Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{61})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 31x^{2} + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.3 | ||
Root | \(-3.40512i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.6.d.h.193.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 11.2410i | − 0.201085i | −0.994933 | − | 0.100543i | \(-0.967942\pi\) | ||||
0.994933 | − | 0.100543i | \(-0.0320579\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −148.205 | −1.14319 | −0.571594 | − | 0.820537i | \(-0.693675\pi\) | ||||
−0.571594 | + | 0.820537i | \(0.693675\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 47.0360i | − 0.117206i | −0.998281 | − | 0.0586028i | \(-0.981335\pi\) | ||||
0.998281 | − | 0.0586028i | \(-0.0186646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 545.374i | − 0.895027i | −0.894277 | − | 0.447513i | \(-0.852310\pi\) | ||||
0.894277 | − | 0.447513i | \(-0.147690\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 101.169 | 0.116097 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1162.53 | −0.975624 | −0.487812 | − | 0.872949i | \(-0.662205\pi\) | ||||
−0.487812 | + | 0.872949i | \(0.662205\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 606.748i | 0.385589i | 0.981239 | + | 0.192794i | \(0.0617550\pi\) | ||||
−0.981239 | + | 0.192794i | \(0.938245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1333.84i | − 0.660020i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1104.70 | 0.435436 | 0.217718 | − | 0.976012i | \(-0.430139\pi\) | ||||
0.217718 | + | 0.976012i | \(0.430139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2998.64 | 0.959565 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 729.000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2355.82i | − 0.520172i | −0.965586 | − | 0.260086i | \(-0.916249\pi\) | ||||
0.965586 | − | 0.260086i | \(-0.0837508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2949.39 | −0.551224 | −0.275612 | − | 0.961269i | \(-0.588880\pi\) | ||||
−0.275612 | + | 0.961269i | \(0.588880\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 423.324 | 0.0676687 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1665.97i | 0.229878i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3567.52i | 0.428413i | 0.976788 | + | 0.214206i | \(0.0687165\pi\) | ||||
−0.976788 | + | 0.214206i | \(0.931283\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4908.37 | 0.516744 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14129.3 | 1.31269 | 0.656343 | − | 0.754463i | \(-0.272103\pi\) | ||||
0.656343 | + | 0.754463i | \(0.272103\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17714.4i | 1.46102i | 0.682902 | + | 0.730510i | \(0.260717\pi\) | ||||
−0.682902 | + | 0.730510i | \(0.739283\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 910.521i | 0.0670284i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11597.8 | 0.765829 | 0.382914 | − | 0.923784i | \(-0.374920\pi\) | ||||
0.382914 | + | 0.923784i | \(0.374920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5157.72 | 0.306879 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 10462.8i | − 0.563277i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1514.95i | 0.0740814i | 0.999314 | + | 0.0370407i | \(0.0117931\pi\) | ||||
−0.999314 | + | 0.0370407i | \(0.988207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −528.732 | −0.0235683 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5460.73 | −0.222620 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 10085.1i | − 0.377181i | −0.982056 | − | 0.188590i | \(-0.939608\pi\) | ||||
0.982056 | − | 0.188590i | \(-0.0603919\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 35214.0i | − 1.21169i | −0.795584 | − | 0.605843i | \(-0.792836\pi\) | ||||
0.795584 | − | 0.605843i | \(-0.207164\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12004.6 | 0.381063 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6130.55 | −0.179977 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 28755.0i | 0.782576i | 0.920268 | + | 0.391288i | \(0.127970\pi\) | ||||
−0.920268 | + | 0.391288i | \(0.872030\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9942.28i | 0.251399i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53443.0 | 1.25819 | 0.629093 | − | 0.777330i | \(-0.283426\pi\) | ||||
0.629093 | + | 0.777330i | \(0.283426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −43934.9 | −0.964944 | −0.482472 | − | 0.875911i | \(-0.660261\pi\) | ||||
−0.482472 | + | 0.875911i | \(0.660261\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 26987.8i | 0.554005i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6970.97i | 0.133988i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26786.0 | 0.482881 | 0.241441 | − | 0.970416i | \(-0.422380\pi\) | ||||
0.241441 | + | 0.970416i | \(0.422380\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 105107.i | 1.67470i | 0.546671 | + | 0.837348i | \(0.315895\pi\) | ||||
−0.546671 | + | 0.837348i | \(0.684105\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13068.0i | 0.196183i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21202.4 | 0.300321 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −47927.2 | −0.641368 | −0.320684 | − | 0.947186i | \(-0.603913\pi\) | ||||
−0.320684 | + | 0.947186i | \(0.603913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 80827.1i | 1.02318i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 26544.5i | − 0.318249i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6820.45 | 0.0775361 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 38270.6 | 0.412986 | 0.206493 | − | 0.978448i | \(-0.433795\pi\) | ||||
0.206493 | + | 0.978448i | \(0.433795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3809.92i | 0.0390686i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 128974.i | 1.25805i | 0.777385 | + | 0.629025i | \(0.216546\pi\) | ||||
−0.777385 | + | 0.629025i | \(0.783454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 202213. | 1.87809 | 0.939044 | − | 0.343798i | \(-0.111713\pi\) | ||||
0.939044 | + | 0.343798i | \(0.111713\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14993.7 | −0.132720 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 50910.8i | 0.429883i | 0.976627 | + | 0.214942i | \(0.0689561\pi\) | ||||
−0.976627 | + | 0.214942i | \(0.931044\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 86786.3i | 0.699656i | 0.936814 | + | 0.349828i | \(0.113760\pi\) | ||||
−0.936814 | + | 0.349828i | \(0.886240\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −32107.7 | −0.247344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10281.4 | 0.0757457 | 0.0378729 | − | 0.999283i | \(-0.487942\pi\) | ||||
0.0378729 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 12417.9i | − 0.0875596i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 44175.3i | 0.298342i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 172293. | 1.11532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 158839. | 0.986263 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 127164.i | 0.757879i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 68835.8i | − 0.394039i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118323. | 0.650966 | 0.325483 | − | 0.945548i | \(-0.394473\pi\) | ||||
0.325483 | + | 0.945548i | \(0.394473\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −159430. | −0.843520 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 328293.i | 1.67141i | 0.549179 | + | 0.835705i | \(0.314940\pi\) | ||||
−0.549179 | + | 0.835705i | \(0.685060\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 89923.1i | − 0.440800i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8194.69 | −0.0386988 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11172.7 | −0.0508579 | −0.0254289 | − | 0.999677i | \(-0.508095\pi\) | ||||
−0.0254289 | + | 0.999677i | \(0.508095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 109510.i | 0.480748i | 0.970680 | + | 0.240374i | \(0.0772701\pi\) | ||||
−0.970680 | + | 0.240374i | \(0.922730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 104380.i | 0.442151i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25652.2 | −0.104902 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26481.7 | −0.104599 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 46419.5i | 0.177177i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 309729.i | − 1.14292i | −0.820629 | − | 0.571461i | \(-0.806377\pi\) | ||||
0.820629 | − | 0.571461i | \(-0.193623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 461953. | 1.64875 | 0.824377 | − | 0.566041i | \(-0.191526\pi\) | ||||
0.824377 | + | 0.566041i | \(0.191526\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 94165.1 | 0.325208 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33154.1i | 0.110843i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 434846.i | − 1.40795i | −0.710227 | − | 0.703973i | \(-0.751408\pi\) | ||||
0.710227 | − | 0.703973i | \(-0.248592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13634.6 | −0.0427709 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −163722. | −0.497785 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 119362.i | 0.351883i | 0.984401 | + | 0.175941i | \(0.0562969\pi\) | ||||
−0.984401 | + | 0.175941i | \(0.943703\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 4758.59i | − 0.0136072i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 460259. | 1.27706 | 0.638530 | − | 0.769597i | \(-0.279543\pi\) | ||||
0.638530 | + | 0.769597i | \(0.279543\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 73860.2 | 0.198927 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 49146.6i | − 0.128530i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 465904.i | 1.18353i | 0.806109 | + | 0.591767i | \(0.201569\pi\) | ||||
−0.806109 | + | 0.591767i | \(0.798431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −444413. | −1.09696 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 90765.8 | 0.217765 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 143810.i | − 0.335471i | −0.985832 | − | 0.167736i | \(-0.946355\pi\) | ||||
0.985832 | − | 0.167736i | \(-0.0536455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 281826.i | − 0.639418i | −0.947516 | − | 0.319709i | \(-0.896415\pi\) | ||||
0.947516 | − | 0.319709i | \(-0.103585\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 316926. | 0.699567 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 40102.5 | 0.0861475 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 54680.9i | 0.114349i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 108041.i | 0.220007i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −319313. | −0.633335 | −0.316667 | − | 0.948537i | \(-0.602564\pi\) | ||||
−0.316667 | + | 0.948537i | \(0.602564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 755250. | 1.45948 | 0.729739 | − | 0.683726i | \(-0.239642\pi\) | ||||
0.729739 | + | 0.683726i | \(0.239642\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 55174.9i | − 0.103910i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 69303.0i | 0.127229i | 0.997975 | + | 0.0636146i | \(0.0202628\pi\) | ||||
−0.997975 | + | 0.0636146i | \(0.979737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16621.2 | 0.0297530 | 0.0148765 | − | 0.999889i | \(-0.495264\pi\) | ||||
0.0148765 | + | 0.999889i | \(0.495264\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −258795. | −0.451821 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 349144.i | 0.594654i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 158827.i | − 0.263962i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −89480.5 | −0.145145 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28539.0 | 0.0451932 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 412143.i | 0.637297i | 0.947873 | + | 0.318648i | \(0.103229\pi\) | ||||
−0.947873 | + | 0.318648i | \(0.896771\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 480987.i | 0.726414i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 199128. | 0.293789 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 437114. | 0.630153 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 395414.i | − 0.557111i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 634015.i | 0.873210i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.19123e6 | −1.60411 | −0.802053 | − | 0.597252i | \(-0.796259\pi\) | ||||
−0.802053 | + | 0.597252i | \(0.796259\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −242890. | −0.319855 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.41130e6i | − 1.81783i | −0.416980 | − | 0.908916i | \(-0.636911\pi\) | ||||
0.416980 | − | 0.908916i | \(-0.363089\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 546374.i | − 0.688496i | −0.938879 | − | 0.344248i | \(-0.888134\pi\) | ||||
0.938879 | − | 0.344248i | \(-0.111866\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −62738.7 | −0.0773581 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −919704. | −1.10984 | −0.554918 | − | 0.831905i | \(-0.687250\pi\) | ||||
−0.554918 | + | 0.831905i | \(0.687250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 130371.i | − 0.153997i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 241074.i | 0.278792i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.38063e6 | −1.56345 | −0.781724 | − | 0.623624i | \(-0.785660\pi\) | ||||
−0.781724 | + | 0.623624i | \(0.785660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 650375. | 0.721308 | 0.360654 | − | 0.932700i | \(-0.382553\pi\) | ||||
0.360654 | + | 0.932700i | \(0.382553\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 57977.9i | − 0.0617089i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 330905. | 0.345112 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −945962. | −0.966886 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 393270.i | − 0.394009i | −0.980403 | − | 0.197005i | \(-0.936879\pi\) | ||||
0.980403 | − | 0.197005i | \(-0.0631214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 51960.6i | − 0.0510355i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −117612. | −0.113267 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.23955e6 | −1.17066 | −0.585331 | − | 0.810794i | \(-0.699036\pi\) | ||||
−0.585331 | + | 0.810794i | \(0.699036\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 528725.i | − 0.489757i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 190821.i | 0.173391i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.47951e6 | 1.31895 | 0.659476 | − | 0.751726i | \(-0.270778\pi\) | ||||
0.659476 | + | 0.751726i | \(0.270778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17029.6 | 0.0148967 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 431345.i | − 0.370294i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 345680.i | − 0.291269i | −0.989338 | − | 0.145634i | \(-0.953478\pi\) | ||||
0.989338 | − | 0.145634i | \(-0.0465223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.53008e6 | −1.26558 | −0.632791 | − | 0.774322i | \(-0.718091\pi\) | ||||
−0.632791 | + | 0.774322i | \(0.718091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −727444. | −0.590736 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 141044.i | − 0.112466i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 464109.i | − 0.363429i | −0.983351 | − | 0.181715i | \(-0.941835\pi\) | ||||
0.983351 | − | 0.181715i | \(-0.0581648\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 238901. | 0.183741 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 847312. | 0.640144 | 0.320072 | − | 0.947393i | \(-0.396293\pi\) | ||||
0.320072 | + | 0.947393i | \(0.396293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.08212e6i | − 1.54540i | −0.634773 | − | 0.772698i | \(-0.718907\pi\) | ||||
0.634773 | − | 0.772698i | \(-0.281093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 61384.1i | 0.0447655i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.09403e6 | −1.50065 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −68376.5 | −0.0481573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 344435.i | 0.238438i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.23146e6i | 0.838017i | 0.907982 | + | 0.419008i | \(0.137622\pi\) | ||||
−0.907982 | + | 0.419008i | \(0.862378\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −113366. | −0.0758454 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34289.2 | −0.0225562 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 602474.i | − 0.389727i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.62537e6i | − 1.67022i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.16076e6 | −0.726335 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −395840. | −0.243652 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.70679e6i | − 1.03356i | −0.856120 | − | 0.516778i | \(-0.827131\pi\) | ||||
0.856120 | − | 0.516778i | \(-0.172869\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.81992e6i | 1.08431i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.97615e6 | −1.74484 | −0.872418 | − | 0.488761i | \(-0.837449\pi\) | ||||
−0.872418 | + | 0.488761i | \(0.837449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.41990e6 | 1.97312 | 0.986558 | − | 0.163411i | \(-0.0522497\pi\) | ||||
0.986558 | + | 0.163411i | \(0.0522497\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 134944.i | − 0.0766260i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.30728e6i | 1.84851i | 0.381770 | + | 0.924257i | \(0.375315\pi\) | ||||
−0.381770 | + | 0.924257i | \(0.624685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −110808. | −0.0609671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −458197. | −0.248193 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 705364.i | − 0.376190i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.63538e6i | − 0.858836i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −781077. | −0.403947 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.71885e6 | −0.875486 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 858062.i | − 0.430476i | −0.976562 | − | 0.215238i | \(-0.930947\pi\) | ||||
0.976562 | − | 0.215238i | \(-0.0690527\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 288969.i | − 0.142804i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 323235. | 0.157364 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.31479e6 | 1.11029 | 0.555146 | − | 0.831753i | \(-0.312662\pi\) | ||||
0.555146 | + | 0.831753i | \(0.312662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 92533.0i | 0.0437318i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 138728.i | 0.0646066i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.72648e6 | 0.792367 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 111761. | 0.0505526 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 42663.1i | 0.0190208i | 0.999955 | + | 0.00951039i | \(0.00302730\pi\) | ||||
−0.999955 | + | 0.00951039i | \(0.996973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 4.06310e6i | − 1.78564i | −0.450413 | − | 0.892820i | \(-0.648723\pi\) | ||||
0.450413 | − | 0.892820i | \(-0.351277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −397578. | −0.172248 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.25470e6 | 0.535922 | 0.267961 | − | 0.963430i | \(-0.413650\pi\) | ||||
0.267961 | + | 0.963430i | \(0.413650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 600752.i | − 0.253002i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.55064e6i | 0.643932i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.93310e6 | 0.791621 | 0.395811 | − | 0.918332i | \(-0.370464\pi\) | ||||
0.395811 | + | 0.918332i | \(0.370464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.10796e6 | 0.851321 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.42955e6i | 0.569419i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 493872.i | 0.194036i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −932855. | −0.361534 | −0.180767 | − | 0.983526i | \(-0.557858\pi\) | ||||
−0.180767 | + | 0.983526i | \(0.557858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.14447e6 | −0.437562 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 224524.i | − 0.0846890i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 636513.i | 0.236884i | 0.992961 | + | 0.118442i | \(0.0377899\pi\) | ||||
−0.992961 | + | 0.118442i | \(0.962210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 619522. | 0.227499 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.28480e6 | −0.465567 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 436637.i | 0.156143i | 0.996948 | + | 0.0780715i | \(0.0248762\pi\) | ||||
−0.996948 | + | 0.0780715i | \(0.975124\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.06490e6i | 0.375835i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.77960e6 | −0.968244 | −0.484122 | − | 0.875001i | \(-0.660861\pi\) | ||||
−0.484122 | + | 0.875001i | \(0.660861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 78360.7 | 0.0269430 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.43487e6i | − 0.487006i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4.22186e6i | − 1.41459i | −0.706919 | − | 0.707294i | \(-0.749916\pi\) | ||||
0.706919 | − | 0.707294i | \(-0.250084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.28425e6 | −0.424822 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.95463e6 | −0.964989 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 301102.i | − 0.0971002i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.89554e6i | − 1.24048i | −0.784411 | − | 0.620242i | \(-0.787034\pi\) | ||||
0.784411 | − | 0.620242i | \(-0.212966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 809308. | 0.254496 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −82294.6 | −0.0255570 | −0.0127785 | − | 0.999918i | \(-0.504068\pi\) | ||||
−0.0127785 | + | 0.999918i | \(0.504068\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.60852e6i | 0.493360i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 73752.2i | − 0.0223428i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 167802. | 0.0502124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −133394. | −0.0394300 | −0.0197150 | − | 0.999806i | \(-0.506276\pi\) | ||||
−0.0197150 | + | 0.999806i | \(0.506276\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 100555.i | − 0.0293628i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.49466e6i | 0.431189i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.18151e6 | 0.336756 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −985591. | −0.277560 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.85459e6i | 1.35088i | 0.737414 | + | 0.675441i | \(0.236047\pi\) | ||||
−0.737414 | + | 0.675441i | \(0.763953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 674802.i | 0.185554i | 0.995687 | + | 0.0927772i | \(0.0295744\pi\) | ||||
−0.995687 | + | 0.0927772i | \(0.970426\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −939423. | −0.255276 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.48601e6 | −0.936175 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.21888e6i | 1.38519i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 230870.i | − 0.0605653i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.62432e6 | 1.45840 | 0.729200 | − | 0.684301i | \(-0.239892\pi\) | ||||
0.729200 | + | 0.684301i | \(0.239892\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.89978e6 | 1.51222 | 0.756112 | − | 0.654442i | \(-0.227097\pi\) | ||||
0.756112 | + | 0.654442i | \(0.227097\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 238336.i | − 0.0603901i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 670273.i | 0.167899i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 417376. | 0.103363 | 0.0516817 | − | 0.998664i | \(-0.483542\pi\) | ||||
0.0516817 | + | 0.998664i | \(0.483542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −417775. | −0.102293 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.30672e6i | − 1.28474i | −0.766393 | − | 0.642372i | \(-0.777950\pi\) | ||||
0.766393 | − | 0.642372i | \(-0.222050\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 538750.i | 0.128969i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.78756e6 | 0.659866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.85104e6 | −0.667402 | −0.333701 | − | 0.942679i | \(-0.608298\pi\) | ||||
−0.333701 | + | 0.942679i | \(0.608298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 664585.i | − 0.153854i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.15758e6i | 0.951909i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 908578. | 0.205747 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.94965e6 | 0.660662 | 0.330331 | − | 0.943865i | \(-0.392840\pi\) | ||||
0.330331 | + | 0.943865i | \(0.392840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 847486.i | 0.187759i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.87075e6i | 1.72490i | 0.506143 | + | 0.862449i | \(0.331071\pi\) | ||||
−0.506143 | + | 0.862449i | \(0.668929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.22083e6 | 0.698257 | 0.349128 | − | 0.937075i | \(-0.386478\pi\) | ||||
0.349128 | + | 0.937075i | \(0.386478\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −298387. | −0.0639952 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.23362e6i | 0.686115i | 0.939314 | + | 0.343057i | \(0.111463\pi\) | ||||
−0.939314 | + | 0.343057i | \(0.888537\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 4.26164e6i | − 0.894632i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.91361e6 | 0.812878 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 833216. | 0.171240 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.81942e6i | 0.369997i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 122711.i | − 0.0246938i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.98448e6 | 1.59004 | 0.795020 | − | 0.606583i | \(-0.207460\pi\) | ||||
0.795020 | + | 0.606583i | \(0.207460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.94563e6 | 0.383441 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.47350e6i | − 0.287396i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 430200.i | − 0.0830454i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.14364e6 | −0.791698 | −0.395849 | − | 0.918316i | \(-0.629550\pi\) | ||||
−0.395849 | + | 0.918316i | \(0.629550\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.07426e6 | −0.203160 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.09427e6i | 1.51521i | 0.652711 | + | 0.757607i | \(0.273632\pi\) | ||||
−0.652711 | + | 0.757607i | \(0.726368\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.73871e6i | 0.507492i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 42827.3 | 0.00785611 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.92052e6 | −1.43834 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.18633e6i | 1.11220i | 0.831117 | + | 0.556098i | \(0.187702\pi\) | ||||
−0.831117 | + | 0.556098i | \(0.812298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.14233e6i | 0.737311i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.12950e6 | −0.199052 | −0.0995260 | − | 0.995035i | \(-0.531733\pi\) | ||||
−0.0995260 | + | 0.995035i | \(0.531733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.44979e6 | 0.252975 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 664742.i | 0.114851i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.44872e6i | 0.932181i | 0.884737 | + | 0.466091i | \(0.154338\pi\) | ||||
−0.884737 | + | 0.466091i | \(0.845662\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.51137e6 | 1.10311 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 442319. | 0.0742066 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.27308e6i | − 0.377655i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 545515.i | − 0.0897595i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.19313e6 | −0.683314 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.87834e6 | 0.948769 | 0.474385 | − | 0.880318i | \(-0.342671\pi\) | ||||
0.474385 | + | 0.880318i | \(0.342671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.00787e7i | 1.61120i | 0.592458 | + | 0.805601i | \(0.298158\pi\) | ||||
−0.592458 | + | 0.805601i | \(0.701842\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3.99972e6i | − 0.633332i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.42876e6 | 0.537787 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.21599e6 | −0.810396 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 816892.i | 0.125727i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.70575e6i | − 1.17489i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 572288. | 0.0864431 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.29429e6 | 0.193684 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 242599.i | − 0.0359680i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.07470e7i | − 1.57869i | −0.613953 | − | 0.789343i | \(-0.710421\pi\) | ||||
0.613953 | − | 0.789343i | \(-0.289579\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.53643e6 | 0.369168 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 975565. | 0.140690 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.90847e6i | 0.272719i | 0.990659 | + | 0.136360i | \(0.0435403\pi\) | ||||
−0.990659 | + | 0.136360i | \(0.956460\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.85233e6i | 0.403895i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.42939e6 | 0.200572 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.96982e6 | −0.552024 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 360923.i | 0.0497373i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.16492e6i | 1.25167i | 0.779954 | + | 0.625837i | \(0.215242\pi\) | ||||
−0.779954 | + | 0.625837i | \(0.784758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.66099e6 | 1.30765 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −492128. | −0.0660193 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.86037e6i | 1.04513i | 0.852598 | + | 0.522567i | \(0.175026\pi\) | ||||
−0.852598 | + | 0.522567i | \(0.824974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 115574.i | − 0.0152313i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −972373. | −0.127021 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.16208e6 | −0.409442 | −0.204721 | − | 0.978820i | \(-0.565629\pi\) | ||||
−0.204721 | + | 0.978820i | \(0.565629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.36016e7i | − 1.74582i | −0.487881 | − | 0.872910i | \(-0.662230\pi\) | ||||
0.487881 | − | 0.872910i | \(-0.337770\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.87382e6i | − 0.365656i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.31259e6 | 0.417829 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.53482e6 | −0.191919 | −0.0959594 | − | 0.995385i | \(-0.530592\pi\) | ||||
−0.0959594 | + | 0.995385i | \(0.530592\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.79725e6i | 0.842630i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.55774e7i | − 1.91449i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 71257.3 | 0.00868277 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 496574. | 0.0599922 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.35171e6i | 0.880629i | 0.897844 | + | 0.440315i | \(0.145133\pi\) | ||||
−0.897844 | + | 0.440315i | \(0.854867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.78954e6i | − 0.212546i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −623727. | −0.0734558 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.72521e6 | 0.902139 | 0.451069 | − | 0.892489i | \(-0.351043\pi\) | ||||
0.451069 | + | 0.892489i | \(0.351043\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.93675e6i | − 0.224275i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 149591.i | 0.0171779i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.53129e7 | −1.74378 | −0.871890 | − | 0.489702i | \(-0.837106\pi\) | ||||
−0.871890 | + | 0.489702i | \(0.837106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.69885e6 | 0.417715 | 0.208857 | − | 0.977946i | \(-0.433026\pi\) | ||||
0.208857 | + | 0.977946i | \(0.433026\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.32916e6i | − 0.260859i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1.78550e6i | − 0.198323i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.37471e6 | 0.481923 | 0.240962 | − | 0.970535i | \(-0.422537\pi\) | ||||
0.240962 | + | 0.970535i | \(0.422537\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.14229e6 | −0.343324 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 6.32515e6i | − 0.685437i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.46082e7i | 1.57016i | 0.619392 | + | 0.785082i | \(0.287379\pi\) | ||||
−0.619392 | + | 0.785082i | \(0.712621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.42945e6 | 0.152398 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 576151. | 0.0609289 | 0.0304644 | − | 0.999536i | \(-0.490301\pi\) | ||||
0.0304644 | + | 0.999536i | \(0.490301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.66461e6i | − 0.489315i | −0.969610 | − | 0.244657i | \(-0.921325\pi\) | ||||
0.969610 | − | 0.244657i | \(-0.0786755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 805325.i | − 0.0837996i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.10305e6 | 0.733204 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.59697e6 | 0.880329 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 256851.i | 0.0260923i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 4.14736e6i | − 0.417970i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.93025e6 | −0.492942 | −0.246471 | − | 0.969150i | \(-0.579271\pi\) | ||||
−0.246471 | + | 0.969150i | \(0.579271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.70929e6 | −0.367944 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.33006e6i | − 0.130900i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.81289e6i | − 0.274665i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.32888e6 | −0.419395 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.42308e6 | 0.713574 | 0.356787 | − | 0.934186i | \(-0.383872\pi\) | ||||
0.356787 | + | 0.934186i | \(0.383872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.28737e6i | − 0.122794i | −0.998113 | − | 0.0613969i | \(-0.980444\pi\) | ||||
0.998113 | − | 0.0613969i | \(-0.0195555\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.79215e6i | 0.169619i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.25779e6 | −0.493790 | −0.246895 | − | 0.969042i | \(-0.579410\pi\) | ||||
−0.246895 | + | 0.969042i | \(0.579410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −474362. | −0.0442077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.93403e6i | 0.363819i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.03822e7i | 0.952811i | 0.879226 | + | 0.476405i | \(0.158061\pi\) | ||||
−0.879226 | + | 0.476405i | \(0.841939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.69034e6 | 0.336096 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.55873e6 | 0.321648 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 5.31093e6i | − 0.476384i | −0.971218 | − | 0.238192i | \(-0.923445\pi\) | ||||
0.971218 | − | 0.238192i | \(-0.0765548\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.12917e6i | 0.456608i | 0.973590 | + | 0.228304i | \(0.0733180\pi\) | ||||
−0.973590 | + | 0.228304i | \(0.926682\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.70613e6 | −0.504148 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.01083e6 | −0.0886384 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.60247e6i | − 0.226501i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.07211e7i | − 0.926132i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.65632e6 | −0.142017 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.93890e6 | 0.675652 | 0.337826 | − | 0.941209i | \(-0.390309\pi\) | ||||
0.337826 | + | 0.941209i | \(0.390309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2.18601e6i | − 0.184668i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 381860.i | − 0.0320208i | −0.999872 | − | 0.0160104i | \(-0.994904\pi\) | ||||
0.999872 | − | 0.0160104i | \(-0.00509649\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.67189e6 | −0.472121 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.27017e7 | 1.04953 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.87069e6i | 0.727621i | 0.931473 | + | 0.363811i | \(0.118524\pi\) | ||||
−0.931473 | + | 0.363811i | \(0.881476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 125593.i | 0.0102268i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.91736e6 | 0.397503 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 826216. | 0.0663049 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.54329e6i | 0.122957i | 0.998108 | + | 0.0614783i | \(0.0195815\pi\) | ||||
−0.998108 | + | 0.0614783i | \(0.980419\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 564649.i | − 0.0446627i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.23100e6 | 0.0966712 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.64258e7 | −1.28069 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 8.27734e6i | − 0.640764i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.51477e6i | 0.577592i | 0.957391 | + | 0.288796i | \(0.0932549\pi\) | ||||
−0.957391 | + | 0.288796i | \(0.906745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.16459e6 | −0.165191 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.17334e6 | 0.0889101 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.91145e7i | − 1.43819i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.54954e7i | 1.15768i | 0.815442 | + | 0.578839i | \(0.196494\pi\) | ||||
−0.815442 | + | 0.578839i | \(0.803506\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.16967e6 | −0.160960 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.25819e6 | −0.240023 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 288356.i | 0.0210943i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.24257e7i | − 0.902657i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.10624e7 | −0.798045 | −0.399022 | − | 0.916941i | \(-0.630650\pi\) | ||||
−0.399022 | + | 0.916941i | \(0.630650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.99690e7 | −2.14701 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.85337e6i | 0.416448i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 7.06425e6i | − 0.499138i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.63858e7 | −1.14982 | −0.574912 | − | 0.818216i | \(-0.694964\pi\) | ||||
−0.574912 | + | 0.818216i | \(0.694964\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.05936e7i | − 1.42541i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.09602e6i | − 0.281580i | −0.990039 | − | 0.140790i | \(-0.955036\pi\) | ||||
0.990039 | − | 0.140790i | \(-0.0449642\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 521801. | 0.0356276 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.35252e6 | 0.0917224 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.35232e7i | − 1.58447i | −0.610213 | − | 0.792237i | \(-0.708916\pi\) | ||||
0.610213 | − | 0.792237i | \(-0.291084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.97814e6i | 0.199251i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.62364e6 | −0.573084 | −0.286542 | − | 0.958068i | \(-0.592506\pi\) | ||||
−0.286542 | + | 0.958068i | \(0.592506\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.48167e6 | −0.229825 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 8.51366e6i | − 0.558232i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 7.54524e6i | − 0.491438i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.62269e7 | −1.04987 | −0.524937 | − | 0.851141i | \(-0.675911\pi\) | ||||
−0.524937 | + | 0.851141i | \(0.675911\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.53943e6 | 0.227481 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 5.19282e6i | − 0.331540i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.05486e7i | 1.30330i | 0.758522 | + | 0.651648i | \(0.225922\pi\) | ||||
−0.758522 | + | 0.651648i | \(0.774078\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 467645. | 0.0294654 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.33531e6 | 0.271368 | 0.135684 | − | 0.990752i | \(-0.456677\pi\) | ||||
0.135684 | + | 0.990752i | \(0.456677\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.28622e7i | − 0.799839i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.05851e6i | − 0.0653945i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.50014e6 | −0.337587 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.72697e7 | −1.05310 | −0.526548 | − | 0.850145i | \(-0.676514\pi\) | ||||
−0.526548 | + | 0.850145i | \(0.676514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.11560e7i | − 0.675882i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2.64326e7i | − 1.59108i | −0.605903 | − | 0.795539i | \(-0.707188\pi\) | ||||
0.605903 | − | 0.795539i | \(-0.292812\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.84416e6 | −0.528935 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.75852e6 | 0.282761 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.57292e6i | 0.506157i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.51374e6i | − 0.147467i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.71739e6 | −0.100107 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.88810e6 | −0.283117 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.17967e7i | 1.25445i | 0.778837 | + | 0.627226i | \(0.215810\pi\) | ||||
−0.778837 | + | 0.627226i | \(0.784190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.33156e7i | 0.761497i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.52376e6 | −0.0865916 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.92048e7 | −1.08449 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 153266.i | 0.00860060i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.45761e7i | 1.37046i | 0.728326 | + | 0.685231i | \(0.240299\pi\) | ||||
−0.728326 | + | 0.685231i | \(0.759701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.34828e7 | −0.747161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.88210e6 | 0.213789 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.06652e6i | 0.113097i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.84040e6i | 0.100097i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.11112e6 | 0.168164 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.10063e7 | 1.12844 | 0.564221 | − | 0.825624i | \(-0.309177\pi\) | ||||
0.564221 | + | 0.825624i | \(0.309177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.68688e7i | 1.43448i | 0.696824 | + | 0.717242i | \(0.254596\pi\) | ||||
−0.696824 | + | 0.717242i | \(0.745404\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.37707e7i | − 0.730685i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.34175e6 | 0.0707583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.07482e7 | −0.563353 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 6.54700e6i | − 0.341061i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.90654e7i | − 0.987161i | −0.869700 | − | 0.493581i | \(-0.835688\pi\) | ||||
0.869700 | − | 0.493581i | \(-0.164312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.64112e6 | −0.187385 | −0.0936926 | − | 0.995601i | \(-0.529867\pi\) | ||||
−0.0936926 | + | 0.995601i | \(0.529867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.26940e6 | 0.0649325 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.44261e7i | − 1.75034i | −0.483812 | − | 0.875172i | \(-0.660748\pi\) | ||||
0.483812 | − | 0.875172i | \(-0.339252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.51490e7i | 1.27097i | 0.772114 | + | 0.635485i | \(0.219200\pi\) | ||||
−0.772114 | + | 0.635485i | \(0.780800\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.17698e6 | 0.209826 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.99601e6 | −0.299399 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 5.17377e6i | − 0.256798i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.15011e6i | 0.106083i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.37585e7 | −0.674785 | −0.337392 | − | 0.941364i | \(-0.609545\pi\) | ||||
−0.337392 | + | 0.941364i | \(0.609545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.49613e7 | 0.729422 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.62581e6i | 0.369587i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 830263.i | − 0.0400013i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.35407e7 | −1.12748 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.87391e7 | 0.892235 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.94104e6i | 0.186546i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.71986e7i | 1.27989i | 0.768419 | + | 0.639946i | \(0.221043\pi\) | ||||
−0.768419 | + | 0.639946i | \(0.778957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −552457. | −0.0258454 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.90034e7 | 0.883851 | 0.441925 | − | 0.897052i | \(-0.354296\pi\) | ||||
0.441925 | + | 0.897052i | \(0.354296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4.23596e7i | − 1.95871i | −0.202157 | − | 0.979353i | \(-0.564795\pi\) | ||||
0.202157 | − | 0.979353i | \(-0.435205\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.88463e7i | − 0.866399i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.43661e6 | −0.0656616 | −0.0328308 | − | 0.999461i | \(-0.510452\pi\) | ||||
−0.0328308 | + | 0.999461i | \(0.510452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.23722e6 | 0.237991 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 615389.i | − 0.0278036i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.25991e6i | − 0.0565964i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.56822e7 | 0.700427 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.09992e6 | −0.137662 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.02018e7i | 0.450461i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.32043e7i | 0.579718i | 0.957069 | + | 0.289859i | \(0.0936085\pi\) | ||||
−0.957069 | + | 0.289859i | \(0.906392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.10832e7 | −0.483829 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.00664e6 | 0.390952 | 0.195476 | − | 0.980709i | \(-0.437375\pi\) | ||||
0.195476 | + | 0.980709i | \(0.437375\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.18359e7i | − 0.942473i | −0.882007 | − | 0.471237i | \(-0.843808\pi\) | ||||
0.882007 | − | 0.471237i | \(-0.156192\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.02030e6i | − 0.0437894i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.58096e7 | 1.95500 | 0.977502 | − | 0.210926i | \(-0.0676479\pi\) | ||||
0.977502 | + | 0.210926i | \(0.0676479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.75360e7 | −0.744176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 308603.i | − 0.0130229i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.03695e6i | 0.295295i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.61656e6 | −0.0674582 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.42226e6 | 0.225009 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.94823e6i | 0.286731i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.76118e6i | − 0.0722757i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.36283e7 | 0.964302 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.16801e6 | −0.128577 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.25677e7i | 1.31452i | 0.753662 | + | 0.657262i | \(0.228286\pi\) | ||||
−0.753662 | + | 0.657262i | \(0.771714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1.04469e7i | − 0.419350i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.24433e7 | −1.69439 | −0.847194 | − | 0.531283i | \(-0.821710\pi\) | ||||
−0.847194 | + | 0.531283i | \(0.821710\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.94381e6 | 0.196284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 3.56256e6i | − 0.140673i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.86546e7i | − 1.91074i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.77474e7 | 1.47434 | 0.737172 | − | 0.675705i | \(-0.236161\pi\) | ||||
0.737172 | + | 0.675705i | \(0.236161\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.53611e7 | 0.596724 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.91464e7i | − 1.12611i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.06977e7i | 0.411090i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.63792e7 | −0.626029 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.41047e7 | 1.29651 | 0.648254 | − | 0.761424i | \(-0.275499\pi\) | ||||
0.648254 | + | 0.761424i | \(0.275499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.12944e6i | 0.118329i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.67854e7i | − 1.00738i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 614667. | 0.0229938 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.26592e7 | −0.843130 | −0.421565 | − | 0.906798i | \(-0.638519\pi\) | ||||
−0.421565 | + | 0.906798i | \(0.638519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.07791e7i | 1.13918i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.44909e7i | − 0.533484i | −0.963768 | − | 0.266742i | \(-0.914053\pi\) | ||||
0.963768 | − | 0.266742i | \(-0.0859471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56086e7 | 0.571590 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.21449e6 | 0.0442401 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.43018e7i | 1.24292i | 0.783447 | + | 0.621459i | \(0.213460\pi\) | ||||
−0.783447 | + | 0.621459i | \(0.786540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.39609e7i | 0.863651i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.97655e7 | −1.06724 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.23134e7 | −1.15252 | −0.576262 | − | 0.817265i | \(-0.695489\pi\) | ||||
−0.576262 | + | 0.817265i | \(0.695489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.58940e6i | 0.127354i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 997274.i | − 0.0351994i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.65586e6 | 0.0581401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.99302e7 | −0.696152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4.12378e6i | − 0.143294i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 8.48976e6i | − 0.293479i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.73182e7 | 0.939477 | 0.469738 | − | 0.882806i | \(-0.344348\pi\) | ||||
0.469738 | + | 0.882806i | \(0.344348\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.34827e6 | 0.217193 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.99922e7i | 1.02085i | 0.859923 | + | 0.510423i | \(0.170511\pi\) | ||||
−0.859923 | + | 0.510423i | \(0.829489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.62300e7i | − 0.549585i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.47184e7 | 0.495849 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.33987e7 | −0.784251 | −0.392126 | − | 0.919912i | \(-0.628260\pi\) | ||||
−0.392126 | + | 0.919912i | \(0.628260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.25430e6i | 0.0751720i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 7.02969e6i | − 0.233219i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.38086e7 | 0.455792 | 0.227896 | − | 0.973686i | \(-0.426815\pi\) | ||||
0.227896 | + | 0.973686i | \(0.426815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 779035. | 0.0255839 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.54697e7i | − 0.505462i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.95691e7i | 0.636180i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.17280e6 | −0.102626 | −0.0513131 | − | 0.998683i | \(-0.516341\pi\) | ||||
−0.0513131 | + | 0.998683i | \(0.516341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.72256e6 | 0.248535 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 186839.i | − 0.00598288i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.02543e6i | 0.128255i | 0.997942 | + | 0.0641276i | \(0.0204265\pi\) | ||||
−0.997942 | + | 0.0641276i | \(0.979574\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.60072e6 | 0.0824481 |
(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 | 384.6.d.h.193.3 | yes | 4 | |
4.3 | odd | 2 | 384.6.d.g.193.1 | ✓ | 4 | ||
8.3 | odd | 2 | 384.6.d.g.193.4 | yes | 4 | ||
8.5 | even | 2 | inner | 384.6.d.h.193.2 | yes | 4 | |
16.3 | odd | 4 | 768.6.a.v.1.1 | 2 | |||
16.5 | even | 4 | 768.6.a.r.1.2 | 2 | |||
16.11 | odd | 4 | 768.6.a.m.1.2 | 2 | |||
16.13 | even | 4 | 768.6.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.d.g.193.1 | ✓ | 4 | 4.3 | odd | 2 | ||
384.6.d.g.193.4 | yes | 4 | 8.3 | odd | 2 | ||
384.6.d.h.193.2 | yes | 4 | 8.5 | even | 2 | inner | |
384.6.d.h.193.3 | yes | 4 | 1.1 | even | 1 | trivial | |
768.6.a.m.1.2 | 2 | 16.11 | odd | 4 | |||
768.6.a.q.1.1 | 2 | 16.13 | even | 4 | |||
768.6.a.r.1.2 | 2 | 16.5 | even | 4 | |||
768.6.a.v.1.1 | 2 | 16.3 | odd | 4 |