Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1100,3,Mod(549,1100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1100.549");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1100.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9728290796\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 85x^{14} + 2456x^{12} + 32605x^{10} + 215801x^{8} + 712960x^{6} + 1098976x^{4} + 633600x^{2} + 92416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{25}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 220) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 549.4 | ||
Root | \(0.465196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1100.549 |
Dual form | 1100.3.e.b.549.14 |
$q$-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 \(\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(551\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.65160i | − | 1.21720i | −0.793478 | − | 0.608600i | \(-0.791732\pi\) | ||
0.793478 | − | 0.608600i | \(-0.208268\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.09184 | 1.29883 | 0.649417 | − | 0.760432i | \(-0.275013\pi\) | ||||
0.649417 | + | 0.760432i | \(0.275013\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.33416 | −0.481573 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.88767 | + | 4.82017i | 0.898879 | + | 0.438198i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.5101 | −1.73155 | −0.865774 | − | 0.500436i | \(-0.833173\pi\) | ||||
−0.865774 | + | 0.500436i | \(0.833173\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.9153 | −1.34796 | −0.673978 | − | 0.738751i | \(-0.735416\pi\) | ||||
−0.673978 | + | 0.738751i | \(0.735416\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 16.0035i | − | 0.842292i | −0.906993 | − | 0.421146i | \(-0.861628\pi\) | ||
0.906993 | − | 0.421146i | \(-0.138372\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 33.1997i | − | 1.58094i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.141697i | − | 0.00616076i | −0.999995 | − | 0.00308038i | \(-0.999019\pi\) | ||
0.999995 | − | 0.00308038i | \(-0.000980517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 17.0378i | − | 0.631028i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 29.8270i | − | 1.02852i | −0.857636 | − | 0.514258i | \(-0.828067\pi\) | ||
0.857636 | − | 0.514258i | \(-0.171933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21.5229 | 0.694287 | 0.347144 | − | 0.937812i | \(-0.387152\pi\) | ||||
0.347144 | + | 0.937812i | \(0.387152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.6013 | − | 36.1058i | 0.533374 | − | 1.09411i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 28.0333i | − | 0.757657i | −0.925467 | − | 0.378829i | \(-0.876327\pi\) | ||
0.925467 | − | 0.378829i | \(-0.123673\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 82.1979i | 2.10764i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 39.5629i | − | 0.964950i | −0.875910 | − | 0.482475i | \(-0.839738\pi\) | ||
0.875910 | − | 0.482475i | \(-0.160262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21.4131 | 0.497979 | 0.248990 | − | 0.968506i | \(-0.419902\pi\) | ||||
0.248990 | + | 0.968506i | \(0.419902\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 15.4239i | − | 0.328167i | −0.986446 | − | 0.164084i | \(-0.947533\pi\) | ||
0.986446 | − | 0.164084i | \(-0.0524667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 33.6616 | 0.686971 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 83.6773i | 1.64073i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 75.9763i | − | 1.43352i | −0.697322 | − | 0.716758i | \(-0.745625\pi\) | ||
0.697322 | − | 0.716758i | \(-0.254375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −58.4385 | −1.02524 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50.4169 | 0.854524 | 0.427262 | − | 0.904128i | \(-0.359478\pi\) | ||||
0.427262 | + | 0.904128i | \(0.359478\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 98.4882i | 1.61456i | 0.590169 | + | 0.807280i | \(0.299061\pi\) | ||||
−0.590169 | + | 0.807280i | \(0.700939\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −39.4055 | −0.625484 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 125.070i | − | 1.86672i | −0.358939 | − | 0.933361i | \(-0.616862\pi\) | ||
0.358939 | − | 0.933361i | \(-0.383138\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.517422 | −0.00749887 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −100.615 | −1.41711 | −0.708556 | − | 0.705654i | \(-0.750653\pi\) | ||||
−0.708556 | + | 0.705654i | \(0.750653\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −128.281 | −1.75728 | −0.878639 | − | 0.477487i | \(-0.841548\pi\) | ||||
−0.878639 | + | 0.477487i | \(0.841548\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 89.8971 | + | 43.8243i | 1.16749 | + | 0.569146i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 103.932i | − | 1.31559i | −0.753197 | − | 0.657795i | \(-0.771489\pi\) | ||
0.753197 | − | 0.657795i | \(-0.228511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.222 | −1.24966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 75.6774 | 0.911776 | 0.455888 | − | 0.890037i | \(-0.349322\pi\) | ||||
0.455888 | + | 0.890037i | \(0.349322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −108.916 | −1.25191 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 58.9162 | 0.661980 | 0.330990 | − | 0.943634i | \(-0.392617\pi\) | ||||
0.330990 | + | 0.943634i | \(0.392617\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −204.658 | −2.24899 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 78.5930i | − | 0.845086i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 62.4540i | 0.643856i | 0.946764 | + | 0.321928i | \(0.104331\pi\) | ||||
−0.946764 | + | 0.321928i | \(0.895669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −42.8547 | − | 20.8914i | −0.432876 | − | 0.211024i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 61.1871i | − | 0.605813i | −0.953020 | − | 0.302906i | \(-0.902043\pi\) | ||
0.953020 | − | 0.302906i | \(-0.0979570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 46.9015i | 0.455354i | 0.973737 | + | 0.227677i | \(0.0731130\pi\) | ||||
−0.973737 | + | 0.227677i | \(0.926887\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −66.2421 | −0.619085 | −0.309542 | − | 0.950886i | \(-0.600176\pi\) | ||||
−0.309542 | + | 0.950886i | \(0.600176\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.2255i | − | 0.167207i | −0.996499 | − | 0.0836033i | \(-0.973357\pi\) | ||
0.996499 | − | 0.0836033i | \(-0.0266429\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −102.366 | −0.922220 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 135.813i | − | 1.20189i | −0.799292 | − | 0.600943i | \(-0.794792\pi\) | ||
0.799292 | − | 0.600943i | \(-0.205208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 97.5625 | 0.833867 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −208.342 | −1.75077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 74.5318 | + | 95.3205i | 0.615966 | + | 0.787773i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −144.468 | −1.17454 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 143.106 | 1.12682 | 0.563410 | − | 0.826177i | \(-0.309489\pi\) | ||||
0.563410 | + | 0.826177i | \(0.309489\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 78.1920i | − | 0.606140i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 49.9179i | 0.381053i | 0.981682 | + | 0.190526i | \(0.0610195\pi\) | ||||
−0.981682 | + | 0.190526i | \(0.938981\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 145.502i | − | 1.09400i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 253.448i | 1.84999i | 0.379981 | + | 0.924994i | \(0.375931\pi\) | ||||
−0.379981 | + | 0.924994i | \(0.624069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 189.435i | 1.36284i | 0.731893 | + | 0.681419i | \(0.238637\pi\) | ||||
−0.731893 | + | 0.681419i | \(0.761363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −56.3217 | −0.399445 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −222.572 | − | 108.503i | −1.55645 | − | 0.758760i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 122.919i | − | 0.836181i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 163.116i | 1.09474i | 0.836892 | + | 0.547368i | \(0.184370\pi\) | ||||
−0.836892 | + | 0.547368i | \(0.815630\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 85.6125i | 0.566970i | 0.958977 | + | 0.283485i | \(0.0914906\pi\) | ||||
−0.958977 | + | 0.283485i | \(0.908509\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 99.3184 | 0.649140 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 105.429i | 0.671524i | 0.941947 | + | 0.335762i | \(0.108994\pi\) | ||||
−0.941947 | + | 0.335762i | \(0.891006\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −277.435 | −1.74487 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.28829i | − | 0.00800181i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 99.9791i | − | 0.613369i | −0.951811 | − | 0.306684i | \(-0.900780\pi\) | ||
0.951811 | − | 0.306684i | \(-0.0992196\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.6434 | 0.0816970 | 0.0408485 | − | 0.999165i | \(-0.486994\pi\) | ||||
0.0408485 | + | 0.999165i | \(0.486994\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 337.705 | 1.99826 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 69.3620i | 0.405625i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −222.063 | −1.28360 | −0.641801 | − | 0.766872i | \(-0.721812\pi\) | ||||
−0.641801 | + | 0.766872i | \(0.721812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 184.102i | − | 1.04013i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.9227 | 0.0777806 | 0.0388903 | − | 0.999243i | \(-0.487618\pi\) | ||||
0.0388903 | + | 0.999243i | \(0.487618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 73.2171 | 0.404515 | 0.202257 | − | 0.979332i | \(-0.435172\pi\) | ||||
0.202257 | + | 0.979332i | \(0.435172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 359.639 | 1.96524 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −226.578 | − | 110.456i | −1.21165 | − | 0.590671i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 154.905i | − | 0.819601i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 79.4081 | 0.415749 | 0.207875 | − | 0.978155i | \(-0.433345\pi\) | ||||
0.207875 | + | 0.978155i | \(0.433345\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 140.214 | 0.726499 | 0.363250 | − | 0.931692i | \(-0.381667\pi\) | ||||
0.363250 | + | 0.931692i | \(0.381667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 76.4700 | 0.388172 | 0.194086 | − | 0.980984i | \(-0.437826\pi\) | ||||
0.194086 | + | 0.980984i | \(0.437826\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.636328 | −0.00319763 | −0.00159881 | − | 0.999999i | \(-0.500509\pi\) | ||||
−0.00159881 | + | 0.999999i | \(0.500509\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −456.707 | −2.27217 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 271.182i | − | 1.33587i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.614140i | 0.00296686i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 77.1399 | − | 158.238i | 0.369090 | − | 0.757118i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 169.636i | − | 0.803962i | −0.915648 | − | 0.401981i | \(-0.868322\pi\) | ||
0.915648 | − | 0.401981i | \(-0.131678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 367.406i | 1.72491i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 195.683 | 0.901764 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 468.432i | 2.13896i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 515.825 | 2.33405 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 149.796i | 0.671731i | 0.941910 | + | 0.335865i | \(0.109029\pi\) | ||||
−0.941910 | + | 0.335865i | \(0.890971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −194.090 | −0.855020 | −0.427510 | − | 0.904011i | \(-0.640609\pi\) | ||||
−0.427510 | + | 0.904011i | \(0.640609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 329.237 | 1.43772 | 0.718859 | − | 0.695156i | \(-0.244665\pi\) | ||||
0.718859 | + | 0.695156i | \(0.244665\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 160.029 | − | 328.268i | 0.692764 | − | 1.42107i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 66.5340 | 0.285554 | 0.142777 | − | 0.989755i | \(-0.454397\pi\) | ||||
0.142777 | + | 0.989755i | \(0.454397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −379.516 | −1.60133 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 90.8230i | − | 0.380012i | −0.981783 | − | 0.190006i | \(-0.939149\pi\) | ||
0.981783 | − | 0.190006i | \(-0.0608508\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 122.137i | 0.506794i | 0.967362 | + | 0.253397i | \(0.0815479\pi\) | ||||
−0.967362 | + | 0.253397i | \(0.918452\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 216.284i | 0.890057i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 360.242i | 1.45847i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 276.343i | − | 1.10981i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 396.928 | 1.58138 | 0.790692 | − | 0.612214i | \(-0.209721\pi\) | ||||
0.790692 | + | 0.612214i | \(0.209721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.683006 | − | 1.40106i | 0.00269963 | − | 0.00553777i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 351.814i | − | 1.36892i | −0.729048 | − | 0.684462i | \(-0.760037\pi\) | ||
0.729048 | − | 0.684462i | \(-0.239963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 254.874i | − | 0.984071i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 129.275i | 0.495306i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −159.720 | −0.607301 | −0.303650 | − | 0.952784i | \(-0.598205\pi\) | ||||
−0.303650 | + | 0.952784i | \(0.598205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 215.138i | − | 0.805762i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −354.272 | −1.31700 | −0.658498 | − | 0.752582i | \(-0.728808\pi\) | ||||
−0.658498 | + | 0.752582i | \(0.728808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 217.764i | − | 0.803559i | −0.915737 | − | 0.401779i | \(-0.868392\pi\) | ||
0.915737 | − | 0.401779i | \(-0.131608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 747.330i | 2.73747i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 425.599 | 1.53646 | 0.768230 | − | 0.640174i | \(-0.221138\pi\) | ||||
0.768230 | + | 0.640174i | \(0.221138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −93.2837 | −0.334350 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 367.218i | − | 1.30682i | −0.757003 | − | 0.653412i | \(-0.773337\pi\) | ||
0.757003 | − | 0.653412i | \(-0.226663\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 424.761 | 1.50092 | 0.750461 | − | 0.660914i | \(-0.229831\pi\) | ||||
0.750461 | + | 0.660914i | \(0.229831\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 359.700i | − | 1.25331i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 236.109 | 0.816985 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 228.057 | 0.783701 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 50.0611 | 0.170857 | 0.0854285 | − | 0.996344i | \(-0.472774\pi\) | ||||
0.0854285 | + | 0.996344i | \(0.472774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 82.1250 | − | 168.464i | 0.276515 | − | 0.567218i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.18963i | 0.0106676i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 194.685 | 0.646793 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −223.431 | −0.737395 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 76.8244 | 0.250242 | 0.125121 | − | 0.992141i | \(-0.460068\pi\) | ||||
0.125121 | + | 0.992141i | \(0.460068\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 171.265 | 0.554257 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −566.867 | −1.82272 | −0.911361 | − | 0.411608i | \(-0.864967\pi\) | ||||
−0.911361 | + | 0.411608i | \(0.864967\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 40.8962i | 0.130659i | 0.997864 | + | 0.0653294i | \(0.0208098\pi\) | ||||
−0.997864 | + | 0.0653294i | \(0.979190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 179.622i | 0.566632i | 0.959027 | + | 0.283316i | \(0.0914345\pi\) | ||||
−0.959027 | + | 0.283316i | \(0.908566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 143.771 | − | 294.919i | 0.450693 | − | 0.924511i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 241.889i | 0.753549i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 366.725i | 1.13537i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −66.5523 | −0.203524 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 140.231i | − | 0.426235i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 504.228 | 1.52335 | 0.761674 | − | 0.647960i | \(-0.224378\pi\) | ||||
0.761674 | + | 0.647960i | \(0.224378\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 121.501i | 0.364868i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −437.742 | −1.29894 | −0.649468 | − | 0.760389i | \(-0.725009\pi\) | ||||
−0.649468 | + | 0.760389i | \(0.725009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −495.935 | −1.46294 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 212.811 | + | 103.744i | 0.624080 | + | 0.304235i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −139.454 | −0.406572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 194.366 | 0.560133 | 0.280067 | − | 0.959981i | \(-0.409643\pi\) | ||||
0.280067 | + | 0.959981i | \(0.409643\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 282.947i | 0.810737i | 0.914153 | + | 0.405369i | \(0.132857\pi\) | ||||
−0.914153 | + | 0.405369i | \(0.867143\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 383.522i | 1.09266i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 156.412i | − | 0.443094i | −0.975150 | − | 0.221547i | \(-0.928889\pi\) | ||
0.975150 | − | 0.221547i | \(-0.0711106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 760.781i | 2.13104i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 614.980i | 1.71304i | 0.516116 | + | 0.856518i | \(0.327377\pi\) | ||||
−0.516116 | + | 0.856518i | \(0.672623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 104.886 | 0.290544 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 348.072 | − | 272.160i | 0.958877 | − | 0.749753i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.10499i | 0.0166349i | 0.999965 | + | 0.00831743i | \(0.00264755\pi\) | ||||
−0.999965 | + | 0.00831743i | \(0.997352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 171.472i | 0.464694i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 690.765i | − | 1.86190i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 358.254 | 0.960467 | 0.480233 | − | 0.877141i | \(-0.340552\pi\) | ||||
0.480233 | + | 0.877141i | \(0.340552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 671.408i | 1.78092i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.7025 | 0.0968405 | 0.0484202 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484202 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 522.566i | − | 1.37157i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 87.9982i | 0.229760i | 0.993379 | + | 0.114880i | \(0.0366484\pi\) | ||||
−0.993379 | + | 0.114880i | \(0.963352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −92.8078 | −0.239814 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −68.1918 | −0.175300 | −0.0876501 | − | 0.996151i | \(-0.527936\pi\) | ||||
−0.0876501 | + | 0.996151i | \(0.527936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.24703i | 0.00830443i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 182.280 | 0.463817 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 575.669i | 1.45005i | 0.688723 | + | 0.725024i | \(0.258172\pi\) | ||||
−0.688723 | + | 0.725024i | \(0.741828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −531.314 | −1.33161 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −119.702 | −0.298509 | −0.149255 | − | 0.988799i | \(-0.547687\pi\) | ||||
−0.149255 | + | 0.988799i | \(0.547687\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −484.483 | −1.20219 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 135.125 | − | 277.184i | 0.332004 | − | 0.681042i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 268.469i | 0.656403i | 0.944608 | + | 0.328201i | \(0.106442\pi\) | ||||
−0.944608 | + | 0.328201i | \(0.893558\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 925.492 | 2.25180 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 458.383 | 1.10989 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 691.739 | 1.65885 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 192.996 | 0.460610 | 0.230305 | − | 0.973118i | \(-0.426028\pi\) | ||||
0.230305 | + | 0.973118i | \(0.426028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −802.207 | −1.90548 | −0.952740 | − | 0.303788i | \(-0.901749\pi\) | ||||
−0.952740 | + | 0.303788i | \(0.901749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 66.8495i | 0.158037i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 895.439i | 2.09705i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −396.208 | + | 812.745i | −0.923562 | + | 1.89451i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 834.575i | 1.93637i | 0.250240 | + | 0.968184i | \(0.419491\pi\) | ||||
−0.250240 | + | 0.968184i | \(0.580509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 678.057i | 1.56595i | 0.622052 | + | 0.782976i | \(0.286299\pi\) | ||||
−0.622052 | + | 0.782976i | \(0.713701\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.26766 | −0.00518916 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 562.372i | − | 1.28103i | −0.767946 | − | 0.640515i | \(-0.778721\pi\) | ||
0.767946 | − | 0.640515i | \(-0.221279\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145.895 | −0.330827 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 597.796i | − | 1.34943i | −0.738080 | − | 0.674713i | \(-0.764267\pi\) | ||
0.738080 | − | 0.674713i | \(-0.235733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 595.633 | 1.33251 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 244.096 | 0.543643 | 0.271821 | − | 0.962348i | \(-0.412374\pi\) | ||||
0.271821 | + | 0.962348i | \(0.412374\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 190.700 | − | 391.185i | 0.422839 | − | 0.867373i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 312.622 | 0.690116 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 457.420 | 1.00092 | 0.500460 | − | 0.865760i | \(-0.333164\pi\) | ||||
0.500460 | + | 0.865760i | \(0.333164\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 390.425i | 0.850598i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 501.488i | − | 1.08783i | −0.839141 | − | 0.543913i | \(-0.816942\pi\) | ||
0.839141 | − | 0.543913i | \(-0.183058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 190.823i | 0.412144i | 0.978537 | + | 0.206072i | \(0.0660681\pi\) | ||||
−0.978537 | + | 0.206072i | \(0.933932\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 627.959i | − | 1.34467i | −0.740249 | − | 0.672333i | \(-0.765292\pi\) | ||
0.740249 | − | 0.672333i | \(-0.234708\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1137.12i | − | 2.42456i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 384.985 | 0.817379 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 211.726 | + | 103.215i | 0.447623 | + | 0.218213i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 329.294i | 0.690343i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 257.075i | − | 0.536691i | −0.963323 | − | 0.268345i | \(-0.913523\pi\) | ||
0.963323 | − | 0.268345i | \(-0.0864768\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 631.033i | 1.31192i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.70432 | −0.00973979 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 387.203i | 0.795079i | 0.917585 | + | 0.397539i | \(0.130136\pi\) | ||||
−0.917585 | + | 0.397539i | \(0.869864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −365.084 | −0.746592 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 905.259i | 1.84370i | 0.387542 | + | 0.921852i | \(0.373324\pi\) | ||||
−0.387542 | + | 0.921852i | \(0.626676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 683.492i | 1.38639i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −914.776 | −1.84060 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 330.636 | 0.662597 | 0.331298 | − | 0.943526i | \(-0.392513\pi\) | ||||
0.331298 | + | 0.943526i | \(0.392513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 49.8202i | − | 0.0994415i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −390.813 | −0.776964 | −0.388482 | − | 0.921456i | \(-0.627000\pi\) | ||||
−0.388482 | + | 0.921456i | \(0.627000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1233.16i | − | 2.43228i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −161.773 | −0.317825 | −0.158912 | − | 0.987293i | \(-0.550799\pi\) | ||||
−0.158912 | + | 0.987293i | \(0.550799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1166.31 | −2.28241 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −272.665 | −0.531510 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 74.3457 | − | 152.506i | 0.143802 | − | 0.294982i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 810.885i | 1.56240i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 49.8047 | 0.0955944 | 0.0477972 | − | 0.998857i | \(-0.484780\pi\) | ||||
0.0477972 | + | 0.998857i | \(0.484780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −750.487 | −1.43497 | −0.717483 | − | 0.696576i | \(-0.754706\pi\) | ||||
−0.717483 | + | 0.696576i | \(0.754706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −493.203 | −0.935869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.980 | 0.999962 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −218.515 | −0.411516 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 890.566i | 1.67086i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 50.8402i | − | 0.0946744i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 332.835 | + | 162.255i | 0.617504 | + | 0.301029i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 749.510i | − | 1.38541i | −0.721219 | − | 0.692707i | \(-0.756418\pi\) | ||
0.721219 | − | 0.692707i | \(-0.243582\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 267.359i | − | 0.492375i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −357.118 | −0.652867 | −0.326433 | − | 0.945220i | \(-0.605847\pi\) | ||||
−0.326433 | + | 0.945220i | \(0.605847\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 426.864i | − | 0.777529i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −477.337 | −0.866311 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 944.929i | − | 1.70873i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 555.491 | 0.997291 | 0.498646 | − | 0.866806i | \(-0.333831\pi\) | ||||
0.498646 | + | 0.866806i | \(0.333831\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −482.011 | −0.862275 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −403.339 | + | 827.373i | −0.718964 | + | 1.47482i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 618.559 | 1.09868 | 0.549342 | − | 0.835598i | \(-0.314878\pi\) | ||||
0.549342 | + | 0.835598i | \(0.314878\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −920.299 | −1.62310 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 873.411i | − | 1.53499i | −0.641054 | − | 0.767496i | \(-0.721502\pi\) | ||
0.641054 | − | 0.767496i | \(-0.278498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1073.95i | − | 1.88082i | −0.340046 | − | 0.940409i | \(-0.610443\pi\) | ||
0.340046 | − | 0.940409i | \(-0.389557\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 289.966i | − | 0.506049i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 136.957i | 0.237360i | 0.992933 | + | 0.118680i | \(0.0378663\pi\) | ||||
−0.992933 | + | 0.118680i | \(0.962134\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 512.006i | − | 0.884294i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 688.047 | 1.18425 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 366.219 | − | 751.229i | 0.628163 | − | 1.28856i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 531.023i | − | 0.904639i | −0.891856 | − | 0.452319i | \(-0.850597\pi\) | ||
0.891856 | − | 0.452319i | \(-0.149403\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 344.443i | − | 0.584792i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 279.237i | − | 0.472483i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −903.516 | −1.52364 | −0.761818 | − | 0.647791i | \(-0.775693\pi\) | ||||
−0.761818 | + | 0.647791i | \(0.775693\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.32361i | 0.00389215i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 800.473 | 1.33635 | 0.668174 | − | 0.744005i | \(-0.267076\pi\) | ||||
0.668174 | + | 0.744005i | \(0.267076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 274.107i | − | 0.456085i | −0.973651 | − | 0.228043i | \(-0.926767\pi\) | ||
0.973651 | − | 0.228043i | \(-0.0732325\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 542.075i | 0.898964i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 591.864 | 0.975064 | 0.487532 | − | 0.873105i | \(-0.337897\pi\) | ||||
0.487532 | + | 0.873105i | \(0.337897\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −990.247 | −1.62602 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 347.193i | 0.568237i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.59994 | 0.0107666 | 0.00538331 | − | 0.999986i | \(-0.498286\pi\) | ||||
0.00538331 | + | 0.999986i | \(0.498286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 719.824i | − | 1.16665i | −0.812238 | − | 0.583326i | \(-0.801751\pi\) | ||
0.812238 | − | 0.583326i | \(-0.198249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 106.000 | 0.171244 | 0.0856219 | − | 0.996328i | \(-0.472712\pi\) | ||||
0.0856219 | + | 0.996328i | \(0.472712\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.41421 | −0.00388761 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 535.657 | 0.859803 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −577.820 | − | 281.684i | −0.921564 | − | 0.449256i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 642.390i | 1.02129i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 651.103 | 1.03186 | 0.515930 | − | 0.856631i | \(-0.327447\pi\) | ||||
0.515930 | + | 0.856631i | \(0.327447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −619.443 | −0.978582 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −757.727 | −1.18952 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 436.082 | 0.682444 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −205.651 | −0.320828 | −0.160414 | − | 0.987050i | \(-0.551283\pi\) | ||||
−0.160414 | + | 0.987050i | \(0.551283\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 612.134i | 0.951997i | 0.879446 | + | 0.475998i | \(0.157913\pi\) | ||||
−0.879446 | + | 0.475998i | \(0.842087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.0151i | 0.0603015i | 0.999545 | + | 0.0301508i | \(0.00959874\pi\) | ||||
−0.999545 | + | 0.0301508i | \(0.990401\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 498.506 | + | 243.018i | 0.768114 | + | 0.374450i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 714.555i | − | 1.09763i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 48.3743i | − | 0.0740801i | −0.999314 | − | 0.0370400i | \(-0.988207\pi\) | ||
0.999314 | − | 0.0370400i | \(-0.0117929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 555.992 | 0.846258 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 546.722i | − | 0.829624i | −0.909907 | − | 0.414812i | \(-0.863847\pi\) | ||
0.909907 | − | 0.414812i | \(-0.136153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 592.309 | 0.896080 | 0.448040 | − | 0.894014i | \(-0.352122\pi\) | ||||
0.448040 | + | 0.894014i | \(0.352122\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1883.58i | − | 2.84100i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.22640 | −0.00633644 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 546.994 | 0.817630 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −474.730 | + | 973.818i | −0.707496 | + | 1.45129i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 566.186 | 0.841287 | 0.420644 | − | 0.907226i | \(-0.361804\pi\) | ||||
0.420644 | + | 0.907226i | \(0.361804\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 728.381 | 1.07590 | 0.537948 | − | 0.842978i | \(-0.319200\pi\) | ||||
0.537948 | + | 0.842978i | \(0.319200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 567.822i | 0.836263i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 708.737i | 1.04073i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.6410i | − | 0.0302211i | −0.999886 | − | 0.0151106i | \(-0.995190\pi\) | ||
0.999886 | − | 0.0151106i | \(-0.00481002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1202.24i | − | 1.74999i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1710.24i | 2.48220i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 727.350 | 1.05260 | 0.526302 | − | 0.850298i | \(-0.323578\pi\) | ||||
0.526302 | + | 0.850298i | \(0.323578\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −389.628 | − | 189.941i | −0.562234 | − | 0.274086i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 906.595i | 1.30071i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 242.955i | − | 0.347576i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 355.389i | 0.506975i | 0.967339 | + | 0.253487i | \(0.0815776\pi\) | ||||
−0.967339 | + | 0.253487i | \(0.918422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −448.632 | −0.638169 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 556.304i | − | 0.786851i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 538.342 | 0.759297 | 0.379649 | − | 0.925131i | \(-0.376045\pi\) | ||||
0.379649 | + | 0.925131i | \(0.376045\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 450.456i | 0.633553i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.04974i | − | 0.00427734i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −331.649 | −0.462551 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 283.789 | 0.394699 | 0.197350 | − | 0.980333i | \(-0.436767\pi\) | ||||
0.197350 | + | 0.980333i | \(0.436767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 426.421i | 0.591430i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 445.997 | 0.616870 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 875.176i | 1.20382i | 0.798565 | + | 0.601909i | \(0.205593\pi\) | ||||
−0.798565 | + | 0.601909i | \(0.794407\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −121.221 | −0.166284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −490.687 | −0.671254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 423.716 | 0.578057 | 0.289028 | − | 0.957321i | \(-0.406668\pi\) | ||||
0.289028 | + | 0.957321i | \(0.406668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 602.861 | − | 1236.65i | 0.817993 | − | 1.67796i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1189.52i | − | 1.60964i | −0.593520 | − | 0.804819i | \(-0.702262\pi\) | ||
0.593520 | − | 0.804819i | \(-0.297738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1315.46 | 1.77525 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 185.550 | 0.249731 | 0.124865 | − | 0.992174i | \(-0.460150\pi\) | ||||
0.124865 | + | 0.992174i | \(0.460150\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −327.998 | −0.439087 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −602.262 | −0.804089 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −495.474 | −0.659753 | −0.329876 | − | 0.944024i | \(-0.607007\pi\) | ||||
−0.329876 | + | 0.944024i | \(0.607007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1449.42i | − | 1.92486i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 183.782i | 0.242777i | 0.992605 | + | 0.121388i | \(0.0387347\pi\) | ||||
−0.992605 | + | 0.121388i | \(0.961265\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.11610 | − | 2.49406i | −0.00674057 | − | 0.00328599i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 902.350i | − | 1.18574i | −0.805298 | − | 0.592871i | \(-0.797994\pi\) | ||
0.805298 | − | 0.592871i | \(-0.202006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 165.704i | − | 0.217174i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1134.89 | −1.47965 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1009.09i | 1.31221i | 0.754668 | + | 0.656107i | \(0.227798\pi\) | ||||
−0.754668 | + | 0.656107i | \(0.772202\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1284.68 | −1.66625 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 645.499i | − | 0.835057i | −0.908664 | − | 0.417529i | \(-0.862896\pi\) | ||
0.908664 | − | 0.417529i | \(-0.137104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −930.699 | −1.19781 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −633.147 | −0.812770 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −994.848 | − | 484.982i | −1.27381 | − | 0.620976i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −508.185 | −0.649023 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 736.556 | 0.935903 | 0.467951 | − | 0.883754i | \(-0.344992\pi\) | ||||
0.467951 | + | 0.883754i | \(0.344992\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 583.233i | 0.739206i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1234.79i | − | 1.56105i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2216.98i | − | 2.79569i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 293.407i | 0.368139i | 0.982913 | + | 0.184070i | \(0.0589272\pi\) | ||||
−0.982913 | + | 0.184070i | \(0.941073\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 353.441i | 0.442355i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −255.352 | −0.318792 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1268.40 | − | 618.338i | −1.57958 | − | 0.770035i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1293.66i | 1.60305i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1076.81i | − | 1.33104i | −0.746379 | − | 0.665522i | \(-0.768209\pi\) | ||
0.746379 | − | 0.665522i | \(-0.231791\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 801.997i | 0.988898i | 0.869207 | + | 0.494449i | \(0.164630\pi\) | ||||
−0.869207 | + | 0.494449i | \(0.835370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −795.188 | −0.978091 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 342.686i | − | 0.419444i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 887.023 | 1.08306 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 644.550i | 0.785079i | 0.919735 | + | 0.392540i | \(0.128403\pi\) | ||||
−0.919735 | + | 0.392540i | \(0.871597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1390.56i | 1.68962i | 0.535065 | + | 0.844811i | \(0.320287\pi\) | ||||
−0.535065 | + | 0.844811i | \(0.679713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 71.7290 | 0.0867340 | 0.0433670 | − | 0.999059i | \(-0.486192\pi\) | ||||
0.0433670 | + | 0.999059i | \(0.486192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1121.23 | −1.35251 | −0.676255 | − | 0.736668i | \(-0.736398\pi\) | ||||
−0.676255 | + | 0.736668i | \(0.736398\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1554.12i | − | 1.87018i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −771.364 | −0.926007 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 366.702i | − | 0.438115i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1527.08 | −1.82012 | −0.910059 | − | 0.414478i | \(-0.863964\pi\) | ||||
−0.910059 | + | 0.414478i | \(0.863964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −48.6473 | −0.0578446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1340.93 | −1.59066 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 677.632 | + | 866.639i | 0.800037 | + | 1.02319i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1551.06i | − | 1.82692i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.97225 | −0.00466774 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −350.340 | −0.410715 | −0.205357 | − | 0.978687i | \(-0.565836\pi\) | ||||
−0.205357 | + | 0.978687i | \(0.565836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1137.89 | −1.32776 | −0.663880 | − | 0.747839i | \(-0.731091\pi\) | ||||
−0.663880 | + | 0.747839i | \(0.731091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1662.27 | −1.93512 | −0.967562 | − | 0.252635i | \(-0.918703\pi\) | ||||
−0.967562 | + | 0.252635i | \(0.918703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1313.48 | −1.52553 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 278.778i | 0.323033i | 0.986870 | + | 0.161517i | \(0.0516385\pi\) | ||||
−0.986870 | + | 0.161517i | \(0.948361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 862.174i | − | 0.994434i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 500.968 | − | 1027.64i | 0.576488 | − | 1.18256i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2815.35i | 3.23232i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 270.686i | − | 0.310064i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1493.74 | 1.70324 | 0.851620 | − | 0.524159i | \(-0.175620\pi\) | ||||
0.851620 | + | 0.524159i | \(0.175620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 182.803i | − | 0.207967i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −814.863 | −0.924929 | −0.462465 | − | 0.886638i | \(-0.653035\pi\) | ||||
−0.462465 | + | 0.886638i | \(0.653035\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 136.873i | − | 0.155009i | −0.996992 | − | 0.0775046i | \(-0.975305\pi\) | ||
0.996992 | − | 0.0775046i | \(-0.0246952\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 274.810 | 0.309820 | 0.154910 | − | 0.987929i | \(-0.450491\pi\) | ||||
0.154910 | + | 0.987929i | \(0.450491\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1301.10 | 1.46355 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1000.85 | − | 487.910i | −1.12329 | − | 0.547598i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −246.836 | −0.276412 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.6472 | 0.0129846 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 641.963i | − | 0.714085i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1741.02i | 1.93232i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 710.910i | − | 0.787275i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 471.112i | − | 0.519417i | −0.965687 | − | 0.259709i | \(-0.916373\pi\) | ||
0.965687 | − | 0.259709i | \(-0.0836265\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 265.195i | 0.291743i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −725.325 | −0.796185 | −0.398093 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398093 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 748.273 | + | 364.778i | 0.819576 | + | 0.399538i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 453.846i | 0.494925i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 598.323i | 0.651058i | 0.945532 | + | 0.325529i | \(0.105542\pi\) | ||||
−0.945532 | + | 0.325529i | \(0.894458\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 280.532i | − | 0.304595i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2264.86 | 2.45380 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 203.279i | − | 0.219286i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1189.14 | −1.28002 | −0.640008 | − | 0.768368i | \(-0.721069\pi\) | ||||
−0.640008 | + | 0.768368i | \(0.721069\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 538.705i | − | 0.578631i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2069.97i | 2.21862i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.72183 | −0.00183759 | −0.000918797 | − | 1.00000i | \(-0.500292\pi\) | ||||
−0.000918797 | 1.00000i | \(0.500292\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 149.336 | 0.159038 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 877.355i | 0.932364i | 0.884689 | + | 0.466182i | \(0.154371\pi\) | ||||
−0.884689 | + | 0.466182i | \(0.845629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.60597 | −0.00594482 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 517.593i | 0.546561i | 0.961934 | + | 0.273281i | \(0.0881088\pi\) | ||||
−0.961934 | + | 0.273281i | \(0.911891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2887.63 | 3.04281 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 655.908 | 0.689703 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 477.486 | 0.501034 | 0.250517 | − | 0.968112i | \(-0.419399\pi\) | ||||
0.250517 | + | 0.968112i | \(0.419399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1076.93 | − | 524.994i | −1.12531 | − | 0.548583i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2304.31i | 2.40283i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −497.765 | −0.517965 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 287.104 | 0.298135 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1766.47 | 1.82675 | 0.913376 | − | 0.407118i | \(-0.133466\pi\) | ||||
0.913376 | + | 0.407118i | \(0.133466\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1339.13 | 1.38197 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 487.722 | 0.502289 | 0.251144 | − | 0.967950i | \(-0.419193\pi\) | ||||
0.251144 | + | 0.967950i | \(0.419193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1722.31i | 1.77010i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 150.791i | − | 0.154341i | −0.997018 | − | 0.0771704i | \(-0.975411\pi\) | ||
0.997018 | − | 0.0771704i | \(-0.0245886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 582.544 | + | 283.987i | 0.595040 | + | 0.290078i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 78.9923i | 0.0805223i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1331.95i | 1.35499i | 0.735528 | + | 0.677494i | \(0.236934\pi\) | ||||
−0.735528 | + | 0.677494i | \(0.763066\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −512.068 | −0.518813 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.03418i | − | 0.00306793i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −780.611 | −0.787700 | −0.393850 | − | 0.919175i | \(-0.628857\pi\) | ||||
−0.393850 | + | 0.919175i | \(0.628857\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1841.24i | − | 1.85422i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 263.034 | 0.263825 | 0.131913 | − | 0.991261i | \(-0.457888\pi\) | ||||
0.131913 | + | 0.991261i | \(0.457888\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −477.625 | −0.478103 |
(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 | 1100.3.e.b.549.4 | 16 | ||
5.2 | odd | 4 | 1100.3.f.f.901.2 | 8 | |||
5.3 | odd | 4 | 220.3.f.a.21.7 | ✓ | 8 | ||
5.4 | even | 2 | inner | 1100.3.e.b.549.13 | 16 | ||
11.10 | odd | 2 | inner | 1100.3.e.b.549.3 | 16 | ||
15.8 | even | 4 | 1980.3.b.a.901.1 | 8 | |||
20.3 | even | 4 | 880.3.j.b.241.2 | 8 | |||
55.32 | even | 4 | 1100.3.f.f.901.1 | 8 | |||
55.43 | even | 4 | 220.3.f.a.21.8 | yes | 8 | ||
55.54 | odd | 2 | inner | 1100.3.e.b.549.14 | 16 | ||
165.98 | odd | 4 | 1980.3.b.a.901.4 | 8 | |||
220.43 | odd | 4 | 880.3.j.b.241.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
220.3.f.a.21.7 | ✓ | 8 | 5.3 | odd | 4 | ||
220.3.f.a.21.8 | yes | 8 | 55.43 | even | 4 | ||
880.3.j.b.241.1 | 8 | 220.43 | odd | 4 | |||
880.3.j.b.241.2 | 8 | 20.3 | even | 4 | |||
1100.3.e.b.549.3 | 16 | 11.10 | odd | 2 | inner | ||
1100.3.e.b.549.4 | 16 | 1.1 | even | 1 | trivial | ||
1100.3.e.b.549.13 | 16 | 5.4 | even | 2 | inner | ||
1100.3.e.b.549.14 | 16 | 55.54 | odd | 2 | inner | ||
1100.3.f.f.901.1 | 8 | 55.32 | even | 4 | |||
1100.3.f.f.901.2 | 8 | 5.2 | odd | 4 | |||
1980.3.b.a.901.1 | 8 | 15.8 | even | 4 | |||
1980.3.b.a.901.4 | 8 | 165.98 | odd | 4 |