Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(95,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, 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("768.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.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: | \(6.13251087523\) |
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 | 95.1 | ||
Character | \(\chi\) | \(=\) | 768.95 |
Dual form | 768.2.o.b.671.1 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 | −0.342024 | − | 0.939691i | \(-0.611112\pi\) |
0.422614 | + | 0.906310i | \(0.361112\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.289055 | − | 0.289055i | −0.109253 | − | 0.109253i | 0.650367 | − | 0.759620i | \(-0.274615\pi\) |
−0.759620 | + | 0.650367i | \(0.774615\pi\) | |||||||
\(8\) | 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 | \(-0.721496\pi\) |
0.995993 | − | 0.0894273i | \(-0.0285037\pi\) | |||||||
\(14\) | 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 | \(-0.983575\pi\) |
−0.0515792 | − | 0.998669i | \(-0.516425\pi\) | |||||||
\(24\) | 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 | \(-0.530388\pi\) |
0.771289 | − | 0.636485i | \(-0.219612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.48336i | − | 1.34405i | −0.740528 | − | 0.672026i | \(-0.765424\pi\) | ||
0.740528 | − | 0.672026i | \(-0.234576\pi\) | |||||||
\(32\) | 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 | 0.997467 | − | 0.0711364i | \(-0.0226626\pi\) |
−0.755616 | + | 0.655014i | \(0.772663\pi\) | |||||||
\(38\) | 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 | \(0.00928208\pi\) | ||||
−0.999575 | + | 0.0291564i | \(0.990718\pi\) | |||||||
\(48\) | 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 | 0.795653 | − | 0.605752i | \(-0.207128\pi\) |
−0.990943 | + | 0.134280i | \(0.957128\pi\) | |||||||
\(54\) | 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 | −0.261015 | − | 0.965335i | \(-0.584057\pi\) |
−0.867160 | + | 0.498029i | \(0.834057\pi\) | |||||||
\(62\) | 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 | −0.516165 | − | 0.856489i | \(-0.672641\pi\) |
0.856489 | + | 0.516165i | \(0.172641\pi\) | |||||||
\(72\) | 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 | \(-0.351076\pi\) | ||||
0.450977 | + | 0.892536i | \(0.351076\pi\) | |||||||
\(80\) | 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 | −0.893633 | − | 0.448798i | \(-0.851852\pi\) |
−0.314546 | + | 0.949242i | \(0.601852\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.46981 | + | 8.46981i | 0.834555 | + | 0.834555i | 0.988136 | − | 0.153581i | \(-0.0490806\pi\) |
−0.153581 | + | 0.988136i | \(0.549081\pi\) | |||||||
\(104\) | 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 | −0.886617 | − | 0.462504i | \(-0.846951\pi\) |
0.953973 | + | 0.299894i | \(0.0969512\pi\) | |||||||
\(110\) | 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 | \(-0.901362\pi\) | ||
0.952370 | − | 0.304944i | \(-0.0986379\pi\) | |||||||
\(128\) | 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 | \(0.119889\pi\) |
−0.397466 | + | 0.917617i | \(0.630111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.50166 | + | 1.50166i | −0.122204 | + | 0.122204i | −0.765564 | − | 0.643360i | \(-0.777540\pi\) |
0.643360 | + | 0.765564i | \(0.277540\pi\) | |||||||
\(152\) | 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 | −0.189830 | − | 0.981817i | \(-0.560794\pi\) |
−0.828480 | + | 0.560019i | \(0.810794\pi\) | |||||||
\(158\) | 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 | −0.640333 | − | 0.768098i | \(-0.721203\pi\) |
0.768098 | + | 0.640333i | \(0.221203\pi\) | |||||||
\(168\) | 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 | 0.723221 | − | 0.690617i | \(-0.242661\pi\) |
0.0230541 | + | 0.999734i | \(0.492661\pi\) | |||||||
\(174\) | 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 | −0.558436 | − | 0.829548i | \(-0.688598\pi\) |
0.191705 | + | 0.981453i | \(0.438598\pi\) | |||||||
\(182\) | 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 | \(-0.361567\pi\) | ||||
0.421318 | + | 0.906913i | \(0.361567\pi\) | |||||||
\(192\) | 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 | −0.361874 | − | 0.932227i | \(-0.617863\pi\) |
0.403300 | + | 0.915068i | \(0.367863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6071 | − | 13.6071i | −0.964583 | − | 0.964583i | 0.0348110 | − | 0.999394i | \(-0.488917\pi\) |
−0.999394 | + | 0.0348110i | \(0.988917\pi\) | |||||||
\(200\) | 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 | \(0.0693086\pi\) | ||||
−0.976388 | + | 0.216023i | \(0.930691\pi\) | |||||||
\(224\) | 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 | \(-0.857096\pi\) |
0.330141 | − | 0.943932i | \(-0.392904\pi\) | |||||||
\(230\) | 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 | \(0.256922\pi\) | ||||
−0.691563 | + | 0.722316i | \(0.743078\pi\) | |||||||
\(240\) | 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 | −0.189241 | − | 0.981931i | \(-0.560603\pi\) |
0.981931 | + | 0.189241i | \(0.0606027\pi\) | |||||||
\(264\) | 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 | −0.00632279 | − | 0.999980i | \(-0.502013\pi\) |
−0.711564 | + | 0.702622i | \(0.752013\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6627 | −0.708457 | −0.354228 | − | 0.935159i | \(-0.615256\pi\) | ||||
−0.354228 | + | 0.935159i | \(0.615256\pi\) | |||||||
\(272\) | 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 | −0.622843 | − | 0.782347i | \(-0.714023\pi\) |
0.112786 | + | 0.993619i | \(0.464023\pi\) | |||||||
\(278\) | 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 | −0.937953 | − | 0.346762i | \(-0.887281\pi\) |
−0.418035 | + | 0.908431i | \(0.637281\pi\) | |||||||
\(294\) | 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 | 0.679998 | − | 0.733214i | \(-0.261981\pi\) |
−0.733214 | + | 0.679998i | \(0.761981\pi\) | |||||||
\(312\) | 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 | \(-0.687412\pi\) |
0.980731 | − | 0.195362i | \(-0.0625881\pi\) | |||||||
\(318\) | 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 | 0.985801 | − | 0.167917i | \(-0.0537039\pi\) |
0.578332 | + | 0.815802i | \(0.303704\pi\) | |||||||
\(350\) | 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 | \(0.510652\pi\) |
−0.999440 | + | 0.0334594i | \(0.989348\pi\) | |||||||
\(360\) | 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 | \(-0.690126\pi\) | ||||
−0.562410 | + | 0.826859i | \(0.690126\pi\) | |||||||
\(368\) | 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 | 0.455910 | − | 0.890026i | \(-0.349314\pi\) |
0.951720 | + | 0.306967i | \(0.0993141\pi\) | |||||||
\(374\) | 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 | \(-0.830016\pi\) | ||||
−0.860768 | + | 0.508998i | \(0.830016\pi\) | |||||||
\(384\) | 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 | \(-0.240849\pi\) |
0.999587 | − | 0.0287433i | \(-0.00915052\pi\) | |||||||
\(390\) | 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 | \(0.393428\pi\) |
−0.900189 | + | 0.435499i | \(0.856572\pi\) | |||||||
\(398\) | 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 | 0.875994 | − | 0.482322i | \(-0.160207\pi\) |
−0.960474 | + | 0.278368i | \(0.910207\pi\) | |||||||
\(422\) | 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 | \(-0.801126\pi\) | ||
0.811092 | − | 0.584919i | \(-0.198874\pi\) | |||||||
\(432\) | 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 | −0.746791 | − | 0.665059i | \(-0.768406\pi\) |
0.665059 | + | 0.746791i | \(0.268406\pi\) | |||||||
\(440\) | 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 | 0.781382 | − | 0.624053i | \(-0.214515\pi\) |
0.111249 | + | 0.993793i | \(0.464515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.9634 | 1.43899 | 0.719496 | − | 0.694496i | \(-0.244373\pi\) | ||||
0.719496 | + | 0.694496i | \(0.244373\pi\) | |||||||
\(464\) | 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 | \(-0.591312\pi\) | ||||
−0.282947 | + | 0.959136i | \(0.591312\pi\) | |||||||
\(480\) | 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 | 0.478220 | − | 0.878240i | \(-0.341282\pi\) |
−0.878240 | + | 0.478220i | \(0.841282\pi\) | |||||||
\(488\) | 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 | 0.686154 | − | 0.727456i | \(-0.259298\pi\) |
−0.727456 | + | 0.686154i | \(0.759298\pi\) | |||||||
\(504\) | 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 | −0.958706 | − | 0.284398i | \(-0.908206\pi\) |
0.879008 | + | 0.476808i | \(0.158206\pi\) | |||||||
\(510\) | 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 | −0.00192927 | − | 0.999998i | \(-0.500614\pi\) |
−0.708470 | + | 0.705741i | \(0.750614\pi\) | |||||||
\(542\) | 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 | −0.0224743 | − | 0.999747i | \(-0.507154\pi\) |
−0.722820 | + | 0.691036i | \(0.757154\pi\) | |||||||
\(558\) | 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 | 0.939407 | − | 0.342803i | \(-0.111376\pi\) |
−0.342803 | + | 0.939407i | \(0.611376\pi\) | |||||||
\(600\) | 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 | \(-0.695563\pi\) | ||
0.576451 | − | 0.817132i | \(-0.304437\pi\) | |||||||
\(608\) | 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 | 0.999613 | − | 0.0278260i | \(-0.00885845\pi\) |
−0.726509 | + | 0.687157i | \(0.758858\pi\) | |||||||
\(614\) | 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 | −0.995171 | − | 0.0981592i | \(-0.968705\pi\) |
0.0981592 | + | 0.995171i | \(0.468705\pi\) | |||||||
\(632\) | 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 | \(0.588583\pi\) |
−0.961526 | + | 0.274714i | \(0.911417\pi\) | |||||||
\(648\) | 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 | 0.274796 | − | 0.961503i | \(-0.411390\pi\) |
−0.485575 | + | 0.874195i | \(0.661390\pi\) | |||||||
\(654\) | 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 | −0.822878 | − | 0.568219i | \(-0.807633\pi\) |
−0.180071 | + | 0.983654i | \(0.557633\pi\) | |||||||
\(662\) | 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 | −0.776749 | − | 0.629810i | \(-0.783133\pi\) |
−0.103901 | + | 0.994588i | \(0.533133\pi\) | |||||||
\(678\) | 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 | −0.998029 | − | 0.0627582i | \(-0.980010\pi\) |
0.750090 | + | 0.661336i | \(0.230010\pi\) | |||||||
\(702\) | 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 | \(0.0693863\pi\) |
−0.537454 | + | 0.843293i | \(0.680614\pi\) | |||||||
\(710\) | 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 | \(-0.791724\pi\) | ||
0.793463 | − | 0.608619i | \(-0.208276\pi\) | |||||||
\(720\) | 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 | −0.892388 | − | 0.451270i | \(-0.850971\pi\) |
0.451270 | + | 0.892388i | \(0.350971\pi\) | |||||||
\(728\) | 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 | 0.629994 | − | 0.776600i | \(-0.283057\pi\) |
−0.103666 | + | 0.994612i | \(0.533057\pi\) | |||||||
\(734\) | 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 | −0.926531 | − | 0.376218i | \(-0.877224\pi\) |
0.376218 | + | 0.926531i | \(0.377224\pi\) | |||||||
\(744\) | 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 | \(-0.436114\pi\) | ||||
0.199360 | + | 0.979926i | \(0.436114\pi\) | |||||||
\(752\) | 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 | 0.00870961 | − | 0.999962i | \(-0.497228\pi\) |
0.713239 | + | 0.700921i | \(0.247228\pi\) | |||||||
\(758\) | 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 | 0.209128 | − | 0.977888i | \(-0.432937\pi\) |
0.839347 | + | 0.543595i | \(0.182937\pi\) | |||||||
\(774\) | 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 | −0.916570 | − | 0.399875i | \(-0.869053\pi\) |
0.930867 | + | 0.365358i | \(0.119053\pi\) | |||||||
\(798\) | 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 | 0.859031 | − | 0.511924i | \(-0.171067\pi\) |
−0.969411 | + | 0.245441i | \(0.921067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.3941 | + | 11.3941i | −0.397173 | + | 0.397173i | −0.877235 | − | 0.480062i | \(-0.840614\pi\) |
0.480062 | + | 0.877235i | \(0.340614\pi\) | |||||||
\(824\) | 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 | 0.501073 | − | 0.865405i | \(-0.332939\pi\) |
−0.257622 | + | 0.966246i | \(0.582939\pi\) | |||||||
\(830\) | 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 | −0.631729 | − | 0.775189i | \(-0.717655\pi\) |
0.775189 | + | 0.631729i | \(0.217655\pi\) | |||||||
\(840\) | 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 | 0.0870255 | − | 0.996206i | \(-0.472264\pi\) |
0.765960 | + | 0.642888i | \(0.222264\pi\) | |||||||
\(854\) | 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 | \(-0.578096\pi\) | ||||
−0.242892 | + | 0.970053i | \(0.578096\pi\) | |||||||
\(864\) | 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 | \(-0.724325\pi\) |
0.996749 | − | 0.0805736i | \(-0.0256752\pi\) | |||||||
\(878\) | 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 | 0.600927 | − | 0.799304i | \(-0.294798\pi\) |
−0.799304 | + | 0.600927i | \(0.794798\pi\) | |||||||
\(888\) | 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 | \(0.162311\pi\) | ||||
−0.872786 | + | 0.488104i | \(0.837689\pi\) | |||||||
\(912\) | 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 | −0.427070 | − | 0.904219i | \(-0.640454\pi\) |
0.904219 | + | 0.427070i | \(0.140454\pi\) | |||||||
\(920\) | 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 | 0.558474 | − | 0.829522i | \(-0.311387\pi\) |
−0.191660 | + | 0.981461i | \(0.561387\pi\) | |||||||
\(942\) | 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 | 0.973585 | − | 0.228324i | \(-0.0733244\pi\) |
−0.228324 | + | 0.973585i | \(0.573324\pi\) | |||||||
\(968\) | 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 | 0.993164 | − | 0.116728i | \(-0.0372406\pi\) |
−0.116728 | + | 0.993164i | \(0.537241\pi\) | |||||||
\(984\) | 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 | \(-0.763384\pi\) | ||
0.736204 | − | 0.676760i | \(-0.236616\pi\) | |||||||
\(992\) | 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 | 0.986995 | − | 0.160748i | \(-0.0513906\pi\) |
−0.811577 | + | 0.584245i | \(0.801391\pi\) | |||||||
\(998\) | 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 | 768.2.o.b.95.1 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.95.11 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.95.14 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.47.1 | 56 | |||
8.5 | even | 2 | 96.2.o.a.35.1 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.95.4 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.35.14 | yes | 56 | ||
24.11 | even | 2 | 384.2.o.a.47.11 | 56 | |||
32.5 | even | 8 | 384.2.o.a.335.11 | 56 | |||
32.11 | odd | 8 | inner | 768.2.o.b.671.11 | 56 | ||
32.21 | even | 8 | 768.2.o.a.671.4 | 56 | |||
32.27 | odd | 8 | 96.2.o.a.11.14 | yes | 56 | ||
96.5 | odd | 8 | 384.2.o.a.335.1 | 56 | |||
96.11 | even | 8 | inner | 768.2.o.b.671.1 | 56 | ||
96.53 | odd | 8 | 768.2.o.a.671.14 | 56 | |||
96.59 | even | 8 | 96.2.o.a.11.1 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.1 | ✓ | 56 | 96.59 | even | 8 | ||
96.2.o.a.11.14 | yes | 56 | 32.27 | odd | 8 | ||
96.2.o.a.35.1 | yes | 56 | 8.5 | even | 2 | ||
96.2.o.a.35.14 | yes | 56 | 24.5 | odd | 2 | ||
384.2.o.a.47.1 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.47.11 | 56 | 24.11 | even | 2 | |||
384.2.o.a.335.1 | 56 | 96.5 | odd | 8 | |||
384.2.o.a.335.11 | 56 | 32.5 | even | 8 | |||
768.2.o.a.95.4 | 56 | 12.11 | even | 2 | |||
768.2.o.a.95.14 | 56 | 4.3 | odd | 2 | |||
768.2.o.a.671.4 | 56 | 32.21 | even | 8 | |||
768.2.o.a.671.14 | 56 | 96.53 | odd | 8 | |||
768.2.o.b.95.1 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.95.11 | 56 | 3.2 | odd | 2 | inner | ||
768.2.o.b.671.1 | 56 | 96.11 | even | 8 | inner | ||
768.2.o.b.671.11 | 56 | 32.11 | odd | 8 | inner |