Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 105x^{3} + 92x^{2} + 1858x - 2576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 616) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-8.22418\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-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 | ||||||||
\(3\) | 8.22418 | 1.58274 | 0.791372 | − | 0.611335i | \(-0.209367\pi\) | ||||
0.791372 | + | 0.611335i | \(0.209367\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.2362 | −1.54166 | −0.770828 | − | 0.637044i | \(-0.780157\pi\) | ||||
−0.770828 | + | 0.637044i | \(0.780157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 40.6371 | 1.50508 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.9306 | 1.34260 | 0.671301 | − | 0.741185i | \(-0.265736\pi\) | ||||
0.671301 | + | 0.741185i | \(0.265736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −141.754 | −2.44005 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −80.9209 | −1.15448 | −0.577241 | − | 0.816574i | \(-0.695871\pi\) | ||||
−0.577241 | + | 0.816574i | \(0.695871\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.9110 | −0.542278 | −0.271139 | − | 0.962540i | \(-0.587400\pi\) | ||||
−0.271139 | + | 0.962540i | \(0.587400\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 57.5693 | 0.598221 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −55.0637 | −0.499199 | −0.249599 | − | 0.968349i | \(-0.580299\pi\) | ||||
−0.249599 | + | 0.968349i | \(0.580299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 172.088 | 1.37670 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 112.154 | 0.799410 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 310.218 | 1.98642 | 0.993208 | − | 0.116349i | \(-0.0371192\pi\) | ||||
0.993208 | + | 0.116349i | \(0.0371192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.80993 | 0.0452486 | 0.0226243 | − | 0.999744i | \(-0.492798\pi\) | ||||
0.0226243 | + | 0.999744i | \(0.492798\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 90.4660 | 0.477215 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −120.654 | −0.582691 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 400.886 | 1.78122 | 0.890612 | − | 0.454764i | \(-0.150276\pi\) | ||||
0.890612 | + | 0.454764i | \(0.150276\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 517.553 | 2.12499 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −470.422 | −1.79189 | −0.895946 | − | 0.444164i | \(-0.853501\pi\) | ||||
−0.895946 | + | 0.444164i | \(0.853501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 551.684 | 1.95653 | 0.978267 | − | 0.207348i | \(-0.0664831\pi\) | ||||
0.978267 | + | 0.207348i | \(0.0664831\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −700.431 | −2.32031 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −36.8998 | −0.114519 | −0.0572594 | − | 0.998359i | \(-0.518236\pi\) | ||||
−0.0572594 | + | 0.998359i | \(0.518236\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −665.508 | −1.82725 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 71.3509 | 0.184921 | 0.0924604 | − | 0.995716i | \(-0.470527\pi\) | ||||
0.0924604 | + | 0.995716i | \(0.470527\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −189.599 | −0.464827 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −369.356 | −0.858287 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 623.175 | 1.37509 | 0.687546 | − | 0.726141i | \(-0.258688\pi\) | ||||
0.687546 | + | 0.726141i | \(0.258688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 326.021 | 0.684307 | 0.342153 | − | 0.939644i | \(-0.388844\pi\) | ||||
0.342153 | + | 0.939644i | \(0.388844\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 284.460 | 0.568866 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1084.69 | −2.06983 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −617.038 | −1.12512 | −0.562561 | − | 0.826756i | \(-0.690184\pi\) | ||||
−0.562561 | + | 0.826756i | \(0.690184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −452.854 | −0.790104 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 719.391 | 1.20248 | 0.601240 | − | 0.799069i | \(-0.294674\pi\) | ||||
0.601240 | + | 0.799069i | \(0.294674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −244.700 | −0.392329 | −0.196164 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196164 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1415.28 | 2.17897 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 232.011 | 0.330422 | 0.165211 | − | 0.986258i | \(-0.447170\pi\) | ||||
0.165211 | + | 0.986258i | \(0.447170\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −174.827 | −0.239818 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1045.98 | −1.38327 | −0.691633 | − | 0.722249i | \(-0.743108\pi\) | ||||
−0.691633 | + | 0.722249i | \(0.743108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1394.77 | 1.77981 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2551.29 | 3.14399 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 927.468 | 1.10462 | 0.552311 | − | 0.833638i | \(-0.313746\pi\) | ||||
0.552311 | + | 0.833638i | \(0.313746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 440.514 | 0.507456 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 64.2303 | 0.0716169 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 774.096 | 0.836006 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1153.90 | 1.20785 | 0.603924 | − | 0.797042i | \(-0.293603\pi\) | ||||
0.603924 | + | 0.797042i | \(0.293603\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 447.008 | 0.453798 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1770.78 | −1.74455 | −0.872273 | − | 0.489019i | \(-0.837355\pi\) | ||||
−0.872273 | + | 0.489019i | \(0.837355\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 673.475 | 0.644266 | 0.322133 | − | 0.946694i | \(-0.395600\pi\) | ||||
0.322133 | + | 0.946694i | \(0.395600\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −992.277 | −0.922251 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 740.840 | 0.669343 | 0.334672 | − | 0.942335i | \(-0.391375\pi\) | ||||
0.334672 | + | 0.942335i | \(0.391375\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 973.956 | 0.855854 | 0.427927 | − | 0.903813i | \(-0.359244\pi\) | ||||
0.427927 | + | 0.903813i | \(0.359244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3296.96 | 2.81922 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1246.55 | 1.03775 | 0.518874 | − | 0.854851i | \(-0.326351\pi\) | ||||
0.518874 | + | 0.854851i | \(0.326351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 949.091 | 0.769593 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2557.32 | 2.02072 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −566.446 | −0.436353 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3868.83 | −2.83610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −811.613 | −0.580743 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2438.63 | 1.70388 | 0.851942 | − | 0.523636i | \(-0.175425\pi\) | ||||
0.851942 | + | 0.523636i | \(0.175425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4537.15 | 3.09669 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1946.49 | 1.29821 | 0.649106 | − | 0.760698i | \(-0.275143\pi\) | ||||
0.649106 | + | 0.760698i | \(0.275143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −314.377 | −0.204962 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1933.11 | −1.23241 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −124.996 | −0.0779500 | −0.0389750 | − | 0.999240i | \(-0.512409\pi\) | ||||
−0.0389750 | + | 0.999240i | \(0.512409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −567.992 | −0.346593 | −0.173297 | − | 0.984870i | \(-0.555442\pi\) | ||||
−0.173297 | + | 0.984870i | \(0.555442\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −303.470 | −0.181254 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 692.237 | 0.404809 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5346.99 | −3.06237 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 402.985 | 0.226106 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.14245 | 0.00172778 | 0.000863890 | − | 1.00000i | \(-0.499725\pi\) | ||||
0.000863890 | 1.00000i | \(0.499725\pi\) | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 506.799 | 0.273130 | 0.136565 | − | 0.990631i | \(-0.456394\pi\) | ||||
0.136565 | + | 0.990631i | \(0.456394\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3288.39 | −1.73759 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −134.614 | −0.0697577 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1390.34 | −0.706759 | −0.353379 | − | 0.935480i | \(-0.614967\pi\) | ||||
−0.353379 | + | 0.935480i | \(0.614967\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 586.803 | 0.292682 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −385.446 | −0.188679 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3101.28 | −1.49025 | −0.745126 | − | 0.666924i | \(-0.767610\pi\) | ||||
−0.745126 | + | 0.666924i | \(0.767610\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1559.29 | −0.735701 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −947.307 | −0.438951 | −0.219475 | − | 0.975618i | \(-0.570435\pi\) | ||||
−0.219475 | + | 0.975618i | \(0.570435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1763.26 | 0.802578 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1825.05 | −0.816171 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1506.99 | 0.662278 | 0.331139 | − | 0.943582i | \(-0.392567\pi\) | ||||
0.331139 | + | 0.943582i | \(0.392567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1204.61 | 0.520344 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5125.10 | 2.17642 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1007.93 | 0.420871 | 0.210436 | − | 0.977608i | \(-0.432512\pi\) | ||||
0.210436 | + | 0.977608i | \(0.432512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −542.440 | −0.222758 | −0.111379 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111379 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2681.25 | 1.08308 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6909.77 | −2.74603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −890.130 | −0.348089 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 785.078 | 0.302148 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −648.159 | −0.245545 | −0.122773 | − | 0.992435i | \(-0.539179\pi\) | ||||
−0.122773 | + | 0.992435i | \(0.539179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3158.55 | 1.17802 | 0.589009 | − | 0.808126i | \(-0.299518\pi\) | ||||
0.589009 | + | 0.808126i | \(0.299518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8920.66 | −3.27601 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2286.70 | 0.827008 | 0.413504 | − | 0.910502i | \(-0.364305\pi\) | ||||
0.413504 | + | 0.910502i | \(0.364305\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2106.32 | 0.750316 | 0.375158 | − | 0.926961i | \(-0.377588\pi\) | ||||
0.375158 | + | 0.926961i | \(0.377588\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5074.63 | −1.78078 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2171.53 | 0.750795 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8108.30 | 2.76248 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2237.63 | −0.751333 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −494.021 | −0.163503 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1304.93 | −0.425759 | −0.212880 | − | 0.977078i | \(-0.568284\pi\) | ||||
−0.212880 | + | 0.977078i | \(0.568284\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5916.40 | 1.90322 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9508.95 | −3.01630 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 54.6695 | 0.0171024 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2012.46 | −0.620956 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5092.40 | −1.55001 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4779.08 | 1.43511 | 0.717557 | − | 0.696499i | \(-0.245260\pi\) | ||||
0.717557 | + | 0.696499i | \(0.245260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6993.15 | 2.07204 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2523.58 | −0.737868 | −0.368934 | − | 0.929456i | \(-0.620277\pi\) | ||||
−0.368934 | + | 0.929456i | \(0.620277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3831.98 | −1.10578 | −0.552892 | − | 0.833253i | \(-0.686476\pi\) | ||||
−0.552892 | + | 0.833253i | \(0.686476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 633.262 | 0.180370 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1317.12 | −0.370333 | −0.185167 | − | 0.982707i | \(-0.559282\pi\) | ||||
−0.185167 | + | 0.982707i | \(0.559282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 636.013 | 0.176549 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1908.10 | 0.522973 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3152.14 | −0.853117 | −0.426559 | − | 0.904460i | \(-0.640274\pi\) | ||||
−0.426559 | + | 0.904460i | \(0.640274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3979.97 | 1.06379 | 0.531893 | − | 0.846812i | \(-0.321481\pi\) | ||||
0.531893 | + | 0.846812i | \(0.321481\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4465.97 | −1.17898 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −844.575 | −0.220236 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2826.27 | −0.728063 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8602.32 | −2.18936 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4434.79 | 1.11522 | 0.557612 | − | 0.830101i | \(-0.311718\pi\) | ||||
0.557612 | + | 0.830101i | \(0.311718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −605.701 | −0.150514 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11470.8 | 2.81699 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4581.08 | −1.11191 | −0.555953 | − | 0.831214i | \(-0.687646\pi\) | ||||
−0.555953 | + | 0.831214i | \(0.687646\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2806.20 | 0.673239 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12606.4 | 2.98971 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2208.39 | 0.517776 | 0.258888 | − | 0.965907i | \(-0.416644\pi\) | ||||
0.258888 | + | 0.965907i | \(0.416644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1229.82 | −0.285084 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7627.66 | 1.74833 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 772.816 | 0.175165 | 0.0875826 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875826 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6671.13 | −1.49536 | −0.747679 | − | 0.664060i | \(-0.768832\pi\) | ||||
−0.747679 | + | 0.664060i | \(0.768832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3622.87 | 0.803172 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1892.96 | 0.415091 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4620.41 | −1.00222 | −0.501108 | − | 0.865385i | \(-0.667074\pi\) | ||||
−0.501108 | + | 0.865385i | \(0.667074\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 317.373 | 0.0681026 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3501.89 | −0.743436 | −0.371718 | − | 0.928346i | \(-0.621231\pi\) | ||||
−0.371718 | + | 0.928346i | \(0.621231\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4388.45 | 0.921789 | 0.460895 | − | 0.887455i | \(-0.347529\pi\) | ||||
0.460895 | + | 0.887455i | \(0.347529\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6366.30 | 1.32318 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3292.95 | −0.677271 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1635.19 | 0.332829 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9489.91 | 1.91171 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 647.804 | 0.129164 | 0.0645821 | − | 0.997912i | \(-0.479429\pi\) | ||||
0.0645821 | + | 0.997912i | \(0.479429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10741.2 | −2.11992 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1233.69 | 0.241031 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3465.19 | −0.670225 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3861.79 | 0.739501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14563.2 | −2.76117 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5619.37 | −1.05497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4964.98 | 0.923017 | 0.461508 | − | 0.887136i | \(-0.347308\pi\) | ||||
0.461508 | + | 0.887136i | \(0.347308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5538.78 | 1.01971 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2882.26 | 0.525524 | 0.262762 | − | 0.964861i | \(-0.415367\pi\) | ||||
0.262762 | + | 0.964861i | \(0.415367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6569.36 | −1.18633 | −0.593167 | − | 0.805080i | \(-0.702123\pi\) | ||||
−0.593167 | + | 0.805080i | \(0.702123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4903.01 | −0.876996 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10191.8 | −1.80576 | −0.902880 | − | 0.429892i | \(-0.858552\pi\) | ||||
−0.902880 | + | 0.429892i | \(0.858552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3412.40 | 0.598927 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6092.80 | 1.05940 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3634.23 | 0.626050 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10829.6 | 1.84836 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8009.99 | 1.35460 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −258.298 | −0.0432840 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8701.15 | −1.44489 | −0.722445 | − | 0.691429i | \(-0.756982\pi\) | ||||
−0.722445 | + | 0.691429i | \(0.756982\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16290.9 | 2.68088 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10635.4 | 1.73455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8820.95 | 1.42584 | 0.712919 | − | 0.701246i | \(-0.247373\pi\) | ||||
0.712919 | + | 0.701246i | \(0.247373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10251.9 | 1.64249 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 85.9093 | 0.0136430 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7805.49 | 1.21807 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 444.321 | 0.0687389 | 0.0343694 | − | 0.999409i | \(-0.489058\pi\) | ||||
0.0343694 | + | 0.999409i | \(0.489058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3522.75 | −0.540311 | −0.270156 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270156 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7057.93 | 1.07329 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8301.61 | −1.25170 | −0.625850 | − | 0.779944i | \(-0.715248\pi\) | ||||
−0.625850 | + | 0.779944i | \(0.715248\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12399.6 | −1.85381 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4658.55 | −0.690635 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 988.600 | 0.145338 | 0.0726690 | − | 0.997356i | \(-0.476848\pi\) | ||||
0.0726690 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4842.01 | −0.705935 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 995.126 | 0.143886 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4217.71 | 0.604835 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −539.911 | −0.0767932 | −0.0383966 | − | 0.999263i | \(-0.512225\pi\) | ||||
−0.0383966 | + | 0.999263i | \(0.512225\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19116.6 | −2.69694 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 499.457 | 0.0698935 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7443.64 | −1.03329 | −0.516645 | − | 0.856200i | \(-0.672819\pi\) | ||||
−0.516645 | + | 0.856200i | \(0.672819\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6674.85 | −0.919168 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19522.2 | 2.66697 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10087.0 | 1.36711 | 0.683553 | − | 0.729901i | \(-0.260434\pi\) | ||||
0.683553 | + | 0.729901i | \(0.260434\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20055.7 | 2.69681 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7400.26 | 0.987299 | 0.493650 | − | 0.869661i | \(-0.335663\pi\) | ||||
0.493650 | + | 0.869661i | \(0.335663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1327.19 | −0.175688 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22418.8 | 2.94474 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 459.213 | 0.0598536 | 0.0299268 | − | 0.999552i | \(-0.490473\pi\) | ||||
0.0299268 | + | 0.999552i | \(0.490473\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4455.80 | 0.576316 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16008.3 | 2.05474 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3999.00 | −0.509397 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5539.55 | 0.700308 | 0.350154 | − | 0.936692i | \(-0.386129\pi\) | ||||
0.350154 | + | 0.936692i | \(0.386129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2585.49 | −0.324402 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5070.83 | −0.631485 | −0.315742 | − | 0.948845i | \(-0.602253\pi\) | ||||
−0.315742 | + | 0.948845i | \(0.602253\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 491.484 | 0.0607508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3013.36 | 0.369716 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4409.75 | 0.537059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10086.7 | −1.21944 | −0.609722 | − | 0.792615i | \(-0.708719\pi\) | ||||
−0.609722 | + | 0.792615i | \(0.708719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1027.99 | −0.123375 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4362.22 | 0.519736 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18028.7 | 2.13252 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4671.27 | −0.548568 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14633.3 | −1.70616 | −0.853081 | − | 0.521779i | \(-0.825269\pi\) | ||||
−0.853081 | + | 0.521779i | \(0.825269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11472.5 | −1.32811 | −0.664054 | − | 0.747685i | \(-0.731165\pi\) | ||||
−0.664054 | + | 0.747685i | \(0.731165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1499.50 | −0.172360 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13925.5 | −1.58938 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2282.15 | 0.258644 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5693.08 | 0.640710 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9873.29 | 1.10343 | 0.551717 | − | 0.834032i | \(-0.313973\pi\) | ||||
0.551717 | + | 0.834032i | \(0.313973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9246.94 | 1.02628 | 0.513140 | − | 0.858305i | \(-0.328482\pi\) | ||||
0.513140 | + | 0.858305i | \(0.328482\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −43974.6 | −4.84695 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2472.96 | 0.270705 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2826.08 | −0.307247 | −0.153624 | − | 0.988129i | \(-0.549094\pi\) | ||||
−0.153624 | + | 0.988129i | \(0.549094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1991.22 | 0.215011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18182.2 | −1.95003 | −0.975014 | − | 0.222142i | \(-0.928695\pi\) | ||||
−0.975014 | + | 0.222142i | \(0.928695\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15986.0 | −1.70295 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.8440 | 0.00273463 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1091.57 | −0.114731 | −0.0573656 | − | 0.998353i | \(-0.518270\pi\) | ||||
−0.0573656 | + | 0.998353i | \(0.518270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5174.64 | −0.540275 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4168.00 | 0.432295 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7592.81 | −0.782321 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7689.22 | −0.787060 | −0.393530 | − | 0.919312i | \(-0.628746\pi\) | ||||
−0.393530 | + | 0.919312i | \(0.628746\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9075.60 | −0.922904 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8159.13 | −0.824313 | −0.412157 | − | 0.911113i | \(-0.635224\pi\) | ||||
−0.412157 | + | 0.911113i | \(0.635224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8483.01 | −0.851488 | −0.425744 | − | 0.904844i | \(-0.639988\pi\) | ||||
−0.425744 | + | 0.904844i | \(0.639988\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1107.09 | −0.110409 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1373.10 | −0.136058 | −0.0680292 | − | 0.997683i | \(-0.521671\pi\) | ||||
−0.0680292 | + | 0.997683i | \(0.521671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4319.27 | −0.425256 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11434.4 | −1.11862 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6068.52 | 0.589917 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7728.62 | −0.746555 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2899.50 | 0.278320 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4492.84 | −0.428566 | −0.214283 | − | 0.976772i | \(-0.568741\pi\) | ||||
−0.214283 | + | 0.976772i | \(0.568741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25228.0 | 2.39147 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3169.98 | −0.298631 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19889.0 | −1.86208 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5602.38 | −0.521290 | −0.260645 | − | 0.965435i | \(-0.583935\pi\) | ||||
−0.260645 | + | 0.965435i | \(0.583935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25505.5 | −2.35869 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10278.7 | 0.944747 | 0.472374 | − | 0.881398i | \(-0.343397\pi\) | ||||
0.472374 | + | 0.881398i | \(0.343397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25103.1 | −2.29328 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7704.74 | −0.699600 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5035.74 | 0.454495 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16802.7 | 1.50740 | 0.753698 | − | 0.657221i | \(-0.228268\pi\) | ||||
0.753698 | + | 0.657221i | \(0.228268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7790.82 | −0.694747 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2510.54 | 0.222543 | 0.111272 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111272 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30521.6 | 2.68949 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14501.4 | 1.27027 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13608.8 | −1.18507 | −0.592533 | − | 0.805546i | \(-0.701872\pi\) | ||||
−0.592533 | + | 0.805546i | \(0.701872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1712.90 | −0.148286 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5036.95 | −0.433502 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11608.2 | −0.993237 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −405.897 | −0.0345287 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12393.7 | 1.04822 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 212.794 | 0.0178938 | 0.00894689 | − | 0.999960i | \(-0.497152\pi\) | ||||
0.00894689 | + | 0.999960i | \(0.497152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −180.086 | −0.0150566 | −0.00752831 | − | 0.999972i | \(-0.502396\pi\) | ||||
−0.00752831 | + | 0.999972i | \(0.502396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9906.96 | 0.823571 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −631.987 | −0.0522387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9134.99 | −0.750800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25324.0 | 2.06962 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29603.9 | −2.40579 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12769.3 | −1.03190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8289.37 | 0.666131 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −913.428 | −0.0725903 | −0.0362951 | − | 0.999341i | \(-0.511556\pi\) | ||||
−0.0362951 | + | 0.999341i | \(0.511556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4461.13 | −0.352570 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16787.3 | −1.31943 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4777.46 | −0.373436 | −0.186718 | − | 0.982414i | \(-0.559785\pi\) | ||||
−0.186718 | + | 0.982414i | \(0.559785\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13248.6 | 1.02994 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13932.2 | −1.07719 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1624.08 | 0.124888 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −56827.2 | −4.34627 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22543.7 | −1.71492 | −0.857458 | − | 0.514553i | \(-0.827958\pi\) | ||||
−0.857458 | + | 0.514553i | \(0.827958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34717.8 | 2.62685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7320.58 | −0.550936 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4815.28 | −0.360462 | −0.180231 | − | 0.983624i | \(-0.557685\pi\) | ||||
−0.180231 | + | 0.983624i | \(0.557685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21485.8 | −1.59985 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1223.79 | −0.0906425 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11312.7 | −0.833482 | −0.416741 | − | 0.909025i | \(-0.636828\pi\) | ||||
−0.416741 | + | 0.909025i | \(0.636828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 709.967 | 0.0520336 | 0.0260168 | − | 0.999662i | \(-0.491718\pi\) | ||||
0.0260168 | + | 0.999662i | \(0.491718\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5330.58 | −0.388635 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9475.78 | −0.687248 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22452.0 | 1.61991 | 0.809956 | − | 0.586490i | \(-0.199491\pi\) | ||||
0.809956 | + | 0.586490i | \(0.199491\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25976.5 | 1.86450 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7321.85 | −0.522825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 784.860 | 0.0557557 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −44078.5 | −3.11525 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6232.49 | 0.438233 | 0.219116 | − | 0.975699i | \(-0.429683\pi\) | ||||
0.219116 | + | 0.975699i | \(0.429683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −350.752 | −0.0245373 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18806.2 | 1.30894 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2650.46 | 0.183544 | 0.0917718 | − | 0.995780i | \(-0.470747\pi\) | ||||
0.0917718 | + | 0.995780i | \(0.470747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9763.40 | 0.672706 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17322.7 | 1.18756 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19416.6 | 1.32444 | 0.662220 | − | 0.749310i | \(-0.269615\pi\) | ||||
0.662220 | + | 0.749310i | \(0.269615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28676.0 | −1.94628 | −0.973142 | − | 0.230204i | \(-0.926061\pi\) | ||||
−0.973142 | + | 0.230204i | \(0.926061\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25074.6 | −1.69340 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2085.58 | −0.140150 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5980.13 | 0.399878 | 0.199939 | − | 0.979808i | \(-0.435926\pi\) | ||||
0.199939 | + | 0.979808i | \(0.435926\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17859.0 | 1.18832 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2322.13 | −0.153753 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24033.0 | −1.58350 | −0.791750 | − | 0.610845i | \(-0.790830\pi\) | ||||
−0.791750 | + | 0.610845i | \(0.790830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 66684.1 | 4.37230 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2485.18 | 0.162155 | 0.0810776 | − | 0.996708i | \(-0.474164\pi\) | ||||
0.0810776 | + | 0.996708i | \(0.474164\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21047.6 | 1.36668 | 0.683339 | − | 0.730101i | \(-0.260527\pi\) | ||||
0.683339 | + | 0.730101i | \(0.260527\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6175.62 | −0.399064 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6492.27 | 0.417508 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7521.80 | −0.481395 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4062.91 | −0.258783 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32440.1 | −2.05639 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3086.63 | −0.194733 | −0.0973667 | − | 0.995249i | \(-0.531042\pi\) | ||||
−0.0973667 | + | 0.995249i | \(0.531042\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10732.0 | −0.673868 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42032.8 | −2.62680 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3083.60 | 0.191800 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29234.0 | 1.80983 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1120.56 | 0.0690475 | 0.0345238 | − | 0.999404i | \(-0.489009\pi\) | ||||
0.0345238 | + | 0.999404i | \(0.489009\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5004.81 | −0.306952 | −0.153476 | − | 0.988152i | \(-0.549047\pi\) | ||||
−0.153476 | + | 0.988152i | \(0.549047\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −78203.3 | −4.77403 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14422.2 | −0.876348 | −0.438174 | − | 0.898890i | \(-0.644375\pi\) | ||||
−0.438174 | + | 0.898890i | \(0.644375\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6854.92 | 0.414606 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 449.612 | 0.0270686 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1456.18 | −0.0872660 | −0.0436330 | − | 0.999048i | \(-0.513893\pi\) | ||||
−0.0436330 | + | 0.999048i | \(0.513893\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33550.2 | −2.00140 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9943.91 | −0.590485 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30655.2 | 1.81207 | 0.906037 | − | 0.423198i | \(-0.139092\pi\) | ||||
0.906037 | + | 0.423198i | \(0.139092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15079.2 | 0.887311 | 0.443656 | − | 0.896197i | \(-0.353681\pi\) | ||||
0.443656 | + | 0.896197i | \(0.353681\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −41880.8 | −2.45327 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5418.67 | 0.315980 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17081.8 | −0.991617 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39304.0 | 2.27142 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3586.23 | 0.206326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1713.08 | 0.0981197 | 0.0490599 | − | 0.998796i | \(-0.484377\pi\) | ||||
0.0490599 | + | 0.998796i | \(0.484377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19300.3 | 1.10055 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26093.5 | 1.48132 | 0.740661 | − | 0.671879i | \(-0.234513\pi\) | ||||
0.740661 | + | 0.671879i | \(0.234513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8077.33 | 0.456523 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20754.4 | −1.16786 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5309.57 | −0.297460 | −0.148730 | − | 0.988878i | \(-0.547518\pi\) | ||||
−0.148730 | + | 0.988878i | \(0.547518\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2154.46 | 0.120172 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31514.9 | −1.75017 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4490.16 | 0.248275 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −658.594 | −0.0362577 | −0.0181289 | − | 0.999836i | \(-0.505771\pi\) | ||||
−0.0181289 | + | 0.999836i | \(0.505771\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3129.06 | 0.171520 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9790.04 | 0.534327 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38066.9 | 2.06871 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10832.3 | −0.586142 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29457.6 | 1.58716 | 0.793580 | − | 0.608466i | \(-0.208215\pi\) | ||||
0.793580 | + | 0.608466i | \(0.208215\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18004.2 | −0.965919 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5230.68 | 0.279431 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12395.5 | −0.659377 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6831.93 | 0.361888 | 0.180944 | − | 0.983493i | \(-0.442085\pi\) | ||||
0.180944 | + | 0.983493i | \(0.442085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9428.28 | 0.497311 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −430.044 | −0.0225880 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11931.6 | −0.624077 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25923.8 | −1.35027 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21721.3 | −1.12666 | −0.563330 | − | 0.826232i | \(-0.690480\pi\) | ||||
−0.563330 | + | 0.826232i | \(0.690480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4714.32 | 0.243510 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32732.0 | 1.68370 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 53384.7 | 2.73470 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19491.9 | −0.994382 | −0.497191 | − | 0.867641i | \(-0.665635\pi\) | ||||
−0.497191 | + | 0.867641i | \(0.665635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32008.6 | −1.62620 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44642.7 | −2.25878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14205.8 | 0.715829 | 0.357915 | − | 0.933754i | \(-0.383488\pi\) | ||||
0.357915 | + | 0.933754i | \(0.383488\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6945.94 | −0.348578 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6787.42 | −0.339237 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12836.5 | 0.638970 | 0.319485 | − | 0.947591i | \(-0.396490\pi\) | ||||
0.319485 | + | 0.947591i | \(0.396490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23243.8 | −1.15234 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19694.2 | 0.972421 | 0.486211 | − | 0.873842i | \(-0.338379\pi\) | ||||
0.486211 | + | 0.873842i | \(0.338379\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −54.1639 | −0.00266364 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −42505.6 | −2.08192 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5185.88 | 0.252988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11383.4 | −0.553111 | −0.276555 | − | 0.960998i | \(-0.589193\pi\) | ||||
−0.276555 | + | 0.960998i | \(0.589193\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36472.5 | 1.76512 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8735.30 | −0.421073 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16665.7 | −0.800165 | −0.400083 | − | 0.916479i | \(-0.631019\pi\) | ||||
−0.400083 | + | 0.916479i | \(0.631019\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4981.39 | −0.238225 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3634.33 | 0.173120 | 0.0865600 | − | 0.996247i | \(-0.472413\pi\) | ||||
0.0865600 | + | 0.996247i | \(0.472413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6817.69 | 0.323482 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56679.5 | 2.67876 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39216.8 | 1.84620 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18467.7 | 0.866012 | 0.433006 | − | 0.901391i | \(-0.357453\pi\) | ||||
0.433006 | + | 0.901391i | \(0.357453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37675.6 | −1.75986 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2076.66 | −0.0966265 | −0.0483133 | − | 0.998832i | \(-0.515385\pi\) | ||||
−0.0483133 | + | 0.998832i | \(0.515385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1343.99 | 0.0622938 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23078.7 | 1.06557 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21127.1 | 0.971703 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7913.31 | 0.362561 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34792.2 | 1.58796 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23964.2 | 1.08958 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 424.318 | 0.0192189 | 0.00960947 | − | 0.999954i | \(-0.496941\pi\) | ||||
0.00960947 | + | 0.999954i | \(0.496941\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18162.2 | 0.819506 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8725.85 | 0.392232 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20516.7 | 0.918751 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10114.3 | −0.451215 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7198.00 | −0.319907 | −0.159954 | − | 0.987125i | \(-0.551134\pi\) | ||||
−0.159954 | + | 0.987125i | \(0.551134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2985.96 | 0.132210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37689.6 | 1.66254 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2691.70 | −0.118292 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6643.63 | 0.290879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6355.78 | 0.277242 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39155.0 | −1.70163 | −0.850813 | − | 0.525469i | \(-0.823890\pi\) | ||||
−0.850813 | + | 0.525469i | \(0.823890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2976.22 | 0.128865 | 0.0644323 | − | 0.997922i | \(-0.479476\pi\) | ||||
0.0644323 | + | 0.997922i | \(0.479476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54864.6 | −2.36677 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53454.4 | 2.29745 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24776.7 | −1.06099 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17901.2 | 0.763760 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35168.0 | 1.49497 | 0.747485 | − | 0.664279i | \(-0.231261\pi\) | ||||
0.747485 | + | 0.664279i | \(0.231261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24599.8 | −1.04192 | −0.520958 | − | 0.853583i | \(-0.674425\pi\) | ||||
−0.520958 | + | 0.853583i | \(0.674425\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15568.1 | 0.656983 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41171.7 | 1.73117 | 0.865586 | − | 0.500760i | \(-0.166946\pi\) | ||||
0.865586 | + | 0.500760i | \(0.166946\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31895.5 | 1.33628 | 0.668141 | − | 0.744035i | \(-0.267090\pi\) | ||||
0.668141 | + | 0.744035i | \(0.267090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37999.1 | −1.58625 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3965.12 | −0.164926 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16328.0 | 0.676711 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 875.916 | 0.0361721 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1010.79 | 0.0415927 | 0.0207964 | − | 0.999784i | \(-0.493380\pi\) | ||||
0.0207964 | + | 0.999784i | \(0.493380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71846.4 | 2.94585 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28800.2 | −1.17667 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30392.0 | −1.23730 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36091.4 | 1.45896 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22074.3 | −0.889185 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25953.4 | 1.04177 | 0.520883 | − | 0.853628i | \(-0.325603\pi\) | ||||
0.520883 | + | 0.853628i | \(0.325603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31457.0 | 1.25825 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30216.2 | 1.20439 | 0.602197 | − | 0.798348i | \(-0.294292\pi\) | ||||
0.602197 | + | 0.798348i | \(0.294292\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 847.560 | 0.0336652 | 0.0168326 | − | 0.999858i | \(-0.494642\pi\) | ||||
0.0168326 | + | 0.999858i | \(0.494642\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27081.8 | −1.07195 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48862.9 | 1.92736 | 0.963680 | − | 0.267060i | \(-0.0860522\pi\) | ||||
0.963680 | + | 0.267060i | \(0.0860522\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25974.8 | −1.02100 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13448.1 | 0.526783 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2552.13 | 0.0996259 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38830.6 | −1.51059 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46891.3 | 1.81790 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5681.29 | −0.219500 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14942.0 | 0.575321 | 0.287660 | − | 0.957733i | \(-0.407123\pi\) | ||||
0.287660 | + | 0.957733i | \(0.407123\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5327.66 | 0.204434 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40955.4 | 1.56620 | 0.783101 | − | 0.621895i | \(-0.213637\pi\) | ||||
0.783101 | + | 0.621895i | \(0.213637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31473.5 | −1.19951 | −0.599755 | − | 0.800184i | \(-0.704735\pi\) | ||||
−0.599755 | + | 0.800184i | \(0.704735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −88337.4 | −3.35529 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29023.6 | 1.09867 | 0.549333 | − | 0.835604i | \(-0.314882\pi\) | ||||
0.549333 | + | 0.835604i | \(0.314882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17070.4 | 0.644008 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1923.10 | −0.0723077 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1657.20 | 0.0621010 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17372.9 | −0.648838 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28498.4 | −1.06079 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2422.78 | 0.0898825 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5773.78 | −0.213488 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31760.0 | 1.17044 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9349.63 | 0.343417 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33337.4 | −1.22045 | −0.610226 | − | 0.792227i | \(-0.708921\pi\) | ||||
−0.610226 | + | 0.792227i | \(0.708921\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −71959.4 | −2.62568 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5676.54 | 0.206446 | 0.103223 | − | 0.994658i | \(-0.467085\pi\) | ||||
0.103223 | + | 0.994658i | \(0.467085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11505.8 | −0.417070 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46214.7 | −1.66974 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13625.5 | 0.490678 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28155.7 | 1.01063 | 0.505316 | − | 0.862934i | \(-0.331376\pi\) | ||||
0.505316 | + | 0.862934i | \(0.331376\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40832.8 | 1.46090 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45271.7 | 1.61445 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 68987.6 | 2.45221 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27368.1 | 0.969671 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30763.7 | −1.08646 | −0.543232 | − | 0.839583i | \(-0.682800\pi\) | ||||
−0.543232 | + | 0.839583i | \(0.682800\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2200.64 | −0.0774683 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23704.2 | 0.831771 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15342.5 | 0.536634 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16888.6 | 0.588824 | 0.294412 | − | 0.955679i | \(-0.404876\pi\) | ||||
0.294412 | + | 0.955679i | \(0.404876\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54027.6 | −1.87766 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42479.9 | −1.47163 | −0.735816 | − | 0.677181i | \(-0.763201\pi\) | ||||
−0.735816 | + | 0.677181i | \(0.763201\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25903.2 | 0.894510 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13531.8 | −0.465809 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47593.1 | −1.63312 | −0.816561 | − | 0.577259i | \(-0.804122\pi\) | ||||
−0.816561 | + | 0.577259i | \(0.804122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15399.1 | −0.526741 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −83818.8 | −2.85806 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31801.0 | 1.08094 | 0.540469 | − | 0.841364i | \(-0.318247\pi\) | ||||
0.540469 | + | 0.841364i | \(0.318247\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11171.8 | 0.378546 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28064.2 | 0.947948 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −874.974 | −0.0294623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29730.0 | −0.997953 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30105.6 | 1.00741 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54441.5 | −1.81610 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45625.3 | −1.51728 | −0.758641 | − | 0.651509i | \(-0.774136\pi\) | ||||
−0.758641 | + | 0.651509i | \(0.774136\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29888.6 | 0.990877 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32698.0 | 1.08067 | 0.540333 | − | 0.841451i | \(-0.318298\pi\) | ||||
0.540333 | + | 0.841451i | \(0.318298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3975.94 | −0.131000 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 89064.4 | 2.92548 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43812.9 | −1.43470 | −0.717349 | − | 0.696714i | \(-0.754645\pi\) | ||||
−0.717349 | + | 0.696714i | \(0.754645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10202.1 | 0.333056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39578.8 | 1.28813 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37190.0 | −1.20669 | −0.603345 | − | 0.797480i | \(-0.706166\pi\) | ||||
−0.603345 | + | 0.797480i | \(0.706166\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39414.1 | −1.27496 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2124.29 | −0.0685076 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30377.7 | −0.976700 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40750.3 | 1.30623 | 0.653115 | − | 0.757258i | \(-0.273462\pi\) | ||||
0.653115 | + | 0.757258i | \(0.273462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −71559.8 | −2.28689 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36305.0 | −1.15673 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22567.1 | 0.716859 | 0.358429 | − | 0.933557i | \(-0.383312\pi\) | ||||
0.358429 | + | 0.933557i | \(0.383312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44961.0 | 1.42393 |
(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 | 1232.4.a.z.1.5 | 5 | ||
4.3 | odd | 2 | 616.4.a.g.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.4.a.g.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
1232.4.a.z.1.5 | 5 | 1.1 | even | 1 | trivial |