Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4 x^{9} - 135 x^{8} + 788 x^{7} + 3323 x^{6} - 26136 x^{5} + 2315 x^{4} + 188664 x^{3} + \cdots + 128592 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-10.8075\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | 0 | ||||||||
\(3\) | −0.0474689 | −0.00913539 | −0.00456769 | − | 0.999990i | \(-0.501454\pi\) | ||||
−0.00456769 | + | 0.999990i | \(0.501454\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.61587 | −0.502299 | −0.251149 | − | 0.967948i | \(-0.580809\pi\) | ||||
−0.251149 | + | 0.967948i | \(0.580809\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.39051 | −0.507040 | −0.253520 | − | 0.967330i | \(-0.581588\pi\) | ||||
−0.253520 | + | 0.967330i | \(0.581588\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.9977 | −0.999917 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.05123 | 0.193275 | 0.0966375 | − | 0.995320i | \(-0.469191\pi\) | ||||
0.0966375 | + | 0.995320i | \(0.469191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.5402 | −0.246207 | −0.123103 | − | 0.992394i | \(-0.539285\pi\) | ||||
−0.123103 | + | 0.992394i | \(0.539285\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.266579 | 0.00458870 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 43.2804 | 0.617473 | 0.308737 | − | 0.951148i | \(-0.400094\pi\) | ||||
0.308737 | + | 0.951148i | \(0.400094\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −94.6522 | −1.14288 | −0.571439 | − | 0.820644i | \(-0.693615\pi\) | ||||
−0.571439 | + | 0.820644i | \(0.693615\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.445757 | 0.00463201 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 183.781 | 1.66613 | 0.833064 | − | 0.553177i | \(-0.186585\pi\) | ||||
0.833064 | + | 0.553177i | \(0.186585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −93.4620 | −0.747696 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.56321 | 0.0182700 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −299.700 | −1.73638 | −0.868189 | − | 0.496233i | \(-0.834716\pi\) | ||||
−0.868189 | + | 0.496233i | \(0.834716\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.334714 | −0.00176564 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 52.7359 | 0.254686 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −116.770 | −0.518834 | −0.259417 | − | 0.965765i | \(-0.583530\pi\) | ||||
−0.259417 | + | 0.965765i | \(0.583530\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.547802 | 0.00224919 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −461.690 | −1.75863 | −0.879316 | − | 0.476239i | \(-0.842000\pi\) | ||||
−0.879316 | + | 0.476239i | \(0.842000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 120.966 | 0.429003 | 0.214502 | − | 0.976724i | \(-0.431187\pi\) | ||||
0.214502 | + | 0.976724i | \(0.431187\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 151.616 | 0.502257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −115.282 | −0.357779 | −0.178890 | − | 0.983869i | \(-0.557250\pi\) | ||||
−0.178890 | + | 0.983869i | \(0.557250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −254.818 | −0.742910 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.05447 | −0.00564086 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.62495 | 0.00421139 | 0.00210570 | − | 0.999998i | \(-0.499330\pi\) | ||||
0.00210570 | + | 0.999998i | \(0.499330\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −39.5988 | −0.0970818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.49303 | 0.0104406 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −167.219 | −0.368984 | −0.184492 | − | 0.982834i | \(-0.559064\pi\) | ||||
−0.184492 | + | 0.982834i | \(0.559064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 753.613 | 1.58181 | 0.790904 | − | 0.611940i | \(-0.209611\pi\) | ||||
0.790904 | + | 0.611940i | \(0.209611\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 253.523 | 0.506998 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 64.8085 | 0.123669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −495.939 | −0.904308 | −0.452154 | − | 0.891940i | \(-0.649344\pi\) | ||||
−0.452154 | + | 0.891940i | \(0.649344\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.72386 | −0.0152207 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 394.893 | 0.660074 | 0.330037 | − | 0.943968i | \(-0.392939\pi\) | ||||
0.330037 | + | 0.943968i | \(0.392939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.7036 | 0.0572438 | 0.0286219 | − | 0.999590i | \(-0.490888\pi\) | ||||
0.0286219 | + | 0.999590i | \(0.490888\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.43654 | 0.00683049 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −66.2147 | −0.0979982 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −659.203 | −0.938811 | −0.469406 | − | 0.882983i | \(-0.655532\pi\) | ||||
−0.469406 | + | 0.882983i | \(0.655532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 728.817 | 0.999750 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1437.34 | 1.90082 | 0.950410 | − | 0.311001i | \(-0.100664\pi\) | ||||
0.950410 | + | 0.311001i | \(0.100664\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −243.057 | −0.310156 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.37660 | −0.00169640 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 171.190 | 0.203889 | 0.101944 | − | 0.994790i | \(-0.467494\pi\) | ||||
0.101944 | + | 0.994790i | \(0.467494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 108.369 | 0.124837 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.2264 | 0.0158625 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 531.554 | 0.574067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −750.095 | −0.785161 | −0.392581 | − | 0.919718i | \(-0.628418\pi\) | ||||
−0.392581 | + | 0.919718i | \(0.628418\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −190.367 | −0.193259 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1587.54 | 1.56402 | 0.782008 | − | 0.623268i | \(-0.214196\pi\) | ||||
0.782008 | + | 0.623268i | \(0.214196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −764.687 | −0.731523 | −0.365762 | − | 0.930709i | \(-0.619191\pi\) | ||||
−0.365762 | + | 0.930709i | \(0.619191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.50332 | −0.00232665 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1366.26 | −1.23440 | −0.617200 | − | 0.786806i | \(-0.711733\pi\) | ||||
−0.617200 | + | 0.786806i | \(0.711733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1652.02 | 1.45169 | 0.725847 | − | 0.687856i | \(-0.241448\pi\) | ||||
0.725847 | + | 0.687856i | \(0.241448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.54294 | 0.00473975 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1170.07 | 0.974077 | 0.487038 | − | 0.873381i | \(-0.338077\pi\) | ||||
0.487038 | + | 0.873381i | \(0.338077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1032.09 | −0.836894 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 311.561 | 0.246186 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −406.425 | −0.313084 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1281.28 | −0.962645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.9159 | 0.0160658 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1226.85 | 0.877866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2522.35 | 1.76238 | 0.881189 | − | 0.472764i | \(-0.156744\pi\) | ||||
0.881189 | + | 0.472764i | \(0.156744\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.74212 | −0.00391911 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2718.35 | 1.81300 | 0.906501 | − | 0.422204i | \(-0.138743\pi\) | ||||
0.906501 | + | 0.422204i | \(0.138743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 888.833 | 0.579485 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.3947 | −0.00917701 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −272.519 | −0.169948 | −0.0849738 | − | 0.996383i | \(-0.527081\pi\) | ||||
−0.0849738 | + | 0.996383i | \(0.527081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2354.00 | −1.43643 | −0.718213 | − | 0.695823i | \(-0.755040\pi\) | ||||
−0.718213 | + | 0.695823i | \(0.755040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.47231 | 0.00326845 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −81.3729 | −0.0475856 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −162.860 | −0.0932746 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0959 | 0.00678678 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2439.00 | 1.34101 | 0.670505 | − | 0.741905i | \(-0.266077\pi\) | ||||
0.670505 | + | 0.741905i | \(0.266077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2649.49 | −1.42790 | −0.713949 | − | 0.700198i | \(-0.753095\pi\) | ||||
−0.713949 | + | 0.700198i | \(0.753095\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1168.47 | −0.617421 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1683.08 | 0.872181 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1504.16 | 0.764619 | 0.382309 | − | 0.924034i | \(-0.375129\pi\) | ||||
0.382309 | + | 0.924034i | \(0.375129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0771345 | −3.84727e−5 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1725.80 | −0.844793 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2016.09 | 0.968788 | 0.484394 | − | 0.874850i | \(-0.339040\pi\) | ||||
0.484394 | + | 0.874850i | \(0.339040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.87971 | 0.000886880 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3547.68 | 1.64388 | 0.821939 | − | 0.569576i | \(-0.192893\pi\) | ||||
0.821939 | + | 0.569576i | \(0.192893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2063.82 | −0.939382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2555.40 | 1.14278 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1916.32 | 0.842168 | 0.421084 | − | 0.907022i | \(-0.361650\pi\) | ||||
0.421084 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 877.656 | 0.379112 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.93770 | 0.00337081 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2799.09 | −1.16879 | −0.584395 | − | 0.811469i | \(-0.698668\pi\) | ||||
−0.584395 | + | 0.811469i | \(0.698668\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1347.05 | −0.553180 | −0.276590 | − | 0.960988i | \(-0.589204\pi\) | ||||
−0.276590 | + | 0.960988i | \(0.589204\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −35.7732 | −0.0144504 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 655.765 | 0.260610 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 305.180 | 0.119342 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −24.0699 | −0.00926363 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2439.45 | 0.924149 | 0.462074 | − | 0.886841i | \(-0.347105\pi\) | ||||
0.462074 | + | 0.886841i | \(0.347105\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3779.81 | 1.40972 | 0.704862 | − | 0.709344i | \(-0.251009\pi\) | ||||
0.704862 | + | 0.709344i | \(0.251009\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.07639 | −0.00112977 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3645.34 | 1.31838 | 0.659188 | − | 0.751979i | \(-0.270900\pi\) | ||||
0.659188 | + | 0.751979i | \(0.270900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4042.15 | −1.43990 | −0.719950 | − | 0.694026i | \(-0.755835\pi\) | ||||
−0.719950 | + | 0.694026i | \(0.755835\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.5417 | 0.00826120 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −272.325 | −0.0941550 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2592.79 | 0.883359 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4961.67 | −1.66599 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −667.414 | −0.220890 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4454.20 | −1.45327 | −0.726634 | − | 0.687024i | \(-0.758917\pi\) | ||||
−0.726634 | + | 0.687024i | \(0.758917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.7451 | −0.00603003 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −679.329 | −0.215488 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2814.34 | 0.880414 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.69481 | −0.000522944 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −499.466 | −0.152026 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 843.600 | 0.253326 | 0.126663 | − | 0.991946i | \(-0.459573\pi\) | ||||
0.126663 | + | 0.991946i | \(0.459573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2523.26 | 0.747633 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −128.667 | −0.0376208 | −0.0188104 | − | 0.999823i | \(-0.505988\pi\) | ||||
−0.0188104 | + | 0.999823i | \(0.505988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1875.55 | 0.541221 | 0.270610 | − | 0.962689i | \(-0.412774\pi\) | ||||
0.270610 | + | 0.962689i | \(0.412774\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.14314 | 0.000895252 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −732.103 | −0.205844 | −0.102922 | − | 0.994689i | \(-0.532819\pi\) | ||||
−0.102922 | + | 0.994689i | \(0.532819\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 647.409 | 0.179712 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.2916 | 0.00857641 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3892.20 | −1.05341 | −0.526706 | − | 0.850047i | \(-0.676573\pi\) | ||||
−0.526706 | + | 0.850047i | \(0.676573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3897.87 | 1.04184 | 0.520920 | − | 0.853605i | \(-0.325589\pi\) | ||||
0.520920 | + | 0.853605i | \(0.325589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −103.803 | −0.0274031 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1431.03 | 0.373163 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1092.31 | 0.281384 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −68.2287 | −0.0173647 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5746.49 | −1.44508 | −0.722540 | − | 0.691329i | \(-0.757026\pi\) | ||||
−0.722540 | + | 0.691329i | \(0.757026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1295.88 | 0.322021 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.5377 | 0.00283340 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4983.07 | 1.20948 | 0.604738 | − | 0.796424i | \(-0.293278\pi\) | ||||
0.604738 | + | 0.796424i | \(0.293278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1096.53 | 0.263070 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −782.935 | −0.185680 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −530.122 | −0.124292 | −0.0621459 | − | 0.998067i | \(-0.519794\pi\) | ||||
−0.0621459 | + | 0.998067i | \(0.519794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.12550 | −0.00211538 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.12619 | −0.00186260 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2205.16 | −0.499817 | −0.249908 | − | 0.968269i | \(-0.580401\pi\) | ||||
−0.249908 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −324.628 | −0.0727666 | −0.0363833 | − | 0.999338i | \(-0.511584\pi\) | ||||
−0.0363833 | + | 0.999338i | \(0.511584\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.14415 | −0.00114043 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −659.022 | −0.144511 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8591.36 | 1.86356 | 0.931778 | − | 0.363028i | \(-0.118257\pi\) | ||||
0.931778 | + | 0.363028i | \(0.118257\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8091.23 | 1.73623 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5176.79 | 1.09901 | 0.549504 | − | 0.835491i | \(-0.314817\pi\) | ||||
0.549504 | + | 0.835491i | \(0.314817\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8331.74 | 1.75007 | 0.875036 | − | 0.484058i | \(-0.160838\pi\) | ||||
0.875036 | + | 0.484058i | \(0.160838\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.2323 | −0.00524432 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4335.51 | 0.891697 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3039.81 | −0.618727 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 35.6062 | 0.00717275 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5137.07 | −1.02427 | −0.512135 | − | 0.858905i | \(-0.671145\pi\) | ||||
−0.512135 | + | 0.858905i | \(0.671145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 939.080 | 0.185340 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.0738 | 0.00353114 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2120.87 | −0.410212 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1135.93 | −0.217522 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −75.3585 | −0.0142879 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4232.20 | −0.794540 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8143.50 | 1.51392 | 0.756961 | − | 0.653460i | \(-0.226683\pi\) | ||||
0.756961 | + | 0.653460i | \(0.226683\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.2989 | 0.00668275 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4108.03 | −0.749020 | −0.374510 | − | 0.927223i | \(-0.622189\pi\) | ||||
−0.374510 | + | 0.927223i | \(0.622189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3593.05 | 0.648853 | 0.324426 | − | 0.945911i | \(-0.394829\pi\) | ||||
0.324426 | + | 0.945911i | \(0.394829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1423.75 | −0.254664 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −819.529 | −0.145203 | −0.0726015 | − | 0.997361i | \(-0.523130\pi\) | ||||
−0.0726015 | + | 0.997361i | \(0.523130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 204.486 | 0.0358903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 64.8546 | 0.0112767 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4096.58 | −0.705697 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1078.57 | 0.184088 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −78.4195 | −0.0132618 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1082.56 | 0.181408 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 826.130 | 0.137185 | 0.0685924 | − | 0.997645i | \(-0.478149\pi\) | ||||
0.0685924 | + | 0.997645i | \(0.478149\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3152.52 | 0.518791 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2785.13 | 0.454233 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6421.60 | 1.03800 | 0.519001 | − | 0.854773i | \(-0.326304\pi\) | ||||
0.519001 | + | 0.854773i | \(0.326304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −55.5418 | −0.00889857 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2113.25 | −0.335599 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5613.82 | 0.883725 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 48.9921 | 0.00764535 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1996.34 | 0.308845 | 0.154423 | − | 0.988005i | \(-0.450648\pi\) | ||||
0.154423 | + | 0.988005i | \(0.450648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5157.51 | 0.791046 | 0.395523 | − | 0.918456i | \(-0.370563\pi\) | ||||
0.395523 | + | 0.918456i | \(0.370563\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.5801 | −0.00449820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8738.74 | 1.31761 | 0.658804 | − | 0.752314i | \(-0.271062\pi\) | ||||
0.658804 | + | 0.752314i | \(0.271062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2217.67 | −0.331554 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.2926 | 0.00286014 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9664.38 | −1.42080 | −0.710399 | − | 0.703799i | \(-0.751485\pi\) | ||||
−0.710399 | + | 0.703799i | \(0.751485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2100.03 | 0.306172 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 60.8209 | 0.00879414 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −200.507 | −0.0287535 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3092.89 | −0.439912 | −0.219956 | − | 0.975510i | \(-0.570591\pi\) | ||||
−0.219956 | + | 0.975510i | \(0.570591\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12464.6 | 1.75849 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.2591 | −0.00213535 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9050.45 | −1.25634 | −0.628170 | − | 0.778076i | \(-0.716196\pi\) | ||||
−0.628170 | + | 0.778076i | \(0.716196\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −58.2374 | −0.00801964 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −334.667 | −0.0457194 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9830.13 | −1.33230 | −0.666148 | − | 0.745820i | \(-0.732058\pi\) | ||||
−0.666148 | + | 0.745820i | \(0.732058\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −119.733 | −0.0161000 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10042.5 | −1.33980 | −0.669902 | − | 0.742449i | \(-0.733664\pi\) | ||||
−0.669902 | + | 0.742449i | \(0.733664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 371.853 | 0.0492244 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3265.81 | −0.428967 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5075.42 | 0.661526 | 0.330763 | − | 0.943714i | \(-0.392694\pi\) | ||||
0.330763 | + | 0.943714i | \(0.392694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7954.10 | 1.02879 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −129.037 | −0.0165625 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3702.00 | 0.471564 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9074.11 | −1.14715 | −0.573573 | − | 0.819155i | \(-0.694443\pi\) | ||||
−0.573573 | + | 0.819155i | \(0.694443\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −42.1919 | −0.00529382 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3865.42 | −0.481372 | −0.240686 | − | 0.970603i | \(-0.577372\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577372\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3458.61 | 0.427508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4092.95 | −0.502173 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −823.371 | −0.100278 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1170.84 | 0.141551 | 0.0707757 | − | 0.997492i | \(-0.477453\pi\) | ||||
0.0707757 | + | 0.997492i | \(0.477453\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.9361 | 0.00155254 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1570.27 | 0.187090 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8071.89 | −0.954779 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 111.742 | 0.0131223 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12741.7 | 1.48562 | 0.742810 | − | 0.669502i | \(-0.233493\pi\) | ||||
0.742810 | + | 0.669502i | \(0.233493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2207.04 | 0.255497 | 0.127749 | − | 0.991807i | \(-0.459225\pi\) | ||||
0.127749 | + | 0.991807i | \(0.459225\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3112.36 | 0.357749 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4045.07 | −0.461682 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7076.82 | −0.802040 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.86268 | 0.000434713 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10293.5 | 1.15039 | 0.575196 | − | 0.818015i | \(-0.304926\pi\) | ||||
0.575196 | + | 0.818015i | \(0.304926\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12374.3 | 1.37337 | 0.686687 | − | 0.726954i | \(-0.259064\pi\) | ||||
0.686687 | + | 0.726954i | \(0.259064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.73080 | 0.000852099 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17395.2 | −1.90418 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2087.57 | −0.226958 | −0.113479 | − | 0.993540i | \(-0.536199\pi\) | ||||
−0.113479 | + | 0.993540i | \(0.536199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6879.52 | 0.742848 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6401.81 | 0.686590 | 0.343295 | − | 0.939228i | \(-0.388457\pi\) | ||||
0.343295 | + | 0.939228i | \(0.388457\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −961.380 | −0.102413 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −115.777 | −0.0122507 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7560.57 | −0.794666 | −0.397333 | − | 0.917674i | \(-0.630064\pi\) | ||||
−0.397333 | + | 0.917674i | \(0.630064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3255.48 | −0.339900 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 125.768 | 0.0130444 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −608.585 | −0.0627053 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11624.1 | 1.18983 | 0.594913 | − | 0.803790i | \(-0.297186\pi\) | ||||
0.594913 | + | 0.803790i | \(0.297186\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 110.937 | 0.0112812 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2487.08 | −0.251269 | −0.125635 | − | 0.992077i | \(-0.540097\pi\) | ||||
−0.125635 | + | 0.992077i | \(0.540097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10489.7 | 1.05291 | 0.526453 | − | 0.850204i | \(-0.323522\pi\) | ||||
0.526453 | + | 0.850204i | \(0.323522\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −79.8938 | −0.00796771 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5870.85 | 0.581735 | 0.290868 | − | 0.956763i | \(-0.406056\pi\) | ||||
0.290868 | + | 0.956763i | \(0.406056\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4657.12 | 0.458520 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −71.4009 | −0.00698509 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 852.959 | 0.0829156 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8846.38 | 0.854526 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −43.8700 | −0.00421104 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11566.3 | 1.10329 | 0.551647 | − | 0.834078i | \(-0.314000\pi\) | ||||
0.551647 | + | 0.834078i | \(0.314000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1347.55 | 0.127740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 81.9216 | 0.00771752 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4212.44 | 0.394386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17667.5 | −1.64392 | −0.821962 | − | 0.569542i | \(-0.807121\pi\) | ||||
−0.821962 | + | 0.569542i | \(0.807121\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −95.7015 | −0.00885025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5200.51 | −0.477996 | −0.238998 | − | 0.971020i | \(-0.576819\pi\) | ||||
−0.238998 | + | 0.971020i | \(0.576819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1255.13 | 0.114662 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1069.08 | 0.0970737 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3708.25 | −0.334684 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19925.1 | −1.78752 | −0.893758 | − | 0.448550i | \(-0.851940\pi\) | ||||
−0.893758 | + | 0.448550i | \(0.851940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −168.404 | −0.0150175 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14124.6 | 1.25206 | 0.626030 | − | 0.779799i | \(-0.284679\pi\) | ||||
0.626030 | + | 0.779799i | \(0.284679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8915.39 | −0.785604 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 97.9674 | 0.00858162 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9959.76 | 0.867305 | 0.433653 | − | 0.901080i | \(-0.357224\pi\) | ||||
0.433653 | + | 0.901080i | \(0.357224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −335.275 | −0.0290249 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −242.614 | −0.0208804 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4294.39 | 0.367443 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −812.880 | −0.0691498 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −90.9655 | −0.00769353 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1656.26 | 0.139275 | 0.0696374 | − | 0.997572i | \(-0.477816\pi\) | ||||
0.0696374 | + | 0.997572i | \(0.477816\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7994.22 | 0.668380 | 0.334190 | − | 0.942506i | \(-0.391537\pi\) | ||||
0.334190 | + | 0.942506i | \(0.391537\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −41.6613 | −0.00346333 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12971.1 | −1.07217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21608.4 | 1.77598 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4514.53 | 0.368953 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5328.02 | 0.432987 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7672.71 | 0.620038 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 132.869 | 0.0106774 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1796.78 | −0.143586 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18621.0 | −1.47981 | −0.739905 | − | 0.672711i | \(-0.765130\pi\) | ||||
−0.739905 | + | 0.672711i | \(0.765130\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 63.9431 | 0.00505352 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9277.52 | −0.729184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19421.9 | −1.51814 | −0.759069 | − | 0.651010i | \(-0.774346\pi\) | ||||
−0.759069 | + | 0.651010i | \(0.774346\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20345.9 | −1.58168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2744.91 | −0.212227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6190.25 | 0.476015 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −31.1284 | −0.00238077 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2156.17 | 0.164021 | 0.0820105 | − | 0.996631i | \(-0.473866\pi\) | ||||
0.0820105 | + | 0.996631i | \(0.473866\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1395.98 | −0.105623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4866 | −0.00109024 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16030.3 | −1.20000 | −0.599998 | − | 0.800001i | \(-0.704832\pi\) | ||||
−0.599998 | + | 0.800001i | \(0.704832\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6570.95 | −0.489278 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6843.97 | −0.506913 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2928.95 | 0.215796 | 0.107898 | − | 0.994162i | \(-0.465588\pi\) | ||||
0.107898 | + | 0.994162i | \(0.465588\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3742.27 | −0.274272 | −0.137136 | − | 0.990552i | \(-0.543790\pi\) | ||||
−0.137136 | + | 0.990552i | \(0.543790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −115.798 | −0.00844246 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17176.5 | −1.24576 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8924.35 | −0.643892 | −0.321946 | − | 0.946758i | \(-0.604337\pi\) | ||||
−0.321946 | + | 0.946758i | \(0.604337\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −179.423 | −0.0128784 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13497.3 | −0.963792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.4579 | 0.000813957 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1749.68 | −0.123659 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −310.349 | −0.0218219 | −0.0109110 | − | 0.999940i | \(-0.503473\pi\) | ||||
−0.0109110 | + | 0.999940i | \(0.503473\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28367.3 | 1.98447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −173.040 | −0.0120439 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27310.8 | 1.89127 | 0.945634 | − | 0.325233i | \(-0.105443\pi\) | ||||
0.945634 | + | 0.325233i | \(0.105443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2282.43 | 0.157262 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 191.876 | 0.0131541 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3123.84 | −0.213083 | −0.106542 | − | 0.994308i | \(-0.533978\pi\) | ||||
−0.106542 | + | 0.994308i | \(0.533978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3130.50 | 0.212472 | 0.106236 | − | 0.994341i | \(-0.466120\pi\) | ||||
0.106236 | + | 0.994341i | \(0.466120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13389.2 | 0.904232 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7195.51 | 0.483535 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9839.02 | 0.657914 | 0.328957 | − | 0.944345i | \(-0.393303\pi\) | ||||
0.328957 | + | 0.944345i | \(0.393303\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.9270 | 0.000860142 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1330.38 | 0.0880876 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1326.74 | −0.0874172 | −0.0437086 | − | 0.999044i | \(-0.513917\pi\) | ||||
−0.0437086 | + | 0.999044i | \(0.513917\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −123.077 | −0.00806983 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18555.3 | −1.21071 | −0.605357 | − | 0.795954i | \(-0.706970\pi\) | ||||
−0.605357 | + | 0.795954i | \(0.706970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8583.21 | 0.557332 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 471.069 | 0.0304402 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1607.56 | −0.103380 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4792.89 | 0.306745 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.6814 | 0.00201792 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5053.85 | −0.320366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13298.9 | −0.839017 | −0.419508 | − | 0.907751i | \(-0.637798\pi\) | ||||
−0.419508 | + | 0.907751i | \(0.637798\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 211.436 | 0.0132762 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14165.2 | −0.885241 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2940.66 | 0.182910 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10661.2 | −0.660018 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25074.9 | −1.54508 | −0.772542 | − | 0.634964i | \(-0.781015\pi\) | ||||
−0.772542 | + | 0.634964i | \(0.781015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2108.13 | 0.129295 | 0.0646475 | − | 0.997908i | \(-0.479408\pi\) | ||||
0.0646475 | + | 0.997908i | \(0.479408\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.2470 | 0.00196857 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19874.2 | 1.20763 | 0.603813 | − | 0.797126i | \(-0.293647\pi\) | ||||
0.603813 | + | 0.797126i | \(0.293647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1179.10 | −0.0713154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −133.593 | −0.00804292 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22531.8 | 1.35029 | 0.675143 | − | 0.737687i | \(-0.264082\pi\) | ||||
0.675143 | + | 0.737687i | \(0.264082\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15265.9 | −0.910669 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −963.918 | −0.0572390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26356.5 | 1.55797 | 0.778984 | − | 0.627043i | \(-0.215735\pi\) | ||||
0.778984 | + | 0.627043i | \(0.215735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22193.4 | −1.30593 | −0.652966 | − | 0.757387i | \(-0.726476\pi\) | ||||
−0.652966 | + | 0.757387i | \(0.726476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.7091 | 0.00138882 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4991.57 | −0.291075 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5329.64 | 0.309392 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40.0448 | −0.00231423 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5313.90 | 0.305724 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1255.70 | −0.0719223 | −0.0359611 | − | 0.999353i | \(-0.511449\pi\) | ||||
−0.0359611 | + | 0.999353i | \(0.511449\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −239.563 | −0.0136604 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5002.40 | 0.283985 | 0.141992 | − | 0.989868i | \(-0.454649\pi\) | ||||
0.141992 | + | 0.989868i | \(0.454649\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7043.78 | 0.398108 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.10768 | 0.000343681 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2701.21 | −0.151331 | −0.0756653 | − | 0.997133i | \(-0.524108\pi\) | ||||
−0.0756653 | + | 0.997133i | \(0.524108\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1530.43 | 0.0853645 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −89.0301 | −0.00494426 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.7523 | −0.00103687 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11622.9 | 0.639879 | 0.319939 | − | 0.947438i | \(-0.396337\pi\) | ||||
0.319939 | + | 0.947438i | \(0.396337\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1787.65 | 0.0979900 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13219.7 | 0.721515 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19982.1 | −1.08591 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.7521 | 0.00188046 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 222.521 | 0.0119893 | 0.00599465 | − | 0.999982i | \(-0.498092\pi\) | ||||
0.00599465 | + | 0.999982i | \(0.498092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11052.5 | 0.592964 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30.7318 | −0.00164174 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14907.8 | −0.793019 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4632.13 | −0.245364 | −0.122682 | − | 0.992446i | \(-0.539150\pi\) | ||||
−0.122682 | + | 0.992446i | \(0.539150\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17797.0 | 0.938733 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −55079.1 | −2.89303 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 456.980 | 0.0239022 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 184.758 | 0.00962333 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29009.9 | 1.50471 | 0.752356 | − | 0.658757i | \(-0.228917\pi\) | ||||
0.752356 | + | 0.658757i | \(0.228917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7180.81 | 0.370912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −185.027 | −0.00951762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2710.40 | −0.138844 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19106.3 | −0.974708 | −0.487354 | − | 0.873204i | \(-0.662038\pi\) | ||||
−0.487354 | + | 0.873204i | \(0.662038\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19673.1 | −0.999499 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5235.46 | 0.264898 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5209.20 | 0.262492 | 0.131246 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131246 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −67.9292 | −0.00340899 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3496.98 | −0.174780 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −318.081 | −0.0158333 | −0.00791664 | − | 0.999969i | \(-0.502520\pi\) | ||||
−0.00791664 | + | 0.999969i | \(0.502520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −51.8507 | −0.00257056 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23407.1 | −1.15575 | −0.577876 | − | 0.816124i | \(-0.696118\pi\) | ||||
−0.577876 | + | 0.816124i | \(0.696118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13697.1 | −0.673588 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −38804.8 | −1.90066 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12829.8 | 0.625891 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6268.91 | −0.304601 | −0.152301 | − | 0.988334i | \(-0.548668\pi\) | ||||
−0.152301 | + | 0.988334i | \(0.548668\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 272.779 | 0.0132014 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14879.2 | 0.717231 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31403.2 | −1.50775 | −0.753877 | − | 0.657016i | \(-0.771818\pi\) | ||||
−0.753877 | + | 0.657016i | \(0.771818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −61.5140 | −0.00294179 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31552.8 | −1.50301 | −0.751504 | − | 0.659729i | \(-0.770671\pi\) | ||||
−0.751504 | + | 0.659729i | \(0.770671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15513.3 | −0.736067 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6562.00 | 0.310130 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1929.75 | 0.0908463 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3893.63 | −0.182585 | −0.0912924 | − | 0.995824i | \(-0.529100\pi\) | ||||
−0.0912924 | + | 0.995824i | \(0.529100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −236.541 | −0.0110490 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11899.3 | −0.553673 | −0.276837 | − | 0.960917i | \(-0.589286\pi\) | ||||
−0.276837 | + | 0.960917i | \(0.589286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28010.6 | 1.29828 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −52.0510 | −0.00240324 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43700.0 | 2.00990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2784.48 | 0.127576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 74.3332 | 0.00339266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8447.18 | −0.384067 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17713.4 | 0.802308 | 0.401154 | − | 0.916011i | \(-0.368609\pi\) | ||||
0.401154 | + | 0.916011i | \(0.368609\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.1643 | 0.00113545 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10987.5 | −0.493896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8696.88 | −0.389452 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.433177 | 1.93248e−5 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28725.3 | 1.27667 | 0.638333 | − | 0.769761i | \(-0.279624\pi\) | ||||
0.638333 | + | 0.769761i | \(0.279624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4989.46 | −0.220919 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4621.74 | −0.203872 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 251.755 | 0.0110638 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9691.85 | 0.424339 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 104.676 | 0.00456602 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34175.7 | −1.48524 | −0.742618 | − | 0.669716i | \(-0.766416\pi\) | ||||
−0.742618 | + | 0.669716i | \(0.766416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24008.9 | 1.03954 | 0.519770 | − | 0.854306i | \(-0.326018\pi\) | ||||
0.519770 | + | 0.854306i | \(0.326018\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.4097 | 0.000664752 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11322.1 | −0.486621 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11449.7 | −0.490299 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2925.71 | −0.124826 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25997.4 | −1.10513 | −0.552567 | − | 0.833468i | \(-0.686352\pi\) | ||||
−0.552567 | + | 0.833468i | \(0.686352\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1210.94 | −0.0512889 | −0.0256444 | − | 0.999671i | \(-0.508164\pi\) | ||||
−0.0256444 | + | 0.999671i | \(0.508164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 31.2830 | 0.00132016 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36601.6 | −1.53901 | −0.769506 | − | 0.638639i | \(-0.779498\pi\) | ||||
−0.769506 | + | 0.638639i | \(0.779498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32943.6 | −1.38019 | −0.690096 | − | 0.723718i | \(-0.742432\pi\) | ||||
−0.690096 | + | 0.723718i | \(0.742432\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −407.822 | −0.0170243 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11028.6 | −0.458727 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19923.3 | −0.825718 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −768.195 | −0.0317237 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16403.5 | −0.674986 | −0.337493 | − | 0.941328i | \(-0.609579\pi\) | ||||
−0.337493 | + | 0.941328i | \(0.609579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −245.736 | −0.0100399 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11590.2 | 0.471851 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12031.9 | 0.488099 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −395.498 | −0.0159876 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21460.1 | −0.864443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4307.51 | −0.172903 | −0.0864515 | − | 0.996256i | \(-0.527553\pi\) | ||||
−0.0864515 | + | 0.996256i | \(0.527553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14350.8 | −0.574019 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32132.7 | −1.28079 | −0.640393 | − | 0.768048i | \(-0.721228\pi\) | ||||
−0.640393 | + | 0.768048i | \(0.721228\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14761.1 | 0.586313 | 0.293157 | − | 0.956064i | \(-0.405294\pi\) | ||||
0.293157 | + | 0.956064i | \(0.405294\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −205.802 | −0.00814600 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7303.62 | −0.288086 | −0.144043 | − | 0.989571i | \(-0.546010\pi\) | ||||
−0.144043 | + | 0.989571i | \(0.546010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10761.8 | −0.423020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 144.296 | 0.00565231 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4648.19 | −0.181449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5723.26 | 0.222647 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20250.9 | 0.785096 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11520.8 | −0.445113 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4634.99 | 0.178464 | 0.0892318 | − | 0.996011i | \(-0.471559\pi\) | ||||
0.0892318 | + | 0.996011i | \(0.471559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 243.851 | 0.00935710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37912.2 | −1.44982 | −0.724911 | − | 0.688842i | \(-0.758119\pi\) | ||||
−0.724911 | + | 0.688842i | \(0.758119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15949.9 | −0.607877 | −0.303939 | − | 0.952692i | \(-0.598302\pi\) | ||||
−0.303939 | + | 0.952692i | \(0.598302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −44.5771 | −0.00169316 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2511.51 | 0.0950712 | 0.0475356 | − | 0.998870i | \(-0.484863\pi\) | ||||
0.0475356 | + | 0.998870i | \(0.484863\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23686.1 | −0.893597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5139.06 | 0.193227 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10911.7 | 0.408898 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15719.3 | 0.587082 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 100.676 | 0.00374744 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8691.30 | −0.322437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 70.3284 | 0.00260042 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 53.9214 | 0.00198715 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7564.87 | 0.277862 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17661.5 | −0.646570 | −0.323285 | − | 0.946302i | \(-0.604787\pi\) | ||||
−0.323285 | + | 0.946302i | \(0.604787\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42859.9 | −1.56389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14133.2 | 0.514002 | 0.257001 | − | 0.966411i | \(-0.417266\pi\) | ||||
0.257001 | + | 0.966411i | \(0.417266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10135.0 | 0.367381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 200.898 | 0.00725844 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25526.7 | −0.919265 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52721.7 | 1.89241 | 0.946207 | − | 0.323561i | \(-0.104880\pi\) | ||||
0.946207 | + | 0.323561i | \(0.104880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −386.563 | −0.0138303 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4557.17 | −0.162515 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10913.5 | 0.387930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20644.8 | 0.731462 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12210.5 | −0.431232 | −0.215616 | − | 0.976478i | \(-0.569176\pi\) | ||||
−0.215616 | + | 0.976478i | \(0.569176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24119.1 | 0.849057 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 195.004 | 0.00684259 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1713.85 | −0.0599454 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31399.0 | 1.09473 | 0.547365 | − | 0.836894i | \(-0.315631\pi\) | ||||
0.547365 | + | 0.836894i | \(0.315631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −170.558 | −0.00592752 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1297.72 | 0.0449568 | 0.0224784 | − | 0.999747i | \(-0.492844\pi\) | ||||
0.0224784 | + | 0.999747i | \(0.492844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −84849.8 | −2.93010 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 135.173 | 0.00465311 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37731.8 | 1.29474 | 0.647370 | − | 0.762176i | \(-0.275869\pi\) | ||||
0.647370 | + | 0.762176i | \(0.275869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −412.029 | −0.0140938 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.9021 | 0.00132649 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1230.12 | 0.0418126 | 0.0209063 | − | 0.999781i | \(-0.493345\pi\) | ||||
0.0209063 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13699.6 | −0.464199 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.70670 | −0.000327872 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2559.09 | 0.0861703 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60029.2 | 2.01501 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36885.8 | 1.23430 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21226.9 | −0.708103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45125.5 | −1.50066 | −0.750329 | − | 0.661064i | \(-0.770105\pi\) | ||||
−0.750329 | + | 0.661064i | \(0.770105\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 194.460 | 0.00644682 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17836.7 | −0.589502 | −0.294751 | − | 0.955574i | \(-0.595237\pi\) | ||||
−0.294751 | + | 0.955574i | \(0.595237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22105.2 | 0.728326 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −51.1987 | −0.00168171 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28809.1 | −0.943384 | −0.471692 | − | 0.881763i | \(-0.656357\pi\) | ||||
−0.471692 | + | 0.881763i | \(0.656357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1207.10 | 0.0394066 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44600.8 | −1.45157 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47625.6 | −1.54529 | −0.772646 | − | 0.634837i | \(-0.781067\pi\) | ||||
−0.772646 | + | 0.634837i | \(0.781067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20471.8 | −0.662218 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −51.3878 | −0.00165724 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22231.2 | 0.714774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24042.4 | 0.770670 | 0.385335 | − | 0.922777i | \(-0.374086\pi\) | ||||
0.385335 | + | 0.922777i | \(0.374086\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.2154 | −0.00125324 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22700.2 | 0.723260 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24316.1 | 0.772415 | 0.386208 | − | 0.922412i | \(-0.373785\pi\) | ||||
0.386208 | + | 0.922412i | \(0.373785\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −299.306 | −0.00947910 |
(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 | 1856.4.a.bi.1.5 | 10 | ||
4.3 | odd | 2 | inner | 1856.4.a.bi.1.6 | 10 | ||
8.3 | odd | 2 | 928.4.a.f.1.5 | ✓ | 10 | ||
8.5 | even | 2 | 928.4.a.f.1.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.f.1.5 | ✓ | 10 | 8.3 | odd | 2 | ||
928.4.a.f.1.6 | yes | 10 | 8.5 | even | 2 | ||
1856.4.a.bi.1.5 | 10 | 1.1 | even | 1 | trivial | ||
1856.4.a.bi.1.6 | 10 | 4.3 | odd | 2 | inner |