Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [55,6,Mod(32,55)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(55, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("55.32");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82111008971\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 32.13 | ||
Character | \(\chi\) | \(=\) | 55.32 |
Dual form | 55.6.e.b.43.13 |
$q$-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 \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).
\(n\) | \(12\) | \(46\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.819850 | + | 0.819850i | −0.144930 | + | 0.144930i | −0.775849 | − | 0.630919i | \(-0.782678\pi\) |
0.630919 | + | 0.775849i | \(0.282678\pi\) | |||||||
\(3\) | −2.25487 | + | 2.25487i | −0.144650 | + | 0.144650i | −0.775723 | − | 0.631073i | \(-0.782615\pi\) |
0.631073 | + | 0.775723i | \(0.282615\pi\) | |||||||
\(4\) | 30.6557i | 0.957990i | ||||||||
\(5\) | 5.74279 | − | 55.6059i | 0.102730 | − | 0.994709i | ||||
\(6\) | − | 3.69731i | − | 0.0419284i | ||||||
\(7\) | −88.0749 | + | 88.0749i | −0.679371 | + | 0.679371i | −0.959858 | − | 0.280487i | \(-0.909504\pi\) |
0.280487 | + | 0.959858i | \(0.409504\pi\) | |||||||
\(8\) | −51.3683 | − | 51.3683i | −0.283772 | − | 0.283772i | ||||
\(9\) | 232.831i | 0.958153i | ||||||||
\(10\) | 40.8803 | + | 50.2967i | 0.129275 | + | 0.159052i | ||||
\(11\) | 68.0926 | − | 395.493i | 0.169675 | − | 0.985500i | ||||
\(12\) | −69.1247 | − | 69.1247i | −0.138573 | − | 0.138573i | ||||
\(13\) | −741.664 | − | 741.664i | −1.21716 | − | 1.21716i | −0.968621 | − | 0.248542i | \(-0.920049\pi\) |
−0.248542 | − | 0.968621i | \(-0.579951\pi\) | |||||||
\(14\) | − | 144.416i | − | 0.196923i | ||||||
\(15\) | 112.435 | + | 138.334i | 0.129025 | + | 0.158745i | ||||
\(16\) | −896.754 | −0.875736 | ||||||||
\(17\) | −805.641 | + | 805.641i | −0.676113 | + | 0.676113i | −0.959118 | − | 0.283005i | \(-0.908669\pi\) |
0.283005 | + | 0.959118i | \(0.408669\pi\) | |||||||
\(18\) | −190.887 | − | 190.887i | −0.138865 | − | 0.138865i | ||||
\(19\) | −1851.56 | −1.17667 | −0.588334 | − | 0.808618i | \(-0.700216\pi\) | ||||
−0.588334 | + | 0.808618i | \(0.700216\pi\) | |||||||
\(20\) | 1704.64 | + | 176.049i | 0.952922 | + | 0.0984145i | ||||
\(21\) | − | 397.196i | − | 0.196542i | ||||||
\(22\) | 268.419 | + | 380.070i | 0.118238 | + | 0.167420i | ||||
\(23\) | −561.188 | + | 561.188i | −0.221202 | + | 0.221202i | −0.809004 | − | 0.587803i | \(-0.799993\pi\) |
0.587803 | + | 0.809004i | \(0.299993\pi\) | |||||||
\(24\) | 231.658 | 0.0820954 | ||||||||
\(25\) | −3059.04 | − | 638.666i | −0.978893 | − | 0.204373i | ||||
\(26\) | 1216.11 | 0.352808 | ||||||||
\(27\) | −1072.94 | − | 1072.94i | −0.283247 | − | 0.283247i | ||||
\(28\) | −2700.00 | − | 2700.00i | −0.650831 | − | 0.650831i | ||||
\(29\) | 3983.79 | 0.879632 | 0.439816 | − | 0.898088i | \(-0.355044\pi\) | ||||
0.439816 | + | 0.898088i | \(0.355044\pi\) | |||||||
\(30\) | −205.593 | − | 21.2329i | −0.0417066 | − | 0.00430731i | ||||
\(31\) | 4011.45 | 0.749717 | 0.374859 | − | 0.927082i | \(-0.377691\pi\) | ||||
0.374859 | + | 0.927082i | \(0.377691\pi\) | |||||||
\(32\) | 2378.99 | − | 2378.99i | 0.410693 | − | 0.410693i | ||||
\(33\) | 738.246 | + | 1045.33i | 0.118009 | + | 0.167096i | ||||
\(34\) | − | 1321.01i | − | 0.195979i | ||||||
\(35\) | 4391.69 | + | 5403.28i | 0.605985 | + | 0.745569i | ||||
\(36\) | −7137.60 | −0.917901 | ||||||||
\(37\) | 5642.57 | + | 5642.57i | 0.677598 | + | 0.677598i | 0.959456 | − | 0.281858i | \(-0.0909507\pi\) |
−0.281858 | + | 0.959456i | \(0.590951\pi\) | |||||||
\(38\) | 1518.00 | − | 1518.00i | 0.170535 | − | 0.170535i | ||||
\(39\) | 3344.72 | 0.352126 | ||||||||
\(40\) | −3151.38 | + | 2561.38i | −0.311423 | + | 0.253119i | ||||
\(41\) | 14226.7i | 1.32174i | 0.750502 | + | 0.660868i | \(0.229812\pi\) | ||||
−0.750502 | + | 0.660868i | \(0.770188\pi\) | |||||||
\(42\) | 325.641 | + | 325.641i | 0.0284849 | + | 0.0284849i | ||||
\(43\) | 3129.47 | + | 3129.47i | 0.258107 | + | 0.258107i | 0.824284 | − | 0.566177i | \(-0.191578\pi\) |
−0.566177 | + | 0.824284i | \(0.691578\pi\) | |||||||
\(44\) | 12124.1 | + | 2087.42i | 0.944100 | + | 0.162547i | ||||
\(45\) | 12946.8 | + | 1337.10i | 0.953083 | + | 0.0984311i | ||||
\(46\) | − | 920.180i | − | 0.0641177i | ||||||
\(47\) | −18434.0 | − | 18434.0i | −1.21724 | − | 1.21724i | −0.968595 | − | 0.248645i | \(-0.920015\pi\) |
−0.248645 | − | 0.968595i | \(-0.579985\pi\) | |||||||
\(48\) | 2022.07 | − | 2022.07i | 0.126675 | − | 0.126675i | ||||
\(49\) | 1292.61i | 0.0769093i | ||||||||
\(50\) | 3031.56 | − | 1984.34i | 0.171491 | − | 0.112251i | ||||
\(51\) | − | 3633.24i | − | 0.195600i | ||||||
\(52\) | 22736.2 | − | 22736.2i | 1.16603 | − | 1.16603i | ||||
\(53\) | −2404.01 | + | 2404.01i | −0.117557 | + | 0.117557i | −0.763438 | − | 0.645881i | \(-0.776490\pi\) |
0.645881 | + | 0.763438i | \(0.276490\pi\) | |||||||
\(54\) | 1759.30 | 0.0821022 | ||||||||
\(55\) | −21600.7 | − | 6057.58i | −0.962855 | − | 0.270018i | ||||
\(56\) | 9048.51 | 0.385573 | ||||||||
\(57\) | 4175.04 | − | 4175.04i | 0.170205 | − | 0.170205i | ||||
\(58\) | −3266.11 | + | 3266.11i | −0.127485 | + | 0.127485i | ||||
\(59\) | 22820.4i | 0.853479i | 0.904375 | + | 0.426739i | \(0.140338\pi\) | ||||
−0.904375 | + | 0.426739i | \(0.859662\pi\) | |||||||
\(60\) | −4240.71 | + | 3446.77i | −0.152076 | + | 0.123605i | ||||
\(61\) | 37872.4i | 1.30316i | 0.758579 | + | 0.651581i | \(0.225894\pi\) | ||||
−0.758579 | + | 0.651581i | \(0.774106\pi\) | |||||||
\(62\) | −3288.79 | + | 3288.79i | −0.108657 | + | 0.108657i | ||||
\(63\) | −20506.6 | − | 20506.6i | −0.650941 | − | 0.650941i | ||||
\(64\) | − | 24795.3i | − | 0.756692i | ||||||
\(65\) | −45500.1 | + | 36981.7i | −1.33576 | + | 1.08568i | ||||
\(66\) | −1462.26 | − | 251.760i | −0.0413204 | − | 0.00711420i | ||||
\(67\) | 5682.77 | + | 5682.77i | 0.154658 | + | 0.154658i | 0.780195 | − | 0.625537i | \(-0.215120\pi\) |
−0.625537 | + | 0.780195i | \(0.715120\pi\) | |||||||
\(68\) | −24697.5 | − | 24697.5i | −0.647710 | − | 0.647710i | ||||
\(69\) | − | 2530.82i | − | 0.0639938i | ||||||
\(70\) | −8030.41 | − | 829.353i | −0.195881 | − | 0.0202299i | ||||
\(71\) | −3271.14 | −0.0770111 | −0.0385056 | − | 0.999258i | \(-0.512260\pi\) | ||||
−0.0385056 | + | 0.999258i | \(0.512260\pi\) | |||||||
\(72\) | 11960.1 | − | 11960.1i | 0.271897 | − | 0.271897i | ||||
\(73\) | −25842.3 | − | 25842.3i | −0.567575 | − | 0.567575i | 0.363873 | − | 0.931449i | \(-0.381454\pi\) |
−0.931449 | + | 0.363873i | \(0.881454\pi\) | |||||||
\(74\) | −9252.11 | −0.196409 | ||||||||
\(75\) | 8337.86 | − | 5457.64i | 0.171160 | − | 0.112034i | ||||
\(76\) | − | 56760.9i | − | 1.12724i | ||||||
\(77\) | 28835.7 | + | 40830.2i | 0.554248 | + | 0.784793i | ||||
\(78\) | −2742.16 | + | 2742.16i | −0.0510337 | + | 0.0510337i | ||||
\(79\) | 41319.9 | 0.744889 | 0.372445 | − | 0.928054i | \(-0.378520\pi\) | ||||
0.372445 | + | 0.928054i | \(0.378520\pi\) | |||||||
\(80\) | −5149.87 | + | 49864.8i | −0.0899645 | + | 0.871103i | ||||
\(81\) | −51739.3 | −0.876209 | ||||||||
\(82\) | −11663.8 | − | 11663.8i | −0.191560 | − | 0.191560i | ||||
\(83\) | −67888.9 | − | 67888.9i | −1.08169 | − | 1.08169i | −0.996352 | − | 0.0853401i | \(-0.972802\pi\) |
−0.0853401 | − | 0.996352i | \(-0.527198\pi\) | |||||||
\(84\) | 12176.3 | 0.188286 | ||||||||
\(85\) | 40171.8 | + | 49425.0i | 0.603079 | + | 0.741993i | ||||
\(86\) | −5131.39 | −0.0748151 | ||||||||
\(87\) | −8982.93 | + | 8982.93i | −0.127239 | + | 0.127239i | ||||
\(88\) | −23813.6 | + | 16818.0i | −0.327807 | + | 0.231508i | ||||
\(89\) | − | 86508.1i | − | 1.15766i | −0.815447 | − | 0.578831i | \(-0.803509\pi\) | ||
0.815447 | − | 0.578831i | \(-0.196491\pi\) | |||||||
\(90\) | −11710.6 | + | 9518.20i | −0.152396 | + | 0.123865i | ||||
\(91\) | 130644. | 1.65381 | ||||||||
\(92\) | −17203.6 | − | 17203.6i | −0.211909 | − | 0.211909i | ||||
\(93\) | −9045.31 | + | 9045.31i | −0.108447 | + | 0.108447i | ||||
\(94\) | 30226.3 | 0.352830 | ||||||||
\(95\) | −10633.1 | + | 102958.i | −0.120879 | + | 1.17044i | ||||
\(96\) | 10728.6i | 0.118814i | ||||||||
\(97\) | −24593.2 | − | 24593.2i | −0.265390 | − | 0.265390i | 0.561849 | − | 0.827240i | \(-0.310090\pi\) |
−0.827240 | + | 0.561849i | \(0.810090\pi\) | |||||||
\(98\) | −1059.75 | − | 1059.75i | −0.0111465 | − | 0.0111465i | ||||
\(99\) | 92083.0 | + | 15854.1i | 0.944260 | + | 0.162575i | ||||
\(100\) | 19578.8 | − | 93777.0i | 0.195788 | − | 0.937770i | ||||
\(101\) | 102376.i | 0.998606i | 0.866427 | + | 0.499303i | \(0.166411\pi\) | ||||
−0.866427 | + | 0.499303i | \(0.833589\pi\) | |||||||
\(102\) | 2978.71 | + | 2978.71i | 0.0283483 | + | 0.0283483i | ||||
\(103\) | −99062.9 | + | 99062.9i | −0.920064 | + | 0.920064i | −0.997033 | − | 0.0769694i | \(-0.975476\pi\) |
0.0769694 | + | 0.997033i | \(0.475476\pi\) | |||||||
\(104\) | 76196.0i | 0.690794i | ||||||||
\(105\) | −22086.4 | − | 2281.01i | −0.195502 | − | 0.0201908i | ||||
\(106\) | − | 3941.86i | − | 0.0340750i | ||||||
\(107\) | 489.464 | − | 489.464i | 0.00413296 | − | 0.00413296i | −0.705037 | − | 0.709170i | \(-0.749070\pi\) |
0.709170 | + | 0.705037i | \(0.249070\pi\) | |||||||
\(108\) | 32891.7 | − | 32891.7i | 0.271348 | − | 0.271348i | ||||
\(109\) | 134140. | 1.08141 | 0.540706 | − | 0.841212i | \(-0.318157\pi\) | ||||
0.540706 | + | 0.841212i | \(0.318157\pi\) | |||||||
\(110\) | 22675.6 | − | 12743.0i | 0.178681 | − | 0.100413i | ||||
\(111\) | −25446.5 | −0.196029 | ||||||||
\(112\) | 78981.5 | − | 78981.5i | 0.594950 | − | 0.594950i | ||||
\(113\) | 113964. | − | 113964.i | 0.839601 | − | 0.839601i | −0.149205 | − | 0.988806i | \(-0.547671\pi\) |
0.988806 | + | 0.149205i | \(0.0476715\pi\) | |||||||
\(114\) | 6845.80i | 0.0493358i | ||||||||
\(115\) | 27982.6 | + | 34428.2i | 0.197307 | + | 0.242756i | ||||
\(116\) | 122126.i | 0.842679i | ||||||||
\(117\) | 172682. | − | 172682.i | 1.16623 | − | 1.16623i | ||||
\(118\) | −18709.3 | − | 18709.3i | −0.123695 | − | 0.123695i | ||||
\(119\) | − | 141914.i | − | 0.918663i | ||||||
\(120\) | 1330.36 | − | 12881.5i | 0.00843367 | − | 0.0816610i | ||||
\(121\) | −151778. | − | 53860.2i | −0.942421 | − | 0.334430i | ||||
\(122\) | −31049.7 | − | 31049.7i | −0.188868 | − | 0.188868i | ||||
\(123\) | −32079.4 | − | 32079.4i | −0.191189 | − | 0.191189i | ||||
\(124\) | 122974.i | 0.718222i | ||||||||
\(125\) | −53081.1 | + | 166433.i | −0.303854 | + | 0.952719i | ||||
\(126\) | 33624.6 | 0.188682 | ||||||||
\(127\) | −72970.4 | + | 72970.4i | −0.401455 | + | 0.401455i | −0.878746 | − | 0.477290i | \(-0.841619\pi\) |
0.477290 | + | 0.878746i | \(0.341619\pi\) | |||||||
\(128\) | 96456.0 | + | 96456.0i | 0.520361 | + | 0.520361i | ||||
\(129\) | −14113.1 | −0.0746704 | ||||||||
\(130\) | 6983.84 | − | 67622.7i | 0.0362440 | − | 0.350941i | ||||
\(131\) | 170832.i | 0.869741i | 0.900493 | + | 0.434871i | \(0.143206\pi\) | ||||
−0.900493 | + | 0.434871i | \(0.856794\pi\) | |||||||
\(132\) | −32045.2 | + | 22631.4i | −0.160077 | + | 0.113052i | ||||
\(133\) | 163076. | − | 163076.i | 0.799395 | − | 0.799395i | ||||
\(134\) | −9318.04 | −0.0448294 | ||||||||
\(135\) | −65823.4 | + | 53500.1i | −0.310847 | + | 0.252651i | ||||
\(136\) | 82768.7 | 0.383724 | ||||||||
\(137\) | 145269. | + | 145269.i | 0.661258 | + | 0.661258i | 0.955677 | − | 0.294418i | \(-0.0951259\pi\) |
−0.294418 | + | 0.955677i | \(0.595126\pi\) | |||||||
\(138\) | 2074.89 | + | 2074.89i | 0.00927464 | + | 0.00927464i | ||||
\(139\) | −361121. | −1.58532 | −0.792659 | − | 0.609665i | \(-0.791304\pi\) | ||||
−0.792659 | + | 0.609665i | \(0.791304\pi\) | |||||||
\(140\) | −165641. | + | 134630.i | −0.714248 | + | 0.580528i | ||||
\(141\) | 83132.9 | 0.352148 | ||||||||
\(142\) | 2681.85 | − | 2681.85i | 0.0111613 | − | 0.0111613i | ||||
\(143\) | −343824. | + | 242821.i | −1.40604 | + | 0.992992i | ||||
\(144\) | − | 208792.i | − | 0.839089i | ||||||
\(145\) | 22878.0 | − | 221522.i | 0.0903647 | − | 0.874978i | ||||
\(146\) | 42373.6 | 0.164518 | ||||||||
\(147\) | −2914.68 | − | 2914.68i | −0.0111249 | − | 0.0111249i | ||||
\(148\) | −172977. | + | 172977.i | −0.649133 | + | 0.649133i | ||||
\(149\) | 157044. | 0.579505 | 0.289752 | − | 0.957102i | \(-0.406427\pi\) | ||||
0.289752 | + | 0.957102i | \(0.406427\pi\) | |||||||
\(150\) | −2361.35 | + | 11310.2i | −0.00856904 | + | 0.0410434i | ||||
\(151\) | − | 406149.i | − | 1.44958i | −0.688968 | − | 0.724792i | \(-0.741936\pi\) | ||
0.688968 | − | 0.724792i | \(-0.258064\pi\) | |||||||
\(152\) | 95111.5 | + | 95111.5i | 0.333906 | + | 0.333906i | ||||
\(153\) | −187578. | − | 187578.i | −0.647819 | − | 0.647819i | ||||
\(154\) | −57115.6 | − | 9833.68i | −0.194068 | − | 0.0334129i | ||||
\(155\) | 23036.9 | − | 223061.i | 0.0770185 | − | 0.745750i | ||||
\(156\) | 102535.i | 0.337333i | ||||||||
\(157\) | −294046. | − | 294046.i | −0.952063 | − | 0.952063i | 0.0468397 | − | 0.998902i | \(-0.485085\pi\) |
−0.998902 | + | 0.0468397i | \(0.985085\pi\) | |||||||
\(158\) | −33876.1 | + | 33876.1i | −0.107957 | + | 0.107957i | ||||
\(159\) | − | 10841.5i | − | 0.0340091i | ||||||
\(160\) | −118624. | − | 145948.i | −0.366330 | − | 0.450711i | ||||
\(161\) | − | 98853.2i | − | 0.300556i | ||||||
\(162\) | 42418.4 | − | 42418.4i | 0.126989 | − | 0.126989i | ||||
\(163\) | 321782. | − | 321782.i | 0.948620 | − | 0.948620i | −0.0501226 | − | 0.998743i | \(-0.515961\pi\) |
0.998743 | + | 0.0501226i | \(0.0159612\pi\) | |||||||
\(164\) | −436130. | −1.26621 | ||||||||
\(165\) | 62365.9 | − | 35047.7i | 0.178335 | − | 0.100219i | ||||
\(166\) | 111317. | 0.313540 | ||||||||
\(167\) | −285860. | + | 285860.i | −0.793164 | + | 0.793164i | −0.982007 | − | 0.188843i | \(-0.939526\pi\) |
0.188843 | + | 0.982007i | \(0.439526\pi\) | |||||||
\(168\) | −20403.2 | + | 20403.2i | −0.0557733 | + | 0.0557733i | ||||
\(169\) | 728838.i | 1.96297i | ||||||||
\(170\) | −73455.9 | − | 7586.28i | −0.194942 | − | 0.0201329i | ||||
\(171\) | − | 431101.i | − | 1.12743i | ||||||
\(172\) | −95936.1 | + | 95936.1i | −0.247264 | + | 0.247264i | ||||
\(173\) | 427806. | + | 427806.i | 1.08675 | + | 1.08675i | 0.995861 | + | 0.0908942i | \(0.0289725\pi\) |
0.0908942 | + | 0.995861i | \(0.471027\pi\) | |||||||
\(174\) | − | 14729.3i | − | 0.0368815i | ||||||
\(175\) | 325675. | − | 213174.i | 0.803877 | − | 0.526187i | ||||
\(176\) | −61062.3 | + | 354659.i | −0.148591 | + | 0.863038i | ||||
\(177\) | −51457.0 | − | 51457.0i | −0.123456 | − | 0.123456i | ||||
\(178\) | 70923.7 | + | 70923.7i | 0.167780 | + | 0.167780i | ||||
\(179\) | − | 241635.i | − | 0.563672i | −0.959463 | − | 0.281836i | \(-0.909057\pi\) | ||
0.959463 | − | 0.281836i | \(-0.0909434\pi\) | |||||||
\(180\) | −40989.7 | + | 396893.i | −0.0942961 | + | 0.913045i | ||||
\(181\) | −632254. | −1.43448 | −0.717241 | − | 0.696825i | \(-0.754595\pi\) | ||||
−0.717241 | + | 0.696825i | \(0.754595\pi\) | |||||||
\(182\) | −107108. | + | 107108.i | −0.239687 | + | 0.239687i | ||||
\(183\) | −85397.4 | − | 85397.4i | −0.188503 | − | 0.188503i | ||||
\(184\) | 57654.5 | 0.125542 | ||||||||
\(185\) | 346164. | − | 281356.i | 0.743623 | − | 0.604404i | ||||
\(186\) | − | 14831.6i | − | 0.0314344i | ||||||
\(187\) | 263767. | + | 373483.i | 0.551590 | + | 0.781029i | ||||
\(188\) | 565108. | − | 565108.i | 1.16610 | − | 1.16610i | ||||
\(189\) | 188998. | 0.384860 | ||||||||
\(190\) | −75692.4 | − | 93127.5i | −0.152114 | − | 0.187152i | ||||
\(191\) | −8107.14 | −0.0160799 | −0.00803997 | − | 0.999968i | \(-0.502559\pi\) | ||||
−0.00803997 | + | 0.999968i | \(0.502559\pi\) | |||||||
\(192\) | 55910.2 | + | 55910.2i | 0.109456 | + | 0.109456i | ||||
\(193\) | 422534. | + | 422534.i | 0.816522 | + | 0.816522i | 0.985602 | − | 0.169080i | \(-0.0540797\pi\) |
−0.169080 | + | 0.985602i | \(0.554080\pi\) | |||||||
\(194\) | 40325.4 | 0.0769263 | ||||||||
\(195\) | 19208.0 | − | 185986.i | 0.0361739 | − | 0.350263i | ||||
\(196\) | −39626.0 | −0.0736783 | ||||||||
\(197\) | −96838.2 | + | 96838.2i | −0.177779 | + | 0.177779i | −0.790387 | − | 0.612608i | \(-0.790121\pi\) |
0.612608 | + | 0.790387i | \(0.290121\pi\) | |||||||
\(198\) | −88492.2 | + | 62496.3i | −0.160414 | + | 0.113290i | ||||
\(199\) | − | 377063.i | − | 0.674965i | −0.941332 | − | 0.337482i | \(-0.890425\pi\) | ||
0.941332 | − | 0.337482i | \(-0.109575\pi\) | |||||||
\(200\) | 124330. | + | 189945.i | 0.219787 | + | 0.335778i | ||||
\(201\) | −25627.9 | −0.0447427 | ||||||||
\(202\) | −83932.9 | − | 83932.9i | −0.144728 | − | 0.144728i | ||||
\(203\) | −350872. | + | 350872.i | −0.597597 | + | 0.597597i | ||||
\(204\) | 111379. | 0.187383 | ||||||||
\(205\) | 791090. | + | 81701.0i | 1.31474 | + | 0.135782i | ||||
\(206\) | − | 162433.i | − | 0.266690i | ||||||
\(207\) | −130662. | − | 130662.i | −0.211945 | − | 0.211945i | ||||
\(208\) | 665090. | + | 665090.i | 1.06591 | + | 1.06591i | ||||
\(209\) | −126078. | + | 732279.i | −0.199651 | + | 1.15961i | ||||
\(210\) | 19977.6 | − | 16237.5i | 0.0312605 | − | 0.0254080i | ||||
\(211\) | − | 737422.i | − | 1.14028i | −0.821549 | − | 0.570138i | \(-0.806890\pi\) | ||
0.821549 | − | 0.570138i | \(-0.193110\pi\) | |||||||
\(212\) | −73696.6 | − | 73696.6i | −0.112618 | − | 0.112618i | ||||
\(213\) | 7376.01 | − | 7376.01i | 0.0111397 | − | 0.0111397i | ||||
\(214\) | 802.574i | 0.00119798i | ||||||||
\(215\) | 191989. | − | 156045.i | 0.283257 | − | 0.230226i | ||||
\(216\) | 110230.i | 0.160755i | ||||||||
\(217\) | −353308. | + | 353308.i | −0.509336 | + | 0.509336i | ||||
\(218\) | −109974. | + | 109974.i | −0.156729 | + | 0.156729i | ||||
\(219\) | 116542. | 0.164200 | ||||||||
\(220\) | 185699. | − | 662184.i | 0.258675 | − | 0.922406i | ||||
\(221\) | 1.19503e6 | 1.64588 | ||||||||
\(222\) | 20862.3 | − | 20862.3i | 0.0284106 | − | 0.0284106i | ||||
\(223\) | 16331.6 | − | 16331.6i | 0.0219921 | − | 0.0219921i | −0.696025 | − | 0.718017i | \(-0.745050\pi\) |
0.718017 | + | 0.696025i | \(0.245050\pi\) | |||||||
\(224\) | 419058.i | 0.558026i | ||||||||
\(225\) | 148701. | − | 712240.i | 0.195821 | − | 0.937929i | ||||
\(226\) | 186867.i | 0.243367i | ||||||||
\(227\) | −355915. | + | 355915.i | −0.458439 | + | 0.458439i | −0.898143 | − | 0.439704i | \(-0.855083\pi\) |
0.439704 | + | 0.898143i | \(0.355083\pi\) | |||||||
\(228\) | 127989. | + | 127989.i | 0.163055 | + | 0.163055i | ||||
\(229\) | − | 1.50015e6i | − | 1.89036i | −0.326544 | − | 0.945182i | \(-0.605884\pi\) | ||
0.326544 | − | 0.945182i | \(-0.394116\pi\) | |||||||
\(230\) | −51167.5 | − | 5284.40i | −0.0637785 | − | 0.00658682i | ||||
\(231\) | −157088. | − | 27046.1i | −0.193692 | − | 0.0333483i | ||||
\(232\) | −204640. | − | 204640.i | −0.249615 | − | 0.249615i | ||||
\(233\) | 191449. | + | 191449.i | 0.231028 | + | 0.231028i | 0.813122 | − | 0.582094i | \(-0.197766\pi\) |
−0.582094 | + | 0.813122i | \(0.697766\pi\) | |||||||
\(234\) | 283147.i | 0.338044i | ||||||||
\(235\) | −1.13091e6 | + | 919180.i | −1.33585 | + | 1.08575i | ||||
\(236\) | −699574. | −0.817625 | ||||||||
\(237\) | −93171.1 | + | 93171.1i | −0.107748 | + | 0.107748i | ||||
\(238\) | 116348. | + | 116348.i | 0.133142 | + | 0.133142i | ||||
\(239\) | −972477. | −1.10125 | −0.550624 | − | 0.834754i | \(-0.685610\pi\) | ||||
−0.550624 | + | 0.834754i | \(0.685610\pi\) | |||||||
\(240\) | −100827. | − | 124051.i | −0.112992 | − | 0.139019i | ||||
\(241\) | − | 169545.i | − | 0.188037i | −0.995570 | − | 0.0940186i | \(-0.970029\pi\) | ||
0.995570 | − | 0.0940186i | \(-0.0299713\pi\) | |||||||
\(242\) | 168592. | − | 80277.7i | 0.185054 | − | 0.0881164i | ||||
\(243\) | 377390. | − | 377390.i | 0.409991 | − | 0.409991i | ||||
\(244\) | −1.16100e6 | −1.24842 | ||||||||
\(245\) | 71877.0 | + | 7423.21i | 0.0765024 | + | 0.00790090i | ||||
\(246\) | 52600.6 | 0.0554183 | ||||||||
\(247\) | 1.37324e6 | + | 1.37324e6i | 1.43220 | + | 1.43220i | ||||
\(248\) | −206061. | − | 206061.i | −0.212749 | − | 0.212749i | ||||
\(249\) | 306162. | 0.312934 | ||||||||
\(250\) | −92931.6 | − | 179969.i | −0.0940402 | − | 0.182115i | ||||
\(251\) | −550651. | −0.551686 | −0.275843 | − | 0.961203i | \(-0.588957\pi\) | ||||
−0.275843 | + | 0.961203i | \(0.588957\pi\) | |||||||
\(252\) | 628643. | − | 628643.i | 0.623596 | − | 0.623596i | ||||
\(253\) | 183733. | + | 260158.i | 0.180462 | + | 0.255527i | ||||
\(254\) | − | 119649.i | − | 0.116366i | ||||||
\(255\) | −202029. | − | 20864.9i | −0.194565 | − | 0.0200940i | ||||
\(256\) | 635291. | 0.605860 | ||||||||
\(257\) | −708471. | − | 708471.i | −0.669097 | − | 0.669097i | 0.288410 | − | 0.957507i | \(-0.406873\pi\) |
−0.957507 | + | 0.288410i | \(0.906873\pi\) | |||||||
\(258\) | 11570.6 | − | 11570.6i | 0.0108220 | − | 0.0108220i | ||||
\(259\) | −993937. | −0.920682 | ||||||||
\(260\) | −1.13370e6 | − | 1.39484e6i | −1.04008 | − | 1.27965i | ||||
\(261\) | 927549.i | 0.842822i | ||||||||
\(262\) | −140056. | − | 140056.i | −0.126052 | − | 0.126052i | ||||
\(263\) | −463210. | − | 463210.i | −0.412942 | − | 0.412942i | 0.469820 | − | 0.882762i | \(-0.344319\pi\) |
−0.882762 | + | 0.469820i | \(0.844319\pi\) | |||||||
\(264\) | 15774.2 | − | 91618.9i | 0.0139295 | − | 0.0809050i | ||||
\(265\) | 119872. | + | 147483.i | 0.104858 | + | 0.129011i | ||||
\(266\) | 267396.i | 0.231713i | ||||||||
\(267\) | 195065. | + | 195065.i | 0.167456 | + | 0.167456i | ||||
\(268\) | −174209. | + | 174209.i | −0.148161 | + | 0.148161i | ||||
\(269\) | 657951.i | 0.554387i | 0.960814 | + | 0.277193i | \(0.0894043\pi\) | ||||
−0.960814 | + | 0.277193i | \(0.910596\pi\) | |||||||
\(270\) | 10103.3 | − | 97827.4i | 0.00843437 | − | 0.0816678i | ||||
\(271\) | − | 162774.i | − | 0.134636i | −0.997732 | − | 0.0673181i | \(-0.978556\pi\) | ||
0.997732 | − | 0.0673181i | \(-0.0214442\pi\) | |||||||
\(272\) | 722461. | − | 722461.i | 0.592096 | − | 0.592096i | ||||
\(273\) | −294586. | + | 294586.i | −0.239224 | + | 0.239224i | ||||
\(274\) | −238197. | −0.191673 | ||||||||
\(275\) | −460886. | + | 1.16634e6i | −0.367504 | + | 0.930022i | ||||
\(276\) | 77583.9 | 0.0613054 | ||||||||
\(277\) | −322956. | + | 322956.i | −0.252897 | + | 0.252897i | −0.822157 | − | 0.569260i | \(-0.807230\pi\) |
0.569260 | + | 0.822157i | \(0.307230\pi\) | |||||||
\(278\) | 296065. | − | 296065.i | 0.229761 | − | 0.229761i | ||||
\(279\) | 933991.i | 0.718343i | ||||||||
\(280\) | 51963.7 | − | 503151.i | 0.0396100 | − | 0.383533i | ||||
\(281\) | − | 135801.i | − | 0.102598i | −0.998683 | − | 0.0512988i | \(-0.983664\pi\) | ||
0.998683 | − | 0.0512988i | \(-0.0163361\pi\) | |||||||
\(282\) | −68156.5 | + | 68156.5i | −0.0510369 | + | 0.0510369i | ||||
\(283\) | −1.20597e6 | − | 1.20597e6i | −0.895099 | − | 0.895099i | 0.0998984 | − | 0.994998i | \(-0.468148\pi\) |
−0.994998 | + | 0.0998984i | \(0.968148\pi\) | |||||||
\(284\) | − | 100279.i | − | 0.0737759i | ||||||
\(285\) | −208180. | − | 256133.i | −0.151820 | − | 0.186790i | ||||
\(286\) | 82807.8 | − | 480961.i | 0.0598627 | − | 0.347692i | ||||
\(287\) | −1.25302e6 | − | 1.25302e6i | −0.897950 | − | 0.897950i | ||||
\(288\) | 553902. | + | 553902.i | 0.393506 | + | 0.393506i | ||||
\(289\) | 121742.i | 0.0857427i | ||||||||
\(290\) | 162858. | + | 200371.i | 0.113714 | + | 0.139907i | ||||
\(291\) | 110909. | 0.0767776 | ||||||||
\(292\) | 792213. | − | 792213.i | 0.543732 | − | 0.543732i | ||||
\(293\) | 251556. | + | 251556.i | 0.171185 | + | 0.171185i | 0.787500 | − | 0.616315i | \(-0.211375\pi\) |
−0.616315 | + | 0.787500i | \(0.711375\pi\) | |||||||
\(294\) | 4779.20 | 0.00322468 | ||||||||
\(295\) | 1.26895e6 | + | 131053.i | 0.848963 | + | 0.0876780i | ||||
\(296\) | − | 579697.i | − | 0.384567i | ||||||
\(297\) | −497398. | + | 351280.i | −0.327200 | + | 0.231080i | ||||
\(298\) | −128753. | + | 128753.i | −0.0839878 | + | 0.0839878i | ||||
\(299\) | 832426. | 0.538478 | ||||||||
\(300\) | 167308. | + | 255603.i | 0.107328 | + | 0.163969i | ||||
\(301\) | −551256. | −0.350701 | ||||||||
\(302\) | 332981. | + | 332981.i | 0.210089 | + | 0.210089i | ||||
\(303\) | −230845. | − | 230845.i | −0.144449 | − | 0.144449i | ||||
\(304\) | 1.66039e6 | 1.03045 | ||||||||
\(305\) | 2.10593e6 | + | 217493.i | 1.29627 | + | 0.133874i | ||||
\(306\) | 307572. | 0.187777 | ||||||||
\(307\) | −1.73184e6 | + | 1.73184e6i | −1.04873 | + | 1.04873i | −0.0499766 | + | 0.998750i | \(0.515915\pi\) |
−0.998750 | + | 0.0499766i | \(0.984085\pi\) | |||||||
\(308\) | −1.25168e6 | + | 883979.i | −0.751824 | + | 0.530964i | ||||
\(309\) | − | 446749.i | − | 0.266175i | ||||||
\(310\) | 163989. | + | 201763.i | 0.0969195 | + | 0.119244i | ||||
\(311\) | 750807. | 0.440177 | 0.220088 | − | 0.975480i | \(-0.429365\pi\) | ||||
0.220088 | + | 0.975480i | \(0.429365\pi\) | |||||||
\(312\) | −171812. | − | 171812.i | −0.0999235 | − | 0.0999235i | ||||
\(313\) | −15556.4 | + | 15556.4i | −0.00897526 | + | 0.00897526i | −0.711580 | − | 0.702605i | \(-0.752020\pi\) |
0.702605 | + | 0.711580i | \(0.252020\pi\) | |||||||
\(314\) | 482146. | 0.275966 | ||||||||
\(315\) | −1.25805e6 | + | 1.02252e6i | −0.714369 | + | 0.580626i | ||||
\(316\) | 1.26669e6i | 0.713597i | ||||||||
\(317\) | 1.39427e6 | + | 1.39427e6i | 0.779289 | + | 0.779289i | 0.979710 | − | 0.200421i | \(-0.0642308\pi\) |
−0.200421 | + | 0.979710i | \(0.564231\pi\) | |||||||
\(318\) | 8888.38 | + | 8888.38i | 0.00492896 | + | 0.00492896i | ||||
\(319\) | 271266. | − | 1.57556e6i | 0.149252 | − | 0.866877i | ||||
\(320\) | −1.37877e6 | − | 142394.i | −0.752689 | − | 0.0777351i | ||||
\(321\) | 2207.36i | 0.00119567i | ||||||||
\(322\) | 81044.8 | + | 81044.8i | 0.0435597 | + | 0.0435597i | ||||
\(323\) | 1.49169e6 | − | 1.49169e6i | 0.795561 | − | 0.795561i | ||||
\(324\) | − | 1.58610e6i | − | 0.839400i | ||||||
\(325\) | 1.79510e6 | + | 2.74246e6i | 0.942717 | + | 1.44023i | ||||
\(326\) | 527626.i | 0.274968i | ||||||||
\(327\) | −302468. | + | 302468.i | −0.156426 | + | 0.156426i | ||||
\(328\) | 730801. | − | 730801.i | 0.375072 | − | 0.375072i | ||||
\(329\) | 3.24715e6 | 1.65391 | ||||||||
\(330\) | −22396.8 | + | 79864.6i | −0.0113214 | + | 0.0403710i | ||||
\(331\) | −1.98487e6 | −0.995779 | −0.497889 | − | 0.867241i | \(-0.665891\pi\) | ||||
−0.497889 | + | 0.867241i | \(0.665891\pi\) | |||||||
\(332\) | 2.08118e6 | − | 2.08118e6i | 1.03625 | − | 1.03625i | ||||
\(333\) | −1.31376e6 | + | 1.31376e6i | −0.649243 | + | 0.649243i | ||||
\(334\) | − | 468725.i | − | 0.229907i | ||||||
\(335\) | 348631. | − | 283361.i | 0.169728 | − | 0.137952i | ||||
\(336\) | 356187.i | 0.172119i | ||||||||
\(337\) | −120865. | + | 120865.i | −0.0579729 | + | 0.0579729i | −0.735499 | − | 0.677526i | \(-0.763052\pi\) |
0.677526 | + | 0.735499i | \(0.263052\pi\) | |||||||
\(338\) | −597538. | − | 597538.i | −0.284494 | − | 0.284494i | ||||
\(339\) | 513950.i | 0.242897i | ||||||||
\(340\) | −1.51516e6 | + | 1.23149e6i | −0.710822 | + | 0.577744i | ||||
\(341\) | 273150. | − | 1.58650e6i | 0.127208 | − | 0.738846i | ||||
\(342\) | 353438. | + | 353438.i | 0.163399 | + | 0.163399i | ||||
\(343\) | −1.59412e6 | − | 1.59412e6i | −0.731621 | − | 0.731621i | ||||
\(344\) | − | 321511.i | − | 0.146487i | ||||||
\(345\) | −140728. | − | 14533.9i | −0.0636552 | − | 0.00657409i | ||||
\(346\) | −701473. | −0.315007 | ||||||||
\(347\) | 1.39645e6 | − | 1.39645e6i | 0.622591 | − | 0.622591i | −0.323602 | − | 0.946193i | \(-0.604894\pi\) |
0.946193 | + | 0.323602i | \(0.104894\pi\) | |||||||
\(348\) | −275378. | − | 275378.i | −0.121894 | − | 0.121894i | ||||
\(349\) | 3.13019e6 | 1.37565 | 0.687824 | − | 0.725878i | \(-0.258566\pi\) | ||||
0.687824 | + | 0.725878i | \(0.258566\pi\) | |||||||
\(350\) | −92233.9 | + | 441776.i | −0.0402458 | + | 0.192767i | ||||
\(351\) | 1.59152e6i | 0.689516i | ||||||||
\(352\) | −778881. | − | 1.10286e6i | −0.335054 | − | 0.474422i | ||||
\(353\) | −23224.5 | + | 23224.5i | −0.00991995 | + | 0.00991995i | −0.712049 | − | 0.702129i | \(-0.752233\pi\) |
0.702129 | + | 0.712049i | \(0.252233\pi\) | |||||||
\(354\) | 84374.1 | 0.0357850 | ||||||||
\(355\) | −18785.5 | + | 181895.i | −0.00791136 | + | 0.0766037i | ||||
\(356\) | 2.65197e6 | 1.10903 | ||||||||
\(357\) | 319997. | + | 319997.i | 0.132885 | + | 0.132885i | ||||
\(358\) | 198104. | + | 198104.i | 0.0816932 | + | 0.0816932i | ||||
\(359\) | 690277. | 0.282675 | 0.141338 | − | 0.989961i | \(-0.454860\pi\) | ||||
0.141338 | + | 0.989961i | \(0.454860\pi\) | |||||||
\(360\) | −596370. | − | 733739.i | −0.242527 | − | 0.298391i | ||||
\(361\) | 952181. | 0.384549 | ||||||||
\(362\) | 518353. | − | 518353.i | 0.207900 | − | 0.207900i | ||||
\(363\) | 463688. | − | 220792.i | 0.184697 | − | 0.0879460i | ||||
\(364\) | 4.00498e6i | 1.58434i | ||||||||
\(365\) | −1.58539e6 | + | 1.28858e6i | −0.622880 | + | 0.506265i | ||||
\(366\) | 140026. | 0.0546395 | ||||||||
\(367\) | −84271.0 | − | 84271.0i | −0.0326597 | − | 0.0326597i | 0.690588 | − | 0.723248i | \(-0.257352\pi\) |
−0.723248 | + | 0.690588i | \(0.757352\pi\) | |||||||
\(368\) | 503247. | − | 503247.i | 0.193714 | − | 0.193714i | ||||
\(369\) | −3.31242e6 | −1.26643 | ||||||||
\(370\) | −53132.9 | + | 514472.i | −0.0201771 | + | 0.195370i | ||||
\(371\) | − | 423466.i | − | 0.159729i | ||||||
\(372\) | −277290. | − | 277290.i | −0.103891 | − | 0.103891i | ||||
\(373\) | −1.52634e6 | − | 1.52634e6i | −0.568042 | − | 0.568042i | 0.363538 | − | 0.931579i | \(-0.381569\pi\) |
−0.931579 | + | 0.363538i | \(0.881569\pi\) | |||||||
\(374\) | −522449. | − | 89950.9i | −0.193137 | − | 0.0332527i | ||||
\(375\) | −255594. | − | 494977.i | −0.0938584 | − | 0.181763i | ||||
\(376\) | 1.89385e6i | 0.690837i | ||||||||
\(377\) | −2.95463e6 | − | 2.95463e6i | −1.07066 | − | 1.07066i | ||||
\(378\) | −154950. | + | 154950.i | −0.0557779 | + | 0.0557779i | ||||
\(379\) | 2.00045e6i | 0.715368i | 0.933843 | + | 0.357684i | \(0.116433\pi\) | ||||
−0.933843 | + | 0.357684i | \(0.883567\pi\) | |||||||
\(380\) | −3.15624e6 | − | 325966.i | −1.12127 | − | 0.115801i | ||||
\(381\) | − | 329078.i | − | 0.116141i | ||||||
\(382\) | 6646.64 | − | 6646.64i | 0.00233047 | − | 0.00233047i | ||||
\(383\) | −3.76908e6 | + | 3.76908e6i | −1.31292 | + | 1.31292i | −0.393665 | + | 0.919254i | \(0.628793\pi\) |
−0.919254 | + | 0.393665i | \(0.871207\pi\) | |||||||
\(384\) | −434992. | −0.150540 | ||||||||
\(385\) | 2.43600e6 | − | 1.36896e6i | 0.837579 | − | 0.470694i | ||||
\(386\) | −692828. | −0.236678 | ||||||||
\(387\) | −728638. | + | 728638.i | −0.247306 | + | 0.247306i | ||||
\(388\) | 753921. | − | 753921.i | 0.254242 | − | 0.254242i | ||||
\(389\) | − | 4.53726e6i | − | 1.52026i | −0.649768 | − | 0.760132i | \(-0.725134\pi\) | ||
0.649768 | − | 0.760132i | \(-0.274866\pi\) | |||||||
\(390\) | 136733. | + | 168228.i | 0.0455210 | + | 0.0560064i | ||||
\(391\) | − | 904232.i | − | 0.299115i | ||||||
\(392\) | 66399.3 | − | 66399.3i | 0.0218247 | − | 0.0218247i | ||||
\(393\) | −385204. | − | 385204.i | −0.125808 | − | 0.125808i | ||||
\(394\) | − | 158786.i | − | 0.0515312i | ||||||
\(395\) | 237291. | − | 2.29763e6i | 0.0765225 | − | 0.740948i | ||||
\(396\) | −486017. | + | 2.82287e6i | −0.155745 | + | 0.904592i | ||||
\(397\) | 3.97395e6 | + | 3.97395e6i | 1.26545 | + | 1.26545i | 0.948412 | + | 0.317041i | \(0.102689\pi\) |
0.317041 | + | 0.948412i | \(0.397311\pi\) | |||||||
\(398\) | 309135. | + | 309135.i | 0.0978228 | + | 0.0978228i | ||||
\(399\) | 735432.i | 0.231265i | ||||||||
\(400\) | 2.74321e6 | + | 572726.i | 0.857252 | + | 0.178977i | ||||
\(401\) | 185273. | 0.0575374 | 0.0287687 | − | 0.999586i | \(-0.490841\pi\) | ||||
0.0287687 | + | 0.999586i | \(0.490841\pi\) | |||||||
\(402\) | 21011.0 | − | 21011.0i | 0.00648457 | − | 0.00648457i | ||||
\(403\) | −2.97515e6 | − | 2.97515e6i | −0.912528 | − | 0.912528i | ||||
\(404\) | −3.13840e6 | −0.956655 | ||||||||
\(405\) | −297128. | + | 2.87701e6i | −0.0900131 | + | 0.871573i | ||||
\(406\) | − | 575324.i | − | 0.173220i | ||||||
\(407\) | 2.61581e6 | − | 1.84738e6i | 0.782745 | − | 0.552802i | ||||
\(408\) | −186633. | + | 186633.i | −0.0555058 | + | 0.0555058i | ||||
\(409\) | 2.72097e6 | 0.804295 | 0.402148 | − | 0.915575i | \(-0.368264\pi\) | ||||
0.402148 | + | 0.915575i | \(0.368264\pi\) | |||||||
\(410\) | −715557. | + | 581592.i | −0.210225 | + | 0.170867i | ||||
\(411\) | −655126. | −0.191302 | ||||||||
\(412\) | −3.03684e6 | − | 3.03684e6i | −0.881413 | − | 0.881413i | ||||
\(413\) | −2.00990e6 | − | 2.00990e6i | −0.579829 | − | 0.579829i | ||||
\(414\) | 214246. | 0.0614346 | ||||||||
\(415\) | −4.16490e6 | + | 3.38515e6i | −1.18709 | + | 0.964847i | ||||
\(416\) | −3.52882e6 | −0.999761 | ||||||||
\(417\) | 814283. | − | 814283.i | 0.229316 | − | 0.229316i | ||||
\(418\) | −496994. | − | 703723.i | −0.139127 | − | 0.196998i | ||||
\(419\) | 3.36223e6i | 0.935604i | 0.883833 | + | 0.467802i | \(0.154954\pi\) | ||||
−0.883833 | + | 0.467802i | \(0.845046\pi\) | |||||||
\(420\) | 69925.9 | − | 677075.i | 0.0193426 | − | 0.187290i | ||||
\(421\) | −798459. | −0.219557 | −0.109778 | − | 0.993956i | \(-0.535014\pi\) | ||||
−0.109778 | + | 0.993956i | \(0.535014\pi\) | |||||||
\(422\) | 604576. | + | 604576.i | 0.165261 | + | 0.165261i | ||||
\(423\) | 4.29202e6 | − | 4.29202e6i | 1.16630 | − | 1.16630i | ||||
\(424\) | 246980. | 0.0667186 | ||||||||
\(425\) | 2.97902e6 | − | 1.94995e6i | 0.800022 | − | 0.523663i | ||||
\(426\) | 12094.4i | 0.00322895i | ||||||||
\(427\) | −3.33561e6 | − | 3.33561e6i | −0.885330 | − | 0.885330i | ||||
\(428\) | 15004.9 | + | 15004.9i | 0.00395934 | + | 0.00395934i | ||||
\(429\) | 227750. | − | 1.32281e6i | 0.0597469 | − | 0.347020i | ||||
\(430\) | −29468.5 | + | 285336.i | −0.00768576 | + | 0.0744192i | ||||
\(431\) | − | 3.94706e6i | − | 1.02348i | −0.859139 | − | 0.511742i | \(-0.829000\pi\) | ||
0.859139 | − | 0.511742i | \(-0.171000\pi\) | |||||||
\(432\) | 962162. | + | 962162.i | 0.248050 | + | 0.248050i | ||||
\(433\) | 1.70841e6 | − | 1.70841e6i | 0.437897 | − | 0.437897i | −0.453407 | − | 0.891304i | \(-0.649792\pi\) |
0.891304 | + | 0.453407i | \(0.149792\pi\) | |||||||
\(434\) | − | 579320.i | − | 0.147637i | ||||||
\(435\) | 447917. | + | 551091.i | 0.113494 | + | 0.139637i | ||||
\(436\) | 4.11214e6i | 1.03598i | ||||||||
\(437\) | 1.03907e6 | − | 1.03907e6i | 0.260281 | − | 0.260281i | ||||
\(438\) | −95547.0 | + | 95547.0i | −0.0237975 | + | 0.0237975i | ||||
\(439\) | −678707. | −0.168082 | −0.0840409 | − | 0.996462i | \(-0.526783\pi\) | ||||
−0.0840409 | + | 0.996462i | \(0.526783\pi\) | |||||||
\(440\) | 798423. | + | 1.42076e6i | 0.196608 | + | 0.349855i | ||||
\(441\) | −300961. | −0.0736908 | ||||||||
\(442\) | −979745. | + | 979745.i | −0.238538 | + | 0.238538i | ||||
\(443\) | −1.67407e6 | + | 1.67407e6i | −0.405289 | + | 0.405289i | −0.880092 | − | 0.474803i | \(-0.842519\pi\) |
0.474803 | + | 0.880092i | \(0.342519\pi\) | |||||||
\(444\) | − | 780081.i | − | 0.187794i | ||||||
\(445\) | −4.81036e6 | − | 496798.i | −1.15154 | − | 0.118927i | ||||
\(446\) | 26779.0i | 0.00637466i | ||||||||
\(447\) | −354115. | + | 354115.i | −0.0838255 | + | 0.0838255i | ||||
\(448\) | 2.18384e6 | + | 2.18384e6i | 0.514075 | + | 0.514075i | ||||
\(449\) | 1.54007e6i | 0.360515i | 0.983619 | + | 0.180258i | \(0.0576931\pi\) | ||||
−0.983619 | + | 0.180258i | \(0.942307\pi\) | |||||||
\(450\) | 462017. | + | 705842.i | 0.107554 | + | 0.164315i | ||||
\(451\) | 5.62656e6 | + | 968733.i | 1.30257 | + | 0.224266i | ||||
\(452\) | 3.49366e6 | + | 3.49366e6i | 0.804330 | + | 0.804330i | ||||
\(453\) | 915815. | + | 915815.i | 0.209683 | + | 0.209683i | ||||
\(454\) | − | 583594.i | − | 0.132884i | ||||||
\(455\) | 750261. | − | 7.26458e6i | 0.169896 | − | 1.64506i | ||||
\(456\) | −428929. | −0.0965991 | ||||||||
\(457\) | −2.37478e6 | + | 2.37478e6i | −0.531904 | + | 0.531904i | −0.921139 | − | 0.389235i | \(-0.872739\pi\) |
0.389235 | + | 0.921139i | \(0.372739\pi\) | |||||||
\(458\) | 1.22990e6 | + | 1.22990e6i | 0.273971 | + | 0.273971i | ||||
\(459\) | 1.72881e6 | 0.383014 | ||||||||
\(460\) | −1.05542e6 | + | 857826.i | −0.232558 | + | 0.189019i | ||||
\(461\) | 4.89233e6i | 1.07217i | 0.844164 | + | 0.536084i | \(0.180097\pi\) | ||||
−0.844164 | + | 0.536084i | \(0.819903\pi\) | |||||||
\(462\) | 150962. | − | 106615.i | 0.0329051 | − | 0.0232387i | ||||
\(463\) | −5.39140e6 | + | 5.39140e6i | −1.16882 | + | 1.16882i | −0.186338 | + | 0.982486i | \(0.559662\pi\) |
−0.982486 | + | 0.186338i | \(0.940338\pi\) | |||||||
\(464\) | −3.57247e6 | −0.770325 | ||||||||
\(465\) | 451028. | + | 554919.i | 0.0967322 | + | 0.119014i | ||||
\(466\) | −313919. | −0.0669659 | ||||||||
\(467\) | 692307. | + | 692307.i | 0.146895 | + | 0.146895i | 0.776729 | − | 0.629835i | \(-0.216877\pi\) |
−0.629835 | + | 0.776729i | \(0.716877\pi\) | |||||||
\(468\) | 5.29370e6 | + | 5.29370e6i | 1.11724 | + | 1.11724i | ||||
\(469\) | −1.00102e6 | −0.210141 | ||||||||
\(470\) | 173583. | − | 1.68076e6i | 0.0362462 | − | 0.350963i | ||||
\(471\) | 1.32607e6 | 0.275432 | ||||||||
\(472\) | 1.17224e6 | − | 1.17224e6i | 0.242194 | − | 0.242194i | ||||
\(473\) | 1.45078e6 | − | 1.02459e6i | 0.298159 | − | 0.210570i | ||||
\(474\) | − | 152773.i | − | 0.0312320i | ||||||
\(475\) | 5.66400e6 | + | 1.18253e6i | 1.15183 | + | 0.240480i | ||||
\(476\) | 4.35046e6 | 0.880071 | ||||||||
\(477\) | −559729. | − | 559729.i | −0.112637 | − | 0.112637i | ||||
\(478\) | 797285. | − | 797285.i | 0.159604 | − | 0.159604i | ||||
\(479\) | 6.45641e6 | 1.28574 | 0.642869 | − | 0.765976i | \(-0.277744\pi\) | ||||
0.642869 | + | 0.765976i | \(0.277744\pi\) | |||||||
\(480\) | 596575. | + | 61612.2i | 0.118185 | + | 0.0122057i | ||||
\(481\) | − | 8.36978e6i | − | 1.64950i | ||||||
\(482\) | 139002. | + | 139002.i | 0.0272523 | + | 0.0272523i | ||||
\(483\) | 222901. | + | 222901.i | 0.0434755 | + | 0.0434755i | ||||
\(484\) | 1.65112e6 | − | 4.65285e6i | 0.320380 | − | 0.902830i | ||||
\(485\) | −1.50876e6 | + | 1.22629e6i | −0.291250 | + | 0.236723i | ||||
\(486\) | 618806.i | 0.118840i | ||||||||
\(487\) | 1.03959e6 | + | 1.03959e6i | 0.198627 | + | 0.198627i | 0.799411 | − | 0.600784i | \(-0.205145\pi\) |
−0.600784 | + | 0.799411i | \(0.705145\pi\) | |||||||
\(488\) | 1.94544e6 | − | 1.94544e6i | 0.369801 | − | 0.369801i | ||||
\(489\) | 1.45115e6i | 0.274436i | ||||||||
\(490\) | −65014.3 | + | 52842.4i | −0.0122326 | + | 0.00994243i | ||||
\(491\) | − | 2.84028e6i | − | 0.531689i | −0.964016 | − | 0.265844i | \(-0.914349\pi\) | ||
0.964016 | − | 0.265844i | \(-0.0856507\pi\) | |||||||
\(492\) | 983417. | − | 983417.i | 0.183158 | − | 0.183158i | ||||
\(493\) | −3.20950e6 | + | 3.20950e6i | −0.594730 | + | 0.594730i | ||||
\(494\) | −2.25170e6 | −0.415138 | ||||||||
\(495\) | 1.41039e6 | − | 5.02931e6i | 0.258718 | − | 0.922562i | ||||
\(496\) | −3.59728e6 | −0.656554 | ||||||||
\(497\) | 288106. | − | 288106.i | 0.0523192 | − | 0.0523192i | ||||
\(498\) | −251007. | + | 251007.i | −0.0453536 | + | 0.0453536i | ||||
\(499\) | − | 3.97737e6i | − | 0.715064i | −0.933901 | − | 0.357532i | \(-0.883618\pi\) | ||
0.933901 | − | 0.357532i | \(-0.116382\pi\) | |||||||
\(500\) | −5.10212e6 | − | 1.62724e6i | −0.912695 | − | 0.291089i | ||||
\(501\) | − | 1.28916e6i | − | 0.229463i | ||||||
\(502\) | 451451. | − | 451451.i | 0.0799560 | − | 0.0799560i | ||||
\(503\) | 6.10079e6 | + | 6.10079e6i | 1.07514 | + | 1.07514i | 0.996937 | + | 0.0782056i | \(0.0249191\pi\) |
0.0782056 | + | 0.996937i | \(0.475081\pi\) | |||||||
\(504\) | 2.10677e6i | 0.369438i | ||||||||
\(505\) | 5.69271e6 | + | 587923.i | 0.993323 | + | 0.102587i | ||||
\(506\) | −363924. | − | 62657.4i | −0.0631880 | − | 0.0108792i | ||||
\(507\) | −1.64344e6 | − | 1.64344e6i | −0.283944 | − | 0.283944i | ||||
\(508\) | −2.23696e6 | − | 2.23696e6i | −0.384590 | − | 0.384590i | ||||
\(509\) | − | 1.28443e6i | − | 0.219743i | −0.993946 | − | 0.109871i | \(-0.964956\pi\) | ||
0.993946 | − | 0.109871i | \(-0.0350439\pi\) | |||||||
\(510\) | 182740. | − | 148528.i | 0.0311106 | − | 0.0252861i | ||||
\(511\) | 4.55211e6 | 0.771189 | ||||||||
\(512\) | −3.60744e6 | + | 3.60744e6i | −0.608168 | + | 0.608168i | ||||
\(513\) | 1.98661e6 | + | 1.98661e6i | 0.333288 | + | 0.333288i | ||||
\(514\) | 1.16168e6 | 0.193945 | ||||||||
\(515\) | 4.93959e6 | + | 6.07738e6i | 0.820678 | + | 1.00971i | ||||
\(516\) | − | 432647.i | − | 0.0715336i | ||||||
\(517\) | −8.54575e6 | + | 6.03531e6i | −1.40612 | + | 0.993054i | ||||
\(518\) | 814879. | − | 814879.i | 0.133435 | − | 0.133435i | ||||
\(519\) | −1.92930e6 | −0.314399 | ||||||||
\(520\) | 4.23695e6 | + | 437577.i | 0.687139 | + | 0.0709654i | ||||
\(521\) | −6.78721e6 | −1.09546 | −0.547731 | − | 0.836655i | \(-0.684508\pi\) | ||||
−0.547731 | + | 0.836655i | \(0.684508\pi\) | |||||||
\(522\) | −760451. | − | 760451.i | −0.122150 | − | 0.122150i | ||||
\(523\) | −2.29263e6 | − | 2.29263e6i | −0.366506 | − | 0.366506i | 0.499695 | − | 0.866201i | \(-0.333445\pi\) |
−0.866201 | + | 0.499695i | \(0.833445\pi\) | |||||||
\(524\) | −5.23696e6 | −0.833204 | ||||||||
\(525\) | −253675. | + | 1.21504e6i | −0.0401680 | + | 0.192394i | ||||
\(526\) | 759526. | 0.119696 | ||||||||
\(527\) | −3.23179e6 | + | 3.23179e6i | −0.506893 | + | 0.506893i | ||||
\(528\) | −662024. | − | 937400.i | −0.103345 | − | 0.146332i | ||||
\(529\) | 5.80648e6i | 0.902139i | ||||||||
\(530\) | −219191. | − | 22637.2i | −0.0338947 | − | 0.00350053i | ||||
\(531\) | −5.31329e6 | −0.817763 | ||||||||
\(532\) | 4.99921e6 | + | 4.99921e6i | 0.765813 | + | 0.765813i | ||||
\(533\) | 1.05514e7 | − | 1.05514e7i | 1.60877 | − | 1.60877i | ||||
\(534\) | −319848. | −0.0485389 | ||||||||
\(535\) | −24406.2 | − | 30028.0i | −0.00368652 | − | 0.00453568i | ||||
\(536\) | − | 583828.i | − | 0.0877755i | ||||||
\(537\) | 544855. | + | 544855.i | 0.0815353 | + | 0.0815353i | ||||
\(538\) | −539421. | − | 539421.i | −0.0803475 | − | 0.0803475i | ||||
\(539\) | 511219. | + | 88017.4i | 0.0757941 | + | 0.0130496i | ||||
\(540\) | −1.64008e6 | − | 2.01786e6i | −0.242037 | − | 0.297788i | ||||
\(541\) | 2.13626e6i | 0.313805i | 0.987614 | + | 0.156903i | \(0.0501509\pi\) | ||||
−0.987614 | + | 0.156903i | \(0.949849\pi\) | |||||||
\(542\) | 133450. | + | 133450.i | 0.0195129 | + | 0.0195129i | ||||
\(543\) | 1.42565e6 | − | 1.42565e6i | 0.207498 | − | 0.207498i | ||||
\(544\) | 3.83322e6i | 0.555350i | ||||||||
\(545\) | 770336. | − | 7.45896e6i | 0.111094 | − | 1.07569i | ||||
\(546\) | − | 483032.i | − | 0.0693417i | ||||||
\(547\) | −3.51247e6 | + | 3.51247e6i | −0.501932 | + | 0.501932i | −0.912038 | − | 0.410106i | \(-0.865492\pi\) |
0.410106 | + | 0.912038i | \(0.365492\pi\) | |||||||
\(548\) | −4.45332e6 | + | 4.45332e6i | −0.633479 | + | 0.633479i | ||||
\(549\) | −8.81787e6 | −1.24863 | ||||||||
\(550\) | −578366. | − | 1.33408e6i | −0.0815260 | − | 0.188051i | ||||
\(551\) | −7.37622e6 | −1.03504 | ||||||||
\(552\) | −130004. | + | 130004.i | −0.0181597 | + | 0.0181597i | ||||
\(553\) | −3.63925e6 | + | 3.63925e6i | −0.506056 | + | 0.506056i | ||||
\(554\) | − | 529550.i | − | 0.0733049i | ||||||
\(555\) | −146134. | + | 1.41498e6i | −0.0201381 | + | 0.194992i | ||||
\(556\) | − | 1.10704e7i | − | 1.51872i | ||||||
\(557\) | −1.23335e6 | + | 1.23335e6i | −0.168442 | + | 0.168442i | −0.786294 | − | 0.617852i | \(-0.788003\pi\) |
0.617852 | + | 0.786294i | \(0.288003\pi\) | |||||||
\(558\) | −765732. | − | 765732.i | −0.104110 | − | 0.104110i | ||||
\(559\) | − | 4.64203e6i | − | 0.628317i | ||||||
\(560\) | −3.93827e6 | − | 4.84542e6i | −0.530683 | − | 0.652921i | ||||
\(561\) | −1.43692e6 | − | 247396.i | −0.192764 | − | 0.0331884i | ||||
\(562\) | 111336. | + | 111336.i | 0.0148695 | + | 0.0148695i | ||||
\(563\) | 4.59650e6 | + | 4.59650e6i | 0.611161 | + | 0.611161i | 0.943249 | − | 0.332087i | \(-0.107753\pi\) |
−0.332087 | + | 0.943249i | \(0.607753\pi\) | |||||||
\(564\) | 2.54850e6i | 0.337354i | ||||||||
\(565\) | −5.68262e6 | − | 6.99157e6i | −0.748907 | − | 0.921411i | ||||
\(566\) | 1.97743e6 | 0.259454 | ||||||||
\(567\) | 4.55693e6 | − | 4.55693e6i | 0.595271 | − | 0.595271i | ||||
\(568\) | 168033. | + | 168033.i | 0.0218536 | + | 0.0218536i | ||||
\(569\) | −1.33573e7 | −1.72957 | −0.864785 | − | 0.502143i | \(-0.832545\pi\) | ||||
−0.864785 | + | 0.502143i | \(0.832545\pi\) | |||||||
\(570\) | 380667. | + | 39314.0i | 0.0490748 | + | 0.00506828i | ||||
\(571\) | − | 9.47840e6i | − | 1.21659i | −0.793711 | − | 0.608296i | \(-0.791854\pi\) | ||
0.793711 | − | 0.608296i | \(-0.208146\pi\) | |||||||
\(572\) | −7.44384e6 | − | 1.05402e7i | −0.951277 | − | 1.34697i | ||||
\(573\) | 18280.6 | − | 18280.6i | 0.00232597 | − | 0.00232597i | ||||
\(574\) | 2.05457e6 | 0.260280 | ||||||||
\(575\) | 2.07511e6 | − | 1.35829e6i | 0.261741 | − | 0.171325i | ||||
\(576\) | 5.77312e6 | 0.725027 | ||||||||
\(577\) | 6.28321e6 | + | 6.28321e6i | 0.785674 | + | 0.785674i | 0.980782 | − | 0.195108i | \(-0.0625057\pi\) |
−0.195108 | + | 0.980782i | \(0.562506\pi\) | |||||||
\(578\) | −99810.5 | − | 99810.5i | −0.0124267 | − | 0.0124267i | ||||
\(579\) | −1.90552e6 | −0.236220 | ||||||||
\(580\) | 6.79091e6 | + | 701342.i | 0.838220 | + | 0.0865685i | ||||
\(581\) | 1.19586e7 | 1.46974 | ||||||||
\(582\) | −90928.7 | + | 90928.7i | −0.0111274 | + | 0.0111274i | ||||
\(583\) | 787073. | + | 1.11446e6i | 0.0959056 | + | 0.135798i | ||||
\(584\) | 2.65494e6i | 0.322124i | ||||||||
\(585\) | −8.61049e6 | − | 1.05938e7i | −1.04025 | − | 1.27986i | ||||
\(586\) | −412476. | −0.0496198 | ||||||||
\(587\) | 4.86606e6 | + | 4.86606e6i | 0.582884 | + | 0.582884i | 0.935695 | − | 0.352811i | \(-0.114774\pi\) |
−0.352811 | + | 0.935695i | \(0.614774\pi\) | |||||||
\(588\) | 89351.6 | − | 89351.6i | 0.0106576 | − | 0.0106576i | ||||
\(589\) | −7.42745e6 | −0.882168 | ||||||||
\(590\) | −1.14779e6 | + | 932904.i | −0.135748 | + | 0.110333i | ||||
\(591\) | − | 436716.i | − | 0.0514316i | ||||||
\(592\) | −5.05999e6 | − | 5.05999e6i | −0.593397 | − | 0.593397i | ||||
\(593\) | 6.68231e6 | + | 6.68231e6i | 0.780351 | + | 0.780351i | 0.979890 | − | 0.199539i | \(-0.0639445\pi\) |
−0.199539 | + | 0.979890i | \(0.563945\pi\) | |||||||
\(594\) | 119795. | − | 695789.i | 0.0139307 | − | 0.0809117i | ||||
\(595\) | −7.89124e6 | − | 814979.i | −0.913803 | − | 0.0943744i | ||||
\(596\) | 4.81431e6i | 0.555160i | ||||||||
\(597\) | 850229. | + | 850229.i | 0.0976337 | + | 0.0976337i | ||||
\(598\) | −682464. | + | 682464.i | −0.0780417 | + | 0.0780417i | ||||
\(599\) | 9.73065e6i | 1.10809i | 0.832487 | + | 0.554045i | \(0.186916\pi\) | ||||
−0.832487 | + | 0.554045i | \(0.813084\pi\) | |||||||
\(600\) | −708651. | − | 147952.i | −0.0803626 | − | 0.0167781i | ||||
\(601\) | − | 1.28500e6i | − | 0.145117i | −0.997364 | − | 0.0725584i | \(-0.976884\pi\) | ||
0.997364 | − | 0.0725584i | \(-0.0231164\pi\) | |||||||
\(602\) | 451947. | − | 451947.i | 0.0508272 | − | 0.0508272i | ||||
\(603\) | −1.32313e6 | + | 1.32313e6i | −0.148186 | + | 0.148186i | ||||
\(604\) | 1.24508e7 | 1.38869 | ||||||||
\(605\) | −3.86658e6 | + | 8.13044e6i | −0.429475 | + | 0.903079i | ||||
\(606\) | 378516. | 0.0418700 | ||||||||
\(607\) | −2.93816e6 | + | 2.93816e6i | −0.323671 | + | 0.323671i | −0.850174 | − | 0.526502i | \(-0.823503\pi\) |
0.526502 | + | 0.850174i | \(0.323503\pi\) | |||||||
\(608\) | −4.40484e6 | + | 4.40484e6i | −0.483249 | + | 0.483249i | ||||
\(609\) | − | 1.58234e6i | − | 0.172885i | ||||||
\(610\) | −1.90486e6 | + | 1.54823e6i | −0.207271 | + | 0.168466i | ||||
\(611\) | 2.73437e7i | 2.96316i | ||||||||
\(612\) | 5.75034e6 | − | 5.75034e6i | 0.620605 | − | 0.620605i | ||||
\(613\) | −2.21322e6 | − | 2.21322e6i | −0.237889 | − | 0.237889i | 0.578087 | − | 0.815975i | \(-0.303800\pi\) |
−0.815975 | + | 0.578087i | \(0.803800\pi\) | |||||||
\(614\) | − | 2.83970e6i | − | 0.303985i | ||||||
\(615\) | −1.96803e6 | + | 1.59958e6i | −0.209819 | + | 0.170537i | ||||
\(616\) | 616136. | − | 3.57862e6i | 0.0654222 | − | 0.379983i | ||||
\(617\) | 1.25927e6 | + | 1.25927e6i | 0.133170 | + | 0.133170i | 0.770550 | − | 0.637380i | \(-0.219982\pi\) |
−0.637380 | + | 0.770550i | \(0.719982\pi\) | |||||||
\(618\) | 366267. | + | 366267.i | 0.0385768 | + | 0.0385768i | ||||
\(619\) | − | 1.33220e7i | − | 1.39747i | −0.715380 | − | 0.698735i | \(-0.753746\pi\) | ||
0.715380 | − | 0.698735i | \(-0.246254\pi\) | |||||||
\(620\) | 6.83808e6 | + | 706213.i | 0.714422 | + | 0.0737830i | ||||
\(621\) | 1.20424e6 | 0.125310 | ||||||||
\(622\) | −615549. | + | 615549.i | −0.0637950 | + | 0.0637950i | ||||
\(623\) | 7.61920e6 | + | 7.61920e6i | 0.786482 | + | 0.786482i | ||||
\(624\) | −2.99939e6 | −0.308369 | ||||||||
\(625\) | 8.94984e6 | + | 3.90741e6i | 0.916463 | + | 0.400119i | ||||
\(626\) | − | 25507.8i | − | 0.00260158i | ||||||
\(627\) | −1.36691e6 | − | 1.93548e6i | −0.138858 | − | 0.196617i | ||||
\(628\) | 9.01417e6 | − | 9.01417e6i | 0.912067 | − | 0.912067i | ||||
\(629\) | −9.09176e6 | −0.916266 | ||||||||
\(630\) | 193099. | − | 1.86973e6i | 0.0193834 | − | 0.187684i | ||||
\(631\) | −9.67806e6 | −0.967642 | −0.483821 | − | 0.875167i | \(-0.660751\pi\) | ||||
−0.483821 | + | 0.875167i | \(0.660751\pi\) | |||||||
\(632\) | −2.12253e6 | − | 2.12253e6i | −0.211379 | − | 0.211379i | ||||
\(633\) | 1.66279e6 | + | 1.66279e6i | 0.164941 | + | 0.164941i | ||||
\(634\) | −2.28618e6 | −0.225885 | ||||||||
\(635\) | 3.63853e6 | + | 4.47664e6i | 0.358090 | + | 0.440573i | ||||
\(636\) | 332353. | 0.0325804 | ||||||||
\(637\) | 958685. | − | 958685.i | 0.0936111 | − | 0.0936111i | ||||
\(638\) | 1.06932e6 | + | 1.51412e6i | 0.104006 | + | 0.147268i | ||||
\(639\) | − | 761624.i | − | 0.0737884i | ||||||
\(640\) | 5.91745e6 | − | 4.80960e6i | 0.571064 | − | 0.464151i | ||||
\(641\) | −4.75399e6 | −0.456997 | −0.228498 | − | 0.973544i | \(-0.573382\pi\) | ||||
−0.228498 | + | 0.973544i | \(0.573382\pi\) | |||||||
\(642\) | −1809.70 | − | 1809.70i | −0.000173288 | − | 0.000173288i | ||||
\(643\) | 8.80966e6 | − | 8.80966e6i | 0.840295 | − | 0.840295i | −0.148602 | − | 0.988897i | \(-0.547477\pi\) |
0.988897 | + | 0.148602i | \(0.0474774\pi\) | |||||||
\(644\) | 3.03041e6 | 0.287930 | ||||||||
\(645\) | −81048.7 | + | 784773.i | −0.00767090 | + | 0.0742754i | ||||
\(646\) | 2.44593e6i | 0.230602i | ||||||||
\(647\) | −4.90324e6 | − | 4.90324e6i | −0.460492 | − | 0.460492i | 0.438325 | − | 0.898817i | \(-0.355572\pi\) |
−0.898817 | + | 0.438325i | \(0.855572\pi\) | |||||||
\(648\) | 2.65776e6 | + | 2.65776e6i | 0.248644 | + | 0.248644i | ||||
\(649\) | 9.02529e6 | + | 1.55390e6i | 0.841103 | + | 0.144814i | ||||
\(650\) | −3.72012e6 | − | 776686.i | −0.345361 | − | 0.0721045i | ||||
\(651\) | − | 1.59333e6i | − | 0.147351i | ||||||
\(652\) | 9.86444e6 | + | 9.86444e6i | 0.908769 | + | 0.908769i | ||||
\(653\) | −9.36700e6 | + | 9.36700e6i | −0.859642 | + | 0.859642i | −0.991296 | − | 0.131653i | \(-0.957971\pi\) |
0.131653 | + | 0.991296i | \(0.457971\pi\) | |||||||
\(654\) | − | 495957.i | − | 0.0453419i | ||||||
\(655\) | 9.49925e6 | + | 981050.i | 0.865140 | + | 0.0893486i | ||||
\(656\) | − | 1.27579e7i | − | 1.15749i | ||||||
\(657\) | 6.01688e6 | − | 6.01688e6i | 0.543824 | − | 0.543824i | ||||
\(658\) | −2.66218e6 | + | 2.66218e6i | −0.239702 | + | 0.239702i | ||||
\(659\) | 1.65001e7 | 1.48004 | 0.740020 | − | 0.672585i | \(-0.234816\pi\) | ||||
0.740020 | + | 0.672585i | \(0.234816\pi\) | |||||||
\(660\) | 1.07441e6 | + | 1.91187e6i | 0.0960089 | + | 0.170844i | ||||
\(661\) | 3.06152e6 | 0.272542 | 0.136271 | − | 0.990672i | \(-0.456488\pi\) | ||||
0.136271 | + | 0.990672i | \(0.456488\pi\) | |||||||
\(662\) | 1.62730e6 | − | 1.62730e6i | 0.144319 | − | 0.144319i | ||||
\(663\) | −2.69464e6 | + | 2.69464e6i | −0.238077 | + | 0.238077i | ||||
\(664\) | 6.97467e6i | 0.613908i | ||||||||
\(665\) | −8.13149e6 | − | 1.00045e7i | −0.713044 | − | 0.877287i | ||||
\(666\) | − | 2.15418e6i | − | 0.188190i | ||||||
\(667\) | −2.23565e6 | + | 2.23565e6i | −0.194576 | + | 0.194576i | ||||
\(668\) | −8.76325e6 | − | 8.76325e6i | −0.759843 | − | 0.759843i | ||||
\(669\) | 73651.5i | 0.00636233i | ||||||||
\(670\) | −53511.5 | + | 518138.i | −0.00460533 | + | 0.0445922i | ||||
\(671\) | 1.49783e7 | + | 2.57883e6i | 1.28427 | + | 0.221114i | ||||
\(672\) | −944923. | − | 944923.i | −0.0807185 | − | 0.0807185i | ||||
\(673\) | −1.46489e6 | − | 1.46489e6i | −0.124672 | − | 0.124672i | 0.642018 | − | 0.766690i | \(-0.278098\pi\) |
−0.766690 | + | 0.642018i | \(0.778098\pi\) | |||||||
\(674\) | − | 198182.i | − | 0.0168041i | ||||||
\(675\) | 2.59691e6 | + | 3.96741e6i | 0.219381 | + | 0.335157i | ||||
\(676\) | −2.23430e7 | −1.88051 | ||||||||
\(677\) | 1.01776e6 | − | 1.01776e6i | 0.0853441 | − | 0.0853441i | −0.663146 | − | 0.748490i | \(-0.730779\pi\) |
0.748490 | + | 0.663146i | \(0.230779\pi\) | |||||||
\(678\) | −421362. | − | 421362.i | −0.0352031 | − | 0.0352031i | ||||
\(679\) | 4.33208e6 | 0.360597 | ||||||||
\(680\) | 475323. | − | 4.60243e6i | 0.0394200 | − | 0.381694i | ||||
\(681\) | − | 1.60509e6i | − | 0.132627i | ||||||
\(682\) | 1.07675e6 | + | 1.52463e6i | 0.0886449 | + | 0.125518i | ||||
\(683\) | 1.70844e7 | − | 1.70844e7i | 1.40136 | − | 1.40136i | 0.605548 | − | 0.795809i | \(-0.292954\pi\) |
0.795809 | − | 0.605548i | \(-0.207046\pi\) | |||||||
\(684\) | 1.32157e7 | 1.08007 | ||||||||
\(685\) | 8.91206e6 | − | 7.24357e6i | 0.725691 | − | 0.589829i | ||||
\(686\) | 2.61388e6 | 0.212068 | ||||||||
\(687\) | 3.38264e6 | + | 3.38264e6i | 0.273441 | + | 0.273441i | ||||
\(688\) | −2.80636e6 | − | 2.80636e6i | −0.226034 | − | 0.226034i | ||||
\(689\) | 3.56594e6 | 0.286171 | ||||||||
\(690\) | 127292. | − | 103460.i | 0.0101784 | − | 0.00827279i | ||||
\(691\) | 1.82141e6 | 0.145115 | 0.0725577 | − | 0.997364i | \(-0.476884\pi\) | ||||
0.0725577 | + | 0.997364i | \(0.476884\pi\) | |||||||
\(692\) | −1.31147e7 | + | 1.31147e7i | −1.04110 | + | 1.04110i | ||||
\(693\) | −9.50655e6 | + | 6.71386e6i | −0.751951 | + | 0.531054i | ||||
\(694\) | 2.28977e6i | 0.180465i | ||||||||
\(695\) | −2.07384e6 | + | 2.00805e7i | −0.162860 | + | 1.57693i | ||||
\(696\) | 922875. | 0.0722137 | ||||||||
\(697\) | −1.14616e7 | − | 1.14616e7i | −0.893643 | − | 0.893643i | ||||
\(698\) | −2.56629e6 | + | 2.56629e6i | −0.199373 | + | 0.199373i | ||||
\(699\) | −863388. | −0.0668364 | ||||||||
\(700\) | 6.53501e6 | + | 9.98380e6i | 0.504082 | + | 0.770107i | ||||
\(701\) | 1.47651e7i | 1.13486i | 0.823422 | + | 0.567429i | \(0.192062\pi\) | ||||
−0.823422 | + | 0.567429i | \(0.807938\pi\) | |||||||
\(702\) | −1.30481e6 | − | 1.30481e6i | −0.0999318 | − | 0.0999318i | ||||
\(703\) | −1.04476e7 | − | 1.04476e7i | −0.797309 | − | 0.797309i | ||||
\(704\) | −9.80636e6 | − | 1.68838e6i | −0.745720 | − | 0.128392i | ||||
\(705\) | 477414. | − | 4.62268e6i | 0.0361762 | − | 0.350285i | ||||
\(706\) | − | 38081.2i | − | 0.00287540i | ||||||
\(707\) | −9.01675e6 | − | 9.01675e6i | −0.678425 | − | 0.678425i | ||||
\(708\) | 1.57745e6 | − | 1.57745e6i | 0.118270 | − | 0.118270i | ||||
\(709\) | 1.67676e7i | 1.25273i | 0.779532 | + | 0.626363i | \(0.215457\pi\) | ||||
−0.779532 | + | 0.626363i | \(0.784543\pi\) | |||||||
\(710\) | −133725. | − | 164528.i | −0.00995560 | − | 0.0122488i | ||||
\(711\) | 9.62056e6i | 0.713717i | ||||||||
\(712\) | −4.44377e6 | + | 4.44377e6i | −0.328512 | + | 0.328512i | ||||
\(713\) | −2.25118e6 | + | 2.25118e6i | −0.165839 | + | 0.165839i | ||||
\(714\) | −524699. | −0.0385181 | ||||||||
\(715\) | 1.15278e7 | + | 2.05131e7i | 0.843296 | + | 1.50061i | ||||
\(716\) | 7.40748e6 | 0.539993 | ||||||||
\(717\) | 2.19281e6 | − | 2.19281e6i | 0.159296 | − | 0.159296i | ||||
\(718\) | −565924. | + | 565924.i | −0.0409682 | + | 0.0409682i | ||||
\(719\) | 1.39297e7i | 1.00489i | 0.864609 | + | 0.502445i | \(0.167566\pi\) | ||||
−0.864609 | + | 0.502445i | \(0.832434\pi\) | |||||||
\(720\) | −1.16101e7 | − | 1.19905e6i | −0.834649 | − | 0.0861997i | ||||
\(721\) | − | 1.74499e7i | − | 1.25013i | ||||||
\(722\) | −780646. | + | 780646.i | −0.0557328 | + | 0.0557328i | ||||
\(723\) | 382304. | + | 382304.i | 0.0271996 | + | 0.0271996i | ||||
\(724\) | − | 1.93822e7i | − | 1.37422i | ||||||
\(725\) | −1.21866e7 | − | 2.54431e6i | −0.861065 | − | 0.179773i | ||||
\(726\) | −199138. | + | 561170.i | −0.0140221 | + | 0.0395142i | ||||
\(727\) | 8.02094e6 | + | 8.02094e6i | 0.562846 | + | 0.562846i | 0.930115 | − | 0.367269i | \(-0.119707\pi\) |
−0.367269 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(728\) | −6.71095e6 | − | 6.71095e6i | −0.469306 | − | 0.469306i | ||||
\(729\) | − | 1.08707e7i | − | 0.757599i | ||||||
\(730\) | 243342. | − | 2.35622e6i | 0.0169009 | − | 0.163647i | ||||
\(731\) | −5.04246e6 | −0.349019 | ||||||||
\(732\) | 2.61792e6 | − | 2.61792e6i | 0.180584 | − | 0.180584i | ||||
\(733\) | −1.26801e7 | − | 1.26801e7i | −0.871691 | − | 0.871691i | 0.120966 | − | 0.992657i | \(-0.461401\pi\) |
−0.992657 | + | 0.120966i | \(0.961401\pi\) | |||||||
\(734\) | 138179. | 0.00946677 | ||||||||
\(735\) | −178812. | + | 145335.i | −0.0122089 | + | 0.00992321i | ||||
\(736\) | 2.67012e6i | 0.181692i | ||||||||
\(737\) | 2.63445e6 | − | 1.86054e6i | 0.178657 | − | 0.126174i | ||||
\(738\) | 2.71569e6 | − | 2.71569e6i | 0.183543 | − | 0.183543i | ||||
\(739\) | 8.77406e6 | 0.591002 | 0.295501 | − | 0.955342i | \(-0.404513\pi\) | ||||
0.295501 | + | 0.955342i | \(0.404513\pi\) | |||||||
\(740\) | 8.62517e6 | + | 1.06119e7i | 0.579013 | + | 0.712384i | ||||
\(741\) | −6.19295e6 | −0.414335 | ||||||||
\(742\) | 347179. | + | 347179.i | 0.0231496 | + | 0.0231496i | ||||
\(743\) | −9.85338e6 | − | 9.85338e6i | −0.654807 | − | 0.654807i | 0.299340 | − | 0.954147i | \(-0.403234\pi\) |
−0.954147 | + | 0.299340i | \(0.903234\pi\) | |||||||
\(744\) | 929284. | 0.0615483 | ||||||||
\(745\) | 901873. | − | 8.73261e6i | 0.0595326 | − | 0.576439i | ||||
\(746\) | 2.50275e6 | 0.164653 | ||||||||
\(747\) | 1.58066e7 | − | 1.58066e7i | 1.03643 | − | 1.03643i | ||||
\(748\) | −1.14494e7 | + | 8.08596e6i | −0.748218 | + | 0.528418i | ||||
\(749\) | 86219.0i | 0.00561563i | ||||||||
\(750\) | 615355. | + | 196257.i | 0.0399460 | + | 0.0127401i | ||||
\(751\) | −3.38585e6 | −0.219063 | −0.109531 | − | 0.993983i | \(-0.534935\pi\) | ||||
−0.109531 | + | 0.993983i | \(0.534935\pi\) | |||||||
\(752\) | 1.65308e7 | + | 1.65308e7i | 1.06598 | + | 1.06598i | ||||
\(753\) | 1.24165e6 | − | 1.24165e6i | 0.0798015 | − | 0.0798015i | ||||
\(754\) | 4.84471e6 | 0.310341 | ||||||||
\(755\) | −2.25843e7 | − | 2.33243e6i | −1.44191 | − | 0.148916i | ||||
\(756\) | 5.79386e6i | 0.368692i | ||||||||
\(757\) | −1.13440e7 | − | 1.13440e7i | −0.719494 | − | 0.719494i | 0.249007 | − | 0.968502i | \(-0.419896\pi\) |
−0.968502 | + | 0.249007i | \(0.919896\pi\) | |||||||
\(758\) | −1.64007e6 | − | 1.64007e6i | −0.103678 | − | 0.103678i | ||||
\(759\) | −1.00092e6 | − | 172330.i | −0.0630659 | − | 0.0108581i | ||||
\(760\) | 5.83497e6 | − | 4.74256e6i | 0.366441 | − | 0.297837i | ||||
\(761\) | − | 1.02068e7i | − | 0.638891i | −0.947605 | − | 0.319446i | \(-0.896503\pi\) | ||
0.947605 | − | 0.319446i | \(-0.103497\pi\) | |||||||
\(762\) | 269794. | + | 269794.i | 0.0168324 | + | 0.0168324i | ||||
\(763\) | −1.18143e7 | + | 1.18143e7i | −0.734680 | + | 0.734680i | ||||
\(764\) | − | 248530.i | − | 0.0154044i | ||||||
\(765\) | −1.15077e7 | + | 9.35324e6i | −0.710942 | + | 0.577841i | ||||
\(766\) | − | 6.18015e6i | − | 0.380563i | ||||||
\(767\) | 1.69251e7 | − | 1.69251e7i | 1.03882 | − | 1.03882i | ||||
\(768\) | −1.43250e6 | + | 1.43250e6i | −0.0876378 | + | 0.0876378i | ||||
\(769\) | −3.02499e7 | −1.84462 | −0.922312 | − | 0.386447i | \(-0.873702\pi\) | ||||
−0.922312 | + | 0.386447i | \(0.873702\pi\) | |||||||
\(770\) | −874814. | + | 3.11950e6i | −0.0531727 | + | 0.189608i | ||||
\(771\) | 3.19502e6 | 0.193570 | ||||||||
\(772\) | −1.29531e7 | + | 1.29531e7i | −0.782220 | + | 0.782220i | ||||
\(773\) | −6.66230e6 | + | 6.66230e6i | −0.401028 | + | 0.401028i | −0.878595 | − | 0.477567i | \(-0.841519\pi\) |
0.477567 | + | 0.878595i | \(0.341519\pi\) | |||||||
\(774\) | − | 1.19475e6i | − | 0.0716843i | ||||||
\(775\) | −1.22712e7 | − | 2.56198e6i | −0.733893 | − | 0.153222i | ||||
\(776\) | 2.52662e6i | 0.150621i | ||||||||
\(777\) | 2.24120e6 | − | 2.24120e6i | 0.133177 | − | 0.133177i | ||||
\(778\) | 3.71987e6 | + | 3.71987e6i | 0.220333 | + | 0.220333i | ||||
\(779\) | − | 2.63416e7i | − | 1.55525i | ||||||
\(780\) | 5.70153e6 | + | 588834.i | 0.335548 | + | 0.0346543i | ||||
\(781\) | −222740. | + | 1.29371e6i | −0.0130669 | + | 0.0758945i | ||||
\(782\) | 741335. | + | 741335.i | 0.0433508 | + | 0.0433508i | ||||
\(783\) | −4.27436e6 | − | 4.27436e6i | −0.249153 | − | 0.249153i | ||||
\(784\) | − | 1.15916e6i | − | 0.0673522i | ||||||
\(785\) | −1.80393e7 | + | 1.46620e7i | −1.04483 | + | 0.849220i | ||||
\(786\) | 631618. | 0.0364669 | ||||||||
\(787\) | 1.23587e6 | − | 1.23587e6i | 0.0711273 | − | 0.0711273i | −0.670648 | − | 0.741776i | \(-0.733984\pi\) |
0.741776 | + | 0.670648i | \(0.233984\pi\) | |||||||
\(788\) | −2.96864e6 | − | 2.96864e6i | −0.170311 | − | 0.170311i | ||||
\(789\) | 2.08896e6 | 0.119464 | ||||||||
\(790\) | 1.68917e6 | + | 2.07826e6i | 0.0962954 | + | 0.118476i | ||||
\(791\) | 2.00748e7i | 1.14080i | ||||||||
\(792\) | −3.91575e6 | − | 5.54454e6i | −0.221820 | − | 0.314089i | ||||
\(793\) | 2.80886e7 | − | 2.80886e7i | 1.58616 | − | 1.58616i | ||||
\(794\) | −6.51608e6 | −0.366805 | ||||||||
\(795\) | −602851. | − | 62260.3i | −0.0338292 | − | 0.00349376i | ||||
\(796\) | 1.15591e7 | 0.646610 | ||||||||
\(797\) | 1.75174e7 | + | 1.75174e7i | 0.976840 | + | 0.976840i | 0.999738 | − | 0.0228981i | \(-0.00728933\pi\) |
−0.0228981 | + | 0.999738i | \(0.507289\pi\) | |||||||
\(798\) | −602944. | − | 602944.i | −0.0335173 | − | 0.0335173i | ||||
\(799\) | 2.97024e7 | 1.64598 | ||||||||
\(800\) | −8.79680e6 | + | 5.75804e6i | −0.485959 | + | 0.318090i | ||||
\(801\) | 2.01418e7 | 1.10922 | ||||||||
\(802\) | −151896. | + | 151896.i | −0.00833891 | + | 0.00833891i | ||||
\(803\) | −1.19801e7 | + | 8.46076e6i | −0.655649 | + | 0.463042i | ||||
\(804\) | − | 785640.i | − | 0.0428631i | ||||||
\(805\) | −5.49682e6 | − | 567693.i | −0.298966 | − | 0.0308762i | ||||
\(806\) | 4.87835e6 | 0.264506 | ||||||||
\(807\) | −1.48360e6 | − | 1.48360e6i | −0.0801922 | − | 0.0801922i | ||||
\(808\) | 5.25887e6 | − | 5.25887e6i | 0.283377 | − | 0.283377i | ||||
\(809\) | 3.44189e6 | 0.184895 | 0.0924477 | − | 0.995718i | \(-0.470531\pi\) | ||||
0.0924477 | + | 0.995718i | \(0.470531\pi\) | |||||||
\(810\) | −2.11512e6 | − | 2.60232e6i | −0.113272 | − | 0.139363i | ||||
\(811\) | − | 1.27797e7i | − | 0.682291i | −0.940010 | − | 0.341146i | \(-0.889185\pi\) | ||
0.940010 | − | 0.341146i | \(-0.110815\pi\) | |||||||
\(812\) | −1.07562e7 | − | 1.07562e7i | −0.572492 | − | 0.572492i | ||||
\(813\) | 367035. | + | 367035.i | 0.0194752 | + | 0.0194752i | ||||
\(814\) | −630000. | + | 3.65914e6i | −0.0333257 | + | 0.193561i | ||||
\(815\) | −1.60451e7 | − | 1.97409e7i | −0.846150 | − | 1.04105i | ||||
\(816\) | 3.25812e6i | 0.171294i | ||||||||
\(817\) | −5.79441e6 | − | 5.79441e6i | −0.303706 | − | 0.303706i | ||||
\(818\) | −2.23079e6 | + | 2.23079e6i | −0.116567 | + | 0.116567i | ||||
\(819\) | 3.04180e7i | 1.58460i | ||||||||
\(820\) | −2.50460e6 | + | 2.42514e7i | −0.130078 | + | 1.25951i | ||||
\(821\) | 2.66295e7i | 1.37881i | 0.724374 | + | 0.689407i | \(0.242129\pi\) | ||||
−0.724374 | + | 0.689407i | \(0.757871\pi\) | |||||||
\(822\) | 537105. | − | 537105.i | 0.0277255 | − | 0.0277255i | ||||
\(823\) | −1.61359e7 | + | 1.61359e7i | −0.830410 | + | 0.830410i | −0.987573 | − | 0.157163i | \(-0.949765\pi\) |
0.157163 | + | 0.987573i | \(0.449765\pi\) | |||||||
\(824\) | 1.01774e7 | 0.522177 | ||||||||
\(825\) | −1.59071e6 | − | 3.66919e6i | −0.0813684 | − | 0.187687i | ||||
\(826\) | 3.29564e6 | 0.168070 | ||||||||
\(827\) | 2.40113e7 | − | 2.40113e7i | 1.22082 | − | 1.22082i | 0.253478 | − | 0.967341i | \(-0.418426\pi\) |
0.967341 | − | 0.253478i | \(-0.0815745\pi\) | |||||||
\(828\) | 4.00554e6 | − | 4.00554e6i | 0.203041 | − | 0.203041i | ||||
\(829\) | 7.97873e6i | 0.403225i | 0.979465 | + | 0.201612i | \(0.0646181\pi\) | ||||
−0.979465 | + | 0.201612i | \(0.935382\pi\) | |||||||
\(830\) | 639272. | − | 6.18991e6i | 0.0322100 | − | 0.311881i | ||||
\(831\) | − | 1.45645e6i | − | 0.0731631i | ||||||
\(832\) | −1.83898e7 | + | 1.83898e7i | −0.921018 | + | 0.921018i | ||||
\(833\) | −1.04138e6 | − | 1.04138e6i | −0.0519994 | − | 0.0519994i | ||||
\(834\) | 1.33518e6i | 0.0664698i | ||||||||
\(835\) | 1.42539e7 | + | 1.75372e7i | 0.707485 | + | 0.870449i | ||||
\(836\) | −2.24485e7 | − | 3.86500e6i | −1.11089 | − | 0.191264i | ||||
\(837\) | −4.30404e6 | − | 4.30404e6i | −0.212355 | − | 0.212355i | ||||
\(838\) | −2.75652e6 | − | 2.75652e6i | −0.135597 | − | 0.135597i | ||||
\(839\) | − | 1.69830e7i | − | 0.832931i | −0.909152 | − | 0.416465i | \(-0.863269\pi\) | ||
0.909152 | − | 0.416465i | \(-0.136731\pi\) | |||||||
\(840\) | 1.01737e6 | + | 1.25171e6i | 0.0497486 | + | 0.0612078i | ||||
\(841\) | −4.64060e6 | −0.226248 | ||||||||
\(842\) | 654616. | − | 654616.i | 0.0318205 | − | 0.0318205i | ||||
\(843\) | 306214. | + | 306214.i | 0.0148408 | + | 0.0148408i | ||||
\(844\) | 2.26062e7 | 1.09237 | ||||||||
\(845\) | 4.05277e7 | + | 4.18556e6i | 1.95259 | + | 0.201656i | ||||
\(846\) | 7.03762e6i | 0.338065i | ||||||||
\(847\) | 1.81116e7 | − | 8.62409e6i | 0.867455 | − | 0.413052i | ||||
\(848\) | 2.15581e6 | − | 2.15581e6i | 0.102948 | − | 0.102948i | ||||
\(849\) | 5.43863e6 | 0.258953 | ||||||||
\(850\) | −843684. | + | 4.04102e6i | −0.0400528 | + | 0.191842i | ||||
\(851\) | −6.33308e6 | −0.299772 | ||||||||
\(852\) | 226117. | + | 226117.i | 0.0106717 | + | 0.0106717i | ||||
\(853\) | 2.49281e7 | + | 2.49281e7i | 1.17305 | + | 1.17305i | 0.981479 | + | 0.191569i | \(0.0613575\pi\) |
0.191569 | + | 0.981479i | \(0.438642\pi\) | |||||||
\(854\) | 5.46940e6 | 0.256622 | ||||||||
\(855\) | −2.39718e7 | − | 2.47572e6i | −1.12146 | − | 0.115821i | ||||
\(856\) | −50285.8 | −0.00234564 | ||||||||
\(857\) | 1.77081e7 | − | 1.77081e7i | 0.823609 | − | 0.823609i | −0.163015 | − | 0.986624i | \(-0.552122\pi\) |
0.986624 | + | 0.163015i | \(0.0521218\pi\) | |||||||
\(858\) | 897785. | + | 1.27123e6i | 0.0416346 | + | 0.0589529i | ||||
\(859\) | − | 2.11987e7i | − | 0.980225i | −0.871659 | − | 0.490113i | \(-0.836956\pi\) | ||
0.871659 | − | 0.490113i | \(-0.163044\pi\) | |||||||
\(860\) | 4.78368e6 | + | 5.88556e6i | 0.220554 | + | 0.271357i | ||||
\(861\) | 5.65079e6 | 0.259777 | ||||||||
\(862\) | 3.23600e6 | + | 3.23600e6i | 0.148334 | + | 0.148334i | ||||
\(863\) | 1.53434e7 | − | 1.53434e7i | 0.701286 | − | 0.701286i | −0.263400 | − | 0.964687i | \(-0.584844\pi\) |
0.964687 | + | 0.263400i | \(0.0848440\pi\) | |||||||
\(864\) | −5.10502e6 | −0.232655 | ||||||||
\(865\) | 2.62454e7 | − | 2.13318e7i | 1.19265 | − | 0.969363i | ||||
\(866\) | 2.80127e6i | 0.126929i | ||||||||
\(867\) | −274514. | − | 274514.i | −0.0124027 | − | 0.0124027i | ||||
\(868\) | −1.08309e7 | − | 1.08309e7i | −0.487939 | − | 0.487939i | ||||
\(869\) | 2.81358e6 | − | 1.63417e7i | 0.126389 | − | 0.734088i | ||||
\(870\) | −819037. | − | 84587.3i | −0.0366864 | − | 0.00378885i | ||||
\(871\) | − | 8.42942e6i | − | 0.376489i | ||||||
\(872\) | −6.89052e6 | − | 6.89052e6i | −0.306875 | − | 0.306875i | ||||
\(873\) | 5.72606e6 | − | 5.72606e6i | 0.254285 | − | 0.254285i | ||||
\(874\) | 1.70377e6i | 0.0754453i | ||||||||
\(875\) | −9.98347e6 | − | 1.93337e7i | −0.440820 | − | 0.853679i | ||||
\(876\) | 3.57268e6i | 0.157302i | ||||||||
\(877\) | −3.15258e7 | + | 3.15258e7i | −1.38410 | + | 1.38410i | −0.546907 | + | 0.837193i | \(0.684195\pi\) |
−0.837193 | + | 0.546907i | \(0.815805\pi\) | |||||||
\(878\) | 556438. | − | 556438.i | 0.0243602 | − | 0.0243602i | ||||
\(879\) | −1.13445e6 | −0.0495239 | ||||||||
\(880\) | 1.93705e7 | + | 5.43216e6i | 0.843207 | + | 0.236464i | ||||
\(881\) | −2.91839e7 | −1.26679 | −0.633394 | − | 0.773829i | \(-0.718339\pi\) | ||||
−0.633394 | + | 0.773829i | \(0.718339\pi\) | |||||||
\(882\) | 246743. | − | 246743.i | 0.0106800 | − | 0.0106800i | ||||
\(883\) | −757927. | + | 757927.i | −0.0327134 | + | 0.0327134i | −0.723274 | − | 0.690561i | \(-0.757364\pi\) |
0.690561 | + | 0.723274i | \(0.257364\pi\) | |||||||
\(884\) | 3.66345e7i | 1.57674i | ||||||||
\(885\) | −3.15682e6 | + | 2.56581e6i | −0.135485 | + | 0.110120i | ||||
\(886\) | − | 2.74498e6i | − | 0.117477i | ||||||
\(887\) | 1.51267e7 | − | 1.51267e7i | 0.645558 | − | 0.645558i | −0.306358 | − | 0.951916i | \(-0.599111\pi\) |
0.951916 | + | 0.306358i | \(0.0991106\pi\) | |||||||
\(888\) | 1.30714e6 | + | 1.30714e6i | 0.0556277 | + | 0.0556277i | ||||
\(889\) | − | 1.28537e7i | − | 0.545475i | ||||||
\(890\) | 4.35108e6 | − | 3.53648e6i | 0.184129 | − | 0.149657i | ||||
\(891\) | −3.52306e6 | + | 2.04625e7i | −0.148671 | + | 0.863504i | ||||
\(892\) | 500658. | + | 500658.i | 0.0210683 | + | 0.0210683i | ||||
\(893\) | 3.41318e7 | + | 3.41318e7i | 1.43229 | + | 1.43229i | ||||
\(894\) | − | 580643.i | − | 0.0242977i | ||||||
\(895\) | −1.34363e7 | − | 1.38766e6i | −0.560690 | − | 0.0579061i | ||||
\(896\) | −1.69907e7 | −0.707036 | ||||||||
\(897\) | −1.87701e6 | + | 1.87701e6i | −0.0778909 | + | 0.0778909i | ||||
\(898\) | −1.26262e6 | − | 1.26262e6i | −0.0522496 | − | 0.0522496i | ||||
\(899\) | 1.59808e7 | 0.659475 | ||||||||
\(900\) | 2.18342e7 | + | 4.55854e6i | 0.898527 | + | 0.187594i | ||||
\(901\) | − | 3.87354e6i | − | 0.158963i | ||||||
\(902\) | −5.40715e6 | + | 3.81872e6i | −0.221285 | + | 0.156279i | ||||
\(903\) | 1.24301e6 | − | 1.24301e6i | 0.0507290 | − | 0.0507290i | ||||
\(904\) | −1.17083e7 | −0.476511 | ||||||||
\(905\) | −3.63090e6 | + | 3.51571e7i | −0.147365 | + | 1.42689i | ||||
\(906\) | −1.50166e6 | −0.0607787 | ||||||||
\(907\) | 2.81619e7 | + | 2.81619e7i | 1.13670 | + | 1.13670i | 0.989039 | + | 0.147657i | \(0.0471731\pi\) |
0.147657 | + | 0.989039i | \(0.452827\pi\) | |||||||
\(908\) | −1.09108e7 | − | 1.09108e7i | −0.439180 | − | 0.439180i | ||||
\(909\) | −2.38363e7 | −0.956817 | ||||||||
\(910\) | 5.34077e6 | + | 6.57097e6i | 0.213796 | + | 0.263042i | ||||
\(911\) | 4.14771e7 | 1.65582 | 0.827908 | − | 0.560864i | \(-0.189531\pi\) | ||||
0.827908 | + | 0.560864i | \(0.189531\pi\) | |||||||
\(912\) | −3.74398e6 | + | 3.74398e6i | −0.149055 | + | 0.149055i | ||||
\(913\) | −3.14723e7 | + | 2.22268e7i | −1.24954 | + | 0.882471i | ||||
\(914\) | − | 3.89393e6i | − | 0.154178i | ||||||
\(915\) | −5.23902e6 | + | 4.25819e6i | −0.206870 | + | 0.168140i | ||||
\(916\) | 4.59881e7 | 1.81095 | ||||||||
\(917\) | −1.50460e7 | − | 1.50460e7i | −0.590877 | − | 0.590877i | ||||
\(918\) | −1.41736e6 | + | 1.41736e6i | −0.0555104 | + | 0.0555104i | ||||
\(919\) | −1.89628e7 | −0.740650 | −0.370325 | − | 0.928902i | \(-0.620754\pi\) | ||||
−0.370325 | + | 0.928902i | \(0.620754\pi\) | |||||||
\(920\) | 331098. | − | 3.20593e6i | 0.0128969 | − | 0.124878i | ||||
\(921\) | − | 7.81017e6i | − | 0.303397i | ||||||
\(922\) | −4.01097e6 | − | 4.01097e6i | −0.155390 | − | 0.155390i | ||||
\(923\) | 2.42609e6 | + | 2.42609e6i | 0.0937351 | + | 0.0937351i | ||||
\(924\) | 829116. | − | 4.81564e6i | 0.0319474 | − | 0.185556i | ||||
\(925\) | −1.36571e7 | − | 2.08646e7i | −0.524813 | − | 0.801779i | ||||
\(926\) | − | 8.84028e6i | − | 0.338796i | ||||||
\(927\) | −2.30649e7 | − | 2.30649e7i | −0.881562 | − | 0.881562i | ||||
\(928\) | 9.47737e6 | − | 9.47737e6i | 0.361259 | − | 0.361259i | ||||
\(929\) | 1.78035e7i | 0.676810i | 0.941001 | + | 0.338405i | \(0.109887\pi\) | ||||
−0.941001 | + | 0.338405i | \(0.890113\pi\) | |||||||
\(930\) | −824725. | − | 85174.7i | −0.0312681 | − | 0.00322926i | ||||
\(931\) | − | 2.39335e6i | − | 0.0904967i | ||||||
\(932\) | −5.86901e6 | + | 5.86901e6i | −0.221322 | + | 0.221322i | ||||
\(933\) | −1.69297e6 | + | 1.69297e6i | −0.0636716 | + | 0.0636716i | ||||
\(934\) | −1.13518e6 | −0.0425790 | ||||||||
\(935\) | 2.22826e7 | − | 1.25222e7i | 0.833561 | − | 0.468436i | ||||
\(936\) | −1.77408e7 | −0.661886 | ||||||||
\(937\) | −1.04846e7 | + | 1.04846e7i | −0.390123 | + | 0.390123i | −0.874731 | − | 0.484608i | \(-0.838962\pi\) |
0.484608 | + | 0.874731i | \(0.338962\pi\) | |||||||
\(938\) | 820686. | − | 820686.i | 0.0304558 | − | 0.0304558i | ||||
\(939\) | − | 70155.2i | − | 0.00259655i | ||||||
\(940\) | −2.81781e7 | − | 3.46687e7i | −1.04014 | − | 1.27973i | ||||
\(941\) | − | 1.69543e7i | − | 0.624173i | −0.950054 | − | 0.312086i | \(-0.898972\pi\) | ||
0.950054 | − | 0.312086i | \(-0.101028\pi\) | |||||||
\(942\) | −1.08718e6 | + | 1.08718e6i | −0.0399185 | + | 0.0399185i | ||||
\(943\) | −7.98386e6 | − | 7.98386e6i | −0.292371 | − | 0.292371i | ||||
\(944\) | − | 2.04643e7i | − | 0.747422i | ||||||
\(945\) | 1.08538e6 | − | 1.05094e7i | 0.0395367 | − | 0.382824i | ||||
\(946\) | −349410. | + | 2.02943e6i | −0.0126942 | + | 0.0737303i | ||||
\(947\) | 1.12252e7 | + | 1.12252e7i | 0.406741 | + | 0.406741i | 0.880600 | − | 0.473860i | \(-0.157140\pi\) |
−0.473860 | + | 0.880600i | \(0.657140\pi\) | |||||||
\(948\) | −2.85623e6 | − | 2.85623e6i | −0.103222 | − | 0.103222i | ||||
\(949\) | 3.83326e7i | 1.38166i | ||||||||
\(950\) | −5.61313e6 | + | 3.67413e6i | −0.201788 | + | 0.132083i | ||||
\(951\) | −6.28780e6 | −0.225449 | ||||||||
\(952\) | −7.28985e6 | + | 7.28985e6i | −0.260691 | + | 0.260691i | ||||
\(953\) | −1.49848e7 | − | 1.49848e7i | −0.534464 | − | 0.534464i | 0.387434 | − | 0.921898i | \(-0.373362\pi\) |
−0.921898 | + | 0.387434i | \(0.873362\pi\) | |||||||
\(954\) | 917787. | 0.0326491 | ||||||||
\(955\) | −46557.6 | + | 450805.i | −0.00165189 | + | 0.0159949i | ||||
\(956\) | − | 2.98120e7i | − | 1.05498i | ||||||
\(957\) | 2.94101e6 | + | 4.16435e6i | 0.103805 | + | 0.146983i | ||||
\(958\) | −5.29329e6 | + | 5.29329e6i | −0.186342 | + | 0.186342i | ||||
\(959\) | −2.55891e7 | −0.898480 | ||||||||
\(960\) | 3.43002e6 | − | 2.78786e6i | 0.120121 | − | 0.0976322i | ||||
\(961\) | −1.25374e7 | −0.437924 | ||||||||
\(962\) | 6.86196e6 | + | 6.86196e6i | 0.239062 | + | 0.239062i | ||||
\(963\) | 113962. | + | 113962.i | 0.00396001 | + | 0.00396001i | ||||
\(964\) | 5.19753e6 | 0.180138 | ||||||||
\(965\) | 2.59219e7 | − | 2.10689e7i | 0.896083 | − | 0.728321i | ||||
\(966\) | −365491. | −0.0126018 | ||||||||
\(967\) | −3.17757e7 | + | 3.17757e7i | −1.09277 | + | 1.09277i | −0.0975384 | + | 0.995232i | \(0.531097\pi\) |
−0.995232 | + | 0.0975384i | \(0.968903\pi\) | |||||||
\(968\) | 5.02986e6 | + | 1.05633e7i | 0.172531 | + | 0.362335i | ||||
\(969\) | 6.72716e6i | 0.230156i | ||||||||
\(970\) | 231580. | − | 2.24233e6i | 0.00790264 | − | 0.0765193i | ||||
\(971\) | −9.35785e6 | −0.318514 | −0.159257 | − | 0.987237i | \(-0.550910\pi\) | ||||
−0.159257 | + | 0.987237i | \(0.550910\pi\) | |||||||
\(972\) | 1.15691e7 | + | 1.15691e7i | 0.392767 | + | 0.392767i | ||||
\(973\) | 3.18057e7 | − | 3.18057e7i | 1.07702 | − | 1.07702i | ||||
\(974\) | −1.70461e6 | −0.0575742 | ||||||||
\(975\) | −1.02316e7 | − | 2.13616e6i | −0.344693 | − | 0.0719651i | ||||
\(976\) | − | 3.39622e7i | − | 1.14123i | ||||||
\(977\) | 1.40931e6 | + | 1.40931e6i | 0.0472355 | + | 0.0472355i | 0.730330 | − | 0.683094i | \(-0.239366\pi\) |
−0.683094 | + | 0.730330i | \(0.739366\pi\) | |||||||
\(978\) | −1.18973e6 | − | 1.18973e6i | −0.0397741 | − | 0.0397741i | ||||
\(979\) | −3.42133e7 | − | 5.89056e6i | −1.14088 | − | 0.196426i | ||||
\(980\) | −227564. | + | 2.20344e6i | −0.00756899 | + | 0.0732885i | ||||
\(981\) | 3.12319e7i | 1.03616i | ||||||||
\(982\) | 2.32860e6 | + | 2.32860e6i | 0.0770578 | + | 0.0770578i | ||||
\(983\) | 2.12347e6 | − | 2.12347e6i | 0.0700910 | − | 0.0700910i | −0.671192 | − | 0.741283i | \(-0.734218\pi\) |
0.741283 | + | 0.671192i | \(0.234218\pi\) | |||||||
\(984\) | 3.29573e6i | 0.108508i | ||||||||
\(985\) | 4.82866e6 | + | 5.94090e6i | 0.158575 | + | 0.195102i | ||||
\(986\) | − | 5.26262e6i | − | 0.172389i | ||||||
\(987\) | −7.32192e6 | + | 7.32192e6i | −0.239239 | + | 0.239239i | ||||
\(988\) | −4.20975e7 | + | 4.20975e7i | −1.37203 | + | 1.37203i | ||||
\(989\) | −3.51244e6 | −0.114188 | ||||||||
\(990\) | 2.96697e6 | + | 5.27959e6i | 0.0962111 | + | 0.171203i | ||||
\(991\) | 7.24962e6 | 0.234494 | 0.117247 | − | 0.993103i | \(-0.462593\pi\) | ||||
0.117247 | + | 0.993103i | \(0.462593\pi\) | |||||||
\(992\) | 9.54319e6 | − | 9.54319e6i | 0.307903 | − | 0.307903i | ||||
\(993\) | 4.47564e6 | − | 4.47564e6i | 0.144040 | − | 0.144040i | ||||
\(994\) | 472407.i | 0.0151653i | ||||||||
\(995\) | −2.09669e7 | − | 2.16539e6i | −0.671394 | − | 0.0693392i | ||||
\(996\) | 9.38560e6i | 0.299788i | ||||||||
\(997\) | −1.80710e7 | + | 1.80710e7i | −0.575764 | + | 0.575764i | −0.933733 | − | 0.357970i | \(-0.883469\pi\) |
0.357970 | + | 0.933733i | \(0.383469\pi\) | |||||||
\(998\) | 3.26085e6 | + | 3.26085e6i | 0.103634 | + | 0.103634i | ||||
\(999\) | − | 1.21083e7i | − | 0.383856i |
(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 | 55.6.e.b.32.13 | ✓ | 52 | |
5.3 | odd | 4 | inner | 55.6.e.b.43.14 | yes | 52 | |
11.10 | odd | 2 | inner | 55.6.e.b.32.14 | yes | 52 | |
55.43 | even | 4 | inner | 55.6.e.b.43.13 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.6.e.b.32.13 | ✓ | 52 | 1.1 | even | 1 | trivial | |
55.6.e.b.32.14 | yes | 52 | 11.10 | odd | 2 | inner | |
55.6.e.b.43.13 | yes | 52 | 55.43 | even | 4 | inner | |
55.6.e.b.43.14 | yes | 52 | 5.3 | odd | 4 | inner |