Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 3.11094 | 1.79610 | 0.898052 | − | 0.439889i | \(-0.144982\pi\) | ||||
0.898052 | + | 0.439889i | \(0.144982\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.12050 | 1.39553 | 0.697764 | − | 0.716327i | \(-0.254178\pi\) | ||||
0.697764 | + | 0.716327i | \(0.254178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.63406 | −0.617618 | −0.308809 | − | 0.951124i | \(-0.599930\pi\) | ||||
−0.308809 | + | 0.951124i | \(0.599930\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.67797 | 2.22599 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.72167 | −0.519103 | −0.259552 | − | 0.965729i | \(-0.583575\pi\) | ||||
−0.259552 | + | 0.965729i | \(0.583575\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82183 | −0.505286 | −0.252643 | − | 0.967560i | \(-0.581300\pi\) | ||||
−0.252643 | + | 0.967560i | \(0.581300\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.70769 | 2.50652 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.18677 | 0.960510 | 0.480255 | − | 0.877129i | \(-0.340544\pi\) | ||||
0.480255 | + | 0.877129i | \(0.340544\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.08348 | −1.10931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.92515 | 1.23548 | 0.617740 | − | 0.786383i | \(-0.288049\pi\) | ||||
0.617740 | + | 0.786383i | \(0.288049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.73750 | 0.947501 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.4420 | 2.20200 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.256534 | −0.0476371 | −0.0238186 | − | 0.999716i | \(-0.507582\pi\) | ||||
−0.0238186 | + | 0.999716i | \(0.507582\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.752999 | 0.135243 | 0.0676213 | − | 0.997711i | \(-0.478459\pi\) | ||||
0.0676213 | + | 0.997711i | \(0.478459\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.35602 | −0.932364 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.09909 | −0.861904 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.71509 | 0.446359 | 0.223179 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223179 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.66762 | −0.907545 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.61114 | 0.251617 | 0.125809 | − | 0.992055i | \(-0.459847\pi\) | ||||
0.125809 | + | 0.992055i | \(0.459847\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.84523 | 0.281395 | 0.140698 | − | 0.990053i | \(-0.455066\pi\) | ||||
0.140698 | + | 0.990053i | \(0.455066\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 20.8386 | 3.10643 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3816 | −1.66017 | −0.830086 | − | 0.557636i | \(-0.811709\pi\) | ||||
−0.830086 | + | 0.557636i | \(0.811709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.32984 | −0.618548 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.11094 | 0.435619 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.07848 | 1.10966 | 0.554832 | − | 0.831962i | \(-0.312783\pi\) | ||||
0.554832 | + | 0.831962i | \(0.312783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.37247 | −0.724424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.0248 | 1.72518 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.80471 | −0.871254 | −0.435627 | − | 0.900127i | \(-0.643473\pi\) | ||||
−0.435627 | + | 0.900127i | \(0.643473\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.9122 | −1.37481 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.68503 | −0.705141 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.90642 | 0.599414 | 0.299707 | − | 0.954031i | \(-0.403111\pi\) | ||||
0.299707 | + | 0.954031i | \(0.403111\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.4328 | 2.21905 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.75393 | −0.445509 | −0.222755 | − | 0.974875i | \(-0.571505\pi\) | ||||
−0.222755 | + | 0.974875i | \(0.571505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.68741 | −1.01678 | −0.508392 | − | 0.861126i | \(-0.669760\pi\) | ||||
−0.508392 | + | 0.861126i | \(0.669760\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.7381 | 1.70181 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.81332 | 0.320608 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.18758 | 0.358631 | 0.179316 | − | 0.983792i | \(-0.442612\pi\) | ||||
0.179316 | + | 0.983792i | \(0.442612\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.5614 | 1.72904 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.57902 | 0.173320 | 0.0866598 | − | 0.996238i | \(-0.472381\pi\) | ||||
0.0866598 | + | 0.996238i | \(0.472381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.12050 | 0.338465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.798062 | −0.0855612 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.7968 | 1.46246 | 0.731229 | − | 0.682132i | \(-0.238947\pi\) | ||||
0.731229 | + | 0.682132i | \(0.238947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.97699 | 0.312073 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.34254 | 0.242910 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.0648 | 1.34042 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.66388 | −0.575080 | −0.287540 | − | 0.957769i | \(-0.592837\pi\) | ||||
−0.287540 | + | 0.957769i | \(0.592837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.4973 | −1.15552 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.1341 | −1.70491 | −0.852455 | − | 0.522800i | \(-0.824887\pi\) | ||||
−0.852455 | + | 0.522800i | \(0.824887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6944 | 1.25082 | 0.625410 | − | 0.780296i | \(-0.284932\pi\) | ||||
0.625410 | + | 0.780296i | \(0.284932\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.8630 | −1.54807 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.43318 | 0.235224 | 0.117612 | − | 0.993060i | \(-0.462476\pi\) | ||||
0.117612 | + | 0.993060i | \(0.462476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.17238 | 0.591207 | 0.295603 | − | 0.955311i | \(-0.404479\pi\) | ||||
0.295603 | + | 0.955311i | \(0.404479\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.44650 | 0.801706 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.42743 | −0.604642 | −0.302321 | − | 0.953206i | \(-0.597761\pi\) | ||||
−0.302321 | + | 0.953206i | \(0.597761\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.4894 | 1.72415 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.1661 | −1.12476 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.63406 | −0.149794 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.03585 | −0.730532 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.01216 | 0.451931 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.819116 | −0.0732640 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.15271 | 0.191022 | 0.0955109 | − | 0.995428i | \(-0.469552\pi\) | ||||
0.0955109 | + | 0.995428i | \(0.469552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.74041 | 0.505415 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.40733 | 0.472440 | 0.236220 | − | 0.971700i | \(-0.424091\pi\) | ||||
0.236220 | + | 0.971700i | \(0.424091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.84144 | −0.593228 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 35.7046 | 3.07296 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.15530 | 0.611319 | 0.305659 | − | 0.952141i | \(-0.401123\pi\) | ||||
0.305659 | + | 0.952141i | \(0.401123\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8663 | 0.921666 | 0.460833 | − | 0.887487i | \(-0.347551\pi\) | ||||
0.460833 | + | 0.887487i | \(0.347551\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −35.4074 | −2.98184 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.13660 | 0.262296 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.800513 | −0.0664790 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.4699 | −1.11098 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.3498 | 1.17559 | 0.587793 | − | 0.809012i | \(-0.299997\pi\) | ||||
0.587793 | + | 0.809012i | \(0.299997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.14548 | −0.255975 | −0.127988 | − | 0.991776i | \(-0.540852\pi\) | ||||
−0.127988 | + | 0.991776i | \(0.540852\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.67797 | 0.539882 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.34973 | 0.188735 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.9883 | −1.59524 | −0.797620 | − | 0.603160i | \(-0.793908\pi\) | ||||
−0.797620 | + | 0.603160i | \(0.793908\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.1317 | 1.99307 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.68207 | −0.763054 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.44363 | 0.426378 | 0.213189 | − | 0.977011i | \(-0.431615\pi\) | ||||
0.213189 | + | 0.977011i | \(0.431615\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.7135 | −1.30114 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.4586 | −0.809307 | −0.404654 | − | 0.914470i | \(-0.632608\pi\) | ||||
−0.404654 | + | 0.914470i | \(0.632608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.68092 | −0.744686 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.9591 | 2.13809 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.2274 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.74138 | −0.585194 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.11094 | 0.233833 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7205 | −0.950778 | −0.475389 | − | 0.879776i | \(-0.657693\pi\) | ||||
−0.475389 | + | 0.879776i | \(0.657693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3344 | 0.768146 | 0.384073 | − | 0.923303i | \(-0.374521\pi\) | ||||
0.384073 | + | 0.923303i | \(0.374521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.1691 | −1.56486 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.47244 | 0.622906 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.72167 | −0.125901 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.6969 | −1.36000 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.5875 | −1.85145 | −0.925723 | − | 0.378203i | \(-0.876542\pi\) | ||||
−0.925723 | + | 0.378203i | \(0.876542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.35915 | 0.673686 | 0.336843 | − | 0.941561i | \(-0.390641\pi\) | ||||
0.336843 | + | 0.941561i | \(0.390641\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.6858 | −1.26651 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.9219 | −1.27688 | −0.638442 | − | 0.769670i | \(-0.720421\pi\) | ||||
−0.638442 | + | 0.769670i | \(0.720421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.06705 | 0.0756413 | 0.0378207 | − | 0.999285i | \(-0.487958\pi\) | ||||
0.0378207 | + | 0.999285i | \(0.487958\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.2636 | 1.07661 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.419192 | 0.0294215 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.02755 | 0.351139 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 39.5680 | 2.75016 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.20824 | −0.498604 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.79572 | 0.674365 | 0.337183 | − | 0.941439i | \(-0.390526\pi\) | ||||
0.337183 | + | 0.941439i | \(0.390526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.6783 | −0.800181 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.75804 | 0.392695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.23045 | −0.0835283 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.0260 | −1.82625 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.82183 | −0.122550 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.4168 | 1.56811 | 0.784054 | − | 0.620693i | \(-0.213148\pi\) | ||||
0.784054 | + | 0.620693i | \(0.213148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 31.6369 | 2.10913 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.58755 | −0.105369 | −0.0526847 | − | 0.998611i | \(-0.516778\pi\) | ||||
−0.0526847 | + | 0.998611i | \(0.516778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.80626 | −0.251525 | −0.125762 | − | 0.992060i | \(-0.540138\pi\) | ||||
−0.125762 | + | 0.992060i | \(0.540138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.75208 | 0.575845 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.0179299 | −0.00117463 | −0.000587313 | − | 1.00000i | \(-0.500187\pi\) | ||||
−0.000587313 | 1.00000i | \(0.500187\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.5161 | −2.31682 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.91639 | 0.644139 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.9482 | 0.902233 | 0.451116 | − | 0.892465i | \(-0.351026\pi\) | ||||
0.451116 | + | 0.892465i | \(0.351026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.02119 | 0.194612 | 0.0973059 | − | 0.995255i | \(-0.468977\pi\) | ||||
0.0973059 | + | 0.995255i | \(0.468977\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.0846 | 0.903530 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.5112 | −0.863202 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.62759 | −0.485332 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.91223 | 0.311300 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.4504 | 1.60642 | 0.803209 | − | 0.595697i | \(-0.203124\pi\) | ||||
0.803209 | + | 0.595697i | \(0.203124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2012 | −0.641342 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.70769 | 0.607919 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.91368 | −0.119372 | −0.0596861 | − | 0.998217i | \(-0.519010\pi\) | ||||
−0.0596861 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.43663 | −0.275679 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.71312 | −0.106040 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.0806 | −1.42321 | −0.711606 | − | 0.702579i | \(-0.752032\pi\) | ||||
−0.711606 | + | 0.702579i | \(0.752032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.2089 | 1.54857 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 42.9211 | 2.62673 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.22239 | −0.501328 | −0.250664 | − | 0.968074i | \(-0.580649\pi\) | ||||
−0.250664 | + | 0.968074i | \(0.580649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.743034 | 0.0451361 | 0.0225680 | − | 0.999745i | \(-0.492816\pi\) | ||||
0.0225680 | + | 0.999745i | \(0.492816\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.26125 | 0.560516 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.15643 | −0.491851 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.4683 | −0.869315 | −0.434658 | − | 0.900596i | \(-0.643131\pi\) | ||||
−0.434658 | + | 0.900596i | \(0.643131\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.02850 | 0.301049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7950 | −1.12121 | −0.560607 | − | 0.828082i | \(-0.689432\pi\) | ||||
−0.560607 | + | 0.828082i | \(0.689432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0143 | −1.66528 | −0.832638 | − | 0.553817i | \(-0.813171\pi\) | ||||
−0.832638 | + | 0.553817i | \(0.813171\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40.6438 | 2.40753 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.63270 | −0.155403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.6200 | −1.03290 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.7345 | −0.802375 | −0.401188 | − | 0.915996i | \(-0.631403\pi\) | ||||
−0.401188 | + | 0.915996i | \(0.631403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.12050 | 0.181682 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.6993 | −1.14307 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.7946 | −0.624270 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.01522 | −0.173795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −53.3033 | −3.06220 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.2341 | −1.21586 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.0064 | −1.08475 | −0.542377 | − | 0.840135i | \(-0.682476\pi\) | ||||
−0.542377 | + | 0.840135i | \(0.682476\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.4917 | 2.24660 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.2402 | −1.43124 | −0.715622 | − | 0.698488i | \(-0.753856\pi\) | ||||
−0.715622 | + | 0.698488i | \(0.753856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4914 | 0.932149 | 0.466075 | − | 0.884745i | \(-0.345668\pi\) | ||||
0.466075 | + | 0.884745i | \(0.345668\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34.0516 | −1.91859 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.57805 | 0.0886320 | 0.0443160 | − | 0.999018i | \(-0.485889\pi\) | ||||
0.0443160 | + | 0.999018i | \(0.485889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.441667 | 0.0247286 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.56947 | 0.422487 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.18677 | 0.232958 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.63094 | −0.478759 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.2019 | 1.06187 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.5982 | 1.02535 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.75710 | −0.316439 | −0.158219 | − | 0.987404i | \(-0.550575\pi\) | ||||
−0.158219 | + | 0.987404i | \(0.550575\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.1313 | 0.993589 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.3105 | 0.836500 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.6952 | 0.909443 | 0.454722 | − | 0.890634i | \(-0.349739\pi\) | ||||
0.454722 | + | 0.890634i | \(0.349739\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.9954 | −1.08600 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.29642 | −0.0702049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5137 | 0.999644 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 57.5195 | 3.09675 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.01346 | −0.161771 | −0.0808854 | − | 0.996723i | \(-0.525775\pi\) | ||||
−0.0808854 | + | 0.996723i | \(0.525775\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.2406 | −1.13698 | −0.568490 | − | 0.822690i | \(-0.692472\pi\) | ||||
−0.568490 | + | 0.822690i | \(0.692472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.8453 | −1.11264 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.5532 | −0.881036 | −0.440518 | − | 0.897744i | \(-0.645205\pi\) | ||||
−0.440518 | + | 0.897744i | \(0.645205\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7141 | −0.621721 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.08348 | −0.269046 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.6883 | −1.03911 | −0.519554 | − | 0.854438i | \(-0.673902\pi\) | ||||
−0.519554 | + | 0.854438i | \(0.673902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.47098 | −0.0774198 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.9991 | −1.31211 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.1090 | −1.41895 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.82074 | −0.356040 | −0.178020 | − | 0.984027i | \(-0.556969\pi\) | ||||
−0.178020 | + | 0.984027i | \(0.556969\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7591 | 0.560098 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.2007 | −0.685348 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.9808 | −1.39701 | −0.698507 | − | 0.715603i | \(-0.746152\pi\) | ||||
−0.698507 | + | 0.715603i | \(0.746152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.54822 | −0.131590 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.467362 | 0.0240703 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3871 | 1.35542 | 0.677708 | − | 0.735331i | \(-0.262973\pi\) | ||||
0.677708 | + | 0.735331i | \(0.262973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.69695 | 0.343095 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.8194 | 0.859431 | 0.429715 | − | 0.902964i | \(-0.358614\pi\) | ||||
0.429715 | + | 0.902964i | \(0.358614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.77896 | 0.447417 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.3224 | 0.626382 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.2679 | 1.53464 | 0.767321 | − | 0.641263i | \(-0.221589\pi\) | ||||
0.767321 | + | 0.641263i | \(0.221589\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.92515 | 0.299648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.8219 | 0.848552 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.94685 | 0.500480 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.85519 | 0.494618 | 0.247309 | − | 0.968937i | \(-0.420454\pi\) | ||||
0.247309 | + | 0.968937i | \(0.420454\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.2833 | −1.06550 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.5047 | −1.12383 | −0.561916 | − | 0.827195i | \(-0.689935\pi\) | ||||
−0.561916 | + | 0.827195i | \(0.689935\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.37184 | −0.0683362 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 48.5592 | 2.41292 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.67450 | −0.231706 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.30743 | 0.410776 | 0.205388 | − | 0.978681i | \(-0.434154\pi\) | ||||
0.205388 | + | 0.978681i | \(0.434154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.2597 | 1.09799 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.63406 | −0.0804070 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.92732 | 0.241872 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.8044 | 1.65541 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4729 | −0.658194 | −0.329097 | − | 0.944296i | \(-0.606744\pi\) | ||||
−0.329097 | + | 0.944296i | \(0.606744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.2479 | −0.743137 | −0.371568 | − | 0.928406i | \(-0.621180\pi\) | ||||
−0.371568 | + | 0.928406i | \(0.621180\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −76.0057 | −3.69552 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.73750 | 0.229803 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1193 | 0.538102 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.75778 | 0.471110 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.19281 | −0.0574555 | −0.0287278 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287278 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.1948 | −0.826331 | −0.413165 | − | 0.910656i | \(-0.635577\pi\) | ||||
−0.413165 | + | 0.910656i | \(0.635577\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.49035 | −0.119403 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.8072 | 1.18669 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.9248 | −0.521413 | −0.260707 | − | 0.965418i | \(-0.583956\pi\) | ||||
−0.260707 | + | 0.965418i | \(0.583956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28.9145 | −1.37688 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7355 | 0.652594 | 0.326297 | − | 0.945267i | \(-0.394199\pi\) | ||||
0.326297 | + | 0.945267i | \(0.394199\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43.0529 | 2.04090 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 44.6416 | 2.11147 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3865 | 0.537362 | 0.268681 | − | 0.963229i | \(-0.413412\pi\) | ||||
0.268681 | + | 0.963229i | \(0.413412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.77385 | −0.130615 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.78540 | −0.459758 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.28969 | 0.435508 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3461 | −0.811414 | −0.405707 | − | 0.914003i | \(-0.632975\pi\) | ||||
−0.405707 | + | 0.914003i | \(0.632975\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.4420 | 0.534065 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.38993 | −0.204460 | −0.102230 | − | 0.994761i | \(-0.532598\pi\) | ||||
−0.102230 | + | 0.994761i | \(0.532598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.45258 | 0.253403 | 0.126702 | − | 0.991941i | \(-0.459561\pi\) | ||||
0.126702 | + | 0.991941i | \(0.459561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.30988 | 0.338988 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5268 | 0.857317 | 0.428658 | − | 0.903467i | \(-0.358986\pi\) | ||||
0.428658 | + | 0.903467i | \(0.358986\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.01740 | −0.370209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −62.1825 | −2.86522 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.17688 | −0.146073 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.8348 | 0.910084 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 53.9478 | 2.47010 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.41160 | 0.110189 | 0.0550945 | − | 0.998481i | \(-0.482454\pi\) | ||||
0.0550945 | + | 0.998481i | \(0.482454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.94645 | −0.225539 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.1204 | −1.37052 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.6741 | −0.802541 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.1865 | 1.77571 | 0.887856 | − | 0.460122i | \(-0.152194\pi\) | ||||
0.887856 | + | 0.460122i | \(0.152194\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.9348 | 0.765819 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.6693 | 1.38408 | 0.692042 | − | 0.721857i | \(-0.256711\pi\) | ||||
0.692042 | + | 0.721857i | \(0.256711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.256534 | −0.0115537 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −35.8772 | −1.61256 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.13415 | 0.275154 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.0417 | −0.941956 | −0.470978 | − | 0.882145i | \(-0.656099\pi\) | ||||
−0.470978 | + | 0.882145i | \(0.656099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.5360 | −1.45360 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0890 | −0.717374 | −0.358687 | − | 0.933458i | \(-0.616775\pi\) | ||||
−0.358687 | + | 0.933458i | \(0.616775\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.4670 | −2.37925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.1168 | −1.33753 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.7446 | 0.963814 | 0.481907 | − | 0.876222i | \(-0.339944\pi\) | ||||
0.481907 | + | 0.876222i | \(0.339944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.1958 | 0.627984 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 47.9048 | 2.11505 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.6130 | 1.74556 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5953 | 0.861801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −47.3717 | −2.07938 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.2214 | 0.973536 | 0.486768 | − | 0.873531i | \(-0.338176\pi\) | ||||
0.486768 | + | 0.873531i | \(0.338176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.66928 | 0.0729927 | 0.0364963 | − | 0.999334i | \(-0.488380\pi\) | ||||
0.0364963 | + | 0.999334i | \(0.488380\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.0830 | −1.05107 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.752999 | 0.0328012 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.1074 | 0.526410 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.67797 | 0.289799 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.93522 | −0.127139 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.59272 | 0.328262 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −39.5729 | −1.70770 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.45456 | 0.321090 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.7624 | −0.677679 | −0.338839 | − | 0.940844i | \(-0.610034\pi\) | ||||
−0.338839 | + | 0.940844i | \(0.610034\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.1496 | 1.37967 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.2609 | 0.825046 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.54160 | 0.279699 | 0.139849 | − | 0.990173i | \(-0.455338\pi\) | ||||
0.139849 | + | 0.990173i | \(0.455338\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −45.4416 | −1.93940 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.07405 | −0.0457559 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.20871 | −0.221497 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.3573 | 1.11880 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.6464 | 1.12904 | 0.564522 | − | 0.825418i | \(-0.309061\pi\) | ||||
0.564522 | + | 0.825418i | \(0.309061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.36170 | −0.142185 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.35602 | −0.226131 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.1636 | 0.639070 | 0.319535 | − | 0.947574i | \(-0.396473\pi\) | ||||
0.319535 | + | 0.947574i | \(0.396473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0568 | −0.843795 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −25.4282 | −1.06789 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.1517 | −0.509427 | −0.254714 | − | 0.967017i | \(-0.581981\pi\) | ||||
−0.254714 | + | 0.967017i | \(0.581981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.1753 | −0.928006 | −0.464003 | − | 0.885834i | \(-0.653587\pi\) | ||||
−0.464003 | + | 0.885834i | \(0.653587\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −79.6012 | −3.32539 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0704 | 1.17062 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.5200 | −1.02078 | −0.510391 | − | 0.859942i | \(-0.670499\pi\) | ||||
−0.510391 | + | 0.859942i | \(0.670499\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.1158 | 1.21001 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.58021 | −0.107045 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9085 | −0.576030 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −37.9644 | −1.56964 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.7090 | 0.524558 | 0.262279 | − | 0.964992i | \(-0.415526\pi\) | ||||
0.262279 | + | 0.964992i | \(0.415526\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.15263 | 0.129902 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −55.7541 | −2.29342 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.68997 | 0.274724 | 0.137362 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137362 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.09909 | −0.209042 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.31954 | 0.135860 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.3707 | −1.40435 | −0.702175 | − | 0.712004i | \(-0.747788\pi\) | ||||
−0.702175 | + | 0.712004i | \(0.747788\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2340 | 1.23327 | 0.616635 | − | 0.787249i | \(-0.288496\pi\) | ||||
0.616635 | + | 0.787249i | \(0.288496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.7649 | 1.33429 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.0758 | −1.01948 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7544 | −0.923571 | −0.461785 | − | 0.886992i | \(-0.652791\pi\) | ||||
−0.461785 | + | 0.886992i | \(0.652791\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.30408 | 0.0528441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7353 | 0.838861 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.83408 | 0.0740779 | 0.0370389 | − | 0.999314i | \(-0.488207\pi\) | ||||
0.0370389 | + | 0.999314i | \(0.488207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.6404 | 0.630683 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.2013 | 0.974306 | 0.487153 | − | 0.873317i | \(-0.338035\pi\) | ||||
0.487153 | + | 0.873317i | \(0.338035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.7256 | 1.67709 | 0.838546 | − | 0.544831i | \(-0.183406\pi\) | ||||
0.838546 | + | 0.544831i | \(0.183406\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 67.7953 | 2.72053 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.5449 | −0.903240 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.2436 | −1.04974 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.4244 | −0.895545 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.71509 | 0.108258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.8422 | −1.18800 | −0.593999 | − | 0.804466i | \(-0.702452\pi\) | ||||
−0.593999 | + | 0.804466i | \(0.702452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.4739 | 1.21123 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.71751 | 0.266576 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.88824 | 0.312543 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.0686 | −0.991699 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.39563 | 0.173617 | 0.0868084 | − | 0.996225i | \(-0.472333\pi\) | ||||
0.0868084 | + | 0.996225i | \(0.472333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.5052 | 1.04526 | 0.522631 | − | 0.852559i | \(-0.324950\pi\) | ||||
0.522631 | + | 0.852559i | \(0.324950\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.9129 | 0.705321 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.2232 | 1.26682 | 0.633412 | − | 0.773814i | \(-0.281654\pi\) | ||||
0.633412 | + | 0.773814i | \(0.281654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.72167 | −0.0675815 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.82785 | −0.150025 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2258 | −0.517564 | −0.258782 | − | 0.965936i | \(-0.583321\pi\) | ||||
−0.258782 | + | 0.965936i | \(0.583321\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.8735 | 0.659304 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −58.0143 | −2.26335 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.7479 | −1.74313 | −0.871564 | − | 0.490281i | \(-0.836894\pi\) | ||||
−0.871564 | + | 0.490281i | \(0.836894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2194 | 0.630861 | 0.315430 | − | 0.948949i | \(-0.397851\pi\) | ||||
0.315430 | + | 0.948949i | \(0.397851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.66762 | −0.220112 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.3487 | −0.827867 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.52000 | −0.0588547 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 72.8485 | 2.81649 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.7155 | 0.452271 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4518 | −1.09674 | −0.548369 | − | 0.836237i | \(-0.684751\pi\) | ||||
−0.548369 | + | 0.836237i | \(0.684751\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 54.2063 | 2.08640 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.14609 | 0.0824808 | 0.0412404 | − | 0.999149i | \(-0.486869\pi\) | ||||
0.0412404 | + | 0.999149i | \(0.486869\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.25514 | 0.355180 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.93878 | −0.189254 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.8845 | 1.14350 | 0.571749 | − | 0.820428i | \(-0.306265\pi\) | ||||
0.571749 | + | 0.820428i | \(0.306265\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.3281 | 0.853113 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8410 | −0.451764 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.7176 | −0.560697 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.57599 | 0.174079 | 0.0870394 | − | 0.996205i | \(-0.472259\pi\) | ||||
0.0870394 | + | 0.996205i | \(0.472259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.7873 | 0.713669 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.9082 | 1.28621 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.61114 | 0.0610262 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0557788 | −0.00210975 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0624 | 0.644438 | 0.322219 | − | 0.946665i | \(-0.395571\pi\) | ||||
0.322219 | + | 0.946665i | \(0.395571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3675 | 0.428732 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −110.489 | −4.16124 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.9983 | 1.05298 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.879464 | 0.0330290 | 0.0165145 | − | 0.999864i | \(-0.494743\pi\) | ||||
0.0165145 | + | 0.999864i | \(0.494743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.2866 | 0.798309 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.46163 | 0.167090 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.78775 | 0.366041 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.3920 | 1.62050 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.2871 | −0.383644 | −0.191822 | − | 0.981430i | \(-0.561440\pi\) | ||||
−0.191822 | + | 0.981430i | \(0.561440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.7435 | −0.772529 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.39874 | 0.349543 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.21533 | −0.0451362 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.3441 | 1.83007 | 0.915036 | − | 0.403373i | \(-0.132162\pi\) | ||||
0.915036 | + | 0.403373i | \(0.132162\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.86754 | −0.106205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.84523 | 0.0682483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.3806 | 1.08520 | 0.542598 | − | 0.839993i | \(-0.317441\pi\) | ||||
0.542598 | + | 0.839993i | \(0.317441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −42.0327 | −1.55040 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.44724 | −0.311158 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.2950 | 1.15120 | 0.575602 | − | 0.817730i | \(-0.304768\pi\) | ||||
0.575602 | + | 0.817730i | \(0.304768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.7290 | −0.871707 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.6344 | −1.45405 | −0.727023 | − | 0.686613i | \(-0.759097\pi\) | ||||
−0.727023 | + | 0.686613i | \(0.759097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.7787 | 1.64056 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.5446 | 0.385808 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.97596 | −0.145279 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.03957 | −0.256878 | −0.128439 | − | 0.991717i | \(-0.540997\pi\) | ||||
−0.128439 | + | 0.991717i | \(0.540997\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 79.1749 | 2.88529 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.81545 | −0.357221 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.4060 | 0.414558 | 0.207279 | − | 0.978282i | \(-0.433539\pi\) | ||||
0.207279 | + | 0.978282i | \(0.433539\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.7352 | −1.15192 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.5123 | 1.50482 | 0.752409 | − | 0.658696i | \(-0.228892\pi\) | ||||
0.752409 | + | 0.658696i | \(0.228892\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0861 | −0.365140 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.8386 | 0.753421 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.82183 | −0.0657826 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.74890 | 0.243372 | 0.121686 | − | 0.992569i | \(-0.461170\pi\) | ||||
0.121686 | + | 0.992569i | \(0.461170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.95336 | −0.214405 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.9701 | 0.574404 | 0.287202 | − | 0.957870i | \(-0.407275\pi\) | ||||
0.287202 | + | 0.957870i | \(0.407275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.56734 | 0.128143 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.8021 | −0.495148 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.74546 | 0.241681 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.46303 | 0.231265 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.93525 | −0.104897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.3735 | −2.22620 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.60301 | −0.342310 | −0.171155 | − | 0.985244i | \(-0.554750\pi\) | ||||
−0.171155 | + | 0.985244i | \(0.554750\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −71.8025 | −2.55624 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.5028 | 0.373438 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3970 | 0.440232 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 78.4233 | 2.78139 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.8184 | 1.65839 | 0.829197 | − | 0.558956i | \(-0.188798\pi\) | ||||
0.829197 | + | 0.558956i | \(0.188798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.3816 | −0.402651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 92.1346 | 3.25542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.9569 | 0.527816 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.2129 | −1.06486 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.5794 | −0.900437 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.0221 | −1.30163 | −0.650814 | − | 0.759237i | \(-0.725572\pi\) | ||||
−0.650814 | + | 0.759237i | \(0.725572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.88874 | −0.312126 | −0.156063 | − | 0.987747i | \(-0.549880\pi\) | ||||
−0.156063 | + | 0.987747i | \(0.549880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.31154 | 0.0810691 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.9868 | 0.595023 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.72555 | 0.270283 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.8803 | 0.694672 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.4325 | −1.72521 | −0.862603 | − | 0.505881i | \(-0.831168\pi\) | ||||
−0.862603 | + | 0.505881i | \(0.831168\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.70614 | −0.303477 | −0.151738 | − | 0.988421i | \(-0.548487\pi\) | ||||
−0.151738 | + | 0.988421i | \(0.548487\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.3742 | −0.883416 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.8666 | 0.969018 | 0.484509 | − | 0.874786i | \(-0.338998\pi\) | ||||
0.484509 | + | 0.874786i | \(0.338998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.13383 | 0.213037 | 0.106518 | − | 0.994311i | \(-0.466030\pi\) | ||||
0.106518 | + | 0.994311i | \(0.466030\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.0100 | −1.56138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.32984 | −0.150020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.6359 | −1.12941 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.61578 | 0.297805 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.0553 | 1.69358 | 0.846789 | − | 0.531930i | \(-0.178533\pi\) | ||||
0.846789 | + | 0.531930i | \(0.178533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9342 | −0.997731 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −58.4701 | −2.01382 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.2093 | −1.03923 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.1311 | 0.451189 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −87.1509 | −2.99101 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0873 | 0.551467 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.2840 | −1.58473 | −0.792367 | − | 0.610044i | \(-0.791152\pi\) | ||||
−0.792367 | + | 0.610044i | \(0.791152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 87.2463 | 2.98376 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.25611 | −0.316183 | −0.158091 | − | 0.987424i | \(-0.550534\pi\) | ||||
−0.158091 | + | 0.987424i | \(0.550534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2033 | 0.348130 | 0.174065 | − | 0.984734i | \(-0.444310\pi\) | ||||
0.174065 | + | 0.984734i | \(0.444310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.19018 | −0.279121 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.27365 | −0.0773960 | −0.0386980 | − | 0.999251i | \(-0.512321\pi\) | ||||
−0.0386980 | + | 0.999251i | \(0.512321\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.5171 | −1.61563 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.11094 | 0.105653 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.48797 | −0.186167 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.93867 | −0.302875 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.8232 | −1.28012 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.33849 | 0.0452491 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.7172 | −0.834641 | −0.417320 | − | 0.908759i | \(-0.637031\pi\) | ||||
−0.417320 | + | 0.908759i | \(0.637031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42.7271 | −1.44115 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.6557 | 1.36972 | 0.684862 | − | 0.728673i | \(-0.259862\pi\) | ||||
0.684862 | + | 0.728673i | \(0.259862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.59522 | 0.289252 | 0.144626 | − | 0.989486i | \(-0.453802\pi\) | ||||
0.144626 | + | 0.989486i | \(0.453802\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.70769 | 0.326320 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.7662 | −0.831566 | −0.415783 | − | 0.909464i | \(-0.636493\pi\) | ||||
−0.415783 | + | 0.909464i | \(0.636493\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.51766 | −0.117978 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.7915 | −0.897550 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −47.6520 | −1.59461 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.6944 | −1.32684 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.5815 | −1.12125 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.193170 | −0.00644257 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.07848 | 0.269133 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.38019 | −0.312153 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.2483 | 1.07197 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0365 | 0.499279 | 0.249640 | − | 0.968339i | \(-0.419688\pi\) | ||||
0.249640 | + | 0.968339i | \(0.419688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −114.421 | −3.79511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.0833 | 0.831046 | 0.415523 | − | 0.909583i | \(-0.363599\pi\) | ||||
0.415523 | + | 0.909583i | \(0.363599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.71855 | −0.0899708 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −66.0580 | −2.18381 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.83591 | −0.291788 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.0181 | −0.693322 | −0.346661 | − | 0.937991i | \(-0.612685\pi\) | ||||
−0.346661 | + | 0.937991i | \(0.612685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −59.1279 | −1.94833 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.83903 | 0.225109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.8628 | 0.422925 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 84.7730 | 2.78431 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.39790 | −0.275526 | −0.137763 | − | 0.990465i | \(-0.543991\pi\) | ||||
−0.137763 | + | 0.990465i | \(0.543991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.1280 | −0.594122 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −78.5210 | −2.57066 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.37247 | −0.175699 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.9004 | −1.14015 | −0.570073 | − | 0.821594i | \(-0.693085\pi\) | ||||
−0.570073 | + | 0.821594i | \(0.693085\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 51.3038 | 1.67424 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.2151 | −1.31097 | −0.655487 | − | 0.755206i | \(-0.727537\pi\) | ||||
−0.655487 | + | 0.755206i | \(0.727537\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.54623 | 0.310868 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −58.3435 | −1.89792 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.15888 | 0.135145 | 0.0675727 | − | 0.997714i | \(-0.478475\pi\) | ||||
0.0675727 | + | 0.997714i | \(0.478475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.8270 | 0.513767 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.90922 | 0.159192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.8759 | 1.51846 | 0.759229 | − | 0.650823i | \(-0.225576\pi\) | ||||
0.759229 | + | 0.650823i | \(0.225576\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −79.8457 | −2.58375 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.37400 | 0.0444151 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6922 | −0.377561 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4330 | −0.981709 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.2487 | 0.523606 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.2052 | 0.940149 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.0541 | 1.22374 | 0.611869 | − | 0.790959i | \(-0.290418\pi\) | ||||
0.611869 | + | 0.790959i | \(0.290418\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.0248 | 0.418417 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8137 | −0.860493 | −0.430246 | − | 0.902711i | \(-0.641573\pi\) | ||||
−0.430246 | + | 0.902711i | \(0.641573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.7562 | −0.569238 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.8504 | −0.859900 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.4495 | 0.686229 | 0.343114 | − | 0.939294i | \(-0.388518\pi\) | ||||
0.343114 | + | 0.939294i | \(0.388518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.7536 | −0.759167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.2190 | 1.31602 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.5036 | 0.558279 | 0.279139 | − | 0.960251i | \(-0.409951\pi\) | ||||
0.279139 | + | 0.960251i | \(0.409951\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −55.9253 | −1.78193 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 57.8579 | 1.84164 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.9333 | 0.347658 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.55287 | −0.0810946 | −0.0405473 | − | 0.999178i | \(-0.512910\pi\) | ||||
−0.0405473 | + | 0.999178i | \(0.512910\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.9100 | −0.568357 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.32973 | 0.105560 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.7604 | −1.57593 | −0.787964 | − | 0.615722i | \(-0.788864\pi\) | ||||
−0.787964 | + | 0.615722i | \(0.788864\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.0660 | 0.982884 |
(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 | 4012.2.a.j.1.19 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.j.1.19 | ✓ | 21 | 1.1 | even | 1 | trivial |