Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,7,Mod(149,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.149");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.b (of order \(2\), degree \(1\), not 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: | \(69.0162250860\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 406 x^{14} + 67561 x^{12} + 5921226 x^{10} + 291565644 x^{8} + 7924637994 x^{6} + 107459649193 x^{4} + 554332708870 x^{2} + \cdots + 276002078881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{18}\cdot 5^{26} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.10 | ||
Root | \(-6.94307i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.149 |
Dual form | 300.7.b.e.149.9 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 9.99060 | + | 25.0836i | 0.370022 | + | 0.929023i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 134.460i | − | 0.392010i | −0.980603 | − | 0.196005i | \(-0.937203\pi\) | ||
0.980603 | − | 0.196005i | \(-0.0627969\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −529.376 | + | 501.201i | −0.726167 | + | 0.687519i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1155.16i | − | 0.867890i | −0.900939 | − | 0.433945i | \(-0.857121\pi\) | ||
0.900939 | − | 0.433945i | \(-0.142879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 78.2272i | − | 0.0356064i | −0.999842 | − | 0.0178032i | \(-0.994333\pi\) | ||
0.999842 | − | 0.0178032i | \(-0.00566723\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −54.6849 | −0.0111306 | −0.00556532 | − | 0.999985i | \(-0.501772\pi\) | ||||
−0.00556532 | + | 0.999985i | \(0.501772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1984.42 | −0.289316 | −0.144658 | − | 0.989482i | \(-0.546208\pi\) | ||||
−0.144658 | + | 0.989482i | \(0.546208\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3372.73 | − | 1343.33i | 0.364186 | − | 0.145053i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16917.8 | 1.39047 | 0.695234 | − | 0.718784i | \(-0.255301\pi\) | ||||
0.695234 | + | 0.718784i | \(0.255301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17860.7 | − | 8271.35i | −0.907418 | − | 0.420228i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18486.2i | 0.757973i | 0.925402 | + | 0.378986i | \(0.123727\pi\) | ||||
−0.925402 | + | 0.378986i | \(0.876273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38367.7 | 1.28789 | 0.643947 | − | 0.765070i | \(-0.277296\pi\) | ||||
0.643947 | + | 0.765070i | \(0.277296\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 28975.6 | − | 11540.8i | 0.806290 | − | 0.321139i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 21242.8i | − | 0.419378i | −0.977768 | − | 0.209689i | \(-0.932755\pi\) | ||
0.977768 | − | 0.209689i | \(-0.0672452\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1962.22 | − | 781.537i | 0.0330791 | − | 0.0131751i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 88980.3i | 1.29105i | 0.763740 | + | 0.645524i | \(0.223361\pi\) | ||||
−0.763740 | + | 0.645524i | \(0.776639\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 65565.7i | − | 0.824654i | −0.911036 | − | 0.412327i | \(-0.864716\pi\) | ||
0.911036 | − | 0.412327i | \(-0.135284\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 163822. | 1.57790 | 0.788950 | − | 0.614457i | \(-0.210625\pi\) | ||||
0.788950 | + | 0.614457i | \(0.210625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 99569.6 | 0.846328 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −546.335 | − | 1371.69i | −0.00411859 | − | 0.0103406i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −97179.1 | −0.652747 | −0.326374 | − | 0.945241i | \(-0.605827\pi\) | ||||
−0.326374 | + | 0.945241i | \(0.605827\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −19825.5 | − | 49776.4i | −0.107053 | − | 0.268781i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 286230.i | − | 1.39367i | −0.717233 | − | 0.696834i | \(-0.754592\pi\) | ||
0.717233 | − | 0.696834i | \(-0.245408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 119504. | 0.526496 | 0.263248 | − | 0.964728i | \(-0.415206\pi\) | ||||
0.263248 | + | 0.964728i | \(0.415206\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 67391.2 | + | 71179.6i | 0.269514 | + | 0.284665i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 142653.i | 0.474304i | 0.971473 | + | 0.237152i | \(0.0762139\pi\) | ||||
−0.971473 | + | 0.237152i | \(0.923786\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 169019. | + | 424360.i | 0.514504 | + | 1.29178i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 363327.i | 1.01513i | 0.861613 | + | 0.507566i | \(0.169455\pi\) | ||||
−0.861613 | + | 0.507566i | \(0.830545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 576517.i | 1.48199i | 0.671513 | + | 0.740993i | \(0.265645\pi\) | ||||
−0.671513 | + | 0.740993i | \(0.734355\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −155322. | −0.340222 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 627119. | 1.27195 | 0.635973 | − | 0.771711i | \(-0.280599\pi\) | ||||
0.635973 | + | 0.771711i | \(0.280599\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29036.1 | − | 530647.i | 0.0546366 | − | 0.998506i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −991316. | −1.73372 | −0.866858 | − | 0.498556i | \(-0.833864\pi\) | ||||
−0.866858 | + | 0.498556i | \(0.833864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −463701. | + | 184688.i | −0.704174 | + | 0.280467i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 827592.i | 1.17394i | 0.809608 | + | 0.586970i | \(0.199679\pi\) | ||||
−0.809608 | + | 0.586970i | \(0.800321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10518.4 | −0.0139581 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 383316. | + | 962400.i | 0.476550 | + | 1.19648i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 848738.i | − | 0.929948i | −0.885324 | − | 0.464974i | \(-0.846064\pi\) | ||
0.885324 | − | 0.464974i | \(-0.153936\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 578968. | + | 611514.i | 0.596690 | + | 0.630233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.11358e6i | − | 1.08083i | −0.841398 | − | 0.540417i | \(-0.818267\pi\) | ||
0.841398 | − | 0.540417i | \(-0.181733\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.09668e6i | 1.91876i | 0.282118 | + | 0.959380i | \(0.408963\pi\) | ||||
−0.282118 | + | 0.959380i | \(0.591037\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 242367. | 0.197844 | 0.0989218 | − | 0.995095i | \(-0.468461\pi\) | ||||
0.0989218 | + | 0.995095i | \(0.468461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.23474e6 | 1.72563 | 0.862816 | − | 0.505519i | \(-0.168699\pi\) | ||||
0.862816 | + | 0.505519i | \(0.168699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 532846. | − | 212228.i | 0.389612 | − | 0.155179i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −245486. | −0.170134 | −0.0850672 | − | 0.996375i | \(-0.527110\pi\) | ||||
−0.0850672 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 39207.5 | + | 41411.6i | 0.0244800 | + | 0.0258562i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7352.90i | 0.00436333i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 437163. | 0.246767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.23195e6 | + | 888967.i | −1.19941 | + | 0.477717i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 484140.i | 0.236352i | 0.992993 | + | 0.118176i | \(0.0377047\pi\) | ||||
−0.992993 | + | 0.118176i | \(0.962295\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.64463e6 | − | 655041.i | 0.766122 | − | 0.305140i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.46823e6i | 1.54274i | 0.636385 | + | 0.771372i | \(0.280429\pi\) | ||||
−0.636385 | + | 0.771372i | \(0.719571\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 266824.i | 0.113415i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.74492e6 | 0.678600 | 0.339300 | − | 0.940678i | \(-0.389810\pi\) | ||||
0.339300 | + | 0.940678i | \(0.389810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.54561e6 | 1.32022 | 0.660111 | − | 0.751168i | \(-0.270509\pi\) | ||||
0.660111 | + | 0.751168i | \(0.270509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.63668e6 | + | 4.10926e6i | 0.583859 | + | 1.46591i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −90365.0 | −0.0309024 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 994761. | + | 2.49757e6i | 0.313160 | + | 0.786258i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.13539e6i | 1.25014i | 0.780570 | + | 0.625069i | \(0.214929\pi\) | ||||
−0.780570 | + | 0.625069i | \(0.785071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.42874e6 | 0.995873 | 0.497937 | − | 0.867213i | \(-0.334091\pi\) | ||||
0.497937 | + | 0.867213i | \(0.334091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 28948.8 | − | 27408.1i | 0.00808270 | − | 0.00765252i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.35519e6i | − | 1.38381i | −0.721990 | − | 0.691904i | \(-0.756772\pi\) | ||
0.721990 | − | 0.691904i | \(-0.243228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −970878. | − | 2.43760e6i | −0.241531 | − | 0.606417i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.27476e6i | − | 0.545078i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 590537.i | 0.136359i | 0.997673 | + | 0.0681796i | \(0.0217191\pi\) | ||||
−0.997673 | + | 0.0681796i | \(0.978281\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.06892e6 | −0.873634 | −0.436817 | − | 0.899550i | \(-0.643894\pi\) | ||||
−0.436817 | + | 0.899550i | \(0.643894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.82069e6 | 0.998732 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.05050e6 | − | 994593.i | 0.210092 | − | 0.198910i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.80964e6 | 0.928912 | 0.464456 | − | 0.885596i | \(-0.346250\pi\) | ||||
0.464456 | + | 0.885596i | \(0.346250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.17968e6 | − | 2.85961e6i | 1.29475 | − | 0.515688i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 616529.i | 0.107496i | 0.998555 | + | 0.0537482i | \(0.0171168\pi\) | ||||
−0.998555 | + | 0.0537482i | \(0.982883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 169854. | 0.0286444 | 0.0143222 | − | 0.999897i | \(-0.495441\pi\) | ||||
0.0143222 | + | 0.999897i | \(0.495441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.19392e6 | + | 2.99760e6i | 0.194815 | + | 0.489126i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 63169.8i | 0.00966017i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.11216e6 | + | 2.40154e6i | −0.164734 | + | 0.355717i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.63748e6i | − | 0.809068i | −0.914523 | − | 0.404534i | \(-0.867434\pi\) | ||
0.914523 | − | 0.404534i | \(-0.132566\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.93534e6i | − | 0.269207i | −0.990900 | − | 0.134603i | \(-0.957024\pi\) | ||
0.990900 | − | 0.134603i | \(-0.0429760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.63667e6 | −0.737265 | −0.368632 | − | 0.929575i | \(-0.620174\pi\) | ||||
−0.368632 | + | 0.929575i | \(0.620174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −661790. | −0.0839772 | −0.0419886 | − | 0.999118i | \(-0.513369\pi\) | ||||
−0.0419886 | + | 0.999118i | \(0.513369\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.57825e6 | + | 1.42519e6i | −0.440639 | + | 0.175503i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.48565e6 | 0.297133 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.95588e6 | + | 8.47923e6i | −1.00971 | + | 0.955972i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.29232e6i | 0.251095i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 726505. | 0.0773376 | 0.0386688 | − | 0.999252i | \(-0.487688\pi\) | ||||
0.0386688 | + | 0.999252i | \(0.487688\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.11355e6 | + | 3.62985e6i | −0.943080 | + | 0.375621i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.15890e6i | − | 0.504868i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.44611e7 | + | 5.75976e6i | −1.37680 | + | 0.548368i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4277.84i | 0.000396322i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19464.1i | 0.00175517i | 1.00000 | 0.000877585i | \(0.000279344\pi\) | |||||
−1.00000 | 0.000877585i | \(0.999721\pi\) | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.74686e6 | −0.149342 | −0.0746708 | − | 0.997208i | \(-0.523791\pi\) | ||||
−0.0746708 | + | 0.997208i | \(0.523791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −803494. | −0.0669077 | −0.0334539 | − | 0.999440i | \(-0.510651\pi\) | ||||
−0.0334539 | + | 0.999440i | \(0.510651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.55177e6 | − | 3.89605e6i | −0.125890 | − | 0.316074i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.41647e7 | −1.11980 | −0.559900 | − | 0.828561i | \(-0.689160\pi\) | ||||
−0.559900 | + | 0.828561i | \(0.689160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.26530e6 | + | 1.57304e7i | 0.470648 | + | 1.18167i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.51609e7i | − | 1.11054i | −0.831672 | − | 0.555268i | \(-0.812616\pi\) | ||
0.831672 | − | 0.555268i | \(-0.187384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.44786e7 | −1.74878 | −0.874391 | − | 0.485222i | \(-0.838739\pi\) | ||||
−0.874391 | + | 0.485222i | \(0.838739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.36006e7 | − | 4.57316e6i | 0.947852 | − | 0.318711i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 155235.i | 0.0103015i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.90384e6 | − | 2.48658e7i | −0.641513 | − | 1.61066i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.38840e6i | 0.340752i | 0.985379 | + | 0.170376i | \(0.0544982\pi\) | ||||
−0.985379 | + | 0.170376i | \(0.945502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.95428e7i | − | 1.20677i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.81725e7 | 1.65969 | 0.829843 | − | 0.557998i | \(-0.188430\pi\) | ||||
0.829843 | + | 0.557998i | \(0.188430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.85629e6 | −0.164401 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.26530e6 | − | 9.78614e6i | −0.521120 | − | 0.550415i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.14892e7 | −0.631570 | −0.315785 | − | 0.948831i | \(-0.602268\pi\) | ||||
−0.315785 | + | 0.948831i | \(0.602268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.07590e7 | + | 8.26814e6i | −1.09062 | + | 0.434384i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.46873e7i | − | 0.754546i | −0.926102 | − | 0.377273i | \(-0.876862\pi\) | ||
0.926102 | − | 0.377273i | \(-0.123138\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.77493e6 | −0.0891812 | −0.0445906 | − | 0.999005i | \(-0.514198\pi\) | ||||
−0.0445906 | + | 0.999005i | \(0.514198\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −105085. | − | 263839.i | −0.00516479 | − | 0.0129674i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.74584e7i | − | 1.29192i | −0.763371 | − | 0.645960i | \(-0.776457\pi\) | ||
0.763371 | − | 0.645960i | \(-0.223543\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.03109e7 | + | 1.92299e7i | −0.935226 | + | 0.885452i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.73409e6i | − | 0.123224i | −0.998100 | − | 0.0616118i | \(-0.980376\pi\) | ||
0.998100 | − | 0.0616118i | \(-0.0196241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.51523e7i | − | 1.55094i | −0.631386 | − | 0.775469i | \(-0.717513\pi\) | ||
0.631386 | − | 0.775469i | \(-0.282487\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.19642e7 | 0.506104 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.41346e7 | −0.999876 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.12894e7 | − | 8.47941e6i | 0.863943 | − | 0.344102i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.66113e7 | 1.85306 | 0.926528 | − | 0.376227i | \(-0.122779\pi\) | ||||
0.926528 | + | 0.376227i | \(0.122779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.55475e6 | + | 2.06320e7i | −0.364712 | + | 0.787539i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.32343e6i | − | 0.0495095i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.81594e6 | −0.323273 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.79327e7 | − | 1.11254e7i | 1.00412 | − | 0.399932i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.11960e7i | − | 1.07816i | −0.842254 | − | 0.539081i | \(-0.818772\pi\) | ||
0.842254 | − | 0.539081i | \(-0.181228\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.25923e7 | + | 2.09471e7i | −1.78257 | + | 0.709984i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.51987e7i | 1.17016i | 0.810975 | + | 0.585081i | \(0.198937\pi\) | ||||
−0.810975 | + | 0.585081i | \(0.801063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.60591e7i | − | 1.17593i | −0.808886 | − | 0.587965i | \(-0.799929\pi\) | ||
0.808886 | − | 0.587965i | \(-0.200071\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.74502e7 | −1.80349 | −0.901745 | − | 0.432269i | \(-0.857713\pi\) | ||||
−0.901745 | + | 0.432269i | \(0.857713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.13545e7 | 0.657837 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.42139e6 | + | 6.07944e6i | 0.0732065 | + | 0.183801i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 108518. | 0.00322027 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.23264e7 | + | 5.60554e7i | 0.638522 | + | 1.60315i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.20275e7i | − | 0.618553i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.26327e7 | 0.899849 | 0.449924 | − | 0.893067i | \(-0.351451\pi\) | ||||
0.449924 | + | 0.893067i | \(0.351451\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.06469e7 | + | 1.12454e7i | 0.288330 | + | 0.304539i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.34020e7i | − | 1.13402i | −0.823712 | − | 0.567009i | \(-0.808100\pi\) | ||
0.823712 | − | 0.567009i | \(-0.191900\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.45256e6 | − | 6.15769e6i | −0.0629535 | − | 0.158059i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.43209e7i | − | 1.11775i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.92071e7i | − | 0.723779i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.50726e7 | 0.839421 | 0.419710 | − | 0.907658i | \(-0.362132\pi\) | ||||
0.419710 | + | 0.907658i | \(0.362132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.41882e7 | −0.333772 | −0.166886 | − | 0.985976i | \(-0.553371\pi\) | ||||
−0.166886 | + | 0.985976i | \(0.553371\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −647045. | + | 1.39719e6i | −0.0149628 | + | 0.0323099i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.86131e7 | 0.423149 | 0.211575 | − | 0.977362i | \(-0.432141\pi\) | ||||
0.211575 | + | 0.977362i | \(0.432141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −184437. | + | 73459.9i | −0.00405363 | + | 0.00161453i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.28748e6i | − | 0.114279i | −0.998366 | − | 0.0571394i | \(-0.981802\pi\) | ||
0.998366 | − | 0.0571394i | \(-0.0181979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.31080e7 | −0.916296 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.36752e6 | + | 1.09656e7i | 0.0913094 | + | 0.229252i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.00133e6i | − | 0.0202571i | −0.999949 | − | 0.0101286i | \(-0.996776\pi\) | ||
0.999949 | − | 0.0101286i | \(-0.00322408\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.45970e7 | − | 4.71040e7i | −0.887619 | − | 0.937516i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.30666e7i | 0.255884i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.27333e7i | 0.823455i | 0.911307 | + | 0.411728i | \(0.135074\pi\) | ||||
−0.911307 | + | 0.411728i | \(0.864926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.44612e6 | 0.0269887 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.05217e8 | 1.93272 | 0.966358 | − | 0.257202i | \(-0.0828006\pi\) | ||||
0.966358 | + | 0.257202i | \(0.0828006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.21440e7 | + | 4.83685e6i | −0.219577 | + | 0.0874556i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.60163e7 | −1.17505 | −0.587523 | − | 0.809208i | \(-0.699897\pi\) | ||||
−0.587523 | + | 0.809208i | \(0.699897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.28616e7 | + | 3.47089e7i | 0.566965 | + | 0.598836i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.54648e7i | 1.11214i | 0.831136 | + | 0.556070i | \(0.187691\pi\) | ||||
−0.831136 | + | 0.556070i | \(0.812309\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −925149. | −0.0154768 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.69957e7 | + | 3.46497e7i | −1.43324 | + | 0.570850i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5.36739e7i | − | 0.857811i | −0.903349 | − | 0.428905i | \(-0.858899\pi\) | ||
0.903349 | − | 0.428905i | \(-0.141101\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.69291e6 | + | 2.66573e6i | −0.105365 | + | 0.0419660i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.82767e6i | − | 0.136903i | −0.997654 | − | 0.0684515i | \(-0.978194\pi\) | ||
0.997654 | − | 0.0684515i | \(-0.0218058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.00139e6i | − | 0.0458572i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.45388e7 | −0.363974 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.11796e8 | 1.63402 | 0.817011 | − | 0.576622i | \(-0.195629\pi\) | ||||
0.817011 | + | 0.576622i | \(0.195629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.74328e7 | + | 4.37689e7i | 0.251097 | + | 0.630435i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.84863e7 | −0.546332 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.54228e7 | + | 8.89368e7i | 0.488512 | + | 1.22652i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.09574e7i | 0.284902i | 0.989802 | + | 0.142451i | \(0.0454983\pi\) | ||||
−0.989802 | + | 0.142451i | \(0.954502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.87381e7 | −0.251118 | −0.125559 | − | 0.992086i | \(-0.540073\pi\) | ||||
−0.125559 | + | 0.992086i | \(0.540073\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.67236e7 | + | 8.21080e7i | −1.14582 | + | 1.08484i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.60685e7i | − | 0.206392i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −902801. | − | 2.26668e6i | −0.0114346 | − | 0.0287090i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7.51443e6i | − | 0.0938565i | −0.998898 | − | 0.0469283i | \(-0.985057\pi\) | ||
0.998898 | − | 0.0469283i | \(-0.0149432\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.88652e7i | 0.848274i | 0.905598 | + | 0.424137i | \(0.139422\pi\) | ||||
−0.905598 | + | 0.424137i | \(0.860578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.35721e7 | −0.402285 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.30096e8 | 1.53769 | 0.768846 | − | 0.639434i | \(-0.220831\pi\) | ||||
0.768846 | + | 0.639434i | \(0.220831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.27097e7 | + | 4.99044e7i | −0.614575 | + | 0.581866i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.19372e8 | 1.37306 | 0.686531 | − | 0.727100i | \(-0.259132\pi\) | ||||
0.686531 | + | 0.727100i | \(0.259132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.03731e8 | + | 4.13151e7i | −1.16141 | + | 0.462579i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.58450e7i | 0.616943i | 0.951234 | + | 0.308471i | \(0.0998174\pi\) | ||||
−0.951234 | + | 0.308471i | \(0.900183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.02787e8 | 1.12049 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.42552e7 | + | 8.60053e7i | 0.368495 | + | 0.925189i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.17246e8i | − | 1.22843i | −0.789140 | − | 0.614213i | \(-0.789473\pi\) | ||
0.789140 | − | 0.614213i | \(-0.210527\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 976711. | + | 452318.i | 0.0101002 | + | 0.00467741i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.77582e8i | − | 1.81258i | −0.422657 | − | 0.906290i | \(-0.638903\pi\) | ||
0.422657 | − | 0.906290i | \(-0.361097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.25613e8i | 1.26558i | 0.774323 | + | 0.632791i | \(0.218091\pi\) | ||||
−0.774323 | + | 0.632791i | \(0.781909\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.66195e7 | −0.261366 | −0.130683 | − | 0.991424i | \(-0.541717\pi\) | ||||
−0.130683 | + | 0.991424i | \(0.541717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.91810e7 | 0.185932 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.34327e8 | − | 5.35016e7i | 1.28559 | − | 0.512040i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.57390e7 | −0.715709 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.14442e7 | − | 4.87062e7i | 0.474003 | − | 0.448776i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.63522e8i | 1.48789i | 0.668242 | + | 0.743944i | \(0.267047\pi\) | ||||
−0.668242 | + | 0.743944i | \(0.732953\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.66176e6 | −0.0149325 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.70593e7 | − | 2.27262e7i | 0.506390 | − | 0.201691i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.56192e6i | 0.0568125i | 0.999596 | + | 0.0284062i | \(0.00904320\pi\) | ||||
−0.999596 | + | 0.0284062i | \(0.990957\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.48128e7 | + | 5.89982e6i | −0.126681 | + | 0.0504559i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.29952e8i | 1.09784i | 0.835874 | + | 0.548921i | \(0.184961\pi\) | ||||
−0.835874 | + | 0.548921i | \(0.815039\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.01092e6i | − | 0.00843673i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.88527e7 | 0.397942 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.09191e8 | 0.878788 | 0.439394 | − | 0.898295i | \(-0.355193\pi\) | ||||
0.439394 | + | 0.898295i | \(0.355193\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.06509e7 | − | 1.02063e8i | −0.323264 | − | 0.811626i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.22774e7 | −0.253626 | −0.126813 | − | 0.991927i | \(-0.540475\pi\) | ||||
−0.126813 | + | 0.991927i | \(0.540475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.81616e7 | + | 1.20920e8i | 0.369553 | + | 0.927845i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.11482e8i | − | 0.845382i | −0.906274 | − | 0.422691i | \(-0.861086\pi\) | ||
0.906274 | − | 0.422691i | \(-0.138914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.75183e7 | 0.580953 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.54432e7 | + | 1.64138e7i | 0.262531 | + | 0.121579i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.89241e8i | − | 1.36944i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.80513e7 | + | 1.20643e8i | 0.343718 | + | 0.862981i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.70153e8i | 1.91028i | 0.296160 | + | 0.955138i | \(0.404294\pi\) | ||||
−0.296160 | + | 0.955138i | \(0.595706\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.29085e8i | − | 0.902341i | −0.892438 | − | 0.451171i | \(-0.851007\pi\) | ||
0.892438 | − | 0.451171i | \(-0.148993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.09813e6 | −0.0143351 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.38177e8 | 0.933401 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.43459e8 | + | 1.51523e8i | 0.958172 | + | 1.01203i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.96068e6 | 0.0459695 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.54648e7 | + | 6.15949e6i | −0.0998667 | + | 0.0397761i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.15019e8i | − | 0.734519i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.19668e8 | −0.755765 | −0.377883 | − | 0.925853i | \(-0.623348\pi\) | ||||
−0.377883 | + | 0.925853i | \(0.623348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.69694e6 | + | 4.26055e6i | 0.0105991 | + | 0.0266113i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.12552e7i | 0.435366i | 0.976020 | + | 0.217683i | \(0.0698499\pi\) | ||||
−0.976020 | + | 0.217683i | \(0.930150\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.32628e7 | + | 5.98958e7i | −0.382324 | + | 0.361975i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.66844e7i | − | 0.219294i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.43221e7i | − | 0.498616i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.53675e8 | 1.46795 | 0.733976 | − | 0.679176i | \(-0.237663\pi\) | ||||
0.733976 | + | 0.679176i | \(0.237663\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.12902e6 | −0.0293629 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.58453e6 | + | 631105.i | −0.00897452 | + | 0.00357448i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.15634e7 | −0.232909 | −0.116454 | − | 0.993196i | \(-0.537153\pi\) | ||||
−0.116454 | + | 0.993196i | \(0.537153\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.13506e7 | − | 3.90418e6i | −0.391425 | − | 0.0214181i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.69480e8i | − | 0.919986i | −0.887923 | − | 0.459993i | \(-0.847852\pi\) | ||
0.887923 | − | 0.459993i | \(-0.152148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.30661e8 | 1.23898 | 0.619492 | − | 0.785003i | \(-0.287338\pi\) | ||||
0.619492 | + | 0.785003i | \(0.287338\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.41408e8 | − | 5.63218e7i | 0.751642 | − | 0.299373i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.38558e7i | − | 0.488578i | −0.969703 | − | 0.244289i | \(-0.921446\pi\) | ||
0.969703 | − | 0.244289i | \(-0.0785545\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.85454e7 | − | 1.93352e7i | 0.250099 | − | 0.0996125i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.33292e8i | 0.679634i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.12258e8i | 0.566513i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.28514e8 | −1.12979 | −0.564897 | − | 0.825162i | \(-0.691084\pi\) | ||||
−0.564897 | + | 0.825162i | \(0.691084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.61376e7 | −0.372609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.63137e7 | − | 1.41388e8i | −0.272805 | − | 0.684936i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.47213e8 | −0.705966 | −0.352983 | − | 0.935630i | \(-0.614833\pi\) | ||||
−0.352983 | + | 0.935630i | \(0.614833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.61169e6 | − | 1.66001e7i | −0.0310734 | − | 0.0780167i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.04762e8i | − | 0.487440i | −0.969846 | − | 0.243720i | \(-0.921632\pi\) | ||
0.969846 | − | 0.243720i | \(-0.0783678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.92674e8 | −1.34822 | −0.674110 | − | 0.738631i | \(-0.735473\pi\) | ||||
−0.674110 | + | 0.738631i | \(0.735473\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.14978e7 | − | 7.55170e7i | −0.326092 | − | 0.344424i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.94250e8i | 1.31568i | 0.753158 | + | 0.657840i | \(0.228530\pi\) | ||||
−0.753158 | + | 0.657840i | \(0.771470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.48331e7 | + | 6.23490e7i | 0.109946 | + | 0.276043i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.28154e7i | − | 0.0561833i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.10142e8i | − | 0.478158i | −0.971000 | − | 0.239079i | \(-0.923155\pi\) | ||
0.971000 | − | 0.239079i | \(-0.0768454\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.60731e8 | 1.53578 | 0.767888 | − | 0.640584i | \(-0.221308\pi\) | ||||
0.767888 | + | 0.640584i | \(0.221308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.02744e8 | −1.69808 | −0.849038 | − | 0.528332i | \(-0.822818\pi\) | ||||
−0.849038 | + | 0.528332i | \(0.822818\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.02164e8 | − | 1.39933e8i | −1.26174 | − | 0.584314i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.11278e8 | 0.460197 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.74998e7 | + | 2.29017e7i | −0.233273 | + | 0.0929106i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.16166e6i | 0.00466795i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.78200e7 | −0.309744 | −0.154872 | − | 0.987935i | \(-0.549497\pi\) | ||||
−0.154872 | + | 0.987935i | \(0.549497\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.25822e6 | + | 1.82234e7i | 0.0286167 | + | 0.0718484i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.78905e6i | − | 0.0301347i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.82100e8 | − | 1.92336e8i | −0.697921 | − | 0.737155i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.82128e8i | − | 1.83058i | −0.402797 | − | 0.915290i | \(-0.631962\pi\) | ||
0.402797 | − | 0.915290i | \(-0.368038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.57608e7i | 0.0592850i | 0.999561 | + | 0.0296425i | \(0.00943688\pi\) | ||||
−0.999561 | + | 0.0296425i | \(0.990563\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.10892e8 | −0.778660 | −0.389330 | − | 0.921098i | \(-0.627293\pi\) | ||||
−0.389330 | + | 0.921098i | \(0.627293\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.30642e8 | −1.20955 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.29404e8 | − | 5.15405e7i | 0.469034 | − | 0.186812i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.03936e8 | −0.732410 | −0.366205 | − | 0.930534i | \(-0.619343\pi\) | ||||
−0.366205 | + | 0.930534i | \(0.619343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.88951e8 | − | 3.05194e8i | −1.01889 | − | 1.07617i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.80405e8i | 1.67862i | 0.543656 | + | 0.839308i | \(0.317040\pi\) | ||||
−0.543656 | + | 0.839308i | \(0.682960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.13313e8 | −0.392351 | −0.196176 | − | 0.980569i | \(-0.562852\pi\) | ||||
−0.196176 | + | 0.980569i | \(0.562852\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −107304. | + | 42738.2i | −0.000368192 | + | 0.000146648i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.12746e8i | 1.05394i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −488229. | + | 194458.i | −0.00163059 | + | 0.000649452i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.38047e8i | − | 0.456940i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 6.78723e7i | − | 0.222663i | −0.993783 | − | 0.111331i | \(-0.964489\pi\) | ||
0.993783 | − | 0.111331i | \(-0.0355115\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.22505e8 | −1.03937 | −0.519685 | − | 0.854358i | \(-0.673951\pi\) | ||||
−0.519685 | + | 0.854358i | \(0.673951\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.14121e8 | −0.364549 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.74522e7 | − | 4.38176e7i | −0.0552598 | − | 0.138742i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.17199e8 | 1.30943 | 0.654714 | − | 0.755877i | \(-0.272789\pi\) | ||||
0.654714 | + | 0.755877i | \(0.272789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.02739e6 | − | 2.01545e7i | −0.0247574 | − | 0.0621588i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.60204e6i | 0.0232420i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.88809e7 | −0.117842 | −0.0589212 | − | 0.998263i | \(-0.518766\pi\) | ||||
−0.0589212 | + | 0.998263i | \(0.518766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.22239e7 | − | 7.78478e7i | 0.247058 | − | 0.233909i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.86587e6i | − | 0.0143702i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.41514e8 | − | 3.55302e8i | −0.414351 | − | 1.04032i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.02379e7i | 0.203900i | 0.994790 | + | 0.101950i | \(0.0325082\pi\) | ||||
−0.994790 | + | 0.101950i | \(0.967492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.21546e7i | 0.121333i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.49732e8 | −0.423698 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.27456e8 | −0.918785 | −0.459393 | − | 0.888233i | \(-0.651933\pi\) | ||||
−0.459393 | + | 0.888233i | \(0.651933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.31981e8 | + | 3.14313e8i | −0.923645 | + | 0.874486i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.49097e8 | 1.79078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.80291e8 | − | 1.51467e8i | 1.03171 | − | 0.410923i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 6.46847e8i | − | 1.74026i | −0.492819 | − | 0.870132i | \(-0.664034\pi\) | ||
0.492819 | − | 0.870132i | \(-0.335966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.81919e8 | 0.752173 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.44556e8 | − | 6.14012e8i | −0.647089 | − | 1.62466i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.36086e8i | 1.13493i | 0.823398 | + | 0.567465i | \(0.192076\pi\) | ||||
−0.823398 | + | 0.567465i | \(0.807924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.50590e8 | + | 2.95465e8i | 0.646816 | + | 0.762646i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.58545e6i | 0.00917893i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.27585e8i | − | 1.08570i | −0.839829 | − | 0.542851i | \(-0.817345\pi\) | ||
0.839829 | − | 0.542851i | \(-0.182655\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.64787e8 | 0.411643 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.65022e8 | −0.904452 | −0.452226 | − | 0.891903i | \(-0.649370\pi\) | ||||
−0.452226 | + | 0.891903i | \(0.649370\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.89387e6 | + | 1.55090e6i | −0.00957032 | + | 0.00381178i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.75024e8 | −1.64571 | −0.822854 | − | 0.568253i | \(-0.807620\pi\) | ||||
−0.822854 | + | 0.568253i | \(0.807620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.24778e8 | − | 4.96848e8i | 1.25897 | − | 1.19196i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.25885e7i | − | 0.0775567i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.14564e8 | −1.21484 | −0.607421 | − | 0.794380i | \(-0.707796\pi\) | ||||
−0.607421 | + | 0.794380i | \(0.707796\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.35161e8 | + | 5.38334e7i | −0.316567 | + | 0.126086i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.32695e8i | 0.536413i | 0.963361 | + | 0.268207i | \(0.0864310\pi\) | ||||
−0.963361 | + | 0.268207i | \(0.913569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.90204e8 | − | 1.95245e8i | 1.12112 | − | 0.446533i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.18044e7i | − | 0.0721661i | −0.999349 | − | 0.0360831i | \(-0.988512\pi\) | ||
0.999349 | − | 0.0360831i | \(-0.0114881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.00482e8i | − | 0.676465i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.23910e7 | −0.0496234 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.46145e8 | −1.42086 | −0.710430 | − | 0.703768i | \(-0.751499\pi\) | ||||
−0.710430 | + | 0.703768i | \(0.751499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.81460e8 | + | 7.06668e8i | 0.614121 | + | 1.54189i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.82196e8 | 0.394457 | 0.197228 | − | 0.980358i | \(-0.436806\pi\) | ||||
0.197228 | + | 0.980358i | \(0.436806\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.85361e7 | − | 7.16462e7i | −0.0608319 | − | 0.152732i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.76574e8i | − | 0.373521i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.19701e8 | 0.881022 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.52906e8 | − | 3.30177e8i | 0.318522 | − | 0.687799i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.57411e8i | 0.322932i | 0.986878 | + | 0.161466i | \(0.0516222\pi\) | ||||
−0.986878 | + | 0.161466i | \(0.948378\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.14784e8 | − | 2.88190e8i | −0.233695 | − | 0.586743i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.30080e7i | 0.0666944i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.34850e6i | − | 0.0187466i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.11553e7 | 0.101045 | 0.0505225 | − | 0.998723i | \(-0.483911\pi\) | ||||
0.0505225 | + | 0.998723i | \(0.483911\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.95860e6 | −0.0175631 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.14790e8 | − | 4.38107e8i | −0.807106 | − | 0.852477i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.65971e8 | 1.28620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.68411e8 | − | 1.46735e8i | 0.700990 | − | 0.279199i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.30177e8i | 0.812459i | 0.913771 | + | 0.406229i | \(0.133157\pi\) | ||||
−0.913771 | + | 0.406229i | \(0.866843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.35268e8 | 0.253590 | 0.126795 | − | 0.991929i | \(-0.459531\pi\) | ||||
0.126795 | + | 0.991929i | \(0.459531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.77326e7 | − | 4.45216e7i | −0.0329990 | − | 0.0828513i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.30110e8i | 0.238586i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.56818e6 | − | 5.27183e6i | 0.0101359 | − | 0.00959642i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.01637e8i | 1.08719i | 0.839348 | + | 0.543595i | \(0.182937\pi\) | ||||
−0.839348 | + | 0.543595i | \(0.817063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.45245e8i | 0.978119i | 0.872250 | + | 0.489060i | \(0.162660\pi\) | ||||
−0.872250 | + | 0.489060i | \(0.837340\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.83751e8 | 0.501673 | 0.250836 | − | 0.968030i | \(-0.419294\pi\) | ||||
0.250836 | + | 0.968030i | \(0.419294\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.17319e7 | −0.161011 | −0.0805057 | − | 0.996754i | \(-0.525654\pi\) | ||||
−0.0805057 | + | 0.996754i | \(0.525654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.88755e8 | − | 2.74326e8i | 1.20022 | − | 0.478039i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.44495e6 | −0.00942018 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.85274e8 | − | 3.17353e8i | −1.16866 | − | 0.541210i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.01084e8i | 1.18709i | 0.804800 | + | 0.593545i | \(0.202272\pi\) | ||||
−0.804800 | + | 0.593545i | \(0.797728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.53084e8 | 0.425477 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.85808e7 | − | 2.73152e7i | 0.114477 | − | 0.0455955i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.87807e7i | − | 0.0967352i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.81747e8 | − | 3.51193e8i | 1.44086 | − | 0.573882i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.59382e8i | − | 0.583132i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.36003e8i | 0.219130i | 0.993980 | + | 0.109565i | \(0.0349457\pi\) | ||||
−0.993980 | + | 0.109565i | \(0.965054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.07337e9 | −1.70532 | −0.852661 | − | 0.522465i | \(-0.825013\pi\) | ||||
−0.852661 | + | 0.522465i | \(0.825013\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00149e8 | 0.631309 | 0.315654 | − | 0.948874i | \(-0.397776\pi\) | ||||
0.315654 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.19530e8 | + | 3.00107e8i | 0.187270 | + | 0.470182i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.98364e8 | −0.775379 | −0.387690 | − | 0.921790i | \(-0.626727\pi\) | ||||
−0.387690 | + | 0.921790i | \(0.626727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.41119e8 | − | 6.05383e8i | −0.369977 | − | 0.928908i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.24424e8i | − | 1.10391i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.11593e7 | 0.0168882 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.25389e8 | + | 4.49301e8i | 0.639356 | + | 0.675297i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06775e9i | 1.58296i | 0.611194 | + | 0.791481i | \(0.290689\pi\) | ||||
−0.611194 | + | 0.791481i | \(0.709311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.65675e8 | + | 1.16918e9i | 0.685672 | + | 1.72153i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.83809e7i | − | 0.114626i | −0.998356 | − | 0.0573129i | \(-0.981747\pi\) | ||
0.998356 | − | 0.0573129i | \(-0.0182533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.34186e8i | 1.21166i | 0.795594 | + | 0.605830i | \(0.207159\pi\) | ||||
−0.795594 | + | 0.605830i | \(0.792841\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.77272e8 | 0.970493 | 0.485247 | − | 0.874377i | \(-0.338730\pi\) | ||||
0.485247 | + | 0.874377i | \(0.338730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.50972e7 | 0.0926525 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.12983e8 | − | 3.35414e7i | −0.866594 | − | 0.0474185i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.25092e8 | −0.456512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.31965e7 | − | 1.32219e7i | 0.0459954 | − | 0.0183196i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.09273e8i | 0.976189i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.31422e6 | 0.00726550 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.80765e7 | − | 2.21136e8i | −0.119618 | − | 0.300328i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.70732e8i | − | 0.496865i | −0.968649 | − | 0.248432i | \(-0.920085\pi\) | ||
0.968649 | − | 0.248432i | \(-0.0799154\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.58129e8 | + | 5.89504e8i | 0.743093 | + | 0.784865i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.03944e8i | − | 0.666541i | −0.942831 | − | 0.333271i | \(-0.891848\pi\) | ||
0.942831 | − | 0.333271i | \(-0.108152\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.14513e9i | 1.50467i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.66336e8 | 0.604771 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.59392e7 | 0.0463043 | 0.0231522 | − | 0.999732i | \(-0.492630\pi\) | ||||
0.0231522 | + | 0.999732i | \(0.492630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.82509e8 | − | 3.11667e8i | 1.00164 | − | 0.398944i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.84220e7 | 0.0361451 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.05086e9 | − | 1.10993e9i | −1.31918 | − | 1.39334i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.60827e8i | 0.574766i | 0.957816 | + | 0.287383i | \(0.0927853\pi\) | ||||
−0.957816 | + | 0.287383i | \(0.907215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.97588e8 | −0.244856 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.82911e8 | + | 3.51656e8i | −1.08711 | + | 0.432986i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.28388e8i | 0.642295i | 0.947029 | + | 0.321147i | \(0.104068\pi\) | ||||
−0.947029 | + | 0.321147i | \(0.895932\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.04492e8 | − | 3.60252e8i | 1.09247 | − | 0.435120i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.96965e8i | 0.356399i | 0.983994 | + | 0.178200i | \(0.0570273\pi\) | ||||
−0.983994 | + | 0.178200i | \(0.942973\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.50535e9i | 1.79516i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.43742e8 | 0.640240 | 0.320120 | − | 0.947377i | \(-0.396277\pi\) | ||||
0.320120 | + | 0.947377i | \(0.396277\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.50993e7 | 0.0527681 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.73962e8 | − | 1.44106e9i | −0.667332 | − | 1.67548i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.43357e9 | −1.65630 | −0.828150 | − | 0.560506i | \(-0.810607\pi\) | ||||
−0.828150 | + | 0.560506i | \(0.810607\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.13345e8 | + | 5.35649e8i | 0.243414 | + | 0.611146i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.34621e8i | − | 0.266018i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.84575e8 | 0.658673 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.28303e8 | + | 1.21475e8i | −0.143667 | + | 0.136021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.86723e8i | − | 0.206500i | −0.994655 | − | 0.103250i | \(-0.967076\pi\) | ||
0.994655 | − | 0.103250i | \(-0.0329241\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.08416e6 | + | 2.72202e6i | 0.00119157 | + | 0.00299171i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.68364e8i | 0.839284i | 0.907690 | + | 0.419642i | \(0.137844\pi\) | ||||
−0.907690 | + | 0.419642i | \(0.862156\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.76741e8i | − | 0.517540i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.60128e7 | 0.0922316 | 0.0461158 | − | 0.998936i | \(-0.485316\pi\) | ||||
0.0461158 | + | 0.998936i | \(0.485316\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.56002e8 | 1.01885 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.18302e9 | + | 1.12006e9i | −1.25310 | + | 1.18640i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.61067e8 | −1.01180 | −0.505898 | − | 0.862593i | \(-0.668839\pi\) | ||||
−0.505898 | + | 0.862593i | \(0.668839\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.52529e8 | − | 2.20068e8i | 0.574650 | − | 0.228879i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.10923e9i | − | 1.14665i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.24596e8 | −0.641768 | −0.320884 | − | 0.947118i | \(-0.603980\pi\) | ||||
−0.320884 | + | 0.947118i | \(0.603980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.26021e8 | + | 8.18547e8i | 0.332964 | + | 0.835980i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.53088e9i | 1.54474i | 0.635171 | + | 0.772371i | \(0.280929\pi\) | ||||
−0.635171 | + | 0.772371i | \(0.719071\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.75707e8 | + | 3.79411e8i | −0.176235 | + | 0.380552i |
(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 | 300.7.b.e.149.10 | 16 | ||
3.2 | odd | 2 | inner | 300.7.b.e.149.8 | 16 | ||
5.2 | odd | 4 | 60.7.g.a.41.7 | ✓ | 8 | ||
5.3 | odd | 4 | 300.7.g.h.101.2 | 8 | |||
5.4 | even | 2 | inner | 300.7.b.e.149.7 | 16 | ||
15.2 | even | 4 | 60.7.g.a.41.8 | yes | 8 | ||
15.8 | even | 4 | 300.7.g.h.101.1 | 8 | |||
15.14 | odd | 2 | inner | 300.7.b.e.149.9 | 16 | ||
20.7 | even | 4 | 240.7.l.c.161.2 | 8 | |||
60.47 | odd | 4 | 240.7.l.c.161.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.g.a.41.7 | ✓ | 8 | 5.2 | odd | 4 | ||
60.7.g.a.41.8 | yes | 8 | 15.2 | even | 4 | ||
240.7.l.c.161.1 | 8 | 60.47 | odd | 4 | |||
240.7.l.c.161.2 | 8 | 20.7 | even | 4 | |||
300.7.b.e.149.7 | 16 | 5.4 | even | 2 | inner | ||
300.7.b.e.149.8 | 16 | 3.2 | odd | 2 | inner | ||
300.7.b.e.149.9 | 16 | 15.14 | odd | 2 | inner | ||
300.7.b.e.149.10 | 16 | 1.1 | even | 1 | trivial | ||
300.7.g.h.101.1 | 8 | 15.8 | even | 4 | |||
300.7.g.h.101.2 | 8 | 5.3 | odd | 4 |