Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(557,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.p (of order \(6\), degree \(2\), 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: | \(16.0218395444\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-35})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} - 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 557.2 | ||
Root | \(2.81174 - 1.04601i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.557 |
Dual form | 588.3.p.d.569.2 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 2.31174 | + | 1.91203i | 0.770579 | + | 0.637344i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.12348 | − | 2.95804i | 1.02470 | − | 0.591608i | 0.109235 | − | 0.994016i | \(-0.465160\pi\) |
0.915460 | + | 0.402408i | \(0.131827\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.68826 | + | 8.84024i | 0.187585 | + | 0.982248i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12348 | − | 2.95804i | −0.465770 | − | 0.268913i | 0.248697 | − | 0.968581i | \(-0.419998\pi\) |
−0.714468 | + | 0.699669i | \(0.753331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 0.461538 | 0.230769 | − | 0.973009i | \(-0.425876\pi\) | ||||
0.230769 | + | 0.973009i | \(0.425876\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 17.5000 | + | 2.95804i | 1.16667 | + | 0.197203i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.12348 | + | 2.95804i | 0.301381 | + | 0.174002i | 0.643063 | − | 0.765813i | \(-0.277663\pi\) |
−0.341682 | + | 0.939816i | \(0.610997\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.5000 | + | 19.9186i | 0.605263 | + | 1.04835i | 0.992010 | + | 0.126161i | \(0.0402654\pi\) |
−0.386747 | + | 0.922186i | \(0.626401\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.8643 | − | 20.7063i | 1.55932 | − | 0.900273i | 0.561996 | − | 0.827140i | \(-0.310033\pi\) |
0.997322 | − | 0.0731333i | \(-0.0232999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | − | 8.66025i | 0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.0000 | + | 23.6643i | −0.481481 | + | 0.876456i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 47.3286i | 1.63202i | 0.578036 | + | 0.816011i | \(0.303819\pi\) | ||||
−0.578036 | + | 0.816011i | \(0.696181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.5000 | − | 33.7750i | 0.629032 | − | 1.08952i | −0.358714 | − | 0.933448i | \(-0.616785\pi\) |
0.987746 | − | 0.156068i | \(-0.0498820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.18826 | − | 16.6345i | −0.187523 | − | 0.504075i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −23.5000 | − | 40.7032i | −0.635135 | − | 1.10009i | −0.986486 | − | 0.163843i | \(-0.947611\pi\) |
0.351351 | − | 0.936244i | \(-0.385722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.8704 | + | 11.4722i | 0.355652 | + | 0.294159i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.0000 | −0.511628 | −0.255814 | − | 0.966726i | \(-0.582343\pi\) | ||||
−0.255814 | + | 0.966726i | \(0.582343\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 34.7995 | + | 40.2988i | 0.773323 | + | 0.895529i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46.1113 | − | 26.6224i | 0.981091 | − | 0.566433i | 0.0784917 | − | 0.996915i | \(-0.474990\pi\) |
0.902599 | + | 0.430482i | \(0.141656\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.18826 | + | 16.6345i | 0.121338 | + | 0.326166i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −46.1113 | − | 26.6224i | −0.870024 | − | 0.502309i | −0.00266787 | − | 0.999996i | \(-0.500849\pi\) |
−0.867356 | + | 0.497688i | \(0.834183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −35.0000 | −0.636364 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.5000 | + | 68.0349i | −0.201754 | + | 1.19360i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 87.0991 | + | 50.2867i | 1.47626 | + | 0.852317i | 0.999641 | − | 0.0267957i | \(-0.00853036\pi\) |
0.476615 | + | 0.879112i | \(0.341864\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.5000 | − | 70.1481i | −0.663934 | − | 1.14997i | −0.979573 | − | 0.201089i | \(-0.935552\pi\) |
0.315639 | − | 0.948879i | \(-0.397781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 30.7409 | − | 17.7482i | 0.472936 | − | 0.273050i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5000 | + | 26.8468i | −0.231343 | + | 0.400698i | −0.958204 | − | 0.286087i | \(-0.907645\pi\) |
0.726860 | + | 0.686785i | \(0.240979\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 122.500 | + | 20.7063i | 1.77536 | + | 0.300091i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 94.6573i | 1.33320i | 0.745415 | + | 0.666601i | \(0.232251\pi\) | ||||
−0.745415 | + | 0.666601i | \(0.767749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.50000 | + | 14.7224i | −0.116438 | + | 0.201677i | −0.918354 | − | 0.395760i | \(-0.870481\pi\) |
0.801915 | + | 0.597438i | \(0.203814\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 28.1174 | − | 10.4601i | 0.374898 | − | 0.139468i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | + | 7.79423i | 0.0569620 | + | 0.0986611i | 0.893100 | − | 0.449858i | \(-0.148525\pi\) |
−0.836138 | + | 0.548519i | \(0.815192\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −75.2995 | + | 29.8493i | −0.929624 | + | 0.368510i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 47.3286i | 0.570225i | 0.958494 | + | 0.285112i | \(0.0920309\pi\) | ||||
−0.958494 | + | 0.285112i | \(0.907969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.0000 | 0.411765 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −90.4939 | + | 109.411i | −1.04016 | + | 1.25760i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −76.8521 | + | 44.3706i | −0.863507 | + | 0.498546i | −0.865185 | − | 0.501453i | \(-0.832799\pi\) |
0.00167806 | + | 0.999999i | \(0.499466\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 109.658 | − | 40.7943i | 1.17912 | − | 0.438648i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 117.840 | + | 68.0349i | 1.24042 | + | 0.716157i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −82.0000 | −0.845361 | −0.422680 | − | 0.906279i | \(-0.638911\pi\) | ||||
−0.422680 | + | 0.906279i | \(0.638911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.5000 | − | 50.2867i | 0.176768 | − | 0.507946i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −35.8643 | − | 20.7063i | −0.355092 | − | 0.205013i | 0.311833 | − | 0.950137i | \(-0.399057\pi\) |
−0.666926 | + | 0.745124i | \(0.732390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5000 | + | 19.9186i | 0.111650 | + | 0.193384i | 0.916436 | − | 0.400182i | \(-0.131053\pi\) |
−0.804785 | + | 0.593566i | \(0.797720\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −46.1113 | + | 26.6224i | −0.430947 | + | 0.248807i | −0.699750 | − | 0.714388i | \(-0.746705\pi\) |
0.268803 | + | 0.963195i | \(0.413372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68.5000 | − | 118.645i | 0.628440 | − | 1.08849i | −0.359424 | − | 0.933174i | \(-0.617027\pi\) |
0.987865 | − | 0.155316i | \(-0.0496397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.5000 | − | 139.028i | 0.211712 | − | 1.25250i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 94.6573i | − | 0.837675i | −0.908061 | − | 0.418838i | \(-0.862438\pi\) | ||
0.908061 | − | 0.418838i | \(-0.137562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 122.500 | − | 212.176i | 1.06522 | − | 1.84501i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.1296 | + | 53.0414i | 0.0865776 | + | 0.453345i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −43.0000 | − | 74.4782i | −0.355372 | − | 0.615522i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 88.7412i | 0.709930i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −78.0000 | −0.614173 | −0.307087 | − | 0.951682i | \(-0.599354\pi\) | ||||
−0.307087 | + | 0.951682i | \(0.599354\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −50.8582 | − | 42.0647i | −0.394250 | − | 0.326083i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 128.087 | − | 73.9510i | 0.977762 | − | 0.564511i | 0.0761686 | − | 0.997095i | \(-0.475731\pi\) |
0.901594 | + | 0.432584i | \(0.142398\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.39482 | + | 159.698i | 0.0251468 | + | 1.18295i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −87.0991 | − | 50.2867i | −0.635760 | − | 0.367056i | 0.147220 | − | 0.989104i | \(-0.452968\pi\) |
−0.782979 | + | 0.622048i | \(0.786301\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −106.000 | −0.762590 | −0.381295 | − | 0.924453i | \(-0.624522\pi\) | ||||
−0.381295 | + | 0.924453i | \(0.624522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 157.500 | + | 26.6224i | 1.11702 | + | 0.188811i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.7409 | − | 17.7482i | −0.214971 | − | 0.124114i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 140.000 | + | 242.487i | 0.965517 | + | 1.67232i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −169.075 | + | 97.6153i | −1.13473 | + | 0.655136i | −0.945120 | − | 0.326723i | \(-0.894055\pi\) |
−0.189609 | + | 0.981860i | \(0.560722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.5000 | − | 35.5070i | 0.135762 | − | 0.235146i | −0.790127 | − | 0.612944i | \(-0.789985\pi\) |
0.925888 | + | 0.377798i | \(0.123319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.5000 | + | 50.2867i | −0.114379 | + | 0.328671i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 230.727i | − | 1.48856i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 83.5000 | − | 144.626i | 0.531847 | − | 0.921186i | −0.467462 | − | 0.884013i | \(-0.654831\pi\) |
0.999309 | − | 0.0371729i | \(-0.0118352\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −55.6944 | − | 149.710i | −0.350279 | − | 0.941573i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −131.500 | − | 227.765i | −0.806748 | − | 1.39733i | −0.915104 | − | 0.403217i | \(-0.867892\pi\) |
0.108356 | − | 0.994112i | \(-0.465441\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −80.9108 | − | 66.9211i | −0.490369 | − | 0.405583i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 189.315i | − | 1.13362i | −0.823849 | − | 0.566810i | \(-0.808177\pi\) | ||
0.823849 | − | 0.566810i | \(-0.191823\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −133.000 | −0.786982 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −156.670 | + | 135.291i | −0.916199 | + | 0.791173i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −240.803 | + | 139.028i | −1.39193 | + | 0.803629i | −0.993528 | − | 0.113583i | \(-0.963767\pi\) |
−0.398398 | + | 0.917212i | \(0.630434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 105.200 | + | 282.786i | 0.594353 | + | 1.59766i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 76.8521 | + | 44.3706i | 0.429342 | + | 0.247880i | 0.699066 | − | 0.715057i | \(-0.253599\pi\) |
−0.269725 | + | 0.962938i | \(0.586933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.0331492 | 0.0165746 | − | 0.999863i | \(-0.494724\pi\) | ||||
0.0165746 | + | 0.999863i | \(0.494724\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 40.5000 | − | 239.601i | 0.221311 | − | 1.30930i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −240.803 | − | 139.028i | −1.30164 | − | 0.751502i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5000 | − | 30.3109i | −0.0935829 | − | 0.162090i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −46.1113 | + | 26.6224i | −0.241420 | + | 0.139384i | −0.615829 | − | 0.787880i | \(-0.711179\pi\) |
0.374409 | + | 0.927264i | \(0.377846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −71.5000 | + | 123.842i | −0.370466 | + | 0.641666i | −0.989637 | − | 0.143590i | \(-0.954135\pi\) |
0.619171 | + | 0.785256i | \(0.287469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 105.000 | + | 17.7482i | 0.538462 | + | 0.0910166i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 47.3286i | − | 0.240247i | −0.992759 | − | 0.120123i | \(-0.961671\pi\) | ||
0.992759 | − | 0.120123i | \(-0.0383290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −84.5000 | + | 146.358i | −0.424623 | + | 0.735469i | −0.996385 | − | 0.0849507i | \(-0.972927\pi\) |
0.571762 | + | 0.820420i | \(0.306260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −87.1639 | + | 32.4262i | −0.433651 | + | 0.161325i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 243.597 | + | 282.091i | 1.17680 | + | 1.36276i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 136.070i | − | 0.651052i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −166.000 | −0.786730 | −0.393365 | − | 0.919382i | \(-0.628689\pi\) | ||||
−0.393365 | + | 0.919382i | \(0.628689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −180.988 | + | 218.823i | −0.849708 | + | 1.02734i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −112.716 | + | 65.0769i | −0.524263 | + | 0.302683i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −47.7995 | + | 17.7821i | −0.218263 | + | 0.0811969i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.7409 | + | 17.7482i | 0.139099 | + | 0.0803088i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 142.000 | 0.636771 | 0.318386 | − | 0.947961i | \(-0.396859\pi\) | ||||
0.318386 | + | 0.947961i | \(0.396859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 85.0000 | + | 29.5804i | 0.377778 | + | 0.131468i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −76.8521 | − | 44.3706i | −0.338556 | − | 0.195465i | 0.321077 | − | 0.947053i | \(-0.395955\pi\) |
−0.659633 | + | 0.751588i | \(0.729288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −128.500 | − | 222.569i | −0.561135 | − | 0.971915i | −0.997398 | − | 0.0720955i | \(-0.977031\pi\) |
0.436262 | − | 0.899820i | \(-0.356302\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 158.828 | − | 91.6992i | 0.681664 | − | 0.393559i | −0.118818 | − | 0.992916i | \(-0.537910\pi\) |
0.800482 | + | 0.599357i | \(0.204577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 157.500 | − | 272.798i | 0.670213 | − | 1.16084i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.50000 | + | 26.6224i | −0.0189873 | + | 0.112331i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 283.972i | − | 1.18817i | −0.804404 | − | 0.594083i | \(-0.797515\pi\) | ||
0.804404 | − | 0.594083i | \(-0.202485\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | + | 0.866025i | −0.00207469 | + | 0.00359347i | −0.867061 | − | 0.498202i | \(-0.833994\pi\) |
0.864986 | + | 0.501796i | \(0.167327\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −231.146 | − | 74.9715i | −0.951216 | − | 0.308525i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 69.0000 | + | 119.512i | 0.279352 | + | 0.483852i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −90.4939 | + | 109.411i | −0.363429 | + | 0.439403i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 141.986i | − | 0.565681i | −0.959167 | − | 0.282840i | \(-0.908723\pi\) | ||
0.959167 | − | 0.282840i | \(-0.0912767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −245.000 | −0.968379 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 80.9108 | + | 66.9211i | 0.317297 | + | 0.262436i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 169.075 | − | 97.6153i | 0.657878 | − | 0.379826i | −0.133590 | − | 0.991037i | \(-0.542650\pi\) |
0.791468 | + | 0.611211i | \(0.209317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −418.396 | + | 79.9032i | −1.60305 | + | 0.306142i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −46.1113 | − | 26.6224i | −0.175328 | − | 0.101226i | 0.409768 | − | 0.912190i | \(-0.365610\pi\) |
−0.585096 | + | 0.810964i | \(0.698943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −315.000 | −1.18868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −262.500 | − | 44.3706i | −0.983146 | − | 0.166182i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −35.8643 | − | 20.7063i | −0.133325 | − | 0.0769750i | 0.431854 | − | 0.901943i | \(-0.357860\pi\) |
−0.565179 | + | 0.824968i | \(0.691193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 43.5000 | + | 75.3442i | 0.160517 | + | 0.278023i | 0.935054 | − | 0.354505i | \(-0.115351\pi\) |
−0.774537 | + | 0.632528i | \(0.782017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −51.2348 | + | 29.5804i | −0.186308 | + | 0.107565i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −155.500 | + | 269.334i | −0.561372 | + | 0.972325i | 0.436005 | + | 0.899944i | \(0.356393\pi\) |
−0.997377 | + | 0.0723804i | \(0.976940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 331.500 | + | 115.364i | 1.18817 | + | 0.413489i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 378.629i | 1.34743i | 0.738989 | + | 0.673717i | \(0.235303\pi\) | ||||
−0.738989 | + | 0.673717i | \(0.764697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 159.500 | − | 276.262i | 0.563604 | − | 0.976191i | −0.433574 | − | 0.901118i | \(-0.642748\pi\) |
0.997178 | − | 0.0750731i | \(-0.0239190\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 142.330 | + | 382.593i | 0.499404 | + | 1.34243i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −127.000 | − | 219.970i | −0.439446 | − | 0.761143i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −189.562 | − | 156.787i | −0.651417 | − | 0.538786i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 141.986i | 0.484594i | 0.970202 | + | 0.242297i | \(0.0779008\pi\) | ||||
−0.970202 | + | 0.242297i | \(0.922099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 595.000 | 2.01695 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 136.605 | − | 82.7890i | 0.459950 | − | 0.278751i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 215.186 | − | 124.238i | 0.719686 | − | 0.415511i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.3178 | − | 116.441i | −0.142963 | − | 0.384295i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −415.002 | − | 239.601i | −1.36066 | − | 0.785578i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −442.000 | −1.43974 | −0.719870 | − | 0.694109i | \(-0.755798\pi\) | ||||
−0.719870 | + | 0.694109i | \(0.755798\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5000 | + | 68.0349i | −0.0372168 | + | 0.220178i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 210.062 | + | 121.280i | 0.675442 | + | 0.389967i | 0.798136 | − | 0.602478i | \(-0.205820\pi\) |
−0.122693 | + | 0.992445i | \(0.539153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −128.500 | − | 222.569i | −0.410543 | − | 0.711082i | 0.584406 | − | 0.811461i | \(-0.301328\pi\) |
−0.994949 | + | 0.100380i | \(0.967994\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 76.8521 | − | 44.3706i | 0.242436 | − | 0.139970i | −0.373860 | − | 0.927485i | \(-0.621966\pi\) |
0.616296 | + | 0.787515i | \(0.288633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 140.000 | − | 242.487i | 0.438871 | − | 0.760148i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −157.500 | − | 26.6224i | −0.490654 | − | 0.0829357i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 136.070i | 0.421269i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.0000 | − | 51.9615i | 0.0923077 | − | 0.159882i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 385.208 | − | 143.303i | 1.17801 | − | 0.438235i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 60.5000 | + | 104.789i | 0.182779 | + | 0.316583i | 0.942826 | − | 0.333285i | \(-0.108157\pi\) |
−0.760047 | + | 0.649869i | \(0.774824\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 320.152 | − | 276.463i | 0.961416 | − | 0.830220i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 183.398i | 0.547458i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −78.0000 | −0.231454 | −0.115727 | − | 0.993281i | \(-0.536920\pi\) | ||||
−0.115727 | + | 0.993281i | \(0.536920\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 180.988 | − | 218.823i | 0.533887 | − | 0.645495i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −199.816 | + | 115.364i | −0.585969 | + | 0.338310i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 688.876 | − | 256.272i | 1.99674 | − | 0.742817i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 568.706 | + | 328.342i | 1.63892 | + | 0.946232i | 0.981205 | + | 0.192966i | \(0.0618106\pi\) |
0.657716 | + | 0.753266i | \(0.271523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 422.000 | 1.20917 | 0.604585 | − | 0.796541i | \(-0.293339\pi\) | ||||
0.604585 | + | 0.796541i | \(0.293339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −78.0000 | + | 141.986i | −0.222222 | + | 0.404518i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 169.075 | + | 97.6153i | 0.478965 | + | 0.276531i | 0.719985 | − | 0.693990i | \(-0.244149\pi\) |
−0.241020 | + | 0.970520i | \(0.577482\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 280.000 | + | 484.974i | 0.788732 | + | 1.36612i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 117.840 | − | 68.0349i | 0.328245 | − | 0.189512i | −0.326817 | − | 0.945088i | \(-0.605976\pi\) |
0.655062 | + | 0.755575i | \(0.272643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −84.0000 | + | 145.492i | −0.232687 | + | 0.403026i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 43.0000 | − | 254.391i | 0.118457 | − | 0.700803i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 100.573i | 0.275543i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.5000 | + | 63.2199i | −0.0994550 | + | 0.172261i | −0.911459 | − | 0.411390i | \(-0.865043\pi\) |
0.812004 | + | 0.583652i | \(0.198377\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 200.500 | + | 347.276i | 0.537534 | + | 0.931035i | 0.999036 | + | 0.0438965i | \(0.0139772\pi\) |
−0.461503 | + | 0.887139i | \(0.652689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −169.676 | + | 205.146i | −0.452470 | + | 0.547057i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 283.972i | 0.753241i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 538.000 | 1.41953 | 0.709763 | − | 0.704441i | \(-0.248802\pi\) | ||||
0.709763 | + | 0.704441i | \(0.248802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −180.316 | − | 149.139i | −0.473269 | − | 0.391440i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 210.062 | − | 121.280i | 0.548466 | − | 0.316657i | −0.200037 | − | 0.979788i | \(-0.564106\pi\) |
0.748503 | + | 0.663131i | \(0.230773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −37.1418 | − | 194.485i | −0.0959736 | − | 0.502546i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.8643 | + | 20.7063i | 0.0921962 | + | 0.0532295i | 0.545389 | − | 0.838183i | \(-0.316382\pi\) |
−0.453193 | + | 0.891412i | \(0.649715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 245.000 | 0.626598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 437.500 | + | 73.9510i | 1.11323 | + | 0.188170i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 46.1113 | + | 26.6224i | 0.116737 | + | 0.0673984i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5000 | − | 28.5788i | −0.0415617 | − | 0.0719870i | 0.844496 | − | 0.535561i | \(-0.179900\pi\) |
−0.886058 | + | 0.463574i | \(0.846567\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 322.779 | − | 186.357i | 0.804935 | − | 0.464729i | −0.0402588 | − | 0.999189i | \(-0.512818\pi\) |
0.845194 | + | 0.534460i | \(0.179485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 117.000 | − | 202.650i | 0.290323 | − | 0.502853i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −297.500 | + | 375.671i | −0.734568 | + | 0.927583i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 278.056i | 0.683184i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −288.500 | + | 499.697i | −0.705379 | + | 1.22175i | 0.261176 | + | 0.965291i | \(0.415890\pi\) |
−0.966555 | + | 0.256461i | \(0.917444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −105.200 | − | 282.786i | −0.255962 | − | 0.688044i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 140.000 | + | 242.487i | 0.337349 | + | 0.584306i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −245.044 | − | 202.675i | −0.587636 | − | 0.486032i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 141.986i | − | 0.338869i | −0.985541 | − | 0.169434i | \(-0.945806\pi\) | ||
0.985541 | − | 0.169434i | \(-0.0541940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −246.000 | −0.584323 | −0.292162 | − | 0.956369i | \(-0.594374\pi\) | ||||
−0.292162 | + | 0.956369i | \(0.594374\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 313.196 | + | 362.689i | 0.740416 | + | 0.857421i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 51.2348 | − | 29.5804i | 0.120552 | − | 0.0696009i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.1296 | − | 99.8068i | −0.0865491 | − | 0.232650i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −537.965 | − | 310.594i | −1.24818 | − | 0.720636i | −0.277433 | − | 0.960745i | \(-0.589483\pi\) |
−0.970746 | + | 0.240109i | \(0.922817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 622.000 | 1.43649 | 0.718245 | − | 0.695790i | \(-0.244946\pi\) | ||||
0.718245 | + | 0.695790i | \(0.244946\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −140.000 | + | 828.251i | −0.321839 | + | 1.90403i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 824.880 | + | 476.244i | 1.88760 | + | 1.08980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −124.500 | − | 215.640i | −0.283599 | − | 0.491208i | 0.688669 | − | 0.725075i | \(-0.258195\pi\) |
−0.972268 | + | 0.233867i | \(0.924862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −210.062 | + | 121.280i | −0.474182 | + | 0.273769i | −0.717989 | − | 0.696055i | \(-0.754937\pi\) |
0.243807 | + | 0.969824i | \(0.421604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −262.500 | + | 454.663i | −0.589888 | + | 1.02172i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −577.500 | − | 97.6153i | −1.29195 | − | 0.218379i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 473.286i | 1.05409i | 0.849837 | + | 0.527045i | \(0.176700\pi\) | ||||
−0.849837 | + | 0.527045i | \(0.823300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 115.281 | − | 42.8863i | 0.254484 | − | 0.0946717i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −303.500 | − | 525.677i | −0.664114 | − | 1.15028i | −0.979525 | − | 0.201324i | \(-0.935476\pi\) |
0.315411 | − | 0.948955i | \(-0.397858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −136.605 | + | 82.7890i | −0.297615 | + | 0.180368i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 520.615i | 1.12932i | 0.825325 | + | 0.564658i | \(0.190992\pi\) | ||||
−0.825325 | + | 0.564658i | \(0.809008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −302.000 | −0.652268 | −0.326134 | − | 0.945324i | \(-0.605746\pi\) | ||||
−0.326134 | + | 0.945324i | \(0.605746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 441.158 | − | 533.381i | 0.948726 | − | 1.14705i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 128.087 | − | 73.9510i | 0.274276 | − | 0.158353i | −0.356553 | − | 0.934275i | \(-0.616048\pi\) |
0.630829 | + | 0.775922i | \(0.282715\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 469.560 | − | 174.683i | 0.996943 | − | 0.370877i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 112.716 | + | 65.0769i | 0.238301 | + | 0.137583i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 230.000 | 0.484211 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 157.500 | − | 452.580i | 0.330189 | − | 0.948805i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 128.087 | + | 73.9510i | 0.267405 | + | 0.154386i | 0.627708 | − | 0.778449i | \(-0.283993\pi\) |
−0.360303 | + | 0.932835i | \(0.617327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −141.000 | − | 244.219i | −0.293139 | − | 0.507732i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −420.125 | + | 242.559i | −0.866237 | + | 0.500122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −323.500 | + | 560.318i | −0.664271 | + | 1.15055i | 0.315211 | + | 0.949021i | \(0.397925\pi\) |
−0.979482 | + | 0.201530i | \(0.935409\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 131.500 | − | 777.964i | 0.268916 | − | 1.59093i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 141.986i | 0.289177i | 0.989492 | + | 0.144589i | \(0.0461858\pi\) | ||||
−0.989492 | + | 0.144589i | \(0.953814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −140.000 | + | 242.487i | −0.283976 | + | 0.491860i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −59.0892 | − | 309.408i | −0.119372 | − | 0.625067i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −51.5000 | − | 89.2006i | −0.103206 | − | 0.178759i | 0.809798 | − | 0.586709i | \(-0.199577\pi\) |
−0.913004 | + | 0.407951i | \(0.866244\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 361.976 | − | 437.646i | 0.722506 | − | 0.873544i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 283.972i | 0.564556i | 0.959333 | + | 0.282278i | \(0.0910901\pi\) | ||||
−0.959333 | + | 0.282278i | \(0.908910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −245.000 | −0.485149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −307.461 | − | 254.300i | −0.606432 | − | 0.501579i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 169.075 | − | 97.6153i | 0.332170 | − | 0.191779i | −0.324634 | − | 0.945840i | \(-0.605241\pi\) |
0.656804 | + | 0.754061i | \(0.271908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −620.860 | + | 13.1981i | −1.21025 | + | 0.0257272i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 117.840 | + | 68.0349i | 0.228815 | + | 0.132107i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −315.000 | −0.609284 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −822.500 | − | 139.028i | −1.58478 | − | 0.267876i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −322.779 | − | 186.357i | −0.619537 | − | 0.357690i | 0.157152 | − | 0.987575i | \(-0.449769\pi\) |
−0.776689 | + | 0.629884i | \(0.783102\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.5000 | + | 19.9186i | 0.0219885 | + | 0.0380852i | 0.876810 | − | 0.480836i | \(-0.159667\pi\) |
−0.854822 | + | 0.518922i | \(0.826334\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 199.816 | − | 115.364i | 0.379157 | − | 0.218906i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 593.000 | − | 1027.11i | 1.12098 | − | 1.94160i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −297.500 | + | 854.874i | −0.560264 | + | 1.60993i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −157.500 | + | 272.798i | −0.294393 | + | 0.509903i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 92.8239 | + | 249.517i | 0.172856 | + | 0.464650i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 256.500 | + | 444.271i | 0.474122 | + | 0.821203i | 0.999561 | − | 0.0296279i | \(-0.00943223\pi\) |
−0.525439 | + | 0.850831i | \(0.676099\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8704 | + | 11.4722i | 0.0255441 | + | 0.0211274i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 810.503i | − | 1.48716i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −54.0000 | −0.0987203 | −0.0493601 | − | 0.998781i | \(-0.515718\pi\) | ||||
−0.0493601 | + | 0.998781i | \(0.515718\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 551.751 | − | 476.458i | 1.00501 | − | 0.867865i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −942.719 | + | 544.279i | −1.71092 | + | 0.987803i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −290.848 | − | 781.820i | −0.524051 | − | 1.40868i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 773.645 | + | 446.664i | 1.38895 | + | 0.801910i | 0.993197 | − | 0.116447i | \(-0.0371505\pi\) |
0.395752 | + | 0.918357i | \(0.370484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −132.000 | −0.236136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.5000 | − | 103.531i | 0.0311943 | − | 0.184548i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −486.730 | − | 281.014i | −0.864530 | − | 0.499136i | 0.000996920 | − | 1.00000i | \(-0.499683\pi\) |
−0.865527 | + | 0.500863i | \(0.833016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −280.000 | − | 484.974i | −0.495575 | − | 0.858361i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 568.706 | − | 328.342i | 0.999483 | − | 0.577052i | 0.0913876 | − | 0.995815i | \(-0.470870\pi\) |
0.908095 | + | 0.418764i | \(0.137536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −463.500 | + | 802.806i | −0.811734 | + | 1.40596i | 0.0999158 | + | 0.994996i | \(0.468143\pi\) |
−0.911650 | + | 0.410968i | \(0.865191\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −157.500 | − | 26.6224i | −0.274869 | − | 0.0464614i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 414.126i | − | 0.720218i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −176.500 | + | 305.707i | −0.305893 | + | 0.529821i | −0.977460 | − | 0.211122i | \(-0.932288\pi\) |
0.671567 | + | 0.740944i | \(0.265621\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −402.078 | + | 149.579i | −0.694436 | + | 0.258340i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 157.500 | + | 272.798i | 0.270154 | + | 0.467921i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 208.797 | + | 241.793i | 0.356918 | + | 0.413321i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 236.643i | − | 0.403140i | −0.979474 | − | 0.201570i | \(-0.935396\pi\) | ||
0.979474 | − | 0.201570i | \(-0.0646044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 897.000 | 1.52292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 90.4939 | − | 109.411i | 0.153120 | − | 0.185129i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 660.928 | − | 381.587i | 1.11455 | − | 0.643486i | 0.174546 | − | 0.984649i | \(-0.444154\pi\) |
0.940004 | + | 0.341163i | \(0.110821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −475.184 | + | 176.775i | −0.795953 | + | 0.296106i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −537.965 | − | 310.594i | −0.898105 | − | 0.518521i | −0.0215201 | − | 0.999768i | \(-0.506851\pi\) |
−0.876585 | + | 0.481247i | \(0.840184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 958.000 | 1.59401 | 0.797005 | − | 0.603973i | \(-0.206416\pi\) | ||||
0.797005 | + | 0.603973i | \(0.206416\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −263.500 | − | 91.6992i | −0.436982 | − | 0.152072i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −440.619 | − | 254.391i | −0.728296 | − | 0.420482i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 403.500 | + | 698.883i | 0.664745 | + | 1.15137i | 0.979354 | + | 0.202150i | \(0.0647930\pi\) |
−0.314610 | + | 0.949221i | \(0.601874\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 276.668 | − | 159.734i | 0.452811 | − | 0.261431i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −259.500 | + | 449.467i | −0.423328 | + | 0.733225i | −0.996263 | − | 0.0863756i | \(-0.972472\pi\) |
0.572935 | + | 0.819601i | \(0.305805\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 757.258i | − | 1.22732i | −0.789569 | − | 0.613661i | \(-0.789696\pi\) | ||
0.789569 | − | 0.613661i | \(-0.210304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −344.500 | + | 596.692i | −0.556543 | + | 0.963960i | 0.441239 | + | 0.897390i | \(0.354539\pi\) |
−0.997782 | + | 0.0665707i | \(0.978794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.7637 | + | 1117.89i | 0.0382669 | + | 1.80014i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 387.500 | + | 671.170i | 0.620000 | + | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 260.170 | − | 314.558i | 0.414944 | − | 0.501687i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 278.056i | − | 0.442060i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 674.000 | 1.06815 | 0.534073 | − | 0.845438i | \(-0.320661\pi\) | ||||
0.534073 | + | 0.845438i | \(0.320661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −383.748 | − | 317.397i | −0.606238 | − | 0.501418i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −399.631 | + | 230.727i | −0.629340 | + | 0.363350i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −836.793 | + | 159.806i | −1.30953 | + | 0.250088i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −742.904 | − | 428.916i | −1.15898 | − | 0.669135i | −0.207918 | − | 0.978146i | \(-0.566669\pi\) |
−0.951059 | + | 0.309011i | \(0.900002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −218.000 | −0.339036 | −0.169518 | − | 0.985527i | \(-0.554221\pi\) | ||||
−0.169518 | + | 0.985527i | \(0.554221\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −385.000 | − | 65.0769i | −0.596899 | − | 0.100894i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −445.742 | − | 257.349i | −0.688937 | − | 0.397758i | 0.114277 | − | 0.993449i | \(-0.463545\pi\) |
−0.803214 | + | 0.595691i | \(0.796878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −297.500 | − | 515.285i | −0.458398 | − | 0.793968i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −906.855 | + | 523.573i | −1.38875 | + | 0.801796i | −0.993175 | − | 0.116636i | \(-0.962789\pi\) |
−0.395577 | + | 0.918433i | \(0.629456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 437.500 | − | 757.772i | 0.667939 | − | 1.15690i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −144.500 | − | 50.2867i | −0.219939 | − | 0.0765398i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 615.272i | − | 0.933645i | −0.884351 | − | 0.466823i | \(-0.845399\pi\) | ||
0.884351 | − | 0.466823i | \(-0.154601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −260.500 | + | 451.199i | −0.394100 | + | 0.682601i | −0.992986 | − | 0.118233i | \(-0.962277\pi\) |
0.598886 | + | 0.800834i | \(0.295610\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.1296 | + | 99.8068i | 0.0560024 | + | 0.150538i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 980.000 | + | 1697.41i | 1.46927 | + | 2.54484i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 328.267 | + | 271.509i | 0.490683 | + | 0.405843i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 479.202i | 0.714162i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 818.000 | 1.21545 | 0.607727 | − | 0.794146i | \(-0.292082\pi\) | ||||
0.607727 | + | 0.794146i | \(0.292082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 139.939 | + | 230.905i | 0.207317 | + | 0.342081i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 660.928 | − | 381.587i | 0.976260 | − | 0.563644i | 0.0751214 | − | 0.997174i | \(-0.476066\pi\) |
0.901139 | + | 0.433530i | \(0.142732\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −92.8239 | − | 249.517i | −0.136305 | − | 0.366398i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −169.075 | − | 97.6153i | −0.247547 | − | 0.142921i | 0.371093 | − | 0.928596i | \(-0.378983\pi\) |
−0.618641 | + | 0.785674i | \(0.712316\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −595.000 | −0.868613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 128.500 | − | 760.216i | 0.187045 | − | 1.10657i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −276.668 | − | 159.734i | −0.401550 | − | 0.231835i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 179.500 | + | 310.903i | 0.259768 | + | 0.449932i | 0.966180 | − | 0.257869i | \(-0.0830204\pi\) |
−0.706411 | + | 0.707802i | \(0.749687\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −543.088 | + | 313.552i | −0.781422 | + | 0.451154i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 542.500 | + | 91.6992i | 0.776109 | + | 0.131186i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 804.587i | − | 1.14777i | −0.818936 | − | 0.573885i | \(-0.805436\pi\) | ||
0.818936 | − | 0.573885i | \(-0.194564\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 540.500 | − | 936.173i | 0.768848 | − | 1.33168i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 885.697 | − | 329.492i | 1.25631 | − | 0.467365i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −215.500 | − | 373.257i | −0.303949 | − | 0.526455i | 0.673078 | − | 0.739572i | \(-0.264972\pi\) |
−0.977027 | + | 0.213116i | \(0.931639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −61.3056 | + | 52.9398i | −0.0862245 | + | 0.0744582i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1615.09i | − | 2.26520i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −210.000 | −0.293706 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 542.963 | − | 656.468i | 0.757271 | − | 0.915577i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −199.816 | + | 115.364i | −0.277908 | + | 0.160450i | −0.632476 | − | 0.774580i | \(-0.717961\pi\) |
0.354568 | + | 0.935030i | \(0.384628\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.81174 | + | 1.04601i | −0.00388899 | + | 0.00144676i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 409.878 | + | 236.643i | 0.565349 | + | 0.326404i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 734.000 | 1.00963 | 0.504814 | − | 0.863228i | \(-0.331561\pi\) | ||||
0.504814 | + | 0.863228i | \(0.331561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −391.000 | − | 615.272i | −0.536351 | − | 0.843995i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −112.716 | − | 65.0769i | −0.154195 | − | 0.0890245i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 151.500 | + | 262.406i | 0.206685 | + | 0.357989i | 0.950668 | − | 0.310209i | \(-0.100399\pi\) |
−0.743983 | + | 0.668198i | \(0.767066\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 158.828 | − | 91.6992i | 0.215506 | − | 0.124422i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −295.500 | + | 511.821i | −0.399865 | + | 0.692586i | −0.993709 | − | 0.111994i | \(-0.964276\pi\) |
0.593844 | + | 0.804580i | \(0.297610\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −69.0000 | + | 408.210i | −0.0931174 | + | 0.550890i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 851.915i | 1.14659i | 0.819349 | + | 0.573294i | \(0.194335\pi\) | ||||
−0.819349 | + | 0.573294i | \(0.805665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −577.500 | + | 1000.26i | −0.775168 | + | 1.34263i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −418.396 | + | 79.9032i | −0.560102 | + | 0.106965i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −499.500 | − | 865.159i | −0.665113 | − | 1.15201i | −0.979255 | − | 0.202634i | \(-0.935050\pi\) |
0.314141 | − | 0.949376i | \(-0.398283\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 271.482 | − | 328.234i | 0.360533 | − | 0.435902i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 242.559i | − | 0.321271i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1398.00 | −1.84676 | −0.923382 | − | 0.383883i | \(-0.874587\pi\) | ||||
−0.923382 | + | 0.383883i | \(0.874587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −566.376 | − | 468.448i | −0.746213 | − | 0.617191i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1142.54 | + | 659.643i | −1.50136 | + | 0.866811i | −0.501361 | + | 0.865238i | \(0.667167\pi\) |
−0.999999 | + | 0.00157261i | \(0.999499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 59.0892 | + | 309.408i | 0.0772408 | + | 0.404455i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 522.594 | + | 301.720i | 0.681349 | + | 0.393377i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −946.000 | −1.23017 | −0.615085 | − | 0.788461i | \(-0.710878\pi\) | ||||
−0.615085 | + | 0.788461i | \(0.710878\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 577.500 | + | 97.6153i | 0.749027 | + | 0.126609i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 455.989 | + | 263.266i | 0.589896 | + | 0.340576i | 0.765056 | − | 0.643963i | \(-0.222711\pi\) |
−0.175161 | + | 0.984540i | \(0.556044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −195.000 | − | 337.750i | −0.251613 | − | 0.435806i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 280.000 | − | 484.974i | 0.358515 | − | 0.620966i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1120.00 | − | 615.272i | −1.43040 | − | 0.785788i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 987.985i | − | 1.25858i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 223.500 | − | 387.113i | 0.283990 | − | 0.491885i | −0.688374 | − | 0.725356i | \(-0.741675\pi\) |
0.972364 | + | 0.233471i | \(0.0750085\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −55.6944 | − | 149.710i | −0.0705885 | − | 0.189747i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −243.000 | − | 420.888i | −0.306431 | − | 0.530755i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −728.197 | − | 602.290i | −0.915972 | − | 0.757598i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1277.87i | 1.60335i | 0.597757 | + | 0.801677i | \(0.296059\pi\) | ||||
−0.597757 | + | 0.801677i | \(0.703941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 315.000 | 0.394243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −521.993 | − | 604.482i | −0.651677 | − | 0.754659i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 87.0991 | − | 50.2867i | 0.108467 | − | 0.0626235i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.3178 | − | 116.441i | −0.0536776 | − | 0.144289i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1142.54 | + | 659.643i | 1.41228 | + | 0.815381i | 0.995603 | − | 0.0936737i | \(-0.0298611\pi\) |
0.416678 | + | 0.909054i | \(0.363194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 86.0000 | 0.106042 | 0.0530210 | − | 0.998593i | \(-0.483115\pi\) | ||||
0.0530210 | + | 0.998593i | \(0.483115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.5000 | + | 257.349i | −0.0535055 | + | 0.316543i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1347.47 | − | 777.964i | −1.65334 | − | 0.954558i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −253.000 | − | 438.209i | −0.309670 | − | 0.536363i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −333.026 | + | 192.273i | −0.405634 | + | 0.234193i | −0.688912 | − | 0.724845i | \(-0.741911\pi\) |
0.283278 | + | 0.959038i | \(0.408578\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 188.500 | − | 326.492i | 0.229040 | − | 0.396709i | −0.728484 | − | 0.685063i | \(-0.759775\pi\) |
0.957524 | + | 0.288354i | \(0.0931080\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −175.000 | − | 29.5804i | −0.212121 | − | 0.0358550i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 141.986i | − | 0.171688i | −0.996309 | − | 0.0858440i | \(-0.972641\pi\) | ||
0.996309 | − | 0.0858440i | \(-0.0273587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 75.5000 | − | 130.770i | 0.0910736 | − | 0.157744i | −0.816890 | − | 0.576794i | \(-0.804303\pi\) |
0.907963 | + | 0.419050i | \(0.137637\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −874.450 | + | 325.308i | −1.05229 | + | 0.391466i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −560.000 | − | 969.948i | −0.670659 | − | 1.16161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 545.762 | + | 900.529i | 0.652046 | + | 1.07590i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 473.286i | 0.564108i | 0.959399 | + | 0.282054i | \(0.0910157\pi\) | ||||
−0.959399 | + | 0.282054i | \(0.908984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1399.00 | −1.66350 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −723.951 | + | 875.291i | −0.858780 | + | 1.03831i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −681.422 | + | 393.419i | −0.806417 | + | 0.465585i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 896.944 | − | 333.676i | 1.05647 | − | 0.393023i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1685.62 | − | 973.195i | −1.98076 | − | 1.14359i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1462.00 | 1.71395 | 0.856975 | − | 0.515357i | \(-0.172341\pi\) | ||||
0.856975 | + | 0.515357i | \(0.172341\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −402.500 | + | 1156.59i | −0.470760 | + | 1.35274i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 169.075 | + | 97.6153i | 0.197287 | + | 0.113904i | 0.595389 | − | 0.803437i | \(-0.296998\pi\) |
−0.398103 | + | 0.917341i | \(0.630331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 491.500 | + | 851.303i | 0.572177 | + | 0.991040i | 0.996342 | + | 0.0854547i | \(0.0272343\pi\) |
−0.424165 | + | 0.905585i | \(0.639432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −128.087 | + | 73.9510i | −0.148420 | + | 0.0856906i | −0.572371 | − | 0.819995i | \(-0.693976\pi\) |
0.423951 | + | 0.905685i | \(0.360643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −822.500 | + | 1424.61i | −0.950867 | + | 1.64695i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 127.000 | − | 751.342i | 0.146482 | − | 0.866600i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 53.2447i | − | 0.0612713i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −93.0000 | + | 161.081i | −0.106774 | + | 0.184938i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −138.438 | − | 724.899i | −0.158577 | − | 0.830354i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 176.500 | + | 305.707i | 0.201254 | + | 0.348583i | 0.948933 | − | 0.315478i | \(-0.102165\pi\) |
−0.747679 | + | 0.664061i | \(0.768832\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −271.482 | + | 328.234i | −0.308853 | + | 0.373418i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 314.000 | 0.355606 | 0.177803 | − | 0.984066i | \(-0.443101\pi\) | ||||
0.177803 | + | 0.984066i | \(0.443101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1375.48 | + | 1137.66i | 1.55422 | + | 1.28549i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 537.965 | − | 310.594i | 0.606499 | − | 0.350163i | −0.165095 | − | 0.986278i | \(-0.552793\pi\) |
0.771594 | + | 0.636115i | \(0.219460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 474.091 | + | 69.8070i | 0.532088 | + | 0.0783468i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1060.56 | + | 612.314i | 1.18764 | + | 0.685682i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 525.000 | 0.586592 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 735.000 | + | 124.238i | 0.819398 | + | 0.138504i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1598.52 | + | 922.908i | 1.77811 | + | 1.02659i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −157.500 | − | 272.798i | −0.174806 | − | 0.302772i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.7409 | − | 17.7482i | 0.0339678 | − | 0.0196113i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 376.500 | − | 652.117i | 0.415105 | − | 0.718983i | −0.580335 | − | 0.814378i | \(-0.697078\pi\) |
0.995439 | + | 0.0953956i | \(0.0304116\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 122.500 | − | 352.007i | 0.134763 | − | 0.387246i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1703.83i | 1.87029i | 0.354270 | + | 0.935143i | \(0.384729\pi\) | ||||
−0.354270 | + | 0.935143i | \(0.615271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 140.000 | − | 242.487i | 0.153341 | − | 0.265594i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −501.249 | − | 1347.39i | −0.547813 | − | 1.47256i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 284.500 | + | 492.768i | 0.309576 | + | 0.536201i | 0.978270 | − | 0.207337i | \(-0.0664797\pi\) |
−0.668694 | + | 0.743538i | \(0.733146\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1021.79 | − | 845.118i | −1.10943 | − | 0.917610i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 567.944i | 0.615324i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −470.000 | −0.508108 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −156.670 | + | 135.291i | −0.169008 | + | 0.145944i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1398.71 | − | 807.545i | 1.50561 | − | 0.869263i | 0.505628 | − | 0.862752i | \(-0.331261\pi\) |
0.999979 | − | 0.00651097i | \(-0.00207252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 253.719 | + | 682.013i | 0.271939 | + | 0.730989i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −179.322 | − | 103.531i | −0.191788 | − | 0.110729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −722.000 | −0.770544 | −0.385272 | − | 0.922803i | \(-0.625892\pi\) | ||||
−0.385272 | + | 0.922803i | \(0.625892\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 128.500 | − | 760.216i | 0.136848 | − | 0.809602i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 455.989 | + | 263.266i | 0.484579 | + | 0.279772i | 0.722323 | − | 0.691556i | \(-0.243074\pi\) |
−0.237743 | + | 0.971328i | \(0.576408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −128.087 | + | 73.9510i | −0.135255 | + | 0.0780898i | −0.566101 | − | 0.824336i | \(-0.691549\pi\) |
0.430845 | + | 0.902426i | \(0.358215\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51.0000 | + | 88.3346i | −0.0537408 | + | 0.0930818i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 262.500 | + | 44.3706i | 0.276025 | + | 0.0466568i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 378.629i | 0.397302i | 0.980070 | + | 0.198651i | \(0.0636561\pi\) | ||||
−0.980070 | + | 0.198651i | \(0.936344\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −157.500 | + | 272.798i | −0.164921 | + | 0.285652i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 787.287 | − | 292.882i | 0.822661 | − | 0.306042i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −280.000 | − | 484.974i | −0.291363 | − | 0.504656i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −313.196 | − | 362.689i | −0.325229 | − | 0.376624i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 845.999i | 0.876683i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 482.000 | 0.498449 | 0.249224 | − | 0.968446i | \(-0.419824\pi\) | ||||
0.249224 | + | 0.968446i | \(0.419824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −260.170 | + | 314.558i | −0.268493 | + | 0.324621i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −199.816 | + | 115.364i | −0.205783 | + | 0.118809i | −0.599350 | − | 0.800487i | \(-0.704574\pi\) |
0.393567 | + | 0.919296i | \(0.371241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 168.704 | − | 62.7604i | 0.173030 | − | 0.0643697i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −169.075 | − | 97.6153i | −0.173055 | − | 0.0999133i | 0.410971 | − | 0.911649i | \(-0.365190\pi\) |
−0.584026 | + | 0.811735i | \(0.698523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 525.000 | 0.536261 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1164.50 | + | 405.251i | 1.18705 | + | 0.413100i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1275.75 | + | 736.552i | 1.29781 | + | 0.749290i | 0.980025 | − | 0.198874i | \(-0.0637283\pi\) |
0.317783 | + | 0.948163i | \(0.397062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −140.000 | − | 242.487i | −0.142132 | − | 0.246180i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −789.015 | + | 455.538i | −0.797791 | + | 0.460605i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 180.500 | − | 312.635i | 0.182139 | − | 0.315474i | −0.760470 | − | 0.649374i | \(-0.775031\pi\) |
0.942609 | + | 0.333899i | \(0.108364\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −60.5000 | + | 357.923i | −0.0609265 | + | 0.360446i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 999.817i | 1.00484i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5000 | + | 63.2199i | −0.0366098 | + | 0.0634101i | −0.883750 | − | 0.467960i | \(-0.844989\pi\) |
0.847140 | + | 0.531370i | \(0.178323\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1268.71 | − | 26.9700i | 1.26998 | − | 0.0269970i |
(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 | 588.3.p.d.557.2 | 4 | ||
3.2 | odd | 2 | inner | 588.3.p.d.557.1 | 4 | ||
7.2 | even | 3 | inner | 588.3.p.d.569.1 | 4 | ||
7.3 | odd | 6 | 588.3.c.e.197.2 | 2 | |||
7.4 | even | 3 | 588.3.c.f.197.1 | 2 | |||
7.5 | odd | 6 | 84.3.p.c.65.2 | yes | 4 | ||
7.6 | odd | 2 | 84.3.p.c.53.1 | ✓ | 4 | ||
21.2 | odd | 6 | inner | 588.3.p.d.569.2 | 4 | ||
21.5 | even | 6 | 84.3.p.c.65.1 | yes | 4 | ||
21.11 | odd | 6 | 588.3.c.f.197.2 | 2 | |||
21.17 | even | 6 | 588.3.c.e.197.1 | 2 | |||
21.20 | even | 2 | 84.3.p.c.53.2 | yes | 4 | ||
28.19 | even | 6 | 336.3.bn.d.65.1 | 4 | |||
28.27 | even | 2 | 336.3.bn.d.305.2 | 4 | |||
84.47 | odd | 6 | 336.3.bn.d.65.2 | 4 | |||
84.83 | odd | 2 | 336.3.bn.d.305.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.3.p.c.53.1 | ✓ | 4 | 7.6 | odd | 2 | ||
84.3.p.c.53.2 | yes | 4 | 21.20 | even | 2 | ||
84.3.p.c.65.1 | yes | 4 | 21.5 | even | 6 | ||
84.3.p.c.65.2 | yes | 4 | 7.5 | odd | 6 | ||
336.3.bn.d.65.1 | 4 | 28.19 | even | 6 | |||
336.3.bn.d.65.2 | 4 | 84.47 | odd | 6 | |||
336.3.bn.d.305.1 | 4 | 84.83 | odd | 2 | |||
336.3.bn.d.305.2 | 4 | 28.27 | even | 2 | |||
588.3.c.e.197.1 | 2 | 21.17 | even | 6 | |||
588.3.c.e.197.2 | 2 | 7.3 | odd | 6 | |||
588.3.c.f.197.1 | 2 | 7.4 | even | 3 | |||
588.3.c.f.197.2 | 2 | 21.11 | odd | 6 | |||
588.3.p.d.557.1 | 4 | 3.2 | odd | 2 | inner | ||
588.3.p.d.557.2 | 4 | 1.1 | even | 1 | trivial | ||
588.3.p.d.569.1 | 4 | 7.2 | even | 3 | inner | ||
588.3.p.d.569.2 | 4 | 21.2 | odd | 6 | inner |