Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(417,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.417");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 34x^{14} + 509x^{12} - 4794x^{10} + 30356x^{8} - 106386x^{6} + 288389x^{4} - 166634x^{2} + 28561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 417.12 | ||
Root | \(2.40873 - 1.69682i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.417 |
Dual form | 1216.3.g.d.417.10 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.53741 | 0.845803 | 0.422902 | − | 0.906176i | \(-0.361012\pi\) | ||||
0.422902 | + | 0.906176i | \(0.361012\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.47540i | 1.29508i | 0.762031 | + | 0.647540i | \(0.224202\pi\) | ||||
−0.762031 | + | 0.647540i | \(0.775798\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41956 | 0.202795 | 0.101397 | − | 0.994846i | \(-0.467669\pi\) | ||||
0.101397 | + | 0.994846i | \(0.467669\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.56155 | −0.284617 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.80776i | − | 0.437069i | −0.975829 | − | 0.218535i | \(-0.929872\pi\) | ||
0.975829 | − | 0.218535i | \(-0.0701277\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.8287 | −0.986827 | −0.493413 | − | 0.869795i | \(-0.664251\pi\) | ||||
−0.493413 | + | 0.869795i | \(0.664251\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.4308i | 1.09538i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.3693 | −0.845254 | −0.422627 | − | 0.906304i | \(-0.638892\pi\) | ||||
−0.422627 | + | 0.906304i | \(0.638892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.9617 | − | 8.56155i | −0.892722 | − | 0.450608i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.60201 | 0.171524 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.4401 | 0.975656 | 0.487828 | − | 0.872940i | \(-0.337789\pi\) | ||||
0.487828 | + | 0.872940i | \(0.337789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16.9309 | −0.677235 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −29.3364 | −1.08653 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.2595 | −1.00895 | −0.504474 | − | 0.863427i | \(-0.668314\pi\) | ||||
−0.504474 | + | 0.863427i | \(0.668314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.22674i | 0.297637i | 0.988865 | + | 0.148818i | \(0.0475470\pi\) | ||||
−0.988865 | + | 0.148818i | \(0.952453\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 12.1993i | − | 0.369675i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.19224i | 0.262635i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −23.6348 | −0.638778 | −0.319389 | − | 0.947624i | \(-0.603478\pi\) | ||||
−0.319389 | + | 0.947624i | \(0.603478\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −32.5518 | −0.834661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.12445i | − | 0.173767i | −0.996218 | − | 0.0868835i | \(-0.972309\pi\) | ||
0.996218 | − | 0.0868835i | \(-0.0276908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.54640i | − | 0.222009i | −0.993820 | − | 0.111005i | \(-0.964593\pi\) | ||
0.993820 | − | 0.111005i | \(-0.0354068\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 16.5871i | − | 0.368602i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.9088 | −0.232103 | −0.116052 | − | 0.993243i | \(-0.537024\pi\) | ||||
−0.116052 | + | 0.993243i | \(0.537024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −46.9848 | −0.958874 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −36.4608 | −0.714918 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 94.9825 | 1.79212 | 0.896061 | − | 0.443930i | \(-0.146416\pi\) | ||||
0.896061 | + | 0.443930i | \(0.146416\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 31.1322 | 0.566040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43.0388 | − | 21.7242i | −0.755067 | − | 0.381126i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −68.3346 | −1.15821 | −0.579107 | − | 0.815251i | \(-0.696599\pi\) | ||||
−0.579107 | + | 0.815251i | \(0.696599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51.3556i | 0.841895i | 0.907085 | + | 0.420947i | \(0.138302\pi\) | ||||
−0.907085 | + | 0.420947i | \(0.861698\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.63628 | −0.0577188 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 83.0713i | − | 1.27802i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.63667 | −0.0990547 | −0.0495274 | − | 0.998773i | \(-0.515772\pi\) | ||||
−0.0495274 | + | 0.998773i | \(0.515772\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 56.9397 | 0.825213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 44.1110i | − | 0.621281i | −0.950527 | − | 0.310641i | \(-0.899456\pi\) | ||
0.950527 | − | 0.310641i | \(-0.100544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 19.3542 | 0.265126 | 0.132563 | − | 0.991175i | \(-0.457679\pi\) | ||||
0.132563 | + | 0.991175i | \(0.457679\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −42.9606 | −0.572807 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.82492i | − | 0.0886353i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 63.7003i | − | 0.806333i | −0.915127 | − | 0.403166i | \(-0.867910\pi\) | ||
0.915127 | − | 0.403166i | \(-0.132090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51.3845 | −0.634376 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 111.970i | 1.34903i | 0.738260 | + | 0.674516i | \(0.235648\pi\) | ||||
−0.738260 | + | 0.674516i | \(0.764352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 93.0471i | − | 1.09467i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −74.2433 | −0.853372 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 60.7224i | − | 0.682274i | −0.940014 | − | 0.341137i | \(-0.889188\pi\) | ||
0.940014 | − | 0.341137i | \(-0.110812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.2112 | −0.200123 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.4120i | 0.251742i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 55.4395 | − | 109.834i | 0.583574 | − | 1.15615i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 136.669i | − | 1.40896i | −0.709723 | − | 0.704481i | \(-0.751180\pi\) | ||
0.709723 | − | 0.704481i | \(-0.248820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.3153i | 0.124397i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 97.9282i | − | 0.969586i | −0.874629 | − | 0.484793i | \(-0.838895\pi\) | ||
0.874629 | − | 0.484793i | \(-0.161105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 72.9270i | 0.708029i | 0.935240 | + | 0.354015i | \(0.115184\pi\) | ||||
−0.935240 | + | 0.354015i | \(0.884816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23.3245i | 0.222138i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −113.032 | −1.05638 | −0.528189 | − | 0.849127i | \(-0.677129\pi\) | ||||
−0.528189 | + | 0.849127i | \(0.677129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −80.5745 | −0.739215 | −0.369608 | − | 0.929188i | \(-0.620508\pi\) | ||||
−0.369608 | + | 0.929188i | \(0.620508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −59.9711 | −0.540280 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 98.1204i | − | 0.868322i | −0.900835 | − | 0.434161i | \(-0.857045\pi\) | ||
0.900835 | − | 0.434161i | \(-0.142955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 145.309i | 1.26355i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32.8615 | 0.280868 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.3981 | −0.171413 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 97.8854 | 0.808970 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 18.0776i | − | 0.146973i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 52.2509i | 0.418007i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 191.988i | 1.51171i | 0.654736 | + | 0.755857i | \(0.272780\pi\) | ||||
−0.654736 | + | 0.755857i | \(0.727220\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 24.2231i | − | 0.187776i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 161.348i | 1.23166i | 0.787879 | + | 0.615830i | \(0.211179\pi\) | ||||
−0.787879 | + | 0.615830i | \(0.788821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0782 | − | 12.1537i | −0.181039 | − | 0.0913808i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 189.965i | − | 1.40715i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −35.5227 | −0.259290 | −0.129645 | − | 0.991560i | \(-0.541384\pi\) | ||||
−0.129645 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.68466i | − | 0.0552853i | −0.999618 | − | 0.0276427i | \(-0.991200\pi\) | ||
0.999618 | − | 0.0276427i | \(-0.00880005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.6802 | −0.196314 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 61.6776i | 0.431312i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 189.467i | − | 1.30667i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −119.220 | −0.811019 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 236.205i | 1.58527i | 0.609697 | + | 0.792634i | \(0.291291\pi\) | ||||
−0.609697 | + | 0.792634i | \(0.708709\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 234.076i | 1.55017i | 0.631856 | + | 0.775086i | \(0.282294\pi\) | ||||
−0.631856 | + | 0.775086i | \(0.717706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36.8078 | 0.240574 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −59.7469 | −0.385464 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 75.7610i | 0.482554i | 0.970456 | + | 0.241277i | \(0.0775663\pi\) | ||||
−0.970456 | + | 0.241277i | \(0.922434\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 241.010 | 1.51578 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 31.8551 | 0.197858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 130.047i | 0.797836i | 0.916987 | + | 0.398918i | \(0.130614\pi\) | ||||
−0.916987 | + | 0.398918i | \(0.869386\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 78.9952 | 0.478759 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 110.970i | − | 0.664490i | −0.943193 | − | 0.332245i | \(-0.892194\pi\) | ||
0.943193 | − | 0.332245i | \(-0.107806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.42329 | −0.0261733 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.4483 | + | 21.9309i | 0.254084 | + | 0.128251i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −117.038 | −0.676520 | −0.338260 | − | 0.941053i | \(-0.609838\pi\) | ||||
−0.338260 | + | 0.941053i | \(0.609838\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.0344 | −0.137339 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −173.393 | −0.979621 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −131.419 | −0.734185 | −0.367092 | − | 0.930185i | \(-0.619647\pi\) | ||||
−0.367092 | + | 0.930185i | \(0.619647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −252.529 | −1.39519 | −0.697595 | − | 0.716492i | \(-0.745747\pi\) | ||||
−0.697595 | + | 0.716492i | \(0.745747\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 130.310i | 0.712077i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 153.045i | − | 0.827269i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 69.0843i | 0.369435i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −41.6448 | −0.220343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −112.648 | −0.589781 | −0.294890 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294890 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 68.6470i | − | 0.355684i | −0.984059 | − | 0.177842i | \(-0.943088\pi\) | ||
0.984059 | − | 0.177842i | \(-0.0569116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 210.786i | − | 1.08095i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 171.200i | − | 0.869034i | −0.900664 | − | 0.434517i | \(-0.856919\pi\) | ||
0.900664 | − | 0.434517i | \(-0.143081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 214.660 | 1.07869 | 0.539347 | − | 0.842083i | \(-0.318671\pi\) | ||||
0.539347 | + | 0.842083i | \(0.318671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.8399 | −0.0837808 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −41.5357 | −0.204609 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 46.1337 | 0.225042 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −57.4815 | −0.277688 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.1619 | + | 81.5479i | −0.196947 | + | 0.390181i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.81208 | −0.0322847 | −0.0161424 | − | 0.999870i | \(-0.505138\pi\) | ||||
−0.0161424 | + | 0.999870i | \(0.505138\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 111.928i | − | 0.525482i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 61.8168 | 0.287520 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.0979i | 0.0603591i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 49.1094 | 0.224244 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 184.340 | 0.834119 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.06815i | 0.0272115i | 0.999907 | + | 0.0136057i | \(0.00433097\pi\) | ||||
−0.999907 | + | 0.0136057i | \(0.995669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 43.3693 | 0.192753 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 191.106 | 0.841876 | 0.420938 | − | 0.907089i | \(-0.361701\pi\) | ||||
0.420938 | + | 0.907089i | \(0.361701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 325.812i | 1.42276i | 0.702807 | + | 0.711380i | \(0.251930\pi\) | ||||
−0.702807 | + | 0.711380i | \(0.748070\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 17.3176i | − | 0.0749680i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7926 | 0.0506121 | 0.0253060 | − | 0.999680i | \(-0.491944\pi\) | ||||
0.0253060 | + | 0.999680i | \(0.491944\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 70.6392i | − | 0.300592i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 161.634i | − | 0.681999i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −224.073 | −0.937544 | −0.468772 | − | 0.883319i | \(-0.655303\pi\) | ||||
−0.468772 | + | 0.883319i | \(0.655303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.77571i | 0.00736810i | 0.999993 | + | 0.00368405i | \(0.00117267\pi\) | ||||
−0.999993 | + | 0.00368405i | \(0.998827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 133.644 | 0.549976 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 304.246i | − | 1.24182i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 217.598 | + | 109.834i | 0.880962 | + | 0.444672i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 284.113i | 1.14102i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 174.747i | − | 0.696204i | −0.937457 | − | 0.348102i | \(-0.886826\pi\) | ||
0.937457 | − | 0.348102i | \(-0.113174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 107.887i | − | 0.426430i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 236.099i | − | 0.925877i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 143.618i | − | 0.558826i | −0.960171 | − | 0.279413i | \(-0.909860\pi\) | ||
0.960171 | − | 0.279413i | \(-0.0901399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −33.5510 | −0.129541 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 74.9498 | 0.287164 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −453.726 | −1.72519 | −0.862597 | − | 0.505892i | \(-0.831164\pi\) | ||||
−0.862597 | + | 0.505892i | \(0.831164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 615.050i | 2.32094i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 154.078i | − | 0.577070i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 323.434 | 1.20236 | 0.601178 | − | 0.799115i | \(-0.294698\pi\) | ||||
0.601178 | + | 0.799115i | \(0.294698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −142.536 | −0.525961 | −0.262981 | − | 0.964801i | \(-0.584706\pi\) | ||||
−0.262981 | + | 0.964801i | \(0.584706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −46.2093 | −0.169265 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 81.3996i | 0.295999i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 515.794i | 1.86207i | 0.364926 | + | 0.931036i | \(0.381094\pi\) | ||||
−0.364926 | + | 0.931036i | \(0.618906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 23.6348i | − | 0.0847124i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 218.140i | 0.776300i | 0.921596 | + | 0.388150i | \(0.126886\pi\) | ||||
−0.921596 | + | 0.388150i | \(0.873114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 244.562i | − | 0.864175i | −0.901832 | − | 0.432088i | \(-0.857777\pi\) | ||
0.901832 | − | 0.432088i | \(-0.142223\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 140.673 | − | 278.694i | 0.493589 | − | 0.977873i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 10.1136i | − | 0.0352390i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −82.5227 | −0.285546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 346.786i | − | 1.19170i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −231.610 | −0.790477 | −0.395239 | − | 0.918578i | \(-0.629338\pi\) | ||||
−0.395239 | + | 0.918578i | \(0.629338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 442.495i | − | 1.49998i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 141.042i | 0.474890i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −287.878 | −0.962804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 13.5517i | − | 0.0450223i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 248.484i | − | 0.820079i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −332.548 | −1.09032 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 100.970 | 0.328893 | 0.164446 | − | 0.986386i | \(-0.447416\pi\) | ||||
0.164446 | + | 0.986386i | \(0.447416\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 185.046i | 0.598854i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 229.402 | 0.737626 | 0.368813 | − | 0.929504i | \(-0.379764\pi\) | ||||
0.368813 | + | 0.929504i | \(0.379764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 397.363 | 1.26953 | 0.634765 | − | 0.772706i | \(-0.281097\pi\) | ||||
0.634765 | + | 0.772706i | \(0.281097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 23.5464i | − | 0.0747505i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 53.7811 | 0.169657 | 0.0848283 | − | 0.996396i | \(-0.472966\pi\) | ||||
0.0848283 | + | 0.996396i | \(0.472966\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 140.673i | 0.440980i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −286.810 | −0.893488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 243.728 | + | 123.024i | 0.754577 | + | 0.380878i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 217.202 | 0.668313 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −204.450 | −0.625231 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.4858 | −0.0470692 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 82.0573 | 0.247907 | 0.123954 | − | 0.992288i | \(-0.460443\pi\) | ||||
0.123954 | + | 0.992288i | \(0.460443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 60.5417 | 0.181807 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 42.9751i | − | 0.128284i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 342.863i | − | 1.01740i | −0.860945 | − | 0.508698i | \(-0.830127\pi\) | ||
0.860945 | − | 0.508698i | \(-0.169873\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 248.972i | − | 0.734429i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 44.3600 | 0.130088 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −136.256 | −0.397249 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 368.708i | 1.06872i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 74.3627i | 0.214302i | 0.994243 | + | 0.107151i | \(0.0341728\pi\) | ||||
−0.994243 | + | 0.107151i | \(0.965827\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 523.416i | − | 1.49976i | −0.661574 | − | 0.749880i | \(-0.730111\pi\) | ||
0.661574 | − | 0.749880i | \(-0.269889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 376.349 | 1.07222 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 355.380 | 1.00674 | 0.503371 | − | 0.864071i | \(-0.332093\pi\) | ||||
0.503371 | + | 0.864071i | \(0.332093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 285.636 | 0.804609 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −51.7584 | −0.144982 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 143.878 | 0.400776 | 0.200388 | − | 0.979717i | \(-0.435780\pi\) | ||||
0.200388 | + | 0.979717i | \(0.435780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 214.400 | + | 290.437i | 0.593905 | + | 0.804535i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 248.375 | 0.684230 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 125.326i | 0.343359i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 574.422 | 1.56518 | 0.782592 | − | 0.622535i | \(-0.213897\pi\) | ||||
0.782592 | + | 0.622535i | \(0.213897\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.2496i | 0.0494570i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 134.834 | 0.363433 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −385.555 | −1.03366 | −0.516829 | − | 0.856088i | \(-0.672888\pi\) | ||||
−0.516829 | + | 0.856088i | \(0.672888\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 132.582i | 0.353552i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 375.363 | 0.995657 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 629.962 | 1.66217 | 0.831085 | − | 0.556146i | \(-0.187720\pi\) | ||||
0.831085 | + | 0.556146i | \(0.187720\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 487.152i | 1.27861i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 445.404i | 1.16293i | 0.813570 | + | 0.581467i | \(0.197521\pi\) | ||||
−0.813570 | + | 0.581467i | \(0.802479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 44.1941 | 0.114790 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.4536i | 0.0631876i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 247.408i | − | 0.636011i | −0.948089 | − | 0.318006i | \(-0.896987\pi\) | ||
0.948089 | − | 0.318006i | \(-0.103013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −322.449 | −0.824677 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 409.405i | 1.04174i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 412.485 | 1.04427 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 84.3335i | 0.212427i | 0.994343 | + | 0.106213i | \(0.0338727\pi\) | ||||
−0.994343 | + | 0.106213i | \(0.966127\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −61.0963 | − | 30.8388i | −0.153123 | − | 0.0772902i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 342.336i | − | 0.853707i | −0.904321 | − | 0.426853i | \(-0.859622\pi\) | ||
0.904321 | − | 0.426853i | \(-0.140378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 118.367i | − | 0.293716i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 332.735i | − | 0.821569i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 113.630i | 0.279190i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 799.815i | 1.95554i | 0.209685 | + | 0.977769i | \(0.432756\pi\) | ||||
−0.209685 | + | 0.977769i | \(0.567244\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −90.1357 | −0.219308 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −97.0052 | −0.234880 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −725.049 | −1.74711 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 19.4991i | − | 0.0467605i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 461.110i | − | 1.10050i | −0.835000 | − | 0.550250i | \(-0.814532\pi\) | ||
0.835000 | − | 0.550250i | \(-0.185468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −763.462 | −1.81345 | −0.906725 | − | 0.421723i | \(-0.861425\pi\) | ||||
−0.906725 | + | 0.421723i | \(0.861425\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 27.9436 | 0.0660605 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 243.285 | 0.572435 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 72.9024i | 0.170732i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 156.501i | 0.364805i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 343.023i | − | 0.795877i | −0.917412 | − | 0.397939i | \(-0.869726\pi\) | ||
0.917412 | − | 0.397939i | \(-0.130274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 608.452i | 1.40520i | 0.711585 | + | 0.702601i | \(0.247978\pi\) | ||||
−0.711585 | + | 0.702601i | \(0.752022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 480.756i | − | 1.10519i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −380.623 | − | 192.122i | −0.870990 | − | 0.439639i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 762.770i | 1.73752i | 0.495236 | + | 0.868758i | \(0.335081\pi\) | ||||
−0.495236 | + | 0.868758i | \(0.664919\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 120.354 | 0.272912 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 333.965i | 0.753871i | 0.926239 | + | 0.376936i | \(0.123022\pi\) | ||||
−0.926239 | + | 0.376936i | \(0.876978\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 393.202 | 0.883601 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 599.349i | 1.34083i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 542.030i | − | 1.20719i | −0.797290 | − | 0.603597i | \(-0.793734\pi\) | ||
0.797290 | − | 0.603597i | \(-0.206266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.2527 | −0.0759483 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 593.947i | 1.31114i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 117.925i | − | 0.259176i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 394.110 | 0.862385 | 0.431192 | − | 0.902260i | \(-0.358093\pi\) | ||||
0.431192 | + | 0.902260i | \(0.358093\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 421.544 | 0.918396 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 545.081i | 1.18239i | 0.806530 | + | 0.591194i | \(0.201343\pi\) | ||||
−0.806530 | + | 0.591194i | \(0.798657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 571.179 | 1.23365 | 0.616824 | − | 0.787101i | \(-0.288419\pi\) | ||||
0.616824 | + | 0.787101i | \(0.288419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −151.602 | −0.326026 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 626.194i | 1.34089i | 0.741961 | + | 0.670443i | \(0.233896\pi\) | ||||
−0.741961 | + | 0.670443i | \(0.766104\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.42116 | −0.0200878 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 192.237i | 0.408146i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −45.8968 | −0.0970335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 287.177 | + | 144.955i | 0.604582 | + | 0.305167i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −243.303 | −0.510069 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 282.428 | 0.589620 | 0.294810 | − | 0.955556i | \(-0.404744\pi\) | ||||
0.294810 | + | 0.955556i | \(0.404744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 303.204 | 0.630363 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 80.8294 | 0.167349 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 884.989 | 1.82472 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 376.771i | − | 0.773658i | −0.922151 | − | 0.386829i | \(-0.873570\pi\) | ||
0.922151 | − | 0.386829i | \(-0.126430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 329.983i | 0.674813i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 778.634i | 1.58581i | 0.609343 | + | 0.792907i | \(0.291433\pi\) | ||||
−0.609343 | + | 0.792907i | \(0.708567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 420.439 | 0.852817 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −79.7468 | −0.161105 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 62.6182i | − | 0.125992i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 445.270i | − | 0.892324i | −0.894952 | − | 0.446162i | \(-0.852790\pi\) | ||
0.894952 | − | 0.446162i | \(-0.147210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 281.576i | − | 0.562028i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 662.359 | 1.31682 | 0.658408 | − | 0.752661i | \(-0.271230\pi\) | ||||
0.658408 | + | 0.752661i | \(0.271230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 634.125 | 1.25569 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2237 | −0.0221375 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −825.583 | −1.62197 | −0.810985 | − | 0.585066i | \(-0.801068\pi\) | ||||
−0.810985 | + | 0.585066i | \(0.801068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.4744 | 0.0537660 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 497.596 | + | 251.165i | 0.969972 | + | 0.489601i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −472.232 | −0.916956 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 52.4472i | 0.101445i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −296.973 | −0.572203 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 467.059i | − | 0.896466i | −0.893917 | − | 0.448233i | \(-0.852053\pi\) | ||
0.893917 | − | 0.448233i | \(-0.147947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 710.261 | 1.35805 | 0.679026 | − | 0.734115i | \(-0.262403\pi\) | ||||
0.679026 | + | 0.734115i | \(0.262403\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −60.9851 | −0.116162 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 132.582i | − | 0.251579i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.4422 | −0.0480949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 175.043 | 0.329647 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 91.3977i | 0.171478i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 731.931i | − | 1.36810i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −333.464 | −0.620976 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 225.892i | 0.419095i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 671.553i | − | 1.24132i | −0.784080 | − | 0.620659i | \(-0.786865\pi\) | ||
0.784080 | − | 0.620659i | \(-0.213135\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −640.771 | −1.18006 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 521.752i | − | 0.957344i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 642.200 | 1.17404 | 0.587020 | − | 0.809572i | \(-0.300301\pi\) | ||||
0.587020 | + | 0.809572i | \(0.300301\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 131.550i | − | 0.239618i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 496.291 | + | 250.507i | 0.900710 | + | 0.454640i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 90.4265i | − | 0.163520i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 388.337i | − | 0.699707i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 160.990i | − | 0.289030i | −0.989503 | − | 0.144515i | \(-0.953838\pi\) | ||
0.989503 | − | 0.144515i | \(-0.0461622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 122.468i | 0.219085i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 175.295i | 0.312469i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −751.993 | −1.33569 | −0.667845 | − | 0.744300i | \(-0.732783\pi\) | ||||
−0.667845 | + | 0.744300i | \(0.732783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 635.369 | 1.12455 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −72.9434 | −0.128648 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 649.303i | 1.14113i | 0.821252 | + | 0.570565i | \(0.193276\pi\) | ||||
−0.821252 | + | 0.570565i | \(0.806724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 298.371i | 0.522541i | 0.965266 | + | 0.261271i | \(0.0841415\pi\) | ||||
−0.965266 | + | 0.261271i | \(0.915858\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −285.834 | −0.498838 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −379.930 | −0.660748 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 233.216 | 0.404187 | 0.202094 | − | 0.979366i | \(-0.435226\pi\) | ||||
0.202094 | + | 0.979366i | \(0.435226\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 174.186i | − | 0.300839i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 158.948i | 0.273576i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 456.654i | − | 0.783282i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 212.792i | 0.363746i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 407.287i | − | 0.693845i | −0.937894 | − | 0.346922i | \(-0.887227\pi\) | ||
0.937894 | − | 0.346922i | \(-0.112773\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 78.9952 | − | 156.501i | 0.134117 | − | 0.265707i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 434.404i | − | 0.735032i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −520.091 | −0.877050 | −0.438525 | − | 0.898719i | \(-0.644499\pi\) | ||||
−0.438525 | + | 0.898719i | \(0.644499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 132.086i | − | 0.221994i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 544.681 | 0.912364 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 38.0428i | − | 0.0635105i | −0.999496 | − | 0.0317553i | \(-0.989890\pi\) | ||
0.999496 | − | 0.0317553i | \(-0.0101097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 194.246i | − | 0.323205i | −0.986856 | − | 0.161603i | \(-0.948334\pi\) | ||
0.986856 | − | 0.161603i | \(-0.0516663\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.0002 | 0.0281927 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 633.848i | 1.04768i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 512.263i | − | 0.843926i | −0.906613 | − | 0.421963i | \(-0.861341\pi\) | ||
0.906613 | − | 0.421963i | \(-0.138659\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −105.393 | −0.173059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 139.947 | 0.229046 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 587.471i | − | 0.958354i | −0.877718 | − | 0.479177i | \(-0.840935\pi\) | ||
0.877718 | − | 0.479177i | \(-0.159065\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 117.060 | 0.190342 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −454.626 | −0.736833 | −0.368416 | − | 0.929661i | \(-0.620100\pi\) | ||||
−0.368416 | + | 0.929661i | \(0.620100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 209.373i | − | 0.338244i | −0.985595 | − | 0.169122i | \(-0.945907\pi\) | ||
0.985595 | − | 0.169122i | \(-0.0540932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −658.311 | −1.06008 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 86.1992i | − | 0.138361i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −761.617 | −1.21859 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −104.445 | + | 206.920i | −0.166578 | + | 0.330017i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 339.616 | 0.539929 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −402.818 | −0.638380 | −0.319190 | − | 0.947691i | \(-0.603411\pi\) | ||||
−0.319190 | + | 0.947691i | \(0.603411\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.2850 | −0.0273065 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1243.20 | −1.95779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 602.757 | 0.946243 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 112.993i | 0.176827i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1104.13i | − | 1.72251i | −0.508173 | − | 0.861255i | \(-0.669679\pi\) | ||
0.508173 | − | 0.861255i | \(-0.330321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.79261i | − | 0.0121191i | −0.999982 | − | 0.00605957i | \(-0.998071\pi\) | ||
0.999982 | − | 0.00605957i | \(-0.00192883\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 156.855 | 0.243185 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −985.289 | −1.52286 | −0.761429 | − | 0.648249i | \(-0.775502\pi\) | ||||
−0.761429 | + | 0.648249i | \(0.775502\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 328.537i | 0.506220i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.2348i | 0.0510519i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 232.471i | − | 0.356004i | −0.984030 | − | 0.178002i | \(-0.943037\pi\) | ||
0.984030 | − | 0.178002i | \(-0.0569634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1044.79 | −1.59510 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −49.5767 | −0.0754592 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −688.832 | −1.04527 | −0.522634 | − | 0.852557i | \(-0.675051\pi\) | ||||
−0.522634 | + | 0.852557i | \(0.675051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 491.343 | 0.743333 | 0.371667 | − | 0.928366i | \(-0.378786\pi\) | ||||
0.371667 | + | 0.928366i | \(0.378786\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 467.747 | 0.705501 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 78.6998 | − | 155.916i | 0.118346 | − | 0.234460i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −656.586 | −0.984387 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.3974i | 0.0230155i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 246.906 | 0.367967 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 856.044i | − | 1.27198i | −0.771696 | − | 0.635991i | \(-0.780591\pi\) | ||
0.771696 | − | 0.635991i | \(-0.219409\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 496.691 | 0.735838 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −431.688 | −0.637649 | −0.318825 | − | 0.947814i | \(-0.603288\pi\) | ||||
−0.318825 | + | 0.947814i | \(0.603288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 194.010i | − | 0.285730i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 484.914 | 0.712061 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.1780 | 0.0676106 | 0.0338053 | − | 0.999428i | \(-0.489237\pi\) | ||||
0.0338053 | + | 0.999428i | \(0.489237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 230.024i | − | 0.335802i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 826.719i | 1.20338i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1218.51 | −1.76851 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 853.715i | 1.23548i | 0.786383 | + | 0.617739i | \(0.211951\pi\) | ||||
−0.786383 | + | 0.617739i | \(0.788049\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.4824i | 0.0252271i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 49.7613 | 0.0715990 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 102.373i | 0.146877i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.9227 | 0.0428078 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 114.570i | − | 0.163439i | −0.996655 | − | 0.0817193i | \(-0.973959\pi\) | ||
0.996655 | − | 0.0817193i | \(-0.0260411\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 400.886 | + | 202.350i | 0.570251 | + | 0.287838i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 179.241i | − | 0.254242i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 139.015i | − | 0.196627i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 300.162i | − | 0.423360i | −0.977339 | − | 0.211680i | \(-0.932107\pi\) | ||
0.977339 | − | 0.211680i | \(-0.0678934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 163.172i | 0.229496i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 207.049i | 0.290391i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −399.387 | −0.558584 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −568.565 | −0.792977 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 489.773 | 0.681186 | 0.340593 | − | 0.940211i | \(-0.389372\pi\) | ||||
0.340593 | + | 0.940211i | \(0.389372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 103.524i | 0.143584i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.50571i | 0.00623197i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 495.389 | 0.683295 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 113.740 | 0.156451 | 0.0782254 | − | 0.996936i | \(-0.475075\pi\) | ||||
0.0782254 | + | 0.996936i | \(0.475075\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 801.570 | 1.09955 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 137.175i | 0.187654i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 845.341i | 1.15326i | 0.817005 | + | 0.576631i | \(0.195633\pi\) | ||||
−0.817005 | + | 0.576631i | \(0.804367\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 771.996i | − | 1.05034i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.9075i | 0.0432938i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1162.20i | − | 1.57266i | −0.617805 | − | 0.786331i | \(-0.711978\pi\) | ||
0.617805 | − | 0.786331i | \(-0.288022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 552.134 | + | 278.694i | 0.745120 | + | 0.376105i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 834.312i | 1.12290i | 0.827512 | + | 0.561448i | \(0.189756\pi\) | ||||
−0.827512 | + | 0.561448i | \(0.810244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1529.52 | −2.05305 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 286.816i | − | 0.383958i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −160.457 | −0.214228 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 46.3827i | − | 0.0617612i | −0.999523 | − | 0.0308806i | \(-0.990169\pi\) | ||
0.999523 | − | 0.0308806i | \(-0.00983117\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 443.405i | − | 0.588851i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1515.74 | −2.00760 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.3077i | 0.0479626i | 0.999712 | + | 0.0239813i | \(0.00763422\pi\) | ||||
−0.999712 | + | 0.0239813i | \(0.992366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 273.753i | − | 0.360675i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −415.212 | −0.545614 | −0.272807 | − | 0.962069i | \(-0.587952\pi\) | ||||
−0.272807 | + | 0.962069i | \(0.587952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −114.380 | −0.149909 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 238.345i | 0.311562i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 876.648 | 1.14296 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −153.051 | −0.199026 | −0.0995130 | − | 0.995036i | \(-0.531729\pi\) | ||||
−0.0995130 | + | 0.995036i | \(0.531729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 364.419i | − | 0.472657i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 187.001 | 0.241916 | 0.120958 | − | 0.992658i | \(-0.461403\pi\) | ||||
0.120958 | + | 0.992658i | \(0.461403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 156.217i | − | 0.201570i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −85.1327 | −0.109566 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −60.9963 | + | 120.843i | −0.0783008 | + | 0.155126i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −212.075 | −0.271543 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 858.368 | 1.09626 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −490.583 | −0.624947 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −942.496 | −1.19758 | −0.598790 | − | 0.800906i | \(-0.704352\pi\) | ||||
−0.598790 | + | 0.800906i | \(0.704352\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1151.29 | −1.45917 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 139.288i | − | 0.176091i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 658.828i | − | 0.830804i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1560.63i | 1.96306i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1285.59 | −1.61304 | −0.806518 | − | 0.591210i | \(-0.798651\pi\) | ||||
−0.806518 | + | 0.591210i | \(0.798651\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 156.753 | 0.196186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 155.544i | 0.194187i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 93.0502i | − | 0.115878i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 206.275i | 0.256242i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 820.684 | 1.01696 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −690.576 | −0.853616 | −0.426808 | − | 0.904342i | \(-0.640362\pi\) | ||||
−0.426808 | + | 0.904342i | \(0.640362\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.7829 | 0.0379567 | 0.0189783 | − | 0.999820i | \(-0.493959\pi\) | ||||
0.0189783 | + | 0.999820i | \(0.493959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −361.671 | −0.444860 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −842.109 | −1.03326 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −81.7320 | + | 161.923i | −0.100039 | + | 0.198193i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 46.6489 | 0.0569584 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 240.639i | 0.293104i | 0.989203 | + | 0.146552i | \(0.0468176\pi\) | ||||
−0.989203 | + | 0.146552i | \(0.953182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −259.890 | −0.315784 | −0.157892 | − | 0.987456i | \(-0.550470\pi\) | ||||
−0.157892 | + | 0.987456i | \(0.550470\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 206.544i | 0.250357i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1062.36 | −1.28460 | −0.642299 | − | 0.766454i | \(-0.722019\pi\) | ||||
−0.642299 | + | 0.766454i | \(0.722019\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 275.721 | 0.332594 | 0.166297 | − | 0.986076i | \(-0.446819\pi\) | ||||
0.166297 | + | 0.986076i | \(0.446819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1308.78i | 1.57495i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 675.140 | 0.810492 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 718.575 | 0.860568 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 270.679i | − | 0.323392i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 411.407i | 0.490354i | 0.969478 | + | 0.245177i | \(0.0788460\pi\) | ||||
−0.969478 | + | 0.245177i | \(0.921154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.1183 | 0.0179766 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 553.511i | 0.656597i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 28.6426i | − | 0.0338966i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 138.954 | 0.164055 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 620.553i | − | 0.730922i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −530.367 | −0.623227 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 386.887i | 0.453560i | 0.973946 | + | 0.226780i | \(0.0728199\pi\) | ||||
−0.973946 | + | 0.226780i | \(0.927180\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −142.011 | + | 281.346i | −0.166095 | + | 0.329059i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1524.48i | − | 1.77886i | −0.457071 | − | 0.889430i | \(-0.651102\pi\) | ||
0.457071 | − | 0.889430i | \(-0.348898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1392.04i | − | 1.62054i | −0.586058 | − | 0.810269i | \(-0.699321\pi\) | ||
0.586058 | − | 0.810269i | \(-0.300679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 25.6623i | − | 0.0298053i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 142.446i | − | 0.165060i | −0.996589 | − | 0.0825298i | \(-0.973700\pi\) | ||
0.996589 | − | 0.0825298i | \(-0.0263000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 757.868i | − | 0.876148i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −209.394 | −0.241516 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −306.256 | −0.352423 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 85.1401 | 0.0977498 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 350.086i | 0.401014i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 74.1733i | 0.0847695i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 937.883 | 1.06942 | 0.534711 | − | 0.845035i | \(-0.320420\pi\) | ||||
0.534711 | + | 0.845035i | \(0.320420\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −587.689 | −0.668588 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 109.435 | 0.124216 | 0.0621082 | − | 0.998069i | \(-0.480218\pi\) | ||||
0.0621082 | + | 0.998069i | \(0.480218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1486.09i | 1.68301i | 0.540253 | + | 0.841503i | \(0.318329\pi\) | ||||
−0.540253 | + | 0.841503i | \(0.681671\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 1122.79i | − | 1.26869i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1714.62i | 1.93305i | 0.256568 | + | 0.966526i | \(0.417408\pi\) | ||||
−0.256568 | + | 0.966526i | \(0.582592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 272.538i | 0.306567i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 247.044i | 0.277266i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 185.033 | + | 93.3967i | 0.207204 | + | 0.104588i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 850.992i | − | 0.950829i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −730.465 | −0.814342 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 269.970i | − | 0.300300i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1364.83 | −1.51480 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 34.3862i | − | 0.0380800i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1635.23i | − | 1.80688i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1409.71 | −1.55425 | −0.777127 | − | 0.629344i | \(-0.783324\pi\) | ||||
−0.777127 | + | 0.629344i | \(0.783324\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 250.848i | 0.275961i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 812.560i | 0.891943i | 0.895047 | + | 0.445971i | \(0.147142\pi\) | ||||
−0.895047 | + | 0.445971i | \(0.852858\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 538.324 | 0.589621 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −843.811 | −0.922198 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 229.043i | 0.249774i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1772.39 | −1.92861 | −0.964306 | − | 0.264792i | \(-0.914697\pi\) | ||||
−0.964306 | + | 0.264792i | \(0.914697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 256.203 | 0.278179 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 565.888i | 0.613097i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 400.157 | 0.432602 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 186.806i | − | 0.201517i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −936.486 | −1.00806 | −0.504029 | − | 0.863687i | \(-0.668150\pi\) | ||||
−0.504029 | + | 0.863687i | \(0.668150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 796.944 | + | 402.263i | 0.856008 | + | 0.432077i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 582.086 | 0.623886 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −447.349 | −0.478448 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1234.01 | −1.31698 | −0.658488 | − | 0.752592i | \(-0.728803\pi\) | ||||
−0.658488 | + | 0.752592i | \(0.728803\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1008.27 | 1.07377 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −327.036 | −0.347541 | −0.173770 | − | 0.984786i | \(-0.555595\pi\) | ||||
−0.173770 | + | 0.984786i | \(0.555595\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 159.873i | − | 0.169537i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 269.667i | − | 0.285362i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1750.53i | 1.84850i | 0.381792 | + | 0.924248i | \(0.375307\pi\) | ||||
−0.381792 | + | 0.924248i | \(0.624693\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −248.290 | −0.261633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 136.465 | 0.143496 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1438.62i | − | 1.50957i | −0.655974 | − | 0.754784i | \(-0.727742\pi\) | ||
0.655974 | − | 0.754784i | \(-0.272258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 729.442i | − | 0.763814i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 356.944i | 0.372983i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −50.4267 | −0.0525826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 875.867 | 0.911412 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 289.539 | 0.300663 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 444.517 | 0.460640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1277.65 | 1.32126 | 0.660628 | − | 0.750714i | \(-0.270290\pi\) | ||||
0.660628 | + | 0.750714i | \(0.270290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 618.438 | + | 312.161i | 0.638223 | + | 0.322148i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −588.097 | −0.605662 | −0.302831 | − | 0.953044i | \(-0.597932\pi\) | ||||
−0.302831 | + | 0.953044i | \(0.597932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.9088i | − | 0.0112116i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 551.130 | 0.565261 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1234.30i | − | 1.26336i | −0.775231 | − | 0.631678i | \(-0.782367\pi\) | ||
0.775231 | − | 0.631678i | \(-0.217633\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −291.939 | −0.298201 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 206.396 | 0.210393 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1642.58i | − | 1.67098i | −0.549502 | − | 0.835492i | \(-0.685183\pi\) | ||
0.549502 | − | 0.835492i | \(-0.314817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1108.59 | 1.12547 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39.2938 | −0.0398113 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 214.222i | − | 0.216605i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1636.51i | − | 1.65137i | −0.564130 | − | 0.825686i | \(-0.690788\pi\) | ||
0.564130 | − | 0.825686i | \(-0.309212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 208.213 | 0.209681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1390.01i | 1.39700i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 457.307i | 0.458683i | 0.973346 | + | 0.229342i | \(0.0736573\pi\) | ||||
−0.973346 | + | 0.229342i | \(0.926343\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 693.359 | 0.694053 |
(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 | 1216.3.g.d.417.12 | yes | 16 | |
4.3 | odd | 2 | inner | 1216.3.g.d.417.7 | yes | 16 | |
8.3 | odd | 2 | inner | 1216.3.g.d.417.9 | yes | 16 | |
8.5 | even | 2 | inner | 1216.3.g.d.417.6 | yes | 16 | |
19.18 | odd | 2 | inner | 1216.3.g.d.417.8 | yes | 16 | |
76.75 | even | 2 | inner | 1216.3.g.d.417.11 | yes | 16 | |
152.37 | odd | 2 | inner | 1216.3.g.d.417.10 | yes | 16 | |
152.75 | even | 2 | inner | 1216.3.g.d.417.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.3.g.d.417.5 | ✓ | 16 | 152.75 | even | 2 | inner | |
1216.3.g.d.417.6 | yes | 16 | 8.5 | even | 2 | inner | |
1216.3.g.d.417.7 | yes | 16 | 4.3 | odd | 2 | inner | |
1216.3.g.d.417.8 | yes | 16 | 19.18 | odd | 2 | inner | |
1216.3.g.d.417.9 | yes | 16 | 8.3 | odd | 2 | inner | |
1216.3.g.d.417.10 | yes | 16 | 152.37 | odd | 2 | inner | |
1216.3.g.d.417.11 | yes | 16 | 76.75 | even | 2 | inner | |
1216.3.g.d.417.12 | yes | 16 | 1.1 | even | 1 | trivial |