2.51977e8 | + | 1.19960e8i | 0.293893 | + | 0.139915i | ||||
\(951\) | − | 7.66853e7i | − | 0.0891602i | ||||||
\(952\) | −3.55723e8 | − | 1.46746e9i | −0.412288 | − | 1.70081i | ||||
\(953\) | −6.70647e8 | −0.774846 | −0.387423 | − | 0.921902i | \(-0.626635\pi\) | ||||
−0.387423 | + | 0.921902i | \(0.626635\pi\) | |||||||
\(954\) | 1.11475e8 | − | 2.34155e8i | 0.128391 | − | 0.269685i | ||||
\(955\) | − | 2.63864e7i | − | 0.0302949i | ||||||
\(956\) | −2.18450e8 | + | 1.77429e8i | −0.250023 | + | 0.203072i | ||||
\(957\) | −3.75170e8 | −0.428047 | ||||||||
\(958\) | 9.56911e7 | + | 4.55562e7i | 0.108837 | + | 0.0518145i | ||||
\(959\) | 1.77159e9i | 2.00866i | ||||||||
\(960\) | 1.04603e8 | + | 2.03081e8i | 0.118231 | + | 0.229539i | ||||
\(961\) | 8.68977e8 | 0.979125 | ||||||||
\(962\) | −3.93740e6 | + | 8.27054e6i | −0.00442267 | + | 0.00928985i | ||||
\(963\) | 2.49438e8i | 0.279308i | ||||||||
\(964\) | −6.94677e8 | − | 8.55286e8i | −0.775446 | − | 0.954729i | ||||
\(965\) | −3.22489e8 | −0.358866 | ||||||||
\(966\) | 6.20881e7 | + | 2.95586e7i | 0.0688774 | + | 0.0327908i | ||||
\(967\) | − | 5.56891e8i | − | 0.615872i | −0.951407 | − | 0.307936i | \(-0.900362\pi\) | ||
0.951407 | − | 0.307936i | \(-0.0996383\pi\) | |||||||
\(968\) | −4.42408e8 | + | 1.07243e8i | −0.487750 | + | 0.118234i | ||||
\(969\) | −1.08721e9 | −1.19493 | ||||||||
\(970\) | 2.77193e8 | − | 5.82246e8i | 0.303716 | − | 0.637957i | ||||
\(971\) | − | 8.52936e8i | − | 0.931663i | −0.884873 | − | 0.465832i | \(-0.845755\pi\) | ||
0.884873 | − | 0.465832i | \(-0.154245\pi\) | |||||||
\(972\) | 4.57279e7 | − | 3.71410e7i | 0.0497947 | − | 0.0404440i | ||||
\(973\) | −1.99442e9 | −2.16510 | ||||||||
\(974\) | 2.92097e8 | + | 1.39060e8i | 0.316119 | + | 0.150496i | ||||
\(975\) | 1.10022e6i | 0.00118704i | ||||||||
\(976\) | −1.72013e8 | + | 8.21095e8i | −0.185017 | + | 0.883169i | ||||
\(977\) | −4.87819e8 | −0.523089 | −0.261544 | − | 0.965191i | \(-0.584232\pi\) | ||||
−0.261544 | + | 0.965191i | \(0.584232\pi\) | |||||||
\(978\) | −1.07578e8 | + | 2.25969e8i | −0.115002 | + | 0.241564i | ||||
\(979\) | 9.44271e8i | 1.00635i | ||||||||
\(980\) | 2.37193e8 | + | 2.92032e8i | 0.252013 | + | 0.310279i | ||||
\(981\) | −1.86973e8 | −0.198049 | ||||||||
\(982\) | 1.47441e9 | + | 7.01931e8i | 1.55698 | + | 0.741242i | ||||
\(983\) | 1.61387e8i | 0.169906i | 0.996385 | + | 0.0849528i | \(0.0270739\pi\) | ||||
−0.996385 | + | 0.0849528i | \(0.972926\pi\) | |||||||
\(984\) | 2.12645e8 | + | 8.77221e8i | 0.223187 | + | 0.920711i | ||||
\(985\) | 5.66309e8 | 0.592577 | ||||||||
\(986\) | 5.50446e8 | − | 1.15622e9i | 0.574228 | − | 1.20617i | ||||
\(987\) | − | 1.35569e9i | − | 1.40997i | ||||||
\(988\) | 1.25249e7 | − | 1.01729e7i | 0.0129868 | − | 0.0105481i | ||||
\(989\) | −1.32854e8 | −0.137336 | ||||||||
\(990\) | −9.21739e7 | − | 4.38817e7i | −0.0949954 | − | 0.0452250i | ||||
\(991\) | − | 8.20569e8i | − | 0.843129i | −0.906798 | − | 0.421564i | \(-0.861481\pi\) | ||
0.906798 | − | 0.421564i | \(-0.138519\pi\) | |||||||
\(992\) | −8.54505e7 | + | 1.12211e8i | −0.0875346 | + | 0.114948i | ||||
\(993\) | −8.35617e8 | −0.853413 | ||||||||
\(994\) | 2.30941e7 | − | 4.85093e7i | 0.0235148 | − | 0.0493931i | ||||
\(995\) | − | 4.86081e8i | − | 0.493446i | ||||||
\(996\) | 5.16155e8 | + | 6.35490e8i | 0.522399 | + | 0.643177i | ||||
\(997\) | −1.48083e9 | −1.49424 | −0.747121 | − | 0.664689i | \(-0.768564\pi\) | ||||
−0.747121 | + | 0.664689i | \(0.768564\pi\) | |||||||
\(998\) | 5.00169e8 | + | 2.38118e8i | 0.503182 | + | 0.239552i | ||||
\(999\) | 1.92037e8i | 0.192615i |
(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.31.15 | ✓ | 24 | |
3.2 | odd | 2 | 180.7.c.b.91.10 | 24 | |||
4.3 | odd | 2 | inner | 60.7.c.a.31.16 | yes | 24 | |
12.11 | even | 2 | 180.7.c.b.91.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.c.a.31.15 | ✓ | 24 | 1.1 | even | 1 | trivial | |
60.7.c.a.31.16 | yes | 24 | 4.3 | odd | 2 | inner | |
180.7.c.b.91.9 | 24 | 12.11 | even | 2 | |||
180.7.c.b.91.10 | 24 | 3.2 | odd | 2 |