Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.5 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.6.d.a.75.6 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.30781 | − | 1.95631i | −0.938297 | − | 0.345830i | ||||
\(3\) | −7.37371 | −0.473024 | −0.236512 | − | 0.971629i | \(-0.576004\pi\) | ||||
−0.236512 | + | 0.971629i | \(0.576004\pi\) | |||||||
\(4\) | 24.3457 | + | 20.7674i | 0.760804 | + | 0.648982i | ||||
\(5\) | 74.1521 | 1.32647 | 0.663237 | − | 0.748410i | \(-0.269182\pi\) | ||||
0.663237 | + | 0.748410i | \(0.269182\pi\) | |||||||
\(6\) | 39.1383 | + | 14.4252i | 0.443837 | + | 0.163586i | ||||
\(7\) | 80.5452i | 0.621290i | 0.950526 | + | 0.310645i | \(0.100545\pi\) | ||||
−0.950526 | + | 0.310645i | \(0.899455\pi\) | |||||||
\(8\) | −88.5950 | − | 157.857i | −0.489423 | − | 0.872046i | ||||
\(9\) | −188.628 | −0.776248 | ||||||||
\(10\) | −393.585 | − | 145.064i | −1.24463 | − | 0.458734i | ||||
\(11\) | − | 299.840i | − | 0.747150i | −0.927600 | − | 0.373575i | \(-0.878132\pi\) | ||
0.927600 | − | 0.373575i | \(-0.121868\pi\) | |||||||
\(12\) | −179.518 | − | 153.133i | −0.359878 | − | 0.306984i | ||||
\(13\) | 472.618i | 0.775625i | 0.921738 | + | 0.387813i | \(0.126769\pi\) | ||||
−0.921738 | + | 0.387813i | \(0.873231\pi\) | |||||||
\(14\) | 157.571 | − | 427.519i | 0.214860 | − | 0.582955i | ||||
\(15\) | −546.776 | −0.627453 | ||||||||
\(16\) | 161.428 | + | 1011.20i | 0.157645 | + | 0.987496i | ||||
\(17\) | 861.194 | 0.722734 | 0.361367 | − | 0.932424i | \(-0.382310\pi\) | ||||
0.361367 | + | 0.932424i | \(0.382310\pi\) | |||||||
\(18\) | 1001.20 | + | 369.015i | 0.728352 | + | 0.268450i | ||||
\(19\) | 115.343 | + | 1569.33i | 0.0733009 | + | 0.997310i | ||||
\(20\) | 1805.29 | + | 1539.95i | 1.00919 | + | 0.860857i | ||||
\(21\) | − | 593.917i | − | 0.293885i | ||||||
\(22\) | −586.579 | + | 1591.49i | −0.258387 | + | 0.701049i | ||||
\(23\) | 840.760i | 0.331400i | 0.986176 | + | 0.165700i | \(0.0529883\pi\) | ||||
−0.986176 | + | 0.165700i | \(0.947012\pi\) | |||||||
\(24\) | 653.274 | + | 1163.99i | 0.231509 | + | 0.412499i | ||||
\(25\) | 2373.54 | 0.759531 | ||||||||
\(26\) | 924.586 | − | 2508.57i | 0.268234 | − | 0.727767i | ||||
\(27\) | 3182.70 | 0.840208 | ||||||||
\(28\) | −1672.72 | + | 1960.93i | −0.403206 | + | 0.472680i | ||||
\(29\) | 5159.61i | 1.13926i | 0.821902 | + | 0.569629i | \(0.192913\pi\) | ||||
−0.821902 | + | 0.569629i | \(0.807087\pi\) | |||||||
\(30\) | 2902.19 | + | 1069.66i | 0.588738 | + | 0.216992i | ||||
\(31\) | 3421.14 | 0.639392 | 0.319696 | − | 0.947520i | \(-0.396419\pi\) | ||||
0.319696 | + | 0.947520i | \(0.396419\pi\) | |||||||
\(32\) | 1121.38 | − | 5683.04i | 0.193587 | − | 0.981083i | ||||
\(33\) | 2210.93i | 0.353420i | ||||||||
\(34\) | −4571.05 | − | 1684.76i | −0.678140 | − | 0.249943i | ||||
\(35\) | 5972.59i | 0.824125i | ||||||||
\(36\) | −4592.29 | − | 3917.32i | −0.590573 | − | 0.503771i | ||||
\(37\) | 4136.40i | 0.496727i | 0.968667 | + | 0.248364i | \(0.0798928\pi\) | ||||
−0.968667 | + | 0.248364i | \(0.920107\pi\) | |||||||
\(38\) | 2457.87 | − | 8555.35i | 0.276121 | − | 0.961123i | ||||
\(39\) | − | 3484.95i | − | 0.366889i | ||||||
\(40\) | −6569.51 | − | 11705.4i | −0.649207 | − | 1.15675i | ||||
\(41\) | 19653.0i | 1.82586i | 0.408112 | + | 0.912932i | \(0.366187\pi\) | ||||
−0.408112 | + | 0.912932i | \(0.633813\pi\) | |||||||
\(42\) | −1161.88 | + | 3152.40i | −0.101634 | + | 0.275752i | ||||
\(43\) | 11970.7i | 0.987302i | 0.869660 | + | 0.493651i | \(0.164338\pi\) | ||||
−0.869660 | + | 0.493651i | \(0.835662\pi\) | |||||||
\(44\) | 6226.90 | − | 7299.82i | 0.484887 | − | 0.568434i | ||||
\(45\) | −13987.2 | −1.02967 | ||||||||
\(46\) | 1644.79 | − | 4462.60i | 0.114608 | − | 0.310952i | ||||
\(47\) | − | 15826.8i | − | 1.04508i | −0.852616 | − | 0.522538i | \(-0.824985\pi\) | ||
0.852616 | − | 0.522538i | \(-0.175015\pi\) | |||||||
\(48\) | −1190.33 | − | 7456.27i | −0.0745698 | − | 0.467109i | ||||
\(49\) | 10319.5 | 0.613999 | ||||||||
\(50\) | −12598.3 | − | 4643.36i | −0.712666 | − | 0.262668i | ||||
\(51\) | −6350.19 | −0.341870 | ||||||||
\(52\) | −9815.06 | + | 11506.2i | −0.503367 | + | 0.590099i | ||||
\(53\) | 4883.58i | 0.238808i | 0.992846 | + | 0.119404i | \(0.0380984\pi\) | ||||
−0.992846 | + | 0.119404i | \(0.961902\pi\) | |||||||
\(54\) | −16893.2 | − | 6226.35i | −0.788365 | − | 0.290569i | ||||
\(55\) | − | 22233.8i | − | 0.991074i | ||||||
\(56\) | 12714.6 | − | 7135.90i | 0.541794 | − | 0.304074i | ||||
\(57\) | −850.510 | − | 11571.8i | −0.0346731 | − | 0.471751i | ||||
\(58\) | 10093.8 | − | 27386.3i | 0.393989 | − | 1.06896i | ||||
\(59\) | 31449.1 | 1.17619 | 0.588097 | − | 0.808790i | \(-0.299877\pi\) | ||||
0.588097 | + | 0.808790i | \(0.299877\pi\) | |||||||
\(60\) | −13311.7 | − | 11355.1i | −0.477369 | − | 0.407206i | ||||
\(61\) | −29401.7 | −1.01169 | −0.505845 | − | 0.862625i | \(-0.668819\pi\) | ||||
−0.505845 | + | 0.862625i | \(0.668819\pi\) | |||||||
\(62\) | −18158.8 | − | 6692.81i | −0.599940 | − | 0.221121i | ||||
\(63\) | − | 15193.1i | − | 0.482275i | ||||||
\(64\) | −17069.8 | + | 27970.7i | −0.520930 | + | 0.853599i | ||||
\(65\) | 35045.6i | 1.02885i | ||||||||
\(66\) | 4325.26 | − | 11735.2i | 0.122223 | − | 0.331613i | ||||
\(67\) | −21728.8 | −0.591355 | −0.295677 | − | 0.955288i | \(-0.595545\pi\) | ||||
−0.295677 | + | 0.955288i | \(0.595545\pi\) | |||||||
\(68\) | 20966.4 | + | 17884.8i | 0.549859 | + | 0.469041i | ||||
\(69\) | − | 6199.52i | − | 0.156760i | ||||||
\(70\) | 11684.2 | − | 31701.4i | 0.285007 | − | 0.773274i | ||||
\(71\) | 2651.65 | 0.0624266 | 0.0312133 | − | 0.999513i | \(-0.490063\pi\) | ||||
0.0312133 | + | 0.999513i | \(0.490063\pi\) | |||||||
\(72\) | 16711.5 | + | 29776.4i | 0.379914 | + | 0.676925i | ||||
\(73\) | −46243.7 | −1.01565 | −0.507826 | − | 0.861460i | \(-0.669551\pi\) | ||||
−0.507826 | + | 0.861460i | \(0.669551\pi\) | |||||||
\(74\) | 8092.07 | − | 21955.2i | 0.171783 | − | 0.466078i | ||||
\(75\) | −17501.8 | −0.359276 | ||||||||
\(76\) | −29782.8 | + | 40601.8i | −0.591469 | + | 0.806328i | ||||
\(77\) | 24150.7 | 0.464197 | ||||||||
\(78\) | −6817.63 | + | 18497.5i | −0.126881 | + | 0.344251i | ||||
\(79\) | 75929.5 | 1.36881 | 0.684404 | − | 0.729103i | \(-0.260062\pi\) | ||||
0.684404 | + | 0.729103i | \(0.260062\pi\) | |||||||
\(80\) | 11970.3 | + | 74982.3i | 0.209112 | + | 1.30989i | ||||
\(81\) | 22368.4 | 0.378810 | ||||||||
\(82\) | 38447.2 | − | 104314.i | 0.631438 | − | 1.71320i | ||||
\(83\) | 35053.8i | 0.558522i | 0.960215 | + | 0.279261i | \(0.0900895\pi\) | ||||
−0.960215 | + | 0.279261i | \(0.909911\pi\) | |||||||
\(84\) | 12334.1 | − | 14459.3i | 0.190726 | − | 0.223589i | ||||
\(85\) | 63859.3 | 0.958687 | ||||||||
\(86\) | 23418.5 | − | 63538.4i | 0.341438 | − | 0.926383i | ||||
\(87\) | − | 38045.5i | − | 0.538896i | ||||||
\(88\) | −47331.9 | + | 26564.3i | −0.651549 | + | 0.365672i | ||||
\(89\) | 61381.1i | 0.821409i | 0.911768 | + | 0.410705i | \(0.134717\pi\) | ||||
−0.911768 | + | 0.410705i | \(0.865283\pi\) | |||||||
\(90\) | 74241.4 | + | 27363.2i | 0.966139 | + | 0.356091i | ||||
\(91\) | −38067.1 | −0.481888 | ||||||||
\(92\) | −17460.4 | + | 20468.9i | −0.215073 | + | 0.252130i | ||||
\(93\) | −25226.5 | −0.302448 | ||||||||
\(94\) | −30962.0 | + | 84005.5i | −0.361418 | + | 0.980591i | ||||
\(95\) | 8552.96 | + | 116369.i | 0.0972316 | + | 1.32290i | ||||
\(96\) | −8268.72 | + | 41905.1i | −0.0915715 | + | 0.464076i | ||||
\(97\) | − | 90996.6i | − | 0.981965i | −0.871169 | − | 0.490983i | \(-0.836638\pi\) | ||
0.871169 | − | 0.490983i | \(-0.163362\pi\) | |||||||
\(98\) | −54773.8 | − | 20188.1i | −0.576113 | − | 0.212339i | ||||
\(99\) | 56558.3i | 0.579974i | ||||||||
\(100\) | 57785.4 | + | 49292.2i | 0.577854 | + | 0.492922i | ||||
\(101\) | 105909. | 1.03307 | 0.516536 | − | 0.856265i | \(-0.327221\pi\) | ||||
0.516536 | + | 0.856265i | \(0.327221\pi\) | |||||||
\(102\) | 33705.6 | + | 12422.9i | 0.320776 | + | 0.118229i | ||||
\(103\) | −200157. | −1.85899 | −0.929497 | − | 0.368829i | \(-0.879759\pi\) | ||||
−0.929497 | + | 0.368829i | \(0.879759\pi\) | |||||||
\(104\) | 74606.2 | − | 41871.6i | 0.676381 | − | 0.379609i | ||||
\(105\) | − | 44040.2i | − | 0.389831i | ||||||
\(106\) | 9553.79 | − | 25921.1i | 0.0825869 | − | 0.224073i | ||||
\(107\) | 36092.6 | 0.304761 | 0.152380 | − | 0.988322i | \(-0.451306\pi\) | ||||
0.152380 | + | 0.988322i | \(0.451306\pi\) | |||||||
\(108\) | 77485.2 | + | 66096.5i | 0.639233 | + | 0.545280i | ||||
\(109\) | − | 239339.i | − | 1.92951i | −0.263145 | − | 0.964756i | \(-0.584760\pi\) | ||
0.263145 | − | 0.964756i | \(-0.415240\pi\) | |||||||
\(110\) | −43496.1 | + | 118013.i | −0.342743 | + | 0.929922i | ||||
\(111\) | − | 30500.6i | − | 0.234964i | ||||||
\(112\) | −81446.9 | + | 13002.3i | −0.613521 | + | 0.0979432i | ||||
\(113\) | − | 94952.4i | − | 0.699535i | −0.936836 | − | 0.349768i | \(-0.886261\pi\) | ||
0.936836 | − | 0.349768i | \(-0.113739\pi\) | |||||||
\(114\) | −18123.6 | + | 63084.7i | −0.130612 | + | 0.454634i | ||||
\(115\) | 62344.1i | 0.439593i | ||||||||
\(116\) | −107152. | + | 125615.i | −0.739358 | + | 0.866752i | ||||
\(117\) | − | 89149.2i | − | 0.602078i | ||||||
\(118\) | −166926. | − | 61524.2i | −1.10362 | − | 0.406763i | ||||
\(119\) | 69365.0i | 0.449028i | ||||||||
\(120\) | 48441.7 | + | 86312.6i | 0.307090 | + | 0.547169i | ||||
\(121\) | 71147.0 | 0.441767 | ||||||||
\(122\) | 156058. | + | 57518.7i | 0.949266 | + | 0.349872i | ||||
\(123\) | − | 144915.i | − | 0.863677i | ||||||
\(124\) | 83290.2 | + | 71048.3i | 0.486452 | + | 0.414954i | ||||
\(125\) | −55722.7 | −0.318975 | ||||||||
\(126\) | −29722.4 | + | 80642.1i | −0.166785 | + | 0.452518i | ||||
\(127\) | −287732. | −1.58299 | −0.791496 | − | 0.611174i | \(-0.790698\pi\) | ||||
−0.791496 | + | 0.611174i | \(0.790698\pi\) | |||||||
\(128\) | 145323. | − | 115070.i | 0.783987 | − | 0.620777i | ||||
\(129\) | − | 88268.8i | − | 0.467017i | ||||||
\(130\) | 68560.0 | − | 186016.i | 0.355805 | − | 0.965364i | ||||
\(131\) | − | 321.169i | − | 0.00163514i | −1.00000 | 0.000817572i | \(-0.999740\pi\) | |||
1.00000 | 0.000817572i | \(-0.000260241\pi\) | ||||||||
\(132\) | −45915.4 | + | 53826.8i | −0.229363 | + | 0.268883i | ||||
\(133\) | −126402. | + | 9290.36i | −0.619619 | + | 0.0455411i | ||||
\(134\) | 115332. | + | 42508.2i | 0.554867 | + | 0.204508i | ||||
\(135\) | 236004. | 1.11451 | ||||||||
\(136\) | −76297.5 | − | 135946.i | −0.353723 | − | 0.630258i | ||||
\(137\) | −44552.3 | −0.202800 | −0.101400 | − | 0.994846i | \(-0.532332\pi\) | ||||
−0.101400 | + | 0.994846i | \(0.532332\pi\) | |||||||
\(138\) | −12128.2 | + | 32905.9i | −0.0542123 | + | 0.147088i | ||||
\(139\) | − | 364472.i | − | 1.60002i | −0.599984 | − | 0.800012i | \(-0.704826\pi\) | ||
0.599984 | − | 0.800012i | \(-0.295174\pi\) | |||||||
\(140\) | −124035. | + | 145407.i | −0.534842 | + | 0.626997i | ||||
\(141\) | 116702.i | 0.494346i | ||||||||
\(142\) | −14074.4 | − | 5187.43i | −0.0585747 | − | 0.0215890i | ||||
\(143\) | 141710. | 0.579508 | ||||||||
\(144\) | −30450.0 | − | 190740.i | −0.122372 | − | 0.766542i | ||||
\(145\) | 382596.i | 1.51120i | ||||||||
\(146\) | 245453. | + | 90466.8i | 0.952984 | + | 0.351243i | ||||
\(147\) | −76092.8 | −0.290436 | ||||||||
\(148\) | −85902.3 | + | 100704.i | −0.322367 | + | 0.377912i | ||||
\(149\) | 40734.1 | 0.150312 | 0.0751558 | − | 0.997172i | \(-0.476055\pi\) | ||||
0.0751558 | + | 0.997172i | \(0.476055\pi\) | |||||||
\(150\) | 92896.1 | + | 34238.8i | 0.337108 | + | 0.124248i | ||||
\(151\) | 311478. | 1.11169 | 0.555846 | − | 0.831285i | \(-0.312394\pi\) | ||||
0.555846 | + | 0.831285i | \(0.312394\pi\) | |||||||
\(152\) | 237511. | − | 157243.i | 0.833825 | − | 0.552028i | ||||
\(153\) | −162446. | −0.561021 | ||||||||
\(154\) | −128187. | − | 47246.1i | −0.435555 | − | 0.160533i | ||||
\(155\) | 253685. | 0.848136 | ||||||||
\(156\) | 72373.4 | − | 84843.6i | 0.238104 | − | 0.279131i | ||||
\(157\) | −113376. | −0.367090 | −0.183545 | − | 0.983011i | \(-0.558757\pi\) | ||||
−0.183545 | + | 0.983011i | \(0.558757\pi\) | |||||||
\(158\) | −403019. | − | 148541.i | −1.28435 | − | 0.473374i | ||||
\(159\) | − | 36010.1i | − | 0.112962i | ||||||
\(160\) | 83152.6 | − | 421409.i | 0.256789 | − | 1.30138i | ||||
\(161\) | −67719.2 | −0.205896 | ||||||||
\(162\) | −118727. | − | 43759.4i | −0.355436 | − | 0.131004i | ||||
\(163\) | 90072.7i | 0.265536i | 0.991147 | + | 0.132768i | \(0.0423866\pi\) | ||||
−0.991147 | + | 0.132768i | \(0.957613\pi\) | |||||||
\(164\) | −408141. | + | 478465.i | −1.18495 | + | 1.38912i | ||||
\(165\) | 163945.i | 0.468802i | ||||||||
\(166\) | 68576.1 | − | 186059.i | 0.193153 | − | 0.524060i | ||||
\(167\) | −513808. | −1.42564 | −0.712820 | − | 0.701347i | \(-0.752582\pi\) | ||||
−0.712820 | + | 0.701347i | \(0.752582\pi\) | |||||||
\(168\) | −93754.1 | + | 52618.1i | −0.256281 | + | 0.143834i | ||||
\(169\) | 147925. | 0.398406 | ||||||||
\(170\) | −338953. | − | 124928.i | −0.899534 | − | 0.331542i | ||||
\(171\) | −21757.1 | − | 296020.i | −0.0568997 | − | 0.774160i | ||||
\(172\) | −248601. | + | 291436.i | −0.640741 | + | 0.751143i | ||||
\(173\) | − | 677354.i | − | 1.72068i | −0.509719 | − | 0.860341i | \(-0.670251\pi\) | ||
0.509719 | − | 0.860341i | \(-0.329749\pi\) | |||||||
\(174\) | −74428.7 | + | 201938.i | −0.186366 | + | 0.505645i | ||||
\(175\) | 191177.i | 0.471889i | ||||||||
\(176\) | 303197. | − | 48402.7i | 0.737807 | − | 0.117784i | ||||
\(177\) | −231897. | −0.556368 | ||||||||
\(178\) | 120080. | − | 325799.i | 0.284068 | − | 0.770726i | ||||
\(179\) | −389094. | −0.907657 | −0.453828 | − | 0.891089i | \(-0.649942\pi\) | ||||
−0.453828 | + | 0.891089i | \(0.649942\pi\) | |||||||
\(180\) | −340528. | − | 290478.i | −0.783379 | − | 0.668239i | ||||
\(181\) | − | 112470.i | − | 0.255176i | −0.991827 | − | 0.127588i | \(-0.959276\pi\) | ||
0.991827 | − | 0.127588i | \(-0.0407235\pi\) | |||||||
\(182\) | 202053. | + | 74471.0i | 0.452154 | + | 0.166651i | ||||
\(183\) | 216799. | 0.478553 | ||||||||
\(184\) | 132720. | − | 74487.2i | 0.288996 | − | 0.162195i | ||||
\(185\) | 306723.i | 0.658896i | ||||||||
\(186\) | 133898. | + | 49350.8i | 0.283786 | + | 0.104595i | ||||
\(187\) | − | 258220.i | − | 0.539991i | ||||||
\(188\) | 328681. | − | 385314.i | 0.678235 | − | 0.795097i | ||||
\(189\) | 256351.i | 0.522013i | ||||||||
\(190\) | 182256. | − | 634397.i | 0.366267 | − | 1.27490i | ||||
\(191\) | 579910.i | 1.15021i | 0.818080 | + | 0.575105i | \(0.195039\pi\) | ||||
−0.818080 | + | 0.575105i | \(0.804961\pi\) | |||||||
\(192\) | 125868. | − | 206248.i | 0.246412 | − | 0.403773i | ||||
\(193\) | 214903.i | 0.415287i | 0.978205 | + | 0.207644i | \(0.0665794\pi\) | ||||
−0.978205 | + | 0.207644i | \(0.933421\pi\) | |||||||
\(194\) | −178017. | + | 482993.i | −0.339593 | + | 0.921375i | ||||
\(195\) | − | 258416.i | − | 0.486669i | ||||||
\(196\) | 251235. | + | 214309.i | 0.467133 | + | 0.398474i | ||||
\(197\) | 753104. | 1.38258 | 0.691288 | − | 0.722579i | \(-0.257043\pi\) | ||||
0.691288 | + | 0.722579i | \(0.257043\pi\) | |||||||
\(198\) | 110645. | − | 300201.i | 0.200572 | − | 0.544188i | ||||
\(199\) | 848329.i | 1.51856i | 0.650765 | + | 0.759279i | \(0.274448\pi\) | ||||
−0.650765 | + | 0.759279i | \(0.725552\pi\) | |||||||
\(200\) | −210283. | − | 374680.i | −0.371732 | − | 0.662347i | ||||
\(201\) | 160222. | 0.279725 | ||||||||
\(202\) | −562147. | − | 207191.i | −0.969330 | − | 0.357267i | ||||
\(203\) | −415582. | −0.707810 | ||||||||
\(204\) | −154600. | − | 131877.i | −0.260096 | − | 0.221868i | ||||
\(205\) | 1.45731e6i | 2.42196i | ||||||||
\(206\) | 1.06240e6 | + | 391569.i | 1.74429 | + | 0.642895i | ||||
\(207\) | − | 158591.i | − | 0.257249i | ||||||
\(208\) | −477909. | + | 76294.0i | −0.765927 | + | 0.122273i | ||||
\(209\) | 470548. | − | 34584.6i | 0.745140 | − | 0.0547667i | ||||
\(210\) | −86156.2 | + | 233757.i | −0.134815 | + | 0.365777i | ||||
\(211\) | 1.02977e6 | 1.59233 | 0.796165 | − | 0.605080i | \(-0.206859\pi\) | ||||
0.796165 | + | 0.605080i | \(0.206859\pi\) | |||||||
\(212\) | −101419. | + | 118894.i | −0.154982 | + | 0.181686i | ||||
\(213\) | −19552.5 | −0.0295293 | ||||||||
\(214\) | −191573. | − | 70608.2i | −0.285956 | − | 0.105395i | ||||
\(215\) | 887656.i | 1.30963i | ||||||||
\(216\) | −281972. | − | 502413.i | −0.411217 | − | 0.732700i | ||||
\(217\) | 275557.i | 0.397248i | ||||||||
\(218\) | −468221. | + | 1.27037e6i | −0.667283 | + | 1.81046i | ||||
\(219\) | 340987. | 0.480428 | ||||||||
\(220\) | 461738. | − | 541297.i | 0.643189 | − | 0.754013i | ||||
\(221\) | 407016.i | 0.560571i | ||||||||
\(222\) | −59668.6 | + | 161891.i | −0.0812575 | + | 0.220466i | ||||
\(223\) | 953172. | 1.28354 | 0.641769 | − | 0.766898i | \(-0.278201\pi\) | ||||
0.641769 | + | 0.766898i | \(0.278201\pi\) | |||||||
\(224\) | 457741. | + | 90321.6i | 0.609537 | + | 0.120274i | ||||
\(225\) | −447716. | −0.589585 | ||||||||
\(226\) | −185756. | + | 503989.i | −0.241920 | + | 0.656372i | ||||
\(227\) | 644020. | 0.829535 | 0.414767 | − | 0.909927i | \(-0.363863\pi\) | ||||
0.414767 | + | 0.909927i | \(0.363863\pi\) | |||||||
\(228\) | 219610. | − | 299386.i | 0.279779 | − | 0.381412i | ||||
\(229\) | −1.08188e6 | −1.36330 | −0.681648 | − | 0.731680i | \(-0.738737\pi\) | ||||
−0.681648 | + | 0.731680i | \(0.738737\pi\) | |||||||
\(230\) | 121964. | − | 330911.i | 0.152024 | − | 0.412469i | ||||
\(231\) | −178080. | −0.219576 | ||||||||
\(232\) | 814483. | − | 457116.i | 0.993486 | − | 0.557579i | ||||
\(233\) | 554996. | 0.669731 | 0.334865 | − | 0.942266i | \(-0.391309\pi\) | ||||
0.334865 | + | 0.942266i | \(0.391309\pi\) | |||||||
\(234\) | −174403. | + | 473187.i | −0.208216 | + | 0.564928i | ||||
\(235\) | − | 1.17359e6i | − | 1.38626i | ||||||
\(236\) | 765652. | + | 653118.i | 0.894853 | + | 0.763329i | ||||
\(237\) | −559882. | −0.647479 | ||||||||
\(238\) | 135699. | − | 368176.i | 0.155287 | − | 0.421321i | ||||
\(239\) | − | 131718.i | − | 0.149159i | −0.997215 | − | 0.0745795i | \(-0.976239\pi\) | ||
0.997215 | − | 0.0745795i | \(-0.0237614\pi\) | |||||||
\(240\) | −88265.2 | − | 552898.i | −0.0989148 | − | 0.619608i | ||||
\(241\) | 635781.i | 0.705123i | 0.935789 | + | 0.352562i | \(0.114689\pi\) | ||||
−0.935789 | + | 0.352562i | \(0.885311\pi\) | |||||||
\(242\) | −377635. | − | 139185.i | −0.414509 | − | 0.152776i | ||||
\(243\) | −938335. | −1.01939 | ||||||||
\(244\) | −715805. | − | 610597.i | −0.769697 | − | 0.656568i | ||||
\(245\) | 765211. | 0.814453 | ||||||||
\(246\) | −283499. | + | 769183.i | −0.298685 | + | 0.810386i | ||||
\(247\) | −741693. | + | 54513.4i | −0.773539 | + | 0.0568540i | ||||
\(248\) | −303096. | − | 540052.i | −0.312933 | − | 0.557579i | ||||
\(249\) | − | 258477.i | − | 0.264194i | ||||||
\(250\) | 295766. | + | 109011.i | 0.299294 | + | 0.110311i | ||||
\(251\) | − | 450280.i | − | 0.451126i | −0.974229 | − | 0.225563i | \(-0.927578\pi\) | ||
0.974229 | − | 0.225563i | \(-0.0724222\pi\) | |||||||
\(252\) | 315522. | − | 369887.i | 0.312988 | − | 0.366917i | ||||
\(253\) | 252093. | 0.247605 | ||||||||
\(254\) | 1.52723e6 | + | 562892.i | 1.48532 | + | 0.547446i | ||||
\(255\) | −470880. | −0.453482 | ||||||||
\(256\) | −996458. | + | 326471.i | −0.950296 | + | 0.311347i | ||||
\(257\) | − | 2.04006e6i | − | 1.92668i | −0.268285 | − | 0.963340i | \(-0.586457\pi\) | ||
0.268285 | − | 0.963340i | \(-0.413543\pi\) | |||||||
\(258\) | −172681. | + | 468514.i | −0.161508 | + | 0.438201i | ||||
\(259\) | −333167. | −0.308612 | ||||||||
\(260\) | −727807. | + | 853211.i | −0.667703 | + | 0.782750i | ||||
\(261\) | − | 973250.i | − | 0.884348i | ||||||
\(262\) | −628.306 | + | 1704.71i | −0.000565481 | + | 0.00153425i | ||||
\(263\) | 1.56262e6i | 1.39304i | 0.717539 | + | 0.696518i | \(0.245269\pi\) | ||||
−0.717539 | + | 0.696518i | \(0.754731\pi\) | |||||||
\(264\) | 349012. | − | 195878.i | 0.308198 | − | 0.172972i | ||||
\(265\) | 362128.i | 0.316772i | ||||||||
\(266\) | 689092. | + | 197970.i | 0.597136 | + | 0.171551i | ||||
\(267\) | − | 452606.i | − | 0.388546i | ||||||
\(268\) | −529003. | − | 451251.i | −0.449905 | − | 0.383779i | ||||
\(269\) | − | 688832.i | − | 0.580407i | −0.956965 | − | 0.290203i | \(-0.906277\pi\) | ||
0.956965 | − | 0.290203i | \(-0.0937230\pi\) | |||||||
\(270\) | −1.25267e6 | − | 461697.i | −1.04574 | − | 0.385432i | ||||
\(271\) | − | 1.09484e6i | − | 0.905580i | −0.891617 | − | 0.452790i | \(-0.850429\pi\) | ||
0.891617 | − | 0.452790i | \(-0.149571\pi\) | |||||||
\(272\) | 139021. | + | 870835.i | 0.113935 | + | 0.713697i | ||||
\(273\) | 280696. | 0.227945 | ||||||||
\(274\) | 236475. | + | 87157.9i | 0.190287 | + | 0.0701343i | ||||
\(275\) | − | 711680.i | − | 0.567484i | ||||||
\(276\) | 128748. | − | 150932.i | 0.101734 | − | 0.119264i | ||||
\(277\) | −855408. | −0.669844 | −0.334922 | − | 0.942246i | \(-0.608710\pi\) | ||||
−0.334922 | + | 0.942246i | \(0.608710\pi\) | |||||||
\(278\) | −713018. | + | 1.93455e6i | −0.553336 | + | 1.50130i | ||||
\(279\) | −645325. | −0.496327 | ||||||||
\(280\) | 942817. | − | 529142.i | 0.718675 | − | 0.403346i | ||||
\(281\) | − | 672672.i | − | 0.508204i | −0.967177 | − | 0.254102i | \(-0.918220\pi\) | ||
0.967177 | − | 0.254102i | \(-0.0817798\pi\) | |||||||
\(282\) | 228305. | − | 619432.i | 0.170959 | − | 0.463843i | ||||
\(283\) | − | 530064.i | − | 0.393425i | −0.980461 | − | 0.196713i | \(-0.936973\pi\) | ||
0.980461 | − | 0.196713i | \(-0.0630266\pi\) | |||||||
\(284\) | 64556.2 | + | 55067.8i | 0.0474944 | + | 0.0405137i | ||||
\(285\) | −63067.1 | − | 858072.i | −0.0459929 | − | 0.625766i | ||||
\(286\) | −752169. | − | 277228.i | −0.543751 | − | 0.200411i | ||||
\(287\) | −1.58295e6 | −1.13439 | ||||||||
\(288\) | −211524. | + | 1.07198e6i | −0.150272 | + | 0.761564i | ||||
\(289\) | −678202. | −0.477655 | ||||||||
\(290\) | 748476. | − | 2.03075e6i | 0.522616 | − | 1.41795i | ||||
\(291\) | 670983.i | 0.464493i | ||||||||
\(292\) | −1.12584e6 | − | 960361.i | −0.772712 | − | 0.659140i | ||||
\(293\) | − | 345695.i | − | 0.235247i | −0.993058 | − | 0.117623i | \(-0.962472\pi\) | ||
0.993058 | − | 0.117623i | \(-0.0375276\pi\) | |||||||
\(294\) | 403886. | + | 148861.i | 0.272515 | + | 0.100441i | ||||
\(295\) | 2.33202e6 | 1.56019 | ||||||||
\(296\) | 652961. | − | 366464.i | 0.433169 | − | 0.243110i | ||||
\(297\) | − | 954301.i | − | 0.627761i | ||||||
\(298\) | −216209. | − | 79688.4i | −0.141037 | − | 0.0519822i | ||||
\(299\) | −397358. | −0.257042 | ||||||||
\(300\) | −426093. | − | 363467.i | −0.273339 | − | 0.233164i | ||||
\(301\) | −964186. | −0.613401 | ||||||||
\(302\) | −1.65327e6 | − | 609346.i | −1.04310 | − | 0.384456i | ||||
\(303\) | −780945. | −0.488668 | ||||||||
\(304\) | −1.56828e6 | + | 369969.i | −0.973284 | + | 0.229605i | ||||
\(305\) | −2.18020e6 | −1.34198 | ||||||||
\(306\) | 862230. | + | 317793.i | 0.526405 | + | 0.194018i | ||||
\(307\) | 120422. | 0.0729225 | 0.0364612 | − | 0.999335i | \(-0.488391\pi\) | ||||
0.0364612 | + | 0.999335i | \(0.488391\pi\) | |||||||
\(308\) | 587965. | + | 501547.i | 0.353163 | + | 0.301255i | ||||
\(309\) | 1.47590e6 | 0.879349 | ||||||||
\(310\) | −1.34651e6 | − | 496286.i | −0.795804 | − | 0.293311i | ||||
\(311\) | − | 932903.i | − | 0.546935i | −0.961881 | − | 0.273467i | \(-0.911829\pi\) | ||
0.961881 | − | 0.273467i | \(-0.0881705\pi\) | |||||||
\(312\) | −550125. | + | 308749.i | −0.319944 | + | 0.179564i | ||||
\(313\) | 1.41695e6 | 0.817509 | 0.408754 | − | 0.912644i | \(-0.365963\pi\) | ||||
0.408754 | + | 0.912644i | \(0.365963\pi\) | |||||||
\(314\) | 601779. | + | 221799.i | 0.344440 | + | 0.126951i | ||||
\(315\) | − | 1.12660e6i | − | 0.639725i | ||||||
\(316\) | 1.84856e6 | + | 1.57686e6i | 1.04139 | + | 0.888332i | ||||
\(317\) | 1.50073e6i | 0.838790i | 0.907804 | + | 0.419395i | \(0.137758\pi\) | ||||
−0.907804 | + | 0.419395i | \(0.862242\pi\) | |||||||
\(318\) | −70446.9 | + | 191135.i | −0.0390656 | + | 0.105992i | ||||
\(319\) | 1.54706e6 | 0.851197 | ||||||||
\(320\) | −1.26576e6 | + | 2.07409e6i | −0.691000 | + | 1.13228i | ||||
\(321\) | −266137. | −0.144159 | ||||||||
\(322\) | 359441. | + | 132480.i | 0.193191 | + | 0.0712048i | ||||
\(323\) | 99333.1 | + | 1.35150e6i | 0.0529770 | + | 0.720790i | ||||
\(324\) | 544574. | + | 464533.i | 0.288200 | + | 0.245841i | ||||
\(325\) | 1.12178e6i | 0.589112i | ||||||||
\(326\) | 176210. | − | 478089.i | 0.0918303 | − | 0.249152i | ||||
\(327\) | 1.76482e6i | 0.912706i | ||||||||
\(328\) | 3.10236e6 | − | 1.74115e6i | 1.59224 | − | 0.893620i | ||||
\(329\) | 1.27477e6 | 0.649295 | ||||||||
\(330\) | 320728. | − | 870191.i | 0.162126 | − | 0.439875i | ||||
\(331\) | 566817. | 0.284363 | 0.142181 | − | 0.989841i | \(-0.454588\pi\) | ||||
0.142181 | + | 0.989841i | \(0.454588\pi\) | |||||||
\(332\) | −727978. | + | 853411.i | −0.362471 | + | 0.424926i | ||||
\(333\) | − | 780242.i | − | 0.385584i | ||||||
\(334\) | 2.72720e6 | + | 1.00517e6i | 1.33767 | + | 0.493029i | ||||
\(335\) | −1.61123e6 | −0.784416 | ||||||||
\(336\) | 600566. | − | 95875.0i | 0.290210 | − | 0.0463295i | ||||
\(337\) | − | 682903.i | − | 0.327555i | −0.986497 | − | 0.163778i | \(-0.947632\pi\) | ||
0.986497 | − | 0.163778i | \(-0.0523680\pi\) | |||||||
\(338\) | −785159. | − | 289387.i | −0.373823 | − | 0.137780i | ||||
\(339\) | 700151.i | 0.330897i | ||||||||
\(340\) | 1.55470e6 | + | 1.32619e6i | 0.729373 | + | 0.622171i | ||||
\(341\) | − | 1.02580e6i | − | 0.477721i | ||||||
\(342\) | −463624. | + | 1.61378e6i | −0.214339 | + | 0.746070i | ||||
\(343\) | 2.18491e6i | 1.00276i | ||||||||
\(344\) | 1.88967e6 | − | 1.06055e6i | 0.860973 | − | 0.483208i | ||||
\(345\) | − | 459708.i | − | 0.207938i | ||||||
\(346\) | −1.32511e6 | + | 3.59527e6i | −0.595063 | + | 1.61451i | ||||
\(347\) | − | 2.93498e6i | − | 1.30852i | −0.756268 | − | 0.654262i | \(-0.772979\pi\) | ||
0.756268 | − | 0.654262i | \(-0.227021\pi\) | |||||||
\(348\) | 790107. | − | 926246.i | 0.349734 | − | 0.409994i | ||||
\(349\) | 3.80401e6 | 1.67178 | 0.835888 | − | 0.548900i | \(-0.184953\pi\) | ||||
0.835888 | + | 0.548900i | \(0.184953\pi\) | |||||||
\(350\) | 374001. | − | 1.01473e6i | 0.163193 | − | 0.442772i | ||||
\(351\) | 1.50420e6i | 0.651686i | ||||||||
\(352\) | −1.70400e6 | − | 336234.i | −0.733016 | − | 0.144639i | ||||
\(353\) | 2.67782e6 | 1.14378 | 0.571892 | − | 0.820329i | \(-0.306210\pi\) | ||||
0.571892 | + | 0.820329i | \(0.306210\pi\) | |||||||
\(354\) | 1.23087e6 | + | 453662.i | 0.522038 | + | 0.192408i | ||||
\(355\) | 196625. | 0.0828072 | ||||||||
\(356\) | −1.27473e6 | + | 1.49437e6i | −0.533080 | + | 0.624931i | ||||
\(357\) | − | 511478.i | − | 0.212401i | ||||||
\(358\) | 2.06524e6 | + | 761187.i | 0.851652 | + | 0.313895i | ||||
\(359\) | 1.10297e6i | 0.451675i | 0.974165 | + | 0.225838i | \(0.0725119\pi\) | ||||
−0.974165 | + | 0.225838i | \(0.927488\pi\) | |||||||
\(360\) | 1.23920e6 | + | 2.20798e6i | 0.503946 | + | 0.897923i | ||||
\(361\) | −2.44949e6 | + | 362024.i | −0.989254 | + | 0.146207i | ||||
\(362\) | −220026. | + | 596969.i | −0.0882475 | + | 0.239431i | ||||
\(363\) | −524618. | −0.208966 | ||||||||
\(364\) | −926771. | − | 790556.i | −0.366622 | − | 0.312737i | ||||
\(365\) | −3.42906e6 | −1.34724 | ||||||||
\(366\) | −1.15073e6 | − | 424126.i | −0.449025 | − | 0.165498i | ||||
\(367\) | − | 1.68764e6i | − | 0.654055i | −0.945015 | − | 0.327028i | \(-0.893953\pi\) | ||
0.945015 | − | 0.327028i | \(-0.106047\pi\) | |||||||
\(368\) | −850173. | + | 135723.i | −0.327256 | + | 0.0522435i | ||||
\(369\) | − | 3.70711e6i | − | 1.41732i | ||||||
\(370\) | 600044. | − | 1.62803e6i | 0.227866 | − | 0.618240i | ||||
\(371\) | −393349. | −0.148369 | ||||||||
\(372\) | −614158. | − | 523890.i | −0.230103 | − | 0.196283i | ||||
\(373\) | 2.23384e6i | 0.831343i | 0.909515 | + | 0.415671i | \(0.136453\pi\) | ||||
−0.909515 | + | 0.415671i | \(0.863547\pi\) | |||||||
\(374\) | −505158. | + | 1.37058e6i | −0.186745 | + | 0.506672i | ||||
\(375\) | 410883. | 0.150883 | ||||||||
\(376\) | −2.49837e6 | + | 1.40217e6i | −0.911354 | + | 0.511484i | ||||
\(377\) | −2.43853e6 | −0.883638 | ||||||||
\(378\) | 501502. | − | 1.36066e6i | 0.180527 | − | 0.489803i | ||||
\(379\) | −5.05682e6 | −1.80834 | −0.904170 | − | 0.427174i | \(-0.859509\pi\) | ||||
−0.904170 | + | 0.427174i | \(0.859509\pi\) | |||||||
\(380\) | −2.20846e6 | + | 3.01071e6i | −0.784567 | + | 1.06957i | ||||
\(381\) | 2.12165e6 | 0.748793 | ||||||||
\(382\) | 1.13448e6 | − | 3.07805e6i | 0.397777 | − | 1.07924i | ||||
\(383\) | 147080. | 0.0512339 | 0.0256169 | − | 0.999672i | \(-0.491845\pi\) | ||||
0.0256169 | + | 0.999672i | \(0.491845\pi\) | |||||||
\(384\) | −1.07157e6 | + | 848490.i | −0.370845 | + | 0.293642i | ||||
\(385\) | 1.79082e6 | 0.615745 | ||||||||
\(386\) | 420416. | − | 1.14066e6i | 0.143619 | − | 0.389663i | ||||
\(387\) | − | 2.25802e6i | − | 0.766392i | ||||||
\(388\) | 1.88977e6 | − | 2.21538e6i | 0.637278 | − | 0.747083i | ||||
\(389\) | −1.65969e6 | −0.556102 | −0.278051 | − | 0.960566i | \(-0.589688\pi\) | ||||
−0.278051 | + | 0.960566i | \(0.589688\pi\) | |||||||
\(390\) | −505542. | + | 1.37163e6i | −0.168304 | + | 0.456640i | ||||
\(391\) | 724057.i | 0.239514i | ||||||||
\(392\) | −914254. | − | 1.62900e6i | −0.300505 | − | 0.535435i | ||||
\(393\) | 2368.21i | 0.000773462i | ||||||||
\(394\) | −3.99733e6 | − | 1.47330e6i | −1.29727 | − | 0.478136i | ||||
\(395\) | 5.63033e6 | 1.81569 | ||||||||
\(396\) | −1.17457e6 | + | 1.37695e6i | −0.376393 | + | 0.441246i | ||||
\(397\) | 380495. | 0.121164 | 0.0605819 | − | 0.998163i | \(-0.480704\pi\) | ||||
0.0605819 | + | 0.998163i | \(0.480704\pi\) | |||||||
\(398\) | 1.65959e6 | − | 4.50277e6i | 0.525162 | − | 1.42486i | ||||
\(399\) | 932051. | − | 68504.5i | 0.293094 | − | 0.0215420i | ||||
\(400\) | 383156. | + | 2.40011e6i | 0.119736 | + | 0.750034i | ||||
\(401\) | 3.81805e6i | 1.18572i | 0.805307 | + | 0.592859i | \(0.202001\pi\) | ||||
−0.805307 | + | 0.592859i | \(0.797999\pi\) | |||||||
\(402\) | −850427. | − | 313443.i | −0.262465 | − | 0.0967372i | ||||
\(403\) | 1.61689e6i | 0.495928i | ||||||||
\(404\) | 2.57844e6 | + | 2.19946e6i | 0.785966 | + | 0.670446i | ||||
\(405\) | 1.65866e6 | 0.502481 | ||||||||
\(406\) | 2.20583e6 | + | 813006.i | 0.664136 | + | 0.244782i | ||||
\(407\) | 1.24026e6 | 0.371130 | ||||||||
\(408\) | 562596. | + | 1.00242e6i | 0.167319 | + | 0.298127i | ||||
\(409\) | 6.20250e6i | 1.83341i | 0.399569 | + | 0.916703i | \(0.369160\pi\) | ||||
−0.399569 | + | 0.916703i | \(0.630840\pi\) | |||||||
\(410\) | 2.85094e6 | − | 7.73512e6i | 0.837585 | − | 2.27252i | ||||
\(411\) | 328515. | 0.0959293 | ||||||||
\(412\) | −4.87297e6 | − | 4.15675e6i | −1.41433 | − | 1.20645i | ||||
\(413\) | 2.53308e6i | 0.730758i | ||||||||
\(414\) | −310253. | + | 841772.i | −0.0889642 | + | 0.241376i | ||||
\(415\) | 2.59932e6i | 0.740865i | ||||||||
\(416\) | 2.68591e6 | + | 529984.i | 0.760953 | + | 0.150151i | ||||
\(417\) | 2.68751e6i | 0.756850i | ||||||||
\(418\) | −2.56524e6 | − | 736967.i | −0.718103 | − | 0.206304i | ||||
\(419\) | 1.54034e6i | 0.428629i | 0.976765 | + | 0.214314i | \(0.0687517\pi\) | ||||
−0.976765 | + | 0.214314i | \(0.931248\pi\) | |||||||
\(420\) | 914601. | − | 1.07219e6i | 0.252993 | − | 0.296585i | ||||
\(421\) | 1.41317e6i | 0.388588i | 0.980943 | + | 0.194294i | \(0.0622416\pi\) | ||||
−0.980943 | + | 0.194294i | \(0.937758\pi\) | |||||||
\(422\) | −5.46581e6 | − | 2.01454e6i | −1.49408 | − | 0.550675i | ||||
\(423\) | 2.98538e6i | 0.811238i | ||||||||
\(424\) | 770909. | − | 432661.i | 0.208252 | − | 0.116878i | ||||
\(425\) | 2.04407e6 | 0.548939 | ||||||||
\(426\) | 103781. | + | 38250.6i | 0.0277072 | + | 0.0102121i | ||||
\(427\) | − | 2.36816e6i | − | 0.628553i | ||||||
\(428\) | 878701. | + | 749550.i | 0.231863 | + | 0.197784i | ||||
\(429\) | −1.04493e6 | −0.274121 | ||||||||
\(430\) | 1.73653e6 | − | 4.71151e6i | 0.452909 | − | 1.22882i | ||||
\(431\) | 3.79553e6 | 0.984192 | 0.492096 | − | 0.870541i | \(-0.336231\pi\) | ||||
0.492096 | + | 0.870541i | \(0.336231\pi\) | |||||||
\(432\) | 513779. | + | 3.21834e6i | 0.132454 | + | 0.829702i | ||||
\(433\) | − | 113030.i | − | 0.0289717i | −0.999895 | − | 0.0144858i | \(-0.995389\pi\) | ||
0.999895 | − | 0.0144858i | \(-0.00461115\pi\) | |||||||
\(434\) | 539073. | − | 1.46260e6i | 0.137380 | − | 0.372737i | ||||
\(435\) | − | 2.82116e6i | − | 0.714832i | ||||||
\(436\) | 4.97046e6 | − | 5.82689e6i | 1.25222 | − | 1.46798i | ||||
\(437\) | −1.31943e6 | + | 96976.2i | −0.330509 | + | 0.0242919i | ||||
\(438\) | −1.80990e6 | − | 667076.i | −0.450784 | − | 0.166146i | ||||
\(439\) | −5.89472e6 | −1.45983 | −0.729914 | − | 0.683539i | \(-0.760440\pi\) | ||||
−0.729914 | + | 0.683539i | \(0.760440\pi\) | |||||||
\(440\) | −3.50976e6 | + | 1.96980e6i | −0.864263 | + | 0.485055i | ||||
\(441\) | −1.94655e6 | −0.476615 | ||||||||
\(442\) | 796248. | − | 2.16036e6i | 0.193862 | − | 0.525982i | ||||
\(443\) | − | 6.87826e6i | − | 1.66521i | −0.553866 | − | 0.832606i | \(-0.686848\pi\) | ||
0.553866 | − | 0.832606i | \(-0.313152\pi\) | |||||||
\(444\) | 633419. | − | 742559.i | 0.152487 | − | 0.178761i | ||||
\(445\) | 4.55154e6i | 1.08958i | ||||||||
\(446\) | −5.05926e6 | − | 1.86470e6i | −1.20434 | − | 0.443886i | ||||
\(447\) | −300362. | −0.0711010 | ||||||||
\(448\) | −2.25291e6 | − | 1.37489e6i | −0.530333 | − | 0.323649i | ||||
\(449\) | − | 3.64357e6i | − | 0.852926i | −0.904505 | − | 0.426463i | \(-0.859759\pi\) | ||
0.904505 | − | 0.426463i | \(-0.140241\pi\) | |||||||
\(450\) | 2.37639e6 | + | 875870.i | 0.553206 | + | 0.203896i | ||||
\(451\) | 5.89274e6 | 1.36419 | ||||||||
\(452\) | 1.97192e6 | − | 2.31168e6i | 0.453986 | − | 0.532209i | ||||
\(453\) | −2.29675e6 | −0.525857 | ||||||||
\(454\) | −3.41834e6 | − | 1.25990e6i | −0.778350 | − | 0.286878i | ||||
\(455\) | −2.82276e6 | −0.639212 | ||||||||
\(456\) | −1.75134e6 | + | 1.15946e6i | −0.394419 | + | 0.261123i | ||||
\(457\) | −6.59770e6 | −1.47775 | −0.738876 | − | 0.673841i | \(-0.764643\pi\) | ||||
−0.738876 | + | 0.673841i | \(0.764643\pi\) | |||||||
\(458\) | 5.74241e6 | + | 2.11649e6i | 1.27918 | + | 0.471468i | ||||
\(459\) | 2.74092e6 | 0.607247 | ||||||||
\(460\) | −1.29473e6 | + | 1.51781e6i | −0.285288 | + | 0.334444i | ||||
\(461\) | 989844. | 0.216927 | 0.108464 | − | 0.994100i | \(-0.465407\pi\) | ||||
0.108464 | + | 0.994100i | \(0.465407\pi\) | |||||||
\(462\) | 945215. | + | 348379.i | 0.206028 | + | 0.0759359i | ||||
\(463\) | 1.18817e6i | 0.257589i | 0.991671 | + | 0.128795i | \(0.0411108\pi\) | ||||
−0.991671 | + | 0.128795i | \(0.958889\pi\) | |||||||
\(464\) | −5.21738e6 | + | 832908.i | −1.12501 | + | 0.179598i | ||||
\(465\) | −1.87060e6 | −0.401189 | ||||||||
\(466\) | −2.94581e6 | − | 1.08574e6i | −0.628407 | − | 0.231613i | ||||
\(467\) | − | 7.10061e6i | − | 1.50662i | −0.657666 | − | 0.753310i | \(-0.728456\pi\) | ||
0.657666 | − | 0.753310i | \(-0.271544\pi\) | |||||||
\(468\) | 1.85140e6 | − | 2.17040e6i | 0.390738 | − | 0.458063i | ||||
\(469\) | − | 1.75015e6i | − | 0.367403i | ||||||
\(470\) | −2.29590e6 | + | 6.22919e6i | −0.479411 | + | 1.30073i | ||||
\(471\) | 836003. | 0.173642 | ||||||||
\(472\) | −2.78624e6 | − | 4.96448e6i | −0.575656 | − | 1.02570i | ||||
\(473\) | 3.58931e6 | 0.737662 | ||||||||
\(474\) | 2.97175e6 | + | 1.09530e6i | 0.607528 | + | 0.223917i | ||||
\(475\) | 273772. | + | 3.72486e6i | 0.0556743 | + | 0.757488i | ||||
\(476\) | −1.44053e6 | + | 1.68874e6i | −0.291411 | + | 0.341622i | ||||
\(477\) | − | 921182.i | − | 0.185374i | ||||||
\(478\) | −257680. | + | 699132.i | −0.0515836 | + | 0.139955i | ||||
\(479\) | 8.66400e6i | 1.72536i | 0.505750 | + | 0.862680i | \(0.331216\pi\) | ||||
−0.505750 | + | 0.862680i | \(0.668784\pi\) | |||||||
\(480\) | −613143. | + | 3.10735e6i | −0.121467 | + | 0.615584i | ||||
\(481\) | −1.95494e6 | −0.385274 | ||||||||
\(482\) | 1.24378e6 | − | 3.37461e6i | 0.243853 | − | 0.661615i | ||||
\(483\) | 499342. | 0.0973935 | ||||||||
\(484\) | 1.73213e6 | + | 1.47754e6i | 0.336098 | + | 0.286699i | ||||
\(485\) | − | 6.74759e6i | − | 1.30255i | ||||||
\(486\) | 4.98050e6 | + | 1.83567e6i | 0.956495 | + | 0.352537i | ||||
\(487\) | 1.53710e6 | 0.293684 | 0.146842 | − | 0.989160i | \(-0.453089\pi\) | ||||
0.146842 | + | 0.989160i | \(0.453089\pi\) | |||||||
\(488\) | 2.60484e6 | + | 4.64127e6i | 0.495144 | + | 0.882240i | ||||
\(489\) | − | 664170.i | − | 0.125605i | ||||||
\(490\) | −4.06159e6 | − | 1.49699e6i | −0.764199 | − | 0.281662i | ||||
\(491\) | − | 9.45899e6i | − | 1.77068i | −0.464941 | − | 0.885342i | \(-0.653925\pi\) | ||
0.464941 | − | 0.885342i | \(-0.346075\pi\) | |||||||
\(492\) | 3.00952e6 | − | 3.52807e6i | 0.560511 | − | 0.657089i | ||||
\(493\) | 4.44343e6i | 0.823381i | ||||||||
\(494\) | 4.04341e6 | + | 1.16163e6i | 0.745471 | + | 0.214167i | ||||
\(495\) | 4.19392e6i | 0.769320i | ||||||||
\(496\) | 552270. | + | 3.45945e6i | 0.100797 | + | 0.631397i | ||||
\(497\) | 213577.i | 0.0387850i | ||||||||
\(498\) | −505660. | + | 1.37195e6i | −0.0913662 | + | 0.247893i | ||||
\(499\) | − | 6.86012e6i | − | 1.23333i | −0.787224 | − | 0.616667i | \(-0.788483\pi\) | ||
0.787224 | − | 0.616667i | \(-0.211517\pi\) | |||||||
\(500\) | −1.35661e6 | − | 1.15722e6i | −0.242678 | − | 0.207009i | ||||
\(501\) | 3.78867e6 | 0.674362 | ||||||||
\(502\) | −880886. | + | 2.39000e6i | −0.156013 | + | 0.423291i | ||||
\(503\) | 7.79162e6i | 1.37312i | 0.727075 | + | 0.686558i | \(0.240879\pi\) | ||||
−0.727075 | + | 0.686558i | \(0.759121\pi\) | |||||||
\(504\) | −2.39834e6 | + | 1.34603e6i | −0.420567 | + | 0.236037i | ||||
\(505\) | 7.85340e6 | 1.37034 | ||||||||
\(506\) | −1.33806e6 | − | 493172.i | −0.232328 | − | 0.0856293i | ||||
\(507\) | −1.09076e6 | −0.188455 | ||||||||
\(508\) | −7.00504e6 | − | 5.97545e6i | −1.20435 | − | 1.02733i | ||||
\(509\) | − | 9.60795e6i | − | 1.64375i | −0.569667 | − | 0.821876i | \(-0.692928\pi\) | ||
0.569667 | − | 0.821876i | \(-0.307072\pi\) | |||||||
\(510\) | 2.49934e6 | + | 921187.i | 0.425501 | + | 0.156828i | ||||
\(511\) | − | 3.72470e6i | − | 0.631015i | ||||||
\(512\) | 5.92769e6 | + | 216529.i | 0.999334 | + | 0.0365041i | ||||
\(513\) | 367104. | + | 4.99471e6i | 0.0615880 | + | 0.837948i | ||||
\(514\) | −3.99098e6 | + | 1.08282e7i | −0.666303 | + | 1.80780i | ||||
\(515\) | −1.48421e7 | −2.46591 | ||||||||
\(516\) | 1.83312e6 | − | 2.14897e6i | 0.303086 | − | 0.355309i | ||||
\(517\) | −4.74550e6 | −0.780828 | ||||||||
\(518\) | 1.76839e6 | + | 651777.i | 0.289570 | + | 0.106727i | ||||
\(519\) | 4.99461e6i | 0.813924i | ||||||||
\(520\) | 5.53221e6 | − | 3.10487e6i | 0.897202 | − | 0.503541i | ||||
\(521\) | 6.64194e6i | 1.07202i | 0.844213 | + | 0.536008i | \(0.180068\pi\) | ||||
−0.844213 | + | 0.536008i | \(0.819932\pi\) | |||||||
\(522\) | −1.90398e6 | + | 5.16583e6i | −0.305834 | + | 0.829781i | ||||
\(523\) | 3.32969e6 | 0.532292 | 0.266146 | − | 0.963933i | \(-0.414250\pi\) | ||||
0.266146 | + | 0.963933i | \(0.414250\pi\) | |||||||
\(524\) | 6669.86 | − | 7819.10i | 0.00106118 | − | 0.00124402i | ||||
\(525\) | − | 1.40968e6i | − | 0.223215i | ||||||
\(526\) | 3.05696e6 | − | 8.29407e6i | 0.481753 | − | 1.30708i | ||||
\(527\) | 2.94627e6 | 0.462110 | ||||||||
\(528\) | −2.23569e6 | + | 356907.i | −0.349000 | + | 0.0557148i | ||||
\(529\) | 5.72947e6 | 0.890174 | ||||||||
\(530\) | 708434. | − | 1.92211e6i | 0.109549 | − | 0.297227i | ||||
\(531\) | −5.93220e6 | −0.913019 | ||||||||
\(532\) | −3.27028e6 | − | 2.39886e6i | −0.500964 | − | 0.367474i | ||||
\(533\) | −9.28834e6 | −1.41619 | ||||||||
\(534\) | −885437. | + | 2.40235e6i | −0.134371 | + | 0.364572i | ||||
\(535\) | 2.67634e6 | 0.404257 | ||||||||
\(536\) | 1.92506e6 | + | 3.43005e6i | 0.289423 | + | 0.515689i | ||||
\(537\) | 2.86906e6 | 0.429343 | ||||||||
\(538\) | −1.34757e6 | + | 3.65619e6i | −0.200722 | + | 0.544594i | ||||
\(539\) | − | 3.09419e6i | − | 0.458749i | ||||||
\(540\) | 5.74569e6 | + | 4.90120e6i | 0.847926 | + | 0.723299i | ||||
\(541\) | 1.36743e6 | 0.200868 | 0.100434 | − | 0.994944i | \(-0.467977\pi\) | ||||
0.100434 | + | 0.994944i | \(0.467977\pi\) | |||||||
\(542\) | −2.14184e6 | + | 5.81119e6i | −0.313176 | + | 0.849703i | ||||
\(543\) | 829321.i | 0.120704i | ||||||||
\(544\) | 965724. | − | 4.89420e6i | 0.139912 | − | 0.709062i | ||||
\(545\) | − | 1.77475e7i | − | 2.55945i | ||||||
\(546\) | −1.48988e6 | − | 549127.i | −0.213880 | − | 0.0788300i | ||||
\(547\) | 5.44793e6 | 0.778509 | 0.389254 | − | 0.921130i | \(-0.372733\pi\) | ||||
0.389254 | + | 0.921130i | \(0.372733\pi\) | |||||||
\(548\) | −1.08466e6 | − | 925235.i | −0.154291 | − | 0.131614i | ||||
\(549\) | 5.54599e6 | 0.785322 | ||||||||
\(550\) | −1.39227e6 | + | 3.77747e6i | −0.196253 | + | 0.532468i | ||||
\(551\) | −8.09714e6 | + | 595128.i | −1.13619 | + | 0.0835086i | ||||
\(552\) | −978640. | + | 549247.i | −0.136702 | + | 0.0767220i | ||||
\(553\) | 6.11575e6i | 0.850427i | ||||||||
\(554\) | 4.54034e6 | + | 1.67344e6i | 0.628513 | + | 0.231652i | ||||
\(555\) | − | 2.26168e6i | − | 0.311673i | ||||||
\(556\) | 7.56913e6 | − | 8.87332e6i | 1.03839 | − | 1.21730i | ||||
\(557\) | −313832. | −0.0428608 | −0.0214304 | − | 0.999770i | \(-0.506822\pi\) | ||||
−0.0214304 | + | 0.999770i | \(0.506822\pi\) | |||||||
\(558\) | 3.42526e6 | + | 1.26245e6i | 0.465702 | + | 0.171645i | ||||
\(559\) | −5.65759e6 | −0.765776 | ||||||||
\(560\) | −6.03946e6 | + | 964146.i | −0.813820 | + | 0.129919i | ||||
\(561\) | 1.90404e6i | 0.255428i | ||||||||
\(562\) | −1.31595e6 | + | 3.57042e6i | −0.175752 | + | 0.476846i | ||||
\(563\) | 2.48402e6 | 0.330282 | 0.165141 | − | 0.986270i | \(-0.447192\pi\) | ||||
0.165141 | + | 0.986270i | \(0.447192\pi\) | |||||||
\(564\) | −2.42360e6 | + | 2.84120e6i | −0.320821 | + | 0.376100i | ||||
\(565\) | − | 7.04092e6i | − | 0.927915i | ||||||
\(566\) | −1.03697e6 | + | 2.81348e6i | −0.136058 | + | 0.369150i | ||||
\(567\) | 1.80166e6i | 0.235351i | ||||||||
\(568\) | −234923. | − | 418582.i | −0.0305530 | − | 0.0544389i | ||||
\(569\) | − | 3.30528e6i | − | 0.427985i | −0.976835 | − | 0.213992i | \(-0.931353\pi\) | ||
0.976835 | − | 0.213992i | \(-0.0686468\pi\) | |||||||
\(570\) | −1.34390e6 | + | 4.67786e6i | −0.173253 | + | 0.603060i | ||||
\(571\) | 1.51598e7i | 1.94582i | 0.231174 | + | 0.972912i | \(0.425743\pi\) | ||||
−0.231174 | + | 0.972912i | \(0.574257\pi\) | |||||||
\(572\) | 3.45003e6 | + | 2.94295e6i | 0.440892 | + | 0.376090i | ||||
\(573\) | − | 4.27609e6i | − | 0.544077i | ||||||
\(574\) | 8.40200e6 | + | 3.09674e6i | 1.06440 | + | 0.392306i | ||||
\(575\) | 1.99557e6i | 0.251709i | ||||||||
\(576\) | 3.21986e6 | − | 5.27608e6i | 0.404371 | − | 0.662605i | ||||
\(577\) | −818742. | −0.102378 | −0.0511891 | − | 0.998689i | \(-0.516301\pi\) | ||||
−0.0511891 | + | 0.998689i | \(0.516301\pi\) | |||||||
\(578\) | 3.59977e6 | + | 1.32677e6i | 0.448183 | + | 0.165187i | ||||
\(579\) | − | 1.58463e6i | − | 0.196441i | ||||||
\(580\) | −7.94554e6 | + | 9.31458e6i | −0.980739 | + | 1.14972i | ||||
\(581\) | −2.82342e6 | −0.347004 | ||||||||
\(582\) | 1.31265e6 | − | 3.56145e6i | 0.160635 | − | 0.435832i | ||||
\(583\) | 1.46429e6 | 0.178425 | ||||||||
\(584\) | 4.09696e6 | + | 7.29990e6i | 0.497084 | + | 0.885696i | ||||
\(585\) | − | 6.61060e6i | − | 0.798640i | ||||||
\(586\) | −676285. | + | 1.83488e6i | −0.0813553 | + | 0.220732i | ||||
\(587\) | − | 2.05576e6i | − | 0.246251i | −0.992391 | − | 0.123126i | \(-0.960708\pi\) | ||
0.992391 | − | 0.123126i | \(-0.0392918\pi\) | |||||||
\(588\) | −1.85254e6 | − | 1.58025e6i | −0.220965 | − | 0.188488i | ||||
\(589\) | 394607. | + | 5.36890e6i | 0.0468680 | + | 0.637672i | ||||
\(590\) | −1.23779e7 | − | 4.56215e6i | −1.46392 | − | 0.539560i | ||||
\(591\) | −5.55317e6 | −0.653992 | ||||||||
\(592\) | −4.18271e6 | + | 667732.i | −0.490516 | + | 0.0783065i | ||||
\(593\) | 8.30825e6 | 0.970226 | 0.485113 | − | 0.874451i | \(-0.338778\pi\) | ||||
0.485113 | + | 0.874451i | \(0.338778\pi\) | |||||||
\(594\) | −1.86691e6 | + | 5.06525e6i | −0.217098 | + | 0.589027i | ||||
\(595\) | 5.14356e6i | 0.595623i | ||||||||
\(596\) | 991701. | + | 845942.i | 0.114358 | + | 0.0975495i | ||||
\(597\) | − | 6.25533e6i | − | 0.718314i | ||||||
\(598\) | 2.10910e6 | + | 777355.i | 0.241182 | + | 0.0888928i | ||||
\(599\) | 1.13233e7 | 1.28945 | 0.644727 | − | 0.764413i | \(-0.276971\pi\) | ||||
0.644727 | + | 0.764413i | \(0.276971\pi\) | |||||||
\(600\) | 1.55057e6 | + | 2.76278e6i | 0.175838 | + | 0.313306i | ||||
\(601\) | − | 2.35047e6i | − | 0.265442i | −0.991153 | − | 0.132721i | \(-0.957629\pi\) | ||
0.991153 | − | 0.132721i | \(-0.0423714\pi\) | |||||||
\(602\) | 5.11771e6 | + | 1.88624e6i | 0.575552 | + | 0.212132i | ||||
\(603\) | 4.09866e6 | 0.459038 | ||||||||
\(604\) | 7.58315e6 | + | 6.46859e6i | 0.845780 | + | 0.721469i | ||||
\(605\) | 5.27570e6 | 0.585992 | ||||||||
\(606\) | 4.14511e6 | + | 1.52777e6i | 0.458516 | + | 0.168996i | ||||
\(607\) | 3.76789e6 | 0.415075 | 0.207537 | − | 0.978227i | \(-0.433455\pi\) | ||||
0.207537 | + | 0.978227i | \(0.433455\pi\) | |||||||
\(608\) | 9.04791e6 | + | 1.10431e6i | 0.992634 | + | 0.121152i | ||||
\(609\) | 3.06438e6 | 0.334811 | ||||||||
\(610\) | 1.15721e7 | + | 4.26513e6i | 1.25918 | + | 0.464096i | ||||
\(611\) | 7.48002e6 | 0.810587 | ||||||||
\(612\) | −3.95485e6 | − | 3.37358e6i | −0.426827 | − | 0.364093i | ||||
\(613\) | 1.48787e7 | 1.59924 | 0.799618 | − | 0.600509i | \(-0.205035\pi\) | ||||
0.799618 | + | 0.600509i | \(0.205035\pi\) | |||||||
\(614\) | −639180. | − | 235583.i | −0.0684230 | − | 0.0252188i | ||||
\(615\) | − | 1.07458e7i | − | 1.14564i | ||||||
\(616\) | −2.13963e6 | − | 3.81236e6i | −0.227189 | − | 0.404801i | ||||
\(617\) | −1.58901e7 | −1.68040 | −0.840200 | − | 0.542276i | \(-0.817563\pi\) | ||||
−0.840200 | + | 0.542276i | \(0.817563\pi\) | |||||||
\(618\) | −7.83381e6 | − | 2.88732e6i | −0.825091 | − | 0.304105i | ||||
\(619\) | 9.96333e6i | 1.04515i | 0.852594 | + | 0.522574i | \(0.175028\pi\) | ||||
−0.852594 | + | 0.522574i | \(0.824972\pi\) | |||||||
\(620\) | 6.17614e6 | + | 5.26838e6i | 0.645265 | + | 0.550425i | ||||
\(621\) | 2.67589e6i | 0.278445i | ||||||||
\(622\) | −1.82504e6 | + | 4.95167e6i | −0.189146 | + | 0.513187i | ||||
\(623\) | −4.94395e6 | −0.510333 | ||||||||
\(624\) | 3.52397e6 | − | 562570.i | 0.362302 | − | 0.0578382i | ||||
\(625\) | −1.15493e7 | −1.18264 | ||||||||
\(626\) | −7.52088e6 | − | 2.77198e6i | −0.767066 | − | 0.282719i | ||||
\(627\) | −3.46968e6 | + | 255017.i | −0.352469 | + | 0.0259060i | ||||
\(628\) | −2.76022e6 | − | 2.35453e6i | −0.279283 | − | 0.238235i | ||||
\(629\) | 3.56224e6i | 0.359002i | ||||||||
\(630\) | −2.20398e6 | + | 5.97978e6i | −0.221236 | + | 0.600253i | ||||
\(631\) | − | 1.50560e7i | − | 1.50535i | −0.658394 | − | 0.752674i | \(-0.728764\pi\) | ||
0.658394 | − | 0.752674i | \(-0.271236\pi\) | |||||||
\(632\) | −6.72697e6 | − | 1.19860e7i | −0.669926 | − | 1.19366i | ||||
\(633\) | −7.59321e6 | −0.753210 | ||||||||
\(634\) | 2.93588e6 | − | 7.96557e6i | 0.290078 | − | 0.787035i | ||||
\(635\) | −2.13359e7 | −2.09980 | ||||||||
\(636\) | 747838. | − | 876693.i | 0.0733102 | − | 0.0859418i | ||||
\(637\) | 4.87717e6i | 0.476233i | ||||||||
\(638\) | −8.21149e6 | − | 3.02652e6i | −0.798676 | − | 0.294369i | ||||
\(639\) | −500176. | −0.0484585 | ||||||||
\(640\) | 1.07760e7 | − | 8.53265e6i | 1.03994 | − | 0.823444i | ||||
\(641\) | 1.52722e6i | 0.146810i | 0.997302 | + | 0.0734051i | \(0.0233866\pi\) | ||||
−0.997302 | + | 0.0734051i | \(0.976613\pi\) | |||||||
\(642\) | 1.41260e6 | + | 520645.i | 0.135264 | + | 0.0498545i | ||||
\(643\) | 4.88237e6i | 0.465696i | 0.972513 | + | 0.232848i | \(0.0748045\pi\) | ||||
−0.972513 | + | 0.232848i | \(0.925195\pi\) | |||||||
\(644\) | −1.64867e6 | − | 1.40635e6i | −0.156646 | − | 0.133622i | ||||
\(645\) | − | 6.54532e6i | − | 0.619486i | ||||||
\(646\) | 2.11670e6 | − | 7.36782e6i | 0.199562 | − | 0.694636i | ||||
\(647\) | − | 1.57872e7i | − | 1.48267i | −0.671136 | − | 0.741334i | \(-0.734193\pi\) | ||
0.671136 | − | 0.741334i | \(-0.265807\pi\) | |||||||
\(648\) | −1.98173e6 | − | 3.53101e6i | −0.185398 | − | 0.330340i | ||||
\(649\) | − | 9.42971e6i | − | 0.878793i | ||||||
\(650\) | 2.19454e6 | − | 5.95417e6i | 0.203732 | − | 0.552762i | ||||
\(651\) | − | 2.03188e6i | − | 0.187908i | ||||||
\(652\) | −1.87058e6 | + | 2.19288e6i | −0.172328 | + | 0.202021i | ||||
\(653\) | −3.17397e6 | −0.291286 | −0.145643 | − | 0.989337i | \(-0.546525\pi\) | ||||
−0.145643 | + | 0.989337i | \(0.546525\pi\) | |||||||
\(654\) | 3.45253e6 | − | 9.36732e6i | 0.315641 | − | 0.856389i | ||||
\(655\) | − | 23815.4i | − | 0.00216897i | ||||||
\(656\) | −1.98730e7 | + | 3.17254e6i | −1.80303 | + | 0.287838i | ||||
\(657\) | 8.72287e6 | 0.788398 | ||||||||
\(658\) | −6.76624e6 | − | 2.49384e6i | −0.609232 | − | 0.224545i | ||||
\(659\) | 1.10241e6 | 0.0988852 | 0.0494426 | − | 0.998777i | \(-0.484256\pi\) | ||||
0.0494426 | + | 0.998777i | \(0.484256\pi\) | |||||||
\(660\) | −3.40472e6 | + | 3.99137e6i | −0.304244 | + | 0.356666i | ||||
\(661\) | 1.07049e7i | 0.952971i | 0.879182 | + | 0.476486i | \(0.158090\pi\) | ||||
−0.879182 | + | 0.476486i | \(0.841910\pi\) | |||||||
\(662\) | −3.00856e6 | − | 1.10887e6i | −0.266817 | − | 0.0983411i | ||||
\(663\) | − | 3.00122e6i | − | 0.265163i | ||||||
\(664\) | 5.53350e6 | − | 3.10560e6i | 0.487057 | − | 0.273354i | ||||
\(665\) | −9.37297e6 | + | 688900.i | −0.821908 | + | 0.0604091i | ||||
\(666\) | −1.52639e6 | + | 4.14138e6i | −0.133346 | + | 0.361792i | ||||
\(667\) | −4.33800e6 | −0.377550 | ||||||||
\(668\) | −1.25090e7 | − | 1.06705e7i | −1.08463 | − | 0.925215i | ||||
\(669\) | −7.02842e6 | −0.607145 | ||||||||
\(670\) | 8.55213e6 | + | 3.15207e6i | 0.736016 | + | 0.271274i | ||||
\(671\) | 8.81579e6i | 0.755884i | ||||||||
\(672\) | −3.37525e6 | − | 666006.i | −0.288326 | − | 0.0568925i | ||||
\(673\) | 1.71375e7i | 1.45851i | 0.684241 | + | 0.729256i | \(0.260134\pi\) | ||||
−0.684241 | + | 0.729256i | \(0.739866\pi\) | |||||||
\(674\) | −1.33597e6 | + | 3.62472e6i | −0.113278 | + | 0.307344i | ||||
\(675\) | 7.55426e6 | 0.638164 | ||||||||
\(676\) | 3.60135e6 | + | 3.07202e6i | 0.303108 | + | 0.258558i | ||||
\(677\) | − | 1.53359e6i | − | 0.128599i | −0.997931 | − | 0.0642995i | \(-0.979519\pi\) | ||
0.997931 | − | 0.0642995i | \(-0.0204813\pi\) | |||||||
\(678\) | 1.36971e6 | − | 3.71627e6i | 0.114434 | − | 0.310480i | ||||
\(679\) | 7.32934e6 | 0.610085 | ||||||||
\(680\) | −5.65762e6 | − | 1.00807e7i | −0.469204 | − | 0.836020i | ||||
\(681\) | −4.74882e6 | −0.392390 | ||||||||
\(682\) | −2.00677e6 | + | 5.44473e6i | −0.165210 | + | 0.448245i | ||||
\(683\) | 1.26404e7 | 1.03683 | 0.518415 | − | 0.855129i | \(-0.326522\pi\) | ||||
0.518415 | + | 0.855129i | \(0.326522\pi\) | |||||||
\(684\) | 5.61788e6 | − | 7.65866e6i | 0.459127 | − | 0.625911i | ||||
\(685\) | −3.30364e6 | −0.269009 | ||||||||
\(686\) | 4.27435e6 | − | 1.15971e7i | 0.346785 | − | 0.940888i | ||||
\(687\) | 7.97747e6 | 0.644872 | ||||||||
\(688\) | −1.21048e7 | + | 1.93242e6i | −0.974956 | + | 0.155643i | ||||
\(689\) | −2.30807e6 | −0.185225 | ||||||||
\(690\) | −899330. | + | 2.44004e6i | −0.0719111 | + | 0.195108i | ||||
\(691\) | 3.64221e6i | 0.290181i | 0.989418 | + | 0.145091i | \(0.0463474\pi\) | ||||
−0.989418 | + | 0.145091i | \(0.953653\pi\) | |||||||
\(692\) | 1.40669e7 | − | 1.64907e7i | 1.11669 | − | 1.30910i | ||||
\(693\) | −4.55550e6 | −0.360332 | ||||||||
\(694\) | −5.74173e6 | + | 1.55783e7i | −0.452527 | + | 1.22779i | ||||
\(695\) | − | 2.70263e7i | − | 2.12239i | ||||||
\(696\) | −6.00576e6 | + | 3.37064e6i | −0.469943 | + | 0.263748i | ||||
\(697\) | 1.69250e7i | 1.31961i | ||||||||
\(698\) | −2.01910e7 | − | 7.44182e6i | −1.56862 | − | 0.578150i | ||||
\(699\) | −4.09238e6 | −0.316799 | ||||||||
\(700\) | −3.97025e6 | + | 4.65434e6i | −0.306248 | + | 0.359015i | ||||
\(701\) | 8.50256e6 | 0.653514 | 0.326757 | − | 0.945108i | \(-0.394044\pi\) | ||||
0.326757 | + | 0.945108i | \(0.394044\pi\) | |||||||
\(702\) | 2.94268e6 | − | 7.98403e6i | 0.225372 | − | 0.611476i | ||||
\(703\) | −6.49137e6 | + | 477107.i | −0.495391 | + | 0.0364105i | ||||
\(704\) | 8.38674e6 | + | 5.11822e6i | 0.637767 | + | 0.389213i | ||||
\(705\) | 8.65370e6i | 0.655736i | ||||||||
\(706\) | −1.42133e7 | − | 5.23863e6i | −1.07321 | − | 0.395554i | ||||
\(707\) | 8.53049e6i | 0.641838i | ||||||||
\(708\) | −5.64570e6 | − | 4.81590e6i | −0.423287 | − | 0.361073i | ||||
\(709\) | 9.45835e6 | 0.706642 | 0.353321 | − | 0.935502i | \(-0.385052\pi\) | ||||
0.353321 | + | 0.935502i | \(0.385052\pi\) | |||||||
\(710\) | −1.04365e6 | − | 384659.i | −0.0776978 | − | 0.0286372i | ||||
\(711\) | −1.43224e7 | −1.06254 | ||||||||
\(712\) | 9.68945e6 | − | 5.43806e6i | 0.716307 | − | 0.402017i | ||||
\(713\) | 2.87636e6i | 0.211894i | ||||||||
\(714\) | −1.00061e6 | + | 2.71483e6i | −0.0734545 | + | 0.199295i | ||||
\(715\) | 1.05081e7 | 0.768702 | ||||||||
\(716\) | −9.47277e6 | − | 8.08047e6i | −0.690549 | − | 0.589053i | ||||
\(717\) | 971248.i | 0.0705557i | ||||||||
\(718\) | 2.15774e6 | − | 5.85434e6i | 0.156203 | − | 0.423806i | ||||
\(719\) | 1.31194e7i | 0.946436i | 0.880945 | + | 0.473218i | \(0.156908\pi\) | ||||
−0.880945 | + | 0.473218i | \(0.843092\pi\) | |||||||
\(720\) | −2.25793e6 | − | 1.41438e7i | −0.162323 | − | 1.01680i | ||||
\(721\) | − | 1.61217e7i | − | 1.15498i | ||||||
\(722\) | 1.37097e7 | + | 2.87040e6i | 0.978777 | + | 0.204927i | ||||
\(723\) | − | 4.68807e6i | − | 0.333540i | ||||||
\(724\) | 2.33571e6 | − | 2.73816e6i | 0.165605 | − | 0.194139i | ||||
\(725\) | 1.22465e7i | 0.865302i | ||||||||
\(726\) | 2.78457e6 | + | 1.02631e6i | 0.196073 | + | 0.0722668i | ||||
\(727\) | − | 2.23602e7i | − | 1.56906i | −0.620092 | − | 0.784529i | \(-0.712905\pi\) | ||
0.620092 | − | 0.784529i | \(-0.287095\pi\) | |||||||
\(728\) | 3.37256e6 | + | 6.00917e6i | 0.235847 | + | 0.420229i | ||||
\(729\) | 1.48350e6 | 0.103388 | ||||||||
\(730\) | 1.82008e7 | + | 6.70830e6i | 1.26411 | + | 0.465914i | ||||
\(731\) | 1.03091e7i | 0.713557i | ||||||||
\(732\) | 5.27814e6 | + | 4.50236e6i | 0.364085 | + | 0.310572i | ||||
\(733\) | −9.88432e6 | −0.679496 | −0.339748 | − | 0.940517i | \(-0.610342\pi\) | ||||
−0.339748 | + | 0.940517i | \(0.610342\pi\) | |||||||
\(734\) | −3.30154e6 | + | 8.95767e6i | −0.226192 | + | 0.613698i | ||||
\(735\) | −5.64244e6 | −0.385256 | ||||||||
\(736\) | 4.77807e6 | + | 942810.i | 0.325131 | + | 0.0641549i | ||||
\(737\) | 6.51515e6i | 0.441831i | ||||||||
\(738\) | −7.25224e6 | + | 1.96766e7i | −0.490152 | + | 1.32987i | ||||
\(739\) | 1.99370e7i | 1.34292i | 0.741042 | + | 0.671459i | \(0.234332\pi\) | ||||
−0.741042 | + | 0.671459i | \(0.765668\pi\) | |||||||
\(740\) | −6.36984e6 | + | 7.46738e6i | −0.427611 | + | 0.501290i | ||||
\(741\) | 5.46903e6 | − | 401966.i | 0.365902 | − | 0.0268933i | ||||
\(742\) | 2.08782e6 | + | 769512.i | 0.139214 | + | 0.0513104i | ||||
\(743\) | 1.15065e6 | 0.0764663 | 0.0382331 | − | 0.999269i | \(-0.487827\pi\) | ||||
0.0382331 | + | 0.999269i | \(0.487827\pi\) | |||||||
\(744\) | 2.23495e6 | + | 3.98219e6i | 0.148025 | + | 0.263748i | ||||
\(745\) | 3.02052e6 | 0.199384 | ||||||||
\(746\) | 4.37008e6 | − | 1.18568e7i | 0.287503 | − | 0.780047i | ||||
\(747\) | − | 6.61215e6i | − | 0.433552i | ||||||
\(748\) | 5.36257e6 | − | 6.28656e6i | 0.350444 | − | 0.410827i | ||||
\(749\) | 2.90709e6i | 0.189345i | ||||||||
\(750\) | −2.18089e6 | − | 803814.i | −0.141573 | − | 0.0521798i | ||||
\(751\) | 1.63685e7 | 1.05903 | 0.529517 | − | 0.848299i | \(-0.322373\pi\) | ||||
0.529517 | + | 0.848299i | \(0.322373\pi\) | |||||||
\(752\) | 1.60040e7 | − | 2.55489e6i | 1.03201 | − | 0.164751i | ||||
\(753\) | 3.32023e6i | 0.213394i | ||||||||
\(754\) | 1.29432e7 | + | 4.77051e6i | 0.829115 | + | 0.305588i | ||||
\(755\) | 2.30967e7 | 1.47463 | ||||||||
\(756\) | −5.32376e6 | + | 6.24106e6i | −0.338777 | + | 0.397149i | ||||
\(757\) | 230669. | 0.0146302 | 0.00731509 | − | 0.999973i | \(-0.497672\pi\) | ||||
0.00731509 | + | 0.999973i | \(0.497672\pi\) | |||||||
\(758\) | 2.68407e7 | + | 9.89270e6i | 1.69676 | + | 0.625377i | ||||
\(759\) | −1.85886e6 | −0.117123 | ||||||||
\(760\) | 1.76120e7 | − | 1.16599e7i | 1.10605 | − | 0.732251i | ||||
\(761\) | 2.58078e7 | 1.61544 | 0.807719 | − | 0.589568i | \(-0.200702\pi\) | ||||
0.807719 | + | 0.589568i | \(0.200702\pi\) | |||||||
\(762\) | −1.12613e7 | − | 4.15061e6i | −0.702591 | − | 0.258955i | ||||
\(763\) | 1.92776e7 | 1.19879 | ||||||||
\(764\) | −1.20432e7 | + | 1.41183e7i | −0.746466 | + | 0.875084i | ||||
\(765\) | −1.20457e7 | −0.744180 | ||||||||
\(766\) | −780674. | − | 287734.i | −0.0480726 | − | 0.0177182i | ||||
\(767\) | 1.48634e7i | 0.912286i | ||||||||
\(768\) | 7.34759e6 | − | 2.40731e6i | 0.449513 | − | 0.147275i | ||||
\(769\) | 1.21242e7 | 0.739329 | 0.369664 | − | 0.929165i | \(-0.379473\pi\) | ||||
0.369664 | + | 0.929165i | \(0.379473\pi\) | |||||||
\(770\) | −9.50535e6 | − | 3.50340e6i | −0.577752 | − | 0.212943i | ||||
\(771\) | 1.50428e7i | 0.911365i | ||||||||
\(772\) | −4.46297e6 | + | 5.23196e6i | −0.269514 | + | 0.315952i | ||||
\(773\) | 1.38975e7i | 0.836541i | 0.908323 | + | 0.418270i | \(0.137364\pi\) | ||||
−0.908323 | + | 0.418270i | \(0.862636\pi\) | |||||||
\(774\) | −4.41738e6 | + | 1.19852e7i | −0.265041 | + | 0.719103i | ||||
\(775\) | 8.12020e6 | 0.485638 | ||||||||
\(776\) | −1.43645e7 | + | 8.06185e6i | −0.856319 | + | 0.480596i | ||||
\(777\) | 2.45668e6 | 0.145981 | ||||||||
\(778\) | 8.80934e6 | + | 3.24687e6i | 0.521789 | + | 0.192316i | ||||
\(779\) | −3.08420e7 | + | 2.26684e6i | −1.82095 | + | 0.133837i | ||||
\(780\) | 5.36664e6 | − | 6.29133e6i | 0.315839 | − | 0.370259i | ||||
\(781\) | − | 795069.i | − | 0.0466420i | ||||||
\(782\) | 1.41648e6 | − | 3.84316e6i | 0.0828311 | − | 0.224735i | ||||
\(783\) | 1.64215e7i | 0.957214i | ||||||||
\(784\) | 1.66586e6 | + | 1.04350e7i | 0.0967937 | + | 0.606321i | ||||
\(785\) | −8.40708e6 | −0.486935 | ||||||||
\(786\) | 4632.95 | − | 12570.0i | 0.000267486 | − | 0.000725737i | ||||
\(787\) | −2.18558e7 | −1.25786 | −0.628928 | − | 0.777464i | \(-0.716506\pi\) | ||||
−0.628928 | + | 0.777464i | \(0.716506\pi\) | |||||||
\(788\) | 1.83349e7 | + | 1.56400e7i | 1.05187 | + | 0.897267i | ||||
\(789\) | − | 1.15223e7i | − | 0.658940i | ||||||
\(790\) | −2.98847e7 | − | 1.10147e7i | −1.70365 | − | 0.627918i | ||||
\(791\) | 7.64795e6 | 0.434614 | ||||||||
\(792\) | 8.92814e6 | − | 5.01079e6i | 0.505764 | − | 0.283853i | ||||
\(793\) | − | 1.38958e7i | − | 0.784692i | ||||||
\(794\) | −2.01960e6 | − | 744366.i | −0.113688 | − | 0.0419020i | ||||
\(795\) | − | 2.67023e6i | − | 0.149841i | ||||||
\(796\) | −1.76176e7 | + | 2.06532e7i | −0.985517 | + | 1.15532i | ||||
\(797\) | 3.40246e7i | 1.89735i | 0.316253 | + | 0.948675i | \(0.397575\pi\) | ||||
−0.316253 | + | 0.948675i | \(0.602425\pi\) | |||||||
\(798\) | −5.08117e6 | − | 1.45977e6i | −0.282460 | − | 0.0811479i | ||||
\(799\) | − | 1.36299e7i | − | 0.755312i | ||||||
\(800\) | 2.66163e6 | − | 1.34889e7i | 0.147036 | − | 0.745163i | ||||
\(801\) | − | 1.15782e7i | − | 0.637618i | ||||||
\(802\) | 7.46929e6 | − | 2.02655e7i | 0.410056 | − | 1.11256i | ||||
\(803\) | 1.38657e7i | 0.758844i | ||||||||
\(804\) | 3.90071e6 | + | 3.32739e6i | 0.212816 | + | 0.181536i | ||||
\(805\) | −5.02152e6 | −0.273115 | ||||||||
\(806\) | 3.16314e6 | − | 8.58217e6i | 0.171507 | − | 0.465328i | ||||
\(807\) | 5.07925e6i | 0.274546i | ||||||||
\(808\) | −9.38305e6 | − | 1.67186e7i | −0.505610 | − | 0.900888i | ||||
\(809\) | 2.78329e7 | 1.49516 | 0.747578 | − | 0.664174i | \(-0.231216\pi\) | ||||
0.747578 | + | 0.664174i | \(0.231216\pi\) | |||||||
\(810\) | −8.80386e6 | − | 3.24485e6i | −0.471477 | − | 0.173773i | ||||
\(811\) | −3.12418e7 | −1.66796 | −0.833978 | − | 0.551798i | \(-0.813942\pi\) | ||||
−0.833978 | + | 0.551798i | \(0.813942\pi\) | |||||||
\(812\) | −1.01176e7 | − | 8.63057e6i | −0.538505 | − | 0.459356i | ||||
\(813\) | 8.07302e6i | 0.428361i | ||||||||
\(814\) | −6.58305e6 | − | 2.42632e6i | −0.348230 | − | 0.128348i | ||||
\(815\) | 6.67908e6i | 0.352227i | ||||||||
\(816\) | −1.02510e6 | − | 6.42129e6i | −0.0538941 | − | 0.337596i | ||||
\(817\) | −1.87860e7 | + | 1.38075e6i | −0.984646 | + | 0.0723701i | ||||
\(818\) | 1.21340e7 | − | 3.29217e7i | 0.634046 | − | 1.72028i | ||||
\(819\) | 7.18054e6 | 0.374065 | ||||||||
\(820\) | −3.02645e7 | + | 3.54792e7i | −1.57181 | + | 1.84264i | ||||
\(821\) | −9.21704e6 | −0.477236 | −0.238618 | − | 0.971113i | \(-0.576694\pi\) | ||||
−0.238618 | + | 0.971113i | \(0.576694\pi\) | |||||||
\(822\) | −1.74370e6 | − | 642677.i | −0.0900102 | − | 0.0331752i | ||||
\(823\) | − | 1.61444e7i | − | 0.830848i | −0.909628 | − | 0.415424i | \(-0.863633\pi\) | ||
0.909628 | − | 0.415424i | \(-0.136367\pi\) | |||||||
\(824\) | 1.77329e7 | + | 3.15963e7i | 0.909835 | + | 1.62113i | ||||
\(825\) | 5.24773e6i | 0.268433i | ||||||||
\(826\) | 4.95548e6 | − | 1.34451e7i | 0.252718 | − | 0.685668i | ||||
\(827\) | 3.64283e7 | 1.85214 | 0.926072 | − | 0.377346i | \(-0.123163\pi\) | ||||
0.926072 | + | 0.377346i | \(0.123163\pi\) | |||||||
\(828\) | 3.29353e6 | − | 3.86102e6i | 0.166950 | − | 0.195716i | ||||
\(829\) | − | 1.47504e7i | − | 0.745447i | −0.927942 | − | 0.372724i | \(-0.878424\pi\) | ||
0.927942 | − | 0.372724i | \(-0.121576\pi\) | |||||||
\(830\) | 5.08506e6 | − | 1.37967e7i | 0.256213 | − | 0.695151i | ||||
\(831\) | 6.30753e6 | 0.316852 | ||||||||
\(832\) | −1.32195e7 | − | 8.06751e6i | −0.662073 | − | 0.404047i | ||||
\(833\) | 8.88707e6 | 0.443758 | ||||||||
\(834\) | 5.25759e6 | − | 1.42648e7i | 0.261741 | − | 0.710150i | ||||
\(835\) | −3.81000e7 | −1.89107 | ||||||||
\(836\) | 1.21741e7 | + | 8.93007e6i | 0.602448 | + | 0.441916i | ||||
\(837\) | 1.08885e7 | 0.537222 | ||||||||
\(838\) | 3.01338e6 | − | 8.17583e6i | 0.148232 | − | 0.402181i | ||||
\(839\) | 1.94790e7 | 0.955349 | 0.477675 | − | 0.878537i | \(-0.341480\pi\) | ||||
0.477675 | + | 0.878537i | \(0.341480\pi\) | |||||||
\(840\) | −6.95206e6 | + | 3.90174e6i | −0.339950 | + | 0.190792i | ||||
\(841\) | −6.11048e6 | −0.297910 | ||||||||
\(842\) | 2.76460e6 | − | 7.50085e6i | 0.134385 | − | 0.364611i | ||||
\(843\) | 4.96009e6i | 0.240392i | ||||||||
\(844\) | 2.50704e7 | + | 2.13856e7i | 1.21145 | + | 1.03339i | ||||
\(845\) | 1.09690e7 | 0.528474 | ||||||||
\(846\) | 5.84032e6 | − | 1.58458e7i | 0.280550 | − | 0.761183i | ||||
\(847\) | 5.73055e6i | 0.274466i | ||||||||
\(848\) | −4.93826e6 | + | 788349.i | −0.235822 | + | 0.0376469i | ||||
\(849\) | 3.90854e6i | 0.186100i | ||||||||
\(850\) | −1.08496e7 | − | 3.99884e6i | −0.515068 | − | 0.189839i | ||||
\(851\) | −3.47772e6 | −0.164615 | ||||||||
\(852\) | −476019. | − | 406054.i | −0.0224660 | − | 0.0191640i | ||||
\(853\) | −2.48591e7 | −1.16980 | −0.584901 | − | 0.811105i | \(-0.698867\pi\) | ||||
−0.584901 | + | 0.811105i | \(0.698867\pi\) | |||||||
\(854\) | −4.63285e6 | + | 1.25698e7i | −0.217372 | + | 0.589769i | ||||
\(855\) | −1.61333e6 | − | 2.19505e7i | −0.0754759 | − | 1.02690i | ||||
\(856\) | −3.19763e6 | − | 5.69748e6i | −0.149157 | − | 0.265765i | ||||
\(857\) | − | 2.33074e6i | − | 0.108403i | −0.998530 | − | 0.0542015i | \(-0.982739\pi\) | ||
0.998530 | − | 0.0542015i | \(-0.0172613\pi\) | |||||||
\(858\) | 5.54627e6 | + | 2.04420e6i | 0.257207 | + | 0.0947992i | ||||
\(859\) | − | 7.46055e6i | − | 0.344975i | −0.985012 | − | 0.172488i | \(-0.944820\pi\) | ||
0.985012 | − | 0.172488i | \(-0.0551805\pi\) | |||||||
\(860\) | −1.84343e7 | + | 2.16106e7i | −0.849926 | + | 0.996371i | ||||
\(861\) | 1.16722e7 | 0.536594 | ||||||||
\(862\) | −2.01460e7 | − | 7.42523e6i | −0.923465 | − | 0.340363i | ||||
\(863\) | −2.11346e7 | −0.965977 | −0.482989 | − | 0.875627i | \(-0.660449\pi\) | ||||
−0.482989 | + | 0.875627i | \(0.660449\pi\) | |||||||
\(864\) | 3.56902e6 | − | 1.80874e7i | 0.162654 | − | 0.824314i | ||||
\(865\) | − | 5.02272e7i | − | 2.28244i | ||||||
\(866\) | −221121. | + | 599942.i | −0.0100193 | + | 0.0271841i | ||||
\(867\) | 5.00087e6 | 0.225942 | ||||||||
\(868\) | −5.72260e6 | + | 6.70862e6i | −0.257807 | + | 0.302228i | ||||
\(869\) | − | 2.27667e7i | − | 1.02270i | ||||||
\(870\) | −5.51905e6 | + | 1.49742e7i | −0.247210 | + | 0.670725i | ||||
\(871\) | − | 1.02694e7i | − | 0.458670i | ||||||
\(872\) | −3.77814e7 | + | 2.12043e7i | −1.68262 | + | 0.944348i | ||||
\(873\) | 1.71645e7i | 0.762249i | ||||||||
\(874\) | 7.19300e6 | + | 2.06648e6i | 0.318516 | + | 0.0915066i | ||||
\(875\) | − | 4.48820e6i | − | 0.198176i | ||||||
\(876\) | 8.30158e6 | + | 7.08143e6i | 0.365511 | + | 0.311789i | ||||
\(877\) | − | 3.31426e7i | − | 1.45508i | −0.686064 | − | 0.727541i | \(-0.740663\pi\) | ||
0.686064 | − | 0.727541i | \(-0.259337\pi\) | |||||||
\(878\) | 3.12881e7 | + | 1.15319e7i | 1.36975 | + | 0.504852i | ||||
\(879\) | 2.54905e6i | 0.111277i | ||||||||
\(880\) | 2.24827e7 | − | 3.58916e6i | 0.978682 | − | 0.156238i | ||||
\(881\) | −2.52197e7 | −1.09471 | −0.547357 | − | 0.836899i | \(-0.684366\pi\) | ||||
−0.547357 | + | 0.836899i | \(0.684366\pi\) | |||||||
\(882\) | 1.03319e7 | + | 3.80804e6i | 0.447207 | + | 0.164828i | ||||
\(883\) | − | 3.20322e7i | − | 1.38256i | −0.722586 | − | 0.691282i | \(-0.757046\pi\) | ||
0.722586 | − | 0.691282i | \(-0.242954\pi\) | |||||||
\(884\) | −8.45267e6 | + | 9.90909e6i | −0.363800 | + | 0.426484i | ||||
\(885\) | −1.71956e7 | −0.738007 | ||||||||
\(886\) | −1.34560e7 | + | 3.65085e7i | −0.575880 | + | 1.56246i | ||||
\(887\) | −2.94824e7 | −1.25821 | −0.629107 | − | 0.777319i | \(-0.716579\pi\) | ||||
−0.629107 | + | 0.777319i | \(0.716579\pi\) | |||||||
\(888\) | −4.81474e6 | + | 2.70220e6i | −0.204899 | + | 0.114997i | ||||
\(889\) | − | 2.31754e7i | − | 0.983498i | ||||||
\(890\) | 8.90421e6 | − | 2.41587e7i | 0.376808 | − | 1.02235i | ||||
\(891\) | − | 6.70693e6i | − | 0.283028i | ||||||
\(892\) | 2.32057e7 | + | 1.97949e7i | 0.976521 | + | 0.832994i | ||||
\(893\) | 2.48374e7 | − | 1.82551e6i | 1.04226 | − | 0.0766049i | ||||
\(894\) | 1.59426e6 | + | 587600.i | 0.0667139 | + | 0.0245888i | ||||
\(895\) | −2.88521e7 | −1.20398 | ||||||||
\(896\) | 9.26830e6 | + | 1.17051e7i | 0.385683 | + | 0.487084i | ||||
\(897\) | 2.93001e6 | 0.121587 | ||||||||
\(898\) | −7.12794e6 | + | 1.93394e7i | −0.294967 | + | 0.800298i | ||||
\(899\) | 1.76518e7i | 0.728433i | ||||||||
\(900\) | −1.09000e7 | − | 9.29791e6i | −0.448558 | − | 0.382630i | ||||
\(901\) | 4.20571e6i | 0.172595i | ||||||||
\(902\) | −3.12776e7 | − | 1.15280e7i | −1.28002 | − | 0.471778i | ||||
\(903\) | 7.10963e6 | 0.290153 | ||||||||
\(904\) | −1.49889e7 | + | 8.41231e6i | −0.610027 | + | 0.342369i | ||||
\(905\) | − | 8.33988e6i | − | 0.338484i | ||||||
\(906\) | 1.21907e7 | + | 4.49315e6i | 0.493410 | + | 0.181857i | ||||
\(907\) | 2.64541e7 | 1.06776 | 0.533882 | − | 0.845559i | \(-0.320733\pi\) | ||||
0.533882 | + | 0.845559i | \(0.320733\pi\) | |||||||
\(908\) | 1.56791e7 | + | 1.33746e7i | 0.631113 | + | 0.538353i | ||||
\(909\) | −1.99775e7 | −0.801921 | ||||||||
\(910\) | 1.49827e7 | + | 5.52218e6i | 0.599771 | + | 0.221058i | ||||
\(911\) | −1.36140e7 | −0.543487 | −0.271744 | − | 0.962370i | \(-0.587600\pi\) | ||||
−0.271744 | + | 0.962370i | \(0.587600\pi\) | |||||||
\(912\) | 1.15640e7 | − | 2.72805e6i | 0.460386 | − | 0.108609i | ||||
\(913\) | 1.05105e7 | 0.417300 | ||||||||
\(914\) | 3.50193e7 | + | 1.29071e7i | 1.38657 | + | 0.511051i | ||||
\(915\) | 1.60761e7 | 0.634788 | ||||||||
\(916\) | −2.63391e7 | − | 2.24679e7i | −1.03720 | − | 0.884755i | ||||
\(917\) | 25868.6 | 0.00101590 | ||||||||
\(918\) | −1.45483e7 | − | 5.36209e6i | −0.569778 | − | 0.210004i | ||||
\(919\) | − | 1.83366e7i | − | 0.716193i | −0.933685 | − | 0.358097i | \(-0.883426\pi\) | ||
0.933685 | − | 0.358097i | \(-0.116574\pi\) | |||||||
\(920\) | 9.84148e6 | − | 5.52338e6i | 0.383346 | − | 0.215147i | ||||
\(921\) | −887960. | −0.0344941 | ||||||||
\(922\) | −5.25391e6 | − | 1.93644e6i | −0.203542 | − | 0.0750199i | ||||
\(923\) | 1.25322e6i | 0.0484196i | ||||||||
\(924\) | −4.33549e6 | − | 3.69826e6i | −0.167054 | − | 0.142501i | ||||
\(925\) | 9.81789e6i | 0.377280i | ||||||||
\(926\) | 2.32444e6 | − | 6.30661e6i | 0.0890820 | − | 0.241695i | ||||
\(927\) | 3.77553e7 | 1.44304 | ||||||||
\(928\) | 2.93223e7 | + | 5.78588e6i | 1.11771 | + | 0.220546i | ||||
\(929\) | −7.07716e6 | −0.269042 | −0.134521 | − | 0.990911i | \(-0.542950\pi\) | ||||
−0.134521 | + | 0.990911i | \(0.542950\pi\) | |||||||
\(930\) | 9.92879e6 | + | 3.65947e6i | 0.376434 | + | 0.138743i | ||||
\(931\) | 1.19028e6 | + | 1.61947e7i | 0.0450066 | + | 0.612347i | ||||
\(932\) | 1.35118e7 | + | 1.15258e7i | 0.509534 | + | 0.434643i | ||||
\(933\) | 6.87896e6i | 0.258713i | ||||||||
\(934\) | −1.38910e7 | + | 3.76887e7i | −0.521034 | + | 1.41366i | ||||
\(935\) | − | 1.91476e7i | − | 0.716283i | ||||||
\(936\) | −1.40728e7 | + | 7.89817e6i | −0.525040 | + | 0.294671i | ||||
\(937\) | −3.32962e7 | −1.23893 | −0.619463 | − | 0.785025i | \(-0.712650\pi\) | ||||
−0.619463 | + | 0.785025i | \(0.712650\pi\) | |||||||
\(938\) | −3.42383e6 | + | 9.28945e6i | −0.127059 | + | 0.344733i | ||||
\(939\) | −1.04482e7 | −0.386701 | ||||||||
\(940\) | 2.43724e7 | − | 2.85719e7i | 0.899661 | − | 1.05468i | ||||
\(941\) | − | 3.92170e7i | − | 1.44378i | −0.692009 | − | 0.721889i | \(-0.743274\pi\) | ||
0.692009 | − | 0.721889i | \(-0.256726\pi\) | |||||||
\(942\) | −4.43735e6 | − | 1.63548e6i | −0.162928 | − | 0.0600506i | ||||
\(943\) | −1.65234e7 | −0.605091 | ||||||||
\(944\) | 5.07678e6 | + | 3.18012e7i | 0.185421 | + | 1.16149i | ||||
\(945\) | 1.90090e7i | 0.692436i | ||||||||
\(946\) | −1.90514e7 | − | 7.02179e6i | −0.692147 | − | 0.255105i | ||||
\(947\) | − | 3.14175e7i | − | 1.13840i | −0.822198 | − | 0.569202i | \(-0.807252\pi\) | ||
0.822198 | − | 0.569202i | \(-0.192748\pi\) | |||||||
\(948\) | −1.36307e7 | − | 1.16273e7i | −0.492604 | − | 0.420202i | ||||
\(949\) | − | 2.18556e7i | − | 0.787765i | ||||||
\(950\) | 5.83384e6 | − | 2.03064e7i | 0.209723 | − | 0.730003i | ||||
\(951\) | − | 1.10659e7i | − | 0.396768i | ||||||
\(952\) | 1.09498e7 | − | 6.14539e6i | 0.391573 | − | 0.219764i | ||||
\(953\) | 1.13168e7i | 0.403638i | 0.979423 | + | 0.201819i | \(0.0646852\pi\) | ||||
−0.979423 | + | 0.201819i | \(0.935315\pi\) | |||||||
\(954\) | −1.80212e6 | + | 4.88946e6i | −0.0641079 | + | 0.173936i | ||||
\(955\) | 4.30016e7i | 1.52572i | ||||||||
\(956\) | 2.73544e6 | − | 3.20676e6i | 0.0968015 | − | 0.113481i | ||||
\(957\) | −1.14076e7 | −0.402636 | ||||||||
\(958\) | 1.69495e7 | − | 4.59869e7i | 0.596681 | − | 1.61890i | ||||
\(959\) | − | 3.58847e6i | − | 0.125998i | ||||||
\(960\) | 9.33338e6 | − | 1.52937e7i | 0.326859 | − | 0.535594i | ||||
\(961\) | −1.69249e7 | −0.591178 | ||||||||
\(962\) | 1.03764e7 | + | 3.82446e6i | 0.361502 | + | 0.133239i | ||||
\(963\) | −6.80809e6 | −0.236570 | ||||||||
\(964\) | −1.32035e7 | + | 1.54786e7i | −0.457612 | + | 0.536461i | ||||
\(965\) | 1.59355e7i | 0.550867i | ||||||||
\(966\) | −2.65041e6 | − | 976866.i | −0.0913841 | − | 0.0336816i | ||||
\(967\) | − | 9.67290e6i | − | 0.332652i | −0.986071 | − | 0.166326i | \(-0.946810\pi\) | ||
0.986071 | − | 0.166326i | \(-0.0531905\pi\) | |||||||
\(968\) | −6.30327e6 | − | 1.12311e7i | −0.216211 | − | 0.385241i | ||||
\(969\) | −732454. | − | 9.96555e6i | −0.0250594 | − | 0.340951i | ||||
\(970\) | −1.32004e7 | + | 3.58150e7i | −0.450460 | + | 1.22218i | ||||
\(971\) | −2.30392e7 | −0.784186 | −0.392093 | − | 0.919926i | \(-0.628249\pi\) | ||||
−0.392093 | + | 0.919926i | \(0.628249\pi\) | |||||||
\(972\) | −2.28444e7 | − | 1.94868e7i | −0.775559 | − | 0.661568i | ||||
\(973\) | 2.93564e7 | 0.994079 | ||||||||
\(974\) | −8.15864e6 | − | 3.00704e6i | −0.275563 | − | 0.101565i | ||||
\(975\) | − | 8.27165e6i | − | 0.278664i | ||||||
\(976\) | −4.74626e6 | − | 2.97308e7i | −0.159488 | − | 0.999039i | ||||
\(977\) | − | 1.94595e7i | − | 0.652220i | −0.945332 | − | 0.326110i | \(-0.894262\pi\) | ||
0.945332 | − | 0.326110i | \(-0.105738\pi\) | |||||||
\(978\) | −1.29932e6 | + | 3.52529e6i | −0.0434379 | + | 0.117855i | ||||
\(979\) | 1.84045e7 | 0.613716 | ||||||||
\(980\) | 1.86296e7 | + | 1.58915e7i | 0.619639 | + | 0.528565i | ||||
\(981\) | 4.51462e7i | 1.49778i | ||||||||
\(982\) | −1.85047e7 | + | 5.02065e7i | −0.612355 | + | 1.66143i | ||||
\(983\) | 4.54651e7 | 1.50070 | 0.750351 | − | 0.661039i | \(-0.229884\pi\) | ||||
0.750351 | + | 0.661039i | \(0.229884\pi\) | |||||||
\(984\) | −2.28759e7 | + | 1.28388e7i | −0.753166 | + | 0.422703i | ||||
\(985\) | 5.58442e7 | 1.83395 | ||||||||
\(986\) | 8.69271e6 | − | 2.35849e7i | 0.284750 | − | 0.772576i | ||||
\(987\) | −9.39979e6 | −0.307132 | ||||||||
\(988\) | −1.91892e7 | − | 1.40759e7i | −0.625408 | − | 0.458758i | ||||
\(989\) | −1.00645e7 | −0.327192 | ||||||||
\(990\) | 8.20459e6 | − | 2.22605e7i | 0.266054 | − | 0.721851i | ||||
\(991\) | 7.45194e6 | 0.241038 | 0.120519 | − | 0.992711i | \(-0.461544\pi\) | ||||
0.120519 | + | 0.992711i | \(0.461544\pi\) | |||||||
\(992\) | 3.83640e6 | − | 1.94425e7i | 0.123778 | − | 0.627296i | ||||
\(993\) | −4.17955e6 | −0.134510 | ||||||||
\(994\) | 417823. | − | 1.13363e6i | 0.0134130 | − | 0.0363919i | ||||
\(995\) | 6.29054e7i | 2.01433i | ||||||||
\(996\) | 5.36790e6 | − | 6.29281e6i | 0.171457 | − | 0.201000i | ||||
\(997\) | 2.53403e7 | 0.807371 | 0.403685 | − | 0.914898i | \(-0.367729\pi\) | ||||
0.403685 | + | 0.914898i | \(0.367729\pi\) | |||||||
\(998\) | −1.34205e7 | + | 3.64122e7i | −0.426523 | + | 1.15723i | ||||
\(999\) | 1.31649e7i | 0.417354i |
(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 | 76.6.d.a.75.5 | ✓ | 48 | |
4.3 | odd | 2 | inner | 76.6.d.a.75.43 | yes | 48 | |
19.18 | odd | 2 | inner | 76.6.d.a.75.44 | yes | 48 | |
76.75 | even | 2 | inner | 76.6.d.a.75.6 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.d.a.75.5 | ✓ | 48 | 1.1 | even | 1 | trivial | |
76.6.d.a.75.6 | yes | 48 | 76.75 | even | 2 | inner | |
76.6.d.a.75.43 | yes | 48 | 4.3 | odd | 2 | inner | |
76.6.d.a.75.44 | yes | 48 | 19.18 | odd | 2 | inner |