Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(703,2016)]
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([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.cs (of order \(6\), 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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 24x^{14} + 218x^{12} + 968x^{10} + 2241x^{8} + 2672x^{6} + 1512x^{4} + 320x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 703.2 | ||
Root | \(1.60698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.703 |
Dual form | 2016.2.cs.c.1279.2 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −2.33837 | + | 1.35006i | −1.04575 | + | 0.603764i | −0.921457 | − | 0.388481i | \(-0.873000\pi\) |
−0.124294 | + | 0.992245i | \(0.539667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63871 | − | 0.192843i | −0.997340 | − | 0.0728877i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.22769 | + | 0.708810i | 0.370164 | + | 0.213714i | 0.673530 | − | 0.739160i | \(-0.264777\pi\) |
−0.303366 | + | 0.952874i | \(0.598111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.69489i | − | 1.57948i | −0.613442 | − | 0.789739i | \(-0.710216\pi\) | ||
0.613442 | − | 0.789739i | \(-0.289784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.69711 | + | 0.979828i | 0.411610 | + | 0.237643i | 0.691481 | − | 0.722394i | \(-0.256958\pi\) |
−0.279871 | + | 0.960038i | \(0.590292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.361646 | + | 0.626389i | 0.0829672 | + | 0.143703i | 0.904523 | − | 0.426424i | \(-0.140227\pi\) |
−0.821556 | + | 0.570128i | \(0.806894\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.562697 | + | 0.324873i | −0.117330 | + | 0.0677407i | −0.557517 | − | 0.830166i | \(-0.688246\pi\) |
0.440186 | + | 0.897906i | \(0.354912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14531 | − | 1.98374i | 0.229063 | − | 0.396749i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.06459 | −1.12617 | −0.563083 | − | 0.826400i | \(-0.690385\pi\) | ||||
−0.563083 | + | 0.826400i | \(0.690385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.49760 | − | 4.32597i | 0.448582 | − | 0.776967i | −0.549712 | − | 0.835354i | \(-0.685262\pi\) |
0.998294 | + | 0.0583872i | \(0.0185958\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.43064 | − | 3.11148i | 1.08698 | − | 0.525936i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.576851 | − | 0.999134i | −0.0948336 | − | 0.164257i | 0.814706 | − | 0.579875i | \(-0.196899\pi\) |
−0.909539 | + | 0.415618i | \(0.863565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.58141i | 0.246975i | 0.992346 | + | 0.123487i | \(0.0394078\pi\) | ||||
−0.992346 | + | 0.123487i | \(0.960592\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8193i | 1.64993i | 0.565185 | + | 0.824965i | \(0.308805\pi\) | ||||
−0.565185 | + | 0.824965i | \(0.691195\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.81485 | + | 8.33956i | 0.702318 | + | 1.21645i | 0.967651 | + | 0.252293i | \(0.0811847\pi\) |
−0.265333 | + | 0.964157i | \(0.585482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92562 | + | 1.01771i | 0.989375 | + | 0.145388i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.26205 | − | 10.8462i | 0.860158 | − | 1.48984i | −0.0116175 | − | 0.999933i | \(-0.503698\pi\) |
0.871776 | − | 0.489905i | \(-0.162969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.82774 | −0.516132 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.434140 | − | 0.751953i | 0.0565202 | − | 0.0978959i | −0.836381 | − | 0.548149i | \(-0.815333\pi\) |
0.892901 | + | 0.450253i | \(0.148666\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7867 | − | 6.80505i | 1.50913 | − | 0.871297i | 0.509188 | − | 0.860655i | \(-0.329946\pi\) |
0.999943 | − | 0.0106419i | \(-0.00338749\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.68844 | + | 13.3168i | 0.953633 | + | 1.65174i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0459751 | − | 0.0265437i | −0.00561675 | − | 0.00324283i | 0.497189 | − | 0.867642i | \(-0.334366\pi\) |
−0.502806 | + | 0.864399i | \(0.667699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0593i | 1.66853i | 0.551362 | + | 0.834266i | \(0.314108\pi\) | ||||
−0.551362 | + | 0.834266i | \(0.685892\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5520 | + | 7.82422i | 1.58614 | + | 0.915756i | 0.993935 | + | 0.109966i | \(0.0350741\pi\) |
0.592201 | + | 0.805790i | \(0.298259\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.10285 | − | 2.10710i | −0.353602 | − | 0.240126i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.95371 | − | 5.74678i | 1.11988 | − | 0.646563i | 0.178510 | − | 0.983938i | \(-0.442872\pi\) |
0.941370 | + | 0.337375i | \(0.109539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.95860 | 0.324749 | 0.162375 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162375 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.29130 | −0.573922 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.13765 | − | 4.12092i | 0.756589 | − | 0.436817i | −0.0714806 | − | 0.997442i | \(-0.522772\pi\) |
0.828070 | + | 0.560625i | \(0.189439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.09822 | + | 15.0272i | −0.115125 | + | 1.57528i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.69132 | − | 0.976486i | −0.173526 | − | 0.100185i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01880i | 0.103444i | 0.998662 | + | 0.0517218i | \(0.0164709\pi\) | ||||
−0.998662 | + | 0.0517218i | \(0.983529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3460 | + | 5.97328i | 1.02947 | + | 0.594364i | 0.916832 | − | 0.399273i | \(-0.130737\pi\) |
0.112636 | + | 0.993636i | \(0.464071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.79513 | + | 15.2336i | 0.866610 | + | 1.50101i | 0.865439 | + | 0.501014i | \(0.167039\pi\) |
0.00117078 | + | 0.999999i | \(0.499627\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6225 | + | 7.28758i | −1.22026 | + | 0.704517i | −0.964973 | − | 0.262349i | \(-0.915503\pi\) |
−0.255286 | + | 0.966866i | \(0.582170\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.70837 | + | 4.69103i | −0.259415 | + | 0.449319i | −0.966085 | − | 0.258223i | \(-0.916863\pi\) |
0.706671 | + | 0.707543i | \(0.250196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.65726 | 0.532190 | 0.266095 | − | 0.963947i | \(-0.414267\pi\) | ||||
0.266095 | + | 0.963947i | \(0.414267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.877195 | − | 1.51935i | 0.0817989 | − | 0.141680i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.28924 | − | 2.91276i | −0.393194 | − | 0.267012i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.49518 | − | 7.78588i | −0.408652 | − | 0.707807i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 7.31562i | − | 0.654329i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7616i | 1.04367i | 0.853046 | + | 0.521835i | \(0.174753\pi\) | ||||
−0.853046 | + | 0.521835i | \(0.825247\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3102 | − | 17.8577i | −0.900804 | − | 1.56024i | −0.826453 | − | 0.563006i | \(-0.809645\pi\) |
−0.0743512 | − | 0.997232i | \(-0.523689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.833485 | − | 1.72260i | −0.0722723 | − | 0.149369i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.78488 | − | 16.9479i | 0.835979 | − | 1.44796i | −0.0572523 | − | 0.998360i | \(-0.518234\pi\) |
0.893231 | − | 0.449598i | \(-0.148433\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4109 | 1.64641 | 0.823205 | − | 0.567745i | \(-0.192184\pi\) | ||||
0.823205 | + | 0.567745i | \(0.192184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.03660 | − | 6.99159i | 0.337557 | − | 0.584666i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1812 | − | 8.18755i | 1.17769 | − | 0.679939i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.60562 | − | 16.6374i | −0.786923 | − | 1.36299i | −0.927843 | − | 0.372970i | \(-0.878339\pi\) |
0.140920 | − | 0.990021i | \(-0.454994\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.45236 | − | 0.838518i | −0.118191 | − | 0.0682376i | 0.439739 | − | 0.898126i | \(-0.355071\pi\) |
−0.557930 | + | 0.829888i | \(0.688404\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.4876i | 1.08335i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.81758 | − | 3.93613i | −0.544102 | − | 0.314137i | 0.202638 | − | 0.979254i | \(-0.435049\pi\) |
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.54744 | − | 0.748735i | 0.121956 | − | 0.0590086i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.08724 | + | 1.78242i | −0.241812 | + | 0.139610i | −0.616009 | − | 0.787739i | \(-0.711252\pi\) |
0.374197 | + | 0.927349i | \(0.377918\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9594 | 0.848063 | 0.424031 | − | 0.905647i | \(-0.360615\pi\) | ||||
0.424031 | + | 0.905647i | \(0.360615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.4318 | −1.49475 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.3996 | + | 9.46830i | −1.24684 | + | 0.719861i | −0.970477 | − | 0.241193i | \(-0.922461\pi\) |
−0.276359 | + | 0.961054i | \(0.589128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.40471 | + | 5.01366i | −0.257372 | + | 0.378997i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.11493 | − | 2.95311i | −0.382308 | − | 0.220726i | 0.296514 | − | 0.955029i | \(-0.404176\pi\) |
−0.678822 | + | 0.734303i | \(0.737509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.5302i | 1.82331i | 0.410953 | + | 0.911656i | \(0.365196\pi\) | ||||
−0.410953 | + | 0.911656i | \(0.634804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.69778 | + | 1.55756i | 0.198345 | + | 0.114514i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.38902 | + | 2.40586i | 0.101575 | + | 0.175934i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.82839 | + | 3.94237i | −0.494085 | + | 0.285260i | −0.726268 | − | 0.687412i | \(-0.758747\pi\) |
0.232182 | + | 0.972672i | \(0.425413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.37464 | − | 9.30915i | 0.386875 | − | 0.670087i | −0.605152 | − | 0.796110i | \(-0.706888\pi\) |
0.992027 | + | 0.126022i | \(0.0402211\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.22489 | −0.443505 | −0.221753 | − | 0.975103i | \(-0.571178\pi\) | ||||
−0.221753 | + | 0.975103i | \(0.571178\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.14111 | − | 3.70852i | 0.151780 | − | 0.262890i | −0.780102 | − | 0.625652i | \(-0.784833\pi\) |
0.931882 | + | 0.362762i | \(0.118166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.0027 | + | 1.16951i | 1.12317 | + | 0.0820836i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.13499 | − | 3.69792i | −0.149114 | − | 0.258274i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.02535i | 0.0709251i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.2858i | − | 1.19001i | −0.803723 | − | 0.595003i | \(-0.797151\pi\) | ||
0.803723 | − | 0.595003i | \(-0.202849\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6067 | − | 25.2995i | −0.996168 | − | 1.72541i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.42468 | + | 10.9334i | −0.504020 | + | 0.742204i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.58001 | − | 9.66487i | 0.375352 | − | 0.650129i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.40635 | −0.295071 | −0.147535 | − | 0.989057i | \(-0.547134\pi\) | ||||
−0.147535 | + | 0.989057i | \(0.547134\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.11039 | + | 5.38735i | −0.206444 | + | 0.357571i | −0.950592 | − | 0.310444i | \(-0.899522\pi\) |
0.744148 | + | 0.668015i | \(0.232856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.98807 | − | 5.76662i | 0.660030 | − | 0.381069i | −0.132258 | − | 0.991215i | \(-0.542223\pi\) |
0.792289 | + | 0.610147i | \(0.208889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.63846 | + | 8.03406i | 0.303876 | + | 0.526328i | 0.977010 | − | 0.213192i | \(-0.0683859\pi\) |
−0.673135 | + | 0.739520i | \(0.735053\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.5178 | − | 13.0006i | −1.46890 | − | 0.848069i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.55540i | 0.229980i | 0.993367 | + | 0.114990i | \(0.0366835\pi\) | ||||
−0.993367 | + | 0.114990i | \(0.963316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.43954 | + | 4.29522i | 0.479223 | + | 0.276679i | 0.720093 | − | 0.693878i | \(-0.244099\pi\) |
−0.240870 | + | 0.970557i | \(0.577433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.5686 | + | 6.97020i | −1.12242 | + | 0.445310i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.56722 | − | 2.05953i | 0.226977 | − | 0.131045i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6135 | 0.669918 | 0.334959 | − | 0.942233i | \(-0.391277\pi\) | ||||
0.334959 | + | 0.942233i | \(0.391277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.921093 | −0.0579086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7058 | + | 7.91303i | −0.854943 | + | 0.493601i | −0.862315 | − | 0.506371i | \(-0.830986\pi\) |
0.00737277 | + | 0.999973i | \(0.497653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.32947 | + | 2.74767i | 0.0826091 | + | 0.170732i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.378909 | + | 0.218763i | 0.0233645 | + | 0.0134895i | 0.511637 | − | 0.859202i | \(-0.329039\pi\) |
−0.488272 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.8165i | 2.07733i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.429647 | − | 0.248057i | −0.0261961 | − | 0.0151243i | 0.486845 | − | 0.873489i | \(-0.338148\pi\) |
−0.513041 | + | 0.858364i | \(0.671481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.68840 | − | 2.92439i | −0.102563 | − | 0.177644i | 0.810177 | − | 0.586185i | \(-0.199371\pi\) |
−0.912740 | + | 0.408541i | \(0.866038\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.81219 | − | 1.62362i | 0.169582 | − | 0.0979080i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.46678 | + | 9.46874i | −0.328467 | + | 0.568921i | −0.982208 | − | 0.187797i | \(-0.939865\pi\) |
0.653741 | + | 0.756718i | \(0.273199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.4932 | 1.58045 | 0.790226 | − | 0.612815i | \(-0.209963\pi\) | ||||
0.790226 | + | 0.612815i | \(0.209963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.08930 | − | 1.88673i | 0.0647524 | − | 0.112154i | −0.831832 | − | 0.555028i | \(-0.812708\pi\) |
0.896584 | + | 0.442873i | \(0.146041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.304963 | − | 4.17289i | 0.0180014 | − | 0.246318i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.57988 | − | 11.3967i | −0.387052 | − | 0.670393i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.82696i | − | 0.398835i | −0.979915 | − | 0.199418i | \(-0.936095\pi\) | ||
0.979915 | − | 0.199418i | \(-0.0639050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34446i | 0.136500i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.85012 | + | 3.20450i | 0.106995 | + | 0.185321i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08642 | − | 28.5491i | 0.120260 | − | 1.64554i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.3744 | + | 31.8254i | −1.05212 | + | 1.82232i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.9855 | 0.741122 | 0.370561 | − | 0.928808i | \(-0.379165\pi\) | ||||
0.370561 | + | 0.928808i | \(0.379165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3818 | − | 28.3741i | 0.928928 | − | 1.60895i | 0.143808 | − | 0.989606i | \(-0.454065\pi\) |
0.785119 | − | 0.619344i | \(-0.212602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.92470 | − | 4.57533i | 0.447930 | − | 0.258613i | −0.259025 | − | 0.965871i | \(-0.583401\pi\) |
0.706956 | + | 0.707258i | \(0.250068\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.2936 | + | 21.2932i | 0.690479 | + | 1.19594i | 0.971681 | + | 0.236296i | \(0.0759334\pi\) |
−0.281203 | + | 0.959648i | \(0.590733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.44546 | − | 4.29864i | −0.416866 | − | 0.240678i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.41740i | 0.0788664i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2972 | − | 6.52244i | −0.626656 | − | 0.361800i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.0968 | − | 22.9342i | −0.611785 | − | 1.26440i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.5039 | − | 10.1059i | 0.962101 | − | 0.555470i | 0.0652823 | − | 0.997867i | \(-0.479205\pi\) |
0.896819 | + | 0.442397i | \(0.145872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.143342 | 0.00783163 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4425 | −0.841209 | −0.420605 | − | 0.907244i | \(-0.638182\pi\) | ||||
−0.420605 | + | 0.907244i | \(0.638182\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.13258 | − | 3.54065i | 0.332098 | − | 0.191737i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0785 | − | 4.02101i | −0.976146 | − | 0.217114i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.8910 | + | 11.4841i | 1.06781 | + | 0.616498i | 0.927581 | − | 0.373621i | \(-0.121884\pi\) |
0.140225 | + | 0.990120i | \(0.455217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.24157i | 0.119988i | 0.998199 | + | 0.0599941i | \(0.0191082\pi\) | ||||
−0.998199 | + | 0.0599941i | \(0.980892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.0621 | + | 6.38674i | 0.588779 | + | 0.339932i | 0.764614 | − | 0.644488i | \(-0.222929\pi\) |
−0.175836 | + | 0.984420i | \(0.556263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.9809 | − | 32.8758i | −1.00740 | − | 1.74487i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.4433 | + | 11.2256i | −1.02618 | + | 0.592464i | −0.915887 | − | 0.401436i | \(-0.868511\pi\) |
−0.110290 | + | 0.993899i | \(0.535178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.23842 | − | 16.0014i | 0.486233 | − | 0.842180i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.2526 | −2.21160 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.98510 | − | 3.43829i | 0.103621 | − | 0.179477i | −0.809553 | − | 0.587047i | \(-0.800290\pi\) |
0.913174 | + | 0.407570i | \(0.133624\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.6154 | + | 27.4124i | −0.966461 | + | 1.42318i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.03872 | − | 15.6555i | −0.468007 | − | 0.810612i | 0.531324 | − | 0.847168i | \(-0.321695\pi\) |
−0.999332 | + | 0.0365562i | \(0.988361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.5372i | 1.77876i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.69206i | − | 0.497848i | −0.968523 | − | 0.248924i | \(-0.919923\pi\) | ||
0.968523 | − | 0.248924i | \(-0.0800769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.93009 | + | 12.0033i | 0.354111 | + | 0.613338i | 0.986965 | − | 0.160932i | \(-0.0514501\pi\) |
−0.632854 | + | 0.774271i | \(0.718117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.1003 | + | 0.738152i | 0.514759 | + | 0.0376197i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.65262 | − | 16.7188i | 0.489407 | − | 0.847678i | −0.510519 | − | 0.859867i | \(-0.670547\pi\) |
0.999926 | + | 0.0121887i | \(0.00387987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.27328 | −0.0643925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.5170 | + | 26.8762i | −0.780743 | + | 1.35229i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.460324 | + | 0.265768i | −0.0231030 | + | 0.0133385i | −0.511507 | − | 0.859279i | \(-0.670913\pi\) |
0.488404 | + | 0.872618i | \(0.337579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.374615 | − | 0.648852i | −0.0187074 | − | 0.0324021i | 0.856520 | − | 0.516114i | \(-0.172622\pi\) |
−0.875228 | + | 0.483711i | \(0.839288\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.6359 | − | 14.2236i | −1.22720 | − | 0.708526i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.63551i | − | 0.0810692i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.68982 | + | 5.01707i | 0.429684 | + | 0.248078i | 0.699212 | − | 0.714914i | \(-0.253534\pi\) |
−0.269528 | + | 0.962993i | \(0.586868\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.29058 | + | 1.90047i | −0.0635053 | + | 0.0935159i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.91831 | + | 3.99429i | −0.339606 | + | 0.196072i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.20727 | 0.107832 | 0.0539160 | − | 0.998545i | \(-0.482830\pi\) | ||||
0.0539160 | + | 0.998545i | \(0.482830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.3916 | −1.04256 | −0.521280 | − | 0.853386i | \(-0.674545\pi\) | ||||
−0.521280 | + | 0.853386i | \(0.674545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.88745 | − | 2.24442i | 0.188569 | − | 0.108870i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.4140 | + | 15.6836i | −1.56862 | + | 0.758983i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3217 | + | 16.3515i | 1.36421 | + | 0.787626i | 0.990181 | − | 0.139791i | \(-0.0446431\pi\) |
0.374028 | + | 0.927417i | \(0.377976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.18695i | − | 0.153155i | −0.997064 | − | 0.0765775i | \(-0.975601\pi\) | ||
0.997064 | − | 0.0765775i | \(-0.0243993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.406994 | − | 0.234978i | −0.0194691 | − | 0.0112405i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.33511 | − | 9.24069i | −0.254631 | − | 0.441034i | 0.710164 | − | 0.704036i | \(-0.248621\pi\) |
−0.964795 | + | 0.263002i | \(0.915287\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.7383 | − | 13.1280i | 1.08033 | − | 0.623729i | 0.149344 | − | 0.988785i | \(-0.452284\pi\) |
0.930985 | + | 0.365057i | \(0.118950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.1270 | + | 19.2725i | −0.527469 | + | 0.913603i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3240 | −0.487220 | −0.243610 | − | 0.969873i | \(-0.578332\pi\) | ||||
−0.243610 | + | 0.969873i | \(0.578332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12092 | + | 1.94149i | −0.0527820 | + | 0.0914211i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.7195 | − | 36.6218i | −0.830705 | − | 1.71686i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6001 | + | 21.8240i | 0.589407 | + | 1.02088i | 0.994310 | + | 0.106523i | \(0.0339718\pi\) |
−0.404903 | + | 0.914359i | \(0.632695\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.7224i | 0.965140i | 0.875857 | + | 0.482570i | \(0.160297\pi\) | ||||
−0.875857 | + | 0.482570i | \(0.839703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.6594i | 1.84313i | 0.388227 | + | 0.921564i | \(0.373088\pi\) | ||||
−0.388227 | + | 0.921564i | \(0.626912\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5981 | − | 28.7487i | −0.768068 | − | 1.33033i | −0.938609 | − | 0.344982i | \(-0.887885\pi\) |
0.170542 | − | 0.985350i | \(-0.445448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.116196 | + | 0.0789073i | 0.00536545 | + | 0.00364360i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.66883 | + | 13.2828i | −0.352613 | + | 0.610744i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.65679 | 0.0760189 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.09367 | + | 15.7507i | −0.415500 | + | 0.719667i | −0.995481 | − | 0.0949628i | \(-0.969727\pi\) |
0.579981 | + | 0.814630i | \(0.303060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.68996 | + | 3.28510i | −0.259440 | + | 0.149788i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.37544 | − | 2.38233i | −0.0624555 | − | 0.108176i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7512 | − | 11.9807i | −0.940326 | − | 0.542897i | −0.0502633 | − | 0.998736i | \(-0.516006\pi\) |
−0.890062 | + | 0.455839i | \(0.849339\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.5449i | − | 0.521016i | −0.965472 | − | 0.260508i | \(-0.916110\pi\) | ||
0.965472 | − | 0.260508i | \(-0.0838900\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2923 | − | 5.94225i | −0.463541 | − | 0.267626i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.71123 | − | 37.0985i | 0.121615 | − | 1.66409i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.2101 | − | 11.0910i | 0.859963 | − | 0.496500i | −0.00403674 | − | 0.999992i | \(-0.501285\pi\) |
0.864000 | + | 0.503492i | \(0.167952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.53547 | 0.0684631 | 0.0342316 | − | 0.999414i | \(-0.489102\pi\) | ||||
0.0342316 | + | 0.999414i | \(0.489102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.2571 | −1.43542 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.40479 | − | 4.85251i | 0.372536 | − | 0.215084i | −0.302030 | − | 0.953298i | \(-0.597664\pi\) |
0.674566 | + | 0.738215i | \(0.264331\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.2509 | − | 23.2593i | −1.51517 | − | 1.02893i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −41.1325 | − | 23.7479i | −1.81252 | − | 1.04646i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6512i | 0.600381i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0675 | − | 13.3180i | −1.01060 | − | 0.583473i | −0.0992356 | − | 0.995064i | \(-0.531640\pi\) |
−0.911368 | + | 0.411591i | \(0.864973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.74401 | − | 8.21687i | −0.207441 | − | 0.359299i | 0.743467 | − | 0.668773i | \(-0.233180\pi\) |
−0.950908 | + | 0.309474i | \(0.899847\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.47741 | − | 4.89444i | 0.369282 | − | 0.213205i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2889 | + | 19.5530i | −0.490822 | + | 0.850129i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.00595 | 0.390091 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.6773 | − | 34.0821i | 0.850724 | − | 1.47350i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.78119 | + | 6.15839i | 0.335159 | + | 0.265261i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5289 | + | 23.4328i | 0.581654 | + | 1.00745i | 0.995283 | + | 0.0970093i | \(0.0309277\pi\) |
−0.413629 | + | 0.910445i | \(0.635739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 14.6258i | − | 0.626501i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.3241i | 1.38208i | 0.722818 | + | 0.691039i | \(0.242847\pi\) | ||||
−0.722818 | + | 0.691039i | \(0.757153\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.19323 | − | 3.79879i | −0.0934349 | − | 0.161834i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.3732 | + | 13.2446i | −1.16403 | + | 0.563218i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.06686 | + | 3.57991i | −0.0875757 | + | 0.151686i | −0.906486 | − | 0.422236i | \(-0.861245\pi\) |
0.818910 | + | 0.573922i | \(0.194579\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 61.6148 | 2.60603 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.0538 | − | 27.8061i | 0.676589 | − | 1.17189i | −0.299413 | − | 0.954124i | \(-0.596791\pi\) |
0.976002 | − | 0.217762i | \(-0.0698758\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.2288 | + | 7.63763i | −0.556538 | + | 0.321317i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.41874 | + | 7.65349i | 0.185243 | + | 0.320851i | 0.943659 | − | 0.330921i | \(-0.107359\pi\) |
−0.758415 | + | 0.651772i | \(0.774026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1203 | + | 13.3485i | 0.967555 | + | 0.558618i | 0.898490 | − | 0.438994i | \(-0.144665\pi\) |
0.0690650 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.48833i | 0.0620675i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.8634 | − | 10.3135i | −0.743665 | − | 0.429355i | 0.0797356 | − | 0.996816i | \(-0.474592\pi\) |
−0.823400 | + | 0.567461i | \(0.807926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.80691 | − | 0.570545i | −0.323885 | − | 0.0236702i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.3758 | − | 8.87720i | 0.636799 | − | 0.367656i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.8831 | −1.27468 | −0.637341 | − | 0.770582i | \(-0.719966\pi\) | ||||
−0.637341 | + | 0.770582i | \(0.719966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.61299 | 0.148871 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.5083 | − | 15.3046i | 1.08856 | − | 0.628483i | 0.155371 | − | 0.987856i | \(-0.450343\pi\) |
0.933194 | + | 0.359373i | \(0.117009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.9622 | + | 1.02039i | 0.572395 | + | 0.0418318i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.35950 | − | 1.36226i | −0.0964068 | − | 0.0556605i | 0.451021 | − | 0.892513i | \(-0.351060\pi\) |
−0.547428 | + | 0.836853i | \(0.684393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.9310i | − | 1.18012i | −0.807360 | − | 0.590059i | \(-0.799104\pi\) | ||
0.807360 | − | 0.590059i | \(-0.200896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.0228 | + | 12.1375i | 0.854697 | + | 0.493460i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.6523 | − | 28.8426i | −0.675896 | − | 1.17069i | −0.976206 | − | 0.216845i | \(-0.930423\pi\) |
0.300310 | − | 0.953842i | \(-0.402910\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 47.4929 | − | 27.4200i | 1.92136 | − | 1.10930i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.928335 | − | 1.60792i | 0.0374951 | − | 0.0649434i | −0.846669 | − | 0.532120i | \(-0.821395\pi\) |
0.884164 | + | 0.467177i | \(0.154729\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.4264 | −1.10415 | −0.552073 | − | 0.833796i | \(-0.686163\pi\) | ||||
−0.552073 | + | 0.833796i | \(0.686163\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.10474 | − | 1.91346i | 0.0444031 | − | 0.0769084i | −0.842970 | − | 0.537961i | \(-0.819195\pi\) |
0.887373 | + | 0.461053i | \(0.152528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.6289 | + | 9.49749i | −0.786415 | + | 0.380509i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6031 | + | 27.0253i | 0.624123 | + | 1.08101i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.26086i | − | 0.0901462i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.7387i | − | 0.785784i | −0.919585 | − | 0.392892i | \(-0.871475\pi\) | ||
0.919585 | − | 0.392892i | \(-0.128525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.8788 | − | 27.5029i | −0.630131 | − | 1.09142i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.79577 | − | 39.4407i | 0.229637 | − | 1.56270i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.48629 | + | 16.4307i | −0.374686 | + | 0.648975i | −0.990280 | − | 0.139088i | \(-0.955583\pi\) |
0.615594 | + | 0.788063i | \(0.288916\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.5988 | −0.694027 | −0.347013 | − | 0.937860i | \(-0.612804\pi\) | ||||
−0.347013 | + | 0.937860i | \(0.612804\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.01648 | + | 5.22469i | −0.118590 | + | 0.205404i | −0.919209 | − | 0.393770i | \(-0.871171\pi\) |
0.800619 | + | 0.599174i | \(0.204504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06598 | − | 0.615446i | 0.0418435 | − | 0.0241584i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.795336 | − | 1.37756i | −0.0311239 | − | 0.0539082i | 0.850044 | − | 0.526712i | \(-0.176575\pi\) |
−0.881168 | + | 0.472804i | \(0.843242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.2180 | + | 27.8387i | 1.88403 | + | 1.08775i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.83213i | − | 0.344051i | −0.985093 | − | 0.172025i | \(-0.944969\pi\) | ||
0.985093 | − | 0.172025i | \(-0.0550311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.26457 | − | 0.730101i | −0.0491862 | − | 0.0283976i | 0.475205 | − | 0.879875i | \(-0.342374\pi\) |
−0.524391 | + | 0.851477i | \(0.675707\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.27461 | + | 2.90283i | 0.165762 | + | 0.112567i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.41252 | − | 1.97022i | 0.132133 | − | 0.0762873i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.2939 | 0.744835 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7279 | −1.22302 | −0.611510 | − | 0.791237i | \(-0.709438\pi\) | ||||
−0.611510 | + | 0.791237i | \(0.709438\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.46898 | − | 3.15752i | 0.210190 | − | 0.121353i | −0.391210 | − | 0.920302i | \(-0.627943\pi\) |
0.601400 | + | 0.798948i | \(0.294610\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.196468 | − | 2.68832i | 0.00753976 | − | 0.103168i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.00339 | + | 1.73401i | 0.114921 | + | 0.0663499i | 0.556359 | − | 0.830942i | \(-0.312198\pi\) |
−0.441438 | + | 0.897292i | \(0.645531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 52.8406i | 2.01894i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −61.7678 | − | 35.6617i | −2.35317 | − | 1.35860i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.28609 | − | 7.42372i | −0.163050 | − | 0.282412i | 0.772911 | − | 0.634515i | \(-0.218800\pi\) |
−0.935961 | + | 0.352103i | \(0.885467\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −45.3898 | + | 26.2058i | −1.72173 | + | 0.994043i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.54951 | + | 2.68383i | −0.0586918 | + | 0.101657i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.08683 | 0.229896 | 0.114948 | − | 0.993371i | \(-0.463330\pi\) | ||||
0.114948 | + | 0.993371i | \(0.463330\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.417231 | − | 0.722665i | 0.0157362 | − | 0.0272558i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.1483 | − | 17.7569i | −0.983408 | − | 0.667818i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4284 | + | 31.9189i | 0.692092 | + | 1.19874i | 0.971151 | + | 0.238464i | \(0.0766439\pi\) |
−0.279060 | + | 0.960274i | \(0.590023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.24561i | 0.121549i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.7986i | 0.815220i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.7917 | + | 39.4764i | 0.849988 | + | 1.47222i | 0.881218 | + | 0.472710i | \(0.156724\pi\) |
−0.0312297 | + | 0.999512i | \(0.509942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.2701 | − | 41.8932i | −0.754900 | − | 1.56019i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.94586 | + | 12.0306i | −0.257963 | + | 0.446805i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.02124 | −0.334579 | −0.167290 | − | 0.985908i | \(-0.553502\pi\) | ||||
−0.167290 | + | 0.985908i | \(0.553502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.6011 | + | 18.3616i | −0.392094 | + | 0.679127i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.9079 | − | 15.5353i | 0.993865 | − | 0.573808i | 0.0874376 | − | 0.996170i | \(-0.472132\pi\) |
0.906427 | + | 0.422362i | \(0.138799\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0376289 | − | 0.0651752i | −0.00138608 | − | 0.00240076i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.6812 | + | 18.8685i | 1.20220 | + | 0.694089i | 0.961043 | − | 0.276398i | \(-0.0891409\pi\) |
0.241154 | + | 0.970487i | \(0.422474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 43.6664i | − | 1.60197i | −0.598687 | − | 0.800983i | \(-0.704311\pi\) | ||
0.598687 | − | 0.800983i | \(-0.295689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.9230 | + | 25.9363i | 1.64585 | + | 0.950233i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.7124 | − | 16.7957i | 1.26836 | − | 0.613701i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.5829 | + | 23.4306i | −1.48089 | + | 0.854993i | −0.999765 | − | 0.0216580i | \(-0.993106\pi\) |
−0.481126 | + | 0.876651i | \(0.659772\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.52819 | 0.164798 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1824 | 0.733543 | 0.366771 | − | 0.930311i | \(-0.380463\pi\) | ||||
0.366771 | + | 0.930311i | \(0.380463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.87020 | − | 2.23446i | 0.140295 | − | 0.0809991i | −0.428210 | − | 0.903679i | \(-0.640856\pi\) |
0.568504 | + | 0.822680i | \(0.307522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.05124 | − | 11.8560i | 0.291474 | − | 0.429216i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.28229 | − | 2.47238i | −0.154625 | − | 0.0892725i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.5449i | 0.921173i | 0.887615 | + | 0.460587i | \(0.152361\pi\) | ||||
−0.887615 | + | 0.460587i | \(0.847639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6854 | + | 9.05597i | 0.564165 | + | 0.325721i | 0.754815 | − | 0.655937i | \(-0.227726\pi\) |
−0.190651 | + | 0.981658i | \(0.561060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.72108 | − | 9.90919i | −0.205507 | − | 0.355949i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.990577 | + | 0.571910i | −0.0354911 | + | 0.0204908i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.96537 | + | 17.2605i | −0.356589 | + | 0.617630i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.2560 | 0.758660 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.3136 | + | 38.6483i | −0.795394 | + | 1.37766i | 0.127195 | + | 0.991878i | \(0.459403\pi\) |
−0.922589 | + | 0.385785i | \(0.873931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.9279 | − | 1.09096i | −0.530774 | − | 0.0387901i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.7540 | − | 67.1239i | −1.37620 | − | 2.38364i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.9941i | 0.885335i | 0.896686 | + | 0.442668i | \(0.145968\pi\) | ||||
−0.896686 | + | 0.442668i | \(0.854032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.8709i | 0.667604i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.0918 | + | 19.2115i | 0.391420 | + | 0.677960i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.60766 | + | 3.83996i | −0.0919080 | + | 0.135341i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.3434 | − | 23.1115i | 0.469129 | − | 0.812556i | −0.530248 | − | 0.847843i | \(-0.677901\pi\) |
0.999377 | + | 0.0352870i | \(0.0112345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1884 | 0.427994 | 0.213997 | − | 0.976834i | \(-0.431352\pi\) | ||||
0.213997 | + | 0.976834i | \(0.431352\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.81274 | − | 8.33592i | 0.168583 | − | 0.291994i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.77709 | + | 3.91276i | −0.237101 | + | 0.136890i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.04570 | + | 13.9356i | 0.280797 | + | 0.486355i | 0.971581 | − | 0.236706i | \(-0.0760679\pi\) |
−0.690784 | + | 0.723061i | \(0.742735\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.9992 | − | 9.23714i | −0.557697 | − | 0.321986i | 0.194524 | − | 0.980898i | \(-0.437684\pi\) |
−0.752221 | + | 0.658911i | \(0.771017\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.1954i | 1.74547i | 0.488198 | + | 0.872733i | \(0.337654\pi\) | ||||
−0.488198 | + | 0.872733i | \(0.662346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6810 | + | 10.2081i | 0.614085 | + | 0.354542i | 0.774563 | − | 0.632497i | \(-0.217970\pi\) |
−0.160477 | + | 0.987040i | \(0.551303\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.7564 | + | 8.51309i | 0.372686 | + | 0.294961i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.6271 | + | 14.7958i | −0.886862 | + | 0.512030i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.8855 | 0.721048 | 0.360524 | − | 0.932750i | \(-0.382598\pi\) | ||||
0.360524 | + | 0.932750i | \(0.382598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.77923 | 0.268249 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.4387 | − | 26.2341i | 1.56314 | − | 0.902479i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3600 | + | 21.4116i | 0.355975 | + | 0.735710i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.649184 | + | 0.374806i | 0.0222537 | + | 0.0128482i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.6666i | − | 0.810329i | −0.914244 | − | 0.405165i | \(-0.867214\pi\) | ||
0.914244 | − | 0.405165i | \(-0.132786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.71294 | + | 1.56631i | 0.0926721 | + | 0.0535043i | 0.545620 | − | 0.838033i | \(-0.316294\pi\) |
−0.452948 | + | 0.891537i | \(0.649628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.15051 | + | 15.8491i | 0.312211 | + | 0.540766i | 0.978841 | − | 0.204623i | \(-0.0655970\pi\) |
−0.666629 | + | 0.745389i | \(0.732264\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.26257 | − | 2.46099i | 0.145099 | − | 0.0837732i | −0.425693 | − | 0.904868i | \(-0.639970\pi\) |
0.570792 | + | 0.821095i | \(0.306636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.5655 | − | 44.2807i | 0.869253 | − | 1.50559i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.2935 | 0.552719 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.151164 | + | 0.261823i | −0.00512199 | + | 0.00887154i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.41076 | + | 19.3038i | −0.0476925 | + | 0.652588i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8882 | + | 34.4474i | 0.671578 | + | 1.16321i | 0.977457 | + | 0.211136i | \(0.0677163\pi\) |
−0.305879 | + | 0.952070i | \(0.598950\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 21.2750i | − | 0.716774i | −0.933573 | − | 0.358387i | \(-0.883327\pi\) | ||
0.933573 | − | 0.358387i | \(-0.116673\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.6054i | 0.760733i | 0.924836 | + | 0.380366i | \(0.124202\pi\) | ||||
−0.924836 | + | 0.380366i | \(0.875798\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.8162 | + | 27.3945i | 0.531057 | + | 0.919817i | 0.999343 | + | 0.0362405i | \(0.0115382\pi\) |
−0.468286 | + | 0.883577i | \(0.655128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.26813 | − | 31.0354i | 0.0760708 | − | 1.04089i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.48254 | + | 6.03193i | −0.116539 | + | 0.201851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.9475 | 0.533065 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.1469 | + | 26.2352i | −0.505178 | + | 0.874994i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.2548 | − | 12.2715i | 0.708099 | − | 0.408821i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.1172 | − | 57.3606i | −1.10085 | − | 1.90673i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.5515 | − | 8.97867i | −0.516380 | − | 0.298132i | 0.219073 | − | 0.975709i | \(-0.429697\pi\) |
−0.735452 | + | 0.677577i | \(0.763030\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.5199i | 1.27622i | 0.769945 | + | 0.638110i | \(0.220284\pi\) | ||||
−0.769945 | + | 0.638110i | \(0.779716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.63226 | + | 2.09709i | 0.120210 | + | 0.0694035i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.7619 | + | 49.1097i | 0.784686 | + | 1.62175i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.26565 | + | 1.88542i | −0.107724 | + | 0.0621944i | −0.552894 | − | 0.833252i | \(-0.686477\pi\) |
0.445170 | + | 0.895446i | \(0.353143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80.0662 | 2.63541 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.64270 | −0.0868915 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.54078 | − | 5.50837i | 0.313023 | − | 0.180724i | −0.335255 | − | 0.942127i | \(-0.608823\pi\) |
0.648278 | + | 0.761403i | \(0.275489\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.86714 | + | 4.70619i | 0.0611930 | + | 0.154239i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.49610 | − | 3.75052i | −0.212445 | − | 0.122655i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.09549i | 0.166462i | 0.996530 | + | 0.0832312i | \(0.0265240\pi\) | ||||
−0.996530 | + | 0.0832312i | \(0.973476\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.96326 | − | 5.17494i | −0.292194 | − | 0.168698i | 0.346737 | − | 0.937962i | \(-0.387290\pi\) |
−0.638931 | + | 0.769264i | \(0.720623\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.513757 | − | 0.889854i | −0.0167302 | − | 0.0289776i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.5816 | − | 23.4298i | 1.31873 | − | 0.761367i | 0.335202 | − | 0.942146i | \(-0.391195\pi\) |
0.983524 | + | 0.180780i | \(0.0578620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.5581 | − | 77.1769i | 1.44642 | − | 2.50527i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.3560 | −1.33965 | −0.669825 | − | 0.742519i | \(-0.733631\pi\) | ||||
−0.669825 | + | 0.742519i | \(0.733631\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.6449 | − | 18.4375i | 0.344460 | − | 0.596622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.0878 | + | 42.8337i | −0.939293 | + | 1.38317i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.02399 | + | 5.23770i | 0.0975479 | + | 0.168958i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.0243i | 0.934326i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.6169i | − | 0.759467i | −0.925096 | − | 0.379733i | \(-0.876016\pi\) | ||
0.925096 | − | 0.379733i | \(-0.123984\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.1664 | − | 40.1254i | −0.743446 | − | 1.28769i | −0.950917 | − | 0.309445i | \(-0.899857\pi\) |
0.207472 | − | 0.978241i | \(-0.433476\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.2198 | − | 3.74325i | −1.64203 | − | 0.120003i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.17019 | + | 10.6871i | −0.197402 | + | 0.341910i | −0.947685 | − | 0.319206i | \(-0.896584\pi\) |
0.750283 | + | 0.661116i | \(0.229917\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.6838 | 0.373416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.59504 | − | 16.6191i | 0.306034 | − | 0.530067i | −0.671457 | − | 0.741044i | \(-0.734331\pi\) |
0.977491 | + | 0.210977i | \(0.0676644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.5561 | − | 8.40396i | 0.463796 | − | 0.267773i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.51490 | − | 6.08799i | −0.111767 | − | 0.193587i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.65548 | + | 4.99724i | 0.274950 | + | 0.158743i | 0.631135 | − | 0.775673i | \(-0.282589\pi\) |
−0.356185 | + | 0.934416i | \(0.615923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.5625i | 0.366556i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.3809 | + | 19.2725i | 1.05718 | + | 0.610365i | 0.924652 | − | 0.380814i | \(-0.124356\pi\) |
0.132532 | + | 0.991179i | \(0.457689\pi\) | |||||||
\(998\) | 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.cs.c.703.2 | 16 | ||
3.2 | odd | 2 | 672.2.bl.b.31.7 | yes | 16 | ||
4.3 | odd | 2 | 2016.2.cs.a.703.2 | 16 | |||
7.5 | odd | 6 | 2016.2.cs.a.1279.2 | 16 | |||
12.11 | even | 2 | 672.2.bl.a.31.7 | ✓ | 16 | ||
21.5 | even | 6 | 672.2.bl.a.607.7 | yes | 16 | ||
21.11 | odd | 6 | 4704.2.b.d.1567.14 | 16 | |||
21.17 | even | 6 | 4704.2.b.e.1567.3 | 16 | |||
24.5 | odd | 2 | 1344.2.bl.k.703.2 | 16 | |||
24.11 | even | 2 | 1344.2.bl.l.703.2 | 16 | |||
28.19 | even | 6 | inner | 2016.2.cs.c.1279.2 | 16 | ||
84.11 | even | 6 | 4704.2.b.e.1567.14 | 16 | |||
84.47 | odd | 6 | 672.2.bl.b.607.7 | yes | 16 | ||
84.59 | odd | 6 | 4704.2.b.d.1567.3 | 16 | |||
168.5 | even | 6 | 1344.2.bl.l.1279.2 | 16 | |||
168.131 | odd | 6 | 1344.2.bl.k.1279.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.bl.a.31.7 | ✓ | 16 | 12.11 | even | 2 | ||
672.2.bl.a.607.7 | yes | 16 | 21.5 | even | 6 | ||
672.2.bl.b.31.7 | yes | 16 | 3.2 | odd | 2 | ||
672.2.bl.b.607.7 | yes | 16 | 84.47 | odd | 6 | ||
1344.2.bl.k.703.2 | 16 | 24.5 | odd | 2 | |||
1344.2.bl.k.1279.2 | 16 | 168.131 | odd | 6 | |||
1344.2.bl.l.703.2 | 16 | 24.11 | even | 2 | |||
1344.2.bl.l.1279.2 | 16 | 168.5 | even | 6 | |||
2016.2.cs.a.703.2 | 16 | 4.3 | odd | 2 | |||
2016.2.cs.a.1279.2 | 16 | 7.5 | odd | 6 | |||
2016.2.cs.c.703.2 | 16 | 1.1 | even | 1 | trivial | ||
2016.2.cs.c.1279.2 | 16 | 28.19 | even | 6 | inner | ||
4704.2.b.d.1567.3 | 16 | 84.59 | odd | 6 | |||
4704.2.b.d.1567.14 | 16 | 21.11 | odd | 6 | |||
4704.2.b.e.1567.3 | 16 | 21.17 | even | 6 | |||
4704.2.b.e.1567.14 | 16 | 84.11 | even | 6 |