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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 338x^{10} + 43555x^{8} + 2692222x^{6} + 81680965x^{4} + 1098257588x^{2} + 4742525956 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{57}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.7 | ||
Root | \(8.76697i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.6.d.j.193.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | − 107.066i | − 1.91525i | −0.288015 | − | 0.957626i | \(-0.592995\pi\) | ||||
0.288015 | − | 0.957626i | \(-0.407005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −150.154 | −1.15822 | −0.579109 | − | 0.815250i | \(-0.696600\pi\) | ||||
−0.579109 | + | 0.815250i | \(0.696600\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 221.870i | − 0.552863i | −0.961034 | − | 0.276432i | \(-0.910848\pi\) | ||||
0.961034 | − | 0.276432i | \(-0.0891519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 504.463i | 0.827887i | 0.910302 | + | 0.413944i | \(0.135849\pi\) | ||||
−0.910302 | + | 0.413944i | \(0.864151\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 963.592 | 1.10577 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1982.75 | −1.66397 | −0.831986 | − | 0.554796i | \(-0.812796\pi\) | ||||
−0.831986 | + | 0.554796i | \(0.812796\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2368.23i | − 1.50501i | −0.658584 | − | 0.752507i | \(-0.728844\pi\) | ||||
0.658584 | − | 0.752507i | \(-0.271156\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1351.38i | − 0.668698i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1143.26 | −0.450634 | −0.225317 | − | 0.974286i | \(-0.572342\pi\) | ||||
−0.225317 | + | 0.974286i | \(0.572342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8338.09 | −2.66819 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 729.000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3900.86i | 0.861321i | 0.902514 | + | 0.430660i | \(0.141719\pi\) | ||||
−0.902514 | + | 0.430660i | \(0.858281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9007.16 | 1.68339 | 0.841693 | − | 0.539957i | \(-0.181559\pi\) | ||||
0.841693 | + | 0.539957i | \(0.181559\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1996.83 | 0.319196 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16076.3i | 2.21828i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 448.595i | − 0.0538704i | −0.999637 | − | 0.0269352i | \(-0.991425\pi\) | ||||
0.999637 | − | 0.0269352i | \(-0.00857477\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4540.17 | −0.477981 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9899.43 | 0.919709 | 0.459855 | − | 0.887994i | \(-0.347901\pi\) | ||||
0.459855 | + | 0.887994i | \(0.347901\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4624.59i | − 0.381419i | −0.981647 | − | 0.190709i | \(-0.938921\pi\) | ||||
0.981647 | − | 0.190709i | \(-0.0610788\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8672.33i | 0.638417i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20086.5 | 1.32635 | 0.663176 | − | 0.748463i | \(-0.269208\pi\) | ||||
0.663176 | + | 0.748463i | \(0.269208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5739.09 | 0.341470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 17844.8i | − 0.960695i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17426.0i | 0.852135i | 0.904691 | + | 0.426068i | \(0.140101\pi\) | ||||
−0.904691 | + | 0.426068i | \(0.859899\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −23754.7 | −1.05887 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21314.1 | 0.868921 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 35967.4i | 1.34517i | 0.740018 | + | 0.672587i | \(0.234817\pi\) | ||||
−0.740018 | + | 0.672587i | \(0.765183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12519.7i | 0.430795i | 0.976526 | + | 0.215397i | \(0.0691047\pi\) | ||||
−0.976526 | + | 0.215397i | \(0.930895\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12162.4 | 0.386073 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 54010.8 | 1.58561 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 35342.5i | − 0.961855i | −0.876760 | − | 0.480928i | \(-0.840300\pi\) | ||||
0.876760 | − | 0.480928i | \(-0.159700\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 10289.3i | − 0.260173i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1761.27 | 0.0414649 | 0.0207325 | − | 0.999785i | \(-0.493400\pi\) | ||||
0.0207325 | + | 0.999785i | \(0.493400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21143.9 | −0.464385 | −0.232193 | − | 0.972670i | \(-0.574590\pi\) | ||||
−0.232193 | + | 0.972670i | \(0.574590\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 75042.8i | − 1.54048i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33314.6i | 0.640337i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46562.3 | 0.839395 | 0.419697 | − | 0.907664i | \(-0.362136\pi\) | ||||
0.419697 | + | 0.907664i | \(0.362136\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 103022.i | 1.64147i | 0.571309 | + | 0.820735i | \(0.306436\pi\) | ||||
−0.571309 | + | 0.820735i | \(0.693564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 212285.i | 3.18693i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −35107.7 | −0.497284 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −111679. | −1.49451 | −0.747253 | − | 0.664540i | \(-0.768628\pi\) | ||||
−0.747253 | + | 0.664540i | \(0.768628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 75747.0i | − 0.958874i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 81064.4i | 0.971903i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −253557. | −2.88248 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −39002.5 | −0.420884 | −0.210442 | − | 0.977606i | \(-0.567490\pi\) | ||||
−0.210442 | + | 0.977606i | \(0.567490\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17971.5i | 0.184288i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 61681.4i | 0.601660i | 0.953678 | + | 0.300830i | \(0.0972636\pi\) | ||||
−0.953678 | + | 0.300830i | \(0.902736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 47754.1 | 0.443524 | 0.221762 | − | 0.975101i | \(-0.428819\pi\) | ||||
0.221762 | + | 0.975101i | \(0.428819\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −144687. | −1.28072 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 70099.5i | 0.591910i | 0.955202 | + | 0.295955i | \(0.0956378\pi\) | ||||
−0.955202 | + | 0.295955i | \(0.904362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 113761.i | − 0.917121i | −0.888663 | − | 0.458561i | \(-0.848365\pi\) | ||||
0.888663 | − | 0.458561i | \(-0.151635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4037.35 | 0.0311021 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −162065. | −1.19397 | −0.596985 | − | 0.802252i | \(-0.703635\pi\) | ||||
−0.596985 | + | 0.802252i | \(0.703635\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 122404.i | 0.863077i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 40861.5i | − 0.275962i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 297717. | 1.92724 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 111824. | 0.694342 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 89094.9i | 0.530994i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 558144.i | 3.19500i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −208540. | −1.14731 | −0.573654 | − | 0.819097i | \(-0.694475\pi\) | ||||
−0.573654 | + | 0.819097i | \(0.694475\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 41621.3 | 0.220212 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 25436.7i | − 0.129504i | −0.997901 | − | 0.0647520i | \(-0.979374\pi\) | ||||
0.997901 | − | 0.0647520i | \(-0.0206256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 355599.i | 1.74314i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −78051.0 | −0.368590 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 249283. | 1.13473 | 0.567363 | − | 0.823468i | \(-0.307964\pi\) | ||||
0.567363 | + | 0.823468i | \(0.307964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 199937.i | − 0.877722i | −0.898555 | − | 0.438861i | \(-0.855382\pi\) | ||||
0.898555 | − | 0.438861i | \(-0.144618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180778.i | 0.765770i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 111926. | 0.457709 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 417648. | 1.64965 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 51651.8i | 0.197148i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 183640.i | − 0.677645i | −0.940850 | − | 0.338823i | \(-0.889971\pi\) | ||||
0.940850 | − | 0.338823i | \(-0.110029\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 319160. | 1.13911 | 0.569555 | − | 0.821953i | \(-0.307116\pi\) | ||||
0.569555 | + | 0.821953i | \(0.307116\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 160603. | 0.554658 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 964359.i | − 3.22411i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 105413.i | 0.341308i | 0.985331 | + | 0.170654i | \(0.0545881\pi\) | ||||
−0.985331 | + | 0.170654i | \(0.945412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −156834. | −0.491981 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 171664. | 0.521932 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 511453.i | 1.50777i | 0.657004 | + | 0.753887i | \(0.271824\pi\) | ||||
−0.657004 | + | 0.753887i | \(0.728176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 213793.i | − 0.611340i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −585529. | −1.62464 | −0.812320 | − | 0.583212i | \(-0.801796\pi\) | ||||
−0.812320 | + | 0.583212i | \(0.801796\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 116810. | 0.314602 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 191827.i | 0.501672i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 149097.i | 0.378751i | 0.981905 | + | 0.189375i | \(0.0606463\pi\) | ||||
−0.981905 | + | 0.189375i | \(0.939354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.25199e6 | 3.09035 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −323706. | −0.776637 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 101335.i | − 0.236390i | −0.992990 | − | 0.118195i | \(-0.962289\pi\) | ||||
0.992990 | − | 0.118195i | \(-0.0377108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 709024.i | 1.60866i | 0.594182 | + | 0.804330i | \(0.297476\pi\) | ||||
−0.594182 | + | 0.804330i | \(0.702524\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −112678. | −0.248719 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −48029.2 | −0.103175 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 439914.i | 0.919950i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 109462.i | 0.222899i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −54546.3 | −0.108189 | −0.0540943 | − | 0.998536i | \(-0.517227\pi\) | ||||
−0.0540943 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −831213. | −1.60627 | −0.803136 | − | 0.595796i | \(-0.796837\pi\) | ||||
−0.803136 | + | 0.595796i | \(0.796837\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 486097.i | 0.915454i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 171308.i | 0.314495i | 0.987559 | + | 0.157247i | \(0.0502620\pi\) | ||||
−0.987559 | + | 0.157247i | \(0.949738\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −119632. | −0.214149 | −0.107075 | − | 0.994251i | \(-0.534148\pi\) | ||||
−0.107075 | + | 0.994251i | \(0.534148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 318082. | 0.555327 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 585727.i | − 0.997598i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.05989e6i | − 1.76148i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 92603.7 | 0.150211 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −525441. | −0.832067 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 877085.i | 1.35624i | 0.734952 | + | 0.678119i | \(0.237204\pi\) | ||||
−0.734952 | + | 0.678119i | \(0.762796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15851.5i | 0.0239398i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −495136. | −0.730513 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.35246e6 | −1.94973 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 190295.i | − 0.268113i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.00023e6i | − 1.37758i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −194513. | −0.261931 | −0.130965 | − | 0.991387i | \(-0.541808\pi\) | ||||
−0.130965 | + | 0.991387i | \(0.541808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 675385. | 0.889397 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 597533.i | 0.769658i | 0.922988 | + | 0.384829i | \(0.125740\pi\) | ||||
−0.922988 | + | 0.384829i | \(0.874260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 794517.i | − 1.00119i | −0.865683 | − | 0.500593i | \(-0.833115\pi\) | ||||
0.865683 | − | 0.500593i | \(-0.166885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −299832. | −0.369698 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 437908. | 0.528437 | 0.264218 | − | 0.964463i | \(-0.414886\pi\) | ||||
0.264218 | + | 0.964463i | \(0.414886\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.15057e6i | − 2.54030i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 419060.i | 0.484625i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 649053. | 0.734997 | 0.367499 | − | 0.930024i | \(-0.380214\pi\) | ||||
0.367499 | + | 0.930024i | \(0.380214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −427372. | −0.473984 | −0.236992 | − | 0.971512i | \(-0.576162\pi\) | ||||
−0.236992 | + | 0.971512i | \(0.576162\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 614460.i | − 0.654001i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.19469e6 | 1.24598 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −927194. | −0.947703 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 514388.i | 0.515355i | 0.966231 | + | 0.257678i | \(0.0829572\pi\) | ||||
−0.966231 | + | 0.257678i | \(0.917043\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 253655.i | 0.249139i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.91057e6 | −1.83997 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −594709. | −0.561657 | −0.280829 | − | 0.959758i | \(-0.590609\pi\) | ||||
−0.280829 | + | 0.959758i | \(0.590609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 67358.1i | 0.0623937i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 315969.i | − 0.287107i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.06496e6 | −1.84087 | −0.920434 | − | 0.390898i | \(-0.872164\pi\) | ||||
−0.920434 | + | 0.390898i | \(0.872164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.86573e6 | 1.63205 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.00511e6i | − 0.862853i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 667420.i | − 0.562365i | −0.959654 | − | 0.281183i | \(-0.909273\pi\) | ||||
0.959654 | − | 0.281183i | \(-0.0907266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 692916. | 0.573136 | 0.286568 | − | 0.958060i | \(-0.407486\pi\) | ||||
0.286568 | + | 0.958060i | \(0.407486\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 681723. | 0.553606 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.84998e6i | 1.47514i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.11671e6i | − 1.65753i | −0.559595 | − | 0.828767i | \(-0.689043\pi\) | ||||
0.559595 | − | 0.828767i | \(-0.310957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −729580. | −0.561128 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.82468e6 | 1.37854 | 0.689271 | − | 0.724504i | \(-0.257931\pi\) | ||||
0.689271 | + | 0.724504i | \(0.257931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.18653e6i | − 0.880665i | −0.897835 | − | 0.440333i | \(-0.854861\pi\) | ||||
0.897835 | − | 0.440333i | \(-0.145139\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2.28201e6i | − 1.66420i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.48643e6 | −1.06522 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.51145e6 | 1.76881 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 351022.i | − 0.242998i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 183945.i | − 0.125175i | −0.998039 | − | 0.0625877i | \(-0.980065\pi\) | ||||
0.998039 | − | 0.0625877i | \(-0.0199353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.85088e6 | 2.57635 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −161744. | −0.106399 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 576730.i | − 0.373074i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 694399.i | 0.441766i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −555133. | −0.347368 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.34044e6 | 0.825080 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 700476.i | − 0.424177i | −0.977250 | − | 0.212089i | \(-0.931973\pi\) | ||||
0.977250 | − | 0.212089i | \(-0.0680265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 429787.i | 0.256069i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.32274e6 | 0.775483 | 0.387741 | − | 0.921768i | \(-0.373255\pi\) | ||||
0.387741 | + | 0.921768i | \(0.373255\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −118214. | −0.0682036 | −0.0341018 | − | 0.999418i | \(-0.510857\pi\) | ||||
−0.0341018 | + | 0.999418i | \(0.510857\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.30218e6i | − 0.739427i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.55712e6i | − 1.42923i | −0.699516 | − | 0.714617i | \(-0.746601\pi\) | ||||
0.699516 | − | 0.714617i | \(-0.253399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 865485. | 0.476193 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −630896. | −0.341739 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.69562e6i | 2.50430i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.20626e6i | − 2.20896i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.02385e6 | 0.529500 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.01605e6 | −1.53621 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.66796e6i | 1.33847i | 0.743049 | + | 0.669237i | \(0.233379\pi\) | ||||
−0.743049 | + | 0.669237i | \(0.766621\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36336.2i | 0.0179568i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.78397e6 | −1.84220 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −352164. | −0.168916 | −0.0844580 | − | 0.996427i | \(-0.526916\pi\) | ||||
−0.0844580 | + | 0.996427i | \(0.526916\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.45859e6i | − 0.689339i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.99842e6i | − 0.930682i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.66189e6 | 0.762722 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.10163e6 | −0.498298 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.65583e6i | 0.738230i | 0.929384 | + | 0.369115i | \(0.120339\pi\) | ||||
−0.929384 | + | 0.369115i | \(0.879661\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.61505e6i | 0.709778i | 0.934908 | + | 0.354889i | \(0.115481\pi\) | ||||
−0.934908 | + | 0.354889i | \(0.884519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 367754. | 0.159327 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.16955e6 | −0.926687 | −0.463343 | − | 0.886179i | \(-0.653350\pi\) | ||||
−0.463343 | + | 0.886179i | \(0.653350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 188572.i | − 0.0794158i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.67946e6i | 1.11269i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −285544. | −0.116933 | −0.0584665 | − | 0.998289i | \(-0.518621\pi\) | ||||
−0.0584665 | + | 0.998289i | \(0.518621\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.13244e6 | −1.26507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00642e6i | 0.400879i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.26379e6i | 0.889414i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.77489e6 | 1.46298 | 0.731491 | − | 0.681851i | \(-0.238825\pi\) | ||||
0.731491 | + | 0.681851i | \(0.238825\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −801854. | −0.306570 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.61658e6i | − 0.986959i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 37031.8i | − 0.0137817i | −0.999976 | − | 0.00689085i | \(-0.997807\pi\) | ||||
0.999976 | − | 0.00689085i | \(-0.00219344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.02330e6 | −1.84464 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.96784e6 | −0.713077 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 4.66986e6i | − 1.66996i | −0.550280 | − | 0.834980i | \(-0.685479\pi\) | ||||
0.550280 | − | 0.834980i | \(-0.314521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1.87686e6i | − 0.662399i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.20726e6 | 0.768878 | 0.384439 | − | 0.923150i | \(-0.374395\pi\) | ||||
0.384439 | + | 0.923150i | \(0.374395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.56686e6 | 1.22641 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 374592.i | 0.127140i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.43408e6i | 1.15063i | 0.817931 | + | 0.575316i | \(0.195121\pi\) | ||||
−0.817931 | + | 0.575316i | \(0.804879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.26679e6 | 0.749842 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 228931. | 0.0747691 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.98523e6i | − 1.60765i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.14935e6i | − 0.684432i | −0.939621 | − | 0.342216i | \(-0.888823\pi\) | ||||
0.939621 | − | 0.342216i | \(-0.111177\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.20039e6 | −1.00640 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.45334e6 | −1.69356 | −0.846782 | − | 0.531940i | \(-0.821463\pi\) | ||||
−0.846782 | + | 0.531940i | \(0.821463\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.54378e6i | 1.39365i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 702459.i | − 0.212806i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −99529.9 | −0.0297829 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.77610e6 | −0.820591 | −0.410296 | − | 0.911953i | \(-0.634574\pi\) | ||||
−0.410296 | + | 0.911953i | \(0.634574\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.24354e6i | 0.655134i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.40063e6i | − 1.55801i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.10301e7 | 3.14383 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.79944e6 | 0.506753 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 5.88907e6i | − 1.63875i | −0.573261 | − | 0.819373i | \(-0.694322\pi\) | ||||
0.573261 | − | 0.819373i | \(-0.305678\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.20288e6i | 0.605740i | 0.953032 | + | 0.302870i | \(0.0979449\pi\) | ||||
−0.953032 | + | 0.302870i | \(0.902055\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.62700e6 | −0.442118 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.65324e7 | 4.43980 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.87988e6i | − 0.498954i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00733e6i | 0.264258i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.86779e6 | −0.743626 | −0.371813 | − | 0.928308i | \(-0.621264\pi\) | ||||
−0.371813 | + | 0.928308i | \(0.621264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.24865e6 | −0.320052 | −0.160026 | − | 0.987113i | \(-0.551158\pi\) | ||||
−0.160026 | + | 0.987113i | \(0.551158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.75884e6i | 0.952424i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.70750e6i | 0.678210i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.67269e6 | −1.40484 | −0.702422 | − | 0.711761i | \(-0.747898\pi\) | ||||
−0.702422 | + | 0.711761i | \(0.747898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −464866. | −0.113823 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.54963e6i | 1.10145i | 0.834685 | + | 0.550727i | \(0.185649\pi\) | ||||
−0.834685 | + | 0.550727i | \(0.814351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.19570e7i | 2.86235i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.65276e6 | 0.391239 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 913805. | 0.213913 | 0.106957 | − | 0.994264i | \(-0.465889\pi\) | ||||
0.106957 | + | 0.994264i | \(0.465889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.19639e6i | − 0.508474i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.87244e6i | 0.657665i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.10991e6 | −1.83649 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.33073e6 | −0.298056 | −0.149028 | − | 0.988833i | \(-0.547614\pi\) | ||||
−0.149028 | + | 0.988833i | \(0.547614\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.44543e6i | 0.320232i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.20403e6i | 0.921327i | 0.887575 | + | 0.460663i | \(0.152388\pi\) | ||||
−0.887575 | + | 0.460663i | \(0.847612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.44968e6 | −1.18146 | −0.590729 | − | 0.806870i | \(-0.701160\pi\) | ||||
−0.590729 | + | 0.806870i | \(0.701160\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.67923e6 | 1.86144 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6.16082e6i | − 1.30721i | −0.756835 | − | 0.653606i | \(-0.773255\pi\) | ||||
0.756835 | − | 0.653606i | \(-0.226745\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.30680e6i | 1.11404i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −948721. | −0.197055 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.02606e6 | −0.210872 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.97466e7i | 4.01566i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.41151e6i | − 0.284045i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.41659e6 | 0.282102 | 0.141051 | − | 0.990002i | \(-0.454952\pi\) | ||||
0.141051 | + | 0.990002i | \(0.454952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 226300. | 0.0445986 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.54497e6i | 0.301338i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.17583e6i | 0.806099i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.72820e6 | 1.09445 | 0.547225 | − | 0.836985i | \(-0.315684\pi\) | ||||
0.547225 | + | 0.836985i | \(0.315684\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.60307e6 | −0.870514 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.89913e6i | − 0.355509i | −0.984075 | − | 0.177755i | \(-0.943117\pi\) | ||||
0.984075 | − | 0.177755i | \(-0.0568833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 7.73443e6i | − 1.43321i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.92413e6 | 0.352957 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −264461. | −0.0480254 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 6.03047e6i | − 1.08418i | −0.840322 | − | 0.542088i | \(-0.817634\pi\) | ||||
0.840322 | − | 0.542088i | \(-0.182366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5.26976e6i | − 0.937986i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.73041e6 | 0.304951 | 0.152475 | − | 0.988307i | \(-0.451276\pi\) | ||||
0.152475 | + | 0.988307i | \(0.451276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.60397e6 | 1.15233 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.05129e6i | 0.181636i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.10086e7i | 1.88337i | 0.336496 | + | 0.941685i | \(0.390758\pi\) | ||||
−0.336496 | + | 0.941685i | \(0.609242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.17483e6 | 0.537859 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.72644e6 | −0.289640 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.11283e6i | − 0.849461i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.45659e6i | − 0.733292i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.34187e6 | −0.218672 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −816327. | −0.131756 | −0.0658779 | − | 0.997828i | \(-0.520985\pi\) | ||||
−0.0658779 | + | 0.997828i | \(0.520985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.59191e6i | − 1.37352i | −0.726883 | − | 0.686761i | \(-0.759032\pi\) | ||||
0.726883 | − | 0.686761i | \(-0.240968\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.12679e7i | 1.78421i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.78590e7 | −2.80111 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.12931e6 | −0.796929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2.91336e6i | − 0.448391i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.99390e6i | 0.761416i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.50526e6 | 1.13366 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 912019. | 0.136480 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.27333e6i | − 0.188786i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.94402e6i | 1.46073i | 0.683059 | + | 0.730363i | \(0.260649\pi\) | ||||
−0.683059 | + | 0.730363i | \(0.739351\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.38122e6 | −0.928761 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.21799e7 | −1.75652 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.99790e6i | 1.42870i | 0.699789 | + | 0.714349i | \(0.253277\pi\) | ||||
−0.699789 | + | 0.714349i | \(0.746723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.01410e6i | − 0.143598i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.23814e6 | 1.29630 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.99149e6 | −0.972203 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 432263.i | − 0.0595683i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.35849e6i | 1.27811i | 0.769161 | + | 0.639055i | \(0.220674\pi\) | ||||
−0.769161 | + | 0.639055i | \(0.779326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.33294e6 | 0.315772 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.95923e6 | −0.531133 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 768517.i | − 0.102184i | −0.998694 | − | 0.0510920i | \(-0.983730\pi\) | ||||
0.998694 | − | 0.0510920i | \(-0.0162702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.73516e7i | 2.28675i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −985157. | −0.128691 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.54628e6 | 0.329704 | 0.164852 | − | 0.986318i | \(-0.447285\pi\) | ||||
0.164852 | + | 0.986318i | \(0.447285\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.88507e6i | 0.755373i | 0.925934 | + | 0.377686i | \(0.123280\pi\) | ||||
−0.925934 | + | 0.377686i | \(0.876720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 490917.i | − 0.0624628i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.53257e6 | 1.20238 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.66115e6 | −0.582846 | −0.291423 | − | 0.956594i | \(-0.594129\pi\) | ||||
−0.291423 | + | 0.956594i | \(0.594129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 7.48092e6i | − 0.927381i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.54691e7i | − 1.90118i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.86632e6 | 0.471114 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.37487e6 | −0.528538 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.05639e7i | 1.26541i | 0.774395 | + | 0.632703i | \(0.218054\pi\) | ||||
−0.774395 | + | 0.632703i | \(0.781946\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.13311e7i | − 2.53352i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.54178e6 | −0.181573 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.02809e6 | −1.05429 | −0.527144 | − | 0.849776i | \(-0.676737\pi\) | ||||
−0.527144 | + | 0.849776i | \(0.676737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.18754e7i | − 3.69116i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.07669e6i | − 0.123639i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.98892e6 | 0.681996 | 0.340998 | − | 0.940064i | \(-0.389235\pi\) | ||||
0.340998 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.66239e6 | −0.639460 | −0.319730 | − | 0.947509i | \(-0.603592\pi\) | ||||
−0.319730 | + | 0.947509i | \(0.603592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.86274e6i | 0.320618i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1.19726e7i | − 1.32984i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.56734e7 | −1.72659 | −0.863297 | − | 0.504697i | \(-0.831604\pi\) | ||||
−0.863297 | + | 0.504697i | \(0.831604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.27155e6 | 0.575963 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.01329e7i | 1.09807i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.52155e7i | 1.63544i | 0.575615 | + | 0.817720i | \(0.304763\pi\) | ||||
−0.575615 | + | 0.817720i | \(0.695237\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.53902e6 | 1.01699 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.91925e6 | 0.520219 | 0.260110 | − | 0.965579i | \(-0.416241\pi\) | ||||
0.260110 | + | 0.965579i | \(0.416241\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.16312e6i | 0.856308i | 0.903706 | + | 0.428154i | \(0.140836\pi\) | ||||
−0.903706 | + | 0.428154i | \(0.859164\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 833433.i | 0.0867245i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.67690e7 | 1.73096 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.37016e7 | 3.45105 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.72897e6i | − 0.480394i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 889453.i | 0.0896388i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.04567e7 | −1.04550 | −0.522749 | − | 0.852487i | \(-0.675093\pi\) | ||||
−0.522749 | + | 0.852487i | \(0.675093\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.89377e6 | −0.783024 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.23275e7i | 2.19739i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.89516e6i | 0.282699i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −142663. | −0.0138216 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.30291e6 | −0.798152 | −0.399076 | − | 0.916918i | \(-0.630669\pi\) | ||||
−0.399076 | + | 0.916918i | \(0.630669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8.73090e6i | − 0.832782i | −0.909186 | − | 0.416391i | \(-0.863295\pi\) | ||||
0.909186 | − | 0.416391i | \(-0.136705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4.45622e6i | − 0.421762i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.10770e7 | −1.04030 | −0.520151 | − | 0.854074i | \(-0.674124\pi\) | ||||
−0.520151 | + | 0.854074i | \(0.674124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.98010e6 | 0.743698 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.21721e7i | − 1.12568i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.70900e6i | 0.707481i | 0.935344 | + | 0.353741i | \(0.115090\pi\) | ||||
−0.935344 | + | 0.353741i | \(0.884910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.72340e6 | −0.248033 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.71266e6 | 0.154795 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.26694e7i | 1.13643i | 0.822881 | + | 0.568214i | \(0.192365\pi\) | ||||
−0.822881 | + | 0.568214i | \(0.807635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.86962e6i | 0.166437i | 0.996531 | + | 0.0832187i | \(0.0265200\pi\) | ||||
−0.996531 | + | 0.0832187i | \(0.973480\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.00204e6 | 0.795347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.80725e7 | 3.33854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.45967e6i | − 0.388140i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.75062e6i | − 0.151226i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.77776e6 | 0.238171 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.99120e7 | 1.69464 | 0.847318 | − | 0.531086i | \(-0.178216\pi\) | ||||
0.847318 | + | 0.531086i | \(0.178216\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.07847e6i | 0.513493i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 652964.i | 0.0547542i | 0.999625 | + | 0.0273771i | \(0.00871550\pi\) | ||||
−0.999625 | + | 0.0273771i | \(0.991285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.85636e6 | 0.487476 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.37780e6 | −0.444362 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.88770e6i | 0.318890i | 0.987207 | + | 0.159445i | \(0.0509705\pi\) | ||||
−0.987207 | + | 0.159445i | \(0.949030\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2.66897e7i | − 2.17329i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.15066e6 | 0.578035 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.79079e6 | −0.705472 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.60215e7i | 1.27647i | 0.769844 | + | 0.638233i | \(0.220334\pi\) | ||||
−0.769844 | + | 0.638233i | \(0.779666\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.69849e6i | − 0.213446i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.14065e7 | −1.68106 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.96281e7 | −1.53037 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.94117e6i | 0.305093i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.68614e6i | − 0.360180i | −0.983650 | − | 0.180090i | \(-0.942361\pi\) | ||||
0.983650 | − | 0.180090i | \(-0.0576390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.06238e6 | −0.0810757 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.93552e7 | 1.46664 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 9.26168e6i | − 0.696853i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.74126e7i | − 1.30091i | −0.759543 | − | 0.650457i | \(-0.774577\pi\) | ||||
0.759543 | − | 0.650457i | \(-0.225423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.77154e6 | −0.279798 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.02975e7 | −0.758590 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.19834e7i | − 0.876627i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.84148e6i | 0.424351i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.20677e7 | 0.870568 | 0.435284 | − | 0.900293i | \(-0.356648\pi\) | ||||
0.435284 | + | 0.900293i | \(0.356648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.17045e6 | −0.513698 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3.84635e6i | − 0.273655i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.25257e7i | − 2.29817i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.76436e6 | −0.123809 | −0.0619044 | − | 0.998082i | \(-0.519717\pi\) | ||||
−0.0619044 | + | 0.998082i | \(0.519717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.16942e6i | 0.634671i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 392726.i | − 0.0269979i | −0.999909 | − | 0.0134989i | \(-0.995703\pi\) | ||||
0.999909 | − | 0.0134989i | \(-0.00429698\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.53014e6 | 0.377588 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.84145e6 | −0.531775 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.06652e7i | − 0.718386i | −0.933263 | − | 0.359193i | \(-0.883052\pi\) | ||||
0.933263 | − | 0.359193i | \(-0.116948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.07522e7i | 0.719368i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.95018e6 | 0.262509 | 0.131255 | − | 0.991349i | \(-0.458099\pi\) | ||||
0.131255 | + | 0.991349i | \(0.458099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.96616e7 | −1.29786 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 8.34475e6i | − 0.547157i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.05257e7i | − 0.685561i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.88791e6 | 0.575042 | 0.287521 | − | 0.957774i | \(-0.407169\pi\) | ||||
0.287521 | + | 0.957774i | \(0.407169\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.62949e6 | −0.297540 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 3.41711e7i | − 2.18168i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 2.27449e7i | − 1.44259i | −0.692626 | − | 0.721297i | \(-0.743546\pi\) | ||||
0.692626 | − | 0.721297i | \(-0.256454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.28289e6 | −0.143840 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.84679e6 | 0.240789 | 0.120395 | − | 0.992726i | \(-0.461584\pi\) | ||||
0.120395 | + | 0.992726i | \(0.461584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.70816e7i | 1.06223i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.71951e7i | − 1.06231i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.81442e7 | −1.11365 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.84393e7 | −1.73421 | −0.867107 | − | 0.498123i | \(-0.834023\pi\) | ||||
−0.867107 | + | 0.498123i | \(0.834023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 5.35238e6i | − 0.324273i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.38002e7i | 0.830686i | 0.909665 | + | 0.415343i | \(0.136338\pi\) | ||||
−0.909665 | + | 0.415343i | \(0.863662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.51025e7 | −4.49159 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −606223. | −0.0360230 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2.34442e7i | − 1.38418i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 390775.i | − 0.0229244i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.84372e6 | 0.165761 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.12862e7 | 0.653692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.48735e6i | 0.373362i | 0.982421 | + | 0.186681i | \(0.0597732\pi\) | ||||
−0.982421 | + | 0.186681i | \(0.940227\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.85847e7i | − 1.06283i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.43347e7 | 1.38288 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.31575e6 | −0.356650 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.67916e7i | 0.942267i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 8.51124e6i | − 0.474621i | −0.971434 | − | 0.237311i | \(-0.923734\pi\) | ||||
0.971434 | − | 0.237311i | \(-0.0762659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.98265e7 | −2.20701 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.04602e6 | 0.498168 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.69121e6i | 0.256741i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.83793e7i | − 0.999632i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.00678e6 | 0.324682 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.40776e7 | −0.756236 | −0.378118 | − | 0.925757i | \(-0.623429\pi\) | ||||
−0.378118 | + | 0.925757i | \(0.623429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.02736e7i | − 1.08238i | −0.840901 | − | 0.541189i | \(-0.817974\pi\) | ||||
0.840901 | − | 0.541189i | \(-0.182026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.23624e6i | 0.330900i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.47591e7 | 2.88777 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.09521e7 | −0.574041 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.13550e6i | 0.319625i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.15969e6i | 0.215379i | 0.994185 | + | 0.107689i | \(0.0343452\pi\) | ||||
−0.994185 | + | 0.107689i | \(0.965655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 755688. | 0.0388904 | 0.0194452 | − | 0.999811i | \(-0.493810\pi\) | ||||
0.0194452 | + | 0.999811i | \(0.493810\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.66498e7 | −0.851675 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.45268e6i | 0.226390i | 0.993573 | + | 0.113195i | \(0.0361085\pi\) | ||||
−0.993573 | + | 0.113195i | \(0.963891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.31726e7i | 0.665712i | 0.942978 | + | 0.332856i | \(0.108012\pi\) | ||||
−0.942978 | + | 0.332856i | \(0.891988\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.90504e7 | 0.956977 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.13792e7 | −0.568197 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.26901e7i | 3.11159i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.56622e6i | − 0.323968i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.34089e7 | 0.657640 | 0.328820 | − | 0.944393i | \(-0.393349\pi\) | ||||
0.328820 | + | 0.944393i | \(0.393349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.29447e6 | 0.258127 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.64221e7i | 0.795902i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.25063e7i | − 0.602543i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.67908e7 | −0.804200 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.06787e7 | 0.508452 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 512858.i | 0.0242758i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.93105e6i | 0.0908699i | 0.998967 | + | 0.0454349i | \(0.0144674\pi\) | ||||
−0.998967 | + | 0.0454349i | \(0.985533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.05381e7 | 0.960827 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.52761e7 | 0.710495 | 0.355248 | − | 0.934772i | \(-0.384397\pi\) | ||||
0.355248 | + | 0.934772i | \(0.384397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.73909e7i | 1.26656i | 0.773925 | + | 0.633278i | \(0.218291\pi\) | ||||
−0.773925 | + | 0.633278i | \(0.781709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.33779e7i | − 0.615008i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.94149e7 | −1.34444 | −0.672219 | − | 0.740352i | \(-0.734659\pi\) | ||||
−0.672219 | + | 0.740352i | \(0.734659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.59632e7 | 0.725403 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.26031e7i | 1.02122i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.03308e7i | − 0.464071i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.78290e7 | 0.796308 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.15920e6 | 0.140295 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 8.38073e7i | − 3.70051i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.48384e7i | 1.52953i | 0.644308 | + | 0.764766i | \(0.277146\pi\) | ||||
−0.644308 | + | 0.764766i | \(0.722854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.65550e6 | 0.0722700 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.80051e7 | −1.21562 | −0.607809 | − | 0.794083i | \(-0.707951\pi\) | ||||
−0.607809 | + | 0.794083i | \(0.707951\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.74027e7i | − 1.18275i | −0.806397 | − | 0.591374i | \(-0.798586\pi\) | ||||
0.806397 | − | 0.591374i | \(-0.201414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.46579e7i | 1.48745i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.87337e7 | 0.799493 | 0.399747 | − | 0.916626i | \(-0.369098\pi\) | ||||
0.399747 | + | 0.916626i | \(0.369098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.13130e7 | 1.32883 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.45569e6i | − 0.0614293i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.75695e7i | − 1.99618i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.08496e7 | −0.452746 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.19057e6 | 0.215394 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.51356e7i | 1.44993i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.45515e7i | − 1.41793i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.24959e6 | −0.255054 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.59122e7 | 3.08099 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.80666e7i | − 0.729219i | −0.931161 | − | 0.364609i | \(-0.881202\pi\) | ||||
0.931161 | − | 0.364609i | \(-0.118798\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 4.99620e6i | − 0.200553i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.90330e7 | −1.15903 | −0.579517 | − | 0.814960i | \(-0.696759\pi\) | ||||
−0.579517 | + | 0.814960i | \(0.696759\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.28575e7 | 0.907509 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.20639e7i | 0.476360i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.81942e6i | 0.149994i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.76004e7 | 0.687437 | 0.343718 | − | 0.939073i | \(-0.388313\pi\) | ||||
0.343718 | + | 0.939073i | \(0.388313\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.30428e6 | 0.244899 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 888498.i | 0.0343283i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.74042e6i | 0.143736i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.86808e6 | −0.147841 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.19603e7 | −0.834834 | −0.417417 | − | 0.908715i | \(-0.637064\pi\) | ||||
−0.417417 | + | 0.908715i | \(0.637064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.35915e7i | − 0.513917i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.19046e7i | 0.447725i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.70998e7 | 1.76194 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.36644e7 | −1.25263 | −0.626314 | − | 0.779571i | \(-0.715437\pi\) | ||||
−0.626314 | + | 0.779571i | \(0.715437\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.06392e6i | − 0.0393774i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.50282e7i | 1.28956i | 0.764366 | + | 0.644782i | \(0.223052\pi\) | ||||
−0.764366 | + | 0.644782i | \(0.776948\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.13176e7 | −0.414452 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.17196e7 | 0.426908 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 8.09345e6i | − 0.293264i | −0.989191 | − | 0.146632i | \(-0.953157\pi\) | ||||
0.989191 | − | 0.146632i | \(-0.0468433\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.06663e7i | − 0.384458i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.30141e7 | 0.825169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.70686e7 | 0.608788 | 0.304394 | − | 0.952546i | \(-0.401546\pi\) | ||||
0.304394 | + | 0.952546i | \(0.401546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.84005e6i | 0.207209i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.78936e6i | 0.274930i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.74307e7 | −1.31426 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.24997e7 | 1.83379 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 5.67806e6i | − 0.197303i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.89945e7i | 3.07641i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.24163e7 | −0.770901 | −0.385450 | − | 0.922729i | \(-0.625954\pi\) | ||||
−0.385450 | + | 0.922729i | \(0.625954\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.22606e7 | −1.44586 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.08206e7i | − 0.708671i | −0.935118 | − | 0.354336i | \(-0.884707\pi\) | ||||
0.935118 | − | 0.354336i | \(-0.115293\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.00213e7i | 1.01659i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.78564e7 | 1.27534 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −817996. | −0.0274167 | −0.0137083 | − | 0.999906i | \(-0.504364\pi\) | ||||
−0.0137083 | + | 0.999906i | \(0.504364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.47783e7i | 0.826257i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.21463e6i | 0.305707i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.17691e7 | 0.388472 | 0.194236 | − | 0.980955i | \(-0.437777\pi\) | ||||
0.194236 | + | 0.980955i | \(0.437777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.83413e7 | 0.602336 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.71445e7i | − 0.886929i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.28709e6i | 0.171880i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.50426e6 | 0.307421 | 0.153711 | − | 0.988116i | \(-0.450878\pi\) | ||||
0.153711 | + | 0.988116i | \(0.450878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.40117e7 | −0.772768 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.28085e7i | 0.410150i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.79258e6i | 0.312003i | 0.987757 | + | 0.156002i | \(0.0498605\pi\) | ||||
−0.987757 | + | 0.156002i | \(0.950139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −327026. | −0.0103674 |
(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.j.193.7 | yes | 12 | |
4.3 | odd | 2 | inner | 384.6.d.j.193.1 | ✓ | 12 | |
8.3 | odd | 2 | inner | 384.6.d.j.193.12 | yes | 12 | |
8.5 | even | 2 | inner | 384.6.d.j.193.6 | yes | 12 | |
16.3 | odd | 4 | 768.6.a.bf.1.1 | 6 | |||
16.5 | even | 4 | 768.6.a.bf.1.6 | 6 | |||
16.11 | odd | 4 | 768.6.a.be.1.6 | 6 | |||
16.13 | even | 4 | 768.6.a.be.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.d.j.193.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
384.6.d.j.193.6 | yes | 12 | 8.5 | even | 2 | inner | |
384.6.d.j.193.7 | yes | 12 | 1.1 | even | 1 | trivial | |
384.6.d.j.193.12 | yes | 12 | 8.3 | odd | 2 | inner | |
768.6.a.be.1.1 | 6 | 16.13 | even | 4 | |||
768.6.a.be.1.6 | 6 | 16.11 | odd | 4 | |||
768.6.a.bf.1.1 | 6 | 16.3 | odd | 4 | |||
768.6.a.bf.1.6 | 6 | 16.5 | even | 4 |