Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,4,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.a (trivial) |
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: | yes |
Analytic conductor: | \(78.0595269376\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 54x^{6} + 887x^{4} - 4176x^{2} + 3136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.959848\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.959848 | −0.339358 | −0.169679 | − | 0.985499i | \(-0.554273\pi\) | ||||
−0.169679 | + | 0.985499i | \(0.554273\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.07869 | −0.884836 | ||||||||
\(5\) | 10.2898 | 0.920346 | 0.460173 | − | 0.887829i | \(-0.347787\pi\) | ||||
0.460173 | + | 0.887829i | \(0.347787\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 14.4733 | 0.639634 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.87663 | −0.312326 | ||||||||
\(11\) | 28.3265 | 0.776432 | 0.388216 | − | 0.921568i | \(-0.373091\pi\) | ||||
0.388216 | + | 0.921568i | \(0.373091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.96269 | 0.127212 | 0.0636058 | − | 0.997975i | \(-0.479740\pi\) | ||||
0.0636058 | + | 0.997975i | \(0.479740\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 42.7374 | 0.667772 | ||||||||
\(17\) | −104.664 | −1.49323 | −0.746613 | − | 0.665259i | \(-0.768321\pi\) | ||||
−0.746613 | + | 0.665259i | \(0.768321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34.0521 | 0.411163 | 0.205581 | − | 0.978640i | \(-0.434091\pi\) | ||||
0.205581 | + | 0.978640i | \(0.434091\pi\) | |||||||
\(20\) | −72.8381 | −0.814355 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −27.1891 | −0.263488 | ||||||||
\(23\) | −103.629 | −0.939484 | −0.469742 | − | 0.882804i | \(-0.655653\pi\) | ||||
−0.469742 | + | 0.882804i | \(0.655653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.1205 | −0.152964 | ||||||||
\(26\) | −5.72328 | −0.0431703 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −195.695 | −1.25309 | −0.626547 | − | 0.779384i | \(-0.715532\pi\) | ||||
−0.626547 | + | 0.779384i | \(0.715532\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.17704 | 0.0531692 | 0.0265846 | − | 0.999647i | \(-0.491537\pi\) | ||||
0.0265846 | + | 0.999647i | \(0.491537\pi\) | |||||||
\(32\) | −156.807 | −0.866247 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 100.462 | 0.506737 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 245.968 | 1.09289 | 0.546444 | − | 0.837496i | \(-0.315981\pi\) | ||||
0.546444 | + | 0.837496i | \(0.315981\pi\) | |||||||
\(38\) | −32.6849 | −0.139531 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 148.927 | 0.588684 | ||||||||
\(41\) | 366.457 | 1.39588 | 0.697939 | − | 0.716157i | \(-0.254101\pi\) | ||||
0.697939 | + | 0.716157i | \(0.254101\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −366.354 | −1.29927 | −0.649633 | − | 0.760248i | \(-0.725078\pi\) | ||||
−0.649633 | + | 0.760248i | \(0.725078\pi\) | |||||||
\(44\) | −200.514 | −0.687015 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 99.4681 | 0.318821 | ||||||||
\(47\) | 244.288 | 0.758152 | 0.379076 | − | 0.925366i | \(-0.376242\pi\) | ||||
0.379076 | + | 0.925366i | \(0.376242\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 18.3528 | 0.0519095 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −42.2080 | −0.112562 | ||||||||
\(53\) | 281.226 | 0.728857 | 0.364428 | − | 0.931231i | \(-0.381264\pi\) | ||||
0.364428 | + | 0.931231i | \(0.381264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 291.473 | 0.714586 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 187.838 | 0.425247 | ||||||||
\(59\) | −181.642 | −0.400810 | −0.200405 | − | 0.979713i | \(-0.564226\pi\) | ||||
−0.200405 | + | 0.979713i | \(0.564226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.1701 | −0.0507323 | −0.0253661 | − | 0.999678i | \(-0.508075\pi\) | ||||
−0.0253661 | + | 0.999678i | \(0.508075\pi\) | |||||||
\(62\) | −8.80857 | −0.0180434 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −191.388 | −0.373804 | ||||||||
\(65\) | 61.3547 | 0.117079 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −336.788 | −0.614108 | −0.307054 | − | 0.951692i | \(-0.599343\pi\) | ||||
−0.307054 | + | 0.951692i | \(0.599343\pi\) | |||||||
\(68\) | 740.886 | 1.32126 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 196.781 | 0.328924 | 0.164462 | − | 0.986383i | \(-0.447411\pi\) | ||||
0.164462 | + | 0.986383i | \(0.447411\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −683.417 | −1.09573 | −0.547863 | − | 0.836568i | \(-0.684558\pi\) | ||||
−0.547863 | + | 0.836568i | \(0.684558\pi\) | |||||||
\(74\) | −236.092 | −0.370880 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −241.044 | −0.363812 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 619.337 | 0.882036 | 0.441018 | − | 0.897498i | \(-0.354617\pi\) | ||||
0.441018 | + | 0.897498i | \(0.354617\pi\) | |||||||
\(80\) | 439.758 | 0.614581 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −351.743 | −0.473702 | ||||||||
\(83\) | −176.475 | −0.233381 | −0.116690 | − | 0.993168i | \(-0.537229\pi\) | ||||
−0.116690 | + | 0.993168i | \(0.537229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1076.97 | −1.37428 | ||||||||
\(86\) | 351.644 | 0.440916 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 409.976 | 0.496632 | ||||||||
\(89\) | −761.046 | −0.906413 | −0.453207 | − | 0.891406i | \(-0.649720\pi\) | ||||
−0.453207 | + | 0.891406i | \(0.649720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 733.557 | 0.831290 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −234.480 | −0.257285 | ||||||||
\(95\) | 350.389 | 0.378412 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1277.59 | −1.33732 | −0.668660 | − | 0.743568i | \(-0.733132\pi\) | ||||
−0.668660 | + | 0.743568i | \(0.733132\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 135.348 | 0.135348 | ||||||||
\(101\) | 1555.82 | 1.53277 | 0.766387 | − | 0.642379i | \(-0.222052\pi\) | ||||
0.766387 | + | 0.642379i | \(0.222052\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 246.314 | 0.235632 | 0.117816 | − | 0.993035i | \(-0.462411\pi\) | ||||
0.117816 | + | 0.993035i | \(0.462411\pi\) | |||||||
\(104\) | 86.2995 | 0.0813689 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −269.935 | −0.247343 | ||||||||
\(107\) | −1621.50 | −1.46501 | −0.732504 | − | 0.680762i | \(-0.761649\pi\) | ||||
−0.732504 | + | 0.680762i | \(0.761649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1906.69 | 1.67548 | 0.837742 | − | 0.546066i | \(-0.183875\pi\) | ||||
0.837742 | + | 0.546066i | \(0.183875\pi\) | |||||||
\(110\) | −279.770 | −0.242500 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1886.64 | −1.57062 | −0.785312 | − | 0.619100i | \(-0.787498\pi\) | ||||
−0.785312 | + | 0.619100i | \(0.787498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1066.32 | −0.864650 | ||||||||
\(116\) | 1385.27 | 1.10878 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 174.349 | 0.136018 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −528.611 | −0.397153 | ||||||||
\(122\) | 23.1997 | 0.0172164 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −64.9614 | −0.0470460 | ||||||||
\(125\) | −1482.97 | −1.06113 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −594.201 | −0.415172 | −0.207586 | − | 0.978217i | \(-0.566561\pi\) | ||||
−0.207586 | + | 0.978217i | \(0.566561\pi\) | |||||||
\(128\) | 1438.16 | 0.993100 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −58.8912 | −0.0397316 | ||||||||
\(131\) | −494.116 | −0.329551 | −0.164775 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164775 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 323.266 | 0.208402 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1514.83 | −0.955117 | ||||||||
\(137\) | 1807.01 | 1.12689 | 0.563443 | − | 0.826155i | \(-0.309477\pi\) | ||||
0.563443 | + | 0.826155i | \(0.309477\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3149.34 | −1.92175 | −0.960876 | − | 0.276979i | \(-0.910667\pi\) | ||||
−0.960876 | + | 0.276979i | \(0.910667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −188.880 | −0.111623 | ||||||||
\(143\) | 168.902 | 0.0987712 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2013.66 | −1.15328 | ||||||||
\(146\) | 655.977 | 0.371843 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1741.13 | −0.967027 | ||||||||
\(149\) | 1899.54 | 1.04441 | 0.522203 | − | 0.852821i | \(-0.325110\pi\) | ||||
0.522203 | + | 0.852821i | \(0.325110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1521.53 | 0.820004 | 0.410002 | − | 0.912085i | \(-0.365528\pi\) | ||||
0.410002 | + | 0.912085i | \(0.365528\pi\) | |||||||
\(152\) | 492.845 | 0.262994 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 94.4297 | 0.0489340 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3606.96 | −1.83355 | −0.916773 | − | 0.399408i | \(-0.869216\pi\) | ||||
−0.916773 | + | 0.399408i | \(0.869216\pi\) | |||||||
\(158\) | −594.470 | −0.299326 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1613.51 | −0.797247 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 887.302 | 0.426373 | 0.213187 | − | 0.977011i | \(-0.431616\pi\) | ||||
0.213187 | + | 0.977011i | \(0.431616\pi\) | |||||||
\(164\) | −2594.04 | −1.23512 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 169.389 | 0.0791996 | ||||||||
\(167\) | 1248.96 | 0.578729 | 0.289364 | − | 0.957219i | \(-0.406556\pi\) | ||||
0.289364 | + | 0.957219i | \(0.406556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2161.45 | −0.983817 | ||||||||
\(170\) | 1033.73 | 0.466374 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2593.31 | 1.14964 | ||||||||
\(173\) | 2130.55 | 0.936318 | 0.468159 | − | 0.883644i | \(-0.344917\pi\) | ||||
0.468159 | + | 0.883644i | \(0.344917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1210.60 | 0.518479 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 730.489 | 0.307598 | ||||||||
\(179\) | −2756.11 | −1.15084 | −0.575422 | − | 0.817857i | \(-0.695162\pi\) | ||||
−0.575422 | + | 0.817857i | \(0.695162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −734.801 | −0.301753 | −0.150877 | − | 0.988553i | \(-0.548210\pi\) | ||||
−0.150877 | + | 0.988553i | \(0.548210\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1499.85 | −0.600926 | ||||||||
\(185\) | 2530.95 | 1.00583 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2964.77 | −1.15939 | ||||||||
\(188\) | −1729.24 | −0.670840 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −336.320 | −0.128417 | ||||||||
\(191\) | −2034.49 | −0.770736 | −0.385368 | − | 0.922763i | \(-0.625925\pi\) | ||||
−0.385368 | + | 0.922763i | \(0.625925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −664.168 | −0.247709 | −0.123855 | − | 0.992300i | \(-0.539526\pi\) | ||||
−0.123855 | + | 0.992300i | \(0.539526\pi\) | |||||||
\(194\) | 1226.30 | 0.453830 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1682.40 | −0.608455 | −0.304228 | − | 0.952599i | \(-0.598398\pi\) | ||||
−0.304228 | + | 0.952599i | \(0.598398\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3778.06 | −1.34583 | −0.672913 | − | 0.739721i | \(-0.734957\pi\) | ||||
−0.672913 | + | 0.739721i | \(0.734957\pi\) | |||||||
\(200\) | −276.736 | −0.0978410 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1493.35 | −0.520159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3770.76 | 1.28469 | ||||||||
\(206\) | −236.425 | −0.0799635 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 254.830 | 0.0849484 | ||||||||
\(209\) | 964.576 | 0.319240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5122.91 | −1.67145 | −0.835725 | − | 0.549148i | \(-0.814952\pi\) | ||||
−0.835725 | + | 0.549148i | \(0.814952\pi\) | |||||||
\(212\) | −1990.71 | −0.644919 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1556.39 | 0.497162 | ||||||||
\(215\) | −3769.70 | −1.19577 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1830.13 | −0.568589 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2063.25 | −0.632291 | ||||||||
\(221\) | −624.081 | −0.189956 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2118.71 | −0.636229 | −0.318115 | − | 0.948052i | \(-0.603050\pi\) | ||||
−0.318115 | + | 0.948052i | \(0.603050\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1810.89 | 0.533004 | ||||||||
\(227\) | −4239.57 | −1.23960 | −0.619802 | − | 0.784758i | \(-0.712787\pi\) | ||||
−0.619802 | + | 0.784758i | \(0.712787\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1518.18 | 0.438098 | 0.219049 | − | 0.975714i | \(-0.429705\pi\) | ||||
0.219049 | + | 0.975714i | \(0.429705\pi\) | |||||||
\(230\) | 1023.50 | 0.293426 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2832.35 | −0.801521 | ||||||||
\(233\) | −4596.37 | −1.29235 | −0.646177 | − | 0.763188i | \(-0.723633\pi\) | ||||
−0.646177 | + | 0.763188i | \(0.723633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2513.67 | 0.697761 | ||||||||
\(236\) | 1285.79 | 0.354651 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2956.83 | 0.800256 | 0.400128 | − | 0.916459i | \(-0.368966\pi\) | ||||
0.400128 | + | 0.916459i | \(0.368966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −113.007 | −0.0302050 | −0.0151025 | − | 0.999886i | \(-0.504807\pi\) | ||||
−0.0151025 | + | 0.999886i | \(0.504807\pi\) | |||||||
\(242\) | 507.387 | 0.134777 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 171.093 | 0.0448897 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 203.042 | 0.0523047 | ||||||||
\(248\) | 132.822 | 0.0340088 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1423.42 | 0.360101 | ||||||||
\(251\) | 6988.70 | 1.75746 | 0.878731 | − | 0.477318i | \(-0.158391\pi\) | ||||
0.878731 | + | 0.477318i | \(0.158391\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2935.44 | −0.729445 | ||||||||
\(254\) | 570.343 | 0.140892 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 150.683 | 0.0367880 | ||||||||
\(257\) | −2969.04 | −0.720637 | −0.360318 | − | 0.932829i | \(-0.617332\pi\) | ||||
−0.360318 | + | 0.932829i | \(0.617332\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −434.311 | −0.103595 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 474.277 | 0.111836 | ||||||||
\(263\) | −4545.72 | −1.06578 | −0.532892 | − | 0.846183i | \(-0.678895\pi\) | ||||
−0.532892 | + | 0.846183i | \(0.678895\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2893.76 | 0.670800 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2384.02 | 0.543385 | ||||||||
\(269\) | −1438.64 | −0.326079 | −0.163040 | − | 0.986620i | \(-0.552130\pi\) | ||||
−0.163040 | + | 0.986620i | \(0.552130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 583.420 | 0.130776 | 0.0653879 | − | 0.997860i | \(-0.479172\pi\) | ||||
0.0653879 | + | 0.997860i | \(0.479172\pi\) | |||||||
\(272\) | −4473.08 | −0.997134 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1734.46 | −0.382417 | ||||||||
\(275\) | −541.616 | −0.118766 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1559.79 | 0.338335 | 0.169168 | − | 0.985587i | \(-0.445892\pi\) | ||||
0.169168 | + | 0.985587i | \(0.445892\pi\) | |||||||
\(278\) | 3022.89 | 0.652161 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8809.34 | 1.87018 | 0.935091 | − | 0.354407i | \(-0.115317\pi\) | ||||
0.935091 | + | 0.354407i | \(0.115317\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8501.27 | −1.78568 | −0.892841 | − | 0.450371i | \(-0.851292\pi\) | ||||
−0.892841 | + | 0.450371i | \(0.851292\pi\) | |||||||
\(284\) | −1392.95 | −0.291044 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −162.120 | −0.0335188 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6041.62 | 1.22972 | ||||||||
\(290\) | 1932.81 | 0.391374 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4837.70 | 0.969537 | ||||||||
\(293\) | −8571.41 | −1.70903 | −0.854517 | − | 0.519423i | \(-0.826147\pi\) | ||||
−0.854517 | + | 0.519423i | \(0.826147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1869.06 | −0.368883 | ||||||||
\(296\) | 3559.95 | 0.699048 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1823.27 | −0.354427 | ||||||||
\(299\) | −617.907 | −0.119513 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1460.44 | −0.278275 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1455.30 | 0.274563 | ||||||||
\(305\) | −248.705 | −0.0466912 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1751.31 | −0.325578 | −0.162789 | − | 0.986661i | \(-0.552049\pi\) | ||||
−0.162789 | + | 0.986661i | \(0.552049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −90.6382 | −0.0166061 | ||||||||
\(311\) | −6681.74 | −1.21829 | −0.609143 | − | 0.793061i | \(-0.708486\pi\) | ||||
−0.609143 | + | 0.793061i | \(0.708486\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6049.69 | −1.09249 | −0.546244 | − | 0.837626i | \(-0.683943\pi\) | ||||
−0.546244 | + | 0.837626i | \(0.683943\pi\) | |||||||
\(314\) | 3462.14 | 0.622228 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4384.10 | −0.780458 | ||||||||
\(317\) | 3678.59 | 0.651767 | 0.325884 | − | 0.945410i | \(-0.394338\pi\) | ||||
0.325884 | + | 0.945410i | \(0.394338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5543.36 | −0.972942 | ||||||||
\(320\) | −1969.34 | −0.344029 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3564.04 | −0.613959 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −114.010 | −0.0194588 | ||||||||
\(326\) | −851.675 | −0.144693 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5303.83 | 0.892850 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10462.0 | 1.73729 | 0.868647 | − | 0.495432i | \(-0.164990\pi\) | ||||
0.868647 | + | 0.495432i | \(0.164990\pi\) | |||||||
\(332\) | 1249.21 | 0.206504 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1198.82 | −0.196396 | ||||||||
\(335\) | −3465.48 | −0.565192 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1072.17 | 0.173308 | 0.0866539 | − | 0.996238i | \(-0.472383\pi\) | ||||
0.0866539 | + | 0.996238i | \(0.472383\pi\) | |||||||
\(338\) | 2074.66 | 0.333866 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7623.56 | 1.21602 | ||||||||
\(341\) | 259.953 | 0.0412823 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5302.34 | −0.831055 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2045.01 | −0.317747 | ||||||||
\(347\) | 9562.41 | 1.47936 | 0.739679 | − | 0.672960i | \(-0.234977\pi\) | ||||
0.739679 | + | 0.672960i | \(0.234977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4159.34 | −0.637950 | −0.318975 | − | 0.947763i | \(-0.603339\pi\) | ||||
−0.318975 | + | 0.947763i | \(0.603339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4441.80 | −0.672582 | ||||||||
\(353\) | 6003.78 | 0.905238 | 0.452619 | − | 0.891704i | \(-0.350490\pi\) | ||||
0.452619 | + | 0.891704i | \(0.350490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2024.83 | 0.302723 | ||||||||
\(356\) | 5387.21 | 0.802027 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2645.44 | 0.390548 | ||||||||
\(359\) | 11515.2 | 1.69290 | 0.846448 | − | 0.532472i | \(-0.178737\pi\) | ||||
0.846448 | + | 0.532472i | \(0.178737\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5699.45 | −0.830945 | ||||||||
\(362\) | 705.298 | 0.102402 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7032.21 | −1.00845 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8631.92 | 1.22774 | 0.613872 | − | 0.789405i | \(-0.289611\pi\) | ||||
0.613872 | + | 0.789405i | \(0.289611\pi\) | |||||||
\(368\) | −4428.83 | −0.627361 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2429.33 | −0.341338 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11586.5 | −1.60838 | −0.804189 | − | 0.594373i | \(-0.797400\pi\) | ||||
−0.804189 | + | 0.594373i | \(0.797400\pi\) | |||||||
\(374\) | 2845.73 | 0.393447 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3535.65 | 0.484939 | ||||||||
\(377\) | −1166.87 | −0.159408 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.3954 | 0.00154443 | 0.000772216 | − | 1.00000i | \(-0.499754\pi\) | ||||
0.000772216 | 1.00000i | \(0.499754\pi\) | ||||||||
\(380\) | −2480.29 | −0.334833 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1952.80 | 0.261555 | ||||||||
\(383\) | −7649.91 | −1.02061 | −0.510303 | − | 0.859995i | \(-0.670467\pi\) | ||||
−0.510303 | + | 0.859995i | \(0.670467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 637.501 | 0.0840620 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9043.69 | 1.18331 | ||||||||
\(389\) | 1018.92 | 0.132805 | 0.0664027 | − | 0.997793i | \(-0.478848\pi\) | ||||
0.0664027 | + | 0.997793i | \(0.478848\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10846.3 | 1.40286 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1614.84 | 0.206484 | ||||||||
\(395\) | 6372.84 | 0.811778 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1213.68 | −0.153433 | −0.0767164 | − | 0.997053i | \(-0.524444\pi\) | ||||
−0.0767164 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(398\) | 3626.36 | 0.456717 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −817.161 | −0.102145 | ||||||||
\(401\) | −7176.55 | −0.893715 | −0.446858 | − | 0.894605i | \(-0.647457\pi\) | ||||
−0.446858 | + | 0.894605i | \(0.647457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 54.7198 | 0.00676374 | ||||||||
\(404\) | −11013.2 | −1.35625 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6967.40 | 0.848553 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14888.8 | −1.80001 | −0.900006 | − | 0.435878i | \(-0.856438\pi\) | ||||
−0.900006 | + | 0.435878i | \(0.856438\pi\) | |||||||
\(410\) | −3619.36 | −0.435969 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1743.58 | −0.208496 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1815.89 | −0.214791 | ||||||||
\(416\) | −934.994 | −0.110197 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −925.847 | −0.108337 | ||||||||
\(419\) | −7504.96 | −0.875039 | −0.437519 | − | 0.899209i | \(-0.644143\pi\) | ||||
−0.437519 | + | 0.899209i | \(0.644143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8568.94 | 0.991983 | 0.495991 | − | 0.868327i | \(-0.334805\pi\) | ||||
0.495991 | + | 0.868327i | \(0.334805\pi\) | |||||||
\(422\) | 4917.22 | 0.567219 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4070.26 | 0.466201 | ||||||||
\(425\) | 2001.23 | 0.228410 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11478.1 | 1.29629 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3618.34 | 0.405795 | ||||||||
\(431\) | 1869.85 | 0.208974 | 0.104487 | − | 0.994526i | \(-0.466680\pi\) | ||||
0.104487 | + | 0.994526i | \(0.466680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11202.1 | −1.24327 | −0.621636 | − | 0.783306i | \(-0.713532\pi\) | ||||
−0.621636 | + | 0.783306i | \(0.713532\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13496.9 | −1.48253 | ||||||||
\(437\) | −3528.79 | −0.386281 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9815.68 | −1.06715 | −0.533573 | − | 0.845754i | \(-0.679151\pi\) | ||||
−0.533573 | + | 0.845754i | \(0.679151\pi\) | |||||||
\(440\) | 4218.56 | 0.457073 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 599.023 | 0.0644629 | ||||||||
\(443\) | 5807.00 | 0.622797 | 0.311399 | − | 0.950279i | \(-0.399203\pi\) | ||||
0.311399 | + | 0.950279i | \(0.399203\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7831.00 | −0.834213 | ||||||||
\(446\) | 2033.64 | 0.215909 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −257.367 | −0.0270510 | −0.0135255 | − | 0.999909i | \(-0.504305\pi\) | ||||
−0.0135255 | + | 0.999909i | \(0.504305\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10380.4 | 1.08380 | ||||||||
\(452\) | 13355.0 | 1.38975 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4069.34 | 0.420669 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1448.74 | 0.148292 | 0.0741458 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741458 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(458\) | −1457.23 | −0.148672 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7548.14 | 0.765074 | ||||||||
\(461\) | −8713.18 | −0.880289 | −0.440144 | − | 0.897927i | \(-0.645073\pi\) | ||||
−0.440144 | + | 0.897927i | \(0.645073\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17766.2 | 1.78329 | 0.891646 | − | 0.452734i | \(-0.149551\pi\) | ||||
0.891646 | + | 0.452734i | \(0.149551\pi\) | |||||||
\(464\) | −8363.51 | −0.836780 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4411.82 | 0.438570 | ||||||||
\(467\) | 13735.0 | 1.36098 | 0.680492 | − | 0.732755i | \(-0.261766\pi\) | ||||
0.680492 | + | 0.732755i | \(0.261766\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2412.74 | −0.236791 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2628.95 | −0.256371 | ||||||||
\(473\) | −10377.5 | −1.00879 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −651.094 | −0.0628931 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2838.11 | −0.271573 | ||||||||
\(479\) | −4821.63 | −0.459929 | −0.229964 | − | 0.973199i | \(-0.573861\pi\) | ||||
−0.229964 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1466.63 | 0.139028 | ||||||||
\(482\) | 108.469 | 0.0102503 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3741.88 | 0.351416 | ||||||||
\(485\) | −13146.2 | −1.23080 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13603.0 | −1.26573 | −0.632864 | − | 0.774263i | \(-0.718121\pi\) | ||||
−0.632864 | + | 0.774263i | \(0.718121\pi\) | |||||||
\(488\) | −349.821 | −0.0324501 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6137.42 | 0.564110 | 0.282055 | − | 0.959398i | \(-0.408984\pi\) | ||||
0.282055 | + | 0.959398i | \(0.408984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20482.3 | 1.87115 | ||||||||
\(494\) | −194.890 | −0.0177500 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 392.203 | 0.0355049 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13674.1 | −1.22673 | −0.613363 | − | 0.789801i | \(-0.710184\pi\) | ||||
−0.613363 | + | 0.789801i | \(0.710184\pi\) | |||||||
\(500\) | 10497.5 | 0.938922 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6708.09 | −0.596408 | ||||||||
\(503\) | −4346.13 | −0.385257 | −0.192629 | − | 0.981272i | \(-0.561701\pi\) | ||||
−0.192629 | + | 0.981272i | \(0.561701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16009.1 | 1.41068 | ||||||||
\(506\) | 2817.58 | 0.247543 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4206.17 | 0.367359 | ||||||||
\(509\) | 19414.9 | 1.69067 | 0.845336 | − | 0.534235i | \(-0.179400\pi\) | ||||
0.845336 | + | 0.534235i | \(0.179400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11649.9 | −1.00558 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2849.83 | 0.244554 | ||||||||
\(515\) | 2534.52 | 0.216863 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6919.83 | 0.588653 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 888.003 | 0.0748875 | ||||||||
\(521\) | 2749.25 | 0.231184 | 0.115592 | − | 0.993297i | \(-0.463124\pi\) | ||||
0.115592 | + | 0.993297i | \(0.463124\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3313.72 | −0.277054 | −0.138527 | − | 0.990359i | \(-0.544237\pi\) | ||||
−0.138527 | + | 0.990359i | \(0.544237\pi\) | |||||||
\(524\) | 3497.70 | 0.291598 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4363.21 | 0.361682 | ||||||||
\(527\) | −960.509 | −0.0793936 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1428.04 | −0.117370 | ||||||||
\(530\) | −2777.57 | −0.227641 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2185.07 | 0.177572 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16684.8 | −1.34831 | ||||||||
\(536\) | −4874.42 | −0.392804 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1380.87 | 0.110657 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1490.04 | −0.118414 | −0.0592069 | − | 0.998246i | \(-0.518857\pi\) | ||||
−0.0592069 | + | 0.998246i | \(0.518857\pi\) | |||||||
\(542\) | −559.995 | −0.0443798 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16412.1 | 1.29350 | ||||||||
\(545\) | 19619.4 | 1.54202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18962.2 | 1.48220 | 0.741102 | − | 0.671392i | \(-0.234303\pi\) | ||||
0.741102 | + | 0.671392i | \(0.234303\pi\) | |||||||
\(548\) | −12791.3 | −0.997109 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 519.870 | 0.0403042 | ||||||||
\(551\) | −6663.84 | −0.515225 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1497.16 | −0.114817 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22293.2 | 1.70044 | ||||||||
\(557\) | −4846.56 | −0.368681 | −0.184341 | − | 0.982862i | \(-0.559015\pi\) | ||||
−0.184341 | + | 0.982862i | \(0.559015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2184.45 | −0.165282 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8455.63 | −0.634661 | ||||||||
\(563\) | −12390.7 | −0.927540 | −0.463770 | − | 0.885956i | \(-0.653504\pi\) | ||||
−0.463770 | + | 0.885956i | \(0.653504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19413.2 | −1.44552 | ||||||||
\(566\) | 8159.93 | 0.605985 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2848.06 | 0.210391 | ||||||||
\(569\) | −8706.19 | −0.641445 | −0.320723 | − | 0.947173i | \(-0.603926\pi\) | ||||
−0.320723 | + | 0.947173i | \(0.603926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22592.6 | −1.65582 | −0.827909 | − | 0.560862i | \(-0.810470\pi\) | ||||
−0.827909 | + | 0.560862i | \(0.810470\pi\) | |||||||
\(572\) | −1195.60 | −0.0873964 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1981.44 | 0.143707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11721.9 | 0.845734 | 0.422867 | − | 0.906192i | \(-0.361024\pi\) | ||||
0.422867 | + | 0.906192i | \(0.361024\pi\) | |||||||
\(578\) | −5799.04 | −0.417315 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14254.1 | 1.02046 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7966.15 | 0.565908 | ||||||||
\(584\) | −9891.27 | −0.700863 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8227.25 | 0.579974 | ||||||||
\(587\) | 18102.6 | 1.27287 | 0.636433 | − | 0.771332i | \(-0.280409\pi\) | ||||
0.636433 | + | 0.771332i | \(0.280409\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 312.498 | 0.0218612 | ||||||||
\(590\) | 1794.01 | 0.125183 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10512.0 | 0.729800 | ||||||||
\(593\) | 538.675 | 0.0373031 | 0.0186516 | − | 0.999826i | \(-0.494063\pi\) | ||||
0.0186516 | + | 0.999826i | \(0.494063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13446.3 | −0.924128 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 593.097 | 0.0405578 | ||||||||
\(599\) | 23628.2 | 1.61172 | 0.805861 | − | 0.592105i | \(-0.201703\pi\) | ||||
0.805861 | + | 0.592105i | \(0.201703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3930.39 | 0.266762 | 0.133381 | − | 0.991065i | \(-0.457417\pi\) | ||||
0.133381 | + | 0.991065i | \(0.457417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10770.5 | −0.725569 | ||||||||
\(605\) | −5439.29 | −0.365518 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9149.06 | 0.611778 | 0.305889 | − | 0.952067i | \(-0.401046\pi\) | ||||
0.305889 | + | 0.952067i | \(0.401046\pi\) | |||||||
\(608\) | −5339.63 | −0.356169 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 238.719 | 0.0158450 | ||||||||
\(611\) | 1456.62 | 0.0964457 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16844.1 | −1.10983 | −0.554917 | − | 0.831905i | \(-0.687250\pi\) | ||||
−0.554917 | + | 0.831905i | \(0.687250\pi\) | |||||||
\(614\) | 1680.99 | 0.110487 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25080.5 | −1.63647 | −0.818235 | − | 0.574884i | \(-0.805047\pi\) | ||||
−0.818235 | + | 0.574884i | \(0.805047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23686.3 | 1.53802 | 0.769009 | − | 0.639238i | \(-0.220750\pi\) | ||||
0.769009 | + | 0.639238i | \(0.220750\pi\) | |||||||
\(620\) | −668.439 | −0.0432986 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6413.46 | 0.413434 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12869.3 | −0.823638 | ||||||||
\(626\) | 5806.78 | 0.370744 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25532.6 | 1.62239 | ||||||||
\(629\) | −25744.0 | −1.63193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11732.0 | 0.740162 | 0.370081 | − | 0.929000i | \(-0.379330\pi\) | ||||
0.370081 | + | 0.929000i | \(0.379330\pi\) | |||||||
\(632\) | 8963.82 | 0.564180 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3530.89 | −0.221182 | ||||||||
\(635\) | −6114.20 | −0.382102 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5320.78 | 0.330175 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14798.4 | 0.913996 | ||||||||
\(641\) | −9158.83 | −0.564356 | −0.282178 | − | 0.959362i | \(-0.591057\pi\) | ||||
−0.282178 | + | 0.959362i | \(0.591057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29594.0 | 1.81504 | 0.907522 | − | 0.420003i | \(-0.137971\pi\) | ||||
0.907522 | + | 0.420003i | \(0.137971\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3420.94 | 0.208352 | ||||||||
\(647\) | 4569.57 | 0.277663 | 0.138832 | − | 0.990316i | \(-0.455665\pi\) | ||||
0.138832 | + | 0.990316i | \(0.455665\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5145.28 | −0.311201 | ||||||||
\(650\) | 109.432 | 0.00660350 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6280.94 | −0.377271 | ||||||||
\(653\) | 21264.7 | 1.27435 | 0.637176 | − | 0.770718i | \(-0.280102\pi\) | ||||
0.637176 | + | 0.770718i | \(0.280102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5084.35 | −0.303300 | ||||||||
\(656\) | 15661.4 | 0.932128 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9214.64 | 0.544691 | 0.272345 | − | 0.962200i | \(-0.412201\pi\) | ||||
0.272345 | + | 0.962200i | \(0.412201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7730.00 | −0.454859 | −0.227430 | − | 0.973794i | \(-0.573032\pi\) | ||||
−0.227430 | + | 0.973794i | \(0.573032\pi\) | |||||||
\(662\) | −10041.9 | −0.589564 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2554.16 | −0.149278 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20279.7 | 1.17726 | ||||||||
\(668\) | −8841.03 | −0.512080 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3326.33 | 0.191802 | ||||||||
\(671\) | −684.654 | −0.0393901 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14627.9 | 0.837835 | 0.418917 | − | 0.908024i | \(-0.362410\pi\) | ||||
0.418917 | + | 0.908024i | \(0.362410\pi\) | |||||||
\(674\) | −1029.12 | −0.0588133 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15300.2 | 0.870517 | ||||||||
\(677\) | 27179.8 | 1.54299 | 0.771496 | − | 0.636234i | \(-0.219509\pi\) | ||||
0.771496 | + | 0.636234i | \(0.219509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −15587.3 | −0.879038 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −249.516 | −0.0140095 | ||||||||
\(683\) | 34448.5 | 1.92992 | 0.964959 | − | 0.262402i | \(-0.0845147\pi\) | ||||
0.964959 | + | 0.262402i | \(0.0845147\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18593.7 | 1.03712 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15657.0 | −0.867614 | ||||||||
\(689\) | 1676.86 | 0.0927191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13766.2 | −0.757872 | −0.378936 | − | 0.925423i | \(-0.623710\pi\) | ||||
−0.378936 | + | 0.925423i | \(0.623710\pi\) | |||||||
\(692\) | −15081.5 | −0.828488 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9178.46 | −0.502031 | ||||||||
\(695\) | −32406.0 | −1.76868 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38355.0 | −2.08436 | ||||||||
\(698\) | 3992.34 | 0.216493 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28107.2 | 1.51440 | 0.757200 | − | 0.653183i | \(-0.226567\pi\) | ||||
0.757200 | + | 0.653183i | \(0.226567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8375.72 | 0.449355 | ||||||||
\(704\) | −5421.34 | −0.290234 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5762.72 | −0.307200 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29866.8 | 1.58205 | 0.791023 | − | 0.611786i | \(-0.209549\pi\) | ||||
0.791023 | + | 0.611786i | \(0.209549\pi\) | |||||||
\(710\) | −1943.53 | −0.102732 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11014.8 | −0.579772 | ||||||||
\(713\) | −951.007 | −0.0499516 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1737.96 | 0.0909037 | ||||||||
\(716\) | 19509.6 | 1.01831 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11052.9 | −0.574497 | ||||||||
\(719\) | −20815.8 | −1.07969 | −0.539845 | − | 0.841764i | \(-0.681517\pi\) | ||||
−0.539845 | + | 0.841764i | \(0.681517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5470.61 | 0.281988 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5201.43 | 0.267002 | ||||||||
\(725\) | 3741.79 | 0.191678 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2638.00 | 0.134578 | 0.0672888 | − | 0.997734i | \(-0.478565\pi\) | ||||
0.0672888 | + | 0.997734i | \(0.478565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6749.86 | 0.342224 | ||||||||
\(731\) | 38344.2 | 1.94010 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19483.1 | 0.981754 | 0.490877 | − | 0.871229i | \(-0.336677\pi\) | ||||
0.490877 | + | 0.871229i | \(0.336677\pi\) | |||||||
\(734\) | −8285.33 | −0.416645 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16249.8 | 0.813825 | ||||||||
\(737\) | −9540.02 | −0.476813 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2190.08 | −0.109017 | −0.0545084 | − | 0.998513i | \(-0.517359\pi\) | ||||
−0.0545084 | + | 0.998513i | \(0.517359\pi\) | |||||||
\(740\) | −17915.8 | −0.889999 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21777.5 | 1.07529 | 0.537644 | − | 0.843172i | \(-0.319315\pi\) | ||||
0.537644 | + | 0.843172i | \(0.319315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19545.8 | 0.961214 | ||||||||
\(746\) | 11121.3 | 0.545815 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20986.7 | 1.02587 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14790.8 | −0.718672 | −0.359336 | − | 0.933208i | \(-0.616997\pi\) | ||||
−0.359336 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(752\) | 10440.2 | 0.506272 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1120.02 | 0.0540964 | ||||||||
\(755\) | 15656.2 | 0.754687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30374.8 | 1.45838 | 0.729188 | − | 0.684313i | \(-0.239898\pi\) | ||||
0.729188 | + | 0.684313i | \(0.239898\pi\) | |||||||
\(758\) | −10.9378 | −0.000524115 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5071.27 | 0.242045 | ||||||||
\(761\) | −14854.4 | −0.707584 | −0.353792 | − | 0.935324i | \(-0.615108\pi\) | ||||
−0.353792 | + | 0.935324i | \(0.615108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14401.5 | 0.681975 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7342.75 | 0.346350 | ||||||||
\(767\) | −1083.07 | −0.0509877 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3016.48 | −0.141453 | −0.0707264 | − | 0.997496i | \(-0.522532\pi\) | ||||
−0.0707264 | + | 0.997496i | \(0.522532\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4701.44 | 0.219182 | ||||||||
\(773\) | −5047.57 | −0.234862 | −0.117431 | − | 0.993081i | \(-0.537466\pi\) | ||||
−0.117431 | + | 0.993081i | \(0.537466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −175.470 | −0.00813298 | ||||||||
\(776\) | −18490.9 | −0.855395 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −978.008 | −0.0450685 | ||||||||
\(779\) | 12478.6 | 0.573933 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5574.11 | 0.255387 | ||||||||
\(782\) | −10410.8 | −0.476072 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37114.8 | −1.68750 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19962.3 | −0.904166 | −0.452083 | − | 0.891976i | \(-0.649319\pi\) | ||||
−0.452083 | + | 0.891976i | \(0.649319\pi\) | |||||||
\(788\) | 11909.2 | 0.538383 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6116.96 | −0.275483 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −144.119 | −0.00645374 | ||||||||
\(794\) | 1164.95 | 0.0520686 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26743.7 | 1.19084 | ||||||||
\(797\) | 806.334 | 0.0358367 | 0.0179183 | − | 0.999839i | \(-0.494296\pi\) | ||||
0.0179183 | + | 0.999839i | \(0.494296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25568.3 | −1.13209 | ||||||||
\(800\) | 2998.24 | 0.132505 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6888.40 | 0.303289 | ||||||||
\(803\) | −19358.8 | −0.850756 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −52.5227 | −0.00229533 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22517.8 | 0.980414 | ||||||||
\(809\) | −42013.3 | −1.82584 | −0.912922 | − | 0.408134i | \(-0.866180\pi\) | ||||
−0.912922 | + | 0.408134i | \(0.866180\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2938.48 | 0.127231 | 0.0636153 | − | 0.997974i | \(-0.479737\pi\) | ||||
0.0636153 | + | 0.997974i | \(0.479737\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6687.64 | −0.287963 | ||||||||
\(815\) | 9130.14 | 0.392411 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12475.1 | −0.534210 | ||||||||
\(818\) | 14291.0 | 0.610848 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26692.1 | −1.13674 | ||||||||
\(821\) | 24232.8 | 1.03012 | 0.515060 | − | 0.857154i | \(-0.327770\pi\) | ||||
0.515060 | + | 0.857154i | \(0.327770\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27959.8 | −1.18422 | −0.592112 | − | 0.805856i | \(-0.701706\pi\) | ||||
−0.592112 | + | 0.805856i | \(0.701706\pi\) | |||||||
\(824\) | 3564.97 | 0.150718 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11855.3 | −0.498487 | −0.249244 | − | 0.968441i | \(-0.580182\pi\) | ||||
−0.249244 | + | 0.968441i | \(0.580182\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43362.5 | −1.81670 | −0.908349 | − | 0.418213i | \(-0.862657\pi\) | ||||
−0.908349 | + | 0.418213i | \(0.862657\pi\) | |||||||
\(830\) | 1742.97 | 0.0728910 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1141.19 | −0.0475523 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12851.6 | 0.532630 | ||||||||
\(836\) | −6827.94 | −0.282475 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7203.62 | 0.296951 | ||||||||
\(839\) | 20467.7 | 0.842221 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13907.7 | 0.570243 | ||||||||
\(842\) | −8224.89 | −0.336637 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 36263.5 | 1.47896 | ||||||||
\(845\) | −22240.8 | −0.905452 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12018.9 | 0.486710 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1920.88 | −0.0775126 | ||||||||
\(851\) | −25489.4 | −1.02675 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17910.2 | −0.718914 | −0.359457 | − | 0.933162i | \(-0.617038\pi\) | ||||
−0.359457 | + | 0.933162i | \(0.617038\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23468.3 | −0.937069 | ||||||||
\(857\) | 4494.31 | 0.179140 | 0.0895698 | − | 0.995981i | \(-0.471451\pi\) | ||||
0.0895698 | + | 0.995981i | \(0.471451\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14367.1 | −0.570663 | −0.285331 | − | 0.958429i | \(-0.592104\pi\) | ||||
−0.285331 | + | 0.958429i | \(0.592104\pi\) | |||||||
\(860\) | 26684.5 | 1.05806 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1794.78 | −0.0709169 | ||||||||
\(863\) | 12240.1 | 0.482802 | 0.241401 | − | 0.970425i | \(-0.422393\pi\) | ||||
0.241401 | + | 0.970425i | \(0.422393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21922.9 | 0.861736 | ||||||||
\(866\) | 10752.3 | 0.421914 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17543.6 | 0.684841 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2008.16 | −0.0781217 | ||||||||
\(872\) | 27596.0 | 1.07170 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3387.10 | 0.131087 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18127.6 | −0.697978 | −0.348989 | − | 0.937127i | \(-0.613475\pi\) | ||||
−0.348989 | + | 0.937127i | \(0.613475\pi\) | |||||||
\(878\) | 9421.57 | 0.362144 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12456.8 | 0.477180 | ||||||||
\(881\) | −28737.3 | −1.09896 | −0.549480 | − | 0.835507i | \(-0.685174\pi\) | ||||
−0.549480 | + | 0.835507i | \(0.685174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29899.7 | 1.13953 | 0.569765 | − | 0.821807i | \(-0.307034\pi\) | ||||
0.569765 | + | 0.821807i | \(0.307034\pi\) | |||||||
\(884\) | 4417.67 | 0.168080 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5573.84 | −0.211351 | ||||||||
\(887\) | 35540.7 | 1.34537 | 0.672683 | − | 0.739931i | \(-0.265142\pi\) | ||||
0.672683 | + | 0.739931i | \(0.265142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7516.57 | 0.283097 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14997.7 | 0.562959 | ||||||||
\(893\) | 8318.54 | 0.311724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28359.7 | −1.05917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 247.034 | 0.00917998 | ||||||||
\(899\) | −1795.90 | −0.0666260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29434.4 | −1.08835 | ||||||||
\(902\) | −9963.64 | −0.367797 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27305.9 | −1.00462 | ||||||||
\(905\) | −7560.94 | −0.277717 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16816.0 | −0.615617 | −0.307808 | − | 0.951448i | \(-0.599596\pi\) | ||||
−0.307808 | + | 0.951448i | \(0.599596\pi\) | |||||||
\(908\) | 30010.6 | 1.09685 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21626.8 | −0.786527 | −0.393264 | − | 0.919426i | \(-0.628654\pi\) | ||||
−0.393264 | + | 0.919426i | \(0.628654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4998.91 | −0.181204 | ||||||||
\(914\) | −1390.57 | −0.0503239 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10746.8 | −0.387645 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31512.2 | 1.13111 | 0.565556 | − | 0.824710i | \(-0.308662\pi\) | ||||
0.565556 | + | 0.824710i | \(0.308662\pi\) | |||||||
\(920\) | −15433.1 | −0.553059 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8363.33 | 0.298733 | ||||||||
\(923\) | 1173.34 | 0.0418429 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4703.03 | −0.167173 | ||||||||
\(926\) | −17052.8 | −0.605174 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30686.5 | 1.08549 | ||||||||
\(929\) | −25267.9 | −0.892373 | −0.446186 | − | 0.894940i | \(-0.647218\pi\) | ||||
−0.446186 | + | 0.894940i | \(0.647218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32536.3 | 1.14352 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13183.5 | −0.461861 | ||||||||
\(935\) | −30506.8 | −1.06704 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14694.4 | −0.512321 | −0.256161 | − | 0.966634i | \(-0.582458\pi\) | ||||
−0.256161 | + | 0.966634i | \(0.582458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17793.5 | −0.617405 | ||||||||
\(941\) | −7004.20 | −0.242647 | −0.121323 | − | 0.992613i | \(-0.538714\pi\) | ||||
−0.121323 | + | 0.992613i | \(0.538714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37975.6 | −1.31140 | ||||||||
\(944\) | −7762.91 | −0.267649 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9960.84 | 0.342341 | ||||||||
\(947\) | 10065.2 | 0.345379 | 0.172690 | − | 0.984976i | \(-0.444754\pi\) | ||||
0.172690 | + | 0.984976i | \(0.444754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4075.00 | −0.139389 | ||||||||
\(950\) | 624.951 | 0.0213433 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15265.2 | −0.518876 | −0.259438 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259438 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20934.5 | −0.709343 | ||||||||
\(956\) | −20930.5 | −0.708096 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4628.03 | 0.156080 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29706.8 | −0.997173 | ||||||||
\(962\) | −1407.74 | −0.0471802 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 799.940 | 0.0267265 | ||||||||
\(965\) | −6834.14 | −0.227978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32705.8 | −1.08764 | −0.543820 | − | 0.839202i | \(-0.683022\pi\) | ||||
−0.543820 | + | 0.839202i | \(0.683022\pi\) | |||||||
\(968\) | −7650.73 | −0.254033 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12618.3 | 0.417680 | ||||||||
\(971\) | 48338.6 | 1.59759 | 0.798795 | − | 0.601603i | \(-0.205471\pi\) | ||||
0.798795 | + | 0.601603i | \(0.205471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13056.8 | 0.429535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1032.97 | −0.0338776 | ||||||||
\(977\) | −21230.1 | −0.695200 | −0.347600 | − | 0.937643i | \(-0.613003\pi\) | ||||
−0.347600 | + | 0.937643i | \(0.613003\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21557.8 | −0.703768 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5890.99 | −0.191435 | ||||||||
\(983\) | −54979.2 | −1.78389 | −0.891946 | − | 0.452142i | \(-0.850660\pi\) | ||||
−0.891946 | + | 0.452142i | \(0.850660\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17311.5 | −0.559989 | ||||||||
\(986\) | −19659.9 | −0.634989 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1437.27 | −0.0462811 | ||||||||
\(989\) | 37964.9 | 1.22064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12954.3 | 0.415245 | 0.207622 | − | 0.978209i | \(-0.433427\pi\) | ||||
0.207622 | + | 0.978209i | \(0.433427\pi\) | |||||||
\(992\) | −1439.03 | −0.0460577 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38875.4 | −1.23863 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13382.0 | −0.425088 | −0.212544 | − | 0.977151i | \(-0.568175\pi\) | ||||
−0.212544 | + | 0.977151i | \(0.568175\pi\) | |||||||
\(998\) | 13125.0 | 0.416299 | ||||||||
\(999\) | 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 | 1323.4.a.bl.1.4 | ✓ | 8 | |
3.2 | odd | 2 | inner | 1323.4.a.bl.1.5 | yes | 8 | |
7.6 | odd | 2 | 1323.4.a.bm.1.4 | yes | 8 | ||
21.20 | even | 2 | 1323.4.a.bm.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.4.a.bl.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1323.4.a.bl.1.5 | yes | 8 | 3.2 | odd | 2 | inner | |
1323.4.a.bm.1.4 | yes | 8 | 7.6 | odd | 2 | ||
1323.4.a.bm.1.5 | yes | 8 | 21.20 | even | 2 |