Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(47,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.o (of order \(8\), degree \(4\), 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: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Character | \(\chi\) | \(=\) | 384.47 |
Dual form | 384.2.o.a.335.1 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.72928 | − | 0.0979076i | −0.998401 | − | 0.0565270i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.180206 | + | 0.0746437i | −0.0805904 | + | 0.0333817i | −0.422614 | − | 0.906310i | \(-0.638888\pi\) |
0.342024 | + | 0.939691i | \(0.388888\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.289055 | + | 0.289055i | 0.109253 | + | 0.109253i | 0.759620 | − | 0.650367i | \(-0.225385\pi\) |
−0.650367 | + | 0.759620i | \(0.725385\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98083 | + | 0.338620i | 0.993609 | + | 0.112873i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.10859 | + | 1.28762i | −0.937276 | + | 0.388232i | −0.798434 | − | 0.602082i | \(-0.794338\pi\) |
−0.138842 | + | 0.990315i | \(0.544338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.27981 | + | 3.08973i | −0.354954 | + | 0.856936i | 0.641039 | + | 0.767508i | \(0.278504\pi\) |
−0.995993 | + | 0.0894273i | \(0.971496\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.318935 | − | 0.111436i | 0.0823486 | − | 0.0287727i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.806332 | −0.195564 | −0.0977822 | − | 0.995208i | \(-0.531175\pi\) | ||||
−0.0977822 | + | 0.995208i | \(0.531175\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.57935 | + | 2.31104i | 1.27999 | + | 0.530190i | 0.915987 | − | 0.401208i | \(-0.131409\pi\) |
0.364004 | + | 0.931397i | \(0.381409\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.471557 | − | 0.528159i | −0.102902 | − | 0.115254i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.03681 | + | 5.03681i | 1.05025 | + | 1.05025i | 0.998669 | + | 0.0515792i | \(0.0164254\pi\) |
0.0515792 | + | 0.998669i | \(0.483575\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50863 | + | 3.50863i | −0.701726 | + | 0.701726i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.12154 | − | 0.877415i | −0.985640 | − | 0.168859i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.64020 | + | 8.78822i | −0.675968 | + | 1.63193i | 0.0953212 | + | 0.995447i | \(0.469612\pi\) |
−0.771289 | + | 0.636485i | \(0.780388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.48336i | 1.34405i | 0.740528 | + | 0.672026i | \(0.234576\pi\) | ||||
−0.740528 | + | 0.672026i | \(0.765424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.50170 | − | 1.92230i | 0.957723 | − | 0.334630i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0736656 | − | 0.0305133i | −0.0124518 | − | 0.00515769i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.47112 | − | 3.55159i | −0.241850 | − | 0.583878i | 0.755616 | − | 0.655014i | \(-0.227337\pi\) |
−0.997467 | + | 0.0711364i | \(0.977337\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.51565 | − | 5.21770i | 0.402827 | − | 0.835501i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.62513 | − | 2.62513i | 0.409976 | − | 0.409976i | −0.471754 | − | 0.881730i | \(-0.656379\pi\) |
0.881730 | + | 0.471754i | \(0.156379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.84744 | − | 6.87432i | −0.434230 | − | 1.04832i | −0.977909 | − | 0.209031i | \(-0.932969\pi\) |
0.543679 | − | 0.839293i | \(-0.317031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.562438 | + | 0.161479i | −0.0838433 | + | 0.0240718i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.399772i | − | 0.0583127i | −0.999575 | − | 0.0291564i | \(-0.990718\pi\) | ||
0.999575 | − | 0.0291564i | \(-0.00928208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.83289i | − | 0.976128i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.39438 | + | 0.0789461i | 0.195252 | + | 0.0110547i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.42173 | + | 3.43237i | 0.195290 | + | 0.471472i | 0.990943 | − | 0.134280i | \(-0.0428723\pi\) |
−0.795653 | + | 0.605752i | \(0.792872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.464073 | − | 0.464073i | 0.0625756 | − | 0.0625756i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.42200 | − | 4.54271i | −1.24797 | − | 0.601696i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.918629 | − | 2.21777i | −0.119595 | − | 0.288729i | 0.852733 | − | 0.522347i | \(-0.174943\pi\) |
−0.972328 | + | 0.233618i | \(0.924943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.81133 | + | 3.64977i | 1.12818 | + | 0.467306i | 0.867160 | − | 0.498029i | \(-0.165943\pi\) |
0.261015 | + | 0.965335i | \(0.415943\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.763745 | + | 0.959504i | 0.0962228 | + | 0.120886i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.652316i | − | 0.0809098i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.76613 | − | 9.09225i | 0.460107 | − | 1.11080i | −0.508247 | − | 0.861212i | \(-0.669706\pi\) |
0.968353 | − | 0.249584i | \(-0.0802938\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.21692 | − | 9.20321i | −0.989201 | − | 1.10794i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.86762 | + | 2.86762i | −0.340324 | + | 0.340324i | −0.856489 | − | 0.516165i | \(-0.827359\pi\) |
0.516165 | + | 0.856489i | \(0.327359\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.97993 | − | 6.97993i | −0.816939 | − | 0.816939i | 0.168725 | − | 0.985663i | \(-0.446035\pi\) |
−0.985663 | + | 0.168725i | \(0.946035\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.41093 | − | 5.72389i | 0.740271 | − | 0.660938i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.27075 | − | 0.526361i | −0.144815 | − | 0.0599845i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.01674 | −0.901954 | −0.450977 | − | 0.892536i | \(-0.648924\pi\) | ||||
−0.450977 | + | 0.892536i | \(0.648924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.77067 | + | 2.01873i | 0.974519 | + | 0.224304i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.47115 | + | 5.96589i | −0.271244 | + | 0.654841i | −0.999537 | − | 0.0304247i | \(-0.990314\pi\) |
0.728293 | + | 0.685266i | \(0.240314\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.145306 | − | 0.0601876i | 0.0157606 | − | 0.00652826i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.15536 | − | 14.8409i | 0.767135 | − | 1.59111i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.43308 | + | 5.43308i | 0.575905 | + | 0.575905i | 0.933773 | − | 0.357867i | \(-0.116496\pi\) |
−0.357867 | + | 0.933773i | \(0.616496\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.26304 | + | 0.523167i | −0.132402 | + | 0.0548428i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.732678 | − | 12.9408i | 0.0759752 | − | 1.34190i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.17794 | −0.120854 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.61408 | 0.265419 | 0.132710 | − | 0.991155i | \(-0.457632\pi\) | ||||
0.132710 | + | 0.991155i | \(0.457632\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.70219 | + | 2.78555i | −0.975107 | + | 0.279958i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1420 | − | 5.02940i | 1.20818 | − | 0.500444i | 0.314546 | − | 0.949242i | \(-0.398148\pi\) |
0.893633 | + | 0.448798i | \(0.148148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.46981 | − | 8.46981i | −0.834555 | − | 0.834555i | 0.153581 | − | 0.988136i | \(-0.450919\pi\) |
−0.988136 | + | 0.153581i | \(0.950919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.124401 | + | 0.0599785i | 0.0121403 | + | 0.00585330i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.03423 | + | 0.428394i | −0.0999833 | + | 0.0414144i | −0.432114 | − | 0.901819i | \(-0.642232\pi\) |
0.332131 | + | 0.943233i | \(0.392232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.703211 | + | 1.69770i | −0.0673554 | + | 0.162610i | −0.953973 | − | 0.299894i | \(-0.903049\pi\) |
0.886617 | + | 0.462504i | \(0.153049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.19625 | + | 6.28573i | 0.208459 | + | 0.596616i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.39540 | −0.131268 | −0.0656339 | − | 0.997844i | \(-0.520907\pi\) | ||||
−0.0656339 | + | 0.997844i | \(0.520907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.28363 | − | 0.531696i | −0.119699 | − | 0.0495809i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.86112 | + | 8.77657i | −0.449411 | + | 0.811394i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.233075 | − | 0.233075i | −0.0213659 | − | 0.0213659i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.227201 | − | 0.227201i | 0.0206547 | − | 0.0206547i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.79661 | + | 4.28257i | −0.432495 | + | 0.386146i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.743597 | − | 1.79520i | 0.0665093 | − | 0.160568i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.87310i | 0.609889i | 0.952370 | + | 0.304944i | \(0.0986379\pi\) | ||||
−0.952370 | + | 0.304944i | \(0.901362\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.25097 | + | 12.1664i | 0.374277 | + | 1.07119i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0581 | + | 6.65149i | 1.40300 | + | 0.581143i | 0.950529 | − | 0.310635i | \(-0.100542\pi\) |
0.452474 | + | 0.891778i | \(0.350542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.944722 | + | 2.28076i | 0.0819178 | + | 0.197767i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.988424 | − | 0.224175i | 0.0850700 | − | 0.0192939i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.7787 | + | 10.7787i | −0.920890 | + | 0.920890i | −0.997092 | − | 0.0762022i | \(-0.975721\pi\) |
0.0762022 | + | 0.997092i | \(0.475721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41183 | + | 3.40847i | 0.119750 | + | 0.289102i | 0.972376 | − | 0.233419i | \(-0.0749914\pi\) |
−0.852626 | + | 0.522521i | \(0.824991\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0391407 | + | 0.691318i | −0.00329624 | + | 0.0582195i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.2526i | − | 0.940990i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.85541i | − | 0.154083i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.668992 | + | 11.8160i | −0.0551776 | + | 0.974567i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.49923 | − | 15.6905i | −0.532438 | − | 1.28542i | −0.929904 | − | 0.367802i | \(-0.880111\pi\) |
0.397466 | − | 0.917617i | \(-0.369889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.50166 | − | 1.50166i | 0.122204 | − | 0.122204i | −0.643360 | − | 0.765564i | \(-0.722460\pi\) |
0.765564 | + | 0.643360i | \(0.222460\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.40354 | − | 0.273040i | −0.194315 | − | 0.0220740i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.558586 | − | 1.34855i | −0.0448667 | − | 0.108318i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7594 | + | 5.28511i | 1.01831 | + | 0.421798i | 0.828480 | − | 0.560019i | \(-0.189206\pi\) |
0.189830 | + | 0.981817i | \(0.439206\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.12252 | − | 6.07473i | −0.168327 | − | 0.481757i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.91184i | 0.229485i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.02496 | + | 7.30291i | −0.236933 | + | 0.572008i | −0.996963 | − | 0.0778809i | \(-0.975185\pi\) |
0.760029 | + | 0.649889i | \(0.225185\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.847950 | + | 0.757077i | −0.0660128 | + | 0.0589384i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.65109 | + | 1.65109i | −0.127765 | + | 0.127765i | −0.768098 | − | 0.640333i | \(-0.778797\pi\) |
0.640333 | + | 0.768098i | \(0.278797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.28389 | + | 1.28389i | 0.0987607 | + | 0.0987607i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.8485 | + | 8.77810i | 1.21197 | + | 0.671278i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.81571 | − | 4.06580i | −0.746275 | − | 0.309117i | −0.0230541 | − | 0.999734i | \(-0.507339\pi\) |
−0.723221 | + | 0.690617i | \(0.757339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.02838 | −0.153331 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.37143 | + | 3.92508i | 0.103083 | + | 0.295027i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.28126 | − | 15.1643i | 0.469484 | − | 1.13343i | −0.494906 | − | 0.868947i | \(-0.664797\pi\) |
0.964389 | − | 0.264487i | \(-0.0852026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.93385 | − | 2.04367i | 0.366730 | − | 0.151905i | −0.191705 | − | 0.981453i | \(-0.561402\pi\) |
0.558436 | + | 0.829548i | \(0.311402\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.8799 | − | 7.17418i | −1.09996 | − | 0.530331i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.530208 | + | 0.530208i | 0.0389816 | + | 0.0389816i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.50656 | − | 1.03825i | 0.183298 | − | 0.0759244i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.22679 | − | 1.73403i | −0.0892356 | − | 0.126132i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6455 | −0.842637 | −0.421318 | − | 0.906913i | \(-0.638433\pi\) | ||||
−0.421318 | + | 0.906913i | \(0.638433\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.03220 | −0.434207 | −0.217104 | − | 0.976149i | \(-0.569661\pi\) | ||||
−0.217104 | + | 0.976149i | \(0.569661\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0638667 | + | 1.12804i | −0.00457359 | + | 0.0807804i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.581435 | + | 0.240838i | −0.0414255 | + | 0.0171590i | −0.403300 | − | 0.915068i | \(-0.632137\pi\) |
0.361874 | + | 0.932227i | \(0.382137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6071 | + | 13.6071i | 0.964583 | + | 0.964583i | 0.999394 | − | 0.0348110i | \(-0.0110829\pi\) |
−0.0348110 | + | 0.999394i | \(0.511083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.40291 | + | 15.3543i | −0.522161 | + | 1.08301i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.59250 | + | 1.48806i | −0.252144 | + | 0.104442i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.277114 | + | 0.669012i | −0.0193545 | + | 0.0467259i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.3083 | + | 16.7194i | 0.924991 | + | 1.16208i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.3197 | −1.40554 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.94196 | + | 2.87545i | 0.477904 | + | 0.197954i | 0.608614 | − | 0.793466i | \(-0.291726\pi\) |
−0.130710 | + | 0.991421i | \(0.541726\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.23969 | − | 4.67816i | 0.359017 | − | 0.320542i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.02625 | + | 1.02625i | 0.0699896 | + | 0.0699896i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.16311 | + | 2.16311i | −0.146841 | + | 0.146841i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.3869 | + | 12.7536i | 0.769453 | + | 0.861811i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.03195 | − | 2.49135i | 0.0694164 | − | 0.167586i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.45182i | − | 0.432046i | −0.976388 | − | 0.216023i | \(-0.930691\pi\) | ||
0.976388 | − | 0.216023i | \(-0.0693086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.6467 | + | 9.27054i | −0.776448 | + | 0.618036i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.16606 | + | 1.31143i | 0.210139 | + | 0.0870424i | 0.485270 | − | 0.874364i | \(-0.338721\pi\) |
−0.275131 | + | 0.961407i | \(0.588721\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.63723 | + | 20.8521i | 0.570764 | + | 1.37795i | 0.900905 | + | 0.434015i | \(0.142904\pi\) |
−0.330141 | + | 0.943932i | \(0.607096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.14595 | + | 1.03464i | 0.141193 | + | 0.0680745i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.5223 | − | 15.5223i | 1.01690 | − | 1.01690i | 0.0170465 | − | 0.999855i | \(-0.494574\pi\) |
0.999855 | − | 0.0170465i | \(-0.00542634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0298404 | + | 0.0720412i | 0.00194658 | + | 0.00469945i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8632 | + | 0.784900i | 0.900512 | + | 0.0509847i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.3335i | − | 1.44463i | −0.691563 | − | 0.722316i | \(-0.743078\pi\) | ||
0.691563 | − | 0.722316i | \(-0.256922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0345i | 0.646380i | 0.946334 | + | 0.323190i | \(0.104755\pi\) | ||||
−0.946334 | + | 0.323190i | \(0.895245\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9693 | − | 4.34968i | −0.960282 | − | 0.279032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.510032 | + | 1.23133i | 0.0325848 | + | 0.0786666i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.2810 | + | 14.2810i | −0.908677 | + | 0.908677i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.85742 | − | 10.0748i | 0.307827 | − | 0.638462i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.23078 | + | 2.97137i | 0.0776862 | + | 0.187551i | 0.957951 | − | 0.286931i | \(-0.0926352\pi\) |
−0.880265 | + | 0.474483i | \(0.842635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.1429 | − | 9.17189i | −1.39211 | − | 0.576632i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.257167 | + | 0.0898547i | −0.0161044 | + | 0.00562692i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.7842i | − | 1.42124i | −0.703576 | − | 0.710620i | \(-0.748415\pi\) | ||
0.703576 | − | 0.710620i | \(-0.251585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.601372 | − | 1.45184i | 0.0373675 | − | 0.0902130i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.8267 | + | 24.9635i | −0.855850 | + | 1.54520i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.8553 | + | 12.8553i | −0.792690 | + | 0.792690i | −0.981931 | − | 0.189241i | \(-0.939397\pi\) |
0.189241 | + | 0.981931i | \(0.439397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.512409 | − | 0.512409i | −0.0314770 | − | 0.0314770i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.86338 | − | 9.92726i | −0.542430 | − | 0.607539i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7742 | + | 4.87704i | 0.717886 | + | 0.297358i | 0.711564 | − | 0.702622i | \(-0.247987\pi\) |
0.00632279 | + | 0.999980i | \(0.497987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6627 | 0.708457 | 0.354228 | − | 0.935159i | \(-0.384744\pi\) | ||||
0.354228 | + | 0.935159i | \(0.384744\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.23537 | − | 0.781042i | 0.135291 | − | 0.0472708i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.38912 | − | 15.4247i | 0.385278 | − | 0.930144i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.48904 | − | 3.51628i | 0.510057 | − | 0.211273i | −0.112786 | − | 0.993619i | \(-0.535977\pi\) |
0.622843 | + | 0.782347i | \(0.285977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.53401 | + | 22.3066i | −0.151707 | + | 1.33546i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.3102 | + | 22.3102i | 1.33091 | + | 1.33091i | 0.904553 | + | 0.426362i | \(0.140205\pi\) |
0.426362 | + | 0.904553i | \(0.359795\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.95203 | − | 4.12227i | 0.591587 | − | 0.245043i | −0.0667462 | − | 0.997770i | \(-0.521262\pi\) |
0.658333 | + | 0.752727i | \(0.271262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.03698 | + | 0.115329i | 0.120660 | + | 0.00683150i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.51762 | 0.0895820 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3498 | −0.961755 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.52048 | − | 0.255938i | −0.264995 | − | 0.0150034i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.2108 | − | 9.61422i | 1.35599 | − | 0.561669i | 0.418035 | − | 0.908431i | \(-0.362719\pi\) |
0.937953 | + | 0.346762i | \(0.112719\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.331084 | + | 0.331084i | 0.0192765 | + | 0.0192765i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.0505 | − | 3.86707i | 0.989373 | − | 0.224390i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.0085 | + | 9.11622i | −1.27279 | + | 0.527205i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.16399 | − | 2.81013i | 0.0670914 | − | 0.161973i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.4894 | + | 7.50845i | −1.23454 | + | 0.431349i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.86029 | −0.106520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.3982 | − | 7.62077i | −1.05004 | − | 0.434940i | −0.210133 | − | 0.977673i | \(-0.567390\pi\) |
−0.839906 | + | 0.542733i | \(0.817390\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8174 | + | 15.4759i | 0.786046 | + | 0.880395i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.938468 | + | 0.938468i | 0.0532157 | + | 0.0532157i | 0.733214 | − | 0.679998i | \(-0.238019\pi\) |
−0.679998 | + | 0.733214i | \(0.738019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2850 | − | 11.2850i | 0.637867 | − | 0.637867i | −0.312162 | − | 0.950029i | \(-0.601053\pi\) |
0.950029 | + | 0.312162i | \(0.101053\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.209252 | − | 0.115899i | −0.0117900 | − | 0.00653020i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.57388 | + | 18.2850i | −0.425391 | + | 1.02699i | 0.555340 | + | 0.831623i | \(0.312588\pi\) |
−0.980731 | + | 0.195362i | \(0.937412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 32.0062i | − | 1.79200i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.83043 | − | 0.639555i | 0.102164 | − | 0.0356965i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.49881 | − | 1.86347i | −0.250321 | − | 0.103686i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.35034 | − | 15.3311i | −0.352253 | − | 0.850415i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.38227 | − | 2.86695i | 0.0764395 | − | 0.158543i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.115556 | − | 0.115556i | 0.00637082 | − | 0.00637082i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.79305 | + | 11.5714i | 0.263450 | + | 0.636024i | 0.999147 | − | 0.0412860i | \(-0.0131455\pi\) |
−0.735698 | + | 0.677310i | \(0.763145\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.18251 | − | 11.0848i | −0.174400 | − | 0.607445i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.91959i | 0.104879i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.03034i | − | 0.382967i | −0.981496 | − | 0.191484i | \(-0.938670\pi\) | ||
0.981496 | − | 0.191484i | \(-0.0613299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.41303 | + | 0.136620i | 0.131058 | + | 0.00742018i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.63574 | − | 23.2627i | −0.521804 | − | 1.25975i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.99847 | − | 3.99847i | 0.215897 | − | 0.215897i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.16770 | + | 1.04513i | 0.116705 | + | 0.0562679i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.70857 | − | 11.3675i | −0.252769 | − | 0.610240i | 0.745656 | − | 0.666331i | \(-0.232136\pi\) |
−0.998426 | + | 0.0560914i | \(0.982136\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.2204 | − | 12.1035i | −1.56413 | − | 0.647885i | −0.578332 | − | 0.815802i | \(-0.696296\pi\) |
−0.985801 | + | 0.167917i | \(0.946296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.26554 | − | 14.7012i | 0.494558 | − | 0.784693i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 14.9632i | − | 0.796411i | −0.917296 | − | 0.398206i | \(-0.869633\pi\) | ||
0.917296 | − | 0.398206i | \(-0.130367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.302712 | − | 0.730811i | 0.0160663 | − | 0.0387874i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.380232 | + | 0.425872i | 0.0201240 | + | 0.0225395i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.5707 | − | 19.5707i | 1.03290 | − | 1.03290i | 0.0334594 | − | 0.999440i | \(-0.489348\pi\) |
0.999440 | − | 0.0334594i | \(-0.0106524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3532 | + | 12.3532i | 0.650170 | + | 0.650170i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.415140 | + | 0.370650i | −0.0217892 | + | 0.0194541i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.77883 | + | 0.736815i | 0.0931082 | + | 0.0385667i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.5484 | 1.12482 | 0.562410 | − | 0.826859i | \(-0.309874\pi\) | ||||
0.562410 | + | 0.826859i | \(0.309874\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.71398 | − | 6.93614i | 0.453632 | − | 0.361081i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.581184 | + | 1.40310i | −0.0301736 | + | 0.0728455i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.1858 | + | 11.2607i | −1.40763 | + | 0.583059i | −0.951720 | − | 0.306967i | \(-0.900686\pi\) |
−0.455910 | + | 0.890026i | \(0.650686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.46165 | + | 3.03160i | −0.0754794 | + | 0.156551i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.4944 | − | 22.4944i | −1.15852 | − | 1.15852i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.5245 | − | 4.77361i | 0.591975 | − | 0.245204i | −0.0665251 | − | 0.997785i | \(-0.521191\pi\) |
0.658500 | + | 0.752581i | \(0.271191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.672929 | − | 11.8855i | 0.0344752 | − | 0.608914i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.6911 | 1.72154 | 0.860768 | − | 0.508998i | \(-0.169984\pi\) | ||||
0.860768 | + | 0.508998i | \(0.169984\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.268286 | 0.0136731 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.15994 | − | 21.4554i | −0.313127 | − | 1.09064i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.0564 | + | 14.1066i | −1.72673 | + | 0.715233i | −0.727139 | + | 0.686490i | \(0.759151\pi\) |
−0.999587 | + | 0.0287433i | \(0.990849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.06135 | − | 4.06135i | −0.205391 | − | 0.205391i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.1178 | − | 13.0745i | −1.36791 | − | 0.659521i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.44466 | − | 0.598399i | 0.0726889 | − | 0.0301087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3891 | − | 27.4958i | 0.571604 | − | 1.37997i | −0.328586 | − | 0.944474i | \(-0.606572\pi\) |
0.900189 | − | 0.435499i | \(-0.143428\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.41039 | − | 4.03657i | −0.0706077 | − | 0.202081i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.31753 | 0.465295 | 0.232648 | − | 0.972561i | \(-0.425261\pi\) | ||||
0.232648 | + | 0.972561i | \(0.425261\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.1215 | − | 9.57726i | −1.15177 | − | 0.477077i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.73121 | + | 0.290888i | −0.0860246 | + | 0.0144543i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.14621 | + | 9.14621i | 0.453361 | + | 0.453361i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7916 | − | 17.7916i | 0.879736 | − | 0.879736i | −0.113771 | − | 0.993507i | \(-0.536293\pi\) |
0.993507 | + | 0.113771i | \(0.0362930\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.6948 | − | 17.5842i | 0.971473 | − | 0.867363i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.375523 | − | 0.906592i | 0.0184783 | − | 0.0446105i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.25954i | − | 0.0618285i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.10774 | − | 6.03242i | −0.103217 | − | 0.295409i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.75715 | − | 4.04154i | −0.476668 | − | 0.197442i | 0.131397 | − | 0.991330i | \(-0.458054\pi\) |
−0.608065 | + | 0.793888i | \(0.708054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.73340 | + | 4.18479i | 0.0844806 | + | 0.203954i | 0.960474 | − | 0.278368i | \(-0.0897935\pi\) |
−0.875994 | + | 0.482322i | \(0.839793\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.135371 | − | 1.19165i | 0.00658195 | − | 0.0579401i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82912 | − | 2.82912i | 0.137233 | − | 0.137233i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.49198 | + | 3.60195i | 0.0722018 | + | 0.174311i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.10172 | + | 19.4589i | −0.0531913 | + | 0.939485i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.2865i | 1.16984i | 0.811092 | + | 0.584919i | \(0.198874\pi\) | ||||
−0.811092 | + | 0.584919i | \(0.801126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.4987i | 1.03316i | 0.856239 | + | 0.516580i | \(0.172795\pi\) | ||||
−0.856239 | + | 0.516580i | \(0.827205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.181658 | + | 3.20852i | −0.00870985 | + | 0.153837i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.4619 | + | 39.7424i | 0.787478 | + | 1.90114i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.71247 | − | 1.71247i | 0.0817316 | − | 0.0817316i | −0.665059 | − | 0.746791i | \(-0.731594\pi\) |
0.746791 | + | 0.665059i | \(0.231594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.31375 | − | 20.3677i | 0.110179 | − | 0.969890i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.69988 | − | 4.10388i | −0.0807639 | − | 0.194981i | 0.878339 | − | 0.478037i | \(-0.158652\pi\) |
−0.959103 | + | 0.283056i | \(0.908652\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.38462 | − | 0.573527i | −0.0656371 | − | 0.0271878i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.70278 | + | 27.7697i | 0.458926 | + | 1.31346i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.34782i | 0.299572i | 0.988718 | + | 0.149786i | \(0.0478585\pi\) | ||||
−0.988718 | + | 0.149786i | \(0.952142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.78028 | + | 11.5406i | −0.225095 | + | 0.543427i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.74382 | + | 2.44977i | −0.128916 | + | 0.115100i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.188555 | − | 0.188555i | 0.00883961 | − | 0.00883961i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0211 | + | 10.0211i | 0.468765 | + | 0.468765i | 0.901514 | − | 0.432749i | \(-0.142456\pi\) |
−0.432749 | + | 0.901514i | \(0.642456\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.12966 | + | 0.707488i | 0.192756 | + | 0.0330227i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.1656 | − | 7.93865i | −0.892631 | − | 0.369740i | −0.111249 | − | 0.993793i | \(-0.535485\pi\) |
−0.781382 | + | 0.624053i | \(0.785485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.9634 | −1.43899 | −0.719496 | − | 0.694496i | \(-0.755627\pi\) | ||||
−0.719496 | + | 0.694496i | \(0.755627\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.833919 | + | 2.38670i | 0.0386721 | + | 0.110681i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.87599 | + | 6.94326i | −0.133085 | + | 0.321296i | −0.976348 | − | 0.216206i | \(-0.930632\pi\) |
0.843263 | + | 0.537502i | \(0.180632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.71679 | − | 1.53954i | 0.171625 | − | 0.0710895i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.5471 | − | 10.3887i | −0.992839 | − | 0.478685i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.7030 | + | 17.7030i | 0.813987 | + | 0.813987i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.6845 | + | 11.4673i | −1.27025 | + | 0.526155i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.07567 | + | 10.7127i | 0.140825 | + | 0.490502i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.3852 | 0.565894 | 0.282947 | − | 0.959136i | \(-0.408688\pi\) | ||||
0.282947 | + | 0.959136i | \(0.408688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8562 | 0.586192 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.285091 | − | 5.03538i | 0.0129721 | − | 0.229118i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.471072 | + | 0.195124i | −0.0213903 | + | 0.00886014i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.82766 | + | 8.82766i | 0.400019 | + | 0.400019i | 0.878240 | − | 0.478220i | \(-0.158718\pi\) |
−0.478220 | + | 0.878240i | \(0.658718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.94602 | − | 12.3326i | 0.268889 | − | 0.557700i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.13225 | − | 3.78270i | 0.412133 | − | 0.170711i | −0.166977 | − | 0.985961i | \(-0.553400\pi\) |
0.579109 | + | 0.815250i | \(0.303400\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.93521 | − | 7.08623i | 0.132195 | − | 0.319148i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.54047 | − | 1.22618i | 0.0692389 | − | 0.0551126i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.65780 | −0.0743626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.86758 | + | 2.01622i | 0.217903 | + | 0.0902583i | 0.488965 | − | 0.872304i | \(-0.337375\pi\) |
−0.271062 | + | 0.962562i | \(0.587375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.01685 | − | 2.69354i | 0.134783 | − | 0.120339i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.926311 | + | 0.926311i | 0.0413022 | + | 0.0413022i | 0.727456 | − | 0.686154i | \(-0.240702\pi\) |
−0.686154 | + | 0.727456i | \(0.740702\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.81265 | + | 1.81265i | −0.0806620 | + | 0.0806620i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.09450 | − | 2.34591i | −0.0930201 | − | 0.104185i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.79808 | − | 4.34096i | 0.0796987 | − | 0.192410i | −0.879008 | − | 0.476808i | \(-0.841794\pi\) |
0.958706 | + | 0.284398i | \(0.0917938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.03517i | − | 0.178505i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.5471 | − | 16.7315i | −1.17208 | − | 0.738714i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.15853 | + | 0.894090i | 0.0951160 | + | 0.0393983i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.514755 | + | 1.24273i | 0.0226389 | + | 0.0546551i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.5761 | + | 7.99195i | 0.727608 | + | 0.350807i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.3969 | + | 12.3969i | −0.543120 | + | 0.543120i | −0.924442 | − | 0.381322i | \(-0.875469\pi\) |
0.381322 | + | 0.924442i | \(0.375469\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.71533 | + | 13.7980i | 0.249914 | + | 0.603346i | 0.998196 | − | 0.0600346i | \(-0.0191211\pi\) |
−0.748282 | + | 0.663380i | \(0.769121\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.50764 | + | 0.198594i | 0.153086 | + | 0.00866734i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 6.03408i | − | 0.262849i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.7390i | 1.20604i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.98730 | − | 6.92184i | −0.0862413 | − | 0.300382i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.75127 | + | 11.4706i | 0.205800 | + | 0.496846i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.154398 | − | 0.154398i | 0.00667521 | − | 0.00667521i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.3468 | + | 25.6084i | −0.532802 | + | 1.10508i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.79818 | + | 21.2407i | 0.378964 | + | 0.914901i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5235 | + | 6.84424i | 0.710399 | + | 0.294257i | 0.708470 | − | 0.705741i | \(-0.249386\pi\) |
0.00192927 | + | 0.999998i | \(0.499386\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.73211 | + | 3.05102i | −0.374731 | + | 0.130932i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 0.358426i | − | 0.0153533i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.24912 | + | 5.42985i | −0.0961654 | + | 0.232164i | −0.964641 | − | 0.263569i | \(-0.915100\pi\) |
0.868475 | + | 0.495733i | \(0.165100\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.0292 | + | 13.8630i | 1.06822 | + | 0.591660i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.6199 | + | 40.6199i | −1.73047 | + | 1.73047i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.31728 | − | 2.31728i | −0.0985409 | − | 0.0985409i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.864967 | − | 0.968789i | −0.0367158 | − | 0.0411228i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5896 | + | 7.28584i | 0.745294 | + | 0.308711i | 0.722820 | − | 0.691036i | \(-0.242846\pi\) |
0.0224743 | + | 0.999747i | \(0.492846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.8839 | 1.05248 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.43620 | + | 1.55002i | −0.187296 | + | 0.0654417i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.04761 | + | 17.0144i | −0.297021 | + | 0.717073i | 0.702962 | + | 0.711228i | \(0.251861\pi\) |
−0.999983 | + | 0.00584493i | \(0.998139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.251458 | − | 0.104157i | 0.0105789 | − | 0.00438194i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.95168 | + | 3.11874i | 0.0819630 | + | 0.130975i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.9856 | − | 15.9856i | −0.670152 | − | 0.670152i | 0.287599 | − | 0.957751i | \(-0.407143\pi\) |
−0.957751 | + | 0.287599i | \(0.907143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2300 | − | 8.79375i | 0.888447 | − | 0.368007i | 0.108680 | − | 0.994077i | \(-0.465337\pi\) |
0.779767 | + | 0.626070i | \(0.215337\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.1383 | + | 1.14018i | 0.841290 | + | 0.0476317i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.3446 | −1.47397 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1703 | 0.881332 | 0.440666 | − | 0.897671i | \(-0.354742\pi\) | ||||
0.440666 | + | 0.897671i | \(0.354742\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.4314 | + | 0.590599i | 0.433513 | + | 0.0245444i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.43877 | + | 1.01017i | −0.101177 | + | 0.0419090i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.83917 | − | 8.83917i | −0.366081 | − | 0.366081i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.220887 | − | 1.94444i | 0.00913255 | − | 0.0803927i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.4081 | + | 5.96803i | −0.594686 | + | 0.246327i | −0.659665 | − | 0.751560i | \(-0.729302\pi\) |
0.0649791 | + | 0.997887i | \(0.479302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.2944 | + | 41.7523i | −0.712603 | + | 1.72037i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.02905 | − | 0.359550i | 0.0423293 | − | 0.0147899i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.5777 | 0.845025 | 0.422512 | − | 0.906357i | \(-0.361148\pi\) | ||||
0.422512 | + | 0.906357i | \(0.361148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0593989 | + | 0.0246038i | 0.00243512 | + | 0.00100866i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.1983 | − | 24.8628i | −0.908516 | − | 1.01757i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6016 | − | 14.6016i | −0.596604 | − | 0.596604i | 0.342803 | − | 0.939407i | \(-0.388624\pi\) |
−0.939407 | + | 0.342803i | \(0.888624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.7394 | + | 22.7394i | −0.927561 | + | 0.927561i | −0.997548 | − | 0.0699869i | \(-0.977704\pi\) |
0.0699869 | + | 0.997548i | \(0.477704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3050 | − | 25.8272i | 0.582545 | − | 1.05176i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0239839 | + | 0.0579021i | −0.000975082 | + | 0.00235406i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.2640i | 1.63426i | 0.576451 | + | 0.817132i | \(0.304437\pi\) | ||||
−0.576451 | + | 0.817132i | \(0.695563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.35814 | − | 2.22155i | 0.257645 | − | 0.0900216i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.23519 | + | 0.511631i | 0.0499703 | + | 0.0206984i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.76173 | − | 16.3243i | −0.273104 | − | 0.659331i | 0.726509 | − | 0.687157i | \(-0.241142\pi\) |
−0.999613 | + | 0.0278260i | \(0.991142\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.544710 | − | 1.12978i | 0.0219648 | − | 0.0455571i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.19834 | − | 5.19834i | 0.209277 | − | 0.209277i | −0.594683 | − | 0.803960i | \(-0.702722\pi\) |
0.803960 | + | 0.594683i | \(0.202722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.07299 | − | 19.4899i | −0.324481 | − | 0.783366i | −0.998983 | − | 0.0450932i | \(-0.985642\pi\) |
0.674502 | − | 0.738273i | \(-0.264358\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.3769 | − | 30.2156i | −0.857824 | − | 1.21251i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.14092i | 0.125838i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 24.4308i | − | 0.977230i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35.1384 | + | 1.98945i | 1.40329 | + | 0.0794510i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.18621 | + | 2.86376i | 0.0472973 | + | 0.114186i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5327 | − | 22.5327i | 0.897012 | − | 0.897012i | −0.0981592 | − | 0.995171i | \(-0.531295\pi\) |
0.995171 | + | 0.0981592i | \(0.0312954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.7231 | − | 5.65214i | −0.465950 | − | 0.224652i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.513033 | − | 1.23857i | −0.0203591 | − | 0.0491512i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.1118 | + | 8.74478i | 0.836479 | + | 0.346481i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.51892 | + | 7.57685i | −0.376563 | + | 0.299736i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.6012i | 1.64315i | 0.570100 | + | 0.821575i | \(0.306904\pi\) | ||||
−0.570100 | + | 0.821575i | \(0.693096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.11746 | + | 17.1831i | −0.280685 | + | 0.677634i | −0.999852 | − | 0.0172036i | \(-0.994524\pi\) |
0.719167 | + | 0.694837i | \(0.244524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.67420 | − | 1.87515i | −0.0659214 | − | 0.0738340i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.4452 | − | 31.4452i | 1.23624 | − | 1.23624i | 0.274714 | − | 0.961526i | \(-0.411417\pi\) |
0.961526 | − | 0.274714i | \(-0.0885833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.71128 | + | 5.71128i | 0.224187 | + | 0.224187i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.95240 | − | 3.52884i | 0.154907 | − | 0.138306i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.38622 | + | 2.23104i | 0.210779 | + | 0.0873075i | 0.485575 | − | 0.874195i | \(-0.338610\pi\) |
−0.274796 | + | 0.961503i | \(0.588610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.39025 | −0.132468 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.4424 | − | 23.1695i | −0.719507 | − | 0.903928i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.05977 | + | 17.0438i | −0.275010 | + | 0.663932i | −0.999683 | − | 0.0251602i | \(-0.991990\pi\) |
0.724674 | + | 0.689092i | \(0.241990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.7857 | − | 10.6808i | 1.00295 | − | 0.415435i | 0.180071 | − | 0.983654i | \(-0.442367\pi\) |
0.822878 | + | 0.568219i | \(0.192367\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.02845 | + | 4.20720i | −0.0787786 | + | 0.163394i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.340489 | − | 0.340489i | −0.0132036 | − | 0.0132036i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −62.5996 | + | 25.9296i | −2.42387 | + | 1.00400i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.631682 | + | 11.1570i | −0.0244222 | + | 0.431355i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.0904 | −1.23883 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5829 | 0.716319 | 0.358160 | − | 0.933660i | \(-0.383404\pi\) | ||||
0.358160 | + | 0.933660i | \(0.383404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.0481 | − | 14.8911i | 0.810142 | − | 0.573157i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9138 | − | 9.49122i | 0.880650 | − | 0.364777i | 0.103901 | − | 0.994588i | \(-0.466867\pi\) |
0.776749 | + | 0.629810i | \(0.216867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.755613 | + | 0.755613i | 0.0289978 | + | 0.0289978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.34661 | − | 2.57781i | −0.204883 | − | 0.0987817i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.5480 | − | 14.3103i | 1.32194 | − | 0.547567i | 0.393597 | − | 0.919283i | \(-0.371231\pi\) |
0.928346 | + | 0.371717i | \(0.121231\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.13783 | − | 2.74696i | 0.0434741 | − | 0.104956i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.8946 | − | 36.9048i | −0.491960 | − | 1.40801i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.4246 | −0.473340 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.9717 | + | 12.4147i | 1.14018 | + | 0.472277i | 0.871228 | − | 0.490878i | \(-0.163324\pi\) |
0.268948 | + | 0.963155i | \(0.413324\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.60965 | − | 1.99929i | −0.137119 | − | 0.0759469i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.508841 | − | 0.508841i | −0.0193014 | − | 0.0193014i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.11673 | + | 2.11673i | −0.0801767 | + | 0.0801767i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.3622 | + | 25.3227i | −1.07276 | + | 0.957793i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.56454 | − | 15.8482i | 0.247939 | − | 0.598578i | −0.750090 | − | 0.661336i | \(-0.769990\pi\) |
0.998029 | + | 0.0627582i | \(0.0199897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 23.2154i | − | 0.875585i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0445491 | − | 0.127501i | −0.00167782 | − | 0.00480197i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.96350 | + | 2.05595i | 0.186672 | + | 0.0773219i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.6861 | − | 28.2128i | −0.438882 | − | 1.05955i | −0.976336 | − | 0.216261i | \(-0.930614\pi\) |
0.537454 | − | 0.843293i | \(-0.319386\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.8965 | − | 2.71463i | −0.896190 | − | 0.101806i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.6923 | + | 37.6923i | −1.41159 | + | 1.41159i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.839935 | + | 2.02778i | 0.0314118 | + | 0.0758348i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.18662 | + | 38.6208i | −0.0816607 | + | 1.44232i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.6392i | 1.21724i | 0.793463 | + | 0.608619i | \(0.208276\pi\) | ||||
−0.793463 | + | 0.608619i | \(0.791724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.89649i | − | 0.182355i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.982456 | − | 17.3525i | 0.0365379 | − | 0.645347i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0625 | − | 43.6067i | −0.670825 | − | 1.61951i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.8938 | − | 11.8938i | 0.441118 | − | 0.441118i | −0.451270 | − | 0.892388i | \(-0.649029\pi\) |
0.892388 | + | 0.451270i | \(0.149029\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.4603 | + | 8.98742i | 0.942974 | + | 0.332867i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.29598 | + | 5.54299i | 0.0849199 | + | 0.205015i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.2498 | − | 5.90246i | −0.526328 | − | 0.218012i | 0.103666 | − | 0.994612i | \(-0.466943\pi\) |
−0.629994 | + | 0.776600i | \(0.716943\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.761433 | − | 2.17925i | −0.0280859 | − | 0.0803827i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.1135i | 1.21975i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.65560 | − | 3.99698i | 0.0609024 | − | 0.147031i | −0.890499 | − | 0.454986i | \(-0.849644\pi\) |
0.951401 | + | 0.307954i | \(0.0996444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.0940 | − | 23.2976i | 0.958589 | − | 0.855859i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.0005 | − | 15.0005i | 0.550313 | − | 0.550313i | −0.376218 | − | 0.926531i | \(-0.622776\pi\) |
0.926531 | + | 0.376218i | \(0.122776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.34240 | + | 2.34240i | 0.0858188 | + | 0.0858188i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.38625 | + | 16.9465i | −0.343425 | + | 0.620040i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.422781 | − | 0.175122i | −0.0154481 | − | 0.00639880i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.9267 | −0.398720 | −0.199360 | − | 0.979926i | \(-0.563886\pi\) | ||||
−0.199360 | + | 0.979926i | \(0.563886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.83745 | − | 5.25884i | −0.0669603 | − | 0.191643i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.158519 | + | 0.382698i | −0.00576908 | + | 0.0139278i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.8634 | + | 8.22770i | −0.721948 | + | 0.299041i | −0.713239 | − | 0.700921i | \(-0.752772\pi\) |
−0.00870961 | + | 0.999962i | \(0.502772\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.3933 | + | 18.0287i | 1.35729 | + | 0.654402i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.07215 | + | 8.07215i | 0.292615 | + | 0.292615i | 0.838112 | − | 0.545497i | \(-0.183659\pi\) |
−0.545497 | + | 0.838112i | \(0.683659\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.693996 | + | 0.287463i | −0.0251243 | + | 0.0104068i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.453512 | − | 0.130206i | 0.0163968 | − | 0.00470759i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.02795 | 0.289873 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.21321 | −0.260115 | −0.130057 | − | 0.991506i | \(-0.541516\pi\) | ||||
−0.130057 | + | 0.991506i | \(0.541516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.23075 | + | 39.4003i | −0.0803384 | + | 1.41897i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.1506 | + | 12.0746i | −1.04848 | + | 0.434293i | −0.839347 | − | 0.543595i | \(-0.817063\pi\) |
−0.209128 | + | 0.977888i | \(0.567063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.2564 | − | 26.2564i | −0.943157 | − | 0.943157i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.18209 | + | 2.45176i | −0.0424072 | + | 0.0879565i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.7133 | − | 8.57973i | 0.742131 | − | 0.307401i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.22185 | − | 12.6067i | 0.186853 | − | 0.451102i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.3543 | − | 41.8152i | 0.941827 | − | 1.49435i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.69382 | −0.0961464 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.5666 | + | 14.3179i | 1.23217 | + | 0.510380i | 0.901258 | − | 0.433283i | \(-0.142645\pi\) |
0.330908 | + | 0.943663i | \(0.392645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.4890 | − | 20.9718i | 0.836231 | − | 0.746614i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.403347 | − | 0.403347i | −0.0143414 | − | 0.0143414i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.5536 | + | 22.5536i | −0.800902 | + | 0.800902i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.835930 | + | 0.936268i | 0.0296474 | + | 0.0332060i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.403632 | + | 0.974454i | −0.0142974 | + | 0.0345169i | −0.930867 | − | 0.365358i | \(-0.880947\pi\) |
0.916570 | + | 0.399875i | \(0.130947\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.322349i | 0.0114039i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3553 | + | 18.0348i | 0.507221 | + | 0.637229i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.6852 | + | 12.7102i | 1.08286 | + | 0.448535i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.217350 | − | 0.524729i | −0.00766058 | − | 0.0184943i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.8834 | − | 9.58656i | −0.699930 | − | 0.337463i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.9129 | − | 34.9129i | 1.22747 | − | 1.22747i | 0.262555 | − | 0.964917i | \(-0.415435\pi\) |
0.964917 | − | 0.262555i | \(-0.0845653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0178 | − | 31.4278i | −0.457117 | − | 1.10358i | −0.969559 | − | 0.244857i | \(-0.921259\pi\) |
0.512442 | − | 0.858722i | \(-0.328741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.1680 | − | 1.14186i | −0.707324 | − | 0.0400469i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.54182i | − | 0.0540076i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 44.9348i | − | 1.57207i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.94205 | + | 1.13178i | −0.137746 | + | 0.0395476i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.16275 | + | 7.63556i | 0.110381 | + | 0.266483i | 0.969411 | − | 0.245441i | \(-0.0789329\pi\) |
−0.859031 | + | 0.511924i | \(0.828933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.3941 | − | 11.3941i | 0.397173 | − | 0.397173i | −0.480062 | − | 0.877235i | \(-0.659386\pi\) |
0.877235 | + | 0.480062i | \(0.159386\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.5588 | + | 26.0481i | −0.437240 | + | 0.906878i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.32108 | + | 20.0889i | 0.289352 | + | 0.698558i | 0.999987 | − | 0.00500239i | \(-0.00159232\pi\) |
−0.710635 | + | 0.703561i | \(0.751592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00953 | − | 2.90344i | −0.243451 | − | 0.100841i | 0.257622 | − | 0.966246i | \(-0.417061\pi\) |
−0.501073 | + | 0.865405i | \(0.667061\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0242 | + | 5.24949i | −0.521184 | + | 0.182103i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.50958i | 0.190896i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.174292 | − | 0.420779i | 0.00603163 | − | 0.0145617i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.56601 | − | 38.3263i | 0.226955 | − | 1.32475i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.15538 | + | 4.15538i | −0.143460 | + | 0.143460i | −0.775189 | − | 0.631729i | \(-0.782345\pi\) |
0.631729 | + | 0.775189i | \(0.282345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.4756 | − | 43.4756i | −1.49916 | − | 1.49916i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.3963 | − | 40.7649i | −1.25355 | − | 1.40402i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.327198 | − | 0.135530i | −0.0112560 | − | 0.00466237i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.131348 | 0.00451316 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6135 | + | 6.15418i | −0.604493 | + | 0.211211i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.4790 | − | 25.2984i | 0.359214 | − | 0.867219i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.9124 | + | 10.3191i | −0.852986 | + | 0.353318i | −0.765960 | − | 0.642888i | \(-0.777736\pi\) |
−0.0870255 | + | 0.996206i | \(0.527736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.51122 | − | 0.398872i | −0.120081 | − | 0.0136411i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.13231 | − | 9.13231i | −0.311954 | − | 0.311954i | 0.533712 | − | 0.845666i | \(-0.320797\pi\) |
−0.845666 | + | 0.533712i | \(0.820797\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.1392 | − | 8.34191i | 0.687139 | − | 0.284622i | −0.0116685 | − | 0.999932i | \(-0.503714\pi\) |
0.698808 | + | 0.715310i | \(0.253714\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.62438 | − | 0.148586i | −0.0894388 | − | 0.00506380i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2708 | 0.485784 | 0.242892 | − | 0.970053i | \(-0.421904\pi\) | ||||
0.242892 | + | 0.970053i | \(0.421904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.07233 | 0.0704614 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.2735 | + | 1.60077i | 0.960217 | + | 0.0543651i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.9208 | − | 10.3225i | 0.845380 | − | 0.350168i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.2726 | + | 23.2726i | 0.788563 | + | 0.788563i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.79212 | + | 0.885178i | 0.263723 | + | 0.0299587i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.733853 | − | 0.303972i | 0.0248088 | − | 0.0102761i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3328 | + | 24.9457i | −0.348915 | + | 0.842355i | 0.647834 | + | 0.761782i | \(0.275675\pi\) |
−0.996749 | + | 0.0805736i | \(0.974325\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.0793 | + | 14.3532i | −1.38557 | + | 0.484121i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.06465 | 0.103251 | 0.0516254 | − | 0.998667i | \(-0.483560\pi\) | ||||
0.0516254 | + | 0.998667i | \(0.483560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.883537 | − | 0.365973i | −0.0297334 | − | 0.0123160i | 0.367767 | − | 0.929918i | \(-0.380122\pi\) |
−0.397501 | + | 0.917602i | \(0.630122\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.540122 | − | 0.604954i | −0.0181560 | − | 0.0203353i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.90816 | + | 5.90816i | 0.198377 | + | 0.198377i | 0.799304 | − | 0.600927i | \(-0.205202\pi\) |
−0.600927 | + | 0.799304i | \(0.705202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.98671 | + | 1.98671i | −0.0666320 | + | 0.0666320i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.8638 | + | 5.01788i | −1.00048 | + | 0.168105i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.923891 | − | 2.23047i | 0.0309168 | − | 0.0746398i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.20155i | 0.107016i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.9515 | − | 13.6097i | 1.30055 | − | 0.454415i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −65.7654 | − | 27.2409i | −2.19340 | − | 0.908536i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.14639 | − | 2.76763i | −0.0381918 | − | 0.0922031i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.28800 | + | 4.74554i | −0.0761400 | + | 0.157922i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.736562 | + | 0.736562i | −0.0244841 | + | 0.0244841i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.83330 | + | 4.42597i | 0.0608736 | + | 0.146962i | 0.951390 | − | 0.307990i | \(-0.0996564\pi\) |
−0.890516 | + | 0.454952i | \(0.849656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.8964 | − | 10.8802i | 1.25694 | − | 0.360875i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 29.4647i | − | 0.976208i | −0.872786 | − | 0.488104i | \(-0.837689\pi\) | ||
0.872786 | − | 0.488104i | \(-0.162311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 21.7274i | − | 0.719073i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.21696 | + | 0.182136i | 0.106349 | + | 0.00602123i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.71903 | + | 6.56433i | 0.0897904 | + | 0.216773i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.4648 | + | 14.4648i | −0.477149 | + | 0.477149i | −0.904219 | − | 0.427070i | \(-0.859546\pi\) |
0.427070 | + | 0.904219i | \(0.359546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.0695 | + | 14.9798i | 1.02377 | + | 0.493600i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.19016 | − | 12.5302i | −0.170836 | − | 0.412435i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.6228 | + | 7.29962i | 0.579435 | + | 0.240010i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.3790 | − | 28.1151i | −0.735023 | − | 0.923421i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 30.4237i | − | 0.998170i | −0.866553 | − | 0.499085i | \(-0.833670\pi\) | ||
0.866553 | − | 0.499085i | \(-0.166330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.7911 | − | 38.1231i | 0.517533 | − | 1.24943i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.53099 | − | 1.71476i | −0.0501225 | − | 0.0561387i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.374197 | + | 0.374197i | −0.0122376 | + | 0.0122376i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7838 | + | 17.7838i | 0.580972 | + | 0.580972i | 0.935170 | − | 0.354199i | \(-0.115246\pi\) |
−0.354199 | + | 0.935170i | \(0.615246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.6199 | + | 18.4101i | −0.672903 | + | 0.600790i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.2523 | − | 4.66086i | −0.366815 | − | 0.151940i | 0.191660 | − | 0.981461i | \(-0.438613\pi\) |
−0.558474 | + | 0.829522i | \(0.688613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.4446 | 0.861154 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.350508 | + | 0.220910i | 0.0114020 | + | 0.00718621i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4459 | + | 37.2898i | −0.501925 | + | 1.21175i | 0.446509 | + | 0.894779i | \(0.352667\pi\) |
−0.948434 | + | 0.316975i | \(0.897333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.4990 | − | 12.6331i | 0.990040 | − | 0.410088i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.8876 | − | 30.8783i | 0.482763 | − | 1.00130i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.9782 | − | 35.9782i | −1.16545 | − | 1.16545i | −0.983264 | − | 0.182184i | \(-0.941683\pi\) |
−0.182184 | − | 0.983264i | \(-0.558317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.09858 | − | 0.869261i | 0.0679085 | − | 0.0281286i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.13365 | + | 55.3477i | −0.101297 | + | 1.78914i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.23131 | −0.201219 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0007 | −0.806476 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.22794 | + | 0.926757i | −0.104019 | + | 0.0298643i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.08704 | − | 0.450266i | 0.0349930 | − | 0.0144946i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.1751 | − | 23.1751i | −0.745262 | − | 0.745262i | 0.228324 | − | 0.973585i | \(-0.426676\pi\) |
−0.973585 | + | 0.228324i | \(0.926676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.59726 | + | 3.66293i | 0.244059 | + | 0.117670i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.6938 | − | 13.9564i | 1.08128 | − | 0.447883i | 0.230325 | − | 0.973114i | \(-0.426021\pi\) |
0.850960 | + | 0.525231i | \(0.176021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.577137 | + | 1.39333i | −0.0185022 | + | 0.0446682i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.48049 | + | 27.1335i | 0.303619 | + | 0.868967i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.1411 | 1.34821 | 0.674106 | − | 0.738635i | \(-0.264529\pi\) | ||||
0.674106 | + | 0.738635i | \(0.264529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.8850 | − | 9.89348i | −0.763367 | − | 0.316197i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.67102 | + | 4.82243i | −0.0852792 | + | 0.153968i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.4787 | − | 27.4787i | −0.876436 | − | 0.876436i | 0.116728 | − | 0.993164i | \(-0.462759\pi\) |
−0.993164 | + | 0.116728i | \(0.962759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0868009 | − | 0.0868009i | 0.00276571 | − | 0.00276571i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.211143 | + | 0.188515i | −0.00672076 | + | 0.00600051i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.2827 | − | 48.9667i | 0.644951 | − | 1.55705i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.6090i | 1.35352i | 0.736204 | + | 0.676760i | \(0.236616\pi\) | ||||
−0.736204 | + | 0.676760i | \(0.763384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.15560 | − | 20.4796i | −0.227076 | − | 0.649899i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.46777 | − | 1.43640i | −0.109936 | − | 0.0455368i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.53889 | − | 13.3721i | −0.175418 | − | 0.423497i | 0.811577 | − | 0.584245i | \(-0.198609\pi\) |
−0.986995 | + | 0.160748i | \(0.948609\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.41816 | + | 19.4804i | 0.139785 | + | 0.616332i |
(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 | 384.2.o.a.47.1 | 56 | ||
3.2 | odd | 2 | inner | 384.2.o.a.47.11 | 56 | ||
4.3 | odd | 2 | 96.2.o.a.35.1 | yes | 56 | ||
8.3 | odd | 2 | 768.2.o.b.95.1 | 56 | |||
8.5 | even | 2 | 768.2.o.a.95.14 | 56 | |||
12.11 | even | 2 | 96.2.o.a.35.14 | yes | 56 | ||
24.5 | odd | 2 | 768.2.o.a.95.4 | 56 | |||
24.11 | even | 2 | 768.2.o.b.95.11 | 56 | |||
32.5 | even | 8 | 768.2.o.b.671.11 | 56 | |||
32.11 | odd | 8 | inner | 384.2.o.a.335.11 | 56 | ||
32.21 | even | 8 | 96.2.o.a.11.14 | yes | 56 | ||
32.27 | odd | 8 | 768.2.o.a.671.4 | 56 | |||
96.5 | odd | 8 | 768.2.o.b.671.1 | 56 | |||
96.11 | even | 8 | inner | 384.2.o.a.335.1 | 56 | ||
96.53 | odd | 8 | 96.2.o.a.11.1 | ✓ | 56 | ||
96.59 | even | 8 | 768.2.o.a.671.14 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.1 | ✓ | 56 | 96.53 | odd | 8 | ||
96.2.o.a.11.14 | yes | 56 | 32.21 | even | 8 | ||
96.2.o.a.35.1 | yes | 56 | 4.3 | odd | 2 | ||
96.2.o.a.35.14 | yes | 56 | 12.11 | even | 2 | ||
384.2.o.a.47.1 | 56 | 1.1 | even | 1 | trivial | ||
384.2.o.a.47.11 | 56 | 3.2 | odd | 2 | inner | ||
384.2.o.a.335.1 | 56 | 96.11 | even | 8 | inner | ||
384.2.o.a.335.11 | 56 | 32.11 | odd | 8 | inner | ||
768.2.o.a.95.4 | 56 | 24.5 | odd | 2 | |||
768.2.o.a.95.14 | 56 | 8.5 | even | 2 | |||
768.2.o.a.671.4 | 56 | 32.27 | odd | 8 | |||
768.2.o.a.671.14 | 56 | 96.59 | even | 8 | |||
768.2.o.b.95.1 | 56 | 8.3 | odd | 2 | |||
768.2.o.b.95.11 | 56 | 24.11 | even | 2 | |||
768.2.o.b.671.1 | 56 | 96.5 | odd | 8 | |||
768.2.o.b.671.11 | 56 | 32.5 | even | 8 |