Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(289,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.s (of order \(3\), degree \(2\), 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: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1445900625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 77x^{4} + 36x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.3 | ||
Root | \(-1.46040 + 2.52950i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.865 |
Dual form | 2016.2.s.x.289.3 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.342371 | + | 0.593004i | 0.153113 | + | 0.265199i | 0.932370 | − | 0.361505i | \(-0.117737\pi\) |
−0.779257 | + | 0.626704i | \(0.784404\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80278 | − | 1.93649i | −0.681385 | − | 0.731925i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.76556 | + | 3.05805i | −0.532338 | + | 0.922036i | 0.466949 | + | 0.884284i | \(0.345353\pi\) |
−0.999287 | + | 0.0377519i | \(0.987980\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.53113 | −0.702009 | −0.351004 | − | 0.936374i | \(-0.614160\pi\) | ||||
−0.351004 | + | 0.936374i | \(0.614160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607 | − | 3.87298i | 0.542326 | − | 0.939336i | −0.456444 | − | 0.889752i | \(-0.650877\pi\) |
0.998770 | − | 0.0495842i | \(-0.0157896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.46040 | + | 2.52950i | 0.335040 | + | 0.580306i | 0.983492 | − | 0.180949i | \(-0.0579169\pi\) |
−0.648453 | + | 0.761255i | \(0.724584\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | + | 1.73205i | 0.208514 | + | 0.361158i | 0.951247 | − | 0.308431i | \(-0.0998038\pi\) |
−0.742732 | + | 0.669588i | \(0.766471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.26556 | − | 3.92407i | 0.453113 | − | 0.784815i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.52636 | 1.21191 | 0.605957 | − | 0.795497i | \(-0.292790\pi\) | ||||
0.605957 | + | 0.795497i | \(0.292790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.433292 | + | 0.750484i | −0.0778216 | + | 0.134791i | −0.902310 | − | 0.431088i | \(-0.858130\pi\) |
0.824488 | + | 0.565879i | \(0.191463\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.531129 | − | 1.73205i | 0.0897772 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.26556 | − | 2.19202i | −0.208058 | − | 0.360366i | 0.743045 | − | 0.669241i | \(-0.233381\pi\) |
−0.951103 | + | 0.308875i | \(0.900047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6832 | 1.82462 | 0.912308 | − | 0.409505i | \(-0.134299\pi\) | ||||
0.912308 | + | 0.409505i | \(0.134299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.39295 | 1.12741 | 0.563707 | − | 0.825975i | \(-0.309375\pi\) | ||||
0.563707 | + | 0.825975i | \(0.309375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.53113 | − | 4.38404i | −0.369203 | − | 0.639479i | 0.620238 | − | 0.784414i | \(-0.287036\pi\) |
−0.989441 | + | 0.144935i | \(0.953703\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 6.98212i | −0.0714286 | + | 0.997446i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.12977 | − | 7.15296i | 0.567267 | − | 0.982535i | −0.429568 | − | 0.903035i | \(-0.641334\pi\) |
0.996835 | − | 0.0795005i | \(-0.0253325\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.41791 | −0.326031 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.76556 | − | 8.25420i | 0.620424 | − | 1.07461i | −0.368983 | − | 0.929436i | \(-0.620294\pi\) |
0.989407 | − | 0.145169i | \(-0.0463727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.53113 | + | 4.38404i | 0.324078 | + | 0.561319i | 0.981325 | − | 0.192356i | \(-0.0616127\pi\) |
−0.657247 | + | 0.753675i | \(0.728279\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.866585 | − | 1.50097i | −0.107487 | − | 0.186172i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.82989 | + | 4.90151i | −0.345726 | + | 0.598815i | −0.985485 | − | 0.169760i | \(-0.945701\pi\) |
0.639760 | + | 0.768575i | \(0.279034\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.06226 | 1.07549 | 0.537746 | − | 0.843107i | \(-0.319276\pi\) | ||||
0.537746 | + | 0.843107i | \(0.319276\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.26556 | − | 2.19202i | 0.148123 | − | 0.256557i | −0.782411 | − | 0.622763i | \(-0.786010\pi\) |
0.930534 | + | 0.366206i | \(0.119343\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.10480 | − | 2.09397i | 1.03759 | − | 0.238630i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.09307 | − | 10.5535i | −0.685524 | − | 1.18736i | −0.973272 | − | 0.229656i | \(-0.926240\pi\) |
0.287748 | − | 0.957706i | \(-0.407093\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.53113 | −1.04618 | −0.523089 | − | 0.852278i | \(-0.675220\pi\) | ||||
−0.523089 | + | 0.852278i | \(0.675220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.06226 | 0.332148 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.05422 | + | 3.55802i | 0.217747 | + | 0.377150i | 0.954119 | − | 0.299428i | \(-0.0967958\pi\) |
−0.736372 | + | 0.676577i | \(0.763462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.56306 | + | 4.90151i | 0.478338 | + | 0.513818i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | + | 1.73205i | −0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.53113 | −0.967740 | −0.483870 | − | 0.875140i | \(-0.660769\pi\) | ||||
−0.483870 | + | 0.875140i | \(0.660769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.15688 | − | 8.93197i | 0.513129 | − | 0.888765i | −0.486756 | − | 0.873538i | \(-0.661820\pi\) |
0.999884 | − | 0.0152264i | \(-0.00484691\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.69647 | − | 6.40248i | −0.364224 | − | 0.630855i | 0.624427 | − | 0.781083i | \(-0.285333\pi\) |
−0.988651 | + | 0.150228i | \(0.951999\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.23444 | + | 5.60221i | 0.312685 | + | 0.541586i | 0.978943 | − | 0.204136i | \(-0.0654384\pi\) |
−0.666258 | + | 0.745721i | \(0.732105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.734436 | + | 1.27208i | −0.0703462 | + | 0.121843i | −0.899053 | − | 0.437840i | \(-0.855744\pi\) |
0.828707 | + | 0.559683i | \(0.189077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7859 | 1.39094 | 0.695470 | − | 0.718555i | \(-0.255196\pi\) | ||||
0.695470 | + | 0.718555i | \(0.255196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.684742 | + | 1.18601i | −0.0638525 | + | 0.110596i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.5311 | + | 2.65199i | −1.05706 | + | 0.243108i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.734436 | − | 1.27208i | −0.0667669 | − | 0.115644i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.52636 | 0.583735 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6525 | −1.38893 | −0.694466 | − | 0.719525i | \(-0.744359\pi\) | ||||
−0.694466 | + | 0.719525i | \(0.744359\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.29669 | + | 12.6382i | 0.637515 | + | 1.10421i | 0.985976 | + | 0.166885i | \(0.0533710\pi\) |
−0.348461 | + | 0.937323i | \(0.613296\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.26556 | − | 7.38817i | 0.196449 | − | 0.640636i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.52636 | − | 11.3040i | 0.557585 | − | 0.965765i | −0.440113 | − | 0.897943i | \(-0.645062\pi\) |
0.997697 | − | 0.0678224i | \(-0.0216051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.4457 | 1.73418 | 0.867089 | − | 0.498152i | \(-0.165988\pi\) | ||||
0.867089 | + | 0.498152i | \(0.165988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.46887 | − | 7.74031i | 0.373706 | − | 0.647277i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.23444 | + | 3.87016i | 0.185560 | + | 0.321399i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.52636 | + | 11.3040i | 0.534660 | + | 0.926059i | 0.999180 | + | 0.0404959i | \(0.0128938\pi\) |
−0.464519 | + | 0.885563i | \(0.653773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.26318 | − | 5.65199i | 0.265554 | − | 0.459953i | −0.702155 | − | 0.712024i | \(-0.747779\pi\) |
0.967709 | + | 0.252072i | \(0.0811119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.593387 | −0.0476620 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53113 | + | 4.38404i | −0.202006 | + | 0.349885i | −0.949175 | − | 0.314750i | \(-0.898079\pi\) |
0.747169 | + | 0.664635i | \(0.231413\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.55133 | − | 5.05899i | 0.122262 | − | 0.398704i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.25953 | + | 14.3059i | 0.646936 | + | 1.12053i | 0.983851 | + | 0.178991i | \(0.0572834\pi\) |
−0.336914 | + | 0.941535i | \(0.609383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.59339 | −0.507184 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.60555 | − | 6.24500i | −0.274125 | − | 0.474798i | 0.695789 | − | 0.718246i | \(-0.255055\pi\) |
−0.969914 | + | 0.243448i | \(0.921722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.6832 | + | 2.68698i | −0.883170 | + | 0.203116i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.46887 | + | 2.54416i | −0.109789 | + | 0.190159i | −0.915685 | − | 0.401898i | \(-0.868351\pi\) |
0.805896 | + | 0.592057i | \(0.201684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5311 | 1.22875 | 0.614375 | − | 0.789015i | \(-0.289408\pi\) | ||||
0.614375 | + | 0.789015i | \(0.289408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.866585 | − | 1.50097i | 0.0637126 | − | 0.110353i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.89584 | + | 13.6760i | 0.577401 | + | 1.00009i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5311 | + | 18.2405i | 0.762006 | + | 1.31983i | 0.941815 | + | 0.336131i | \(0.109119\pi\) |
−0.179809 | + | 0.983701i | \(0.557548\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.968871 | − | 1.67813i | 0.0697409 | − | 0.120795i | −0.829046 | − | 0.559180i | \(-0.811116\pi\) |
0.898787 | + | 0.438385i | \(0.144449\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.73317 | −0.123483 | −0.0617416 | − | 0.998092i | \(-0.519665\pi\) | ||||
−0.0617416 | + | 0.998092i | \(0.519665\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.21110 | − | 12.4900i | 0.511182 | − | 0.885392i | −0.488735 | − | 0.872433i | \(-0.662541\pi\) |
0.999916 | − | 0.0129598i | \(-0.00412534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.7656 | − | 12.6382i | −0.825781 | − | 0.887031i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 6.92820i | 0.279372 | + | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3138 | −0.713417 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.53113 | + | 4.38404i | 0.172622 | + | 0.298989i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.23444 | − | 0.513888i | 0.151683 | − | 0.0348850i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.65978 | + | 9.80302i | −0.380718 | + | 0.659422i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1011 | −0.944283 | −0.472141 | − | 0.881523i | \(-0.656519\pi\) | ||||
−0.472141 | + | 0.881523i | \(0.656519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.7656 | − | 20.3786i | 0.780908 | − | 1.35257i | −0.150505 | − | 0.988609i | \(-0.548090\pi\) |
0.931413 | − | 0.363963i | \(-0.118577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3278 | − | 23.0845i | −0.880727 | − | 1.52546i | −0.850534 | − | 0.525920i | \(-0.823721\pi\) |
−0.0301934 | − | 0.999544i | \(-0.509612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.866585 | + | 1.50097i | 0.0567718 | + | 0.0983317i | 0.893015 | − | 0.450028i | \(-0.148586\pi\) |
−0.836243 | + | 0.548359i | \(0.815253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.73317 | − | 3.00194i | 0.113060 | − | 0.195825i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.93774 | 0.319396 | 0.159698 | − | 0.987166i | \(-0.448948\pi\) | ||||
0.159698 | + | 0.987166i | \(0.448948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.76556 | − | 8.25420i | 0.306977 | − | 0.531700i | −0.670723 | − | 0.741708i | \(-0.734016\pi\) |
0.977700 | + | 0.210009i | \(0.0673492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.31161 | + | 2.09397i | −0.275459 | + | 0.133779i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.69647 | − | 6.40248i | −0.235201 | − | 0.407380i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.593387 | 0.0374542 | 0.0187271 | − | 0.999825i | \(-0.494039\pi\) | ||||
0.0187271 | + | 0.999825i | \(0.494039\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.06226 | −0.444000 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.60555 | + | 6.24500i | 0.224908 | + | 0.389552i | 0.956292 | − | 0.292414i | \(-0.0944585\pi\) |
−0.731384 | + | 0.681966i | \(0.761125\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.96330 | + | 6.40248i | −0.121994 | + | 0.397831i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.06226 | − | 1.83988i | 0.0655016 | − | 0.113452i | −0.831415 | − | 0.555652i | \(-0.812469\pi\) |
0.896916 | + | 0.442200i | \(0.145802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.65564 | 0.347423 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.36583 | + | 11.0259i | −0.388132 | + | 0.672264i | −0.992198 | − | 0.124670i | \(-0.960213\pi\) |
0.604067 | + | 0.796934i | \(0.293546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.78954 | − | 16.9560i | −0.594672 | − | 1.03000i | −0.993593 | − | 0.113017i | \(-0.963948\pi\) |
0.398921 | − | 0.916985i | \(-0.369385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.00000 | + | 13.8564i | 0.482418 | + | 0.835573i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3278 | + | 23.0845i | −0.800791 | + | 1.38701i | 0.118305 | + | 0.992977i | \(0.462254\pi\) |
−0.919096 | + | 0.394034i | \(0.871079\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.8386 | −1.66071 | −0.830356 | − | 0.557233i | \(-0.811863\pi\) | ||||
−0.830356 | + | 0.557233i | \(0.811863\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.24780 | − | 9.08945i | 0.311949 | − | 0.540312i | −0.666835 | − | 0.745205i | \(-0.732351\pi\) |
0.978784 | + | 0.204893i | \(0.0656848\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.0623 | − | 22.6245i | −1.24327 | − | 1.33548i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.50000 | − | 2.59808i | −0.0882353 | − | 0.152828i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.69054 | −0.0987623 | −0.0493812 | − | 0.998780i | \(-0.515725\pi\) | ||||
−0.0493812 | + | 0.998780i | \(0.515725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.52636 | 0.379979 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.53113 | − | 4.38404i | −0.146379 | − | 0.253536i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3278 | − | 14.3164i | −0.768203 | − | 0.825182i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.73317 | + | 3.00194i | −0.0992410 | + | 0.171890i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5014 | −0.656419 | −0.328210 | − | 0.944605i | \(-0.606445\pi\) | ||||
−0.328210 | + | 0.944605i | \(0.606445\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0000 | − | 24.2487i | 0.793867 | − | 1.37502i | −0.129689 | − | 0.991555i | \(-0.541398\pi\) |
0.923556 | − | 0.383464i | \(-0.125269\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.03113 | + | 10.4462i | 0.340900 | + | 0.590455i | 0.984600 | − | 0.174822i | \(-0.0559351\pi\) |
−0.643700 | + | 0.765278i | \(0.722602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3159 | − | 28.2600i | −0.916392 | − | 1.58724i | −0.804850 | − | 0.593478i | \(-0.797754\pi\) |
−0.111543 | − | 0.993760i | \(-0.535579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.5227 | + | 19.9579i | −0.645148 | + | 1.11743i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.0623 | 0.726803 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.73444 | + | 9.93233i | −0.318089 | + | 0.550947i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.92661 | + | 12.8050i | −0.216481 | + | 0.705960i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.96330 | + | 3.40054i | 0.107913 | + | 0.186911i | 0.914925 | − | 0.403625i | \(-0.132250\pi\) |
−0.807012 | + | 0.590536i | \(0.798917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.87548 | −0.211740 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.1245 | 1.04178 | 0.520889 | − | 0.853624i | \(-0.325600\pi\) | ||||
0.520889 | + | 0.853624i | \(0.325600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.53001 | − | 2.65006i | −0.0828547 | − | 0.143509i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4222 | − | 11.6190i | 0.778726 | − | 0.627364i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.53113 | + | 11.3122i | −0.350609 | + | 0.607273i | −0.986356 | − | 0.164624i | \(-0.947359\pi\) |
0.635747 | + | 0.771898i | \(0.280692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.1245 | 1.29136 | 0.645678 | − | 0.763610i | \(-0.276575\pi\) | ||||
0.645678 | + | 0.763610i | \(0.276575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4956 | + | 18.1789i | −0.558624 | + | 0.967566i | 0.438987 | + | 0.898493i | \(0.355337\pi\) |
−0.997612 | + | 0.0690725i | \(0.977996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.10265 | + | 5.37395i | 0.164672 | + | 0.285220i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4689 | + | 18.1326i | 0.552526 | + | 0.957003i | 0.998091 | + | 0.0617536i | \(0.0196693\pi\) |
−0.445566 | + | 0.895249i | \(0.646997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.23444 | − | 9.06631i | 0.275497 | − | 0.477174i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.73317 | 0.0907182 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.51098 | + | 14.7414i | −0.444270 | + | 0.769497i | −0.998001 | − | 0.0631979i | \(-0.979870\pi\) |
0.553731 | + | 0.832695i | \(0.313203\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.2967 | + | 4.89793i | −1.10567 | + | 0.254288i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.32782 | + | 16.1563i | 0.482976 | + | 0.836540i | 0.999809 | − | 0.0195469i | \(-0.00622238\pi\) |
−0.516833 | + | 0.856086i | \(0.672889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.5191 | −0.850775 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.1788 | 1.13925 | 0.569625 | − | 0.821905i | \(-0.307088\pi\) | ||||
0.569625 | + | 0.821905i | \(0.307088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.00000 | + | 12.1244i | 0.357683 | + | 0.619526i | 0.987573 | − | 0.157159i | \(-0.0502334\pi\) |
−0.629890 | + | 0.776684i | \(0.716900\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.35895 | + | 4.68226i | 0.222153 | + | 0.238630i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.6525 | + | 27.1109i | −0.793612 | + | 1.37458i | 0.130105 | + | 0.991500i | \(0.458469\pi\) |
−0.923717 | + | 0.383076i | \(0.874865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.94427 | 0.452331 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.17218 | − | 7.22642i | 0.209925 | − | 0.363601i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.73444 | − | 9.93233i | −0.287803 | − | 0.498490i | 0.685482 | − | 0.728090i | \(-0.259592\pi\) |
−0.973285 | + | 0.229600i | \(0.926258\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.39295 | + | 12.8050i | 0.369186 | + | 0.639449i | 0.989439 | − | 0.144953i | \(-0.0463032\pi\) |
−0.620252 | + | 0.784402i | \(0.712970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.09672 | − | 1.89957i | 0.0546315 | − | 0.0946245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.93774 | 0.443027 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0934 | + | 19.2143i | −0.548533 | + | 0.950086i | 0.449843 | + | 0.893108i | \(0.351480\pi\) |
−0.998375 | + | 0.0569787i | \(0.981853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.5754 | + | 5.65199i | −1.20928 | + | 0.278116i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.26318 | − | 5.65199i | −0.160183 | − | 0.277445i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.1245 | −1.86250 | −0.931252 | − | 0.364375i | \(-0.881283\pi\) | ||||
−0.931252 | + | 0.364375i | \(0.881283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.5934 | −1.05240 | −0.526199 | − | 0.850362i | \(-0.676383\pi\) | ||||
−0.526199 | + | 0.850362i | \(0.676383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.1319 | − | 17.5490i | −0.491470 | − | 0.851251i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.92661 | − | 12.8050i | 0.190022 | − | 0.619675i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5934 | + | 30.4726i | −0.847444 | + | 1.46782i | 0.0360384 | + | 0.999350i | \(0.488526\pi\) |
−0.883482 | + | 0.468465i | \(0.844807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.5934 | −1.71051 | −0.855255 | − | 0.518208i | \(-0.826599\pi\) | ||||
−0.855255 | + | 0.518208i | \(0.826599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.92081 | + | 5.05899i | −0.139721 | + | 0.242004i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.63266 | + | 8.02401i | 0.221105 | + | 0.382965i | 0.955144 | − | 0.296142i | \(-0.0957003\pi\) |
−0.734039 | + | 0.679108i | \(0.762367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.8278 | + | 30.8787i | 0.847025 | + | 1.46709i | 0.883851 | + | 0.467769i | \(0.154942\pi\) |
−0.0368252 | + | 0.999322i | \(0.511724\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.40661 | + | 2.43633i | −0.0666799 | + | 0.115493i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.3723 | −1.15020 | −0.575099 | − | 0.818084i | \(-0.695037\pi\) | ||||
−0.575099 | + | 0.818084i | \(0.695037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.6275 | + | 35.7279i | −0.971312 | + | 1.68236i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.34436 | + | 4.38404i | −0.0630244 | + | 0.205527i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0311 | − | 17.3744i | −0.469236 | − | 0.812741i | 0.530145 | − | 0.847907i | \(-0.322137\pi\) |
−0.999381 | + | 0.0351656i | \(0.988804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.9413 | −1.44108 | −0.720539 | − | 0.693414i | \(-0.756106\pi\) | ||||
−0.720539 | + | 0.693414i | \(0.756106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.92661 | −0.182485 | −0.0912424 | − | 0.995829i | \(-0.529084\pi\) | ||||
−0.0912424 | + | 0.995829i | \(0.529084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.53113 | − | 4.38404i | −0.117127 | − | 0.202869i | 0.801501 | − | 0.597993i | \(-0.204035\pi\) |
−0.918628 | + | 0.395124i | \(0.870702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.5934 | − | 3.35627i | 0.673860 | − | 0.154978i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.0527 | + | 22.6080i | −0.600165 | + | 1.03952i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.2346 | 0.607243 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.5934 | − | 37.4008i | 0.986627 | − | 1.70889i | 0.352156 | − | 0.935941i | \(-0.385449\pi\) |
0.634471 | − | 0.772947i | \(-0.281218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.20331 | + | 5.54829i | 0.146058 | + | 0.252980i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.26318 | − | 5.65199i | −0.148173 | − | 0.256644i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.2192 | − | 26.3604i | 0.689647 | − | 1.19450i | −0.282305 | − | 0.959325i | \(-0.591099\pi\) |
0.971952 | − | 0.235179i | \(-0.0755676\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.6556 | 1.33834 | 0.669170 | − | 0.743109i | \(-0.266650\pi\) | ||||
0.669170 | + | 0.743109i | \(0.266650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.5934 | − | 25.2765i | 0.657253 | − | 1.13840i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.3372 | − | 17.5490i | −0.732824 | − | 0.787180i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.9560 | − | 20.7084i | −0.535224 | − | 0.927036i | −0.999152 | − | 0.0411627i | \(-0.986894\pi\) |
0.463928 | − | 0.885873i | \(-0.346440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.3113 | −1.75280 | −0.876402 | − | 0.481580i | \(-0.840063\pi\) | ||||
−0.876402 | + | 0.481580i | \(0.840063\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.06226 | 0.314266 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.4435 | + | 25.0169i | 0.640198 | + | 1.10886i | 0.985388 | + | 0.170322i | \(0.0544809\pi\) |
−0.345191 | + | 0.938533i | \(0.612186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.52636 | + | 1.50097i | −0.288709 | + | 0.0663989i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.53113 | − | 4.38404i | 0.111535 | − | 0.193184i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.8755 | 0.786163 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.10265 | + | 5.37395i | −0.135930 | + | 0.235437i | −0.925952 | − | 0.377641i | \(-0.876735\pi\) |
0.790023 | + | 0.613078i | \(0.210069\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.82989 | − | 4.90151i | −0.123742 | − | 0.214328i | 0.797498 | − | 0.603321i | \(-0.206156\pi\) |
−0.921241 | + | 0.388993i | \(0.872823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.93774 | + | 3.35627i | 0.0844094 | + | 0.146201i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.5718 | −1.28090 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.21475 | + | 3.83606i | −0.0957521 | + | 0.165848i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.4689 | − | 13.8564i | −0.881657 | − | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.73444 | + | 9.93233i | 0.246543 | + | 0.427024i | 0.962564 | − | 0.271054i | \(-0.0873721\pi\) |
−0.716022 | + | 0.698078i | \(0.754039\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.00580 | −0.0430836 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.1582 | −1.67428 | −0.837141 | − | 0.546987i | \(-0.815775\pi\) | ||||
−0.837141 | + | 0.546987i | \(0.815775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.53113 | + | 16.5084i | 0.406040 | + | 0.703281i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.45234 | + | 30.8248i | −0.401954 | + | 1.31080i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.26318 | − | 5.65199i | 0.138265 | − | 0.239483i | −0.788575 | − | 0.614939i | \(-0.789181\pi\) |
0.926840 | + | 0.375456i | \(0.122514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.7125 | −0.791454 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.7656 | − | 32.5029i | 0.790874 | − | 1.36983i | −0.134552 | − | 0.990907i | \(-0.542960\pi\) |
0.925426 | − | 0.378928i | \(-0.123707\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.06226 | + | 8.76809i | 0.212971 | + | 0.368876i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.79319 | − | 8.30205i | −0.200941 | − | 0.348040i | 0.747891 | − | 0.663822i | \(-0.231067\pi\) |
−0.948832 | + | 0.315782i | \(0.897733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.35625 | − | 16.2055i | 0.391547 | − | 0.678179i | −0.601107 | − | 0.799169i | \(-0.705273\pi\) |
0.992654 | + | 0.120990i | \(0.0386068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.06226 | 0.377922 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5000 | − | 18.1865i | 0.437121 | − | 0.757115i | −0.560345 | − | 0.828259i | \(-0.689332\pi\) |
0.997466 | + | 0.0711438i | \(0.0226649\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.1825 | + | 18.4570i | 0.712850 | + | 0.765723i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5827 | + | 25.2580i | 0.603955 | + | 1.04608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.4066 | −0.553350 | −0.276675 | − | 0.960964i | \(-0.589233\pi\) | ||||
−0.276675 | + | 0.960964i | \(0.589233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.53113 | −0.104293 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.05422 | − | 3.55802i | −0.0843569 | − | 0.146110i | 0.820760 | − | 0.571273i | \(-0.193550\pi\) |
−0.905117 | + | 0.425163i | \(0.860217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.52056 | − | 5.93004i | −0.226321 | − | 0.243108i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.468871 | − | 0.812109i | 0.0191576 | − | 0.0331819i | −0.856288 | − | 0.516499i | \(-0.827235\pi\) |
0.875445 | + | 0.483317i | \(0.160568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.2490 | −1.68258 | −0.841292 | − | 0.540582i | \(-0.818204\pi\) | ||||
−0.841292 | + | 0.540582i | \(0.818204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.502899 | − | 0.871046i | 0.0204457 | − | 0.0354131i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8497 | + | 23.9884i | 0.562142 | + | 0.973658i | 0.997309 | + | 0.0733089i | \(0.0233559\pi\) |
−0.435167 | + | 0.900350i | \(0.643311\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.40661 | + | 11.0966i | 0.259184 | + | 0.448920i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.00000 | + | 8.66025i | −0.201948 | + | 0.349784i | −0.949156 | − | 0.314806i | \(-0.898061\pi\) |
0.747208 | + | 0.664590i | \(0.231394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.1054 | 1.05097 | 0.525483 | − | 0.850804i | \(-0.323885\pi\) | ||||
0.525483 | + | 0.850804i | \(0.323885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4824 | − | 32.0124i | 0.742869 | − | 1.28669i | −0.208315 | − | 0.978062i | \(-0.566798\pi\) |
0.951184 | − | 0.308625i | \(-0.0998688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.18677 | − | 10.3923i | 0.127675 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.09339 | − | 15.7502i | −0.363735 | − | 0.630008i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.3196 | −0.451340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.6318 | 1.29905 | 0.649526 | − | 0.760340i | \(-0.274967\pi\) | ||||
0.649526 | + | 0.760340i | \(0.274967\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.35895 | − | 9.28198i | −0.212663 | − | 0.368344i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.26556 | − | 17.6726i | 0.0501435 | − | 0.700216i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.65978 | − | 9.80302i | 0.223548 | − | 0.387196i | −0.732335 | − | 0.680944i | \(-0.761569\pi\) |
0.955883 | + | 0.293748i | \(0.0949028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.7095 | −1.60543 | −0.802713 | − | 0.596366i | \(-0.796611\pi\) | ||||
−0.802713 | + | 0.596366i | \(0.796611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.0623 | − | 33.0168i | 0.749415 | − | 1.29802i | −0.198689 | − | 0.980063i | \(-0.563668\pi\) |
0.948104 | − | 0.317962i | \(-0.102998\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.8278 | + | 29.1466i | 0.660550 | + | 1.14411i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0491 | + | 31.2619i | 0.706315 | + | 1.22337i | 0.966215 | + | 0.257738i | \(0.0829770\pi\) |
−0.259900 | + | 0.965635i | \(0.583690\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.99635 | + | 8.65393i | −0.195224 | + | 0.338137i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.0623 | 1.13210 | 0.566052 | − | 0.824369i | \(-0.308470\pi\) | ||||
0.566052 | + | 0.824369i | \(0.308470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.73444 | + | 9.93233i | −0.223044 | + | 0.386323i | −0.955731 | − | 0.294243i | \(-0.904933\pi\) |
0.732687 | + | 0.680566i | \(0.238266\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.15688 | − | 1.18601i | 0.199975 | − | 0.0459914i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.52636 | + | 11.3040i | 0.252702 | + | 0.437692i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.8755 | −0.690075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0623 | 1.00463 | 0.502313 | − | 0.864686i | \(-0.332482\pi\) | ||||
0.502313 | + | 0.864686i | \(0.332482\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.8365 | − | 37.8219i | −0.839244 | − | 1.45361i | −0.890528 | − | 0.454928i | \(-0.849665\pi\) |
0.0512845 | − | 0.998684i | \(-0.483668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.1825 | + | 18.4570i | 0.659403 | + | 0.708313i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.7656 | + | 25.5747i | −0.564989 | + | 0.978589i | 0.432062 | + | 0.901844i | \(0.357786\pi\) |
−0.997051 | + | 0.0767452i | \(0.975547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.93774 | 0.341494 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.4530 | + | 18.1051i | −0.398226 | + | 0.689748i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.1421 | − | 41.8154i | −0.918410 | − | 1.59073i | −0.801830 | − | 0.597552i | \(-0.796140\pi\) |
−0.116580 | − | 0.993181i | \(-0.537193\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.00000 | + | 12.1244i | 0.265525 | + | 0.459903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.1245 | − | 45.2490i | 0.989537 | − | 1.71393i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.25953 | −0.311958 | −0.155979 | − | 0.987760i | \(-0.549853\pi\) | ||||
−0.155979 | + | 0.987760i | \(0.549853\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.69647 | − | 6.40248i | 0.139415 | − | 0.241474i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.5934 | + | 6.11609i | −1.00015 | + | 0.230019i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.1245 | − | 22.7323i | −0.492902 | − | 0.853730i | 0.507065 | − | 0.861908i | \(-0.330730\pi\) |
−0.999967 | + | 0.00817731i | \(0.997397\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.73317 | −0.0649077 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.12004 | 0.228877 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.46887 | − | 7.74031i | −0.166661 | − | 0.288665i | 0.770583 | − | 0.637340i | \(-0.219965\pi\) |
−0.937244 | + | 0.348675i | \(0.886632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.73444 | + | 18.7004i | −0.213562 | + | 0.696440i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.7859 | − | 25.6099i | 0.549134 | − | 0.951128i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.2243 | 1.67727 | 0.838637 | − | 0.544690i | \(-0.183353\pi\) | ||||
0.838637 | + | 0.544690i | \(0.183353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5311 | − | 28.6328i | 0.611426 | − | 1.05902i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.26556 | − | 14.3164i | −0.305296 | − | 0.528787i | 0.672032 | − | 0.740523i | \(-0.265422\pi\) |
−0.977327 | + | 0.211735i | \(0.932089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.99270 | − | 17.3079i | −0.368086 | − | 0.637543i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.0087 | + | 43.3164i | −0.919961 | + | 1.59342i | −0.120490 | + | 0.992715i | \(0.538446\pi\) |
−0.799471 | + | 0.600704i | \(0.794887\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.93774 | 0.181148 | 0.0905741 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905741 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.46887 | + | 7.74031i | −0.163727 | + | 0.283583i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.01767 | − | 16.3630i | 0.183341 | − | 0.597890i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.8790 | + | 36.1634i | 0.761884 | + | 1.31962i | 0.941878 | + | 0.335954i | \(0.109059\pi\) |
−0.179994 | + | 0.983668i | \(0.557608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.46887 | 0.162639 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.9377 | −0.397539 | −0.198770 | − | 0.980046i | \(-0.563695\pi\) | ||||
−0.198770 | + | 0.980046i | \(0.563695\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6583 | + | 28.8530i | 0.603862 | + | 1.04592i | 0.992230 | + | 0.124415i | \(0.0397055\pi\) |
−0.388368 | + | 0.921504i | \(0.626961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.78739 | − | 0.871046i | 0.137113 | − | 0.0315340i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0623 | + | 20.8924i | −0.435543 | + | 0.754382i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.9377 | −1.07958 | −0.539791 | − | 0.841799i | \(-0.681497\pi\) | ||||
−0.539791 | + | 0.841799i | \(0.681497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.42371 | + | 5.93004i | −0.123142 | + | 0.213289i | −0.921005 | − | 0.389550i | \(-0.872630\pi\) |
0.797863 | + | 0.602839i | \(0.205964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.96330 | + | 3.40054i | 0.0705239 | + | 0.122151i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.0623 | + | 29.5527i | 0.611319 | + | 1.05884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | + | 27.7128i | −0.572525 | + | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.46634 | −0.123719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.3196 | − | 19.6060i | 0.403498 | − | 0.698880i | −0.590647 | − | 0.806930i | \(-0.701127\pi\) |
0.994145 | + | 0.108050i | \(0.0344607\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.6556 | − | 28.6328i | −0.947766 | − | 1.01806i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.40661 | − | 11.0966i | −0.227506 | − | 0.394051i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.5819 | 1.50833 | 0.754164 | − | 0.656686i | \(-0.228043\pi\) | ||||
0.754164 | + | 0.656686i | \(0.228043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.6391 | −0.800914 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.46887 | + | 7.74031i | 0.157703 | + | 0.273150i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.53113 | − | 0.812109i | 0.124456 | − | 0.0286231i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.65978 | + | 9.80302i | −0.198987 | + | 0.344656i | −0.948200 | − | 0.317673i | \(-0.897099\pi\) |
0.749213 | + | 0.662329i | \(0.230432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0527 | −0.458343 | −0.229172 | − | 0.973386i | \(-0.573602\pi\) | ||||
−0.229172 | + | 0.973386i | \(0.573602\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.65564 | + | 9.79586i | −0.198109 | + | 0.343134i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7967 | + | 18.7004i | 0.377728 | + | 0.654245i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.39660 | + | 4.15103i | 0.0836418 | + | 0.144872i | 0.904812 | − | 0.425812i | \(-0.140012\pi\) |
−0.821170 | + | 0.570684i | \(0.806678\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.73317 | − | 3.00194i | 0.0604145 | − | 0.104641i | −0.834236 | − | 0.551407i | \(-0.814091\pi\) |
0.894651 | + | 0.446766i | \(0.147424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.53113 | −0.192336 | −0.0961681 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961681 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.85895 | + | 15.3442i | −0.307684 | + | 0.532924i | −0.977855 | − | 0.209282i | \(-0.932887\pi\) |
0.670171 | + | 0.742207i | \(0.266221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.9236 | + | 17.5490i | 0.898200 | + | 0.608036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.79319 | − | 8.30205i | −0.165875 | − | 0.287304i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.93774 | −0.308565 | −0.154283 | − | 0.988027i | \(-0.549307\pi\) | ||||
−0.154283 | + | 0.988027i | \(0.549307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5934 | 0.468737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.25738 | − | 3.90990i | −0.0776563 | − | 0.134505i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.13935 | + | 3.71550i | −0.0391485 | + | 0.127666i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.53113 | − | 4.38404i | 0.0867660 | − | 0.150283i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.4066 | 0.698709 | 0.349355 | − | 0.936991i | \(-0.386401\pi\) | ||||
0.349355 | + | 0.936991i | \(0.386401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.4749 | − | 47.5880i | 0.938526 | − | 1.62557i | 0.170303 | − | 0.985392i | \(-0.445525\pi\) |
0.768223 | − | 0.640182i | \(-0.221141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.8885 | − | 30.9839i | −0.610349 | − | 1.05716i | −0.991181 | − | 0.132512i | \(-0.957696\pi\) |
0.380832 | − | 0.924644i | \(-0.375638\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.6556 | + | 47.9010i | 0.941409 | + | 1.63057i | 0.762786 | + | 0.646651i | \(0.223831\pi\) |
0.178623 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.46887 | − | 4.27621i | 0.0839441 | − | 0.145396i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.0308 | 1.45972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.16281 | − | 12.4064i | 0.242703 | − | 0.420373i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.7656 | − | 12.6382i | −0.397749 | − | 0.427251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.5934 | + | 44.3290i | 0.864227 | + | 1.49689i | 0.867812 | + | 0.496892i | \(0.165525\pi\) |
−0.00358516 | + | 0.999994i | \(0.501141\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.6217 | 0.661072 | 0.330536 | − | 0.943793i | \(-0.392770\pi\) | ||||
0.330536 | + | 0.943793i | \(0.392770\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.9647 | −1.24396 | −0.621981 | − | 0.783032i | \(-0.713672\pi\) | ||||
−0.621981 | + | 0.783032i | \(0.713672\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.53113 | + | 16.5084i | 0.320024 | + | 0.554298i | 0.980493 | − | 0.196556i | \(-0.0629757\pi\) |
−0.660469 | + | 0.750854i | \(0.729642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.2179 | + | 30.3109i | 0.946398 | + | 1.01659i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.39295 | − | 12.8050i | 0.247395 | − | 0.428502i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.01159 | −0.0672402 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.82782 | + | 4.89793i | −0.0943132 | + | 0.163355i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.4689 | − | 31.9890i | −0.615287 | − | 1.06571i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.65978 | + | 9.80302i | 0.188137 | + | 0.325863i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.2756 | − | 40.3144i | 0.772852 | − | 1.33862i | −0.163142 | − | 0.986603i | \(-0.552163\pi\) |
0.935994 | − | 0.352017i | \(-0.114504\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.1868 | −0.370634 | −0.185317 | − | 0.982679i | \(-0.559331\pi\) | ||||
−0.185317 | + | 0.982679i | \(0.559331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.8278 | − | 29.1466i | 0.556920 | − | 0.964613i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.3196 | − | 36.9139i | 0.373805 | − | 1.21900i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.96330 | + | 3.40054i | 0.0647634 | + | 0.112174i | 0.896589 | − | 0.442864i | \(-0.146037\pi\) |
−0.831826 | + | 0.555037i | \(0.812704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.9377 | −0.755005 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.4689 | −0.377094 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.18764 | − | 2.05705i | −0.0389652 | − | 0.0674897i | 0.845885 | − | 0.533365i | \(-0.179073\pi\) |
−0.884850 | + | 0.465875i | \(0.845739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.3914 | + | 8.93197i | −0.602755 | + | 0.292734i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.40661 | + | 9.36453i | −0.176815 | + | 0.306253i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.8755 | −0.355287 | −0.177643 | − | 0.984095i | \(-0.556847\pi\) | ||||
−0.177643 | + | 0.984095i | \(0.556847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.7588 | − | 23.8309i | 0.448523 | − | 0.776865i | −0.549767 | − | 0.835318i | \(-0.685283\pi\) |
0.998290 | + | 0.0584529i | \(0.0186168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6832 | + | 20.2360i | 0.380459 | + | 0.658974i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.00000 | + | 10.3923i | 0.194974 | + | 0.337705i | 0.946892 | − | 0.321552i | \(-0.104204\pi\) |
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.20331 | + | 5.54829i | −0.103984 | + | 0.180105i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.8913 | 1.32460 | 0.662300 | − | 0.749239i | \(-0.269580\pi\) | ||||
0.662300 | + | 0.749239i | \(0.269580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.21110 | + | 12.4900i | −0.233346 | + | 0.404167i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.6556 | + | 7.74031i | −1.08680 | + | 0.249948i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1245 | + | 26.1964i | 0.487888 | + | 0.845046i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.32685 | 0.0427129 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.6525 | 0.503350 | 0.251675 | − | 0.967812i | \(-0.419019\pi\) | ||||
0.251675 | + | 0.967812i | \(0.419019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.35895 | + | 9.28198i | 0.171977 | + | 0.297873i | 0.939111 | − | 0.343614i | \(-0.111651\pi\) |
−0.767134 | + | 0.641487i | \(0.778318\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.8590 | − | 39.5929i | −1.18164 | − | 1.26929i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.5191 | − | 28.6119i | 0.528492 | − | 0.915374i | −0.470957 | − | 0.882156i | \(-0.656091\pi\) |
0.999448 | − | 0.0332178i | \(-0.0105755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.5075 | −0.463661 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.4689 | − | 19.8647i | 0.365800 | − | 0.633584i | −0.623104 | − | 0.782139i | \(-0.714129\pi\) |
0.988904 | + | 0.148554i | \(0.0474620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.593387 | − | 1.02778i | −0.0189069 | − | 0.0327477i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.39295 | + | 12.8050i | 0.235082 | + | 0.407174i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.29988 | − | 2.25145i | 0.0412920 | − | 0.0715198i | −0.844641 | − | 0.535333i | \(-0.820186\pi\) |
0.885933 | + | 0.463814i | \(0.153519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.87548 | 0.313074 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.2656 | + | 26.4407i | −0.483465 | + | 0.837386i | −0.999820 | − | 0.0189886i | \(-0.993955\pi\) |
0.516354 | + | 0.856375i | \(0.327289\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2016.2.s.x.865.3 | yes | 8 | |
3.2 | odd | 2 | 2016.2.s.w.865.2 | yes | 8 | ||
4.3 | odd | 2 | 2016.2.s.w.865.3 | yes | 8 | ||
7.2 | even | 3 | inner | 2016.2.s.x.289.3 | yes | 8 | |
12.11 | even | 2 | inner | 2016.2.s.x.865.2 | yes | 8 | |
21.2 | odd | 6 | 2016.2.s.w.289.2 | ✓ | 8 | ||
28.23 | odd | 6 | 2016.2.s.w.289.3 | yes | 8 | ||
84.23 | even | 6 | inner | 2016.2.s.x.289.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.s.w.289.2 | ✓ | 8 | 21.2 | odd | 6 | ||
2016.2.s.w.289.3 | yes | 8 | 28.23 | odd | 6 | ||
2016.2.s.w.865.2 | yes | 8 | 3.2 | odd | 2 | ||
2016.2.s.w.865.3 | yes | 8 | 4.3 | odd | 2 | ||
2016.2.s.x.289.2 | yes | 8 | 84.23 | even | 6 | inner | |
2016.2.s.x.289.3 | yes | 8 | 7.2 | even | 3 | inner | |
2016.2.s.x.865.2 | yes | 8 | 12.11 | even | 2 | inner | |
2016.2.s.x.865.3 | yes | 8 | 1.1 | even | 1 | trivial |