Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61741 | −1.14368 | −0.571842 | − | 0.820363i | \(-0.693771\pi\) | ||||
−0.571842 | + | 0.820363i | \(0.693771\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.616031 | 0.308015 | ||||||||
\(5\) | −3.81830 | −1.70759 | −0.853797 | − | 0.520605i | \(-0.825706\pi\) | ||||
−0.853797 | + | 0.520605i | \(0.825706\pi\) | |||||||
\(6\) | 1.61741 | 0.660307 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23845 | 0.791413 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.17577 | 1.95295 | ||||||||
\(11\) | −5.83242 | −1.75854 | −0.879270 | − | 0.476324i | \(-0.841969\pi\) | ||||
−0.879270 | + | 0.476324i | \(0.841969\pi\) | |||||||
\(12\) | −0.616031 | −0.177833 | ||||||||
\(13\) | 2.66196 | 0.738294 | 0.369147 | − | 0.929371i | \(-0.379650\pi\) | ||||
0.369147 | + | 0.929371i | \(0.379650\pi\) | |||||||
\(14\) | −1.61741 | −0.432272 | ||||||||
\(15\) | 3.81830 | 0.985880 | ||||||||
\(16\) | −4.85257 | −1.21314 | ||||||||
\(17\) | 1.83267 | 0.444488 | 0.222244 | − | 0.974991i | \(-0.428662\pi\) | ||||
0.222244 | + | 0.974991i | \(0.428662\pi\) | |||||||
\(18\) | −1.61741 | −0.381228 | ||||||||
\(19\) | −1.69967 | −0.389930 | −0.194965 | − | 0.980810i | \(-0.562459\pi\) | ||||
−0.194965 | + | 0.980810i | \(0.562459\pi\) | |||||||
\(20\) | −2.35219 | −0.525965 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 9.43344 | 2.01122 | ||||||||
\(23\) | −8.47805 | −1.76779 | −0.883897 | − | 0.467681i | \(-0.845090\pi\) | ||||
−0.883897 | + | 0.467681i | \(0.845090\pi\) | |||||||
\(24\) | −2.23845 | −0.456922 | ||||||||
\(25\) | 9.57940 | 1.91588 | ||||||||
\(26\) | −4.30549 | −0.844376 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.616031 | 0.116419 | ||||||||
\(29\) | −1.07148 | −0.198969 | −0.0994844 | − | 0.995039i | \(-0.531719\pi\) | ||||
−0.0994844 | + | 0.995039i | \(0.531719\pi\) | |||||||
\(30\) | −6.17577 | −1.12754 | ||||||||
\(31\) | −2.20955 | −0.396847 | −0.198424 | − | 0.980116i | \(-0.563582\pi\) | ||||
−0.198424 | + | 0.980116i | \(0.563582\pi\) | |||||||
\(32\) | 3.37171 | 0.596040 | ||||||||
\(33\) | 5.83242 | 1.01529 | ||||||||
\(34\) | −2.96419 | −0.508354 | ||||||||
\(35\) | −3.81830 | −0.645410 | ||||||||
\(36\) | 0.616031 | 0.102672 | ||||||||
\(37\) | −8.02038 | −1.31854 | −0.659271 | − | 0.751905i | \(-0.729135\pi\) | ||||
−0.659271 | + | 0.751905i | \(0.729135\pi\) | |||||||
\(38\) | 2.74907 | 0.445958 | ||||||||
\(39\) | −2.66196 | −0.426254 | ||||||||
\(40\) | −8.54708 | −1.35141 | ||||||||
\(41\) | −3.22910 | −0.504301 | −0.252151 | − | 0.967688i | \(-0.581138\pi\) | ||||
−0.252151 | + | 0.967688i | \(0.581138\pi\) | |||||||
\(42\) | 1.61741 | 0.249573 | ||||||||
\(43\) | 3.13100 | 0.477474 | 0.238737 | − | 0.971084i | \(-0.423267\pi\) | ||||
0.238737 | + | 0.971084i | \(0.423267\pi\) | |||||||
\(44\) | −3.59295 | −0.541657 | ||||||||
\(45\) | −3.81830 | −0.569198 | ||||||||
\(46\) | 13.7125 | 2.02180 | ||||||||
\(47\) | −0.289107 | −0.0421705 | −0.0210853 | − | 0.999778i | \(-0.506712\pi\) | ||||
−0.0210853 | + | 0.999778i | \(0.506712\pi\) | |||||||
\(48\) | 4.85257 | 0.700408 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −15.4939 | −2.19116 | ||||||||
\(51\) | −1.83267 | −0.256625 | ||||||||
\(52\) | 1.63985 | 0.227406 | ||||||||
\(53\) | 6.72259 | 0.923418 | 0.461709 | − | 0.887031i | \(-0.347236\pi\) | ||||
0.461709 | + | 0.887031i | \(0.347236\pi\) | |||||||
\(54\) | 1.61741 | 0.220102 | ||||||||
\(55\) | 22.2699 | 3.00287 | ||||||||
\(56\) | 2.23845 | 0.299126 | ||||||||
\(57\) | 1.69967 | 0.225126 | ||||||||
\(58\) | 1.73303 | 0.227558 | ||||||||
\(59\) | 7.98601 | 1.03969 | 0.519845 | − | 0.854260i | \(-0.325990\pi\) | ||||
0.519845 | + | 0.854260i | \(0.325990\pi\) | |||||||
\(60\) | 2.35219 | 0.303666 | ||||||||
\(61\) | 6.92080 | 0.886118 | 0.443059 | − | 0.896492i | \(-0.353893\pi\) | ||||
0.443059 | + | 0.896492i | \(0.353893\pi\) | |||||||
\(62\) | 3.57376 | 0.453868 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 4.25168 | 0.531460 | ||||||||
\(65\) | −10.1641 | −1.26071 | ||||||||
\(66\) | −9.43344 | −1.16118 | ||||||||
\(67\) | 2.40863 | 0.294261 | 0.147130 | − | 0.989117i | \(-0.452996\pi\) | ||||
0.147130 | + | 0.989117i | \(0.452996\pi\) | |||||||
\(68\) | 1.12898 | 0.136909 | ||||||||
\(69\) | 8.47805 | 1.02064 | ||||||||
\(70\) | 6.17577 | 0.738146 | ||||||||
\(71\) | −11.3491 | −1.34689 | −0.673443 | − | 0.739239i | \(-0.735185\pi\) | ||||
−0.673443 | + | 0.739239i | \(0.735185\pi\) | |||||||
\(72\) | 2.23845 | 0.263804 | ||||||||
\(73\) | −4.36922 | −0.511378 | −0.255689 | − | 0.966759i | \(-0.582302\pi\) | ||||
−0.255689 | + | 0.966759i | \(0.582302\pi\) | |||||||
\(74\) | 12.9723 | 1.50800 | ||||||||
\(75\) | −9.57940 | −1.10613 | ||||||||
\(76\) | −1.04705 | −0.120105 | ||||||||
\(77\) | −5.83242 | −0.664666 | ||||||||
\(78\) | 4.30549 | 0.487501 | ||||||||
\(79\) | −4.87186 | −0.548127 | −0.274064 | − | 0.961712i | \(-0.588368\pi\) | ||||
−0.274064 | + | 0.961712i | \(0.588368\pi\) | |||||||
\(80\) | 18.5286 | 2.07155 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.22280 | 0.576762 | ||||||||
\(83\) | −5.97861 | −0.656238 | −0.328119 | − | 0.944636i | \(-0.606415\pi\) | ||||
−0.328119 | + | 0.944636i | \(0.606415\pi\) | |||||||
\(84\) | −0.616031 | −0.0672144 | ||||||||
\(85\) | −6.99768 | −0.759005 | ||||||||
\(86\) | −5.06413 | −0.546080 | ||||||||
\(87\) | 1.07148 | 0.114875 | ||||||||
\(88\) | −13.0556 | −1.39173 | ||||||||
\(89\) | −14.2467 | −1.51015 | −0.755073 | − | 0.655641i | \(-0.772399\pi\) | ||||
−0.755073 | + | 0.655641i | \(0.772399\pi\) | |||||||
\(90\) | 6.17577 | 0.650984 | ||||||||
\(91\) | 2.66196 | 0.279049 | ||||||||
\(92\) | −5.22274 | −0.544508 | ||||||||
\(93\) | 2.20955 | 0.229120 | ||||||||
\(94\) | 0.467605 | 0.0482298 | ||||||||
\(95\) | 6.48984 | 0.665843 | ||||||||
\(96\) | −3.37171 | −0.344124 | ||||||||
\(97\) | 8.87913 | 0.901539 | 0.450769 | − | 0.892640i | \(-0.351150\pi\) | ||||
0.450769 | + | 0.892640i | \(0.351150\pi\) | |||||||
\(98\) | −1.61741 | −0.163384 | ||||||||
\(99\) | −5.83242 | −0.586180 | ||||||||
\(100\) | 5.90120 | 0.590120 | ||||||||
\(101\) | −0.314415 | −0.0312855 | −0.0156427 | − | 0.999878i | \(-0.504979\pi\) | ||||
−0.0156427 | + | 0.999878i | \(0.504979\pi\) | |||||||
\(102\) | 2.96419 | 0.293498 | ||||||||
\(103\) | −12.9244 | −1.27348 | −0.636740 | − | 0.771079i | \(-0.719717\pi\) | ||||
−0.636740 | + | 0.771079i | \(0.719717\pi\) | |||||||
\(104\) | 5.95867 | 0.584295 | ||||||||
\(105\) | 3.81830 | 0.372628 | ||||||||
\(106\) | −10.8732 | −1.05610 | ||||||||
\(107\) | 2.85690 | 0.276187 | 0.138093 | − | 0.990419i | \(-0.455903\pi\) | ||||
0.138093 | + | 0.990419i | \(0.455903\pi\) | |||||||
\(108\) | −0.616031 | −0.0592776 | ||||||||
\(109\) | −6.91442 | −0.662282 | −0.331141 | − | 0.943581i | \(-0.607434\pi\) | ||||
−0.331141 | + | 0.943581i | \(0.607434\pi\) | |||||||
\(110\) | −36.0197 | −3.43434 | ||||||||
\(111\) | 8.02038 | 0.761261 | ||||||||
\(112\) | −4.85257 | −0.458525 | ||||||||
\(113\) | −15.9840 | −1.50365 | −0.751824 | − | 0.659363i | \(-0.770826\pi\) | ||||
−0.751824 | + | 0.659363i | \(0.770826\pi\) | |||||||
\(114\) | −2.74907 | −0.257474 | ||||||||
\(115\) | 32.3717 | 3.01868 | ||||||||
\(116\) | −0.660064 | −0.0612854 | ||||||||
\(117\) | 2.66196 | 0.246098 | ||||||||
\(118\) | −12.9167 | −1.18908 | ||||||||
\(119\) | 1.83267 | 0.168001 | ||||||||
\(120\) | 8.54708 | 0.780238 | ||||||||
\(121\) | 23.0171 | 2.09246 | ||||||||
\(122\) | −11.1938 | −1.01344 | ||||||||
\(123\) | 3.22910 | 0.291158 | ||||||||
\(124\) | −1.36115 | −0.122235 | ||||||||
\(125\) | −17.4855 | −1.56395 | ||||||||
\(126\) | −1.61741 | −0.144091 | ||||||||
\(127\) | −18.0523 | −1.60188 | −0.800940 | − | 0.598745i | \(-0.795666\pi\) | ||||
−0.800940 | + | 0.598745i | \(0.795666\pi\) | |||||||
\(128\) | −13.6202 | −1.20386 | ||||||||
\(129\) | −3.13100 | −0.275670 | ||||||||
\(130\) | 16.4396 | 1.44185 | ||||||||
\(131\) | −22.4093 | −1.95791 | −0.978954 | − | 0.204083i | \(-0.934579\pi\) | ||||
−0.978954 | + | 0.204083i | \(0.934579\pi\) | |||||||
\(132\) | 3.59295 | 0.312726 | ||||||||
\(133\) | −1.69967 | −0.147380 | ||||||||
\(134\) | −3.89575 | −0.336542 | ||||||||
\(135\) | 3.81830 | 0.328627 | ||||||||
\(136\) | 4.10235 | 0.351773 | ||||||||
\(137\) | −6.03905 | −0.515951 | −0.257975 | − | 0.966152i | \(-0.583055\pi\) | ||||
−0.257975 | + | 0.966152i | \(0.583055\pi\) | |||||||
\(138\) | −13.7125 | −1.16729 | ||||||||
\(139\) | −5.20717 | −0.441666 | −0.220833 | − | 0.975312i | \(-0.570878\pi\) | ||||
−0.220833 | + | 0.975312i | \(0.570878\pi\) | |||||||
\(140\) | −2.35219 | −0.198796 | ||||||||
\(141\) | 0.289107 | 0.0243472 | ||||||||
\(142\) | 18.3561 | 1.54041 | ||||||||
\(143\) | −15.5256 | −1.29832 | ||||||||
\(144\) | −4.85257 | −0.404381 | ||||||||
\(145\) | 4.09123 | 0.339758 | ||||||||
\(146\) | 7.06684 | 0.584856 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −4.94080 | −0.406131 | ||||||||
\(149\) | 1.54488 | 0.126562 | 0.0632808 | − | 0.997996i | \(-0.479844\pi\) | ||||
0.0632808 | + | 0.997996i | \(0.479844\pi\) | |||||||
\(150\) | 15.4939 | 1.26507 | ||||||||
\(151\) | 6.02046 | 0.489938 | 0.244969 | − | 0.969531i | \(-0.421222\pi\) | ||||
0.244969 | + | 0.969531i | \(0.421222\pi\) | |||||||
\(152\) | −3.80462 | −0.308596 | ||||||||
\(153\) | 1.83267 | 0.148163 | ||||||||
\(154\) | 9.43344 | 0.760168 | ||||||||
\(155\) | 8.43673 | 0.677654 | ||||||||
\(156\) | −1.63985 | −0.131293 | ||||||||
\(157\) | −17.5234 | −1.39852 | −0.699262 | − | 0.714866i | \(-0.746488\pi\) | ||||
−0.699262 | + | 0.714866i | \(0.746488\pi\) | |||||||
\(158\) | 7.87982 | 0.626885 | ||||||||
\(159\) | −6.72259 | −0.533136 | ||||||||
\(160\) | −12.8742 | −1.01779 | ||||||||
\(161\) | −8.47805 | −0.668164 | ||||||||
\(162\) | −1.61741 | −0.127076 | ||||||||
\(163\) | −22.0962 | −1.73071 | −0.865353 | − | 0.501163i | \(-0.832906\pi\) | ||||
−0.865353 | + | 0.501163i | \(0.832906\pi\) | |||||||
\(164\) | −1.98923 | −0.155332 | ||||||||
\(165\) | −22.2699 | −1.73371 | ||||||||
\(166\) | 9.66989 | 0.750529 | ||||||||
\(167\) | −9.14586 | −0.707728 | −0.353864 | − | 0.935297i | \(-0.615132\pi\) | ||||
−0.353864 | + | 0.935297i | \(0.615132\pi\) | |||||||
\(168\) | −2.23845 | −0.172700 | ||||||||
\(169\) | −5.91398 | −0.454922 | ||||||||
\(170\) | 11.3182 | 0.868063 | ||||||||
\(171\) | −1.69967 | −0.129977 | ||||||||
\(172\) | 1.92879 | 0.147069 | ||||||||
\(173\) | −0.552490 | −0.0420050 | −0.0210025 | − | 0.999779i | \(-0.506686\pi\) | ||||
−0.0210025 | + | 0.999779i | \(0.506686\pi\) | |||||||
\(174\) | −1.73303 | −0.131380 | ||||||||
\(175\) | 9.57940 | 0.724135 | ||||||||
\(176\) | 28.3022 | 2.13336 | ||||||||
\(177\) | −7.98601 | −0.600266 | ||||||||
\(178\) | 23.0428 | 1.72713 | ||||||||
\(179\) | 6.60544 | 0.493714 | 0.246857 | − | 0.969052i | \(-0.420602\pi\) | ||||
0.246857 | + | 0.969052i | \(0.420602\pi\) | |||||||
\(180\) | −2.35219 | −0.175322 | ||||||||
\(181\) | 14.3503 | 1.06665 | 0.533326 | − | 0.845909i | \(-0.320942\pi\) | ||||
0.533326 | + | 0.845909i | \(0.320942\pi\) | |||||||
\(182\) | −4.30549 | −0.319144 | ||||||||
\(183\) | −6.92080 | −0.511600 | ||||||||
\(184\) | −18.9777 | −1.39906 | ||||||||
\(185\) | 30.6242 | 2.25154 | ||||||||
\(186\) | −3.57376 | −0.262041 | ||||||||
\(187\) | −10.6889 | −0.781649 | ||||||||
\(188\) | −0.178098 | −0.0129892 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −10.4968 | −0.761515 | ||||||||
\(191\) | 11.1348 | 0.805684 | 0.402842 | − | 0.915269i | \(-0.368022\pi\) | ||||
0.402842 | + | 0.915269i | \(0.368022\pi\) | |||||||
\(192\) | −4.25168 | −0.306839 | ||||||||
\(193\) | −8.74547 | −0.629513 | −0.314757 | − | 0.949172i | \(-0.601923\pi\) | ||||
−0.314757 | + | 0.949172i | \(0.601923\pi\) | |||||||
\(194\) | −14.3612 | −1.03108 | ||||||||
\(195\) | 10.1641 | 0.727870 | ||||||||
\(196\) | 0.616031 | 0.0440022 | ||||||||
\(197\) | 1.79970 | 0.128224 | 0.0641118 | − | 0.997943i | \(-0.479579\pi\) | ||||
0.0641118 | + | 0.997943i | \(0.479579\pi\) | |||||||
\(198\) | 9.43344 | 0.670405 | ||||||||
\(199\) | −9.09677 | −0.644853 | −0.322426 | − | 0.946595i | \(-0.604498\pi\) | ||||
−0.322426 | + | 0.946595i | \(0.604498\pi\) | |||||||
\(200\) | 21.4430 | 1.51625 | ||||||||
\(201\) | −2.40863 | −0.169892 | ||||||||
\(202\) | 0.508540 | 0.0357807 | ||||||||
\(203\) | −1.07148 | −0.0752031 | ||||||||
\(204\) | −1.12898 | −0.0790445 | ||||||||
\(205\) | 12.3297 | 0.861142 | ||||||||
\(206\) | 20.9041 | 1.45646 | ||||||||
\(207\) | −8.47805 | −0.589265 | ||||||||
\(208\) | −12.9173 | −0.895656 | ||||||||
\(209\) | 9.91317 | 0.685708 | ||||||||
\(210\) | −6.17577 | −0.426169 | ||||||||
\(211\) | 6.97807 | 0.480390 | 0.240195 | − | 0.970725i | \(-0.422789\pi\) | ||||
0.240195 | + | 0.970725i | \(0.422789\pi\) | |||||||
\(212\) | 4.14132 | 0.284427 | ||||||||
\(213\) | 11.3491 | 0.777625 | ||||||||
\(214\) | −4.62079 | −0.315871 | ||||||||
\(215\) | −11.9551 | −0.815332 | ||||||||
\(216\) | −2.23845 | −0.152307 | ||||||||
\(217\) | −2.20955 | −0.149994 | ||||||||
\(218\) | 11.1835 | 0.757442 | ||||||||
\(219\) | 4.36922 | 0.295244 | ||||||||
\(220\) | 13.7189 | 0.924931 | ||||||||
\(221\) | 4.87849 | 0.328163 | ||||||||
\(222\) | −12.9723 | −0.870642 | ||||||||
\(223\) | −16.3296 | −1.09351 | −0.546757 | − | 0.837291i | \(-0.684138\pi\) | ||||
−0.546757 | + | 0.837291i | \(0.684138\pi\) | |||||||
\(224\) | 3.37171 | 0.225282 | ||||||||
\(225\) | 9.57940 | 0.638627 | ||||||||
\(226\) | 25.8528 | 1.71970 | ||||||||
\(227\) | −3.43480 | −0.227976 | −0.113988 | − | 0.993482i | \(-0.536362\pi\) | ||||
−0.113988 | + | 0.993482i | \(0.536362\pi\) | |||||||
\(228\) | 1.04705 | 0.0693424 | ||||||||
\(229\) | −1.08011 | −0.0713757 | −0.0356879 | − | 0.999363i | \(-0.511362\pi\) | ||||
−0.0356879 | + | 0.999363i | \(0.511362\pi\) | |||||||
\(230\) | −52.3585 | −3.45242 | ||||||||
\(231\) | 5.83242 | 0.383745 | ||||||||
\(232\) | −2.39846 | −0.157466 | ||||||||
\(233\) | 14.9222 | 0.977588 | 0.488794 | − | 0.872399i | \(-0.337437\pi\) | ||||
0.488794 | + | 0.872399i | \(0.337437\pi\) | |||||||
\(234\) | −4.30549 | −0.281459 | ||||||||
\(235\) | 1.10389 | 0.0720102 | ||||||||
\(236\) | 4.91963 | 0.320241 | ||||||||
\(237\) | 4.87186 | 0.316462 | ||||||||
\(238\) | −2.96419 | −0.192140 | ||||||||
\(239\) | −10.8737 | −0.703361 | −0.351680 | − | 0.936120i | \(-0.614390\pi\) | ||||
−0.351680 | + | 0.936120i | \(0.614390\pi\) | |||||||
\(240\) | −18.5286 | −1.19601 | ||||||||
\(241\) | 12.7179 | 0.819233 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(242\) | −37.2282 | −2.39312 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.26343 | 0.272938 | ||||||||
\(245\) | −3.81830 | −0.243942 | ||||||||
\(246\) | −5.22280 | −0.332994 | ||||||||
\(247\) | −4.52444 | −0.287883 | ||||||||
\(248\) | −4.94598 | −0.314070 | ||||||||
\(249\) | 5.97861 | 0.378879 | ||||||||
\(250\) | 28.2813 | 1.78867 | ||||||||
\(251\) | −16.1665 | −1.02042 | −0.510209 | − | 0.860051i | \(-0.670432\pi\) | ||||
−0.510209 | + | 0.860051i | \(0.670432\pi\) | |||||||
\(252\) | 0.616031 | 0.0388063 | ||||||||
\(253\) | 49.4475 | 3.10874 | ||||||||
\(254\) | 29.1980 | 1.83205 | ||||||||
\(255\) | 6.99768 | 0.438212 | ||||||||
\(256\) | 13.5261 | 0.845379 | ||||||||
\(257\) | −21.9692 | −1.37040 | −0.685202 | − | 0.728353i | \(-0.740286\pi\) | ||||
−0.685202 | + | 0.728353i | \(0.740286\pi\) | |||||||
\(258\) | 5.06413 | 0.315279 | ||||||||
\(259\) | −8.02038 | −0.498362 | ||||||||
\(260\) | −6.26143 | −0.388317 | ||||||||
\(261\) | −1.07148 | −0.0663229 | ||||||||
\(262\) | 36.2451 | 2.23923 | ||||||||
\(263\) | −16.8388 | −1.03833 | −0.519163 | − | 0.854675i | \(-0.673756\pi\) | ||||
−0.519163 | + | 0.854675i | \(0.673756\pi\) | |||||||
\(264\) | 13.0556 | 0.803516 | ||||||||
\(265\) | −25.6688 | −1.57682 | ||||||||
\(266\) | 2.74907 | 0.168556 | ||||||||
\(267\) | 14.2467 | 0.871883 | ||||||||
\(268\) | 1.48379 | 0.0906368 | ||||||||
\(269\) | −0.655115 | −0.0399430 | −0.0199715 | − | 0.999801i | \(-0.506358\pi\) | ||||
−0.0199715 | + | 0.999801i | \(0.506358\pi\) | |||||||
\(270\) | −6.17577 | −0.375846 | ||||||||
\(271\) | 4.32325 | 0.262619 | 0.131309 | − | 0.991341i | \(-0.458082\pi\) | ||||
0.131309 | + | 0.991341i | \(0.458082\pi\) | |||||||
\(272\) | −8.89315 | −0.539227 | ||||||||
\(273\) | −2.66196 | −0.161109 | ||||||||
\(274\) | 9.76764 | 0.590085 | ||||||||
\(275\) | −55.8711 | −3.36915 | ||||||||
\(276\) | 5.22274 | 0.314372 | ||||||||
\(277\) | 19.2556 | 1.15696 | 0.578479 | − | 0.815698i | \(-0.303647\pi\) | ||||
0.578479 | + | 0.815698i | \(0.303647\pi\) | |||||||
\(278\) | 8.42215 | 0.505127 | ||||||||
\(279\) | −2.20955 | −0.132282 | ||||||||
\(280\) | −8.54708 | −0.510786 | ||||||||
\(281\) | −14.4857 | −0.864142 | −0.432071 | − | 0.901840i | \(-0.642217\pi\) | ||||
−0.432071 | + | 0.901840i | \(0.642217\pi\) | |||||||
\(282\) | −0.467605 | −0.0278455 | ||||||||
\(283\) | −23.0964 | −1.37294 | −0.686469 | − | 0.727159i | \(-0.740840\pi\) | ||||
−0.686469 | + | 0.727159i | \(0.740840\pi\) | |||||||
\(284\) | −6.99137 | −0.414861 | ||||||||
\(285\) | −6.48984 | −0.384425 | ||||||||
\(286\) | 25.1114 | 1.48487 | ||||||||
\(287\) | −3.22910 | −0.190608 | ||||||||
\(288\) | 3.37171 | 0.198680 | ||||||||
\(289\) | −13.6413 | −0.802431 | ||||||||
\(290\) | −6.61721 | −0.388576 | ||||||||
\(291\) | −8.87913 | −0.520504 | ||||||||
\(292\) | −2.69157 | −0.157512 | ||||||||
\(293\) | 28.0899 | 1.64103 | 0.820516 | − | 0.571624i | \(-0.193686\pi\) | ||||
0.820516 | + | 0.571624i | \(0.193686\pi\) | |||||||
\(294\) | 1.61741 | 0.0943295 | ||||||||
\(295\) | −30.4930 | −1.77537 | ||||||||
\(296\) | −17.9532 | −1.04351 | ||||||||
\(297\) | 5.83242 | 0.338431 | ||||||||
\(298\) | −2.49871 | −0.144747 | ||||||||
\(299\) | −22.5682 | −1.30515 | ||||||||
\(300\) | −5.90120 | −0.340706 | ||||||||
\(301\) | 3.13100 | 0.180468 | ||||||||
\(302\) | −9.73758 | −0.560335 | ||||||||
\(303\) | 0.314415 | 0.0180627 | ||||||||
\(304\) | 8.24775 | 0.473041 | ||||||||
\(305\) | −26.4257 | −1.51313 | ||||||||
\(306\) | −2.96419 | −0.169451 | ||||||||
\(307\) | −13.8386 | −0.789809 | −0.394905 | − | 0.918722i | \(-0.629222\pi\) | ||||
−0.394905 | + | 0.918722i | \(0.629222\pi\) | |||||||
\(308\) | −3.59295 | −0.204727 | ||||||||
\(309\) | 12.9244 | 0.735244 | ||||||||
\(310\) | −13.6457 | −0.775023 | ||||||||
\(311\) | 15.6609 | 0.888049 | 0.444024 | − | 0.896015i | \(-0.353550\pi\) | ||||
0.444024 | + | 0.896015i | \(0.353550\pi\) | |||||||
\(312\) | −5.95867 | −0.337343 | ||||||||
\(313\) | −9.07104 | −0.512725 | −0.256363 | − | 0.966581i | \(-0.582524\pi\) | ||||
−0.256363 | + | 0.966581i | \(0.582524\pi\) | |||||||
\(314\) | 28.3427 | 1.59947 | ||||||||
\(315\) | −3.81830 | −0.215137 | ||||||||
\(316\) | −3.00122 | −0.168832 | ||||||||
\(317\) | 28.5237 | 1.60205 | 0.801026 | − | 0.598630i | \(-0.204288\pi\) | ||||
0.801026 | + | 0.598630i | \(0.204288\pi\) | |||||||
\(318\) | 10.8732 | 0.609739 | ||||||||
\(319\) | 6.24932 | 0.349895 | ||||||||
\(320\) | −16.2342 | −0.907519 | ||||||||
\(321\) | −2.85690 | −0.159457 | ||||||||
\(322\) | 13.7125 | 0.764169 | ||||||||
\(323\) | −3.11493 | −0.173319 | ||||||||
\(324\) | 0.616031 | 0.0342239 | ||||||||
\(325\) | 25.5000 | 1.41448 | ||||||||
\(326\) | 35.7387 | 1.97938 | ||||||||
\(327\) | 6.91442 | 0.382369 | ||||||||
\(328\) | −7.22820 | −0.399110 | ||||||||
\(329\) | −0.289107 | −0.0159390 | ||||||||
\(330\) | 36.0197 | 1.98282 | ||||||||
\(331\) | 17.1939 | 0.945065 | 0.472532 | − | 0.881313i | \(-0.343340\pi\) | ||||
0.472532 | + | 0.881313i | \(0.343340\pi\) | |||||||
\(332\) | −3.68301 | −0.202131 | ||||||||
\(333\) | −8.02038 | −0.439514 | ||||||||
\(334\) | 14.7926 | 0.809418 | ||||||||
\(335\) | −9.19686 | −0.502478 | ||||||||
\(336\) | 4.85257 | 0.264729 | ||||||||
\(337\) | −28.5883 | −1.55730 | −0.778651 | − | 0.627458i | \(-0.784096\pi\) | ||||
−0.778651 | + | 0.627458i | \(0.784096\pi\) | |||||||
\(338\) | 9.56536 | 0.520287 | ||||||||
\(339\) | 15.9840 | 0.868132 | ||||||||
\(340\) | −4.31079 | −0.233785 | ||||||||
\(341\) | 12.8870 | 0.697872 | ||||||||
\(342\) | 2.74907 | 0.148653 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 7.00861 | 0.377879 | ||||||||
\(345\) | −32.3717 | −1.74283 | ||||||||
\(346\) | 0.893605 | 0.0480405 | ||||||||
\(347\) | −17.8369 | −0.957534 | −0.478767 | − | 0.877942i | \(-0.658916\pi\) | ||||
−0.478767 | + | 0.877942i | \(0.658916\pi\) | |||||||
\(348\) | 0.660064 | 0.0353832 | ||||||||
\(349\) | 6.53762 | 0.349951 | 0.174975 | − | 0.984573i | \(-0.444015\pi\) | ||||
0.174975 | + | 0.984573i | \(0.444015\pi\) | |||||||
\(350\) | −15.4939 | −0.828182 | ||||||||
\(351\) | −2.66196 | −0.142085 | ||||||||
\(352\) | −19.6652 | −1.04816 | ||||||||
\(353\) | −2.52280 | −0.134275 | −0.0671375 | − | 0.997744i | \(-0.521387\pi\) | ||||
−0.0671375 | + | 0.997744i | \(0.521387\pi\) | |||||||
\(354\) | 12.9167 | 0.686515 | ||||||||
\(355\) | 43.3341 | 2.29994 | ||||||||
\(356\) | −8.77640 | −0.465148 | ||||||||
\(357\) | −1.83267 | −0.0969952 | ||||||||
\(358\) | −10.6837 | −0.564653 | ||||||||
\(359\) | −4.77378 | −0.251950 | −0.125975 | − | 0.992033i | \(-0.540206\pi\) | ||||
−0.125975 | + | 0.992033i | \(0.540206\pi\) | |||||||
\(360\) | −8.54708 | −0.450471 | ||||||||
\(361\) | −16.1111 | −0.847954 | ||||||||
\(362\) | −23.2105 | −1.21991 | ||||||||
\(363\) | −23.0171 | −1.20808 | ||||||||
\(364\) | 1.63985 | 0.0859513 | ||||||||
\(365\) | 16.6830 | 0.873227 | ||||||||
\(366\) | 11.1938 | 0.585110 | ||||||||
\(367\) | 2.61693 | 0.136602 | 0.0683012 | − | 0.997665i | \(-0.478242\pi\) | ||||
0.0683012 | + | 0.997665i | \(0.478242\pi\) | |||||||
\(368\) | 41.1403 | 2.14459 | ||||||||
\(369\) | −3.22910 | −0.168100 | ||||||||
\(370\) | −49.5320 | −2.57505 | ||||||||
\(371\) | 6.72259 | 0.349019 | ||||||||
\(372\) | 1.36115 | 0.0705724 | ||||||||
\(373\) | 3.48855 | 0.180630 | 0.0903150 | − | 0.995913i | \(-0.471213\pi\) | ||||
0.0903150 | + | 0.995913i | \(0.471213\pi\) | |||||||
\(374\) | 17.2884 | 0.893961 | ||||||||
\(375\) | 17.4855 | 0.902949 | ||||||||
\(376\) | −0.647151 | −0.0333743 | ||||||||
\(377\) | −2.85223 | −0.146897 | ||||||||
\(378\) | 1.61741 | 0.0831908 | ||||||||
\(379\) | 3.43946 | 0.176673 | 0.0883367 | − | 0.996091i | \(-0.471845\pi\) | ||||
0.0883367 | + | 0.996091i | \(0.471845\pi\) | |||||||
\(380\) | 3.99794 | 0.205090 | ||||||||
\(381\) | 18.0523 | 0.924846 | ||||||||
\(382\) | −18.0096 | −0.921449 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 13.6202 | 0.695051 | ||||||||
\(385\) | 22.2699 | 1.13498 | ||||||||
\(386\) | 14.1451 | 0.719965 | ||||||||
\(387\) | 3.13100 | 0.159158 | ||||||||
\(388\) | 5.46981 | 0.277688 | ||||||||
\(389\) | −0.775682 | −0.0393286 | −0.0196643 | − | 0.999807i | \(-0.506260\pi\) | ||||
−0.0196643 | + | 0.999807i | \(0.506260\pi\) | |||||||
\(390\) | −16.4396 | −0.832454 | ||||||||
\(391\) | −15.5375 | −0.785763 | ||||||||
\(392\) | 2.23845 | 0.113059 | ||||||||
\(393\) | 22.4093 | 1.13040 | ||||||||
\(394\) | −2.91087 | −0.146647 | ||||||||
\(395\) | 18.6022 | 0.935980 | ||||||||
\(396\) | −3.59295 | −0.180552 | ||||||||
\(397\) | 18.2597 | 0.916430 | 0.458215 | − | 0.888841i | \(-0.348489\pi\) | ||||
0.458215 | + | 0.888841i | \(0.348489\pi\) | |||||||
\(398\) | 14.7132 | 0.737509 | ||||||||
\(399\) | 1.69967 | 0.0850898 | ||||||||
\(400\) | −46.4847 | −2.32423 | ||||||||
\(401\) | 37.2852 | 1.86193 | 0.930967 | − | 0.365104i | \(-0.118967\pi\) | ||||
0.930967 | + | 0.365104i | \(0.118967\pi\) | |||||||
\(402\) | 3.89575 | 0.194302 | ||||||||
\(403\) | −5.88173 | −0.292990 | ||||||||
\(404\) | −0.193689 | −0.00963641 | ||||||||
\(405\) | −3.81830 | −0.189733 | ||||||||
\(406\) | 1.73303 | 0.0860087 | ||||||||
\(407\) | 46.7782 | 2.31871 | ||||||||
\(408\) | −4.10235 | −0.203096 | ||||||||
\(409\) | 7.77100 | 0.384251 | 0.192125 | − | 0.981370i | \(-0.438462\pi\) | ||||
0.192125 | + | 0.981370i | \(0.438462\pi\) | |||||||
\(410\) | −19.9422 | −0.984875 | ||||||||
\(411\) | 6.03905 | 0.297884 | ||||||||
\(412\) | −7.96183 | −0.392251 | ||||||||
\(413\) | 7.98601 | 0.392966 | ||||||||
\(414\) | 13.7125 | 0.673933 | ||||||||
\(415\) | 22.8281 | 1.12059 | ||||||||
\(416\) | 8.97535 | 0.440053 | ||||||||
\(417\) | 5.20717 | 0.254996 | ||||||||
\(418\) | −16.0337 | −0.784234 | ||||||||
\(419\) | 18.3597 | 0.896932 | 0.448466 | − | 0.893800i | \(-0.351970\pi\) | ||||
0.448466 | + | 0.893800i | \(0.351970\pi\) | |||||||
\(420\) | 2.35219 | 0.114775 | ||||||||
\(421\) | −15.4350 | −0.752257 | −0.376129 | − | 0.926567i | \(-0.622745\pi\) | ||||
−0.376129 | + | 0.926567i | \(0.622745\pi\) | |||||||
\(422\) | −11.2864 | −0.549415 | ||||||||
\(423\) | −0.289107 | −0.0140568 | ||||||||
\(424\) | 15.0482 | 0.730805 | ||||||||
\(425\) | 17.5559 | 0.851585 | ||||||||
\(426\) | −18.3561 | −0.889358 | ||||||||
\(427\) | 6.92080 | 0.334921 | ||||||||
\(428\) | 1.75994 | 0.0850698 | ||||||||
\(429\) | 15.5256 | 0.749585 | ||||||||
\(430\) | 19.3364 | 0.932483 | ||||||||
\(431\) | −20.3818 | −0.981755 | −0.490878 | − | 0.871229i | \(-0.663324\pi\) | ||||
−0.490878 | + | 0.871229i | \(0.663324\pi\) | |||||||
\(432\) | 4.85257 | 0.233469 | ||||||||
\(433\) | 34.7468 | 1.66983 | 0.834913 | − | 0.550382i | \(-0.185518\pi\) | ||||
0.834913 | + | 0.550382i | \(0.185518\pi\) | |||||||
\(434\) | 3.57376 | 0.171546 | ||||||||
\(435\) | −4.09123 | −0.196159 | ||||||||
\(436\) | −4.25950 | −0.203993 | ||||||||
\(437\) | 14.4099 | 0.689317 | ||||||||
\(438\) | −7.06684 | −0.337667 | ||||||||
\(439\) | 5.86283 | 0.279817 | 0.139909 | − | 0.990164i | \(-0.455319\pi\) | ||||
0.139909 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(440\) | 49.8501 | 2.37651 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −7.89054 | −0.375315 | ||||||||
\(443\) | 40.3266 | 1.91597 | 0.957987 | − | 0.286812i | \(-0.0925956\pi\) | ||||
0.957987 | + | 0.286812i | \(0.0925956\pi\) | |||||||
\(444\) | 4.94080 | 0.234480 | ||||||||
\(445\) | 54.3981 | 2.57872 | ||||||||
\(446\) | 26.4118 | 1.25064 | ||||||||
\(447\) | −1.54488 | −0.0730704 | ||||||||
\(448\) | 4.25168 | 0.200873 | ||||||||
\(449\) | −6.84391 | −0.322984 | −0.161492 | − | 0.986874i | \(-0.551631\pi\) | ||||
−0.161492 | + | 0.986874i | \(0.551631\pi\) | |||||||
\(450\) | −15.4939 | −0.730388 | ||||||||
\(451\) | 18.8335 | 0.886834 | ||||||||
\(452\) | −9.84664 | −0.463147 | ||||||||
\(453\) | −6.02046 | −0.282866 | ||||||||
\(454\) | 5.55549 | 0.260732 | ||||||||
\(455\) | −10.1641 | −0.476503 | ||||||||
\(456\) | 3.80462 | 0.178168 | ||||||||
\(457\) | −19.1964 | −0.897971 | −0.448985 | − | 0.893539i | \(-0.648214\pi\) | ||||
−0.448985 | + | 0.893539i | \(0.648214\pi\) | |||||||
\(458\) | 1.74699 | 0.0816313 | ||||||||
\(459\) | −1.83267 | −0.0855417 | ||||||||
\(460\) | 19.9420 | 0.929799 | ||||||||
\(461\) | −9.48991 | −0.441989 | −0.220995 | − | 0.975275i | \(-0.570930\pi\) | ||||
−0.220995 | + | 0.975275i | \(0.570930\pi\) | |||||||
\(462\) | −9.43344 | −0.438883 | ||||||||
\(463\) | 21.7366 | 1.01018 | 0.505092 | − | 0.863066i | \(-0.331459\pi\) | ||||
0.505092 | + | 0.863066i | \(0.331459\pi\) | |||||||
\(464\) | 5.19943 | 0.241377 | ||||||||
\(465\) | −8.43673 | −0.391244 | ||||||||
\(466\) | −24.1354 | −1.11805 | ||||||||
\(467\) | 10.3772 | 0.480202 | 0.240101 | − | 0.970748i | \(-0.422819\pi\) | ||||
0.240101 | + | 0.970748i | \(0.422819\pi\) | |||||||
\(468\) | 1.63985 | 0.0758020 | ||||||||
\(469\) | 2.40863 | 0.111220 | ||||||||
\(470\) | −1.78546 | −0.0823569 | ||||||||
\(471\) | 17.5234 | 0.807438 | ||||||||
\(472\) | 17.8763 | 0.822824 | ||||||||
\(473\) | −18.2613 | −0.839657 | ||||||||
\(474\) | −7.87982 | −0.361932 | ||||||||
\(475\) | −16.2818 | −0.747060 | ||||||||
\(476\) | 1.12898 | 0.0517467 | ||||||||
\(477\) | 6.72259 | 0.307806 | ||||||||
\(478\) | 17.5873 | 0.804423 | ||||||||
\(479\) | −26.4060 | −1.20652 | −0.603262 | − | 0.797543i | \(-0.706132\pi\) | ||||
−0.603262 | + | 0.797543i | \(0.706132\pi\) | |||||||
\(480\) | 12.8742 | 0.587624 | ||||||||
\(481\) | −21.3499 | −0.973472 | ||||||||
\(482\) | −20.5701 | −0.936944 | ||||||||
\(483\) | 8.47805 | 0.385764 | ||||||||
\(484\) | 14.1792 | 0.644510 | ||||||||
\(485\) | −33.9031 | −1.53946 | ||||||||
\(486\) | 1.61741 | 0.0733674 | ||||||||
\(487\) | 37.9905 | 1.72151 | 0.860756 | − | 0.509018i | \(-0.169991\pi\) | ||||
0.860756 | + | 0.509018i | \(0.169991\pi\) | |||||||
\(488\) | 15.4919 | 0.701285 | ||||||||
\(489\) | 22.0962 | 0.999224 | ||||||||
\(490\) | 6.17577 | 0.278993 | ||||||||
\(491\) | −12.1865 | −0.549968 | −0.274984 | − | 0.961449i | \(-0.588673\pi\) | ||||
−0.274984 | + | 0.961449i | \(0.588673\pi\) | |||||||
\(492\) | 1.98923 | 0.0896812 | ||||||||
\(493\) | −1.96367 | −0.0884392 | ||||||||
\(494\) | 7.31790 | 0.329248 | ||||||||
\(495\) | 22.2699 | 1.00096 | ||||||||
\(496\) | 10.7220 | 0.481432 | ||||||||
\(497\) | −11.3491 | −0.509075 | ||||||||
\(498\) | −9.66989 | −0.433318 | ||||||||
\(499\) | −20.6727 | −0.925438 | −0.462719 | − | 0.886505i | \(-0.653126\pi\) | ||||
−0.462719 | + | 0.886505i | \(0.653126\pi\) | |||||||
\(500\) | −10.7716 | −0.481721 | ||||||||
\(501\) | 9.14586 | 0.408607 | ||||||||
\(502\) | 26.1479 | 1.16704 | ||||||||
\(503\) | −17.1737 | −0.765739 | −0.382870 | − | 0.923802i | \(-0.625064\pi\) | ||||
−0.382870 | + | 0.923802i | \(0.625064\pi\) | |||||||
\(504\) | 2.23845 | 0.0997086 | ||||||||
\(505\) | 1.20053 | 0.0534229 | ||||||||
\(506\) | −79.9771 | −3.55542 | ||||||||
\(507\) | 5.91398 | 0.262649 | ||||||||
\(508\) | −11.1207 | −0.493403 | ||||||||
\(509\) | −2.98112 | −0.132136 | −0.0660679 | − | 0.997815i | \(-0.521045\pi\) | ||||
−0.0660679 | + | 0.997815i | \(0.521045\pi\) | |||||||
\(510\) | −11.3182 | −0.501176 | ||||||||
\(511\) | −4.36922 | −0.193283 | ||||||||
\(512\) | 5.36304 | 0.237015 | ||||||||
\(513\) | 1.69967 | 0.0750421 | ||||||||
\(514\) | 35.5334 | 1.56731 | ||||||||
\(515\) | 49.3492 | 2.17459 | ||||||||
\(516\) | −1.92879 | −0.0849104 | ||||||||
\(517\) | 1.68619 | 0.0741585 | ||||||||
\(518\) | 12.9723 | 0.569969 | ||||||||
\(519\) | 0.552490 | 0.0242516 | ||||||||
\(520\) | −22.7520 | −0.997740 | ||||||||
\(521\) | −31.0279 | −1.35936 | −0.679678 | − | 0.733510i | \(-0.737881\pi\) | ||||
−0.679678 | + | 0.733510i | \(0.737881\pi\) | |||||||
\(522\) | 1.73303 | 0.0758525 | ||||||||
\(523\) | −8.67493 | −0.379328 | −0.189664 | − | 0.981849i | \(-0.560740\pi\) | ||||
−0.189664 | + | 0.981849i | \(0.560740\pi\) | |||||||
\(524\) | −13.8048 | −0.603065 | ||||||||
\(525\) | −9.57940 | −0.418079 | ||||||||
\(526\) | 27.2353 | 1.18752 | ||||||||
\(527\) | −4.04938 | −0.176394 | ||||||||
\(528\) | −28.3022 | −1.23169 | ||||||||
\(529\) | 48.8773 | 2.12510 | ||||||||
\(530\) | 41.5172 | 1.80339 | ||||||||
\(531\) | 7.98601 | 0.346563 | ||||||||
\(532\) | −1.04705 | −0.0453952 | ||||||||
\(533\) | −8.59574 | −0.372323 | ||||||||
\(534\) | −23.0428 | −0.997160 | ||||||||
\(535\) | −10.9085 | −0.471615 | ||||||||
\(536\) | 5.39160 | 0.232882 | ||||||||
\(537\) | −6.60544 | −0.285046 | ||||||||
\(538\) | 1.05959 | 0.0456823 | ||||||||
\(539\) | −5.83242 | −0.251220 | ||||||||
\(540\) | 2.35219 | 0.101222 | ||||||||
\(541\) | −2.47586 | −0.106446 | −0.0532228 | − | 0.998583i | \(-0.516949\pi\) | ||||
−0.0532228 | + | 0.998583i | \(0.516949\pi\) | |||||||
\(542\) | −6.99249 | −0.300353 | ||||||||
\(543\) | −14.3503 | −0.615832 | ||||||||
\(544\) | 6.17923 | 0.264932 | ||||||||
\(545\) | 26.4013 | 1.13091 | ||||||||
\(546\) | 4.30549 | 0.184258 | ||||||||
\(547\) | 3.95202 | 0.168976 | 0.0844881 | − | 0.996424i | \(-0.473074\pi\) | ||||
0.0844881 | + | 0.996424i | \(0.473074\pi\) | |||||||
\(548\) | −3.72024 | −0.158921 | ||||||||
\(549\) | 6.92080 | 0.295373 | ||||||||
\(550\) | 90.3667 | 3.85325 | ||||||||
\(551\) | 1.82116 | 0.0775840 | ||||||||
\(552\) | 18.9777 | 0.807745 | ||||||||
\(553\) | −4.87186 | −0.207173 | ||||||||
\(554\) | −31.1443 | −1.32319 | ||||||||
\(555\) | −30.6242 | −1.29993 | ||||||||
\(556\) | −3.20777 | −0.136040 | ||||||||
\(557\) | −19.8735 | −0.842066 | −0.421033 | − | 0.907045i | \(-0.638332\pi\) | ||||
−0.421033 | + | 0.907045i | \(0.638332\pi\) | |||||||
\(558\) | 3.57376 | 0.151289 | ||||||||
\(559\) | 8.33460 | 0.352516 | ||||||||
\(560\) | 18.5286 | 0.782974 | ||||||||
\(561\) | 10.6889 | 0.451285 | ||||||||
\(562\) | 23.4293 | 0.988306 | ||||||||
\(563\) | 37.8407 | 1.59480 | 0.797399 | − | 0.603453i | \(-0.206209\pi\) | ||||
0.797399 | + | 0.603453i | \(0.206209\pi\) | |||||||
\(564\) | 0.178098 | 0.00749930 | ||||||||
\(565\) | 61.0317 | 2.56762 | ||||||||
\(566\) | 37.3564 | 1.57021 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −25.4043 | −1.06594 | ||||||||
\(569\) | 38.8416 | 1.62833 | 0.814163 | − | 0.580637i | \(-0.197196\pi\) | ||||
0.814163 | + | 0.580637i | \(0.197196\pi\) | |||||||
\(570\) | 10.4968 | 0.439661 | ||||||||
\(571\) | −0.300788 | −0.0125876 | −0.00629379 | − | 0.999980i | \(-0.502003\pi\) | ||||
−0.00629379 | + | 0.999980i | \(0.502003\pi\) | |||||||
\(572\) | −9.56427 | −0.399902 | ||||||||
\(573\) | −11.1348 | −0.465162 | ||||||||
\(574\) | 5.22280 | 0.217995 | ||||||||
\(575\) | −81.2146 | −3.38688 | ||||||||
\(576\) | 4.25168 | 0.177153 | ||||||||
\(577\) | −20.5200 | −0.854258 | −0.427129 | − | 0.904191i | \(-0.640475\pi\) | ||||
−0.427129 | + | 0.904191i | \(0.640475\pi\) | |||||||
\(578\) | 22.0637 | 0.917728 | ||||||||
\(579\) | 8.74547 | 0.363450 | ||||||||
\(580\) | 2.52032 | 0.104651 | ||||||||
\(581\) | −5.97861 | −0.248035 | ||||||||
\(582\) | 14.3612 | 0.595292 | ||||||||
\(583\) | −39.2089 | −1.62387 | ||||||||
\(584\) | −9.78029 | −0.404711 | ||||||||
\(585\) | −10.1641 | −0.420236 | ||||||||
\(586\) | −45.4331 | −1.87682 | ||||||||
\(587\) | 17.7252 | 0.731597 | 0.365798 | − | 0.930694i | \(-0.380796\pi\) | ||||
0.365798 | + | 0.930694i | \(0.380796\pi\) | |||||||
\(588\) | −0.616031 | −0.0254047 | ||||||||
\(589\) | 3.75550 | 0.154743 | ||||||||
\(590\) | 49.3198 | 2.03046 | ||||||||
\(591\) | −1.79970 | −0.0740300 | ||||||||
\(592\) | 38.9194 | 1.59958 | ||||||||
\(593\) | −19.5349 | −0.802202 | −0.401101 | − | 0.916034i | \(-0.631372\pi\) | ||||
−0.401101 | + | 0.916034i | \(0.631372\pi\) | |||||||
\(594\) | −9.43344 | −0.387059 | ||||||||
\(595\) | −6.99768 | −0.286877 | ||||||||
\(596\) | 0.951694 | 0.0389829 | ||||||||
\(597\) | 9.09677 | 0.372306 | ||||||||
\(598\) | 36.5021 | 1.49268 | ||||||||
\(599\) | −12.9827 | −0.530459 | −0.265230 | − | 0.964185i | \(-0.585448\pi\) | ||||
−0.265230 | + | 0.964185i | \(0.585448\pi\) | |||||||
\(600\) | −21.4430 | −0.875408 | ||||||||
\(601\) | 21.3752 | 0.871911 | 0.435956 | − | 0.899968i | \(-0.356410\pi\) | ||||
0.435956 | + | 0.899968i | \(0.356410\pi\) | |||||||
\(602\) | −5.06413 | −0.206399 | ||||||||
\(603\) | 2.40863 | 0.0980870 | ||||||||
\(604\) | 3.70879 | 0.150908 | ||||||||
\(605\) | −87.8861 | −3.57308 | ||||||||
\(606\) | −0.508540 | −0.0206580 | ||||||||
\(607\) | −22.5833 | −0.916627 | −0.458313 | − | 0.888791i | \(-0.651546\pi\) | ||||
−0.458313 | + | 0.888791i | \(0.651546\pi\) | |||||||
\(608\) | −5.73078 | −0.232414 | ||||||||
\(609\) | 1.07148 | 0.0434185 | ||||||||
\(610\) | 42.7413 | 1.73054 | ||||||||
\(611\) | −0.769589 | −0.0311342 | ||||||||
\(612\) | 1.12898 | 0.0456363 | ||||||||
\(613\) | −36.6141 | −1.47883 | −0.739414 | − | 0.673251i | \(-0.764897\pi\) | ||||
−0.739414 | + | 0.673251i | \(0.764897\pi\) | |||||||
\(614\) | 22.3827 | 0.903293 | ||||||||
\(615\) | −12.3297 | −0.497181 | ||||||||
\(616\) | −13.0556 | −0.526025 | ||||||||
\(617\) | −35.0818 | −1.41234 | −0.706170 | − | 0.708042i | \(-0.749579\pi\) | ||||
−0.706170 | + | 0.708042i | \(0.749579\pi\) | |||||||
\(618\) | −20.9041 | −0.840887 | ||||||||
\(619\) | −39.3616 | −1.58208 | −0.791039 | − | 0.611766i | \(-0.790460\pi\) | ||||
−0.791039 | + | 0.611766i | \(0.790460\pi\) | |||||||
\(620\) | 5.19728 | 0.208728 | ||||||||
\(621\) | 8.47805 | 0.340212 | ||||||||
\(622\) | −25.3302 | −1.01565 | ||||||||
\(623\) | −14.2467 | −0.570782 | ||||||||
\(624\) | 12.9173 | 0.517107 | ||||||||
\(625\) | 18.8679 | 0.754718 | ||||||||
\(626\) | 14.6716 | 0.586396 | ||||||||
\(627\) | −9.91317 | −0.395894 | ||||||||
\(628\) | −10.7950 | −0.430767 | ||||||||
\(629\) | −14.6987 | −0.586076 | ||||||||
\(630\) | 6.17577 | 0.246049 | ||||||||
\(631\) | 41.2313 | 1.64139 | 0.820695 | − | 0.571366i | \(-0.193586\pi\) | ||||
0.820695 | + | 0.571366i | \(0.193586\pi\) | |||||||
\(632\) | −10.9054 | −0.433795 | ||||||||
\(633\) | −6.97807 | −0.277353 | ||||||||
\(634\) | −46.1347 | −1.83224 | ||||||||
\(635\) | 68.9289 | 2.73536 | ||||||||
\(636\) | −4.14132 | −0.164214 | ||||||||
\(637\) | 2.66196 | 0.105471 | ||||||||
\(638\) | −10.1077 | −0.400169 | ||||||||
\(639\) | −11.3491 | −0.448962 | ||||||||
\(640\) | 52.0058 | 2.05571 | ||||||||
\(641\) | −23.8154 | −0.940653 | −0.470327 | − | 0.882492i | \(-0.655864\pi\) | ||||
−0.470327 | + | 0.882492i | \(0.655864\pi\) | |||||||
\(642\) | 4.62079 | 0.182368 | ||||||||
\(643\) | 17.1991 | 0.678268 | 0.339134 | − | 0.940738i | \(-0.389866\pi\) | ||||
0.339134 | + | 0.940738i | \(0.389866\pi\) | |||||||
\(644\) | −5.22274 | −0.205805 | ||||||||
\(645\) | 11.9551 | 0.470732 | ||||||||
\(646\) | 5.03813 | 0.198223 | ||||||||
\(647\) | 36.9235 | 1.45161 | 0.725806 | − | 0.687899i | \(-0.241467\pi\) | ||||
0.725806 | + | 0.687899i | \(0.241467\pi\) | |||||||
\(648\) | 2.23845 | 0.0879347 | ||||||||
\(649\) | −46.5778 | −1.82834 | ||||||||
\(650\) | −41.2440 | −1.61772 | ||||||||
\(651\) | 2.20955 | 0.0865992 | ||||||||
\(652\) | −13.6119 | −0.533084 | ||||||||
\(653\) | 21.7155 | 0.849795 | 0.424897 | − | 0.905242i | \(-0.360310\pi\) | ||||
0.424897 | + | 0.905242i | \(0.360310\pi\) | |||||||
\(654\) | −11.1835 | −0.437309 | ||||||||
\(655\) | 85.5653 | 3.34331 | ||||||||
\(656\) | 15.6694 | 0.611789 | ||||||||
\(657\) | −4.36922 | −0.170459 | ||||||||
\(658\) | 0.467605 | 0.0182291 | ||||||||
\(659\) | 24.6953 | 0.961994 | 0.480997 | − | 0.876722i | \(-0.340275\pi\) | ||||
0.480997 | + | 0.876722i | \(0.340275\pi\) | |||||||
\(660\) | −13.7189 | −0.534009 | ||||||||
\(661\) | 7.53059 | 0.292906 | 0.146453 | − | 0.989218i | \(-0.453214\pi\) | ||||
0.146453 | + | 0.989218i | \(0.453214\pi\) | |||||||
\(662\) | −27.8097 | −1.08086 | ||||||||
\(663\) | −4.87849 | −0.189465 | ||||||||
\(664\) | −13.3828 | −0.519355 | ||||||||
\(665\) | 6.48984 | 0.251665 | ||||||||
\(666\) | 12.9723 | 0.502666 | ||||||||
\(667\) | 9.08405 | 0.351736 | ||||||||
\(668\) | −5.63413 | −0.217991 | ||||||||
\(669\) | 16.3296 | 0.631340 | ||||||||
\(670\) | 14.8751 | 0.574677 | ||||||||
\(671\) | −40.3650 | −1.55827 | ||||||||
\(672\) | −3.37171 | −0.130066 | ||||||||
\(673\) | 48.9265 | 1.88598 | 0.942989 | − | 0.332824i | \(-0.108002\pi\) | ||||
0.942989 | + | 0.332824i | \(0.108002\pi\) | |||||||
\(674\) | 46.2391 | 1.78106 | ||||||||
\(675\) | −9.57940 | −0.368711 | ||||||||
\(676\) | −3.64319 | −0.140123 | ||||||||
\(677\) | 41.4004 | 1.59115 | 0.795574 | − | 0.605857i | \(-0.207170\pi\) | ||||
0.795574 | + | 0.605857i | \(0.207170\pi\) | |||||||
\(678\) | −25.8528 | −0.992870 | ||||||||
\(679\) | 8.87913 | 0.340750 | ||||||||
\(680\) | −15.6640 | −0.600686 | ||||||||
\(681\) | 3.43480 | 0.131622 | ||||||||
\(682\) | −20.8437 | −0.798145 | ||||||||
\(683\) | −42.0704 | −1.60978 | −0.804890 | − | 0.593423i | \(-0.797776\pi\) | ||||
−0.804890 | + | 0.593423i | \(0.797776\pi\) | |||||||
\(684\) | −1.04705 | −0.0400348 | ||||||||
\(685\) | 23.0589 | 0.881035 | ||||||||
\(686\) | −1.61741 | −0.0617532 | ||||||||
\(687\) | 1.08011 | 0.0412088 | ||||||||
\(688\) | −15.1934 | −0.579243 | ||||||||
\(689\) | 17.8952 | 0.681754 | ||||||||
\(690\) | 52.3585 | 1.99325 | ||||||||
\(691\) | −39.7522 | −1.51224 | −0.756122 | − | 0.654431i | \(-0.772908\pi\) | ||||
−0.756122 | + | 0.654431i | \(0.772908\pi\) | |||||||
\(692\) | −0.340350 | −0.0129382 | ||||||||
\(693\) | −5.83242 | −0.221555 | ||||||||
\(694\) | 28.8496 | 1.09512 | ||||||||
\(695\) | 19.8825 | 0.754187 | ||||||||
\(696\) | 2.39846 | 0.0909133 | ||||||||
\(697\) | −5.91788 | −0.224156 | ||||||||
\(698\) | −10.5740 | −0.400233 | ||||||||
\(699\) | −14.9222 | −0.564411 | ||||||||
\(700\) | 5.90120 | 0.223045 | ||||||||
\(701\) | 0.473823 | 0.0178961 | 0.00894803 | − | 0.999960i | \(-0.497152\pi\) | ||||
0.00894803 | + | 0.999960i | \(0.497152\pi\) | |||||||
\(702\) | 4.30549 | 0.162500 | ||||||||
\(703\) | 13.6320 | 0.514140 | ||||||||
\(704\) | −24.7976 | −0.934594 | ||||||||
\(705\) | −1.10389 | −0.0415751 | ||||||||
\(706\) | 4.08041 | 0.153568 | ||||||||
\(707\) | −0.314415 | −0.0118248 | ||||||||
\(708\) | −4.91963 | −0.184891 | ||||||||
\(709\) | 44.3251 | 1.66466 | 0.832332 | − | 0.554277i | \(-0.187005\pi\) | ||||
0.832332 | + | 0.554277i | \(0.187005\pi\) | |||||||
\(710\) | −70.0892 | −2.63040 | ||||||||
\(711\) | −4.87186 | −0.182709 | ||||||||
\(712\) | −31.8905 | −1.19515 | ||||||||
\(713\) | 18.7327 | 0.701545 | ||||||||
\(714\) | 2.96419 | 0.110932 | ||||||||
\(715\) | 59.2815 | 2.21700 | ||||||||
\(716\) | 4.06915 | 0.152071 | ||||||||
\(717\) | 10.8737 | 0.406086 | ||||||||
\(718\) | 7.72118 | 0.288152 | ||||||||
\(719\) | −32.8297 | −1.22434 | −0.612171 | − | 0.790725i | \(-0.709704\pi\) | ||||
−0.612171 | + | 0.790725i | \(0.709704\pi\) | |||||||
\(720\) | 18.5286 | 0.690518 | ||||||||
\(721\) | −12.9244 | −0.481330 | ||||||||
\(722\) | 26.0584 | 0.969793 | ||||||||
\(723\) | −12.7179 | −0.472984 | ||||||||
\(724\) | 8.84025 | 0.328545 | ||||||||
\(725\) | −10.2641 | −0.381200 | ||||||||
\(726\) | 37.2282 | 1.38167 | ||||||||
\(727\) | 24.9801 | 0.926461 | 0.463231 | − | 0.886238i | \(-0.346690\pi\) | ||||
0.463231 | + | 0.886238i | \(0.346690\pi\) | |||||||
\(728\) | 5.95867 | 0.220843 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −26.9833 | −0.998697 | ||||||||
\(731\) | 5.73810 | 0.212231 | ||||||||
\(732\) | −4.26343 | −0.157581 | ||||||||
\(733\) | −8.97575 | −0.331527 | −0.165763 | − | 0.986166i | \(-0.553009\pi\) | ||||
−0.165763 | + | 0.986166i | \(0.553009\pi\) | |||||||
\(734\) | −4.23265 | −0.156230 | ||||||||
\(735\) | 3.81830 | 0.140840 | ||||||||
\(736\) | −28.5855 | −1.05368 | ||||||||
\(737\) | −14.0481 | −0.517469 | ||||||||
\(738\) | 5.22280 | 0.192254 | ||||||||
\(739\) | 5.18372 | 0.190686 | 0.0953430 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953430 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(740\) | 18.8654 | 0.693508 | ||||||||
\(741\) | 4.52444 | 0.166210 | ||||||||
\(742\) | −10.8732 | −0.399168 | ||||||||
\(743\) | 26.6816 | 0.978852 | 0.489426 | − | 0.872045i | \(-0.337206\pi\) | ||||
0.489426 | + | 0.872045i | \(0.337206\pi\) | |||||||
\(744\) | 4.94598 | 0.181328 | ||||||||
\(745\) | −5.89882 | −0.216116 | ||||||||
\(746\) | −5.64243 | −0.206584 | ||||||||
\(747\) | −5.97861 | −0.218746 | ||||||||
\(748\) | −6.58469 | −0.240760 | ||||||||
\(749\) | 2.85690 | 0.104389 | ||||||||
\(750\) | −28.2813 | −1.03269 | ||||||||
\(751\) | 8.72133 | 0.318246 | 0.159123 | − | 0.987259i | \(-0.449133\pi\) | ||||
0.159123 | + | 0.987259i | \(0.449133\pi\) | |||||||
\(752\) | 1.40291 | 0.0511588 | ||||||||
\(753\) | 16.1665 | 0.589138 | ||||||||
\(754\) | 4.61324 | 0.168004 | ||||||||
\(755\) | −22.9879 | −0.836615 | ||||||||
\(756\) | −0.616031 | −0.0224048 | ||||||||
\(757\) | −4.40542 | −0.160118 | −0.0800589 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800589 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(758\) | −5.56304 | −0.202059 | ||||||||
\(759\) | −49.4475 | −1.79483 | ||||||||
\(760\) | 14.5272 | 0.526957 | ||||||||
\(761\) | −20.1386 | −0.730025 | −0.365013 | − | 0.931003i | \(-0.618935\pi\) | ||||
−0.365013 | + | 0.931003i | \(0.618935\pi\) | |||||||
\(762\) | −29.1980 | −1.05773 | ||||||||
\(763\) | −6.91442 | −0.250319 | ||||||||
\(764\) | 6.85936 | 0.248163 | ||||||||
\(765\) | −6.99768 | −0.253002 | ||||||||
\(766\) | 1.61741 | 0.0584396 | ||||||||
\(767\) | 21.2584 | 0.767597 | ||||||||
\(768\) | −13.5261 | −0.488080 | ||||||||
\(769\) | 15.5277 | 0.559941 | 0.279971 | − | 0.960009i | \(-0.409675\pi\) | ||||
0.279971 | + | 0.960009i | \(0.409675\pi\) | |||||||
\(770\) | −36.0197 | −1.29806 | ||||||||
\(771\) | 21.9692 | 0.791203 | ||||||||
\(772\) | −5.38748 | −0.193900 | ||||||||
\(773\) | −45.9176 | −1.65154 | −0.825771 | − | 0.564006i | \(-0.809260\pi\) | ||||
−0.825771 | + | 0.564006i | \(0.809260\pi\) | |||||||
\(774\) | −5.06413 | −0.182027 | ||||||||
\(775\) | −21.1662 | −0.760312 | ||||||||
\(776\) | 19.8755 | 0.713489 | ||||||||
\(777\) | 8.02038 | 0.287730 | ||||||||
\(778\) | 1.25460 | 0.0449796 | ||||||||
\(779\) | 5.48840 | 0.196642 | ||||||||
\(780\) | 6.26143 | 0.224195 | ||||||||
\(781\) | 66.1925 | 2.36855 | ||||||||
\(782\) | 25.1305 | 0.898666 | ||||||||
\(783\) | 1.07148 | 0.0382916 | ||||||||
\(784\) | −4.85257 | −0.173306 | ||||||||
\(785\) | 66.9097 | 2.38811 | ||||||||
\(786\) | −36.2451 | −1.29282 | ||||||||
\(787\) | −47.2905 | −1.68572 | −0.842862 | − | 0.538130i | \(-0.819131\pi\) | ||||
−0.842862 | + | 0.538130i | \(0.819131\pi\) | |||||||
\(788\) | 1.10867 | 0.0394948 | ||||||||
\(789\) | 16.8388 | 0.599477 | ||||||||
\(790\) | −30.0875 | −1.07047 | ||||||||
\(791\) | −15.9840 | −0.568326 | ||||||||
\(792\) | −13.0556 | −0.463910 | ||||||||
\(793\) | 18.4229 | 0.654216 | ||||||||
\(794\) | −29.5336 | −1.04811 | ||||||||
\(795\) | 25.6688 | 0.910380 | ||||||||
\(796\) | −5.60389 | −0.198625 | ||||||||
\(797\) | 35.1234 | 1.24413 | 0.622066 | − | 0.782964i | \(-0.286293\pi\) | ||||
0.622066 | + | 0.782964i | \(0.286293\pi\) | |||||||
\(798\) | −2.74907 | −0.0973159 | ||||||||
\(799\) | −0.529837 | −0.0187443 | ||||||||
\(800\) | 32.2990 | 1.14194 | ||||||||
\(801\) | −14.2467 | −0.503382 | ||||||||
\(802\) | −60.3056 | −2.12947 | ||||||||
\(803\) | 25.4831 | 0.899279 | ||||||||
\(804\) | −1.48379 | −0.0523292 | ||||||||
\(805\) | 32.3717 | 1.14095 | ||||||||
\(806\) | 9.51320 | 0.335088 | ||||||||
\(807\) | 0.655115 | 0.0230611 | ||||||||
\(808\) | −0.703804 | −0.0247597 | ||||||||
\(809\) | 19.1133 | 0.671987 | 0.335994 | − | 0.941864i | \(-0.390928\pi\) | ||||
0.335994 | + | 0.941864i | \(0.390928\pi\) | |||||||
\(810\) | 6.17577 | 0.216995 | ||||||||
\(811\) | 10.1460 | 0.356273 | 0.178136 | − | 0.984006i | \(-0.442993\pi\) | ||||
0.178136 | + | 0.984006i | \(0.442993\pi\) | |||||||
\(812\) | −0.660064 | −0.0231637 | ||||||||
\(813\) | −4.32325 | −0.151623 | ||||||||
\(814\) | −75.6597 | −2.65187 | ||||||||
\(815\) | 84.3698 | 2.95534 | ||||||||
\(816\) | 8.89315 | 0.311323 | ||||||||
\(817\) | −5.32167 | −0.186182 | ||||||||
\(818\) | −12.5689 | −0.439462 | ||||||||
\(819\) | 2.66196 | 0.0930163 | ||||||||
\(820\) | 7.59546 | 0.265245 | ||||||||
\(821\) | −40.6747 | −1.41956 | −0.709779 | − | 0.704425i | \(-0.751205\pi\) | ||||
−0.709779 | + | 0.704425i | \(0.751205\pi\) | |||||||
\(822\) | −9.76764 | −0.340686 | ||||||||
\(823\) | 31.2483 | 1.08925 | 0.544624 | − | 0.838681i | \(-0.316673\pi\) | ||||
0.544624 | + | 0.838681i | \(0.316673\pi\) | |||||||
\(824\) | −28.9307 | −1.00785 | ||||||||
\(825\) | 55.8711 | 1.94518 | ||||||||
\(826\) | −12.9167 | −0.449429 | ||||||||
\(827\) | 46.0537 | 1.60144 | 0.800721 | − | 0.599037i | \(-0.204450\pi\) | ||||
0.800721 | + | 0.599037i | \(0.204450\pi\) | |||||||
\(828\) | −5.22274 | −0.181503 | ||||||||
\(829\) | −30.8646 | −1.07197 | −0.535986 | − | 0.844227i | \(-0.680060\pi\) | ||||
−0.535986 | + | 0.844227i | \(0.680060\pi\) | |||||||
\(830\) | −36.9225 | −1.28160 | ||||||||
\(831\) | −19.2556 | −0.667970 | ||||||||
\(832\) | 11.3178 | 0.392374 | ||||||||
\(833\) | 1.83267 | 0.0634983 | ||||||||
\(834\) | −8.42215 | −0.291635 | ||||||||
\(835\) | 34.9216 | 1.20851 | ||||||||
\(836\) | 6.10681 | 0.211209 | ||||||||
\(837\) | 2.20955 | 0.0763733 | ||||||||
\(838\) | −29.6953 | −1.02581 | ||||||||
\(839\) | −8.46162 | −0.292128 | −0.146064 | − | 0.989275i | \(-0.546660\pi\) | ||||
−0.146064 | + | 0.989275i | \(0.546660\pi\) | |||||||
\(840\) | 8.54708 | 0.294902 | ||||||||
\(841\) | −27.8519 | −0.960411 | ||||||||
\(842\) | 24.9648 | 0.860345 | ||||||||
\(843\) | 14.4857 | 0.498912 | ||||||||
\(844\) | 4.29870 | 0.147968 | ||||||||
\(845\) | 22.5814 | 0.776822 | ||||||||
\(846\) | 0.467605 | 0.0160766 | ||||||||
\(847\) | 23.0171 | 0.790876 | ||||||||
\(848\) | −32.6218 | −1.12024 | ||||||||
\(849\) | 23.0964 | 0.792666 | ||||||||
\(850\) | −28.3951 | −0.973945 | ||||||||
\(851\) | 67.9971 | 2.33091 | ||||||||
\(852\) | 6.99137 | 0.239520 | ||||||||
\(853\) | 6.03293 | 0.206563 | 0.103282 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103282 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(854\) | −11.1938 | −0.383044 | ||||||||
\(855\) | 6.48984 | 0.221948 | ||||||||
\(856\) | 6.39503 | 0.218578 | ||||||||
\(857\) | 12.3878 | 0.423159 | 0.211579 | − | 0.977361i | \(-0.432139\pi\) | ||||
0.211579 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(858\) | −25.1114 | −0.857289 | ||||||||
\(859\) | −35.3322 | −1.20552 | −0.602760 | − | 0.797922i | \(-0.705932\pi\) | ||||
−0.602760 | + | 0.797922i | \(0.705932\pi\) | |||||||
\(860\) | −7.36471 | −0.251135 | ||||||||
\(861\) | 3.22910 | 0.110048 | ||||||||
\(862\) | 32.9658 | 1.12282 | ||||||||
\(863\) | −18.1617 | −0.618230 | −0.309115 | − | 0.951025i | \(-0.600033\pi\) | ||||
−0.309115 | + | 0.951025i | \(0.600033\pi\) | |||||||
\(864\) | −3.37171 | −0.114708 | ||||||||
\(865\) | 2.10957 | 0.0717275 | ||||||||
\(866\) | −56.2000 | −1.90975 | ||||||||
\(867\) | 13.6413 | 0.463284 | ||||||||
\(868\) | −1.36115 | −0.0462005 | ||||||||
\(869\) | 28.4147 | 0.963904 | ||||||||
\(870\) | 6.61721 | 0.224345 | ||||||||
\(871\) | 6.41167 | 0.217251 | ||||||||
\(872\) | −15.4776 | −0.524138 | ||||||||
\(873\) | 8.87913 | 0.300513 | ||||||||
\(874\) | −23.3067 | −0.788361 | ||||||||
\(875\) | −17.4855 | −0.591119 | ||||||||
\(876\) | 2.69157 | 0.0909398 | ||||||||
\(877\) | −26.9720 | −0.910780 | −0.455390 | − | 0.890292i | \(-0.650500\pi\) | ||||
−0.455390 | + | 0.890292i | \(0.650500\pi\) | |||||||
\(878\) | −9.48262 | −0.320023 | ||||||||
\(879\) | −28.0899 | −0.947450 | ||||||||
\(880\) | −108.066 | −3.64291 | ||||||||
\(881\) | 29.9656 | 1.00957 | 0.504783 | − | 0.863246i | \(-0.331572\pi\) | ||||
0.504783 | + | 0.863246i | \(0.331572\pi\) | |||||||
\(882\) | −1.61741 | −0.0544612 | ||||||||
\(883\) | −11.7049 | −0.393903 | −0.196951 | − | 0.980413i | \(-0.563104\pi\) | ||||
−0.196951 | + | 0.980413i | \(0.563104\pi\) | |||||||
\(884\) | 3.00530 | 0.101079 | ||||||||
\(885\) | 30.4930 | 1.02501 | ||||||||
\(886\) | −65.2248 | −2.19127 | ||||||||
\(887\) | −1.49587 | −0.0502263 | −0.0251132 | − | 0.999685i | \(-0.507995\pi\) | ||||
−0.0251132 | + | 0.999685i | \(0.507995\pi\) | |||||||
\(888\) | 17.9532 | 0.602471 | ||||||||
\(889\) | −18.0523 | −0.605454 | ||||||||
\(890\) | −87.9843 | −2.94924 | ||||||||
\(891\) | −5.83242 | −0.195393 | ||||||||
\(892\) | −10.0596 | −0.336819 | ||||||||
\(893\) | 0.491385 | 0.0164436 | ||||||||
\(894\) | 2.49871 | 0.0835695 | ||||||||
\(895\) | −25.2216 | −0.843063 | ||||||||
\(896\) | −13.6202 | −0.455017 | ||||||||
\(897\) | 22.5682 | 0.753530 | ||||||||
\(898\) | 11.0694 | 0.369392 | ||||||||
\(899\) | 2.36749 | 0.0789602 | ||||||||
\(900\) | 5.90120 | 0.196707 | ||||||||
\(901\) | 12.3203 | 0.410448 | ||||||||
\(902\) | −30.4615 | −1.01426 | ||||||||
\(903\) | −3.13100 | −0.104193 | ||||||||
\(904\) | −35.7794 | −1.19001 | ||||||||
\(905\) | −54.7939 | −1.82141 | ||||||||
\(906\) | 9.73758 | 0.323509 | ||||||||
\(907\) | 36.7886 | 1.22154 | 0.610772 | − | 0.791806i | \(-0.290859\pi\) | ||||
0.610772 | + | 0.791806i | \(0.290859\pi\) | |||||||
\(908\) | −2.11594 | −0.0702200 | ||||||||
\(909\) | −0.314415 | −0.0104285 | ||||||||
\(910\) | 16.4396 | 0.544969 | ||||||||
\(911\) | −4.99085 | −0.165354 | −0.0826771 | − | 0.996576i | \(-0.526347\pi\) | ||||
−0.0826771 | + | 0.996576i | \(0.526347\pi\) | |||||||
\(912\) | −8.24775 | −0.273110 | ||||||||
\(913\) | 34.8697 | 1.15402 | ||||||||
\(914\) | 31.0486 | 1.02700 | ||||||||
\(915\) | 26.4257 | 0.873606 | ||||||||
\(916\) | −0.665381 | −0.0219848 | ||||||||
\(917\) | −22.4093 | −0.740019 | ||||||||
\(918\) | 2.96419 | 0.0978328 | ||||||||
\(919\) | −9.44433 | −0.311540 | −0.155770 | − | 0.987793i | \(-0.549786\pi\) | ||||
−0.155770 | + | 0.987793i | \(0.549786\pi\) | |||||||
\(920\) | 72.4625 | 2.38902 | ||||||||
\(921\) | 13.8386 | 0.455997 | ||||||||
\(922\) | 15.3491 | 0.505497 | ||||||||
\(923\) | −30.2107 | −0.994398 | ||||||||
\(924\) | 3.59295 | 0.118199 | ||||||||
\(925\) | −76.8304 | −2.52617 | ||||||||
\(926\) | −35.1570 | −1.15533 | ||||||||
\(927\) | −12.9244 | −0.424493 | ||||||||
\(928\) | −3.61272 | −0.118593 | ||||||||
\(929\) | −46.1310 | −1.51351 | −0.756755 | − | 0.653699i | \(-0.773216\pi\) | ||||
−0.756755 | + | 0.653699i | \(0.773216\pi\) | |||||||
\(930\) | 13.6457 | 0.447460 | ||||||||
\(931\) | −1.69967 | −0.0557043 | ||||||||
\(932\) | 9.19255 | 0.301112 | ||||||||
\(933\) | −15.6609 | −0.512715 | ||||||||
\(934\) | −16.7843 | −0.549199 | ||||||||
\(935\) | 40.8134 | 1.33474 | ||||||||
\(936\) | 5.95867 | 0.194765 | ||||||||
\(937\) | 19.8670 | 0.649026 | 0.324513 | − | 0.945881i | \(-0.394800\pi\) | ||||
0.324513 | + | 0.945881i | \(0.394800\pi\) | |||||||
\(938\) | −3.89575 | −0.127201 | ||||||||
\(939\) | 9.07104 | 0.296022 | ||||||||
\(940\) | 0.680033 | 0.0221802 | ||||||||
\(941\) | −11.9238 | −0.388703 | −0.194352 | − | 0.980932i | \(-0.562260\pi\) | ||||
−0.194352 | + | 0.980932i | \(0.562260\pi\) | |||||||
\(942\) | −28.3427 | −0.923454 | ||||||||
\(943\) | 27.3765 | 0.891501 | ||||||||
\(944\) | −38.7527 | −1.26129 | ||||||||
\(945\) | 3.81830 | 0.124209 | ||||||||
\(946\) | 29.5361 | 0.960303 | ||||||||
\(947\) | 36.3155 | 1.18009 | 0.590047 | − | 0.807369i | \(-0.299109\pi\) | ||||
0.590047 | + | 0.807369i | \(0.299109\pi\) | |||||||
\(948\) | 3.00122 | 0.0974750 | ||||||||
\(949\) | −11.6307 | −0.377548 | ||||||||
\(950\) | 26.3344 | 0.854401 | ||||||||
\(951\) | −28.5237 | −0.924945 | ||||||||
\(952\) | 4.10235 | 0.132958 | ||||||||
\(953\) | 32.9455 | 1.06721 | 0.533605 | − | 0.845734i | \(-0.320837\pi\) | ||||
0.533605 | + | 0.845734i | \(0.320837\pi\) | |||||||
\(954\) | −10.8732 | −0.352033 | ||||||||
\(955\) | −42.5159 | −1.37578 | ||||||||
\(956\) | −6.69853 | −0.216646 | ||||||||
\(957\) | −6.24932 | −0.202012 | ||||||||
\(958\) | 42.7095 | 1.37988 | ||||||||
\(959\) | −6.03905 | −0.195011 | ||||||||
\(960\) | 16.2342 | 0.523956 | ||||||||
\(961\) | −26.1179 | −0.842512 | ||||||||
\(962\) | 34.5317 | 1.11335 | ||||||||
\(963\) | 2.85690 | 0.0920623 | ||||||||
\(964\) | 7.83462 | 0.252336 | ||||||||
\(965\) | 33.3928 | 1.07495 | ||||||||
\(966\) | −13.7125 | −0.441193 | ||||||||
\(967\) | 20.0960 | 0.646245 | 0.323123 | − | 0.946357i | \(-0.395267\pi\) | ||||
0.323123 | + | 0.946357i | \(0.395267\pi\) | |||||||
\(968\) | 51.5226 | 1.65600 | ||||||||
\(969\) | 3.11493 | 0.100066 | ||||||||
\(970\) | 54.8355 | 1.76066 | ||||||||
\(971\) | 32.6097 | 1.04649 | 0.523247 | − | 0.852181i | \(-0.324721\pi\) | ||||
0.523247 | + | 0.852181i | \(0.324721\pi\) | |||||||
\(972\) | −0.616031 | −0.0197592 | ||||||||
\(973\) | −5.20717 | −0.166934 | ||||||||
\(974\) | −61.4463 | −1.96887 | ||||||||
\(975\) | −25.5000 | −0.816652 | ||||||||
\(976\) | −33.5837 | −1.07499 | ||||||||
\(977\) | 44.6229 | 1.42761 | 0.713807 | − | 0.700342i | \(-0.246969\pi\) | ||||
0.713807 | + | 0.700342i | \(0.246969\pi\) | |||||||
\(978\) | −35.7387 | −1.14280 | ||||||||
\(979\) | 83.0926 | 2.65565 | ||||||||
\(980\) | −2.35219 | −0.0751379 | ||||||||
\(981\) | −6.91442 | −0.220761 | ||||||||
\(982\) | 19.7106 | 0.628991 | ||||||||
\(983\) | −21.0947 | −0.672815 | −0.336408 | − | 0.941716i | \(-0.609212\pi\) | ||||
−0.336408 | + | 0.941716i | \(0.609212\pi\) | |||||||
\(984\) | 7.22820 | 0.230426 | ||||||||
\(985\) | −6.87181 | −0.218954 | ||||||||
\(986\) | 3.17607 | 0.101147 | ||||||||
\(987\) | 0.289107 | 0.00920236 | ||||||||
\(988\) | −2.78719 | −0.0886725 | ||||||||
\(989\) | −26.5448 | −0.844076 | ||||||||
\(990\) | −36.0197 | −1.14478 | ||||||||
\(991\) | 14.6930 | 0.466739 | 0.233369 | − | 0.972388i | \(-0.425025\pi\) | ||||
0.233369 | + | 0.972388i | \(0.425025\pi\) | |||||||
\(992\) | −7.44997 | −0.236537 | ||||||||
\(993\) | −17.1939 | −0.545633 | ||||||||
\(994\) | 18.3561 | 0.582221 | ||||||||
\(995\) | 34.7342 | 1.10115 | ||||||||
\(996\) | 3.68301 | 0.116701 | ||||||||
\(997\) | 22.1576 | 0.701740 | 0.350870 | − | 0.936424i | \(-0.385886\pi\) | ||||
0.350870 | + | 0.936424i | \(0.385886\pi\) | |||||||
\(998\) | 33.4364 | 1.05841 | ||||||||
\(999\) | 8.02038 | 0.253754 |
(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 | 8043.2.a.t.1.14 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.14 | ✓ | 52 | 1.1 | even | 1 | trivial |