Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(1,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("403.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 9x^{5} + 12x^{4} + 22x^{3} - 18x^{2} - 13x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.0890306\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 403.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58972 | 1.83121 | 0.915604 | − | 0.402081i | \(-0.131713\pi\) | ||||
0.915604 | + | 0.402081i | \(0.131713\pi\) | |||||||
\(3\) | 1.08903 | 0.628752 | 0.314376 | − | 0.949299i | \(-0.398205\pi\) | ||||
0.314376 | + | 0.949299i | \(0.398205\pi\) | |||||||
\(4\) | 4.70665 | 2.35332 | ||||||||
\(5\) | −1.22264 | −0.546780 | −0.273390 | − | 0.961903i | \(-0.588145\pi\) | ||||
−0.273390 | + | 0.961903i | \(0.588145\pi\) | |||||||
\(6\) | 2.82028 | 1.15138 | ||||||||
\(7\) | −0.573038 | −0.216588 | −0.108294 | − | 0.994119i | \(-0.534539\pi\) | ||||
−0.108294 | + | 0.994119i | \(0.534539\pi\) | |||||||
\(8\) | 7.00945 | 2.47822 | ||||||||
\(9\) | −1.81401 | −0.604671 | ||||||||
\(10\) | −3.16629 | −1.00127 | ||||||||
\(11\) | −1.53337 | −0.462328 | −0.231164 | − | 0.972915i | \(-0.574253\pi\) | ||||
−0.231164 | + | 0.972915i | \(0.574253\pi\) | |||||||
\(12\) | 5.12568 | 1.47966 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.48401 | −0.396618 | ||||||||
\(15\) | −1.33149 | −0.343789 | ||||||||
\(16\) | 8.73922 | 2.18480 | ||||||||
\(17\) | 3.04458 | 0.738418 | 0.369209 | − | 0.929346i | \(-0.379629\pi\) | ||||
0.369209 | + | 0.929346i | \(0.379629\pi\) | |||||||
\(18\) | −4.69778 | −1.10728 | ||||||||
\(19\) | −0.170684 | −0.0391575 | −0.0195787 | − | 0.999808i | \(-0.506233\pi\) | ||||
−0.0195787 | + | 0.999808i | \(0.506233\pi\) | |||||||
\(20\) | −5.75452 | −1.28675 | ||||||||
\(21\) | −0.624056 | −0.136180 | ||||||||
\(22\) | −3.97100 | −0.846620 | ||||||||
\(23\) | −1.04732 | −0.218381 | −0.109190 | − | 0.994021i | \(-0.534826\pi\) | ||||
−0.109190 | + | 0.994021i | \(0.534826\pi\) | |||||||
\(24\) | 7.63351 | 1.55818 | ||||||||
\(25\) | −3.50516 | −0.701031 | ||||||||
\(26\) | −2.58972 | −0.507886 | ||||||||
\(27\) | −5.24261 | −1.00894 | ||||||||
\(28\) | −2.69709 | −0.509701 | ||||||||
\(29\) | −0.554872 | −0.103037 | −0.0515185 | − | 0.998672i | \(-0.516406\pi\) | ||||
−0.0515185 | + | 0.998672i | \(0.516406\pi\) | |||||||
\(30\) | −3.44819 | −0.629550 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 8.61322 | 1.52262 | ||||||||
\(33\) | −1.66989 | −0.290690 | ||||||||
\(34\) | 7.88460 | 1.35220 | ||||||||
\(35\) | 0.700618 | 0.118426 | ||||||||
\(36\) | −8.53791 | −1.42299 | ||||||||
\(37\) | 5.10806 | 0.839760 | 0.419880 | − | 0.907580i | \(-0.362072\pi\) | ||||
0.419880 | + | 0.907580i | \(0.362072\pi\) | |||||||
\(38\) | −0.442022 | −0.0717055 | ||||||||
\(39\) | −1.08903 | −0.174384 | ||||||||
\(40\) | −8.57002 | −1.35504 | ||||||||
\(41\) | 3.94545 | 0.616176 | 0.308088 | − | 0.951358i | \(-0.400311\pi\) | ||||
0.308088 | + | 0.951358i | \(0.400311\pi\) | |||||||
\(42\) | −1.61613 | −0.249374 | ||||||||
\(43\) | 3.89592 | 0.594122 | 0.297061 | − | 0.954858i | \(-0.403993\pi\) | ||||
0.297061 | + | 0.954858i | \(0.403993\pi\) | |||||||
\(44\) | −7.21703 | −1.08801 | ||||||||
\(45\) | 2.21788 | 0.330622 | ||||||||
\(46\) | −2.71225 | −0.399900 | ||||||||
\(47\) | 6.79810 | 0.991604 | 0.495802 | − | 0.868435i | \(-0.334874\pi\) | ||||
0.495802 | + | 0.868435i | \(0.334874\pi\) | |||||||
\(48\) | 9.51728 | 1.37370 | ||||||||
\(49\) | −6.67163 | −0.953090 | ||||||||
\(50\) | −9.07737 | −1.28373 | ||||||||
\(51\) | 3.31564 | 0.464282 | ||||||||
\(52\) | −4.70665 | −0.652694 | ||||||||
\(53\) | −7.17642 | −0.985757 | −0.492879 | − | 0.870098i | \(-0.664055\pi\) | ||||
−0.492879 | + | 0.870098i | \(0.664055\pi\) | |||||||
\(54\) | −13.5769 | −1.84758 | ||||||||
\(55\) | 1.87476 | 0.252792 | ||||||||
\(56\) | −4.01668 | −0.536752 | ||||||||
\(57\) | −0.185880 | −0.0246204 | ||||||||
\(58\) | −1.43696 | −0.188682 | ||||||||
\(59\) | 7.05962 | 0.919084 | 0.459542 | − | 0.888156i | \(-0.348014\pi\) | ||||
0.459542 | + | 0.888156i | \(0.348014\pi\) | |||||||
\(60\) | −6.26685 | −0.809047 | ||||||||
\(61\) | 7.06306 | 0.904332 | 0.452166 | − | 0.891934i | \(-0.350651\pi\) | ||||
0.452166 | + | 0.891934i | \(0.350651\pi\) | |||||||
\(62\) | 2.58972 | 0.328895 | ||||||||
\(63\) | 1.03950 | 0.130964 | ||||||||
\(64\) | 4.82738 | 0.603423 | ||||||||
\(65\) | 1.22264 | 0.151650 | ||||||||
\(66\) | −4.32454 | −0.532314 | ||||||||
\(67\) | −8.47608 | −1.03552 | −0.517759 | − | 0.855526i | \(-0.673234\pi\) | ||||
−0.517759 | + | 0.855526i | \(0.673234\pi\) | |||||||
\(68\) | 14.3297 | 1.73774 | ||||||||
\(69\) | −1.14056 | −0.137307 | ||||||||
\(70\) | 1.81440 | 0.216863 | ||||||||
\(71\) | −3.61508 | −0.429032 | −0.214516 | − | 0.976721i | \(-0.568817\pi\) | ||||
−0.214516 | + | 0.976721i | \(0.568817\pi\) | |||||||
\(72\) | −12.7152 | −1.49850 | ||||||||
\(73\) | 3.02639 | 0.354212 | 0.177106 | − | 0.984192i | \(-0.443326\pi\) | ||||
0.177106 | + | 0.984192i | \(0.443326\pi\) | |||||||
\(74\) | 13.2284 | 1.53778 | ||||||||
\(75\) | −3.81722 | −0.440775 | ||||||||
\(76\) | −0.803347 | −0.0921502 | ||||||||
\(77\) | 0.878679 | 0.100135 | ||||||||
\(78\) | −2.82028 | −0.319334 | ||||||||
\(79\) | 5.15645 | 0.580146 | 0.290073 | − | 0.957005i | \(-0.406320\pi\) | ||||
0.290073 | + | 0.957005i | \(0.406320\pi\) | |||||||
\(80\) | −10.6849 | −1.19461 | ||||||||
\(81\) | −0.267323 | −0.0297025 | ||||||||
\(82\) | 10.2176 | 1.12835 | ||||||||
\(83\) | 13.5688 | 1.48937 | 0.744685 | − | 0.667416i | \(-0.232600\pi\) | ||||
0.744685 | + | 0.667416i | \(0.232600\pi\) | |||||||
\(84\) | −2.93721 | −0.320476 | ||||||||
\(85\) | −3.72241 | −0.403753 | ||||||||
\(86\) | 10.0893 | 1.08796 | ||||||||
\(87\) | −0.604272 | −0.0647848 | ||||||||
\(88\) | −10.7481 | −1.14575 | ||||||||
\(89\) | 6.51329 | 0.690408 | 0.345204 | − | 0.938528i | \(-0.387810\pi\) | ||||
0.345204 | + | 0.938528i | \(0.387810\pi\) | |||||||
\(90\) | 5.74369 | 0.605438 | ||||||||
\(91\) | 0.573038 | 0.0600707 | ||||||||
\(92\) | −4.92935 | −0.513920 | ||||||||
\(93\) | 1.08903 | 0.112927 | ||||||||
\(94\) | 17.6052 | 1.81583 | ||||||||
\(95\) | 0.208684 | 0.0214105 | ||||||||
\(96\) | 9.38006 | 0.957348 | ||||||||
\(97\) | −18.1121 | −1.83900 | −0.919500 | − | 0.393090i | \(-0.871406\pi\) | ||||
−0.919500 | + | 0.393090i | \(0.871406\pi\) | |||||||
\(98\) | −17.2776 | −1.74531 | ||||||||
\(99\) | 2.78155 | 0.279556 | ||||||||
\(100\) | −16.4975 | −1.64975 | ||||||||
\(101\) | 0.768329 | 0.0764516 | 0.0382258 | − | 0.999269i | \(-0.487829\pi\) | ||||
0.0382258 | + | 0.999269i | \(0.487829\pi\) | |||||||
\(102\) | 8.58657 | 0.850197 | ||||||||
\(103\) | −12.6231 | −1.24379 | −0.621897 | − | 0.783099i | \(-0.713638\pi\) | ||||
−0.621897 | + | 0.783099i | \(0.713638\pi\) | |||||||
\(104\) | −7.00945 | −0.687333 | ||||||||
\(105\) | 0.762994 | 0.0744606 | ||||||||
\(106\) | −18.5849 | −1.80513 | ||||||||
\(107\) | −6.76222 | −0.653729 | −0.326864 | − | 0.945071i | \(-0.605992\pi\) | ||||
−0.326864 | + | 0.945071i | \(0.605992\pi\) | |||||||
\(108\) | −24.6751 | −2.37436 | ||||||||
\(109\) | 10.7442 | 1.02911 | 0.514556 | − | 0.857457i | \(-0.327957\pi\) | ||||
0.514556 | + | 0.857457i | \(0.327957\pi\) | |||||||
\(110\) | 4.85509 | 0.462915 | ||||||||
\(111\) | 5.56284 | 0.528001 | ||||||||
\(112\) | −5.00790 | −0.473202 | ||||||||
\(113\) | 11.4364 | 1.07585 | 0.537924 | − | 0.842993i | \(-0.319209\pi\) | ||||
0.537924 | + | 0.842993i | \(0.319209\pi\) | |||||||
\(114\) | −0.481376 | −0.0450850 | ||||||||
\(115\) | 1.28049 | 0.119406 | ||||||||
\(116\) | −2.61158 | −0.242479 | ||||||||
\(117\) | 1.81401 | 0.167705 | ||||||||
\(118\) | 18.2824 | 1.68303 | ||||||||
\(119\) | −1.74466 | −0.159933 | ||||||||
\(120\) | −9.33301 | −0.851984 | ||||||||
\(121\) | −8.64878 | −0.786252 | ||||||||
\(122\) | 18.2913 | 1.65602 | ||||||||
\(123\) | 4.29672 | 0.387422 | ||||||||
\(124\) | 4.70665 | 0.422669 | ||||||||
\(125\) | 10.3987 | 0.930090 | ||||||||
\(126\) | 2.69201 | 0.239823 | ||||||||
\(127\) | −3.13744 | −0.278403 | −0.139201 | − | 0.990264i | \(-0.544454\pi\) | ||||
−0.139201 | + | 0.990264i | \(0.544454\pi\) | |||||||
\(128\) | −4.72487 | −0.417624 | ||||||||
\(129\) | 4.24278 | 0.373556 | ||||||||
\(130\) | 3.16629 | 0.277702 | ||||||||
\(131\) | 1.73537 | 0.151620 | 0.0758101 | − | 0.997122i | \(-0.475846\pi\) | ||||
0.0758101 | + | 0.997122i | \(0.475846\pi\) | |||||||
\(132\) | −7.85957 | −0.684087 | ||||||||
\(133\) | 0.0978081 | 0.00848104 | ||||||||
\(134\) | −21.9507 | −1.89625 | ||||||||
\(135\) | 6.40981 | 0.551669 | ||||||||
\(136\) | 21.3408 | 1.82996 | ||||||||
\(137\) | 8.66597 | 0.740384 | 0.370192 | − | 0.928955i | \(-0.379292\pi\) | ||||
0.370192 | + | 0.928955i | \(0.379292\pi\) | |||||||
\(138\) | −2.95373 | −0.251438 | ||||||||
\(139\) | −11.8869 | −1.00823 | −0.504116 | − | 0.863636i | \(-0.668182\pi\) | ||||
−0.504116 | + | 0.863636i | \(0.668182\pi\) | |||||||
\(140\) | 3.29756 | 0.278695 | ||||||||
\(141\) | 7.40334 | 0.623473 | ||||||||
\(142\) | −9.36205 | −0.785646 | ||||||||
\(143\) | 1.53337 | 0.128227 | ||||||||
\(144\) | −15.8530 | −1.32109 | ||||||||
\(145\) | 0.678407 | 0.0563386 | ||||||||
\(146\) | 7.83749 | 0.648636 | ||||||||
\(147\) | −7.26561 | −0.599257 | ||||||||
\(148\) | 24.0418 | 1.97623 | ||||||||
\(149\) | −7.07496 | −0.579603 | −0.289801 | − | 0.957087i | \(-0.593589\pi\) | ||||
−0.289801 | + | 0.957087i | \(0.593589\pi\) | |||||||
\(150\) | −9.88554 | −0.807151 | ||||||||
\(151\) | 16.6729 | 1.35682 | 0.678412 | − | 0.734682i | \(-0.262669\pi\) | ||||
0.678412 | + | 0.734682i | \(0.262669\pi\) | |||||||
\(152\) | −1.19640 | −0.0970407 | ||||||||
\(153\) | −5.52290 | −0.446500 | ||||||||
\(154\) | 2.27553 | 0.183368 | ||||||||
\(155\) | −1.22264 | −0.0982046 | ||||||||
\(156\) | −5.12568 | −0.410383 | ||||||||
\(157\) | 16.5464 | 1.32055 | 0.660273 | − | 0.751026i | \(-0.270441\pi\) | ||||
0.660273 | + | 0.751026i | \(0.270441\pi\) | |||||||
\(158\) | 13.3538 | 1.06237 | ||||||||
\(159\) | −7.81534 | −0.619797 | ||||||||
\(160\) | −10.5308 | −0.832537 | ||||||||
\(161\) | 0.600152 | 0.0472986 | ||||||||
\(162\) | −0.692291 | −0.0543915 | ||||||||
\(163\) | −15.3279 | −1.20057 | −0.600287 | − | 0.799785i | \(-0.704947\pi\) | ||||
−0.600287 | + | 0.799785i | \(0.704947\pi\) | |||||||
\(164\) | 18.5698 | 1.45006 | ||||||||
\(165\) | 2.04167 | 0.158944 | ||||||||
\(166\) | 35.1394 | 2.72735 | ||||||||
\(167\) | 19.2837 | 1.49222 | 0.746108 | − | 0.665825i | \(-0.231920\pi\) | ||||
0.746108 | + | 0.665825i | \(0.231920\pi\) | |||||||
\(168\) | −4.37429 | −0.337484 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −9.64001 | −0.739355 | ||||||||
\(171\) | 0.309622 | 0.0236774 | ||||||||
\(172\) | 18.3367 | 1.39816 | ||||||||
\(173\) | −14.0195 | −1.06588 | −0.532942 | − | 0.846152i | \(-0.678914\pi\) | ||||
−0.532942 | + | 0.846152i | \(0.678914\pi\) | |||||||
\(174\) | −1.56490 | −0.118634 | ||||||||
\(175\) | 2.00859 | 0.151835 | ||||||||
\(176\) | −13.4005 | −1.01010 | ||||||||
\(177\) | 7.68814 | 0.577876 | ||||||||
\(178\) | 16.8676 | 1.26428 | ||||||||
\(179\) | −22.7717 | −1.70203 | −0.851017 | − | 0.525137i | \(-0.824014\pi\) | ||||
−0.851017 | + | 0.525137i | \(0.824014\pi\) | |||||||
\(180\) | 10.4388 | 0.778060 | ||||||||
\(181\) | 15.8733 | 1.17985 | 0.589926 | − | 0.807457i | \(-0.299157\pi\) | ||||
0.589926 | + | 0.807457i | \(0.299157\pi\) | |||||||
\(182\) | 1.48401 | 0.110002 | ||||||||
\(183\) | 7.69189 | 0.568601 | ||||||||
\(184\) | −7.34111 | −0.541194 | ||||||||
\(185\) | −6.24531 | −0.459164 | ||||||||
\(186\) | 2.82028 | 0.206793 | ||||||||
\(187\) | −4.66846 | −0.341392 | ||||||||
\(188\) | 31.9962 | 2.33357 | ||||||||
\(189\) | 3.00421 | 0.218524 | ||||||||
\(190\) | 0.540433 | 0.0392072 | ||||||||
\(191\) | −8.17952 | −0.591849 | −0.295925 | − | 0.955211i | \(-0.595628\pi\) | ||||
−0.295925 | + | 0.955211i | \(0.595628\pi\) | |||||||
\(192\) | 5.25717 | 0.379403 | ||||||||
\(193\) | −14.7608 | −1.06251 | −0.531253 | − | 0.847213i | \(-0.678279\pi\) | ||||
−0.531253 | + | 0.847213i | \(0.678279\pi\) | |||||||
\(194\) | −46.9051 | −3.36759 | ||||||||
\(195\) | 1.33149 | 0.0953500 | ||||||||
\(196\) | −31.4010 | −2.24293 | ||||||||
\(197\) | 10.2450 | 0.729929 | 0.364965 | − | 0.931021i | \(-0.381081\pi\) | ||||
0.364965 | + | 0.931021i | \(0.381081\pi\) | |||||||
\(198\) | 7.20344 | 0.511926 | ||||||||
\(199\) | −8.45228 | −0.599166 | −0.299583 | − | 0.954070i | \(-0.596848\pi\) | ||||
−0.299583 | + | 0.954070i | \(0.596848\pi\) | |||||||
\(200\) | −24.5692 | −1.73731 | ||||||||
\(201\) | −9.23071 | −0.651084 | ||||||||
\(202\) | 1.98976 | 0.139999 | ||||||||
\(203\) | 0.317962 | 0.0223166 | ||||||||
\(204\) | 15.6055 | 1.09261 | ||||||||
\(205\) | −4.82386 | −0.336913 | ||||||||
\(206\) | −32.6903 | −2.27764 | ||||||||
\(207\) | 1.89984 | 0.132048 | ||||||||
\(208\) | −8.73922 | −0.605956 | ||||||||
\(209\) | 0.261721 | 0.0181036 | ||||||||
\(210\) | 1.97594 | 0.136353 | ||||||||
\(211\) | 17.8589 | 1.22946 | 0.614729 | − | 0.788738i | \(-0.289265\pi\) | ||||
0.614729 | + | 0.788738i | \(0.289265\pi\) | |||||||
\(212\) | −33.7769 | −2.31980 | ||||||||
\(213\) | −3.93694 | −0.269755 | ||||||||
\(214\) | −17.5123 | −1.19711 | ||||||||
\(215\) | −4.76330 | −0.324854 | ||||||||
\(216\) | −36.7478 | −2.50037 | ||||||||
\(217\) | −0.573038 | −0.0389003 | ||||||||
\(218\) | 27.8246 | 1.88452 | ||||||||
\(219\) | 3.29583 | 0.222712 | ||||||||
\(220\) | 8.82381 | 0.594901 | ||||||||
\(221\) | −3.04458 | −0.204800 | ||||||||
\(222\) | 14.4062 | 0.966880 | ||||||||
\(223\) | −13.0448 | −0.873547 | −0.436773 | − | 0.899572i | \(-0.643879\pi\) | ||||
−0.436773 | + | 0.899572i | \(0.643879\pi\) | |||||||
\(224\) | −4.93570 | −0.329780 | ||||||||
\(225\) | 6.35840 | 0.423893 | ||||||||
\(226\) | 29.6171 | 1.97010 | ||||||||
\(227\) | 12.3606 | 0.820400 | 0.410200 | − | 0.911996i | \(-0.365459\pi\) | ||||
0.410200 | + | 0.911996i | \(0.365459\pi\) | |||||||
\(228\) | −0.874869 | −0.0579396 | ||||||||
\(229\) | 6.65491 | 0.439769 | 0.219884 | − | 0.975526i | \(-0.429432\pi\) | ||||
0.219884 | + | 0.975526i | \(0.429432\pi\) | |||||||
\(230\) | 3.31611 | 0.218658 | ||||||||
\(231\) | 0.956909 | 0.0629600 | ||||||||
\(232\) | −3.88935 | −0.255348 | ||||||||
\(233\) | −18.4220 | −1.20686 | −0.603432 | − | 0.797415i | \(-0.706200\pi\) | ||||
−0.603432 | + | 0.797415i | \(0.706200\pi\) | |||||||
\(234\) | 4.69778 | 0.307104 | ||||||||
\(235\) | −8.31161 | −0.542190 | ||||||||
\(236\) | 33.2271 | 2.16290 | ||||||||
\(237\) | 5.61553 | 0.364768 | ||||||||
\(238\) | −4.51817 | −0.292870 | ||||||||
\(239\) | −24.7696 | −1.60221 | −0.801107 | − | 0.598521i | \(-0.795755\pi\) | ||||
−0.801107 | + | 0.598521i | \(0.795755\pi\) | |||||||
\(240\) | −11.6362 | −0.751112 | ||||||||
\(241\) | 16.7239 | 1.07728 | 0.538641 | − | 0.842536i | \(-0.318938\pi\) | ||||
0.538641 | + | 0.842536i | \(0.318938\pi\) | |||||||
\(242\) | −22.3979 | −1.43979 | ||||||||
\(243\) | 15.4367 | 0.990265 | ||||||||
\(244\) | 33.2433 | 2.12819 | ||||||||
\(245\) | 8.15698 | 0.521131 | ||||||||
\(246\) | 11.1273 | 0.709451 | ||||||||
\(247\) | 0.170684 | 0.0108603 | ||||||||
\(248\) | 7.00945 | 0.445101 | ||||||||
\(249\) | 14.7768 | 0.936444 | ||||||||
\(250\) | 26.9298 | 1.70319 | ||||||||
\(251\) | −14.3980 | −0.908794 | −0.454397 | − | 0.890799i | \(-0.650145\pi\) | ||||
−0.454397 | + | 0.890799i | \(0.650145\pi\) | |||||||
\(252\) | 4.89255 | 0.308202 | ||||||||
\(253\) | 1.60592 | 0.100964 | ||||||||
\(254\) | −8.12509 | −0.509814 | ||||||||
\(255\) | −4.05382 | −0.253860 | ||||||||
\(256\) | −21.8909 | −1.36818 | ||||||||
\(257\) | 26.7350 | 1.66768 | 0.833841 | − | 0.552005i | \(-0.186137\pi\) | ||||
0.833841 | + | 0.552005i | \(0.186137\pi\) | |||||||
\(258\) | 10.9876 | 0.684058 | ||||||||
\(259\) | −2.92711 | −0.181882 | ||||||||
\(260\) | 5.75452 | 0.356880 | ||||||||
\(261\) | 1.00654 | 0.0623035 | ||||||||
\(262\) | 4.49413 | 0.277648 | ||||||||
\(263\) | 13.1232 | 0.809213 | 0.404606 | − | 0.914491i | \(-0.367409\pi\) | ||||
0.404606 | + | 0.914491i | \(0.367409\pi\) | |||||||
\(264\) | −11.7050 | −0.720392 | ||||||||
\(265\) | 8.77416 | 0.538993 | ||||||||
\(266\) | 0.253296 | 0.0155305 | ||||||||
\(267\) | 7.09318 | 0.434095 | ||||||||
\(268\) | −39.8939 | −2.43691 | ||||||||
\(269\) | 16.7183 | 1.01933 | 0.509666 | − | 0.860372i | \(-0.329769\pi\) | ||||
0.509666 | + | 0.860372i | \(0.329769\pi\) | |||||||
\(270\) | 16.5996 | 1.01022 | ||||||||
\(271\) | −11.6958 | −0.710469 | −0.355235 | − | 0.934777i | \(-0.615599\pi\) | ||||
−0.355235 | + | 0.934777i | \(0.615599\pi\) | |||||||
\(272\) | 26.6072 | 1.61330 | ||||||||
\(273\) | 0.624056 | 0.0377696 | ||||||||
\(274\) | 22.4424 | 1.35580 | ||||||||
\(275\) | 5.37470 | 0.324107 | ||||||||
\(276\) | −5.36821 | −0.323128 | ||||||||
\(277\) | 21.4797 | 1.29059 | 0.645295 | − | 0.763934i | \(-0.276735\pi\) | ||||
0.645295 | + | 0.763934i | \(0.276735\pi\) | |||||||
\(278\) | −30.7837 | −1.84628 | ||||||||
\(279\) | −1.81401 | −0.108602 | ||||||||
\(280\) | 4.91095 | 0.293485 | ||||||||
\(281\) | 4.91202 | 0.293026 | 0.146513 | − | 0.989209i | \(-0.453195\pi\) | ||||
0.146513 | + | 0.989209i | \(0.453195\pi\) | |||||||
\(282\) | 19.1726 | 1.14171 | ||||||||
\(283\) | −8.94867 | −0.531943 | −0.265972 | − | 0.963981i | \(-0.585693\pi\) | ||||
−0.265972 | + | 0.963981i | \(0.585693\pi\) | |||||||
\(284\) | −17.0149 | −1.00965 | ||||||||
\(285\) | 0.227263 | 0.0134619 | ||||||||
\(286\) | 3.97100 | 0.234810 | ||||||||
\(287\) | −2.26089 | −0.133456 | ||||||||
\(288\) | −15.6245 | −0.920682 | ||||||||
\(289\) | −7.73055 | −0.454738 | ||||||||
\(290\) | 1.75688 | 0.103168 | ||||||||
\(291\) | −19.7246 | −1.15628 | ||||||||
\(292\) | 14.2441 | 0.833575 | ||||||||
\(293\) | 5.86850 | 0.342842 | 0.171421 | − | 0.985198i | \(-0.445164\pi\) | ||||
0.171421 | + | 0.985198i | \(0.445164\pi\) | |||||||
\(294\) | −18.8159 | −1.09736 | ||||||||
\(295\) | −8.63136 | −0.502537 | ||||||||
\(296\) | 35.8047 | 2.08111 | ||||||||
\(297\) | 8.03886 | 0.466462 | ||||||||
\(298\) | −18.3221 | −1.06137 | ||||||||
\(299\) | 1.04732 | 0.0605679 | ||||||||
\(300\) | −17.9663 | −1.03729 | ||||||||
\(301\) | −2.23251 | −0.128680 | ||||||||
\(302\) | 43.1782 | 2.48463 | ||||||||
\(303\) | 0.836734 | 0.0480691 | ||||||||
\(304\) | −1.49164 | −0.0855515 | ||||||||
\(305\) | −8.63557 | −0.494471 | ||||||||
\(306\) | −14.3028 | −0.817634 | ||||||||
\(307\) | −30.0293 | −1.71386 | −0.856931 | − | 0.515432i | \(-0.827632\pi\) | ||||
−0.856931 | + | 0.515432i | \(0.827632\pi\) | |||||||
\(308\) | 4.13563 | 0.235649 | ||||||||
\(309\) | −13.7470 | −0.782038 | ||||||||
\(310\) | −3.16629 | −0.179833 | ||||||||
\(311\) | 11.6620 | 0.661290 | 0.330645 | − | 0.943755i | \(-0.392734\pi\) | ||||
0.330645 | + | 0.943755i | \(0.392734\pi\) | |||||||
\(312\) | −7.63351 | −0.432162 | ||||||||
\(313\) | −20.7436 | −1.17250 | −0.586248 | − | 0.810131i | \(-0.699396\pi\) | ||||
−0.586248 | + | 0.810131i | \(0.699396\pi\) | |||||||
\(314\) | 42.8505 | 2.41819 | ||||||||
\(315\) | −1.27093 | −0.0716088 | ||||||||
\(316\) | 24.2696 | 1.36527 | ||||||||
\(317\) | 20.3042 | 1.14040 | 0.570198 | − | 0.821507i | \(-0.306866\pi\) | ||||
0.570198 | + | 0.821507i | \(0.306866\pi\) | |||||||
\(318\) | −20.2395 | −1.13498 | ||||||||
\(319\) | 0.850823 | 0.0476370 | ||||||||
\(320\) | −5.90214 | −0.329940 | ||||||||
\(321\) | −7.36427 | −0.411033 | ||||||||
\(322\) | 1.55422 | 0.0866136 | ||||||||
\(323\) | −0.519659 | −0.0289146 | ||||||||
\(324\) | −1.25819 | −0.0698996 | ||||||||
\(325\) | 3.50516 | 0.194431 | ||||||||
\(326\) | −39.6949 | −2.19850 | ||||||||
\(327\) | 11.7008 | 0.647056 | ||||||||
\(328\) | 27.6555 | 1.52702 | ||||||||
\(329\) | −3.89557 | −0.214770 | ||||||||
\(330\) | 5.28734 | 0.291059 | ||||||||
\(331\) | −24.9050 | −1.36890 | −0.684452 | − | 0.729058i | \(-0.739958\pi\) | ||||
−0.684452 | + | 0.729058i | \(0.739958\pi\) | |||||||
\(332\) | 63.8636 | 3.50497 | ||||||||
\(333\) | −9.26609 | −0.507779 | ||||||||
\(334\) | 49.9393 | 2.73256 | ||||||||
\(335\) | 10.3632 | 0.566201 | ||||||||
\(336\) | −5.45376 | −0.297527 | ||||||||
\(337\) | 4.24298 | 0.231130 | 0.115565 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115565 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(338\) | 2.58972 | 0.140862 | ||||||||
\(339\) | 12.4546 | 0.676442 | ||||||||
\(340\) | −17.5201 | −0.950160 | ||||||||
\(341\) | −1.53337 | −0.0830366 | ||||||||
\(342\) | 0.801834 | 0.0433582 | ||||||||
\(343\) | 7.83436 | 0.423016 | ||||||||
\(344\) | 27.3083 | 1.47236 | ||||||||
\(345\) | 1.39449 | 0.0750769 | ||||||||
\(346\) | −36.3066 | −1.95186 | ||||||||
\(347\) | −27.8347 | −1.49424 | −0.747122 | − | 0.664687i | \(-0.768565\pi\) | ||||
−0.747122 | + | 0.664687i | \(0.768565\pi\) | |||||||
\(348\) | −2.84409 | −0.152459 | ||||||||
\(349\) | −15.2791 | −0.817873 | −0.408937 | − | 0.912563i | \(-0.634100\pi\) | ||||
−0.408937 | + | 0.912563i | \(0.634100\pi\) | |||||||
\(350\) | 5.20168 | 0.278041 | ||||||||
\(351\) | 5.24261 | 0.279830 | ||||||||
\(352\) | −13.2073 | −0.703949 | ||||||||
\(353\) | 15.7131 | 0.836327 | 0.418163 | − | 0.908372i | \(-0.362674\pi\) | ||||
0.418163 | + | 0.908372i | \(0.362674\pi\) | |||||||
\(354\) | 19.9101 | 1.05821 | ||||||||
\(355\) | 4.41994 | 0.234586 | ||||||||
\(356\) | 30.6558 | 1.62475 | ||||||||
\(357\) | −1.89999 | −0.100558 | ||||||||
\(358\) | −58.9722 | −3.11678 | ||||||||
\(359\) | 10.0405 | 0.529918 | 0.264959 | − | 0.964260i | \(-0.414642\pi\) | ||||
0.264959 | + | 0.964260i | \(0.414642\pi\) | |||||||
\(360\) | 15.5461 | 0.819353 | ||||||||
\(361\) | −18.9709 | −0.998467 | ||||||||
\(362\) | 41.1073 | 2.16055 | ||||||||
\(363\) | −9.41878 | −0.494358 | ||||||||
\(364\) | 2.69709 | 0.141366 | ||||||||
\(365\) | −3.70018 | −0.193676 | ||||||||
\(366\) | 19.9198 | 1.04123 | ||||||||
\(367\) | −2.39645 | −0.125094 | −0.0625469 | − | 0.998042i | \(-0.519922\pi\) | ||||
−0.0625469 | + | 0.998042i | \(0.519922\pi\) | |||||||
\(368\) | −9.15272 | −0.477119 | ||||||||
\(369\) | −7.15710 | −0.372584 | ||||||||
\(370\) | −16.1736 | −0.840826 | ||||||||
\(371\) | 4.11236 | 0.213503 | ||||||||
\(372\) | 5.12568 | 0.265754 | ||||||||
\(373\) | −29.7360 | −1.53967 | −0.769835 | − | 0.638243i | \(-0.779661\pi\) | ||||
−0.769835 | + | 0.638243i | \(0.779661\pi\) | |||||||
\(374\) | −12.0900 | −0.625159 | ||||||||
\(375\) | 11.3245 | 0.584796 | ||||||||
\(376\) | 47.6509 | 2.45741 | ||||||||
\(377\) | 0.554872 | 0.0285773 | ||||||||
\(378\) | 7.78007 | 0.400163 | ||||||||
\(379\) | −0.122804 | −0.00630802 | −0.00315401 | − | 0.999995i | \(-0.501004\pi\) | ||||
−0.00315401 | + | 0.999995i | \(0.501004\pi\) | |||||||
\(380\) | 0.982202 | 0.0503859 | ||||||||
\(381\) | −3.41677 | −0.175046 | ||||||||
\(382\) | −21.1827 | −1.08380 | ||||||||
\(383\) | −35.9159 | −1.83522 | −0.917608 | − | 0.397487i | \(-0.869882\pi\) | ||||
−0.917608 | + | 0.397487i | \(0.869882\pi\) | |||||||
\(384\) | −5.14553 | −0.262582 | ||||||||
\(385\) | −1.07431 | −0.0547517 | ||||||||
\(386\) | −38.2263 | −1.94567 | ||||||||
\(387\) | −7.06725 | −0.359248 | ||||||||
\(388\) | −85.2470 | −4.32776 | ||||||||
\(389\) | 6.97889 | 0.353844 | 0.176922 | − | 0.984225i | \(-0.443386\pi\) | ||||
0.176922 | + | 0.984225i | \(0.443386\pi\) | |||||||
\(390\) | 3.44819 | 0.174606 | ||||||||
\(391\) | −3.18863 | −0.161256 | ||||||||
\(392\) | −46.7644 | −2.36196 | ||||||||
\(393\) | 1.88987 | 0.0953315 | ||||||||
\(394\) | 26.5318 | 1.33665 | ||||||||
\(395\) | −6.30447 | −0.317212 | ||||||||
\(396\) | 13.0918 | 0.657887 | ||||||||
\(397\) | −5.41099 | −0.271570 | −0.135785 | − | 0.990738i | \(-0.543356\pi\) | ||||
−0.135785 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(398\) | −21.8890 | −1.09720 | ||||||||
\(399\) | 0.106516 | 0.00533247 | ||||||||
\(400\) | −30.6323 | −1.53162 | ||||||||
\(401\) | 6.50195 | 0.324692 | 0.162346 | − | 0.986734i | \(-0.448094\pi\) | ||||
0.162346 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(402\) | −23.9050 | −1.19227 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | 3.61625 | 0.179915 | ||||||||
\(405\) | 0.326839 | 0.0162408 | ||||||||
\(406\) | 0.823433 | 0.0408663 | ||||||||
\(407\) | −7.83255 | −0.388245 | ||||||||
\(408\) | 23.2408 | 1.15059 | ||||||||
\(409\) | −32.5096 | −1.60750 | −0.803749 | − | 0.594969i | \(-0.797164\pi\) | ||||
−0.803749 | + | 0.594969i | \(0.797164\pi\) | |||||||
\(410\) | −12.4924 | −0.616958 | ||||||||
\(411\) | 9.43750 | 0.465518 | ||||||||
\(412\) | −59.4126 | −2.92705 | ||||||||
\(413\) | −4.04543 | −0.199063 | ||||||||
\(414\) | 4.92006 | 0.241808 | ||||||||
\(415\) | −16.5897 | −0.814358 | ||||||||
\(416\) | −8.61322 | −0.422298 | ||||||||
\(417\) | −12.9452 | −0.633928 | ||||||||
\(418\) | 0.677784 | 0.0331515 | ||||||||
\(419\) | 9.90498 | 0.483890 | 0.241945 | − | 0.970290i | \(-0.422215\pi\) | ||||
0.241945 | + | 0.970290i | \(0.422215\pi\) | |||||||
\(420\) | 3.59114 | 0.175230 | ||||||||
\(421\) | −18.3445 | −0.894057 | −0.447029 | − | 0.894520i | \(-0.647518\pi\) | ||||
−0.447029 | + | 0.894520i | \(0.647518\pi\) | |||||||
\(422\) | 46.2496 | 2.25140 | ||||||||
\(423\) | −12.3318 | −0.599594 | ||||||||
\(424\) | −50.3028 | −2.44292 | ||||||||
\(425\) | −10.6717 | −0.517654 | ||||||||
\(426\) | −10.1956 | −0.493977 | ||||||||
\(427\) | −4.04740 | −0.195867 | ||||||||
\(428\) | −31.8274 | −1.53843 | ||||||||
\(429\) | 1.66989 | 0.0806229 | ||||||||
\(430\) | −12.3356 | −0.594876 | ||||||||
\(431\) | −4.17716 | −0.201207 | −0.100603 | − | 0.994927i | \(-0.532077\pi\) | ||||
−0.100603 | + | 0.994927i | \(0.532077\pi\) | |||||||
\(432\) | −45.8163 | −2.20434 | ||||||||
\(433\) | 11.2781 | 0.541989 | 0.270995 | − | 0.962581i | \(-0.412647\pi\) | ||||
0.270995 | + | 0.962581i | \(0.412647\pi\) | |||||||
\(434\) | −1.48401 | −0.0712346 | ||||||||
\(435\) | 0.738806 | 0.0354230 | ||||||||
\(436\) | 50.5693 | 2.42183 | ||||||||
\(437\) | 0.178760 | 0.00855123 | ||||||||
\(438\) | 8.53527 | 0.407831 | ||||||||
\(439\) | −32.7529 | −1.56321 | −0.781606 | − | 0.623772i | \(-0.785599\pi\) | ||||
−0.781606 | + | 0.623772i | \(0.785599\pi\) | |||||||
\(440\) | 13.1410 | 0.626473 | ||||||||
\(441\) | 12.1024 | 0.576305 | ||||||||
\(442\) | −7.88460 | −0.375032 | ||||||||
\(443\) | −15.3591 | −0.729731 | −0.364865 | − | 0.931060i | \(-0.618885\pi\) | ||||
−0.364865 | + | 0.931060i | \(0.618885\pi\) | |||||||
\(444\) | 26.1823 | 1.24256 | ||||||||
\(445\) | −7.96340 | −0.377501 | ||||||||
\(446\) | −33.7825 | −1.59965 | ||||||||
\(447\) | −7.70484 | −0.364427 | ||||||||
\(448\) | −2.76627 | −0.130694 | ||||||||
\(449\) | 6.85235 | 0.323382 | 0.161691 | − | 0.986841i | \(-0.448305\pi\) | ||||
0.161691 | + | 0.986841i | \(0.448305\pi\) | |||||||
\(450\) | 16.4665 | 0.776236 | ||||||||
\(451\) | −6.04984 | −0.284876 | ||||||||
\(452\) | 53.8272 | 2.53182 | ||||||||
\(453\) | 18.1573 | 0.853106 | ||||||||
\(454\) | 32.0104 | 1.50232 | ||||||||
\(455\) | −0.700618 | −0.0328455 | ||||||||
\(456\) | −1.30291 | −0.0610145 | ||||||||
\(457\) | 11.6216 | 0.543634 | 0.271817 | − | 0.962349i | \(-0.412375\pi\) | ||||
0.271817 | + | 0.962349i | \(0.412375\pi\) | |||||||
\(458\) | 17.2344 | 0.805308 | ||||||||
\(459\) | −15.9615 | −0.745020 | ||||||||
\(460\) | 6.02680 | 0.281001 | ||||||||
\(461\) | 22.0155 | 1.02536 | 0.512681 | − | 0.858579i | \(-0.328652\pi\) | ||||
0.512681 | + | 0.858579i | \(0.328652\pi\) | |||||||
\(462\) | 2.47812 | 0.115293 | ||||||||
\(463\) | −12.6323 | −0.587074 | −0.293537 | − | 0.955948i | \(-0.594832\pi\) | ||||
−0.293537 | + | 0.955948i | \(0.594832\pi\) | |||||||
\(464\) | −4.84914 | −0.225116 | ||||||||
\(465\) | −1.33149 | −0.0617464 | ||||||||
\(466\) | −47.7077 | −2.21002 | ||||||||
\(467\) | −8.71567 | −0.403313 | −0.201657 | − | 0.979456i | \(-0.564633\pi\) | ||||
−0.201657 | + | 0.979456i | \(0.564633\pi\) | |||||||
\(468\) | 8.53791 | 0.394665 | ||||||||
\(469\) | 4.85712 | 0.224281 | ||||||||
\(470\) | −21.5247 | −0.992862 | ||||||||
\(471\) | 18.0195 | 0.830296 | ||||||||
\(472\) | 49.4840 | 2.27769 | ||||||||
\(473\) | −5.97389 | −0.274680 | ||||||||
\(474\) | 14.5427 | 0.667966 | ||||||||
\(475\) | 0.598272 | 0.0274506 | ||||||||
\(476\) | −8.21149 | −0.376373 | ||||||||
\(477\) | 13.0181 | 0.596059 | ||||||||
\(478\) | −64.1464 | −2.93399 | ||||||||
\(479\) | 16.9032 | 0.772325 | 0.386162 | − | 0.922431i | \(-0.373800\pi\) | ||||
0.386162 | + | 0.922431i | \(0.373800\pi\) | |||||||
\(480\) | −11.4684 | −0.523459 | ||||||||
\(481\) | −5.10806 | −0.232908 | ||||||||
\(482\) | 43.3102 | 1.97273 | ||||||||
\(483\) | 0.653584 | 0.0297391 | ||||||||
\(484\) | −40.7067 | −1.85031 | ||||||||
\(485\) | 22.1445 | 1.00553 | ||||||||
\(486\) | 39.9767 | 1.81338 | ||||||||
\(487\) | −0.0858727 | −0.00389127 | −0.00194563 | − | 0.999998i | \(-0.500619\pi\) | ||||
−0.00194563 | + | 0.999998i | \(0.500619\pi\) | |||||||
\(488\) | 49.5082 | 2.24113 | ||||||||
\(489\) | −16.6925 | −0.754863 | ||||||||
\(490\) | 21.1243 | 0.954299 | ||||||||
\(491\) | −39.9349 | −1.80224 | −0.901118 | − | 0.433574i | \(-0.857252\pi\) | ||||
−0.901118 | + | 0.433574i | \(0.857252\pi\) | |||||||
\(492\) | 20.2231 | 0.911729 | ||||||||
\(493\) | −1.68935 | −0.0760845 | ||||||||
\(494\) | 0.442022 | 0.0198875 | ||||||||
\(495\) | −3.40083 | −0.152856 | ||||||||
\(496\) | 8.73922 | 0.392402 | ||||||||
\(497\) | 2.07158 | 0.0929231 | ||||||||
\(498\) | 38.2679 | 1.71482 | ||||||||
\(499\) | 9.38080 | 0.419942 | 0.209971 | − | 0.977708i | \(-0.432663\pi\) | ||||
0.209971 | + | 0.977708i | \(0.432663\pi\) | |||||||
\(500\) | 48.9431 | 2.18880 | ||||||||
\(501\) | 21.0005 | 0.938234 | ||||||||
\(502\) | −37.2868 | −1.66419 | ||||||||
\(503\) | −27.4528 | −1.22406 | −0.612031 | − | 0.790834i | \(-0.709647\pi\) | ||||
−0.612031 | + | 0.790834i | \(0.709647\pi\) | |||||||
\(504\) | 7.28631 | 0.324558 | ||||||||
\(505\) | −0.939388 | −0.0418022 | ||||||||
\(506\) | 4.15889 | 0.184885 | ||||||||
\(507\) | 1.08903 | 0.0483655 | ||||||||
\(508\) | −14.7668 | −0.655172 | ||||||||
\(509\) | 10.8524 | 0.481026 | 0.240513 | − | 0.970646i | \(-0.422684\pi\) | ||||
0.240513 | + | 0.970646i | \(0.422684\pi\) | |||||||
\(510\) | −10.4983 | −0.464871 | ||||||||
\(511\) | −1.73424 | −0.0767180 | ||||||||
\(512\) | −47.2414 | −2.08780 | ||||||||
\(513\) | 0.894827 | 0.0395076 | ||||||||
\(514\) | 69.2361 | 3.05387 | ||||||||
\(515\) | 15.4335 | 0.680082 | ||||||||
\(516\) | 19.9692 | 0.879097 | ||||||||
\(517\) | −10.4240 | −0.458447 | ||||||||
\(518\) | −7.58040 | −0.333064 | ||||||||
\(519\) | −15.2677 | −0.670177 | ||||||||
\(520\) | 8.57002 | 0.375820 | ||||||||
\(521\) | 9.07911 | 0.397763 | 0.198882 | − | 0.980024i | \(-0.436269\pi\) | ||||
0.198882 | + | 0.980024i | \(0.436269\pi\) | |||||||
\(522\) | 2.60667 | 0.114091 | ||||||||
\(523\) | 3.83179 | 0.167552 | 0.0837762 | − | 0.996485i | \(-0.473302\pi\) | ||||
0.0837762 | + | 0.996485i | \(0.473302\pi\) | |||||||
\(524\) | 8.16778 | 0.356811 | ||||||||
\(525\) | 2.18741 | 0.0954666 | ||||||||
\(526\) | 33.9855 | 1.48184 | ||||||||
\(527\) | 3.04458 | 0.132624 | ||||||||
\(528\) | −14.5935 | −0.635101 | ||||||||
\(529\) | −21.9031 | −0.952310 | ||||||||
\(530\) | 22.7226 | 0.987008 | ||||||||
\(531\) | −12.8062 | −0.555743 | ||||||||
\(532\) | 0.460348 | 0.0199586 | ||||||||
\(533\) | −3.94545 | −0.170897 | ||||||||
\(534\) | 18.3693 | 0.794919 | ||||||||
\(535\) | 8.26775 | 0.357446 | ||||||||
\(536\) | −59.4127 | −2.56624 | ||||||||
\(537\) | −24.7991 | −1.07016 | ||||||||
\(538\) | 43.2957 | 1.86661 | ||||||||
\(539\) | 10.2301 | 0.440640 | ||||||||
\(540\) | 30.1687 | 1.29825 | ||||||||
\(541\) | 40.1608 | 1.72665 | 0.863324 | − | 0.504650i | \(-0.168378\pi\) | ||||
0.863324 | + | 0.504650i | \(0.168378\pi\) | |||||||
\(542\) | −30.2888 | −1.30102 | ||||||||
\(543\) | 17.2865 | 0.741834 | ||||||||
\(544\) | 26.2236 | 1.12433 | ||||||||
\(545\) | −13.1363 | −0.562698 | ||||||||
\(546\) | 1.61613 | 0.0691640 | ||||||||
\(547\) | 38.1661 | 1.63186 | 0.815931 | − | 0.578149i | \(-0.196225\pi\) | ||||
0.815931 | + | 0.578149i | \(0.196225\pi\) | |||||||
\(548\) | 40.7876 | 1.74236 | ||||||||
\(549\) | −12.8125 | −0.546823 | ||||||||
\(550\) | 13.9190 | 0.593507 | ||||||||
\(551\) | 0.0947074 | 0.00403467 | ||||||||
\(552\) | −7.99469 | −0.340277 | ||||||||
\(553\) | −2.95484 | −0.125653 | ||||||||
\(554\) | 55.6263 | 2.36334 | ||||||||
\(555\) | −6.80134 | −0.288701 | ||||||||
\(556\) | −55.9473 | −2.37269 | ||||||||
\(557\) | 41.3959 | 1.75400 | 0.877001 | − | 0.480489i | \(-0.159541\pi\) | ||||
0.877001 | + | 0.480489i | \(0.159541\pi\) | |||||||
\(558\) | −4.69778 | −0.198873 | ||||||||
\(559\) | −3.89592 | −0.164780 | ||||||||
\(560\) | 6.12285 | 0.258738 | ||||||||
\(561\) | −5.08410 | −0.214651 | ||||||||
\(562\) | 12.7207 | 0.536592 | ||||||||
\(563\) | 16.6148 | 0.700232 | 0.350116 | − | 0.936706i | \(-0.386142\pi\) | ||||
0.350116 | + | 0.936706i | \(0.386142\pi\) | |||||||
\(564\) | 34.8449 | 1.46723 | ||||||||
\(565\) | −13.9826 | −0.588253 | ||||||||
\(566\) | −23.1745 | −0.974098 | ||||||||
\(567\) | 0.153186 | 0.00643321 | ||||||||
\(568\) | −25.3398 | −1.06323 | ||||||||
\(569\) | 44.4229 | 1.86230 | 0.931152 | − | 0.364631i | \(-0.118805\pi\) | ||||
0.931152 | + | 0.364631i | \(0.118805\pi\) | |||||||
\(570\) | 0.588548 | 0.0246516 | ||||||||
\(571\) | 11.7168 | 0.490332 | 0.245166 | − | 0.969481i | \(-0.421157\pi\) | ||||
0.245166 | + | 0.969481i | \(0.421157\pi\) | |||||||
\(572\) | 7.21703 | 0.301759 | ||||||||
\(573\) | −8.90775 | −0.372127 | ||||||||
\(574\) | −5.85508 | −0.244386 | ||||||||
\(575\) | 3.67101 | 0.153092 | ||||||||
\(576\) | −8.75693 | −0.364872 | ||||||||
\(577\) | −9.27400 | −0.386082 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(578\) | −20.0200 | −0.832721 | ||||||||
\(579\) | −16.0750 | −0.668053 | ||||||||
\(580\) | 3.19302 | 0.132583 | ||||||||
\(581\) | −7.77544 | −0.322580 | ||||||||
\(582\) | −51.0811 | −2.11738 | ||||||||
\(583\) | 11.0041 | 0.455744 | ||||||||
\(584\) | 21.2133 | 0.877813 | ||||||||
\(585\) | −2.21788 | −0.0916981 | ||||||||
\(586\) | 15.1978 | 0.627814 | ||||||||
\(587\) | −26.9865 | −1.11385 | −0.556927 | − | 0.830562i | \(-0.688020\pi\) | ||||
−0.556927 | + | 0.830562i | \(0.688020\pi\) | |||||||
\(588\) | −34.1966 | −1.41025 | ||||||||
\(589\) | −0.170684 | −0.00703289 | ||||||||
\(590\) | −22.3528 | −0.920250 | ||||||||
\(591\) | 11.1572 | 0.458945 | ||||||||
\(592\) | 44.6405 | 1.83471 | ||||||||
\(593\) | 12.8406 | 0.527299 | 0.263649 | − | 0.964619i | \(-0.415074\pi\) | ||||
0.263649 | + | 0.964619i | \(0.415074\pi\) | |||||||
\(594\) | 20.8184 | 0.854188 | ||||||||
\(595\) | 2.13308 | 0.0874480 | ||||||||
\(596\) | −33.2993 | −1.36399 | ||||||||
\(597\) | −9.20479 | −0.376727 | ||||||||
\(598\) | 2.71225 | 0.110912 | ||||||||
\(599\) | −33.5314 | −1.37006 | −0.685029 | − | 0.728516i | \(-0.740210\pi\) | ||||
−0.685029 | + | 0.728516i | \(0.740210\pi\) | |||||||
\(600\) | −26.7566 | −1.09234 | ||||||||
\(601\) | −36.7391 | −1.49862 | −0.749310 | − | 0.662220i | \(-0.769615\pi\) | ||||
−0.749310 | + | 0.662220i | \(0.769615\pi\) | |||||||
\(602\) | −5.78157 | −0.235639 | ||||||||
\(603\) | 15.3757 | 0.626148 | ||||||||
\(604\) | 78.4735 | 3.19304 | ||||||||
\(605\) | 10.5743 | 0.429907 | ||||||||
\(606\) | 2.16691 | 0.0880245 | ||||||||
\(607\) | 6.49000 | 0.263421 | 0.131710 | − | 0.991288i | \(-0.457953\pi\) | ||||
0.131710 | + | 0.991288i | \(0.457953\pi\) | |||||||
\(608\) | −1.47013 | −0.0596218 | ||||||||
\(609\) | 0.346271 | 0.0140316 | ||||||||
\(610\) | −22.3637 | −0.905479 | ||||||||
\(611\) | −6.79810 | −0.275022 | ||||||||
\(612\) | −25.9943 | −1.05076 | ||||||||
\(613\) | −23.9687 | −0.968088 | −0.484044 | − | 0.875044i | \(-0.660833\pi\) | ||||
−0.484044 | + | 0.875044i | \(0.660833\pi\) | |||||||
\(614\) | −77.7674 | −3.13844 | ||||||||
\(615\) | −5.25333 | −0.211835 | ||||||||
\(616\) | 6.15906 | 0.248156 | ||||||||
\(617\) | −31.1849 | −1.25546 | −0.627729 | − | 0.778432i | \(-0.716015\pi\) | ||||
−0.627729 | + | 0.778432i | \(0.716015\pi\) | |||||||
\(618\) | −35.6008 | −1.43207 | ||||||||
\(619\) | −3.32672 | −0.133712 | −0.0668561 | − | 0.997763i | \(-0.521297\pi\) | ||||
−0.0668561 | + | 0.997763i | \(0.521297\pi\) | |||||||
\(620\) | −5.75452 | −0.231107 | ||||||||
\(621\) | 5.49067 | 0.220333 | ||||||||
\(622\) | 30.2012 | 1.21096 | ||||||||
\(623\) | −3.73236 | −0.149534 | ||||||||
\(624\) | −9.51728 | −0.380996 | ||||||||
\(625\) | 4.81191 | 0.192476 | ||||||||
\(626\) | −53.7201 | −2.14709 | ||||||||
\(627\) | 0.285022 | 0.0113827 | ||||||||
\(628\) | 77.8780 | 3.10767 | ||||||||
\(629\) | 15.5519 | 0.620094 | ||||||||
\(630\) | −3.29135 | −0.131131 | ||||||||
\(631\) | 26.4173 | 1.05166 | 0.525829 | − | 0.850590i | \(-0.323755\pi\) | ||||
0.525829 | + | 0.850590i | \(0.323755\pi\) | |||||||
\(632\) | 36.1439 | 1.43773 | ||||||||
\(633\) | 19.4489 | 0.773025 | ||||||||
\(634\) | 52.5821 | 2.08830 | ||||||||
\(635\) | 3.83595 | 0.152225 | ||||||||
\(636\) | −36.7840 | −1.45858 | ||||||||
\(637\) | 6.67163 | 0.264340 | ||||||||
\(638\) | 2.20339 | 0.0872332 | ||||||||
\(639\) | 6.55781 | 0.259423 | ||||||||
\(640\) | 5.77681 | 0.228348 | ||||||||
\(641\) | 30.9803 | 1.22365 | 0.611825 | − | 0.790993i | \(-0.290436\pi\) | ||||
0.611825 | + | 0.790993i | \(0.290436\pi\) | |||||||
\(642\) | −19.0714 | −0.752687 | ||||||||
\(643\) | −34.9166 | −1.37698 | −0.688488 | − | 0.725248i | \(-0.741725\pi\) | ||||
−0.688488 | + | 0.725248i | \(0.741725\pi\) | |||||||
\(644\) | 2.82470 | 0.111309 | ||||||||
\(645\) | −5.18738 | −0.204253 | ||||||||
\(646\) | −1.34577 | −0.0529487 | ||||||||
\(647\) | 46.6829 | 1.83529 | 0.917647 | − | 0.397396i | \(-0.130086\pi\) | ||||
0.917647 | + | 0.397396i | \(0.130086\pi\) | |||||||
\(648\) | −1.87378 | −0.0736092 | ||||||||
\(649\) | −10.8250 | −0.424919 | ||||||||
\(650\) | 9.07737 | 0.356044 | ||||||||
\(651\) | −0.624056 | −0.0244587 | ||||||||
\(652\) | −72.1430 | −2.82534 | ||||||||
\(653\) | 25.1719 | 0.985053 | 0.492526 | − | 0.870297i | \(-0.336073\pi\) | ||||
0.492526 | + | 0.870297i | \(0.336073\pi\) | |||||||
\(654\) | 30.3018 | 1.18489 | ||||||||
\(655\) | −2.12173 | −0.0829029 | ||||||||
\(656\) | 34.4802 | 1.34622 | ||||||||
\(657\) | −5.48990 | −0.214182 | ||||||||
\(658\) | −10.0884 | −0.393288 | ||||||||
\(659\) | −22.6064 | −0.880620 | −0.440310 | − | 0.897846i | \(-0.645131\pi\) | ||||
−0.440310 | + | 0.897846i | \(0.645131\pi\) | |||||||
\(660\) | 9.60940 | 0.374045 | ||||||||
\(661\) | 28.2947 | 1.10054 | 0.550268 | − | 0.834988i | \(-0.314525\pi\) | ||||
0.550268 | + | 0.834988i | \(0.314525\pi\) | |||||||
\(662\) | −64.4970 | −2.50675 | ||||||||
\(663\) | −3.31564 | −0.128769 | ||||||||
\(664\) | 95.1099 | 3.69098 | ||||||||
\(665\) | −0.119584 | −0.00463727 | ||||||||
\(666\) | −23.9966 | −0.929848 | ||||||||
\(667\) | 0.581126 | 0.0225013 | ||||||||
\(668\) | 90.7614 | 3.51166 | ||||||||
\(669\) | −14.2062 | −0.549244 | ||||||||
\(670\) | 26.8377 | 1.03683 | ||||||||
\(671\) | −10.8303 | −0.418099 | ||||||||
\(672\) | −5.37513 | −0.207350 | ||||||||
\(673\) | −15.4671 | −0.596212 | −0.298106 | − | 0.954533i | \(-0.596355\pi\) | ||||
−0.298106 | + | 0.954533i | \(0.596355\pi\) | |||||||
\(674\) | 10.9881 | 0.423247 | ||||||||
\(675\) | 18.3762 | 0.707299 | ||||||||
\(676\) | 4.70665 | 0.181025 | ||||||||
\(677\) | −5.14548 | −0.197757 | −0.0988785 | − | 0.995100i | \(-0.531526\pi\) | ||||
−0.0988785 | + | 0.995100i | \(0.531526\pi\) | |||||||
\(678\) | 32.2540 | 1.23871 | ||||||||
\(679\) | 10.3789 | 0.398305 | ||||||||
\(680\) | −26.0921 | −1.00059 | ||||||||
\(681\) | 13.4610 | 0.515828 | ||||||||
\(682\) | −3.97100 | −0.152057 | ||||||||
\(683\) | 48.3922 | 1.85168 | 0.925838 | − | 0.377920i | \(-0.123361\pi\) | ||||
0.925838 | + | 0.377920i | \(0.123361\pi\) | |||||||
\(684\) | 1.45728 | 0.0557205 | ||||||||
\(685\) | −10.5953 | −0.404827 | ||||||||
\(686\) | 20.2888 | 0.774630 | ||||||||
\(687\) | 7.24740 | 0.276506 | ||||||||
\(688\) | 34.0473 | 1.29804 | ||||||||
\(689\) | 7.17642 | 0.273400 | ||||||||
\(690\) | 3.61134 | 0.137481 | ||||||||
\(691\) | 26.0413 | 0.990658 | 0.495329 | − | 0.868705i | \(-0.335047\pi\) | ||||
0.495329 | + | 0.868705i | \(0.335047\pi\) | |||||||
\(692\) | −65.9849 | −2.50837 | ||||||||
\(693\) | −1.59393 | −0.0605486 | ||||||||
\(694\) | −72.0840 | −2.73627 | ||||||||
\(695\) | 14.5333 | 0.551281 | ||||||||
\(696\) | −4.23562 | −0.160551 | ||||||||
\(697\) | 12.0122 | 0.454996 | ||||||||
\(698\) | −39.5687 | −1.49770 | ||||||||
\(699\) | −20.0621 | −0.758818 | ||||||||
\(700\) | 9.45371 | 0.357317 | ||||||||
\(701\) | 29.0404 | 1.09684 | 0.548420 | − | 0.836203i | \(-0.315230\pi\) | ||||
0.548420 | + | 0.836203i | \(0.315230\pi\) | |||||||
\(702\) | 13.5769 | 0.512426 | ||||||||
\(703\) | −0.871862 | −0.0328829 | ||||||||
\(704\) | −7.40216 | −0.278980 | ||||||||
\(705\) | −9.05160 | −0.340903 | ||||||||
\(706\) | 40.6926 | 1.53149 | ||||||||
\(707\) | −0.440282 | −0.0165585 | ||||||||
\(708\) | 36.1853 | 1.35993 | ||||||||
\(709\) | 8.70581 | 0.326953 | 0.163477 | − | 0.986547i | \(-0.447729\pi\) | ||||
0.163477 | + | 0.986547i | \(0.447729\pi\) | |||||||
\(710\) | 11.4464 | 0.429576 | ||||||||
\(711\) | −9.35387 | −0.350797 | ||||||||
\(712\) | 45.6546 | 1.71098 | ||||||||
\(713\) | −1.04732 | −0.0392223 | ||||||||
\(714\) | −4.92043 | −0.184142 | ||||||||
\(715\) | −1.87476 | −0.0701119 | ||||||||
\(716\) | −107.178 | −4.00544 | ||||||||
\(717\) | −26.9749 | −1.00740 | ||||||||
\(718\) | 26.0021 | 0.970389 | ||||||||
\(719\) | 20.1480 | 0.751392 | 0.375696 | − | 0.926743i | \(-0.377404\pi\) | ||||
0.375696 | + | 0.926743i | \(0.377404\pi\) | |||||||
\(720\) | 19.3825 | 0.722345 | ||||||||
\(721\) | 7.23353 | 0.269391 | ||||||||
\(722\) | −49.1292 | −1.82840 | ||||||||
\(723\) | 18.2128 | 0.677343 | ||||||||
\(724\) | 74.7099 | 2.77657 | ||||||||
\(725\) | 1.94491 | 0.0722322 | ||||||||
\(726\) | −24.3920 | −0.905272 | ||||||||
\(727\) | 10.3774 | 0.384876 | 0.192438 | − | 0.981309i | \(-0.438361\pi\) | ||||
0.192438 | + | 0.981309i | \(0.438361\pi\) | |||||||
\(728\) | 4.01668 | 0.148868 | ||||||||
\(729\) | 17.6130 | 0.652334 | ||||||||
\(730\) | −9.58242 | −0.354661 | ||||||||
\(731\) | 11.8614 | 0.438711 | ||||||||
\(732\) | 36.2030 | 1.33810 | ||||||||
\(733\) | 50.8688 | 1.87888 | 0.939441 | − | 0.342712i | \(-0.111345\pi\) | ||||
0.939441 | + | 0.342712i | \(0.111345\pi\) | |||||||
\(734\) | −6.20614 | −0.229073 | ||||||||
\(735\) | 8.88321 | 0.327662 | ||||||||
\(736\) | −9.02076 | −0.332510 | ||||||||
\(737\) | 12.9970 | 0.478749 | ||||||||
\(738\) | −18.5349 | −0.682278 | ||||||||
\(739\) | 35.0783 | 1.29038 | 0.645189 | − | 0.764023i | \(-0.276779\pi\) | ||||
0.645189 | + | 0.764023i | \(0.276779\pi\) | |||||||
\(740\) | −29.3945 | −1.08056 | ||||||||
\(741\) | 0.185880 | 0.00682846 | ||||||||
\(742\) | 10.6499 | 0.390969 | ||||||||
\(743\) | 22.5151 | 0.825998 | 0.412999 | − | 0.910732i | \(-0.364481\pi\) | ||||
0.412999 | + | 0.910732i | \(0.364481\pi\) | |||||||
\(744\) | 7.63351 | 0.279858 | ||||||||
\(745\) | 8.65011 | 0.316915 | ||||||||
\(746\) | −77.0078 | −2.81946 | ||||||||
\(747\) | −24.6140 | −0.900578 | ||||||||
\(748\) | −21.9728 | −0.803405 | ||||||||
\(749\) | 3.87501 | 0.141590 | ||||||||
\(750\) | 29.3274 | 1.07088 | ||||||||
\(751\) | −43.8171 | −1.59891 | −0.799454 | − | 0.600727i | \(-0.794878\pi\) | ||||
−0.799454 | + | 0.600727i | \(0.794878\pi\) | |||||||
\(752\) | 59.4101 | 2.16646 | ||||||||
\(753\) | −15.6799 | −0.571406 | ||||||||
\(754\) | 1.43696 | 0.0523311 | ||||||||
\(755\) | −20.3849 | −0.741884 | ||||||||
\(756\) | 14.1398 | 0.514258 | ||||||||
\(757\) | 42.2912 | 1.53710 | 0.768550 | − | 0.639790i | \(-0.220979\pi\) | ||||
0.768550 | + | 0.639790i | \(0.220979\pi\) | |||||||
\(758\) | −0.318028 | −0.0115513 | ||||||||
\(759\) | 1.74890 | 0.0634810 | ||||||||
\(760\) | 1.46276 | 0.0530599 | ||||||||
\(761\) | −42.8193 | −1.55220 | −0.776099 | − | 0.630611i | \(-0.782804\pi\) | ||||
−0.776099 | + | 0.630611i | \(0.782804\pi\) | |||||||
\(762\) | −8.84847 | −0.320546 | ||||||||
\(763\) | −6.15685 | −0.222893 | ||||||||
\(764\) | −38.4981 | −1.39281 | ||||||||
\(765\) | 6.75251 | 0.244137 | ||||||||
\(766\) | −93.0120 | −3.36066 | ||||||||
\(767\) | −7.05962 | −0.254908 | ||||||||
\(768\) | −23.8398 | −0.860245 | ||||||||
\(769\) | 25.3392 | 0.913754 | 0.456877 | − | 0.889530i | \(-0.348968\pi\) | ||||
0.456877 | + | 0.889530i | \(0.348968\pi\) | |||||||
\(770\) | −2.78215 | −0.100262 | ||||||||
\(771\) | 29.1152 | 1.04856 | ||||||||
\(772\) | −69.4739 | −2.50042 | ||||||||
\(773\) | −11.6925 | −0.420551 | −0.210276 | − | 0.977642i | \(-0.567436\pi\) | ||||
−0.210276 | + | 0.977642i | \(0.567436\pi\) | |||||||
\(774\) | −18.3022 | −0.657859 | ||||||||
\(775\) | −3.50516 | −0.125909 | ||||||||
\(776\) | −126.956 | −4.55744 | ||||||||
\(777\) | −3.18772 | −0.114359 | ||||||||
\(778\) | 18.0734 | 0.647961 | ||||||||
\(779\) | −0.673424 | −0.0241279 | ||||||||
\(780\) | 6.26685 | 0.224389 | ||||||||
\(781\) | 5.54326 | 0.198354 | ||||||||
\(782\) | −8.25767 | −0.295294 | ||||||||
\(783\) | 2.90897 | 0.103958 | ||||||||
\(784\) | −58.3048 | −2.08231 | ||||||||
\(785\) | −20.2302 | −0.722048 | ||||||||
\(786\) | 4.89424 | 0.174572 | ||||||||
\(787\) | 18.3689 | 0.654782 | 0.327391 | − | 0.944889i | \(-0.393831\pi\) | ||||
0.327391 | + | 0.944889i | \(0.393831\pi\) | |||||||
\(788\) | 48.2198 | 1.71776 | ||||||||
\(789\) | 14.2916 | 0.508794 | ||||||||
\(790\) | −16.3268 | −0.580882 | ||||||||
\(791\) | −6.55351 | −0.233016 | ||||||||
\(792\) | 19.4972 | 0.692801 | ||||||||
\(793\) | −7.06306 | −0.250817 | ||||||||
\(794\) | −14.0129 | −0.497301 | ||||||||
\(795\) | 9.55533 | 0.338893 | ||||||||
\(796\) | −39.7819 | −1.41003 | ||||||||
\(797\) | 11.0461 | 0.391272 | 0.195636 | − | 0.980677i | \(-0.437323\pi\) | ||||
0.195636 | + | 0.980677i | \(0.437323\pi\) | |||||||
\(798\) | 0.275847 | 0.00976487 | ||||||||
\(799\) | 20.6973 | 0.732219 | ||||||||
\(800\) | −30.1907 | −1.06740 | ||||||||
\(801\) | −11.8152 | −0.417469 | ||||||||
\(802\) | 16.8382 | 0.594578 | ||||||||
\(803\) | −4.64057 | −0.163762 | ||||||||
\(804\) | −43.4457 | −1.53221 | ||||||||
\(805\) | −0.733768 | −0.0258619 | ||||||||
\(806\) | −2.58972 | −0.0912190 | ||||||||
\(807\) | 18.2067 | 0.640907 | ||||||||
\(808\) | 5.38557 | 0.189464 | ||||||||
\(809\) | −25.8647 | −0.909355 | −0.454678 | − | 0.890656i | \(-0.650246\pi\) | ||||
−0.454678 | + | 0.890656i | \(0.650246\pi\) | |||||||
\(810\) | 0.846421 | 0.0297402 | ||||||||
\(811\) | 41.7130 | 1.46474 | 0.732372 | − | 0.680905i | \(-0.238413\pi\) | ||||
0.732372 | + | 0.680905i | \(0.238413\pi\) | |||||||
\(812\) | 1.49654 | 0.0525181 | ||||||||
\(813\) | −12.7371 | −0.446709 | ||||||||
\(814\) | −20.2841 | −0.710958 | ||||||||
\(815\) | 18.7405 | 0.656450 | ||||||||
\(816\) | 28.9761 | 1.01437 | ||||||||
\(817\) | −0.664969 | −0.0232643 | ||||||||
\(818\) | −84.1908 | −2.94366 | ||||||||
\(819\) | −1.03950 | −0.0363230 | ||||||||
\(820\) | −22.7042 | −0.792865 | ||||||||
\(821\) | 42.4540 | 1.48166 | 0.740828 | − | 0.671695i | \(-0.234434\pi\) | ||||
0.740828 | + | 0.671695i | \(0.234434\pi\) | |||||||
\(822\) | 24.4405 | 0.852460 | ||||||||
\(823\) | −29.0780 | −1.01359 | −0.506797 | − | 0.862065i | \(-0.669171\pi\) | ||||
−0.506797 | + | 0.862065i | \(0.669171\pi\) | |||||||
\(824\) | −88.4812 | −3.08239 | ||||||||
\(825\) | 5.85322 | 0.203783 | ||||||||
\(826\) | −10.4765 | −0.364525 | ||||||||
\(827\) | −36.4739 | −1.26832 | −0.634161 | − | 0.773201i | \(-0.718654\pi\) | ||||
−0.634161 | + | 0.773201i | \(0.718654\pi\) | |||||||
\(828\) | 8.94189 | 0.310752 | ||||||||
\(829\) | −43.6715 | −1.51678 | −0.758388 | − | 0.651804i | \(-0.774013\pi\) | ||||
−0.758388 | + | 0.651804i | \(0.774013\pi\) | |||||||
\(830\) | −42.9628 | −1.49126 | ||||||||
\(831\) | 23.3920 | 0.811461 | ||||||||
\(832\) | −4.82738 | −0.167359 | ||||||||
\(833\) | −20.3123 | −0.703779 | ||||||||
\(834\) | −33.5244 | −1.16085 | ||||||||
\(835\) | −23.5770 | −0.815914 | ||||||||
\(836\) | 1.23183 | 0.0426037 | ||||||||
\(837\) | −5.24261 | −0.181211 | ||||||||
\(838\) | 25.6511 | 0.886103 | ||||||||
\(839\) | 1.66526 | 0.0574912 | 0.0287456 | − | 0.999587i | \(-0.490849\pi\) | ||||
0.0287456 | + | 0.999587i | \(0.490849\pi\) | |||||||
\(840\) | 5.34817 | 0.184529 | ||||||||
\(841\) | −28.6921 | −0.989383 | ||||||||
\(842\) | −47.5072 | −1.63721 | ||||||||
\(843\) | 5.34934 | 0.184241 | ||||||||
\(844\) | 84.0556 | 2.89331 | ||||||||
\(845\) | −1.22264 | −0.0420600 | ||||||||
\(846\) | −31.9360 | −1.09798 | ||||||||
\(847\) | 4.95608 | 0.170293 | ||||||||
\(848\) | −62.7163 | −2.15369 | ||||||||
\(849\) | −9.74537 | −0.334460 | ||||||||
\(850\) | −27.6368 | −0.947933 | ||||||||
\(851\) | −5.34976 | −0.183387 | ||||||||
\(852\) | −18.5298 | −0.634819 | ||||||||
\(853\) | 43.2903 | 1.48223 | 0.741116 | − | 0.671377i | \(-0.234297\pi\) | ||||
0.741116 | + | 0.671377i | \(0.234297\pi\) | |||||||
\(854\) | −10.4816 | −0.358674 | ||||||||
\(855\) | −0.378556 | −0.0129463 | ||||||||
\(856\) | −47.3995 | −1.62008 | ||||||||
\(857\) | 49.8064 | 1.70135 | 0.850677 | − | 0.525688i | \(-0.176192\pi\) | ||||
0.850677 | + | 0.525688i | \(0.176192\pi\) | |||||||
\(858\) | 4.32454 | 0.147637 | ||||||||
\(859\) | −29.5928 | −1.00969 | −0.504846 | − | 0.863209i | \(-0.668451\pi\) | ||||
−0.504846 | + | 0.863209i | \(0.668451\pi\) | |||||||
\(860\) | −22.4192 | −0.764487 | ||||||||
\(861\) | −2.46218 | −0.0839110 | ||||||||
\(862\) | −10.8177 | −0.368451 | ||||||||
\(863\) | 6.55697 | 0.223202 | 0.111601 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111601 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(864\) | −45.1557 | −1.53623 | ||||||||
\(865\) | 17.1408 | 0.582805 | ||||||||
\(866\) | 29.2070 | 0.992495 | ||||||||
\(867\) | −8.41881 | −0.285918 | ||||||||
\(868\) | −2.69709 | −0.0915451 | ||||||||
\(869\) | −7.90675 | −0.268218 | ||||||||
\(870\) | 1.91330 | 0.0648669 | ||||||||
\(871\) | 8.47608 | 0.287201 | ||||||||
\(872\) | 75.3112 | 2.55036 | ||||||||
\(873\) | 32.8555 | 1.11199 | ||||||||
\(874\) | 0.462937 | 0.0156591 | ||||||||
\(875\) | −5.95886 | −0.201446 | ||||||||
\(876\) | 15.5123 | 0.524112 | ||||||||
\(877\) | −9.40850 | −0.317703 | −0.158851 | − | 0.987303i | \(-0.550779\pi\) | ||||
−0.158851 | + | 0.987303i | \(0.550779\pi\) | |||||||
\(878\) | −84.8209 | −2.86257 | ||||||||
\(879\) | 6.39098 | 0.215562 | ||||||||
\(880\) | 16.3839 | 0.552301 | ||||||||
\(881\) | −42.2031 | −1.42186 | −0.710930 | − | 0.703263i | \(-0.751726\pi\) | ||||
−0.710930 | + | 0.703263i | \(0.751726\pi\) | |||||||
\(882\) | 31.3419 | 1.05534 | ||||||||
\(883\) | 24.4614 | 0.823192 | 0.411596 | − | 0.911366i | \(-0.364971\pi\) | ||||
0.411596 | + | 0.911366i | \(0.364971\pi\) | |||||||
\(884\) | −14.3297 | −0.481961 | ||||||||
\(885\) | −9.39981 | −0.315971 | ||||||||
\(886\) | −39.7756 | −1.33629 | ||||||||
\(887\) | 22.2383 | 0.746690 | 0.373345 | − | 0.927693i | \(-0.378211\pi\) | ||||
0.373345 | + | 0.927693i | \(0.378211\pi\) | |||||||
\(888\) | 38.9924 | 1.30850 | ||||||||
\(889\) | 1.79787 | 0.0602987 | ||||||||
\(890\) | −20.6230 | −0.691283 | ||||||||
\(891\) | 0.409905 | 0.0137323 | ||||||||
\(892\) | −61.3974 | −2.05574 | ||||||||
\(893\) | −1.16032 | −0.0388287 | ||||||||
\(894\) | −19.9534 | −0.667341 | ||||||||
\(895\) | 27.8415 | 0.930639 | ||||||||
\(896\) | 2.70753 | 0.0904523 | ||||||||
\(897\) | 1.14056 | 0.0380822 | ||||||||
\(898\) | 17.7457 | 0.592180 | ||||||||
\(899\) | −0.554872 | −0.0185060 | ||||||||
\(900\) | 29.9267 | 0.997557 | ||||||||
\(901\) | −21.8492 | −0.727901 | ||||||||
\(902\) | −15.6674 | −0.521667 | ||||||||
\(903\) | −2.43127 | −0.0809077 | ||||||||
\(904\) | 80.1631 | 2.66618 | ||||||||
\(905\) | −19.4073 | −0.645120 | ||||||||
\(906\) | 47.0224 | 1.56221 | ||||||||
\(907\) | 47.7520 | 1.58558 | 0.792790 | − | 0.609495i | \(-0.208628\pi\) | ||||
0.792790 | + | 0.609495i | \(0.208628\pi\) | |||||||
\(908\) | 58.1768 | 1.93067 | ||||||||
\(909\) | −1.39376 | −0.0462280 | ||||||||
\(910\) | −1.81440 | −0.0601469 | ||||||||
\(911\) | −0.138448 | −0.00458697 | −0.00229349 | − | 0.999997i | \(-0.500730\pi\) | ||||
−0.00229349 | + | 0.999997i | \(0.500730\pi\) | |||||||
\(912\) | −1.62444 | −0.0537907 | ||||||||
\(913\) | −20.8060 | −0.688578 | ||||||||
\(914\) | 30.0966 | 0.995507 | ||||||||
\(915\) | −9.40440 | −0.310900 | ||||||||
\(916\) | 31.3223 | 1.03492 | ||||||||
\(917\) | −0.994434 | −0.0328391 | ||||||||
\(918\) | −41.3358 | −1.36429 | ||||||||
\(919\) | 9.66845 | 0.318933 | 0.159466 | − | 0.987203i | \(-0.449023\pi\) | ||||
0.159466 | + | 0.987203i | \(0.449023\pi\) | |||||||
\(920\) | 8.97552 | 0.295914 | ||||||||
\(921\) | −32.7028 | −1.07759 | ||||||||
\(922\) | 57.0139 | 1.87765 | ||||||||
\(923\) | 3.61508 | 0.118992 | ||||||||
\(924\) | 4.50383 | 0.148165 | ||||||||
\(925\) | −17.9046 | −0.588698 | ||||||||
\(926\) | −32.7142 | −1.07505 | ||||||||
\(927\) | 22.8985 | 0.752085 | ||||||||
\(928\) | −4.77923 | −0.156886 | ||||||||
\(929\) | −11.9193 | −0.391061 | −0.195531 | − | 0.980698i | \(-0.562643\pi\) | ||||
−0.195531 | + | 0.980698i | \(0.562643\pi\) | |||||||
\(930\) | −3.44819 | −0.113070 | ||||||||
\(931\) | 1.13874 | 0.0373206 | ||||||||
\(932\) | −86.7057 | −2.84014 | ||||||||
\(933\) | 12.7002 | 0.415787 | ||||||||
\(934\) | −22.5711 | −0.738550 | ||||||||
\(935\) | 5.70784 | 0.186666 | ||||||||
\(936\) | 12.7152 | 0.415610 | ||||||||
\(937\) | 9.05049 | 0.295667 | 0.147833 | − | 0.989012i | \(-0.452770\pi\) | ||||
0.147833 | + | 0.989012i | \(0.452770\pi\) | |||||||
\(938\) | 12.5786 | 0.410705 | ||||||||
\(939\) | −22.5904 | −0.737210 | ||||||||
\(940\) | −39.1198 | −1.27595 | ||||||||
\(941\) | 17.7185 | 0.577607 | 0.288804 | − | 0.957388i | \(-0.406743\pi\) | ||||
0.288804 | + | 0.957388i | \(0.406743\pi\) | |||||||
\(942\) | 46.6655 | 1.52044 | ||||||||
\(943\) | −4.13214 | −0.134561 | ||||||||
\(944\) | 61.6955 | 2.00802 | ||||||||
\(945\) | −3.67306 | −0.119485 | ||||||||
\(946\) | −15.4707 | −0.502996 | ||||||||
\(947\) | 57.5147 | 1.86898 | 0.934489 | − | 0.355993i | \(-0.115857\pi\) | ||||
0.934489 | + | 0.355993i | \(0.115857\pi\) | |||||||
\(948\) | 26.4303 | 0.858417 | ||||||||
\(949\) | −3.02639 | −0.0982407 | ||||||||
\(950\) | 1.54936 | 0.0502678 | ||||||||
\(951\) | 22.1119 | 0.717026 | ||||||||
\(952\) | −12.2291 | −0.396347 | ||||||||
\(953\) | 4.03295 | 0.130640 | 0.0653201 | − | 0.997864i | \(-0.479193\pi\) | ||||
0.0653201 | + | 0.997864i | \(0.479193\pi\) | |||||||
\(954\) | 33.7133 | 1.09151 | ||||||||
\(955\) | 10.0006 | 0.323612 | ||||||||
\(956\) | −116.582 | −3.77053 | ||||||||
\(957\) | 0.926573 | 0.0299518 | ||||||||
\(958\) | 43.7744 | 1.41429 | ||||||||
\(959\) | −4.96593 | −0.160358 | ||||||||
\(960\) | −6.42761 | −0.207450 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −13.2284 | −0.426502 | ||||||||
\(963\) | 12.2668 | 0.395291 | ||||||||
\(964\) | 78.7135 | 2.53519 | ||||||||
\(965\) | 18.0471 | 0.580957 | ||||||||
\(966\) | 1.69260 | 0.0544585 | ||||||||
\(967\) | −12.5674 | −0.404141 | −0.202071 | − | 0.979371i | \(-0.564767\pi\) | ||||
−0.202071 | + | 0.979371i | \(0.564767\pi\) | |||||||
\(968\) | −60.6232 | −1.94850 | ||||||||
\(969\) | −0.565925 | −0.0181801 | ||||||||
\(970\) | 57.3480 | 1.84133 | ||||||||
\(971\) | −12.9635 | −0.416018 | −0.208009 | − | 0.978127i | \(-0.566698\pi\) | ||||
−0.208009 | + | 0.978127i | \(0.566698\pi\) | |||||||
\(972\) | 72.6551 | 2.33041 | ||||||||
\(973\) | 6.81163 | 0.218371 | ||||||||
\(974\) | −0.222386 | −0.00712572 | ||||||||
\(975\) | 3.81722 | 0.122249 | ||||||||
\(976\) | 61.7256 | 1.97579 | ||||||||
\(977\) | 52.5757 | 1.68205 | 0.841024 | − | 0.540999i | \(-0.181954\pi\) | ||||
0.841024 | + | 0.540999i | \(0.181954\pi\) | |||||||
\(978\) | −43.2290 | −1.38231 | ||||||||
\(979\) | −9.98729 | −0.319195 | ||||||||
\(980\) | 38.3920 | 1.22639 | ||||||||
\(981\) | −19.4902 | −0.622273 | ||||||||
\(982\) | −103.420 | −3.30027 | ||||||||
\(983\) | 7.56545 | 0.241300 | 0.120650 | − | 0.992695i | \(-0.461502\pi\) | ||||
0.120650 | + | 0.992695i | \(0.461502\pi\) | |||||||
\(984\) | 30.1176 | 0.960115 | ||||||||
\(985\) | −12.5260 | −0.399111 | ||||||||
\(986\) | −4.37494 | −0.139326 | ||||||||
\(987\) | −4.24239 | −0.135037 | ||||||||
\(988\) | 0.803347 | 0.0255579 | ||||||||
\(989\) | −4.08026 | −0.129745 | ||||||||
\(990\) | −8.80720 | −0.279911 | ||||||||
\(991\) | 39.4600 | 1.25349 | 0.626745 | − | 0.779225i | \(-0.284387\pi\) | ||||
0.626745 | + | 0.779225i | \(0.284387\pi\) | |||||||
\(992\) | 8.61322 | 0.273470 | ||||||||
\(993\) | −27.1223 | −0.860701 | ||||||||
\(994\) | 5.36481 | 0.170162 | ||||||||
\(995\) | 10.3341 | 0.327612 | ||||||||
\(996\) | 69.5494 | 2.20376 | ||||||||
\(997\) | 39.6484 | 1.25568 | 0.627839 | − | 0.778344i | \(-0.283940\pi\) | ||||
0.627839 | + | 0.778344i | \(0.283940\pi\) | |||||||
\(998\) | 24.2936 | 0.769002 | ||||||||
\(999\) | −26.7796 | −0.847268 |
(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 | 403.2.a.c.1.7 | ✓ | 7 | |
3.2 | odd | 2 | 3627.2.a.n.1.1 | 7 | |||
4.3 | odd | 2 | 6448.2.a.ba.1.4 | 7 | |||
13.12 | even | 2 | 5239.2.a.h.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.a.c.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial | |
3627.2.a.n.1.1 | 7 | 3.2 | odd | 2 | |||
5239.2.a.h.1.1 | 7 | 13.12 | even | 2 | |||
6448.2.a.ba.1.4 | 7 | 4.3 | odd | 2 |