Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.49813\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49813 | −1.76645 | −0.883224 | − | 0.468952i | \(-0.844632\pi\) | ||||
−0.883224 | + | 0.468952i | \(0.844632\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.24068 | 2.12034 | ||||||||
\(5\) | −2.35199 | −1.05184 | −0.525920 | − | 0.850534i | \(-0.676279\pi\) | ||||
−0.525920 | + | 0.850534i | \(0.676279\pi\) | |||||||
\(6\) | −2.49813 | −1.01986 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −5.59751 | −1.97902 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.87558 | 1.85802 | ||||||||
\(11\) | −5.16537 | −1.55742 | −0.778709 | − | 0.627385i | \(-0.784125\pi\) | ||||
−0.778709 | + | 0.627385i | \(0.784125\pi\) | |||||||
\(12\) | 4.24068 | 1.22418 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.49813 | −0.667654 | ||||||||
\(15\) | −2.35199 | −0.607280 | ||||||||
\(16\) | 5.50198 | 1.37549 | ||||||||
\(17\) | −1.70559 | −0.413665 | −0.206833 | − | 0.978376i | \(-0.566316\pi\) | ||||
−0.206833 | + | 0.978376i | \(0.566316\pi\) | |||||||
\(18\) | −2.49813 | −0.588816 | ||||||||
\(19\) | 8.02484 | 1.84102 | 0.920512 | − | 0.390715i | \(-0.127772\pi\) | ||||
0.920512 | + | 0.390715i | \(0.127772\pi\) | |||||||
\(20\) | −9.97401 | −2.23026 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 12.9038 | 2.75110 | ||||||||
\(23\) | 4.21818 | 0.879552 | 0.439776 | − | 0.898108i | \(-0.355058\pi\) | ||||
0.439776 | + | 0.898108i | \(0.355058\pi\) | |||||||
\(24\) | −5.59751 | −1.14259 | ||||||||
\(25\) | 0.531841 | 0.106368 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.24068 | 0.801412 | ||||||||
\(29\) | −5.24033 | −0.973104 | −0.486552 | − | 0.873652i | \(-0.661746\pi\) | ||||
−0.486552 | + | 0.873652i | \(0.661746\pi\) | |||||||
\(30\) | 5.87558 | 1.07273 | ||||||||
\(31\) | −1.11538 | −0.200328 | −0.100164 | − | 0.994971i | \(-0.531937\pi\) | ||||
−0.100164 | + | 0.994971i | \(0.531937\pi\) | |||||||
\(32\) | −2.54966 | −0.450720 | ||||||||
\(33\) | −5.16537 | −0.899176 | ||||||||
\(34\) | 4.26078 | 0.730718 | ||||||||
\(35\) | −2.35199 | −0.397558 | ||||||||
\(36\) | 4.24068 | 0.706779 | ||||||||
\(37\) | −8.21263 | −1.35015 | −0.675074 | − | 0.737750i | \(-0.735888\pi\) | ||||
−0.675074 | + | 0.737750i | \(0.735888\pi\) | |||||||
\(38\) | −20.0471 | −3.25207 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.1653 | 2.08161 | ||||||||
\(41\) | 6.75466 | 1.05490 | 0.527450 | − | 0.849586i | \(-0.323148\pi\) | ||||
0.527450 | + | 0.849586i | \(0.323148\pi\) | |||||||
\(42\) | −2.49813 | −0.385470 | ||||||||
\(43\) | −0.965145 | −0.147183 | −0.0735916 | − | 0.997288i | \(-0.523446\pi\) | ||||
−0.0735916 | + | 0.997288i | \(0.523446\pi\) | |||||||
\(44\) | −21.9047 | −3.30225 | ||||||||
\(45\) | −2.35199 | −0.350613 | ||||||||
\(46\) | −10.5376 | −1.55368 | ||||||||
\(47\) | −9.18662 | −1.34001 | −0.670003 | − | 0.742358i | \(-0.733707\pi\) | ||||
−0.670003 | + | 0.742358i | \(0.733707\pi\) | |||||||
\(48\) | 5.50198 | 0.794142 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.32861 | −0.187894 | ||||||||
\(51\) | −1.70559 | −0.238830 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9257 | 1.63812 | 0.819059 | − | 0.573709i | \(-0.194496\pi\) | ||||
0.819059 | + | 0.573709i | \(0.194496\pi\) | |||||||
\(54\) | −2.49813 | −0.339953 | ||||||||
\(55\) | 12.1489 | 1.63816 | ||||||||
\(56\) | −5.59751 | −0.747998 | ||||||||
\(57\) | 8.02484 | 1.06292 | ||||||||
\(58\) | 13.0910 | 1.71894 | ||||||||
\(59\) | 2.98003 | 0.387966 | 0.193983 | − | 0.981005i | \(-0.437859\pi\) | ||||
0.193983 | + | 0.981005i | \(0.437859\pi\) | |||||||
\(60\) | −9.97401 | −1.28764 | ||||||||
\(61\) | −14.6034 | −1.86977 | −0.934884 | − | 0.354954i | \(-0.884497\pi\) | ||||
−0.934884 | + | 0.354954i | \(0.884497\pi\) | |||||||
\(62\) | 2.78637 | 0.353869 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −4.63456 | −0.579320 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.9038 | 1.58835 | ||||||||
\(67\) | 13.5464 | 1.65496 | 0.827478 | − | 0.561499i | \(-0.189775\pi\) | ||||
0.827478 | + | 0.561499i | \(0.189775\pi\) | |||||||
\(68\) | −7.23283 | −0.877110 | ||||||||
\(69\) | 4.21818 | 0.507809 | ||||||||
\(70\) | 5.87558 | 0.702266 | ||||||||
\(71\) | −0.318196 | −0.0377629 | −0.0188814 | − | 0.999822i | \(-0.506011\pi\) | ||||
−0.0188814 | + | 0.999822i | \(0.506011\pi\) | |||||||
\(72\) | −5.59751 | −0.659673 | ||||||||
\(73\) | 0.542709 | 0.0635193 | 0.0317596 | − | 0.999496i | \(-0.489889\pi\) | ||||
0.0317596 | + | 0.999496i | \(0.489889\pi\) | |||||||
\(74\) | 20.5162 | 2.38496 | ||||||||
\(75\) | 0.531841 | 0.0614117 | ||||||||
\(76\) | 34.0307 | 3.90359 | ||||||||
\(77\) | −5.16537 | −0.588649 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.2301 | −1.48850 | −0.744249 | − | 0.667903i | \(-0.767192\pi\) | ||||
−0.744249 | + | 0.667903i | \(0.767192\pi\) | |||||||
\(80\) | −12.9406 | −1.44680 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.8740 | −1.86343 | ||||||||
\(83\) | −5.79295 | −0.635859 | −0.317930 | − | 0.948114i | \(-0.602988\pi\) | ||||
−0.317930 | + | 0.948114i | \(0.602988\pi\) | |||||||
\(84\) | 4.24068 | 0.462696 | ||||||||
\(85\) | 4.01151 | 0.435110 | ||||||||
\(86\) | 2.41106 | 0.259991 | ||||||||
\(87\) | −5.24033 | −0.561822 | ||||||||
\(88\) | 28.9132 | 3.08216 | ||||||||
\(89\) | 7.80950 | 0.827805 | 0.413902 | − | 0.910321i | \(-0.364165\pi\) | ||||
0.413902 | + | 0.910321i | \(0.364165\pi\) | |||||||
\(90\) | 5.87558 | 0.619340 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 17.8879 | 1.86495 | ||||||||
\(93\) | −1.11538 | −0.115660 | ||||||||
\(94\) | 22.9494 | 2.36705 | ||||||||
\(95\) | −18.8743 | −1.93646 | ||||||||
\(96\) | −2.54966 | −0.260224 | ||||||||
\(97\) | 0.287042 | 0.0291447 | 0.0145723 | − | 0.999894i | \(-0.495361\pi\) | ||||
0.0145723 | + | 0.999894i | \(0.495361\pi\) | |||||||
\(98\) | −2.49813 | −0.252350 | ||||||||
\(99\) | −5.16537 | −0.519140 | ||||||||
\(100\) | 2.25536 | 0.225536 | ||||||||
\(101\) | 12.9536 | 1.28893 | 0.644467 | − | 0.764632i | \(-0.277079\pi\) | ||||
0.644467 | + | 0.764632i | \(0.277079\pi\) | |||||||
\(102\) | 4.26078 | 0.421880 | ||||||||
\(103\) | −6.53676 | −0.644086 | −0.322043 | − | 0.946725i | \(-0.604370\pi\) | ||||
−0.322043 | + | 0.946725i | \(0.604370\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.35199 | −0.229530 | ||||||||
\(106\) | −29.7919 | −2.89365 | ||||||||
\(107\) | −3.73899 | −0.361462 | −0.180731 | − | 0.983533i | \(-0.557846\pi\) | ||||
−0.180731 | + | 0.983533i | \(0.557846\pi\) | |||||||
\(108\) | 4.24068 | 0.408059 | ||||||||
\(109\) | 10.1278 | 0.970066 | 0.485033 | − | 0.874496i | \(-0.338808\pi\) | ||||
0.485033 | + | 0.874496i | \(0.338808\pi\) | |||||||
\(110\) | −30.3496 | −2.89372 | ||||||||
\(111\) | −8.21263 | −0.779508 | ||||||||
\(112\) | 5.50198 | 0.519888 | ||||||||
\(113\) | 16.5267 | 1.55471 | 0.777353 | − | 0.629065i | \(-0.216562\pi\) | ||||
0.777353 | + | 0.629065i | \(0.216562\pi\) | |||||||
\(114\) | −20.0471 | −1.87758 | ||||||||
\(115\) | −9.92111 | −0.925148 | ||||||||
\(116\) | −22.2225 | −2.06331 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.44450 | −0.685322 | ||||||||
\(119\) | −1.70559 | −0.156351 | ||||||||
\(120\) | 13.1653 | 1.20182 | ||||||||
\(121\) | 15.6811 | 1.42555 | ||||||||
\(122\) | 36.4811 | 3.30285 | ||||||||
\(123\) | 6.75466 | 0.609047 | ||||||||
\(124\) | −4.72996 | −0.424763 | ||||||||
\(125\) | 10.5091 | 0.939958 | ||||||||
\(126\) | −2.49813 | −0.222551 | ||||||||
\(127\) | 13.8279 | 1.22703 | 0.613516 | − | 0.789682i | \(-0.289755\pi\) | ||||
0.613516 | + | 0.789682i | \(0.289755\pi\) | |||||||
\(128\) | 16.6771 | 1.47406 | ||||||||
\(129\) | −0.965145 | −0.0849762 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.92612 | 0.867249 | 0.433624 | − | 0.901094i | \(-0.357234\pi\) | ||||
0.433624 | + | 0.901094i | \(0.357234\pi\) | |||||||
\(132\) | −21.9047 | −1.90656 | ||||||||
\(133\) | 8.02484 | 0.695842 | ||||||||
\(134\) | −33.8407 | −2.92339 | ||||||||
\(135\) | −2.35199 | −0.202427 | ||||||||
\(136\) | 9.54703 | 0.818651 | ||||||||
\(137\) | −8.60954 | −0.735563 | −0.367781 | − | 0.929912i | \(-0.619883\pi\) | ||||
−0.367781 | + | 0.929912i | \(0.619883\pi\) | |||||||
\(138\) | −10.5376 | −0.897019 | ||||||||
\(139\) | −9.92269 | −0.841631 | −0.420816 | − | 0.907146i | \(-0.638256\pi\) | ||||
−0.420816 | + | 0.907146i | \(0.638256\pi\) | |||||||
\(140\) | −9.97401 | −0.842958 | ||||||||
\(141\) | −9.18662 | −0.773653 | ||||||||
\(142\) | 0.794896 | 0.0667062 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.50198 | 0.458498 | ||||||||
\(145\) | 12.3252 | 1.02355 | ||||||||
\(146\) | −1.35576 | −0.112203 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −34.8271 | −2.86277 | ||||||||
\(149\) | 0.253154 | 0.0207392 | 0.0103696 | − | 0.999946i | \(-0.496699\pi\) | ||||
0.0103696 | + | 0.999946i | \(0.496699\pi\) | |||||||
\(150\) | −1.32861 | −0.108481 | ||||||||
\(151\) | 19.1942 | 1.56200 | 0.780999 | − | 0.624532i | \(-0.214710\pi\) | ||||
0.780999 | + | 0.624532i | \(0.214710\pi\) | |||||||
\(152\) | −44.9191 | −3.64342 | ||||||||
\(153\) | −1.70559 | −0.137888 | ||||||||
\(154\) | 12.9038 | 1.03982 | ||||||||
\(155\) | 2.62336 | 0.210713 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.8981 | −1.18900 | −0.594500 | − | 0.804096i | \(-0.702650\pi\) | ||||
−0.594500 | + | 0.804096i | \(0.702650\pi\) | |||||||
\(158\) | 33.0505 | 2.62935 | ||||||||
\(159\) | 11.9257 | 0.945768 | ||||||||
\(160\) | 5.99676 | 0.474086 | ||||||||
\(161\) | 4.21818 | 0.332439 | ||||||||
\(162\) | −2.49813 | −0.196272 | ||||||||
\(163\) | 5.80688 | 0.454830 | 0.227415 | − | 0.973798i | \(-0.426973\pi\) | ||||
0.227415 | + | 0.973798i | \(0.426973\pi\) | |||||||
\(164\) | 28.6443 | 2.23674 | ||||||||
\(165\) | 12.1489 | 0.945790 | ||||||||
\(166\) | 14.4716 | 1.12321 | ||||||||
\(167\) | −21.4231 | −1.65777 | −0.828885 | − | 0.559419i | \(-0.811024\pi\) | ||||
−0.828885 | + | 0.559419i | \(0.811024\pi\) | |||||||
\(168\) | −5.59751 | −0.431857 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −10.0213 | −0.768599 | ||||||||
\(171\) | 8.02484 | 0.613675 | ||||||||
\(172\) | −4.09286 | −0.312078 | ||||||||
\(173\) | 21.4128 | 1.62798 | 0.813991 | − | 0.580878i | \(-0.197290\pi\) | ||||
0.813991 | + | 0.580878i | \(0.197290\pi\) | |||||||
\(174\) | 13.0910 | 0.992429 | ||||||||
\(175\) | 0.531841 | 0.0402034 | ||||||||
\(176\) | −28.4198 | −2.14222 | ||||||||
\(177\) | 2.98003 | 0.223992 | ||||||||
\(178\) | −19.5092 | −1.46227 | ||||||||
\(179\) | 5.04689 | 0.377222 | 0.188611 | − | 0.982052i | \(-0.439601\pi\) | ||||
0.188611 | + | 0.982052i | \(0.439601\pi\) | |||||||
\(180\) | −9.97401 | −0.743419 | ||||||||
\(181\) | 15.8878 | 1.18093 | 0.590464 | − | 0.807064i | \(-0.298945\pi\) | ||||
0.590464 | + | 0.807064i | \(0.298945\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.6034 | −1.07951 | ||||||||
\(184\) | −23.6113 | −1.74065 | ||||||||
\(185\) | 19.3160 | 1.42014 | ||||||||
\(186\) | 2.78637 | 0.204306 | ||||||||
\(187\) | 8.80999 | 0.644250 | ||||||||
\(188\) | −38.9575 | −2.84127 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 47.1506 | 3.42066 | ||||||||
\(191\) | 13.3753 | 0.967801 | 0.483901 | − | 0.875123i | \(-0.339220\pi\) | ||||
0.483901 | + | 0.875123i | \(0.339220\pi\) | |||||||
\(192\) | −4.63456 | −0.334471 | ||||||||
\(193\) | 6.66748 | 0.479935 | 0.239968 | − | 0.970781i | \(-0.422863\pi\) | ||||
0.239968 | + | 0.970781i | \(0.422863\pi\) | |||||||
\(194\) | −0.717068 | −0.0514825 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.24068 | 0.302905 | ||||||||
\(197\) | −12.3543 | −0.880210 | −0.440105 | − | 0.897946i | \(-0.645059\pi\) | ||||
−0.440105 | + | 0.897946i | \(0.645059\pi\) | |||||||
\(198\) | 12.9038 | 0.917033 | ||||||||
\(199\) | −14.5437 | −1.03098 | −0.515488 | − | 0.856897i | \(-0.672389\pi\) | ||||
−0.515488 | + | 0.856897i | \(0.672389\pi\) | |||||||
\(200\) | −2.97698 | −0.210505 | ||||||||
\(201\) | 13.5464 | 0.955489 | ||||||||
\(202\) | −32.3599 | −2.27683 | ||||||||
\(203\) | −5.24033 | −0.367799 | ||||||||
\(204\) | −7.23283 | −0.506400 | ||||||||
\(205\) | −15.8869 | −1.10959 | ||||||||
\(206\) | 16.3297 | 1.13774 | ||||||||
\(207\) | 4.21818 | 0.293184 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.4513 | −2.86725 | ||||||||
\(210\) | 5.87558 | 0.405453 | ||||||||
\(211\) | 25.6088 | 1.76298 | 0.881491 | − | 0.472200i | \(-0.156540\pi\) | ||||
0.881491 | + | 0.472200i | \(0.156540\pi\) | |||||||
\(212\) | 50.5729 | 3.47336 | ||||||||
\(213\) | −0.318196 | −0.0218024 | ||||||||
\(214\) | 9.34050 | 0.638503 | ||||||||
\(215\) | 2.27001 | 0.154813 | ||||||||
\(216\) | −5.59751 | −0.380862 | ||||||||
\(217\) | −1.11538 | −0.0757169 | ||||||||
\(218\) | −25.3006 | −1.71357 | ||||||||
\(219\) | 0.542709 | 0.0366729 | ||||||||
\(220\) | 51.5195 | 3.47344 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 20.5162 | 1.37696 | ||||||||
\(223\) | −8.99291 | −0.602210 | −0.301105 | − | 0.953591i | \(-0.597355\pi\) | ||||
−0.301105 | + | 0.953591i | \(0.597355\pi\) | |||||||
\(224\) | −2.54966 | −0.170356 | ||||||||
\(225\) | 0.531841 | 0.0354561 | ||||||||
\(226\) | −41.2860 | −2.74631 | ||||||||
\(227\) | −4.16233 | −0.276263 | −0.138132 | − | 0.990414i | \(-0.544110\pi\) | ||||
−0.138132 | + | 0.990414i | \(0.544110\pi\) | |||||||
\(228\) | 34.0307 | 2.25374 | ||||||||
\(229\) | −8.47202 | −0.559847 | −0.279924 | − | 0.960022i | \(-0.590309\pi\) | ||||
−0.279924 | + | 0.960022i | \(0.590309\pi\) | |||||||
\(230\) | 24.7843 | 1.63423 | ||||||||
\(231\) | −5.16537 | −0.339857 | ||||||||
\(232\) | 29.3328 | 1.92579 | ||||||||
\(233\) | −18.5357 | −1.21432 | −0.607158 | − | 0.794581i | \(-0.707691\pi\) | ||||
−0.607158 | + | 0.794581i | \(0.707691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.6068 | 1.40947 | ||||||||
\(236\) | 12.6373 | 0.822620 | ||||||||
\(237\) | −13.2301 | −0.859384 | ||||||||
\(238\) | 4.26078 | 0.276185 | ||||||||
\(239\) | 0.176911 | 0.0114434 | 0.00572171 | − | 0.999984i | \(-0.498179\pi\) | ||||
0.00572171 | + | 0.999984i | \(0.498179\pi\) | |||||||
\(240\) | −12.9406 | −0.835310 | ||||||||
\(241\) | 4.99572 | 0.321803 | 0.160901 | − | 0.986970i | \(-0.448560\pi\) | ||||
0.160901 | + | 0.986970i | \(0.448560\pi\) | |||||||
\(242\) | −39.1735 | −2.51817 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −61.9281 | −3.96454 | ||||||||
\(245\) | −2.35199 | −0.150263 | ||||||||
\(246\) | −16.8740 | −1.07585 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.24335 | 0.396453 | ||||||||
\(249\) | −5.79295 | −0.367113 | ||||||||
\(250\) | −26.2530 | −1.66039 | ||||||||
\(251\) | 0.560900 | 0.0354037 | 0.0177019 | − | 0.999843i | \(-0.494365\pi\) | ||||
0.0177019 | + | 0.999843i | \(0.494365\pi\) | |||||||
\(252\) | 4.24068 | 0.267137 | ||||||||
\(253\) | −21.7885 | −1.36983 | ||||||||
\(254\) | −34.5441 | −2.16749 | ||||||||
\(255\) | 4.01151 | 0.251211 | ||||||||
\(256\) | −32.3924 | −2.02453 | ||||||||
\(257\) | −16.9596 | −1.05791 | −0.528954 | − | 0.848650i | \(-0.677416\pi\) | ||||
−0.528954 | + | 0.848650i | \(0.677416\pi\) | |||||||
\(258\) | 2.41106 | 0.150106 | ||||||||
\(259\) | −8.21263 | −0.510308 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.24033 | −0.324368 | ||||||||
\(262\) | −24.7968 | −1.53195 | ||||||||
\(263\) | 7.29257 | 0.449679 | 0.224839 | − | 0.974396i | \(-0.427814\pi\) | ||||
0.224839 | + | 0.974396i | \(0.427814\pi\) | |||||||
\(264\) | 28.9132 | 1.77949 | ||||||||
\(265\) | −28.0490 | −1.72304 | ||||||||
\(266\) | −20.0471 | −1.22917 | ||||||||
\(267\) | 7.80950 | 0.477933 | ||||||||
\(268\) | 57.4459 | 3.50906 | ||||||||
\(269\) | 1.71166 | 0.104362 | 0.0521809 | − | 0.998638i | \(-0.483383\pi\) | ||||
0.0521809 | + | 0.998638i | \(0.483383\pi\) | |||||||
\(270\) | 5.87558 | 0.357576 | ||||||||
\(271\) | 12.2573 | 0.744575 | 0.372288 | − | 0.928117i | \(-0.378573\pi\) | ||||
0.372288 | + | 0.928117i | \(0.378573\pi\) | |||||||
\(272\) | −9.38409 | −0.568994 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.5078 | 1.29933 | ||||||||
\(275\) | −2.74716 | −0.165660 | ||||||||
\(276\) | 17.8879 | 1.07673 | ||||||||
\(277\) | 32.0290 | 1.92444 | 0.962218 | − | 0.272279i | \(-0.0877775\pi\) | ||||
0.962218 | + | 0.272279i | \(0.0877775\pi\) | |||||||
\(278\) | 24.7882 | 1.48670 | ||||||||
\(279\) | −1.11538 | −0.0667761 | ||||||||
\(280\) | 13.1653 | 0.786775 | ||||||||
\(281\) | 25.3153 | 1.51018 | 0.755091 | − | 0.655620i | \(-0.227592\pi\) | ||||
0.755091 | + | 0.655620i | \(0.227592\pi\) | |||||||
\(282\) | 22.9494 | 1.36662 | ||||||||
\(283\) | −8.29593 | −0.493142 | −0.246571 | − | 0.969125i | \(-0.579304\pi\) | ||||
−0.246571 | + | 0.969125i | \(0.579304\pi\) | |||||||
\(284\) | −1.34937 | −0.0800701 | ||||||||
\(285\) | −18.8743 | −1.11802 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.75466 | 0.398715 | ||||||||
\(288\) | −2.54966 | −0.150240 | ||||||||
\(289\) | −14.0910 | −0.828881 | ||||||||
\(290\) | −30.7900 | −1.80805 | ||||||||
\(291\) | 0.287042 | 0.0168267 | ||||||||
\(292\) | 2.30145 | 0.134682 | ||||||||
\(293\) | 26.9892 | 1.57672 | 0.788362 | − | 0.615211i | \(-0.210929\pi\) | ||||
0.788362 | + | 0.615211i | \(0.210929\pi\) | |||||||
\(294\) | −2.49813 | −0.145694 | ||||||||
\(295\) | −7.00898 | −0.408079 | ||||||||
\(296\) | 45.9702 | 2.67197 | ||||||||
\(297\) | −5.16537 | −0.299725 | ||||||||
\(298\) | −0.632414 | −0.0366348 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.25536 | 0.130214 | ||||||||
\(301\) | −0.965145 | −0.0556300 | ||||||||
\(302\) | −47.9496 | −2.75919 | ||||||||
\(303\) | 12.9536 | 0.744166 | ||||||||
\(304\) | 44.1525 | 2.53232 | ||||||||
\(305\) | 34.3469 | 1.96670 | ||||||||
\(306\) | 4.26078 | 0.243573 | ||||||||
\(307\) | 7.63819 | 0.435935 | 0.217967 | − | 0.975956i | \(-0.430057\pi\) | ||||
0.217967 | + | 0.975956i | \(0.430057\pi\) | |||||||
\(308\) | −21.9047 | −1.24813 | ||||||||
\(309\) | −6.53676 | −0.371863 | ||||||||
\(310\) | −6.55350 | −0.372214 | ||||||||
\(311\) | −3.99085 | −0.226301 | −0.113150 | − | 0.993578i | \(-0.536094\pi\) | ||||
−0.113150 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.1267 | 0.628920 | 0.314460 | − | 0.949271i | \(-0.398177\pi\) | ||||
0.314460 | + | 0.949271i | \(0.398177\pi\) | |||||||
\(314\) | 37.2175 | 2.10031 | ||||||||
\(315\) | −2.35199 | −0.132519 | ||||||||
\(316\) | −56.1044 | −3.15612 | ||||||||
\(317\) | −6.72186 | −0.377537 | −0.188769 | − | 0.982022i | \(-0.560450\pi\) | ||||
−0.188769 | + | 0.982022i | \(0.560450\pi\) | |||||||
\(318\) | −29.7919 | −1.67065 | ||||||||
\(319\) | 27.0682 | 1.51553 | ||||||||
\(320\) | 10.9004 | 0.609352 | ||||||||
\(321\) | −3.73899 | −0.208690 | ||||||||
\(322\) | −10.5376 | −0.587237 | ||||||||
\(323\) | −13.6870 | −0.761567 | ||||||||
\(324\) | 4.24068 | 0.235593 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.5064 | −0.803434 | ||||||||
\(327\) | 10.1278 | 0.560068 | ||||||||
\(328\) | −37.8092 | −2.08767 | ||||||||
\(329\) | −9.18662 | −0.506475 | ||||||||
\(330\) | −30.3496 | −1.67069 | ||||||||
\(331\) | 19.4811 | 1.07078 | 0.535390 | − | 0.844605i | \(-0.320165\pi\) | ||||
0.535390 | + | 0.844605i | \(0.320165\pi\) | |||||||
\(332\) | −24.5660 | −1.34824 | ||||||||
\(333\) | −8.21263 | −0.450049 | ||||||||
\(334\) | 53.5178 | 2.92836 | ||||||||
\(335\) | −31.8609 | −1.74075 | ||||||||
\(336\) | 5.50198 | 0.300157 | ||||||||
\(337\) | −6.57866 | −0.358362 | −0.179181 | − | 0.983816i | \(-0.557345\pi\) | ||||
−0.179181 | + | 0.983816i | \(0.557345\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.5267 | 0.897609 | ||||||||
\(340\) | 17.0115 | 0.922580 | ||||||||
\(341\) | 5.76136 | 0.311995 | ||||||||
\(342\) | −20.0471 | −1.08402 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.40240 | 0.291278 | ||||||||
\(345\) | −9.92111 | −0.534134 | ||||||||
\(346\) | −53.4920 | −2.87575 | ||||||||
\(347\) | 13.4028 | 0.719498 | 0.359749 | − | 0.933049i | \(-0.382862\pi\) | ||||
0.359749 | + | 0.933049i | \(0.382862\pi\) | |||||||
\(348\) | −22.2225 | −1.19125 | ||||||||
\(349\) | 16.3285 | 0.874045 | 0.437022 | − | 0.899451i | \(-0.356033\pi\) | ||||
0.437022 | + | 0.899451i | \(0.356033\pi\) | |||||||
\(350\) | −1.32861 | −0.0710172 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.1699 | 0.701960 | ||||||||
\(353\) | 21.5374 | 1.14632 | 0.573161 | − | 0.819443i | \(-0.305717\pi\) | ||||
0.573161 | + | 0.819443i | \(0.305717\pi\) | |||||||
\(354\) | −7.44450 | −0.395671 | ||||||||
\(355\) | 0.748392 | 0.0397205 | ||||||||
\(356\) | 33.1175 | 1.75523 | ||||||||
\(357\) | −1.70559 | −0.0902691 | ||||||||
\(358\) | −12.6078 | −0.666344 | ||||||||
\(359\) | −31.8829 | −1.68272 | −0.841358 | − | 0.540478i | \(-0.818243\pi\) | ||||
−0.841358 | + | 0.540478i | \(0.818243\pi\) | |||||||
\(360\) | 13.1653 | 0.693870 | ||||||||
\(361\) | 45.3980 | 2.38937 | ||||||||
\(362\) | −39.6898 | −2.08605 | ||||||||
\(363\) | 15.6811 | 0.823044 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.27644 | −0.0668122 | ||||||||
\(366\) | 36.4811 | 1.90690 | ||||||||
\(367\) | 14.9500 | 0.780381 | 0.390191 | − | 0.920734i | \(-0.372409\pi\) | ||||
0.390191 | + | 0.920734i | \(0.372409\pi\) | |||||||
\(368\) | 23.2083 | 1.20982 | ||||||||
\(369\) | 6.75466 | 0.351633 | ||||||||
\(370\) | −48.2539 | −2.50860 | ||||||||
\(371\) | 11.9257 | 0.619150 | ||||||||
\(372\) | −4.72996 | −0.245237 | ||||||||
\(373\) | 1.74166 | 0.0901798 | 0.0450899 | − | 0.998983i | \(-0.485643\pi\) | ||||
0.0450899 | + | 0.998983i | \(0.485643\pi\) | |||||||
\(374\) | −22.0085 | −1.13803 | ||||||||
\(375\) | 10.5091 | 0.542685 | ||||||||
\(376\) | 51.4222 | 2.65190 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.49813 | −0.128490 | ||||||||
\(379\) | 35.4778 | 1.82237 | 0.911186 | − | 0.411995i | \(-0.135168\pi\) | ||||
0.911186 | + | 0.411995i | \(0.135168\pi\) | |||||||
\(380\) | −80.0398 | −4.10596 | ||||||||
\(381\) | 13.8279 | 0.708427 | ||||||||
\(382\) | −33.4132 | −1.70957 | ||||||||
\(383\) | 22.1971 | 1.13422 | 0.567109 | − | 0.823642i | \(-0.308062\pi\) | ||||
0.567109 | + | 0.823642i | \(0.308062\pi\) | |||||||
\(384\) | 16.6771 | 0.851048 | ||||||||
\(385\) | 12.1489 | 0.619165 | ||||||||
\(386\) | −16.6563 | −0.847781 | ||||||||
\(387\) | −0.965145 | −0.0490611 | ||||||||
\(388\) | 1.21725 | 0.0617965 | ||||||||
\(389\) | 3.44035 | 0.174433 | 0.0872163 | − | 0.996189i | \(-0.472203\pi\) | ||||
0.0872163 | + | 0.996189i | \(0.472203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.19447 | −0.363840 | ||||||||
\(392\) | −5.59751 | −0.282717 | ||||||||
\(393\) | 9.92612 | 0.500706 | ||||||||
\(394\) | 30.8628 | 1.55484 | ||||||||
\(395\) | 31.1169 | 1.56566 | ||||||||
\(396\) | −21.9047 | −1.10075 | ||||||||
\(397\) | 17.9477 | 0.900767 | 0.450384 | − | 0.892835i | \(-0.351287\pi\) | ||||
0.450384 | + | 0.892835i | \(0.351287\pi\) | |||||||
\(398\) | 36.3321 | 1.82116 | ||||||||
\(399\) | 8.02484 | 0.401744 | ||||||||
\(400\) | 2.92618 | 0.146309 | ||||||||
\(401\) | −19.7564 | −0.986587 | −0.493293 | − | 0.869863i | \(-0.664207\pi\) | ||||
−0.493293 | + | 0.869863i | \(0.664207\pi\) | |||||||
\(402\) | −33.8407 | −1.68782 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 54.9321 | 2.73297 | ||||||||
\(405\) | −2.35199 | −0.116871 | ||||||||
\(406\) | 13.0910 | 0.649697 | ||||||||
\(407\) | 42.4213 | 2.10275 | ||||||||
\(408\) | 9.54703 | 0.472648 | ||||||||
\(409\) | 20.3407 | 1.00578 | 0.502891 | − | 0.864350i | \(-0.332270\pi\) | ||||
0.502891 | + | 0.864350i | \(0.332270\pi\) | |||||||
\(410\) | 39.6875 | 1.96003 | ||||||||
\(411\) | −8.60954 | −0.424677 | ||||||||
\(412\) | −27.7203 | −1.36568 | ||||||||
\(413\) | 2.98003 | 0.146637 | ||||||||
\(414\) | −10.5376 | −0.517894 | ||||||||
\(415\) | 13.6249 | 0.668822 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.92269 | −0.485916 | ||||||||
\(418\) | 103.551 | 5.06484 | ||||||||
\(419\) | 14.0084 | 0.684356 | 0.342178 | − | 0.939635i | \(-0.388835\pi\) | ||||
0.342178 | + | 0.939635i | \(0.388835\pi\) | |||||||
\(420\) | −9.97401 | −0.486682 | ||||||||
\(421\) | 5.93566 | 0.289286 | 0.144643 | − | 0.989484i | \(-0.453797\pi\) | ||||
0.144643 | + | 0.989484i | \(0.453797\pi\) | |||||||
\(422\) | −63.9742 | −3.11422 | ||||||||
\(423\) | −9.18662 | −0.446669 | ||||||||
\(424\) | −66.7541 | −3.24186 | ||||||||
\(425\) | −0.907100 | −0.0440008 | ||||||||
\(426\) | 0.794896 | 0.0385128 | ||||||||
\(427\) | −14.6034 | −0.706706 | ||||||||
\(428\) | −15.8558 | −0.766421 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.67078 | −0.273469 | ||||||||
\(431\) | 10.9820 | 0.528982 | 0.264491 | − | 0.964388i | \(-0.414796\pi\) | ||||
0.264491 | + | 0.964388i | \(0.414796\pi\) | |||||||
\(432\) | 5.50198 | 0.264714 | ||||||||
\(433\) | 6.59353 | 0.316865 | 0.158432 | − | 0.987370i | \(-0.449356\pi\) | ||||
0.158432 | + | 0.987370i | \(0.449356\pi\) | |||||||
\(434\) | 2.78637 | 0.133750 | ||||||||
\(435\) | 12.3252 | 0.590947 | ||||||||
\(436\) | 42.9487 | 2.05687 | ||||||||
\(437\) | 33.8502 | 1.61928 | ||||||||
\(438\) | −1.35576 | −0.0647807 | ||||||||
\(439\) | −4.55826 | −0.217554 | −0.108777 | − | 0.994066i | \(-0.534693\pi\) | ||||
−0.108777 | + | 0.994066i | \(0.534693\pi\) | |||||||
\(440\) | −68.0035 | −3.24194 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.84511 | 0.325221 | 0.162610 | − | 0.986690i | \(-0.448009\pi\) | ||||
0.162610 | + | 0.986690i | \(0.448009\pi\) | |||||||
\(444\) | −34.8271 | −1.65282 | ||||||||
\(445\) | −18.3678 | −0.870719 | ||||||||
\(446\) | 22.4655 | 1.06377 | ||||||||
\(447\) | 0.253154 | 0.0119738 | ||||||||
\(448\) | −4.63456 | −0.218962 | ||||||||
\(449\) | −15.9302 | −0.751791 | −0.375896 | − | 0.926662i | \(-0.622665\pi\) | ||||
−0.375896 | + | 0.926662i | \(0.622665\pi\) | |||||||
\(450\) | −1.32861 | −0.0626313 | ||||||||
\(451\) | −34.8903 | −1.64292 | ||||||||
\(452\) | 70.0845 | 3.29650 | ||||||||
\(453\) | 19.1942 | 0.901820 | ||||||||
\(454\) | 10.3981 | 0.488005 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −44.9191 | −2.10353 | ||||||||
\(457\) | −11.3437 | −0.530638 | −0.265319 | − | 0.964161i | \(-0.585477\pi\) | ||||
−0.265319 | + | 0.964161i | \(0.585477\pi\) | |||||||
\(458\) | 21.1643 | 0.988941 | ||||||||
\(459\) | −1.70559 | −0.0796099 | ||||||||
\(460\) | −42.0722 | −1.96163 | ||||||||
\(461\) | 37.9495 | 1.76749 | 0.883743 | − | 0.467973i | \(-0.155016\pi\) | ||||
0.883743 | + | 0.467973i | \(0.155016\pi\) | |||||||
\(462\) | 12.9038 | 0.600339 | ||||||||
\(463\) | −33.4984 | −1.55680 | −0.778401 | − | 0.627767i | \(-0.783969\pi\) | ||||
−0.778401 | + | 0.627767i | \(0.783969\pi\) | |||||||
\(464\) | −28.8322 | −1.33850 | ||||||||
\(465\) | 2.62336 | 0.121655 | ||||||||
\(466\) | 46.3047 | 2.14503 | ||||||||
\(467\) | 11.6371 | 0.538500 | 0.269250 | − | 0.963070i | \(-0.413224\pi\) | ||||
0.269250 | + | 0.963070i | \(0.413224\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5464 | 0.625514 | ||||||||
\(470\) | −53.9767 | −2.48976 | ||||||||
\(471\) | −14.8981 | −0.686469 | ||||||||
\(472\) | −16.6807 | −0.767792 | ||||||||
\(473\) | 4.98533 | 0.229226 | ||||||||
\(474\) | 33.0505 | 1.51806 | ||||||||
\(475\) | 4.26794 | 0.195826 | ||||||||
\(476\) | −7.23283 | −0.331516 | ||||||||
\(477\) | 11.9257 | 0.546039 | ||||||||
\(478\) | −0.441948 | −0.0202142 | ||||||||
\(479\) | 26.2836 | 1.20093 | 0.600465 | − | 0.799651i | \(-0.294982\pi\) | ||||
0.600465 | + | 0.799651i | \(0.294982\pi\) | |||||||
\(480\) | 5.99676 | 0.273714 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.4800 | −0.568448 | ||||||||
\(483\) | 4.21818 | 0.191934 | ||||||||
\(484\) | 66.4984 | 3.02266 | ||||||||
\(485\) | −0.675118 | −0.0306555 | ||||||||
\(486\) | −2.49813 | −0.113318 | ||||||||
\(487\) | −13.9247 | −0.630990 | −0.315495 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315495 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(488\) | 81.7424 | 3.70030 | ||||||||
\(489\) | 5.80688 | 0.262596 | ||||||||
\(490\) | 5.87558 | 0.265432 | ||||||||
\(491\) | −23.3848 | −1.05534 | −0.527670 | − | 0.849449i | \(-0.676934\pi\) | ||||
−0.527670 | + | 0.849449i | \(0.676934\pi\) | |||||||
\(492\) | 28.6443 | 1.29139 | ||||||||
\(493\) | 8.93782 | 0.402539 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.1489 | 0.546052 | ||||||||
\(496\) | −6.13679 | −0.275550 | ||||||||
\(497\) | −0.318196 | −0.0142730 | ||||||||
\(498\) | 14.4716 | 0.648487 | ||||||||
\(499\) | −4.20079 | −0.188053 | −0.0940266 | − | 0.995570i | \(-0.529974\pi\) | ||||
−0.0940266 | + | 0.995570i | \(0.529974\pi\) | |||||||
\(500\) | 44.5655 | 1.99303 | ||||||||
\(501\) | −21.4231 | −0.957114 | ||||||||
\(502\) | −1.40120 | −0.0625388 | ||||||||
\(503\) | 5.60179 | 0.249772 | 0.124886 | − | 0.992171i | \(-0.460144\pi\) | ||||
0.124886 | + | 0.992171i | \(0.460144\pi\) | |||||||
\(504\) | −5.59751 | −0.249333 | ||||||||
\(505\) | −30.4668 | −1.35575 | ||||||||
\(506\) | 54.4306 | 2.41973 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 58.6398 | 2.60172 | ||||||||
\(509\) | −7.88662 | −0.349568 | −0.174784 | − | 0.984607i | \(-0.555923\pi\) | ||||
−0.174784 | + | 0.984607i | \(0.555923\pi\) | |||||||
\(510\) | −10.0213 | −0.443751 | ||||||||
\(511\) | 0.542709 | 0.0240080 | ||||||||
\(512\) | 47.5665 | 2.10216 | ||||||||
\(513\) | 8.02484 | 0.354305 | ||||||||
\(514\) | 42.3673 | 1.86874 | ||||||||
\(515\) | 15.3744 | 0.677475 | ||||||||
\(516\) | −4.09286 | −0.180178 | ||||||||
\(517\) | 47.4523 | 2.08695 | ||||||||
\(518\) | 20.5162 | 0.901432 | ||||||||
\(519\) | 21.4128 | 0.939916 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.5215 | 1.33717 | 0.668585 | − | 0.743635i | \(-0.266900\pi\) | ||||
0.668585 | + | 0.743635i | \(0.266900\pi\) | |||||||
\(522\) | 13.0910 | 0.572979 | ||||||||
\(523\) | 26.1984 | 1.14557 | 0.572787 | − | 0.819704i | \(-0.305862\pi\) | ||||
0.572787 | + | 0.819704i | \(0.305862\pi\) | |||||||
\(524\) | 42.0934 | 1.83886 | ||||||||
\(525\) | 0.531841 | 0.0232114 | ||||||||
\(526\) | −18.2178 | −0.794334 | ||||||||
\(527\) | 1.90238 | 0.0828688 | ||||||||
\(528\) | −28.4198 | −1.23681 | ||||||||
\(529\) | −5.20695 | −0.226389 | ||||||||
\(530\) | 70.0703 | 3.04366 | ||||||||
\(531\) | 2.98003 | 0.129322 | ||||||||
\(532\) | 34.0307 | 1.47542 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −19.5092 | −0.844244 | ||||||||
\(535\) | 8.79405 | 0.380200 | ||||||||
\(536\) | −75.8260 | −3.27519 | ||||||||
\(537\) | 5.04689 | 0.217789 | ||||||||
\(538\) | −4.27596 | −0.184350 | ||||||||
\(539\) | −5.16537 | −0.222488 | ||||||||
\(540\) | −9.97401 | −0.429213 | ||||||||
\(541\) | 6.76840 | 0.290996 | 0.145498 | − | 0.989359i | \(-0.453522\pi\) | ||||
0.145498 | + | 0.989359i | \(0.453522\pi\) | |||||||
\(542\) | −30.6203 | −1.31525 | ||||||||
\(543\) | 15.8878 | 0.681810 | ||||||||
\(544\) | 4.34866 | 0.186447 | ||||||||
\(545\) | −23.8204 | −1.02035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8930 | −1.70570 | −0.852851 | − | 0.522155i | \(-0.825128\pi\) | ||||
−0.852851 | + | 0.522155i | \(0.825128\pi\) | |||||||
\(548\) | −36.5103 | −1.55964 | ||||||||
\(549\) | −14.6034 | −0.623256 | ||||||||
\(550\) | 6.86277 | 0.292629 | ||||||||
\(551\) | −42.0528 | −1.79151 | ||||||||
\(552\) | −23.6113 | −1.00496 | ||||||||
\(553\) | −13.2301 | −0.562599 | ||||||||
\(554\) | −80.0128 | −3.39942 | ||||||||
\(555\) | 19.3160 | 0.819918 | ||||||||
\(556\) | −42.0789 | −1.78454 | ||||||||
\(557\) | −20.7410 | −0.878825 | −0.439412 | − | 0.898285i | \(-0.644813\pi\) | ||||
−0.439412 | + | 0.898285i | \(0.644813\pi\) | |||||||
\(558\) | 2.78637 | 0.117956 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −12.9406 | −0.546839 | ||||||||
\(561\) | 8.80999 | 0.371958 | ||||||||
\(562\) | −63.2410 | −2.66766 | ||||||||
\(563\) | 46.2754 | 1.95027 | 0.975137 | − | 0.221602i | \(-0.0711287\pi\) | ||||
0.975137 | + | 0.221602i | \(0.0711287\pi\) | |||||||
\(564\) | −38.9575 | −1.64041 | ||||||||
\(565\) | −38.8707 | −1.63530 | ||||||||
\(566\) | 20.7243 | 0.871109 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 1.78110 | 0.0747334 | ||||||||
\(569\) | −13.9515 | −0.584879 | −0.292439 | − | 0.956284i | \(-0.594467\pi\) | ||||
−0.292439 | + | 0.956284i | \(0.594467\pi\) | |||||||
\(570\) | 47.1506 | 1.97492 | ||||||||
\(571\) | 25.4059 | 1.06320 | 0.531602 | − | 0.846994i | \(-0.321590\pi\) | ||||
0.531602 | + | 0.846994i | \(0.321590\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.3753 | 0.558760 | ||||||||
\(574\) | −16.8740 | −0.704309 | ||||||||
\(575\) | 2.24340 | 0.0935563 | ||||||||
\(576\) | −4.63456 | −0.193107 | ||||||||
\(577\) | 44.9472 | 1.87118 | 0.935588 | − | 0.353093i | \(-0.114870\pi\) | ||||
0.935588 | + | 0.353093i | \(0.114870\pi\) | |||||||
\(578\) | 35.2012 | 1.46418 | ||||||||
\(579\) | 6.66748 | 0.277091 | ||||||||
\(580\) | 52.2671 | 2.17027 | ||||||||
\(581\) | −5.79295 | −0.240332 | ||||||||
\(582\) | −0.717068 | −0.0297234 | ||||||||
\(583\) | −61.6006 | −2.55124 | ||||||||
\(584\) | −3.03782 | −0.125706 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −67.4226 | −2.78520 | ||||||||
\(587\) | −23.2272 | −0.958688 | −0.479344 | − | 0.877627i | \(-0.659125\pi\) | ||||
−0.479344 | + | 0.877627i | \(0.659125\pi\) | |||||||
\(588\) | 4.24068 | 0.174882 | ||||||||
\(589\) | −8.95074 | −0.368809 | ||||||||
\(590\) | 17.5094 | 0.720850 | ||||||||
\(591\) | −12.3543 | −0.508189 | ||||||||
\(592\) | −45.1857 | −1.85712 | ||||||||
\(593\) | 9.16296 | 0.376278 | 0.188139 | − | 0.982142i | \(-0.439755\pi\) | ||||
0.188139 | + | 0.982142i | \(0.439755\pi\) | |||||||
\(594\) | 12.9038 | 0.529449 | ||||||||
\(595\) | 4.01151 | 0.164456 | ||||||||
\(596\) | 1.07355 | 0.0439742 | ||||||||
\(597\) | −14.5437 | −0.595234 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.8168 | 1.05485 | 0.527424 | − | 0.849602i | \(-0.323158\pi\) | ||||
0.527424 | + | 0.849602i | \(0.323158\pi\) | |||||||
\(600\) | −2.97698 | −0.121535 | ||||||||
\(601\) | 17.8496 | 0.728102 | 0.364051 | − | 0.931379i | \(-0.381393\pi\) | ||||
0.364051 | + | 0.931379i | \(0.381393\pi\) | |||||||
\(602\) | 2.41106 | 0.0982675 | ||||||||
\(603\) | 13.5464 | 0.551652 | ||||||||
\(604\) | 81.3962 | 3.31196 | ||||||||
\(605\) | −36.8817 | −1.49946 | ||||||||
\(606\) | −32.3599 | −1.31453 | ||||||||
\(607\) | 34.2992 | 1.39216 | 0.696081 | − | 0.717963i | \(-0.254925\pi\) | ||||
0.696081 | + | 0.717963i | \(0.254925\pi\) | |||||||
\(608\) | −20.4606 | −0.829787 | ||||||||
\(609\) | −5.24033 | −0.212349 | ||||||||
\(610\) | −85.8031 | −3.47407 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.23283 | −0.292370 | ||||||||
\(613\) | −0.143589 | −0.00579952 | −0.00289976 | − | 0.999996i | \(-0.500923\pi\) | ||||
−0.00289976 | + | 0.999996i | \(0.500923\pi\) | |||||||
\(614\) | −19.0812 | −0.770056 | ||||||||
\(615\) | −15.8869 | −0.640620 | ||||||||
\(616\) | 28.9132 | 1.16495 | ||||||||
\(617\) | 18.3135 | 0.737272 | 0.368636 | − | 0.929574i | \(-0.379825\pi\) | ||||
0.368636 | + | 0.929574i | \(0.379825\pi\) | |||||||
\(618\) | 16.3297 | 0.656877 | ||||||||
\(619\) | 0.301686 | 0.0121258 | 0.00606289 | − | 0.999982i | \(-0.498070\pi\) | ||||
0.00606289 | + | 0.999982i | \(0.498070\pi\) | |||||||
\(620\) | 11.1248 | 0.446783 | ||||||||
\(621\) | 4.21818 | 0.169270 | ||||||||
\(622\) | 9.96969 | 0.399748 | ||||||||
\(623\) | 7.80950 | 0.312881 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.3764 | −1.09505 | ||||||||
\(626\) | −27.7961 | −1.11095 | ||||||||
\(627\) | −41.4513 | −1.65540 | ||||||||
\(628\) | −63.1781 | −2.52108 | ||||||||
\(629\) | 14.0073 | 0.558509 | ||||||||
\(630\) | 5.87558 | 0.234089 | ||||||||
\(631\) | −20.3829 | −0.811432 | −0.405716 | − | 0.913999i | \(-0.632978\pi\) | ||||
−0.405716 | + | 0.913999i | \(0.632978\pi\) | |||||||
\(632\) | 74.0553 | 2.94576 | ||||||||
\(633\) | 25.6088 | 1.01786 | ||||||||
\(634\) | 16.7921 | 0.666900 | ||||||||
\(635\) | −32.5231 | −1.29064 | ||||||||
\(636\) | 50.5729 | 2.00535 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −67.6201 | −2.67711 | ||||||||
\(639\) | −0.318196 | −0.0125876 | ||||||||
\(640\) | −39.2243 | −1.55047 | ||||||||
\(641\) | 20.7666 | 0.820233 | 0.410116 | − | 0.912033i | \(-0.365488\pi\) | ||||
0.410116 | + | 0.912033i | \(0.365488\pi\) | |||||||
\(642\) | 9.34050 | 0.368640 | ||||||||
\(643\) | 11.0348 | 0.435171 | 0.217585 | − | 0.976041i | \(-0.430182\pi\) | ||||
0.217585 | + | 0.976041i | \(0.430182\pi\) | |||||||
\(644\) | 17.8879 | 0.704883 | ||||||||
\(645\) | 2.27001 | 0.0893814 | ||||||||
\(646\) | 34.1921 | 1.34527 | ||||||||
\(647\) | −37.5007 | −1.47430 | −0.737152 | − | 0.675727i | \(-0.763830\pi\) | ||||
−0.737152 | + | 0.675727i | \(0.763830\pi\) | |||||||
\(648\) | −5.59751 | −0.219891 | ||||||||
\(649\) | −15.3929 | −0.604226 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11538 | −0.0437152 | ||||||||
\(652\) | 24.6251 | 0.964394 | ||||||||
\(653\) | −26.8688 | −1.05146 | −0.525729 | − | 0.850652i | \(-0.676207\pi\) | ||||
−0.525729 | + | 0.850652i | \(0.676207\pi\) | |||||||
\(654\) | −25.3006 | −0.989331 | ||||||||
\(655\) | −23.3461 | −0.912207 | ||||||||
\(656\) | 37.1640 | 1.45101 | ||||||||
\(657\) | 0.542709 | 0.0211731 | ||||||||
\(658\) | 22.9494 | 0.894662 | ||||||||
\(659\) | 10.8847 | 0.424008 | 0.212004 | − | 0.977269i | \(-0.432001\pi\) | ||||
0.212004 | + | 0.977269i | \(0.432001\pi\) | |||||||
\(660\) | 51.5195 | 2.00539 | ||||||||
\(661\) | 10.7257 | 0.417181 | 0.208590 | − | 0.978003i | \(-0.433112\pi\) | ||||
0.208590 | + | 0.978003i | \(0.433112\pi\) | |||||||
\(662\) | −48.6665 | −1.89148 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.4261 | 1.25838 | ||||||||
\(665\) | −18.8743 | −0.731914 | ||||||||
\(666\) | 20.5162 | 0.794988 | ||||||||
\(667\) | −22.1046 | −0.855895 | ||||||||
\(668\) | −90.8485 | −3.51503 | ||||||||
\(669\) | −8.99291 | −0.347686 | ||||||||
\(670\) | 79.5929 | 3.07494 | ||||||||
\(671\) | 75.4318 | 2.91201 | ||||||||
\(672\) | −2.54966 | −0.0983552 | ||||||||
\(673\) | −22.2093 | −0.856104 | −0.428052 | − | 0.903754i | \(-0.640800\pi\) | ||||
−0.428052 | + | 0.903754i | \(0.640800\pi\) | |||||||
\(674\) | 16.4344 | 0.633028 | ||||||||
\(675\) | 0.531841 | 0.0204706 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.83321 | 0.147322 | 0.0736612 | − | 0.997283i | \(-0.476532\pi\) | ||||
0.0736612 | + | 0.997283i | \(0.476532\pi\) | |||||||
\(678\) | −41.2860 | −1.58558 | ||||||||
\(679\) | 0.287042 | 0.0110156 | ||||||||
\(680\) | −22.4545 | −0.861090 | ||||||||
\(681\) | −4.16233 | −0.159501 | ||||||||
\(682\) | −14.3926 | −0.551123 | ||||||||
\(683\) | −6.80946 | −0.260557 | −0.130278 | − | 0.991477i | \(-0.541587\pi\) | ||||
−0.130278 | + | 0.991477i | \(0.541587\pi\) | |||||||
\(684\) | 34.0307 | 1.30120 | ||||||||
\(685\) | 20.2495 | 0.773695 | ||||||||
\(686\) | −2.49813 | −0.0953792 | ||||||||
\(687\) | −8.47202 | −0.323228 | ||||||||
\(688\) | −5.31020 | −0.202450 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 24.7843 | 0.943520 | ||||||||
\(691\) | −1.14161 | −0.0434288 | −0.0217144 | − | 0.999764i | \(-0.506912\pi\) | ||||
−0.0217144 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(692\) | 90.8046 | 3.45187 | ||||||||
\(693\) | −5.16537 | −0.196216 | ||||||||
\(694\) | −33.4819 | −1.27096 | ||||||||
\(695\) | 23.3380 | 0.885262 | ||||||||
\(696\) | 29.3328 | 1.11186 | ||||||||
\(697\) | −11.5206 | −0.436375 | ||||||||
\(698\) | −40.7908 | −1.54395 | ||||||||
\(699\) | −18.5357 | −0.701086 | ||||||||
\(700\) | 2.25536 | 0.0852448 | ||||||||
\(701\) | 8.44188 | 0.318845 | 0.159423 | − | 0.987210i | \(-0.449037\pi\) | ||||
0.159423 | + | 0.987210i | \(0.449037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −65.9050 | −2.48565 | ||||||||
\(704\) | 23.9392 | 0.902244 | ||||||||
\(705\) | 21.6068 | 0.813760 | ||||||||
\(706\) | −53.8034 | −2.02492 | ||||||||
\(707\) | 12.9536 | 0.487171 | ||||||||
\(708\) | 12.6373 | 0.474940 | ||||||||
\(709\) | 7.11295 | 0.267133 | 0.133566 | − | 0.991040i | \(-0.457357\pi\) | ||||
0.133566 | + | 0.991040i | \(0.457357\pi\) | |||||||
\(710\) | −1.86958 | −0.0701643 | ||||||||
\(711\) | −13.2301 | −0.496166 | ||||||||
\(712\) | −43.7137 | −1.63824 | ||||||||
\(713\) | −4.70487 | −0.176199 | ||||||||
\(714\) | 4.26078 | 0.159456 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.4022 | 0.799839 | ||||||||
\(717\) | 0.176911 | 0.00660687 | ||||||||
\(718\) | 79.6478 | 2.97243 | ||||||||
\(719\) | 6.74382 | 0.251502 | 0.125751 | − | 0.992062i | \(-0.459866\pi\) | ||||
0.125751 | + | 0.992062i | \(0.459866\pi\) | |||||||
\(720\) | −12.9406 | −0.482267 | ||||||||
\(721\) | −6.53676 | −0.243442 | ||||||||
\(722\) | −113.410 | −4.22069 | ||||||||
\(723\) | 4.99572 | 0.185793 | ||||||||
\(724\) | 67.3749 | 2.50397 | ||||||||
\(725\) | −2.78702 | −0.103507 | ||||||||
\(726\) | −39.1735 | −1.45386 | ||||||||
\(727\) | −23.9650 | −0.888811 | −0.444406 | − | 0.895826i | \(-0.646585\pi\) | ||||
−0.444406 | + | 0.895826i | \(0.646585\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.18873 | 0.118020 | ||||||||
\(731\) | 1.64614 | 0.0608846 | ||||||||
\(732\) | −61.9281 | −2.28893 | ||||||||
\(733\) | −5.63526 | −0.208143 | −0.104072 | − | 0.994570i | \(-0.533187\pi\) | ||||
−0.104072 | + | 0.994570i | \(0.533187\pi\) | |||||||
\(734\) | −37.3470 | −1.37850 | ||||||||
\(735\) | −2.35199 | −0.0867543 | ||||||||
\(736\) | −10.7549 | −0.396432 | ||||||||
\(737\) | −69.9722 | −2.57746 | ||||||||
\(738\) | −16.8740 | −0.621142 | ||||||||
\(739\) | −18.7986 | −0.691518 | −0.345759 | − | 0.938323i | \(-0.612378\pi\) | ||||
−0.345759 | + | 0.938323i | \(0.612378\pi\) | |||||||
\(740\) | 81.9128 | 3.01118 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −29.7919 | −1.09370 | ||||||||
\(743\) | −27.2365 | −0.999209 | −0.499604 | − | 0.866254i | \(-0.666521\pi\) | ||||
−0.499604 | + | 0.866254i | \(0.666521\pi\) | |||||||
\(744\) | 6.24335 | 0.228892 | ||||||||
\(745\) | −0.595416 | −0.0218144 | ||||||||
\(746\) | −4.35090 | −0.159298 | ||||||||
\(747\) | −5.79295 | −0.211953 | ||||||||
\(748\) | 37.3603 | 1.36603 | ||||||||
\(749\) | −3.73899 | −0.136620 | ||||||||
\(750\) | −26.2530 | −0.958625 | ||||||||
\(751\) | 17.2816 | 0.630615 | 0.315308 | − | 0.948989i | \(-0.397892\pi\) | ||||
0.315308 | + | 0.948989i | \(0.397892\pi\) | |||||||
\(752\) | −50.5446 | −1.84317 | ||||||||
\(753\) | 0.560900 | 0.0204403 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.1444 | −1.64297 | ||||||||
\(756\) | 4.24068 | 0.154232 | ||||||||
\(757\) | −10.1844 | −0.370160 | −0.185080 | − | 0.982723i | \(-0.559254\pi\) | ||||
−0.185080 | + | 0.982723i | \(0.559254\pi\) | |||||||
\(758\) | −88.6283 | −3.21913 | ||||||||
\(759\) | −21.7885 | −0.790872 | ||||||||
\(760\) | 105.649 | 3.83230 | ||||||||
\(761\) | −51.1035 | −1.85250 | −0.926251 | − | 0.376908i | \(-0.876987\pi\) | ||||
−0.926251 | + | 0.376908i | \(0.876987\pi\) | |||||||
\(762\) | −34.5441 | −1.25140 | ||||||||
\(763\) | 10.1278 | 0.366651 | ||||||||
\(764\) | 56.7202 | 2.05206 | ||||||||
\(765\) | 4.01151 | 0.145037 | ||||||||
\(766\) | −55.4513 | −2.00354 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −32.3924 | −1.16886 | ||||||||
\(769\) | −26.3949 | −0.951823 | −0.475911 | − | 0.879493i | \(-0.657882\pi\) | ||||
−0.475911 | + | 0.879493i | \(0.657882\pi\) | |||||||
\(770\) | −30.3496 | −1.09372 | ||||||||
\(771\) | −16.9596 | −0.610784 | ||||||||
\(772\) | 28.2746 | 1.01763 | ||||||||
\(773\) | 10.1413 | 0.364758 | 0.182379 | − | 0.983228i | \(-0.441620\pi\) | ||||
0.182379 | + | 0.983228i | \(0.441620\pi\) | |||||||
\(774\) | 2.41106 | 0.0866638 | ||||||||
\(775\) | −0.593205 | −0.0213085 | ||||||||
\(776\) | −1.60672 | −0.0576778 | ||||||||
\(777\) | −8.21263 | −0.294626 | ||||||||
\(778\) | −8.59445 | −0.308126 | ||||||||
\(779\) | 54.2050 | 1.94210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.64360 | 0.0588127 | ||||||||
\(782\) | 17.9727 | 0.642704 | ||||||||
\(783\) | −5.24033 | −0.187274 | ||||||||
\(784\) | 5.50198 | 0.196499 | ||||||||
\(785\) | 35.0402 | 1.25064 | ||||||||
\(786\) | −24.7968 | −0.884472 | ||||||||
\(787\) | −51.5981 | −1.83927 | −0.919636 | − | 0.392771i | \(-0.871516\pi\) | ||||
−0.919636 | + | 0.392771i | \(0.871516\pi\) | |||||||
\(788\) | −52.3907 | −1.86634 | ||||||||
\(789\) | 7.29257 | 0.259622 | ||||||||
\(790\) | −77.7342 | −2.76566 | ||||||||
\(791\) | 16.5267 | 0.587623 | ||||||||
\(792\) | 28.9132 | 1.02739 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −44.8357 | −1.59116 | ||||||||
\(795\) | −28.0490 | −0.994797 | ||||||||
\(796\) | −61.6751 | −2.18602 | ||||||||
\(797\) | −15.1299 | −0.535928 | −0.267964 | − | 0.963429i | \(-0.586351\pi\) | ||||
−0.267964 | + | 0.963429i | \(0.586351\pi\) | |||||||
\(798\) | −20.0471 | −0.709660 | ||||||||
\(799\) | 15.6686 | 0.554314 | ||||||||
\(800\) | −1.35601 | −0.0479423 | ||||||||
\(801\) | 7.80950 | 0.275935 | ||||||||
\(802\) | 49.3541 | 1.74275 | ||||||||
\(803\) | −2.80330 | −0.0989261 | ||||||||
\(804\) | 57.4459 | 2.02596 | ||||||||
\(805\) | −9.92111 | −0.349673 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.71166 | 0.0602533 | ||||||||
\(808\) | −72.5080 | −2.55082 | ||||||||
\(809\) | 4.43586 | 0.155956 | 0.0779782 | − | 0.996955i | \(-0.475154\pi\) | ||||
0.0779782 | + | 0.996955i | \(0.475154\pi\) | |||||||
\(810\) | 5.87558 | 0.206447 | ||||||||
\(811\) | 3.05676 | 0.107337 | 0.0536686 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536686 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(812\) | −22.2225 | −0.779858 | ||||||||
\(813\) | 12.2573 | 0.429881 | ||||||||
\(814\) | −105.974 | −3.71439 | ||||||||
\(815\) | −13.6577 | −0.478409 | ||||||||
\(816\) | −9.38409 | −0.328509 | ||||||||
\(817\) | −7.74513 | −0.270968 | ||||||||
\(818\) | −50.8138 | −1.77666 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −67.3710 | −2.35270 | ||||||||
\(821\) | −11.0373 | −0.385204 | −0.192602 | − | 0.981277i | \(-0.561693\pi\) | ||||
−0.192602 | + | 0.981277i | \(0.561693\pi\) | |||||||
\(822\) | 21.5078 | 0.750170 | ||||||||
\(823\) | 49.7386 | 1.73378 | 0.866890 | − | 0.498499i | \(-0.166115\pi\) | ||||
0.866890 | + | 0.498499i | \(0.166115\pi\) | |||||||
\(824\) | 36.5895 | 1.27466 | ||||||||
\(825\) | −2.74716 | −0.0956438 | ||||||||
\(826\) | −7.44450 | −0.259027 | ||||||||
\(827\) | −42.7670 | −1.48715 | −0.743577 | − | 0.668650i | \(-0.766872\pi\) | ||||
−0.743577 | + | 0.668650i | \(0.766872\pi\) | |||||||
\(828\) | 17.8879 | 0.621649 | ||||||||
\(829\) | −11.5052 | −0.399591 | −0.199796 | − | 0.979838i | \(-0.564028\pi\) | ||||
−0.199796 | + | 0.979838i | \(0.564028\pi\) | |||||||
\(830\) | −34.0369 | −1.18144 | ||||||||
\(831\) | 32.0290 | 1.11107 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.70559 | −0.0590950 | ||||||||
\(834\) | 24.7882 | 0.858345 | ||||||||
\(835\) | 50.3869 | 1.74371 | ||||||||
\(836\) | −175.781 | −6.07953 | ||||||||
\(837\) | −1.11538 | −0.0385532 | ||||||||
\(838\) | −34.9949 | −1.20888 | ||||||||
\(839\) | 10.5561 | 0.364436 | 0.182218 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182218 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(840\) | 13.1653 | 0.454245 | ||||||||
\(841\) | −1.53898 | −0.0530681 | ||||||||
\(842\) | −14.8281 | −0.511009 | ||||||||
\(843\) | 25.3153 | 0.871904 | ||||||||
\(844\) | 108.599 | 3.73812 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22.9494 | 0.789017 | ||||||||
\(847\) | 15.6811 | 0.538809 | ||||||||
\(848\) | 65.6148 | 2.25322 | ||||||||
\(849\) | −8.29593 | −0.284715 | ||||||||
\(850\) | 2.26606 | 0.0777251 | ||||||||
\(851\) | −34.6423 | −1.18752 | ||||||||
\(852\) | −1.34937 | −0.0462285 | ||||||||
\(853\) | 2.34131 | 0.0801648 | 0.0400824 | − | 0.999196i | \(-0.487238\pi\) | ||||
0.0400824 | + | 0.999196i | \(0.487238\pi\) | |||||||
\(854\) | 36.4811 | 1.24836 | ||||||||
\(855\) | −18.8743 | −0.645488 | ||||||||
\(856\) | 20.9290 | 0.715339 | ||||||||
\(857\) | −47.5469 | −1.62417 | −0.812086 | − | 0.583537i | \(-0.801668\pi\) | ||||
−0.812086 | + | 0.583537i | \(0.801668\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.5483 | 1.69057 | 0.845284 | − | 0.534318i | \(-0.179431\pi\) | ||||
0.845284 | + | 0.534318i | \(0.179431\pi\) | |||||||
\(860\) | 9.62636 | 0.328256 | ||||||||
\(861\) | 6.75466 | 0.230198 | ||||||||
\(862\) | −27.4344 | −0.934419 | ||||||||
\(863\) | −0.233810 | −0.00795899 | −0.00397949 | − | 0.999992i | \(-0.501267\pi\) | ||||
−0.00397949 | + | 0.999992i | \(0.501267\pi\) | |||||||
\(864\) | −2.54966 | −0.0867412 | ||||||||
\(865\) | −50.3625 | −1.71238 | ||||||||
\(866\) | −16.4715 | −0.559725 | ||||||||
\(867\) | −14.0910 | −0.478555 | ||||||||
\(868\) | −4.72996 | −0.160545 | ||||||||
\(869\) | 68.3382 | 2.31821 | ||||||||
\(870\) | −30.7900 | −1.04388 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −56.6904 | −1.91978 | ||||||||
\(873\) | 0.287042 | 0.00971489 | ||||||||
\(874\) | −84.5624 | −2.86037 | ||||||||
\(875\) | 10.5091 | 0.355271 | ||||||||
\(876\) | 2.30145 | 0.0777589 | ||||||||
\(877\) | −21.2880 | −0.718845 | −0.359423 | − | 0.933175i | \(-0.617026\pi\) | ||||
−0.359423 | + | 0.933175i | \(0.617026\pi\) | |||||||
\(878\) | 11.3872 | 0.384298 | ||||||||
\(879\) | 26.9892 | 0.910322 | ||||||||
\(880\) | 66.8429 | 2.25327 | ||||||||
\(881\) | 17.0535 | 0.574546 | 0.287273 | − | 0.957849i | \(-0.407251\pi\) | ||||
0.287273 | + | 0.957849i | \(0.407251\pi\) | |||||||
\(882\) | −2.49813 | −0.0841166 | ||||||||
\(883\) | 15.7586 | 0.530319 | 0.265160 | − | 0.964205i | \(-0.414575\pi\) | ||||
0.265160 | + | 0.964205i | \(0.414575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.00898 | −0.235604 | ||||||||
\(886\) | −17.1000 | −0.574486 | ||||||||
\(887\) | −19.6096 | −0.658425 | −0.329212 | − | 0.944256i | \(-0.606783\pi\) | ||||
−0.329212 | + | 0.944256i | \(0.606783\pi\) | |||||||
\(888\) | 45.9702 | 1.54266 | ||||||||
\(889\) | 13.8279 | 0.463774 | ||||||||
\(890\) | 45.8853 | 1.53808 | ||||||||
\(891\) | −5.16537 | −0.173047 | ||||||||
\(892\) | −38.1360 | −1.27689 | ||||||||
\(893\) | −73.7212 | −2.46698 | ||||||||
\(894\) | −0.632414 | −0.0211511 | ||||||||
\(895\) | −11.8702 | −0.396778 | ||||||||
\(896\) | 16.6771 | 0.557142 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.7957 | 1.32800 | ||||||||
\(899\) | 5.84496 | 0.194940 | ||||||||
\(900\) | 2.25536 | 0.0751788 | ||||||||
\(901\) | −20.3403 | −0.677632 | ||||||||
\(902\) | 87.1607 | 2.90214 | ||||||||
\(903\) | −0.965145 | −0.0321180 | ||||||||
\(904\) | −92.5086 | −3.07679 | ||||||||
\(905\) | −37.3678 | −1.24215 | ||||||||
\(906\) | −47.9496 | −1.59302 | ||||||||
\(907\) | 8.16378 | 0.271074 | 0.135537 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135537 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(908\) | −17.6511 | −0.585772 | ||||||||
\(909\) | 12.9536 | 0.429645 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0348 | 1.32641 | 0.663206 | − | 0.748437i | \(-0.269195\pi\) | ||||
0.663206 | + | 0.748437i | \(0.269195\pi\) | |||||||
\(912\) | 44.1525 | 1.46203 | ||||||||
\(913\) | 29.9228 | 0.990299 | ||||||||
\(914\) | 28.3382 | 0.937345 | ||||||||
\(915\) | 34.3469 | 1.13547 | ||||||||
\(916\) | −35.9271 | −1.18706 | ||||||||
\(917\) | 9.92612 | 0.327789 | ||||||||
\(918\) | 4.26078 | 0.140627 | ||||||||
\(919\) | −34.0730 | −1.12396 | −0.561982 | − | 0.827149i | \(-0.689961\pi\) | ||||
−0.561982 | + | 0.827149i | \(0.689961\pi\) | |||||||
\(920\) | 55.5335 | 1.83088 | ||||||||
\(921\) | 7.63819 | 0.251687 | ||||||||
\(922\) | −94.8030 | −3.12217 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −21.9047 | −0.720611 | ||||||||
\(925\) | −4.36781 | −0.143613 | ||||||||
\(926\) | 83.6835 | 2.75001 | ||||||||
\(927\) | −6.53676 | −0.214695 | ||||||||
\(928\) | 13.3610 | 0.438598 | ||||||||
\(929\) | 20.8776 | 0.684972 | 0.342486 | − | 0.939523i | \(-0.388731\pi\) | ||||
0.342486 | + | 0.939523i | \(0.388731\pi\) | |||||||
\(930\) | −6.55350 | −0.214898 | ||||||||
\(931\) | 8.02484 | 0.263003 | ||||||||
\(932\) | −78.6040 | −2.57476 | ||||||||
\(933\) | −3.99085 | −0.130655 | ||||||||
\(934\) | −29.0710 | −0.951232 | ||||||||
\(935\) | −20.7210 | −0.677648 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.5927 | 0.672734 | 0.336367 | − | 0.941731i | \(-0.390802\pi\) | ||||
0.336367 | + | 0.941731i | \(0.390802\pi\) | |||||||
\(938\) | −33.8407 | −1.10494 | ||||||||
\(939\) | 11.1267 | 0.363107 | ||||||||
\(940\) | 91.6275 | 2.98856 | ||||||||
\(941\) | −18.7149 | −0.610089 | −0.305045 | − | 0.952338i | \(-0.598671\pi\) | ||||
−0.305045 | + | 0.952338i | \(0.598671\pi\) | |||||||
\(942\) | 37.2175 | 1.21261 | ||||||||
\(943\) | 28.4924 | 0.927839 | ||||||||
\(944\) | 16.3960 | 0.533645 | ||||||||
\(945\) | −2.35199 | −0.0765101 | ||||||||
\(946\) | −12.4540 | −0.404915 | ||||||||
\(947\) | 5.23110 | 0.169988 | 0.0849939 | − | 0.996381i | \(-0.472913\pi\) | ||||
0.0849939 | + | 0.996381i | \(0.472913\pi\) | |||||||
\(948\) | −56.1044 | −1.82218 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −10.6619 | −0.345917 | ||||||||
\(951\) | −6.72186 | −0.217971 | ||||||||
\(952\) | 9.54703 | 0.309421 | ||||||||
\(953\) | −49.7229 | −1.61068 | −0.805341 | − | 0.592812i | \(-0.798018\pi\) | ||||
−0.805341 | + | 0.592812i | \(0.798018\pi\) | |||||||
\(954\) | −29.7919 | −0.964550 | ||||||||
\(955\) | −31.4585 | −1.01797 | ||||||||
\(956\) | 0.750222 | 0.0242639 | ||||||||
\(957\) | 27.0682 | 0.874992 | ||||||||
\(958\) | −65.6601 | −2.12138 | ||||||||
\(959\) | −8.60954 | −0.278017 | ||||||||
\(960\) | 10.9004 | 0.351810 | ||||||||
\(961\) | −29.7559 | −0.959869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.73899 | −0.120487 | ||||||||
\(964\) | 21.1852 | 0.682330 | ||||||||
\(965\) | −15.6818 | −0.504815 | ||||||||
\(966\) | −10.5376 | −0.339041 | ||||||||
\(967\) | 4.55490 | 0.146476 | 0.0732379 | − | 0.997314i | \(-0.476667\pi\) | ||||
0.0732379 | + | 0.997314i | \(0.476667\pi\) | |||||||
\(968\) | −87.7750 | −2.82120 | ||||||||
\(969\) | −13.6870 | −0.439691 | ||||||||
\(970\) | 1.68654 | 0.0541514 | ||||||||
\(971\) | 33.4767 | 1.07432 | 0.537159 | − | 0.843481i | \(-0.319497\pi\) | ||||
0.537159 | + | 0.843481i | \(0.319497\pi\) | |||||||
\(972\) | 4.24068 | 0.136020 | ||||||||
\(973\) | −9.92269 | −0.318107 | ||||||||
\(974\) | 34.7859 | 1.11461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −80.3473 | −2.57185 | ||||||||
\(977\) | 48.7454 | 1.55950 | 0.779752 | − | 0.626089i | \(-0.215345\pi\) | ||||
0.779752 | + | 0.626089i | \(0.215345\pi\) | |||||||
\(978\) | −14.5064 | −0.463863 | ||||||||
\(979\) | −40.3390 | −1.28924 | ||||||||
\(980\) | −9.97401 | −0.318608 | ||||||||
\(981\) | 10.1278 | 0.323355 | ||||||||
\(982\) | 58.4183 | 1.86420 | ||||||||
\(983\) | −5.57582 | −0.177841 | −0.0889205 | − | 0.996039i | \(-0.528342\pi\) | ||||
−0.0889205 | + | 0.996039i | \(0.528342\pi\) | |||||||
\(984\) | −37.8092 | −1.20531 | ||||||||
\(985\) | 29.0572 | 0.925840 | ||||||||
\(986\) | −22.3279 | −0.711065 | ||||||||
\(987\) | −9.18662 | −0.292413 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.07115 | −0.129455 | ||||||||
\(990\) | −30.3496 | −0.964572 | ||||||||
\(991\) | 39.8543 | 1.26601 | 0.633006 | − | 0.774147i | \(-0.281821\pi\) | ||||
0.633006 | + | 0.774147i | \(0.281821\pi\) | |||||||
\(992\) | 2.84384 | 0.0902920 | ||||||||
\(993\) | 19.4811 | 0.618216 | ||||||||
\(994\) | 0.794896 | 0.0252126 | ||||||||
\(995\) | 34.2066 | 1.08442 | ||||||||
\(996\) | −24.5660 | −0.778404 | ||||||||
\(997\) | −39.1045 | −1.23845 | −0.619226 | − | 0.785213i | \(-0.712554\pi\) | ||||
−0.619226 | + | 0.785213i | \(0.712554\pi\) | |||||||
\(998\) | 10.4941 | 0.332186 | ||||||||
\(999\) | −8.21263 | −0.259836 |
(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 | 3549.2.a.bg.1.3 | ✓ | 15 | |
13.12 | even | 2 | 3549.2.a.bh.1.13 | yes | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.bg.1.3 | ✓ | 15 | 1.1 | even | 1 | trivial | |
3549.2.a.bh.1.13 | yes | 15 | 13.12 | even | 2 |