Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,3,Mod(449,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.d (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: | \(109.864042590\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 44x^{10} + 719x^{8} + 5356x^{6} + 17809x^{4} + 20000x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 2016) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.10 | ||
Root | \(2.61146i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.449 |
Dual form | 4032.3.d.o.449.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.81315i | 1.36263i | 0.731990 | + | 0.681315i | \(0.238592\pi\) | ||||
−0.731990 | + | 0.681315i | \(0.761408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.61241i | − 0.146583i | −0.997311 | − | 0.0732913i | \(-0.976650\pi\) | ||||
0.997311 | − | 0.0732913i | \(-0.0233503\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.520800 | −0.0400616 | −0.0200308 | − | 0.999799i | \(-0.506376\pi\) | ||||
−0.0200308 | + | 0.999799i | \(0.506376\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.9683i | 1.58637i | 0.608980 | + | 0.793186i | \(0.291579\pi\) | ||||
−0.608980 | + | 0.793186i | \(0.708421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.8871 | −0.941427 | −0.470713 | − | 0.882286i | \(-0.656003\pi\) | ||||
−0.470713 | + | 0.882286i | \(0.656003\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 12.1896i | − 0.529982i | −0.964251 | − | 0.264991i | \(-0.914631\pi\) | ||||
0.964251 | − | 0.264991i | \(-0.0853690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.4191 | −0.856763 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 47.9985i | − 1.65512i | −0.561377 | − | 0.827560i | \(-0.689728\pi\) | ||||
0.561377 | − | 0.827560i | \(-0.310272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.8270 | −1.51055 | −0.755274 | − | 0.655409i | \(-0.772496\pi\) | ||||
−0.755274 | + | 0.655409i | \(0.772496\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 18.0259i | − 0.515026i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.85849 | 0.0502295 | 0.0251148 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251148 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.6825i | 1.01665i | 0.861166 | + | 0.508324i | \(0.169735\pi\) | ||||
−0.861166 | + | 0.508324i | \(0.830265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.33064 | 0.0542009 | 0.0271005 | − | 0.999633i | \(-0.491373\pi\) | ||||
0.0271005 | + | 0.999633i | \(0.491373\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 91.9001i | − 1.95532i | −0.210188 | − | 0.977661i | \(-0.567408\pi\) | ||||
0.210188 | − | 0.977661i | \(-0.432592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 30.2708i | − 0.571147i | −0.958357 | − | 0.285574i | \(-0.907816\pi\) | ||||
0.958357 | − | 0.285574i | \(-0.0921841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.9856 | 0.199738 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 72.1273i | − 1.22250i | −0.791439 | − | 0.611249i | \(-0.790668\pi\) | ||||
0.791439 | − | 0.611249i | \(-0.209332\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32.1019 | 0.526261 | 0.263131 | − | 0.964760i | \(-0.415245\pi\) | ||||
0.263131 | + | 0.964760i | \(0.415245\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 3.54829i | − 0.0545891i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −45.0801 | −0.672837 | −0.336419 | − | 0.941713i | \(-0.609216\pi\) | ||||
−0.336419 | + | 0.941713i | \(0.609216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 111.454i | 1.56978i | 0.619635 | + | 0.784890i | \(0.287281\pi\) | ||||
−0.619635 | + | 0.784890i | \(0.712719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 99.9042 | 1.36855 | 0.684276 | − | 0.729223i | \(-0.260119\pi\) | ||||
0.684276 | + | 0.729223i | \(0.260119\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.26603i | 0.0554030i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.78325 | −0.0478892 | −0.0239446 | − | 0.999713i | \(-0.507623\pi\) | ||||
−0.0239446 | + | 0.999713i | \(0.507623\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 35.2017i | − 0.424117i | −0.977257 | − | 0.212059i | \(-0.931983\pi\) | ||||
0.977257 | − | 0.212059i | \(-0.0680168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −183.739 | −2.16164 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 48.7809i | 0.548100i | 0.961716 | + | 0.274050i | \(0.0883633\pi\) | ||||
−0.961716 | + | 0.274050i | \(0.911637\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.37791 | 0.0151418 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 121.868i | − 1.28282i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1334 | 0.125087 | 0.0625434 | − | 0.998042i | \(-0.480079\pi\) | ||||
0.0625434 | + | 0.998042i | \(0.480079\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7469i | 0.116306i | 0.998308 | + | 0.0581529i | \(0.0185211\pi\) | ||||
−0.998308 | + | 0.0581529i | \(0.981479\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 153.740 | 1.49262 | 0.746310 | − | 0.665599i | \(-0.231824\pi\) | ||||
0.746310 | + | 0.665599i | \(0.231824\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 54.3156i | 0.507622i | 0.967254 | + | 0.253811i | \(0.0816841\pi\) | ||||
−0.967254 | + | 0.253811i | \(0.918316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −172.032 | −1.57828 | −0.789139 | − | 0.614215i | \(-0.789473\pi\) | ||||
−0.789139 | + | 0.614215i | \(0.789473\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 64.8360i | − 0.573770i | −0.957965 | − | 0.286885i | \(-0.907380\pi\) | ||||
0.957965 | − | 0.286885i | \(-0.0926198\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.0496 | 0.722170 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 71.3515i | − 0.599592i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 118.400 | 0.978514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.3974i | 0.195179i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −185.124 | −1.45767 | −0.728834 | − | 0.684690i | \(-0.759938\pi\) | ||||
−0.728834 | + | 0.684690i | \(0.759938\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 31.0619i | − 0.237114i | −0.992947 | − | 0.118557i | \(-0.962173\pi\) | ||||
0.992947 | − | 0.118557i | \(-0.0378268\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47.3248 | 0.355826 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 85.6561i | 0.625227i | 0.949880 | + | 0.312614i | \(0.101204\pi\) | ||||
−0.949880 | + | 0.312614i | \(0.898796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.59091 | −0.0186396 | −0.00931982 | − | 0.999957i | \(-0.502967\pi\) | ||||
−0.00931982 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.839742i | 0.00587232i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 327.021 | 2.25532 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 113.941i | − 0.764703i | −0.924017 | − | 0.382351i | \(-0.875114\pi\) | ||||
0.924017 | − | 0.382351i | \(-0.124886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2688 | −0.0746277 | −0.0373138 | − | 0.999304i | \(-0.511880\pi\) | ||||
−0.0373138 | + | 0.999304i | \(0.511880\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 319.039i | − 2.05832i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −41.7543 | −0.265951 | −0.132976 | − | 0.991119i | \(-0.542453\pi\) | ||||
−0.132976 | + | 0.991119i | \(0.542453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.2506i | 0.200314i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −141.787 | −0.869860 | −0.434930 | − | 0.900464i | \(-0.643227\pi\) | ||||
−0.434930 | + | 0.900464i | \(0.643227\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 166.816i | − 0.998897i | −0.866344 | − | 0.499449i | \(-0.833536\pi\) | ||||
0.866344 | − | 0.499449i | \(-0.166464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.729 | −0.998395 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0306i | 0.0579805i | 0.999580 | + | 0.0289903i | \(0.00922918\pi\) | ||||
−0.999580 | + | 0.0289903i | \(0.990771\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 56.6695 | 0.323826 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 99.4270i | − 0.555458i | −0.960659 | − | 0.277729i | \(-0.910418\pi\) | ||||
0.960659 | − | 0.277729i | \(-0.0895817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −217.242 | −1.20023 | −0.600115 | − | 0.799914i | \(-0.704878\pi\) | ||||
−0.600115 | + | 0.799914i | \(0.704878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.6622i | 0.0684443i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 43.4839 | 0.232534 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 237.181i | − 1.24179i | −0.783895 | − | 0.620893i | \(-0.786770\pi\) | ||||
0.783895 | − | 0.620893i | \(-0.213230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 234.019 | 1.21253 | 0.606266 | − | 0.795262i | \(-0.292667\pi\) | ||||
0.606266 | + | 0.795262i | \(0.292667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 277.878i | − 1.41055i | −0.708934 | − | 0.705274i | \(-0.750824\pi\) | ||||
0.708934 | − | 0.705274i | \(-0.249176\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 169.646 | 0.852494 | 0.426247 | − | 0.904607i | \(-0.359836\pi\) | ||||
0.426247 | + | 0.904607i | \(0.359836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 126.992i | 0.625576i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −283.990 | −1.38531 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.8413i | 0.137997i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 307.022 | 1.45508 | 0.727540 | − | 0.686066i | \(-0.240664\pi\) | ||||
0.727540 | + | 0.686066i | \(0.240664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.8790i | 0.0738559i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 123.893 | 0.570933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 14.0451i | − 0.0635525i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 317.188 | 1.42237 | 0.711185 | − | 0.703005i | \(-0.248159\pi\) | ||||
0.711185 | + | 0.703005i | \(0.248159\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 205.937i | − 0.907214i | −0.891202 | − | 0.453607i | \(-0.850137\pi\) | ||||
0.891202 | − | 0.453607i | \(-0.149863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 55.1812 | 0.240966 | 0.120483 | − | 0.992715i | \(-0.461556\pi\) | ||||
0.120483 | + | 0.992715i | \(0.461556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0717i | 0.0646855i | 0.999477 | + | 0.0323427i | \(0.0102968\pi\) | ||||
−0.999477 | + | 0.0323427i | \(0.989703\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 626.130 | 2.66438 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 106.732i | 0.446576i | 0.974753 | + | 0.223288i | \(0.0716790\pi\) | ||||
−0.974753 | + | 0.223288i | \(0.928321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9793 | 0.0912005 | 0.0456003 | − | 0.998960i | \(-0.485480\pi\) | ||||
0.0456003 | + | 0.998960i | \(0.485480\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 47.6921i | 0.194662i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.31561 | 0.0377150 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 389.193i | 1.55057i | 0.631613 | + | 0.775284i | \(0.282393\pi\) | ||||
−0.631613 | + | 0.775284i | \(0.717607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.6546 | −0.0776861 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 409.681i | 1.59409i | 0.603920 | + | 0.797045i | \(0.293605\pi\) | ||||
−0.603920 | + | 0.797045i | \(0.706395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.91711 | −0.0189850 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 288.396i | 1.09656i | 0.836294 | + | 0.548281i | \(0.184718\pi\) | ||||
−0.836294 | + | 0.548281i | \(0.815282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 206.240 | 0.778263 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 264.656i | − 0.983852i | −0.870637 | − | 0.491926i | \(-0.836293\pi\) | ||||
0.870637 | − | 0.491926i | \(-0.163707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 437.788 | 1.61545 | 0.807727 | − | 0.589556i | \(-0.200697\pi\) | ||||
0.807727 | + | 0.589556i | \(0.200697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 34.5363i | 0.125586i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 438.941 | 1.58462 | 0.792312 | − | 0.610116i | \(-0.208877\pi\) | ||||
0.792312 | + | 0.610116i | \(0.208877\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 62.8497i | 0.223664i | 0.993727 | + | 0.111832i | \(0.0356719\pi\) | ||||
−0.993727 | + | 0.111832i | \(0.964328\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 427.199 | 1.50954 | 0.754769 | − | 0.655990i | \(-0.227749\pi\) | ||||
0.754769 | + | 0.655990i | \(0.227749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 110.282i | − 0.384256i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −438.290 | −1.51657 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 375.101i | − 1.28021i | −0.768288 | − | 0.640104i | \(-0.778891\pi\) | ||||
0.768288 | − | 0.640104i | \(-0.221109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 491.415 | 1.66581 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.34834i | 0.0212319i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.16629 | −0.0204860 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 218.716i | 0.717100i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −268.463 | −0.874473 | −0.437237 | − | 0.899347i | \(-0.644043\pi\) | ||||
−0.437237 | + | 0.899347i | \(0.644043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 156.940i | − 0.504629i | −0.967645 | − | 0.252314i | \(-0.918808\pi\) | ||||
0.967645 | − | 0.252314i | \(-0.0811917\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −39.3100 | −0.125591 | −0.0627956 | − | 0.998026i | \(-0.520002\pi\) | ||||
−0.0627956 | + | 0.998026i | \(0.520002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 491.176i | − 1.54945i | −0.632298 | − | 0.774725i | \(-0.717888\pi\) | ||||
0.632298 | − | 0.774725i | \(-0.282112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −77.3931 | −0.242612 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 482.385i | − 1.49345i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.1551 | 0.0343233 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 243.145i | 0.739042i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 571.594 | 1.72687 | 0.863435 | − | 0.504460i | \(-0.168308\pi\) | ||||
0.863435 | + | 0.504460i | \(0.168308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 307.138i | − 0.916829i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 176.364 | 0.523334 | 0.261667 | − | 0.965158i | \(-0.415728\pi\) | ||||
0.261667 | + | 0.965158i | \(0.415728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 75.5042i | 0.221420i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 518.445i | − 1.49408i | −0.664780 | − | 0.747039i | \(-0.731475\pi\) | ||||
0.664780 | − | 0.747039i | \(-0.268525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.55868 | −0.00733145 | −0.00366573 | − | 0.999993i | \(-0.501167\pi\) | ||||
−0.00366573 | + | 0.999993i | \(0.501167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 44.1821i | − 0.125162i | −0.998040 | − | 0.0625809i | \(-0.980067\pi\) | ||||
0.998040 | − | 0.0625809i | \(-0.0199332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −759.356 | −2.13903 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 24.3091i | − 0.0677134i | −0.999427 | − | 0.0338567i | \(-0.989221\pi\) | ||||
0.999427 | − | 0.0338567i | \(-0.0107790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −41.0514 | −0.113716 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 680.663i | 1.86483i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −271.257 | −0.739121 | −0.369560 | − | 0.929207i | \(-0.620492\pi\) | ||||
−0.369560 | + | 0.929207i | \(0.620492\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 80.0890i | 0.215873i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −479.051 | −1.28432 | −0.642159 | − | 0.766571i | \(-0.721961\pi\) | ||||
−0.642159 | + | 0.766571i | \(0.721961\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.9976i | 0.0663067i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 286.046 | 0.754740 | 0.377370 | − | 0.926063i | \(-0.376829\pi\) | ||||
0.377370 | + | 0.926063i | \(0.376829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 453.990i | − 1.18535i | −0.805440 | − | 0.592677i | \(-0.798071\pi\) | ||||
0.805440 | − | 0.592677i | \(-0.201929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.0651 | −0.0754938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 556.266i | 1.42999i | 0.699129 | + | 0.714995i | \(0.253571\pi\) | ||||
−0.699129 | + | 0.714995i | \(0.746429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 328.733 | 0.840749 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 25.7758i | − 0.0652553i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 65.9114 | 0.166024 | 0.0830118 | − | 0.996549i | \(-0.473546\pi\) | ||||
0.0830118 | + | 0.996549i | \(0.473546\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 706.777i | − 1.76253i | −0.472618 | − | 0.881267i | \(-0.656691\pi\) | ||||
0.472618 | − | 0.881267i | \(-0.343309\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.3875 | 0.0605149 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.99665i | − 0.00736277i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 541.836 | 1.32478 | 0.662391 | − | 0.749159i | \(-0.269542\pi\) | ||||
0.662391 | + | 0.749159i | \(0.269542\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 190.831i | 0.462061i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 239.835 | 0.577915 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 529.656i | − 1.26410i | −0.774930 | − | 0.632048i | \(-0.782215\pi\) | ||||
0.774930 | − | 0.632048i | \(-0.217785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −251.002 | −0.596205 | −0.298103 | − | 0.954534i | \(-0.596354\pi\) | ||||
−0.298103 | + | 0.954534i | \(0.596354\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 577.636i | − 1.35914i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −84.9338 | −0.198908 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 631.431i | − 1.46504i | −0.680747 | − | 0.732519i | \(-0.738345\pi\) | ||||
0.680747 | − | 0.732519i | \(-0.261655\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −645.417 | −1.49057 | −0.745285 | − | 0.666746i | \(-0.767687\pi\) | ||||
−0.745285 | + | 0.666746i | \(0.767687\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 218.037i | 0.498939i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 66.3355 | 0.151106 | 0.0755529 | − | 0.997142i | \(-0.475928\pi\) | ||||
0.0755529 | + | 0.997142i | \(0.475928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 52.3648i | − 0.118205i | −0.998252 | − | 0.0591025i | \(-0.981176\pi\) | ||||
0.998252 | − | 0.0591025i | \(-0.0188239\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −332.352 | −0.746857 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 460.715i | 1.02609i | 0.858361 | + | 0.513045i | \(0.171483\pi\) | ||||
−0.858361 | + | 0.513045i | \(0.828517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 67.2092 | 0.149023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.38790i | 0.0206327i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −609.343 | −1.33335 | −0.666677 | − | 0.745346i | \(-0.732284\pi\) | ||||
−0.666677 | + | 0.745346i | \(0.732284\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 244.657i | 0.530709i | 0.964151 | + | 0.265354i | \(0.0854890\pi\) | ||||
−0.964151 | + | 0.265354i | \(0.914511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −241.775 | −0.522191 | −0.261096 | − | 0.965313i | \(-0.584084\pi\) | ||||
−0.261096 | + | 0.965313i | \(0.584084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 449.911i | − 0.963408i | −0.876334 | − | 0.481704i | \(-0.840018\pi\) | ||||
0.876334 | − | 0.481704i | \(-0.159982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 119.271 | 0.254309 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.75794i | − 0.00794491i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 383.125 | 0.806579 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 159.741i | − 0.333489i | −0.986000 | − | 0.166744i | \(-0.946675\pi\) | ||||
0.986000 | − | 0.166744i | \(-0.0533255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.967903 | −0.00201227 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 82.6669i | 0.170447i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −320.830 | −0.658788 | −0.329394 | − | 0.944193i | \(-0.606844\pi\) | ||||
−0.329394 | + | 0.944193i | \(0.606844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 786.947i | − 1.60274i | −0.598167 | − | 0.801372i | \(-0.704104\pi\) | ||||
0.598167 | − | 0.801372i | \(-0.295896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1294.44 | 2.62563 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 294.881i | − 0.593321i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 560.988 | 1.12422 | 0.562112 | − | 0.827061i | \(-0.309989\pi\) | ||||
0.562112 | + | 0.827061i | \(0.309989\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 63.4623i | 0.126168i | 0.998008 | + | 0.0630838i | \(0.0200936\pi\) | ||||
−0.998008 | + | 0.0630838i | \(0.979906\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −80.0333 | −0.158482 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 114.008i | 0.223985i | 0.993709 | + | 0.111992i | \(0.0357233\pi\) | ||||
−0.993709 | + | 0.111992i | \(0.964277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −264.322 | −0.517264 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1047.45i | 2.03389i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −148.180 | −0.286616 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 179.557i | 0.344640i | 0.985041 | + | 0.172320i | \(0.0551262\pi\) | ||||
−0.985041 | + | 0.172320i | \(0.944874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −378.737 | −0.724163 | −0.362082 | − | 0.932146i | \(-0.617934\pi\) | ||||
−0.362082 | + | 0.932146i | \(0.617934\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1262.84i | − 2.39629i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 380.414 | 0.719119 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 21.7083i | − 0.0407285i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −370.060 | −0.691701 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 11.2869i | − 0.0209404i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −466.858 | −0.862954 | −0.431477 | − | 0.902124i | \(-0.642007\pi\) | ||||
−0.431477 | + | 0.902124i | \(0.642007\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1172.08i | − 2.15061i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1068.48 | −1.95335 | −0.976675 | − | 0.214721i | \(-0.931116\pi\) | ||||
−0.976675 | + | 0.214721i | \(0.931116\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 858.554i | 1.55817i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0095 | 0.0181004 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 374.378i | − 0.672132i | −0.941838 | − | 0.336066i | \(-0.890903\pi\) | ||||
0.941838 | − | 0.336066i | \(-0.109097\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.21380 | −0.00217137 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 74.2058i | 0.131804i | 0.997826 | + | 0.0659021i | \(0.0209925\pi\) | ||||
−0.997826 | + | 0.0659021i | \(0.979007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 441.738 | 0.781837 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 674.188i | − 1.18486i | −0.805620 | − | 0.592432i | \(-0.798168\pi\) | ||||
0.805620 | − | 0.592432i | \(-0.201832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −193.792 | −0.339390 | −0.169695 | − | 0.985497i | \(-0.554278\pi\) | ||||
−0.169695 | + | 0.985497i | \(0.554278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 261.090i | 0.454069i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 458.303 | 0.794286 | 0.397143 | − | 0.917757i | \(-0.370002\pi\) | ||||
0.397143 | + | 0.917757i | \(0.370002\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 93.1351i | 0.160301i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −48.8089 | −0.0837202 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 980.515i | − 1.67038i | −0.549959 | − | 0.835192i | \(-0.685357\pi\) | ||||
0.549959 | − | 0.835192i | \(-0.314643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 837.599 | 1.42207 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.9429i | 0.0656710i | 0.999461 | + | 0.0328355i | \(0.0104537\pi\) | ||||
−0.999461 | + | 0.0328355i | \(0.989546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 486.128 | 0.817023 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 937.594i | − 1.56527i | −0.622483 | − | 0.782633i | \(-0.713876\pi\) | ||||
0.622483 | − | 0.782633i | \(-0.286124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −898.370 | −1.49479 | −0.747396 | − | 0.664379i | \(-0.768696\pi\) | ||||
−0.747396 | + | 0.664379i | \(0.768696\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 806.678i | 1.33335i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 957.285 | 1.57708 | 0.788538 | − | 0.614986i | \(-0.210838\pi\) | ||||
0.788538 | + | 0.614986i | \(0.210838\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 47.8616i | 0.0783333i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 602.677 | 0.983160 | 0.491580 | − | 0.870832i | \(-0.336419\pi\) | ||||
0.491580 | + | 0.870832i | \(0.336419\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 248.867i | − 0.403350i | −0.979453 | − | 0.201675i | \(-0.935362\pi\) | ||||
0.979453 | − | 0.201675i | \(-0.0646384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 63.7190 | 0.102939 | 0.0514693 | − | 0.998675i | \(-0.483610\pi\) | ||||
0.0514693 | + | 0.998675i | \(0.483610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 129.062i | − 0.207162i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −701.700 | −1.12272 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.1204i | 0.0796827i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −191.480 | −0.303455 | −0.151728 | − | 0.988422i | \(-0.548484\pi\) | ||||
−0.151728 | + | 0.988422i | \(0.548484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1261.28i | − 1.98626i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.64560 | −0.00572308 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 276.684i | 0.431644i | 0.976433 | + | 0.215822i | \(0.0692431\pi\) | ||||
−0.976433 | + | 0.215822i | \(0.930757\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 154.293 | 0.239958 | 0.119979 | − | 0.992776i | \(-0.461717\pi\) | ||||
0.119979 | + | 0.992776i | \(0.461717\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 198.767i | 0.307214i | 0.988132 | + | 0.153607i | \(0.0490890\pi\) | ||||
−0.988132 | + | 0.153607i | \(0.950911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −116.299 | −0.179197 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 703.030i | − 1.07662i | −0.842748 | − | 0.538308i | \(-0.819064\pi\) | ||||
0.842748 | − | 0.538308i | \(-0.180936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 211.629 | 0.323098 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 964.242i | 1.46319i | 0.681740 | + | 0.731595i | \(0.261224\pi\) | ||||
−0.681740 | + | 0.731595i | \(0.738776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 777.062 | 1.17559 | 0.587793 | − | 0.809011i | \(-0.299997\pi\) | ||||
0.587793 | + | 0.809011i | \(0.299997\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 322.431i | 0.484859i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −585.082 | −0.877184 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 51.7614i | − 0.0771407i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −249.025 | −0.370022 | −0.185011 | − | 0.982736i | \(-0.559232\pi\) | ||||
−0.185011 | + | 0.982736i | \(0.559232\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 500.574i | 0.739401i | 0.929151 | + | 0.369700i | \(0.120540\pi\) | ||||
−0.929151 | + | 0.369700i | \(0.879460\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.1020 | −0.0472784 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 549.601i | 0.804687i | 0.915489 | + | 0.402344i | \(0.131804\pi\) | ||||
−0.915489 | + | 0.402344i | \(0.868196\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −583.588 | −0.851954 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.7650i | 0.0228811i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 206.279 | 0.298522 | 0.149261 | − | 0.988798i | \(-0.452310\pi\) | ||||
0.149261 | + | 0.988798i | \(0.452310\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 17.6523i | − 0.0253990i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1124.11 | −1.61278 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 246.956i | 0.352291i | 0.984364 | + | 0.176146i | \(0.0563630\pi\) | ||||
−0.984364 | + | 0.176146i | \(0.943637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.2430 | −0.0472874 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 31.0793i | − 0.0439594i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1086.05 | 1.53180 | 0.765901 | − | 0.642958i | \(-0.222293\pi\) | ||||
0.765901 | + | 0.642958i | \(0.222293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 570.802i | 0.800564i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.72129 | −0.00800181 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 563.186i | 0.783291i | 0.920116 | + | 0.391645i | \(0.128094\pi\) | ||||
−0.920116 | + | 0.391645i | \(0.871906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −406.757 | −0.564157 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1028.08i | 1.41805i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −619.737 | −0.852458 | −0.426229 | − | 0.904615i | \(-0.640158\pi\) | ||||
−0.426229 | + | 0.904615i | \(0.640158\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 62.8534i | 0.0859828i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 807.509 | 1.10165 | 0.550825 | − | 0.834621i | \(-0.314313\pi\) | ||||
0.550825 | + | 0.834621i | \(0.314313\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 72.6875i | 0.0986261i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 653.350 | 0.884101 | 0.442050 | − | 0.896990i | \(-0.354251\pi\) | ||||
0.442050 | + | 0.896990i | \(0.354251\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 388.142i | − 0.522399i | −0.965285 | − | 0.261199i | \(-0.915882\pi\) | ||||
0.965285 | − | 0.261199i | \(-0.0841180\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 776.296 | 1.04201 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 143.705i | − 0.191863i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1366.13 | −1.81909 | −0.909543 | − | 0.415610i | \(-0.863568\pi\) | ||||
−0.909543 | + | 0.415610i | \(0.863568\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 76.7759i | − 0.101690i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −556.658 | −0.735348 | −0.367674 | − | 0.929955i | \(-0.619846\pi\) | ||||
−0.367674 | + | 0.929955i | \(0.619846\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 393.624i | 0.517246i | 0.965978 | + | 0.258623i | \(0.0832687\pi\) | ||||
−0.965978 | + | 0.258623i | \(0.916731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 455.154 | 0.596533 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.5639i | 0.0489752i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1150.26 | −1.49578 | −0.747892 | − | 0.663821i | \(-0.768934\pi\) | ||||
−0.747892 | + | 0.663821i | \(0.768934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 961.972i | − 1.24447i | −0.782832 | − | 0.622233i | \(-0.786226\pi\) | ||||
0.782832 | − | 0.622233i | \(-0.213774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1002.99 | 1.29418 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 745.580i | − 0.957099i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 179.710 | 0.230102 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 284.479i | − 0.362393i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −512.863 | −0.651669 | −0.325834 | − | 0.945427i | \(-0.605645\pi\) | ||||
−0.325834 | + | 0.945427i | \(0.605645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 171.540i | 0.216865i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.7187 | −0.0210829 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 322.873i | − 0.405111i | −0.979271 | − | 0.202555i | \(-0.935075\pi\) | ||||
0.979271 | − | 0.202555i | \(-0.0649246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2478.39 | 3.10187 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 161.086i | − 0.200606i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −219.729 | −0.272955 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 243.580i | − 0.301088i | −0.988603 | − | 0.150544i | \(-0.951898\pi\) | ||||
0.988603 | − | 0.150544i | \(-0.0481024\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −834.792 | −1.02934 | −0.514668 | − | 0.857389i | \(-0.672085\pi\) | ||||
−0.514668 | + | 0.857389i | \(0.672085\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 966.018i | − 1.18530i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.6884 | −0.0510262 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 465.749i | − 0.567295i | −0.958929 | − | 0.283647i | \(-0.908456\pi\) | ||||
0.958929 | − | 0.283647i | \(-0.0915445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1471.89 | −1.78844 | −0.894221 | − | 0.447626i | \(-0.852270\pi\) | ||||
−0.894221 | + | 0.447626i | \(0.852270\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 770.034i | 0.931118i | 0.885017 | + | 0.465559i | \(0.154147\pi\) | ||||
−0.885017 | + | 0.465559i | \(0.845853\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1130.62 | 1.36383 | 0.681915 | − | 0.731431i | \(-0.261147\pi\) | ||||
0.681915 | + | 0.731431i | \(0.261147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 188.778i | 0.226625i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1136.54 | 1.36113 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1258.96i | 1.50054i | 0.661129 | + | 0.750272i | \(0.270078\pi\) | ||||
−0.661129 | + | 0.750272i | \(0.729922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1462.85 | −1.73942 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1149.58i | − 1.36044i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −313.257 | −0.369843 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 22.6543i | − 0.0266208i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −595.267 | −0.697851 | −0.348925 | − | 0.937150i | \(-0.613453\pi\) | ||||
−0.348925 | + | 0.937150i | \(0.613453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1319.66i | − 1.53986i | −0.638130 | − | 0.769929i | \(-0.720292\pi\) | ||||
0.638130 | − | 0.769929i | \(-0.279708\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1519.85 | −1.76932 | −0.884662 | − | 0.466233i | \(-0.845611\pi\) | ||||
−0.884662 | + | 0.466233i | \(0.845611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 921.628i | 1.06793i | 0.845505 | + | 0.533967i | \(0.179299\pi\) | ||||
−0.845505 | + | 0.533967i | \(0.820701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −68.3403 | −0.0790061 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.10014i | 0.00701972i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.4777 | 0.0269549 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 64.5495i | − 0.0737709i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −300.963 | −0.343173 | −0.171587 | − | 0.985169i | \(-0.554889\pi\) | ||||
−0.171587 | + | 0.985169i | \(0.554889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 950.730i | 1.07915i | 0.841938 | + | 0.539574i | \(0.181415\pi\) | ||||
−0.841938 | + | 0.539574i | \(0.818585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1486.55 | −1.68352 | −0.841761 | − | 0.539850i | \(-0.818481\pi\) | ||||
−0.841761 | + | 0.539850i | \(0.818481\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1500.35i | 1.69149i | 0.533590 | + | 0.845743i | \(0.320843\pi\) | ||||
−0.533590 | + | 0.845743i | \(0.679157\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 489.792 | 0.550947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1643.83i | 1.84079i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 677.411 | 0.756884 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2247.62i | 2.50014i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 816.353 | 0.906052 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1480.10i | − 1.63547i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1353.09 | 1.49183 | 0.745914 | − | 0.666043i | \(-0.232013\pi\) | ||||
0.745914 | + | 0.666043i | \(0.232013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 405.043i | − 0.444613i | −0.974977 | − | 0.222307i | \(-0.928641\pi\) | ||||
0.974977 | − | 0.222307i | \(-0.0713586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.7596 | −0.0621682 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 82.1820i | 0.0896205i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1523.01 | −1.65724 | −0.828621 | − | 0.559810i | \(-0.810874\pi\) | ||||
−0.828621 | + | 0.559810i | \(0.810874\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 58.0455i | − 0.0628879i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.8072 | −0.0430348 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1044.12i | − 1.12391i | −0.827166 | − | 0.561957i | \(-0.810049\pi\) | ||||
0.827166 | − | 0.561957i | \(-0.189951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −125.210 | −0.134490 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 296.263i | 0.316858i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1563.83 | 1.66897 | 0.834487 | − | 0.551027i | \(-0.185764\pi\) | ||||
0.834487 | + | 0.551027i | \(0.185764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 75.2579i | 0.0799765i | 0.999200 | + | 0.0399882i | \(0.0127320\pi\) | ||||
−0.999200 | + | 0.0399882i | \(0.987268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 508.093 | 0.538805 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1441.19i | 1.52185i | 0.648842 | + | 0.760923i | \(0.275253\pi\) | ||||
−0.648842 | + | 0.760923i | \(0.724747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.0302 | −0.0548263 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 156.478i | 0.164195i | 0.996624 | + | 0.0820974i | \(0.0261618\pi\) | ||||
−0.996624 | + | 0.0820974i | \(0.973838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1615.95 | 1.69210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 226.625i | − 0.236314i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1231.77 | 1.28175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1594.41i | 1.65223i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 704.516 | 0.728558 | 0.364279 | − | 0.931290i | \(-0.381315\pi\) | ||||
0.364279 | + | 0.931290i | \(0.381315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 984.744i | − 1.01415i | −0.861901 | − | 0.507077i | \(-0.830726\pi\) | ||||
0.861901 | − | 0.507077i | \(-0.169274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.85490 | 0.00704512 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1235.23i | 1.26431i | 0.774841 | + | 0.632156i | \(0.217830\pi\) | ||||
−0.774841 | + | 0.632156i | \(0.782170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78.6546 | 0.0803418 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 873.904i | − 0.889017i | −0.895775 | − | 0.444509i | \(-0.853378\pi\) | ||||
0.895775 | − | 0.444509i | \(-0.146622\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1893.23 | 1.92206 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 28.4096i | − 0.0287255i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −421.680 | −0.425509 | −0.212755 | − | 0.977106i | \(-0.568244\pi\) | ||||
−0.212755 | + | 0.977106i | \(0.568244\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1155.83i | 1.16163i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1500.34 | −1.50486 | −0.752428 | − | 0.658674i | \(-0.771117\pi\) | ||||
−0.752428 | + | 0.658674i | \(0.771117\pi\) | |||||||
\(998\) | 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 | 4032.3.d.o.449.10 | 12 | ||
3.2 | odd | 2 | inner | 4032.3.d.o.449.3 | 12 | ||
4.3 | odd | 2 | 4032.3.d.n.449.10 | 12 | |||
8.3 | odd | 2 | 2016.3.d.f.449.3 | yes | 12 | ||
8.5 | even | 2 | 2016.3.d.e.449.3 | ✓ | 12 | ||
12.11 | even | 2 | 4032.3.d.n.449.3 | 12 | |||
24.5 | odd | 2 | 2016.3.d.e.449.10 | yes | 12 | ||
24.11 | even | 2 | 2016.3.d.f.449.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.3.d.e.449.3 | ✓ | 12 | 8.5 | even | 2 | ||
2016.3.d.e.449.10 | yes | 12 | 24.5 | odd | 2 | ||
2016.3.d.f.449.3 | yes | 12 | 8.3 | odd | 2 | ||
2016.3.d.f.449.10 | yes | 12 | 24.11 | even | 2 | ||
4032.3.d.n.449.3 | 12 | 12.11 | even | 2 | |||
4032.3.d.n.449.10 | 12 | 4.3 | odd | 2 | |||
4032.3.d.o.449.3 | 12 | 3.2 | odd | 2 | inner | ||
4032.3.d.o.449.10 | 12 | 1.1 | even | 1 | trivial |