Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.13215\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.13215 | −1.50766 | −0.753830 | − | 0.657069i | \(-0.771796\pi\) | ||||
−0.753830 | + | 0.657069i | \(0.771796\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.54608 | 1.27304 | ||||||||
\(5\) | −2.91322 | −1.30283 | −0.651417 | − | 0.758720i | \(-0.725825\pi\) | ||||
−0.651417 | + | 0.758720i | \(0.725825\pi\) | |||||||
\(6\) | 2.13215 | 0.870448 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.16433 | −0.411654 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.21144 | 1.96423 | ||||||||
\(11\) | −1.50055 | −0.452434 | −0.226217 | − | 0.974077i | \(-0.572636\pi\) | ||||
−0.226217 | + | 0.974077i | \(0.572636\pi\) | |||||||
\(12\) | −2.54608 | −0.734991 | ||||||||
\(13\) | 2.14723 | 0.595535 | 0.297768 | − | 0.954638i | \(-0.403758\pi\) | ||||
0.297768 | + | 0.954638i | \(0.403758\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.91322 | 0.752191 | ||||||||
\(16\) | −2.60963 | −0.652407 | ||||||||
\(17\) | −2.46605 | −0.598105 | −0.299053 | − | 0.954237i | \(-0.596671\pi\) | ||||
−0.299053 | + | 0.954237i | \(0.596671\pi\) | |||||||
\(18\) | −2.13215 | −0.502554 | ||||||||
\(19\) | 7.23455 | 1.65972 | 0.829860 | − | 0.557972i | \(-0.188420\pi\) | ||||
0.829860 | + | 0.557972i | \(0.188420\pi\) | |||||||
\(20\) | −7.41731 | −1.65856 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.19941 | 0.682117 | ||||||||
\(23\) | 4.49416 | 0.937097 | 0.468548 | − | 0.883438i | \(-0.344777\pi\) | ||||
0.468548 | + | 0.883438i | \(0.344777\pi\) | |||||||
\(24\) | 1.16433 | 0.237668 | ||||||||
\(25\) | 3.48687 | 0.697374 | ||||||||
\(26\) | −4.57823 | −0.897866 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.11879 | −1.69332 | −0.846659 | − | 0.532136i | \(-0.821389\pi\) | ||||
−0.846659 | + | 0.532136i | \(0.821389\pi\) | |||||||
\(30\) | −6.21144 | −1.13405 | ||||||||
\(31\) | 7.76497 | 1.39463 | 0.697315 | − | 0.716765i | \(-0.254378\pi\) | ||||
0.697315 | + | 0.716765i | \(0.254378\pi\) | |||||||
\(32\) | 7.89280 | 1.39526 | ||||||||
\(33\) | 1.50055 | 0.261213 | ||||||||
\(34\) | 5.25800 | 0.901740 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.54608 | 0.424347 | ||||||||
\(37\) | 1.76746 | 0.290569 | 0.145285 | − | 0.989390i | \(-0.453590\pi\) | ||||
0.145285 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(38\) | −15.4252 | −2.50229 | ||||||||
\(39\) | −2.14723 | −0.343833 | ||||||||
\(40\) | 3.39196 | 0.536316 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47180 | 0.986941 | 0.493470 | − | 0.869763i | \(-0.335728\pi\) | ||||
0.493470 | + | 0.869763i | \(0.335728\pi\) | |||||||
\(44\) | −3.82053 | −0.575967 | ||||||||
\(45\) | −2.91322 | −0.434278 | ||||||||
\(46\) | −9.58224 | −1.41282 | ||||||||
\(47\) | 1.43939 | 0.209957 | 0.104979 | − | 0.994474i | \(-0.466523\pi\) | ||||
0.104979 | + | 0.994474i | \(0.466523\pi\) | |||||||
\(48\) | 2.60963 | 0.376667 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.43455 | −1.05140 | ||||||||
\(51\) | 2.46605 | 0.345316 | ||||||||
\(52\) | 5.46703 | 0.758141 | ||||||||
\(53\) | 3.74917 | 0.514988 | 0.257494 | − | 0.966280i | \(-0.417103\pi\) | ||||
0.257494 | + | 0.966280i | \(0.417103\pi\) | |||||||
\(54\) | 2.13215 | 0.290149 | ||||||||
\(55\) | 4.37145 | 0.589446 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.23455 | −0.958240 | ||||||||
\(58\) | 19.4427 | 2.55295 | ||||||||
\(59\) | 7.69935 | 1.00237 | 0.501185 | − | 0.865340i | \(-0.332898\pi\) | ||||
0.501185 | + | 0.865340i | \(0.332898\pi\) | |||||||
\(60\) | 7.41731 | 0.957570 | ||||||||
\(61\) | −5.74045 | −0.734990 | −0.367495 | − | 0.930026i | \(-0.619784\pi\) | ||||
−0.367495 | + | 0.930026i | \(0.619784\pi\) | |||||||
\(62\) | −16.5561 | −2.10263 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.6094 | −1.45118 | ||||||||
\(65\) | −6.25537 | −0.775883 | ||||||||
\(66\) | −3.19941 | −0.393821 | ||||||||
\(67\) | −13.0781 | −1.59775 | −0.798874 | − | 0.601499i | \(-0.794571\pi\) | ||||
−0.798874 | + | 0.601499i | \(0.794571\pi\) | |||||||
\(68\) | −6.27877 | −0.761413 | ||||||||
\(69\) | −4.49416 | −0.541033 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.11377 | −0.488215 | −0.244107 | − | 0.969748i | \(-0.578495\pi\) | ||||
−0.244107 | + | 0.969748i | \(0.578495\pi\) | |||||||
\(72\) | −1.16433 | −0.137218 | ||||||||
\(73\) | −2.78408 | −0.325852 | −0.162926 | − | 0.986638i | \(-0.552093\pi\) | ||||
−0.162926 | + | 0.986638i | \(0.552093\pi\) | |||||||
\(74\) | −3.76851 | −0.438080 | ||||||||
\(75\) | −3.48687 | −0.402629 | ||||||||
\(76\) | 18.4198 | 2.11289 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.57823 | 0.518383 | ||||||||
\(79\) | 15.6156 | 1.75690 | 0.878448 | − | 0.477838i | \(-0.158580\pi\) | ||||
0.878448 | + | 0.477838i | \(0.158580\pi\) | |||||||
\(80\) | 7.60243 | 0.849977 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.13215 | −0.235457 | ||||||||
\(83\) | 1.23966 | 0.136071 | 0.0680353 | − | 0.997683i | \(-0.478327\pi\) | ||||
0.0680353 | + | 0.997683i | \(0.478327\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.18416 | 0.779232 | ||||||||
\(86\) | −13.7989 | −1.48797 | ||||||||
\(87\) | 9.11879 | 0.977637 | ||||||||
\(88\) | 1.74714 | 0.186246 | ||||||||
\(89\) | 10.2933 | 1.09109 | 0.545546 | − | 0.838081i | \(-0.316322\pi\) | ||||
0.545546 | + | 0.838081i | \(0.316322\pi\) | |||||||
\(90\) | 6.21144 | 0.654744 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 11.4425 | 1.19296 | ||||||||
\(93\) | −7.76497 | −0.805190 | ||||||||
\(94\) | −3.06901 | −0.316544 | ||||||||
\(95\) | −21.0759 | −2.16234 | ||||||||
\(96\) | −7.89280 | −0.805555 | ||||||||
\(97\) | −2.93804 | −0.298312 | −0.149156 | − | 0.988814i | \(-0.547656\pi\) | ||||
−0.149156 | + | 0.988814i | \(0.547656\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50055 | −0.150811 | ||||||||
\(100\) | 8.87786 | 0.887786 | ||||||||
\(101\) | 9.85932 | 0.981039 | 0.490520 | − | 0.871430i | \(-0.336807\pi\) | ||||
0.490520 | + | 0.871430i | \(0.336807\pi\) | |||||||
\(102\) | −5.25800 | −0.520620 | ||||||||
\(103\) | −5.59038 | −0.550836 | −0.275418 | − | 0.961325i | \(-0.588816\pi\) | ||||
−0.275418 | + | 0.961325i | \(0.588816\pi\) | |||||||
\(104\) | −2.50010 | −0.245155 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.99380 | −0.776427 | ||||||||
\(107\) | 13.7382 | 1.32812 | 0.664062 | − | 0.747678i | \(-0.268831\pi\) | ||||
0.664062 | + | 0.747678i | \(0.268831\pi\) | |||||||
\(108\) | −2.54608 | −0.244997 | ||||||||
\(109\) | −16.8992 | −1.61865 | −0.809323 | − | 0.587364i | \(-0.800166\pi\) | ||||
−0.809323 | + | 0.587364i | \(0.800166\pi\) | |||||||
\(110\) | −9.32061 | −0.888685 | ||||||||
\(111\) | −1.76746 | −0.167760 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.2739 | −1.15463 | −0.577315 | − | 0.816522i | \(-0.695899\pi\) | ||||
−0.577315 | + | 0.816522i | \(0.695899\pi\) | |||||||
\(114\) | 15.4252 | 1.44470 | ||||||||
\(115\) | −13.0925 | −1.22088 | ||||||||
\(116\) | −23.2172 | −2.15566 | ||||||||
\(117\) | 2.14723 | 0.198512 | ||||||||
\(118\) | −16.4162 | −1.51123 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.39196 | −0.309642 | ||||||||
\(121\) | −8.74834 | −0.795303 | ||||||||
\(122\) | 12.2395 | 1.10811 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 19.7703 | 1.77542 | ||||||||
\(125\) | 4.40808 | 0.394271 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.83504 | 0.872719 | 0.436359 | − | 0.899773i | \(-0.356268\pi\) | ||||
0.436359 | + | 0.899773i | \(0.356268\pi\) | |||||||
\(128\) | 8.96745 | 0.792618 | ||||||||
\(129\) | −6.47180 | −0.569811 | ||||||||
\(130\) | 13.3374 | 1.16977 | ||||||||
\(131\) | 1.68941 | 0.147605 | 0.0738024 | − | 0.997273i | \(-0.476487\pi\) | ||||
0.0738024 | + | 0.997273i | \(0.476487\pi\) | |||||||
\(132\) | 3.82053 | 0.332535 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 27.8846 | 2.40886 | ||||||||
\(135\) | 2.91322 | 0.250730 | ||||||||
\(136\) | 2.87131 | 0.246212 | ||||||||
\(137\) | −18.7959 | −1.60584 | −0.802921 | − | 0.596085i | \(-0.796722\pi\) | ||||
−0.802921 | + | 0.596085i | \(0.796722\pi\) | |||||||
\(138\) | 9.58224 | 0.815695 | ||||||||
\(139\) | −3.46444 | −0.293850 | −0.146925 | − | 0.989148i | \(-0.546938\pi\) | ||||
−0.146925 | + | 0.989148i | \(0.546938\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.43939 | −0.121219 | ||||||||
\(142\) | 8.77120 | 0.736062 | ||||||||
\(143\) | −3.22204 | −0.269441 | ||||||||
\(144\) | −2.60963 | −0.217469 | ||||||||
\(145\) | 26.5651 | 2.20611 | ||||||||
\(146\) | 5.93610 | 0.491275 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.50011 | 0.369907 | ||||||||
\(149\) | −22.5119 | −1.84424 | −0.922121 | − | 0.386901i | \(-0.873546\pi\) | ||||
−0.922121 | + | 0.386901i | \(0.873546\pi\) | |||||||
\(150\) | 7.43455 | 0.607028 | ||||||||
\(151\) | −15.5398 | −1.26461 | −0.632307 | − | 0.774718i | \(-0.717892\pi\) | ||||
−0.632307 | + | 0.774718i | \(0.717892\pi\) | |||||||
\(152\) | −8.42343 | −0.683230 | ||||||||
\(153\) | −2.46605 | −0.199368 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.6211 | −1.81697 | ||||||||
\(156\) | −5.46703 | −0.437713 | ||||||||
\(157\) | 20.4910 | 1.63536 | 0.817680 | − | 0.575674i | \(-0.195260\pi\) | ||||
0.817680 | + | 0.575674i | \(0.195260\pi\) | |||||||
\(158\) | −33.2949 | −2.64880 | ||||||||
\(159\) | −3.74917 | −0.297328 | ||||||||
\(160\) | −22.9935 | −1.81779 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.13215 | −0.167518 | ||||||||
\(163\) | 11.4712 | 0.898495 | 0.449247 | − | 0.893407i | \(-0.351692\pi\) | ||||
0.449247 | + | 0.893407i | \(0.351692\pi\) | |||||||
\(164\) | 2.54608 | 0.198816 | ||||||||
\(165\) | −4.37145 | −0.340317 | ||||||||
\(166\) | −2.64315 | −0.205148 | ||||||||
\(167\) | −1.21433 | −0.0939673 | −0.0469837 | − | 0.998896i | \(-0.514961\pi\) | ||||
−0.0469837 | + | 0.998896i | \(0.514961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.38939 | −0.645338 | ||||||||
\(170\) | −15.3177 | −1.17482 | ||||||||
\(171\) | 7.23455 | 0.553240 | ||||||||
\(172\) | 16.4778 | 1.25642 | ||||||||
\(173\) | −18.3164 | −1.39257 | −0.696285 | − | 0.717765i | \(-0.745165\pi\) | ||||
−0.696285 | + | 0.717765i | \(0.745165\pi\) | |||||||
\(174\) | −19.4427 | −1.47395 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.91589 | 0.295171 | ||||||||
\(177\) | −7.69935 | −0.578719 | ||||||||
\(178\) | −21.9470 | −1.64500 | ||||||||
\(179\) | 7.80070 | 0.583052 | 0.291526 | − | 0.956563i | \(-0.405837\pi\) | ||||
0.291526 | + | 0.956563i | \(0.405837\pi\) | |||||||
\(180\) | −7.41731 | −0.552854 | ||||||||
\(181\) | −2.11732 | −0.157379 | −0.0786894 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786894 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.74045 | 0.424346 | ||||||||
\(184\) | −5.23270 | −0.385760 | ||||||||
\(185\) | −5.14902 | −0.378563 | ||||||||
\(186\) | 16.5561 | 1.21395 | ||||||||
\(187\) | 3.70044 | 0.270603 | ||||||||
\(188\) | 3.66481 | 0.267284 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 44.9370 | 3.26007 | ||||||||
\(191\) | −20.0465 | −1.45051 | −0.725256 | − | 0.688479i | \(-0.758279\pi\) | ||||
−0.725256 | + | 0.688479i | \(0.758279\pi\) | |||||||
\(192\) | 11.6094 | 0.837837 | ||||||||
\(193\) | −8.66357 | −0.623618 | −0.311809 | − | 0.950145i | \(-0.600935\pi\) | ||||
−0.311809 | + | 0.950145i | \(0.600935\pi\) | |||||||
\(194\) | 6.26435 | 0.449754 | ||||||||
\(195\) | 6.25537 | 0.447956 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9064 | 0.777051 | 0.388525 | − | 0.921438i | \(-0.372985\pi\) | ||||
0.388525 | + | 0.921438i | \(0.372985\pi\) | |||||||
\(198\) | 3.19941 | 0.227372 | ||||||||
\(199\) | 18.3904 | 1.30366 | 0.651829 | − | 0.758366i | \(-0.274002\pi\) | ||||
0.651829 | + | 0.758366i | \(0.274002\pi\) | |||||||
\(200\) | −4.05988 | −0.287077 | ||||||||
\(201\) | 13.0781 | 0.922460 | ||||||||
\(202\) | −21.0216 | −1.47907 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.27877 | 0.439602 | ||||||||
\(205\) | −2.91322 | −0.203468 | ||||||||
\(206\) | 11.9195 | 0.830474 | ||||||||
\(207\) | 4.49416 | 0.312366 | ||||||||
\(208\) | −5.60348 | −0.388531 | ||||||||
\(209\) | −10.8558 | −0.750914 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.2561 | 1.66986 | 0.834928 | − | 0.550358i | \(-0.185509\pi\) | ||||
0.834928 | + | 0.550358i | \(0.185509\pi\) | |||||||
\(212\) | 9.54569 | 0.655601 | ||||||||
\(213\) | 4.11377 | 0.281871 | ||||||||
\(214\) | −29.2920 | −2.00236 | ||||||||
\(215\) | −18.8538 | −1.28582 | ||||||||
\(216\) | 1.16433 | 0.0792228 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 36.0316 | 2.44037 | ||||||||
\(219\) | 2.78408 | 0.188131 | ||||||||
\(220\) | 11.1301 | 0.750389 | ||||||||
\(221\) | −5.29519 | −0.356193 | ||||||||
\(222\) | 3.76851 | 0.252926 | ||||||||
\(223\) | 10.0523 | 0.673149 | 0.336574 | − | 0.941657i | \(-0.390732\pi\) | ||||
0.336574 | + | 0.941657i | \(0.390732\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.48687 | 0.232458 | ||||||||
\(226\) | 26.1698 | 1.74079 | ||||||||
\(227\) | 3.70831 | 0.246129 | 0.123065 | − | 0.992399i | \(-0.460728\pi\) | ||||
0.123065 | + | 0.992399i | \(0.460728\pi\) | |||||||
\(228\) | −18.4198 | −1.21988 | ||||||||
\(229\) | 0.627708 | 0.0414801 | 0.0207401 | − | 0.999785i | \(-0.493398\pi\) | ||||
0.0207401 | + | 0.999785i | \(0.493398\pi\) | |||||||
\(230\) | 27.9152 | 1.84067 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.6173 | 0.697061 | ||||||||
\(233\) | −5.69247 | −0.372926 | −0.186463 | − | 0.982462i | \(-0.559702\pi\) | ||||
−0.186463 | + | 0.982462i | \(0.559702\pi\) | |||||||
\(234\) | −4.57823 | −0.299289 | ||||||||
\(235\) | −4.19327 | −0.273539 | ||||||||
\(236\) | 19.6032 | 1.27606 | ||||||||
\(237\) | −15.6156 | −1.01434 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.28786 | −0.147989 | −0.0739947 | − | 0.997259i | \(-0.523575\pi\) | ||||
−0.0739947 | + | 0.997259i | \(0.523575\pi\) | |||||||
\(240\) | −7.60243 | −0.490735 | ||||||||
\(241\) | −9.22536 | −0.594258 | −0.297129 | − | 0.954837i | \(-0.596029\pi\) | ||||
−0.297129 | + | 0.954837i | \(0.596029\pi\) | |||||||
\(242\) | 18.6528 | 1.19905 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.6157 | −0.935672 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.13215 | 0.135941 | ||||||||
\(247\) | 15.5343 | 0.988422 | ||||||||
\(248\) | −9.04101 | −0.574105 | ||||||||
\(249\) | −1.23966 | −0.0785604 | ||||||||
\(250\) | −9.39871 | −0.594427 | ||||||||
\(251\) | 3.04049 | 0.191914 | 0.0959569 | − | 0.995385i | \(-0.469409\pi\) | ||||
0.0959569 | + | 0.995385i | \(0.469409\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.74373 | −0.423975 | ||||||||
\(254\) | −20.9698 | −1.31576 | ||||||||
\(255\) | −7.18416 | −0.449890 | ||||||||
\(256\) | 4.09881 | 0.256176 | ||||||||
\(257\) | −21.7197 | −1.35484 | −0.677418 | − | 0.735599i | \(-0.736901\pi\) | ||||
−0.677418 | + | 0.735599i | \(0.736901\pi\) | |||||||
\(258\) | 13.7989 | 0.859081 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −15.9267 | −0.987732 | ||||||||
\(261\) | −9.11879 | −0.564439 | ||||||||
\(262\) | −3.60209 | −0.222538 | ||||||||
\(263\) | −0.758785 | −0.0467887 | −0.0233944 | − | 0.999726i | \(-0.507447\pi\) | ||||
−0.0233944 | + | 0.999726i | \(0.507447\pi\) | |||||||
\(264\) | −1.74714 | −0.107529 | ||||||||
\(265\) | −10.9222 | −0.670943 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.2933 | −0.629942 | ||||||||
\(268\) | −33.2980 | −2.03400 | ||||||||
\(269\) | 9.21857 | 0.562066 | 0.281033 | − | 0.959698i | \(-0.409323\pi\) | ||||
0.281033 | + | 0.959698i | \(0.409323\pi\) | |||||||
\(270\) | −6.21144 | −0.378016 | ||||||||
\(271\) | −21.9651 | −1.33429 | −0.667143 | − | 0.744930i | \(-0.732483\pi\) | ||||
−0.667143 | + | 0.744930i | \(0.732483\pi\) | |||||||
\(272\) | 6.43548 | 0.390208 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 40.0758 | 2.42107 | ||||||||
\(275\) | −5.23224 | −0.315516 | ||||||||
\(276\) | −11.4425 | −0.688758 | ||||||||
\(277\) | 17.9529 | 1.07869 | 0.539343 | − | 0.842086i | \(-0.318673\pi\) | ||||
0.539343 | + | 0.842086i | \(0.318673\pi\) | |||||||
\(278\) | 7.38672 | 0.443026 | ||||||||
\(279\) | 7.76497 | 0.464877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.5886 | −1.34752 | −0.673761 | − | 0.738949i | \(-0.735322\pi\) | ||||
−0.673761 | + | 0.738949i | \(0.735322\pi\) | |||||||
\(282\) | 3.06901 | 0.182757 | ||||||||
\(283\) | −13.7918 | −0.819835 | −0.409917 | − | 0.912123i | \(-0.634442\pi\) | ||||
−0.409917 | + | 0.912123i | \(0.634442\pi\) | |||||||
\(284\) | −10.4740 | −0.621518 | ||||||||
\(285\) | 21.0759 | 1.24843 | ||||||||
\(286\) | 6.86989 | 0.406225 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.89280 | 0.465087 | ||||||||
\(289\) | −10.9186 | −0.642270 | ||||||||
\(290\) | −56.6409 | −3.32607 | ||||||||
\(291\) | 2.93804 | 0.172231 | ||||||||
\(292\) | −7.08851 | −0.414824 | ||||||||
\(293\) | 7.85590 | 0.458947 | 0.229473 | − | 0.973315i | \(-0.426300\pi\) | ||||
0.229473 | + | 0.973315i | \(0.426300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.4299 | −1.30592 | ||||||||
\(296\) | −2.05792 | −0.119614 | ||||||||
\(297\) | 1.50055 | 0.0870710 | ||||||||
\(298\) | 47.9988 | 2.78049 | ||||||||
\(299\) | 9.65001 | 0.558074 | ||||||||
\(300\) | −8.87786 | −0.512564 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 33.1333 | 1.90661 | ||||||||
\(303\) | −9.85932 | −0.566403 | ||||||||
\(304\) | −18.8795 | −1.08281 | ||||||||
\(305\) | 16.7232 | 0.957569 | ||||||||
\(306\) | 5.25800 | 0.300580 | ||||||||
\(307\) | 12.8613 | 0.734035 | 0.367018 | − | 0.930214i | \(-0.380379\pi\) | ||||
0.367018 | + | 0.930214i | \(0.380379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.59038 | 0.318025 | ||||||||
\(310\) | 48.2317 | 2.73937 | ||||||||
\(311\) | −15.5497 | −0.881742 | −0.440871 | − | 0.897570i | \(-0.645330\pi\) | ||||
−0.440871 | + | 0.897570i | \(0.645330\pi\) | |||||||
\(312\) | 2.50010 | 0.141540 | ||||||||
\(313\) | 27.1677 | 1.53561 | 0.767804 | − | 0.640685i | \(-0.221349\pi\) | ||||
0.767804 | + | 0.640685i | \(0.221349\pi\) | |||||||
\(314\) | −43.6900 | −2.46557 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 39.7587 | 2.23660 | ||||||||
\(317\) | 2.98972 | 0.167920 | 0.0839598 | − | 0.996469i | \(-0.473243\pi\) | ||||
0.0839598 | + | 0.996469i | \(0.473243\pi\) | |||||||
\(318\) | 7.99380 | 0.448270 | ||||||||
\(319\) | 13.6832 | 0.766114 | ||||||||
\(320\) | 33.8208 | 1.89064 | ||||||||
\(321\) | −13.7382 | −0.766792 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8408 | −0.992687 | ||||||||
\(324\) | 2.54608 | 0.141449 | ||||||||
\(325\) | 7.48713 | 0.415311 | ||||||||
\(326\) | −24.4584 | −1.35463 | ||||||||
\(327\) | 16.8992 | 0.934526 | ||||||||
\(328\) | −1.16433 | −0.0642895 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.32061 | 0.513082 | ||||||||
\(331\) | 11.4220 | 0.627809 | 0.313904 | − | 0.949455i | \(-0.398363\pi\) | ||||
0.313904 | + | 0.949455i | \(0.398363\pi\) | |||||||
\(332\) | 3.15628 | 0.173224 | ||||||||
\(333\) | 1.76746 | 0.0968564 | ||||||||
\(334\) | 2.58913 | 0.141671 | ||||||||
\(335\) | 38.0995 | 2.08160 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.89417 | 0.321076 | 0.160538 | − | 0.987030i | \(-0.448677\pi\) | ||||
0.160538 | + | 0.987030i | \(0.448677\pi\) | |||||||
\(338\) | 17.8875 | 0.972950 | ||||||||
\(339\) | 12.2739 | 0.666626 | ||||||||
\(340\) | 18.2915 | 0.991994 | ||||||||
\(341\) | −11.6518 | −0.630978 | ||||||||
\(342\) | −15.4252 | −0.834098 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.53534 | −0.406278 | ||||||||
\(345\) | 13.0925 | 0.704876 | ||||||||
\(346\) | 39.0534 | 2.09952 | ||||||||
\(347\) | −4.45569 | −0.239194 | −0.119597 | − | 0.992823i | \(-0.538160\pi\) | ||||
−0.119597 | + | 0.992823i | \(0.538160\pi\) | |||||||
\(348\) | 23.2172 | 1.24457 | ||||||||
\(349\) | −12.0671 | −0.645940 | −0.322970 | − | 0.946409i | \(-0.604681\pi\) | ||||
−0.322970 | + | 0.946409i | \(0.604681\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.14723 | −0.114611 | ||||||||
\(352\) | −11.8436 | −0.631264 | ||||||||
\(353\) | 28.3315 | 1.50793 | 0.753966 | − | 0.656913i | \(-0.228138\pi\) | ||||
0.753966 | + | 0.656913i | \(0.228138\pi\) | |||||||
\(354\) | 16.4162 | 0.872512 | ||||||||
\(355\) | 11.9843 | 0.636063 | ||||||||
\(356\) | 26.2077 | 1.38901 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.6323 | −0.879044 | ||||||||
\(359\) | 15.1427 | 0.799203 | 0.399601 | − | 0.916689i | \(-0.369149\pi\) | ||||
0.399601 | + | 0.916689i | \(0.369149\pi\) | |||||||
\(360\) | 3.39196 | 0.178772 | ||||||||
\(361\) | 33.3387 | 1.75467 | ||||||||
\(362\) | 4.51444 | 0.237274 | ||||||||
\(363\) | 8.74834 | 0.459169 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.11066 | 0.424531 | ||||||||
\(366\) | −12.2395 | −0.639770 | ||||||||
\(367\) | −15.8017 | −0.824844 | −0.412422 | − | 0.910993i | \(-0.635317\pi\) | ||||
−0.412422 | + | 0.910993i | \(0.635317\pi\) | |||||||
\(368\) | −11.7281 | −0.611369 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 10.9785 | 0.570745 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19.7703 | −1.02504 | ||||||||
\(373\) | 12.4879 | 0.646601 | 0.323301 | − | 0.946296i | \(-0.395207\pi\) | ||||
0.323301 | + | 0.946296i | \(0.395207\pi\) | |||||||
\(374\) | −7.88992 | −0.407978 | ||||||||
\(375\) | −4.40808 | −0.227632 | ||||||||
\(376\) | −1.67593 | −0.0864296 | ||||||||
\(377\) | −19.5802 | −1.00843 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.92589 | 0.201659 | 0.100830 | − | 0.994904i | \(-0.467850\pi\) | ||||
0.100830 | + | 0.994904i | \(0.467850\pi\) | |||||||
\(380\) | −53.6609 | −2.75275 | ||||||||
\(381\) | −9.83504 | −0.503864 | ||||||||
\(382\) | 42.7422 | 2.18688 | ||||||||
\(383\) | 12.8664 | 0.657443 | 0.328721 | − | 0.944427i | \(-0.393382\pi\) | ||||
0.328721 | + | 0.944427i | \(0.393382\pi\) | |||||||
\(384\) | −8.96745 | −0.457618 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.4721 | 0.940204 | ||||||||
\(387\) | 6.47180 | 0.328980 | ||||||||
\(388\) | −7.48049 | −0.379764 | ||||||||
\(389\) | 24.1359 | 1.22374 | 0.611868 | − | 0.790960i | \(-0.290418\pi\) | ||||
0.611868 | + | 0.790960i | \(0.290418\pi\) | |||||||
\(390\) | −13.3374 | −0.675366 | ||||||||
\(391\) | −11.0828 | −0.560483 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.68941 | −0.0852197 | ||||||||
\(394\) | −23.2542 | −1.17153 | ||||||||
\(395\) | −45.4918 | −2.28894 | ||||||||
\(396\) | −3.82053 | −0.191989 | ||||||||
\(397\) | −16.9939 | −0.852902 | −0.426451 | − | 0.904511i | \(-0.640236\pi\) | ||||
−0.426451 | + | 0.904511i | \(0.640236\pi\) | |||||||
\(398\) | −39.2111 | −1.96547 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.09944 | −0.454972 | ||||||||
\(401\) | 16.8777 | 0.842830 | 0.421415 | − | 0.906868i | \(-0.361534\pi\) | ||||
0.421415 | + | 0.906868i | \(0.361534\pi\) | |||||||
\(402\) | −27.8846 | −1.39076 | ||||||||
\(403\) | 16.6732 | 0.830551 | ||||||||
\(404\) | 25.1026 | 1.24890 | ||||||||
\(405\) | −2.91322 | −0.144759 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.65217 | −0.131463 | ||||||||
\(408\) | −2.87131 | −0.142151 | ||||||||
\(409\) | 23.3733 | 1.15573 | 0.577867 | − | 0.816131i | \(-0.303885\pi\) | ||||
0.577867 | + | 0.816131i | \(0.303885\pi\) | |||||||
\(410\) | 6.21144 | 0.306761 | ||||||||
\(411\) | 18.7959 | 0.927133 | ||||||||
\(412\) | −14.2336 | −0.701237 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.58224 | −0.470941 | ||||||||
\(415\) | −3.61141 | −0.177277 | ||||||||
\(416\) | 16.9477 | 0.830928 | ||||||||
\(417\) | 3.46444 | 0.169654 | ||||||||
\(418\) | 23.1463 | 1.13212 | ||||||||
\(419\) | −0.638417 | −0.0311887 | −0.0155944 | − | 0.999878i | \(-0.504964\pi\) | ||||
−0.0155944 | + | 0.999878i | \(0.504964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.1543 | −1.66458 | −0.832290 | − | 0.554340i | \(-0.812971\pi\) | ||||
−0.832290 | + | 0.554340i | \(0.812971\pi\) | |||||||
\(422\) | −51.7177 | −2.51758 | ||||||||
\(423\) | 1.43939 | 0.0699857 | ||||||||
\(424\) | −4.36528 | −0.211997 | ||||||||
\(425\) | −8.59881 | −0.417103 | ||||||||
\(426\) | −8.77120 | −0.424966 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 34.9786 | 1.69076 | ||||||||
\(429\) | 3.22204 | 0.155562 | ||||||||
\(430\) | 40.1992 | 1.93858 | ||||||||
\(431\) | −17.8141 | −0.858073 | −0.429036 | − | 0.903287i | \(-0.641147\pi\) | ||||
−0.429036 | + | 0.903287i | \(0.641147\pi\) | |||||||
\(432\) | 2.60963 | 0.125556 | ||||||||
\(433\) | 18.6108 | 0.894379 | 0.447189 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447189 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.5651 | −1.27370 | ||||||||
\(436\) | −43.0267 | −2.06060 | ||||||||
\(437\) | 32.5132 | 1.55532 | ||||||||
\(438\) | −5.93610 | −0.283638 | ||||||||
\(439\) | −30.0312 | −1.43331 | −0.716654 | − | 0.697428i | \(-0.754327\pi\) | ||||
−0.716654 | + | 0.697428i | \(0.754327\pi\) | |||||||
\(440\) | −5.08982 | −0.242648 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.2902 | 0.537018 | ||||||||
\(443\) | 10.6865 | 0.507730 | 0.253865 | − | 0.967240i | \(-0.418298\pi\) | ||||
0.253865 | + | 0.967240i | \(0.418298\pi\) | |||||||
\(444\) | −4.50011 | −0.213566 | ||||||||
\(445\) | −29.9868 | −1.42151 | ||||||||
\(446\) | −21.4330 | −1.01488 | ||||||||
\(447\) | 22.5119 | 1.06477 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0579 | −0.474660 | −0.237330 | − | 0.971429i | \(-0.576272\pi\) | ||||
−0.237330 | + | 0.971429i | \(0.576272\pi\) | |||||||
\(450\) | −7.43455 | −0.350468 | ||||||||
\(451\) | −1.50055 | −0.0706583 | ||||||||
\(452\) | −31.2503 | −1.46989 | ||||||||
\(453\) | 15.5398 | 0.730125 | ||||||||
\(454\) | −7.90670 | −0.371080 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.42343 | 0.394463 | ||||||||
\(457\) | 28.5745 | 1.33666 | 0.668330 | − | 0.743865i | \(-0.267010\pi\) | ||||
0.668330 | + | 0.743865i | \(0.267010\pi\) | |||||||
\(458\) | −1.33837 | −0.0625380 | ||||||||
\(459\) | 2.46605 | 0.115105 | ||||||||
\(460\) | −33.3346 | −1.55423 | ||||||||
\(461\) | 9.51845 | 0.443318 | 0.221659 | − | 0.975124i | \(-0.428853\pi\) | ||||
0.221659 | + | 0.975124i | \(0.428853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.0602 | 1.44349 | 0.721745 | − | 0.692159i | \(-0.243340\pi\) | ||||
0.721745 | + | 0.692159i | \(0.243340\pi\) | |||||||
\(464\) | 23.7967 | 1.10473 | ||||||||
\(465\) | 22.6211 | 1.04903 | ||||||||
\(466\) | 12.1372 | 0.562246 | ||||||||
\(467\) | 22.7912 | 1.05465 | 0.527325 | − | 0.849663i | \(-0.323195\pi\) | ||||
0.527325 | + | 0.849663i | \(0.323195\pi\) | |||||||
\(468\) | 5.46703 | 0.252714 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.94071 | 0.412404 | ||||||||
\(471\) | −20.4910 | −0.944175 | ||||||||
\(472\) | −8.96461 | −0.412630 | ||||||||
\(473\) | −9.71129 | −0.446526 | ||||||||
\(474\) | 33.2949 | 1.52929 | ||||||||
\(475\) | 25.2260 | 1.15745 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.74917 | 0.171663 | ||||||||
\(478\) | 4.87807 | 0.223118 | ||||||||
\(479\) | 34.2503 | 1.56493 | 0.782467 | − | 0.622692i | \(-0.213961\pi\) | ||||
0.782467 | + | 0.622692i | \(0.213961\pi\) | |||||||
\(480\) | 22.9935 | 1.04950 | ||||||||
\(481\) | 3.79516 | 0.173044 | ||||||||
\(482\) | 19.6699 | 0.895939 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.2740 | −1.01245 | ||||||||
\(485\) | 8.55916 | 0.388651 | ||||||||
\(486\) | 2.13215 | 0.0967165 | ||||||||
\(487\) | −9.18232 | −0.416091 | −0.208045 | − | 0.978119i | \(-0.566710\pi\) | ||||
−0.208045 | + | 0.978119i | \(0.566710\pi\) | |||||||
\(488\) | 6.68380 | 0.302561 | ||||||||
\(489\) | −11.4712 | −0.518746 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.8804 | −0.806931 | −0.403465 | − | 0.914995i | \(-0.632194\pi\) | ||||
−0.403465 | + | 0.914995i | \(0.632194\pi\) | |||||||
\(492\) | −2.54608 | −0.114786 | ||||||||
\(493\) | 22.4874 | 1.01278 | ||||||||
\(494\) | −33.1215 | −1.49021 | ||||||||
\(495\) | 4.37145 | 0.196482 | ||||||||
\(496\) | −20.2637 | −0.909866 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.64315 | 0.118442 | ||||||||
\(499\) | −23.6303 | −1.05784 | −0.528919 | − | 0.848672i | \(-0.677402\pi\) | ||||
−0.528919 | + | 0.848672i | \(0.677402\pi\) | |||||||
\(500\) | 11.2233 | 0.501923 | ||||||||
\(501\) | 1.21433 | 0.0542521 | ||||||||
\(502\) | −6.48278 | −0.289341 | ||||||||
\(503\) | −37.0939 | −1.65394 | −0.826968 | − | 0.562249i | \(-0.809936\pi\) | ||||
−0.826968 | + | 0.562249i | \(0.809936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.7224 | −1.27813 | ||||||||
\(506\) | 14.3787 | 0.639210 | ||||||||
\(507\) | 8.38939 | 0.372586 | ||||||||
\(508\) | 25.0408 | 1.11101 | ||||||||
\(509\) | 35.2024 | 1.56032 | 0.780158 | − | 0.625582i | \(-0.215138\pi\) | ||||
0.780158 | + | 0.625582i | \(0.215138\pi\) | |||||||
\(510\) | 15.3177 | 0.678281 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −26.6742 | −1.17884 | ||||||||
\(513\) | −7.23455 | −0.319413 | ||||||||
\(514\) | 46.3097 | 2.04263 | ||||||||
\(515\) | 16.2860 | 0.717648 | ||||||||
\(516\) | −16.4778 | −0.725393 | ||||||||
\(517\) | −2.15989 | −0.0949917 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.3164 | 0.804001 | ||||||||
\(520\) | 7.28334 | 0.319395 | ||||||||
\(521\) | −24.0907 | −1.05543 | −0.527715 | − | 0.849421i | \(-0.676951\pi\) | ||||
−0.527715 | + | 0.849421i | \(0.676951\pi\) | |||||||
\(522\) | 19.4427 | 0.850983 | ||||||||
\(523\) | −10.2611 | −0.448687 | −0.224343 | − | 0.974510i | \(-0.572024\pi\) | ||||
−0.224343 | + | 0.974510i | \(0.572024\pi\) | |||||||
\(524\) | 4.30139 | 0.187907 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.61785 | 0.0705415 | ||||||||
\(527\) | −19.1488 | −0.834136 | ||||||||
\(528\) | −3.91589 | −0.170417 | ||||||||
\(529\) | −2.80253 | −0.121849 | ||||||||
\(530\) | 23.2877 | 1.01155 | ||||||||
\(531\) | 7.69935 | 0.334123 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.14723 | 0.0930070 | ||||||||
\(534\) | 21.9470 | 0.949739 | ||||||||
\(535\) | −40.0225 | −1.73032 | ||||||||
\(536\) | 15.2273 | 0.657719 | ||||||||
\(537\) | −7.80070 | −0.336625 | ||||||||
\(538\) | −19.6554 | −0.847406 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.41731 | 0.319190 | ||||||||
\(541\) | 34.4179 | 1.47974 | 0.739870 | − | 0.672750i | \(-0.234887\pi\) | ||||
0.739870 | + | 0.672750i | \(0.234887\pi\) | |||||||
\(542\) | 46.8330 | 2.01165 | ||||||||
\(543\) | 2.11732 | 0.0908627 | ||||||||
\(544\) | −19.4640 | −0.834514 | ||||||||
\(545\) | 49.2310 | 2.10883 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.2749 | 1.25171 | 0.625853 | − | 0.779941i | \(-0.284751\pi\) | ||||
0.625853 | + | 0.779941i | \(0.284751\pi\) | |||||||
\(548\) | −47.8559 | −2.04430 | ||||||||
\(549\) | −5.74045 | −0.244997 | ||||||||
\(550\) | 11.1559 | 0.475691 | ||||||||
\(551\) | −65.9704 | −2.81043 | ||||||||
\(552\) | 5.23270 | 0.222718 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −38.2784 | −1.62629 | ||||||||
\(555\) | 5.14902 | 0.218564 | ||||||||
\(556\) | −8.82075 | −0.374083 | ||||||||
\(557\) | 33.6058 | 1.42392 | 0.711961 | − | 0.702219i | \(-0.247807\pi\) | ||||
0.711961 | + | 0.702219i | \(0.247807\pi\) | |||||||
\(558\) | −16.5561 | −0.700876 | ||||||||
\(559\) | 13.8965 | 0.587758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.70044 | −0.156233 | ||||||||
\(562\) | 48.1623 | 2.03161 | ||||||||
\(563\) | 37.6392 | 1.58630 | 0.793152 | − | 0.609024i | \(-0.208439\pi\) | ||||
0.793152 | + | 0.609024i | \(0.208439\pi\) | |||||||
\(564\) | −3.66481 | −0.154316 | ||||||||
\(565\) | 35.7566 | 1.50429 | ||||||||
\(566\) | 29.4062 | 1.23603 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.78980 | 0.200976 | ||||||||
\(569\) | 16.5430 | 0.693520 | 0.346760 | − | 0.937954i | \(-0.387282\pi\) | ||||
0.346760 | + | 0.937954i | \(0.387282\pi\) | |||||||
\(570\) | −44.9370 | −1.88220 | ||||||||
\(571\) | −8.67402 | −0.362997 | −0.181498 | − | 0.983391i | \(-0.558095\pi\) | ||||
−0.181498 | + | 0.983391i | \(0.558095\pi\) | |||||||
\(572\) | −8.20358 | −0.343009 | ||||||||
\(573\) | 20.0465 | 0.837454 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.6706 | 0.653507 | ||||||||
\(576\) | −11.6094 | −0.483725 | ||||||||
\(577\) | −13.6404 | −0.567857 | −0.283929 | − | 0.958845i | \(-0.591638\pi\) | ||||
−0.283929 | + | 0.958845i | \(0.591638\pi\) | |||||||
\(578\) | 23.2801 | 0.968325 | ||||||||
\(579\) | 8.66357 | 0.360046 | ||||||||
\(580\) | 67.6369 | 2.80847 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.26435 | −0.259666 | ||||||||
\(583\) | −5.62583 | −0.232998 | ||||||||
\(584\) | 3.24160 | 0.134138 | ||||||||
\(585\) | −6.25537 | −0.258628 | ||||||||
\(586\) | −16.7500 | −0.691936 | ||||||||
\(587\) | 8.81891 | 0.363996 | 0.181998 | − | 0.983299i | \(-0.441744\pi\) | ||||
0.181998 | + | 0.983299i | \(0.441744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.1761 | 2.31469 | ||||||||
\(590\) | 47.8241 | 1.96889 | ||||||||
\(591\) | −10.9064 | −0.448631 | ||||||||
\(592\) | −4.61242 | −0.189569 | ||||||||
\(593\) | −39.9050 | −1.63870 | −0.819351 | − | 0.573292i | \(-0.805666\pi\) | ||||
−0.819351 | + | 0.573292i | \(0.805666\pi\) | |||||||
\(594\) | −3.19941 | −0.131274 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −57.3170 | −2.34780 | ||||||||
\(597\) | −18.3904 | −0.752667 | ||||||||
\(598\) | −20.5753 | −0.841387 | ||||||||
\(599\) | 10.0955 | 0.412493 | 0.206246 | − | 0.978500i | \(-0.433875\pi\) | ||||
0.206246 | + | 0.978500i | \(0.433875\pi\) | |||||||
\(600\) | 4.05988 | 0.165744 | ||||||||
\(601\) | −9.21459 | −0.375871 | −0.187935 | − | 0.982181i | \(-0.560180\pi\) | ||||
−0.187935 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0781 | −0.532583 | ||||||||
\(604\) | −39.5657 | −1.60991 | ||||||||
\(605\) | 25.4859 | 1.03615 | ||||||||
\(606\) | 21.0216 | 0.853944 | ||||||||
\(607\) | 39.5129 | 1.60378 | 0.801890 | − | 0.597471i | \(-0.203828\pi\) | ||||
0.801890 | + | 0.597471i | \(0.203828\pi\) | |||||||
\(608\) | 57.1008 | 2.31574 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −35.6565 | −1.44369 | ||||||||
\(611\) | 3.09071 | 0.125037 | ||||||||
\(612\) | −6.27877 | −0.253804 | ||||||||
\(613\) | −19.9530 | −0.805895 | −0.402947 | − | 0.915223i | \(-0.632014\pi\) | ||||
−0.402947 | + | 0.915223i | \(0.632014\pi\) | |||||||
\(614\) | −27.4224 | −1.10668 | ||||||||
\(615\) | 2.91322 | 0.117473 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.18441 | 0.208716 | 0.104358 | − | 0.994540i | \(-0.466721\pi\) | ||||
0.104358 | + | 0.994540i | \(0.466721\pi\) | |||||||
\(618\) | −11.9195 | −0.479475 | ||||||||
\(619\) | −13.6896 | −0.550233 | −0.275117 | − | 0.961411i | \(-0.588716\pi\) | ||||
−0.275117 | + | 0.961411i | \(0.588716\pi\) | |||||||
\(620\) | −57.5952 | −2.31308 | ||||||||
\(621\) | −4.49416 | −0.180344 | ||||||||
\(622\) | 33.1543 | 1.32937 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.60348 | 0.224319 | ||||||||
\(625\) | −30.2761 | −1.21104 | ||||||||
\(626\) | −57.9257 | −2.31518 | ||||||||
\(627\) | 10.8558 | 0.433540 | ||||||||
\(628\) | 52.1718 | 2.08188 | ||||||||
\(629\) | −4.35866 | −0.173791 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1111 | 1.67642 | 0.838209 | − | 0.545350i | \(-0.183603\pi\) | ||||
0.838209 | + | 0.545350i | \(0.183603\pi\) | |||||||
\(632\) | −18.1818 | −0.723233 | ||||||||
\(633\) | −24.2561 | −0.964092 | ||||||||
\(634\) | −6.37455 | −0.253166 | ||||||||
\(635\) | −28.6517 | −1.13701 | ||||||||
\(636\) | −9.54569 | −0.378511 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29.1748 | −1.15504 | ||||||||
\(639\) | −4.11377 | −0.162738 | ||||||||
\(640\) | −26.1242 | −1.03265 | ||||||||
\(641\) | −3.51098 | −0.138676 | −0.0693378 | − | 0.997593i | \(-0.522089\pi\) | ||||
−0.0693378 | + | 0.997593i | \(0.522089\pi\) | |||||||
\(642\) | 29.2920 | 1.15606 | ||||||||
\(643\) | 36.4566 | 1.43771 | 0.718854 | − | 0.695161i | \(-0.244667\pi\) | ||||
0.718854 | + | 0.695161i | \(0.244667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.8538 | 0.742368 | ||||||||
\(646\) | 38.0393 | 1.49664 | ||||||||
\(647\) | 14.4875 | 0.569564 | 0.284782 | − | 0.958592i | \(-0.408079\pi\) | ||||
0.284782 | + | 0.958592i | \(0.408079\pi\) | |||||||
\(648\) | −1.16433 | −0.0457393 | ||||||||
\(649\) | −11.5533 | −0.453507 | ||||||||
\(650\) | −15.9637 | −0.626148 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.2067 | 1.14382 | ||||||||
\(653\) | 26.6506 | 1.04292 | 0.521458 | − | 0.853277i | \(-0.325388\pi\) | ||||
0.521458 | + | 0.853277i | \(0.325388\pi\) | |||||||
\(654\) | −36.0316 | −1.40895 | ||||||||
\(655\) | −4.92164 | −0.192304 | ||||||||
\(656\) | −2.60963 | −0.101889 | ||||||||
\(657\) | −2.78408 | −0.108617 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.9262 | −1.43844 | −0.719220 | − | 0.694782i | \(-0.755501\pi\) | ||||
−0.719220 | + | 0.694782i | \(0.755501\pi\) | |||||||
\(660\) | −11.1301 | −0.433237 | ||||||||
\(661\) | 22.7844 | 0.886210 | 0.443105 | − | 0.896470i | \(-0.353877\pi\) | ||||
0.443105 | + | 0.896470i | \(0.353877\pi\) | |||||||
\(662\) | −24.3534 | −0.946523 | ||||||||
\(663\) | 5.29519 | 0.205648 | ||||||||
\(664\) | −1.44338 | −0.0560140 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.76851 | −0.146027 | ||||||||
\(667\) | −40.9813 | −1.58680 | ||||||||
\(668\) | −3.09177 | −0.119624 | ||||||||
\(669\) | −10.0523 | −0.388642 | ||||||||
\(670\) | −81.2340 | −3.13834 | ||||||||
\(671\) | 8.61386 | 0.332534 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.6835 | −0.874384 | −0.437192 | − | 0.899368i | \(-0.644027\pi\) | ||||
−0.437192 | + | 0.899368i | \(0.644027\pi\) | |||||||
\(674\) | −12.5673 | −0.484074 | ||||||||
\(675\) | −3.48687 | −0.134210 | ||||||||
\(676\) | −21.3601 | −0.821541 | ||||||||
\(677\) | 47.1910 | 1.81370 | 0.906848 | − | 0.421457i | \(-0.138481\pi\) | ||||
0.906848 | + | 0.421457i | \(0.138481\pi\) | |||||||
\(678\) | −26.1698 | −1.00505 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.36476 | −0.320774 | ||||||||
\(681\) | −3.70831 | −0.142103 | ||||||||
\(682\) | 24.8433 | 0.951301 | ||||||||
\(683\) | 45.3118 | 1.73381 | 0.866904 | − | 0.498476i | \(-0.166107\pi\) | ||||
0.866904 | + | 0.498476i | \(0.166107\pi\) | |||||||
\(684\) | 18.4198 | 0.704297 | ||||||||
\(685\) | 54.7567 | 2.09214 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.627708 | −0.0239486 | ||||||||
\(688\) | −16.8890 | −0.643887 | ||||||||
\(689\) | 8.05034 | 0.306693 | ||||||||
\(690\) | −27.9152 | −1.06271 | ||||||||
\(691\) | −23.4256 | −0.891151 | −0.445576 | − | 0.895244i | \(-0.647001\pi\) | ||||
−0.445576 | + | 0.895244i | \(0.647001\pi\) | |||||||
\(692\) | −46.6351 | −1.77280 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.50022 | 0.360623 | ||||||||
\(695\) | 10.0927 | 0.382838 | ||||||||
\(696\) | −10.6173 | −0.402448 | ||||||||
\(697\) | −2.46605 | −0.0934084 | ||||||||
\(698\) | 25.7290 | 0.973858 | ||||||||
\(699\) | 5.69247 | 0.215309 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.95291 | 0.149299 | 0.0746496 | − | 0.997210i | \(-0.476216\pi\) | ||||
0.0746496 | + | 0.997210i | \(0.476216\pi\) | |||||||
\(702\) | 4.57823 | 0.172794 | ||||||||
\(703\) | 12.7868 | 0.482264 | ||||||||
\(704\) | 17.4205 | 0.656561 | ||||||||
\(705\) | 4.19327 | 0.157928 | ||||||||
\(706\) | −60.4071 | −2.27345 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −19.6032 | −0.736733 | ||||||||
\(709\) | −43.7509 | −1.64310 | −0.821549 | − | 0.570137i | \(-0.806890\pi\) | ||||
−0.821549 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(710\) | −25.5525 | −0.958967 | ||||||||
\(711\) | 15.6156 | 0.585632 | ||||||||
\(712\) | −11.9849 | −0.449152 | ||||||||
\(713\) | 34.8970 | 1.30690 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.38652 | 0.351036 | ||||||||
\(716\) | 19.8612 | 0.742249 | ||||||||
\(717\) | 2.28786 | 0.0854417 | ||||||||
\(718\) | −32.2867 | −1.20493 | ||||||||
\(719\) | 39.2991 | 1.46561 | 0.732805 | − | 0.680439i | \(-0.238211\pi\) | ||||
0.732805 | + | 0.680439i | \(0.238211\pi\) | |||||||
\(720\) | 7.60243 | 0.283326 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −71.0833 | −2.64545 | ||||||||
\(723\) | 9.22536 | 0.343095 | ||||||||
\(724\) | −5.39086 | −0.200350 | ||||||||
\(725\) | −31.7961 | −1.18088 | ||||||||
\(726\) | −18.6528 | −0.692271 | ||||||||
\(727\) | −6.63007 | −0.245896 | −0.122948 | − | 0.992413i | \(-0.539235\pi\) | ||||
−0.122948 | + | 0.992413i | \(0.539235\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.2932 | −0.640049 | ||||||||
\(731\) | −15.9598 | −0.590295 | ||||||||
\(732\) | 14.6157 | 0.540211 | ||||||||
\(733\) | 18.4143 | 0.680149 | 0.340074 | − | 0.940399i | \(-0.389548\pi\) | ||||
0.340074 | + | 0.940399i | \(0.389548\pi\) | |||||||
\(734\) | 33.6918 | 1.24359 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.4715 | 1.30750 | ||||||||
\(737\) | 19.6244 | 0.722875 | ||||||||
\(738\) | −2.13215 | −0.0784857 | ||||||||
\(739\) | 45.5824 | 1.67678 | 0.838388 | − | 0.545073i | \(-0.183498\pi\) | ||||
0.838388 | + | 0.545073i | \(0.183498\pi\) | |||||||
\(740\) | −13.1098 | −0.481927 | ||||||||
\(741\) | −15.5343 | −0.570666 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.83501 | 0.140693 | 0.0703465 | − | 0.997523i | \(-0.477590\pi\) | ||||
0.0703465 | + | 0.997523i | \(0.477590\pi\) | |||||||
\(744\) | 9.04101 | 0.331460 | ||||||||
\(745\) | 65.5821 | 2.40274 | ||||||||
\(746\) | −26.6262 | −0.974855 | ||||||||
\(747\) | 1.23966 | 0.0453569 | ||||||||
\(748\) | 9.42164 | 0.344489 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.39871 | 0.343192 | ||||||||
\(751\) | −15.3335 | −0.559528 | −0.279764 | − | 0.960069i | \(-0.590256\pi\) | ||||
−0.279764 | + | 0.960069i | \(0.590256\pi\) | |||||||
\(752\) | −3.75628 | −0.136977 | ||||||||
\(753\) | −3.04049 | −0.110801 | ||||||||
\(754\) | 41.7480 | 1.52037 | ||||||||
\(755\) | 45.2710 | 1.64758 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.5275 | −1.47300 | −0.736499 | − | 0.676439i | \(-0.763522\pi\) | ||||
−0.736499 | + | 0.676439i | \(0.763522\pi\) | |||||||
\(758\) | −8.37060 | −0.304034 | ||||||||
\(759\) | 6.74373 | 0.244782 | ||||||||
\(760\) | 24.5393 | 0.890135 | ||||||||
\(761\) | 49.4612 | 1.79297 | 0.896483 | − | 0.443077i | \(-0.146113\pi\) | ||||
0.896483 | + | 0.443077i | \(0.146113\pi\) | |||||||
\(762\) | 20.9698 | 0.759656 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −51.0400 | −1.84656 | ||||||||
\(765\) | 7.18416 | 0.259744 | ||||||||
\(766\) | −27.4332 | −0.991201 | ||||||||
\(767\) | 16.5323 | 0.596947 | ||||||||
\(768\) | −4.09881 | −0.147903 | ||||||||
\(769\) | 30.7710 | 1.10963 | 0.554815 | − | 0.831974i | \(-0.312789\pi\) | ||||
0.554815 | + | 0.831974i | \(0.312789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7197 | 0.782215 | ||||||||
\(772\) | −22.0582 | −0.793891 | ||||||||
\(773\) | 31.6733 | 1.13921 | 0.569605 | − | 0.821919i | \(-0.307096\pi\) | ||||
0.569605 | + | 0.821919i | \(0.307096\pi\) | |||||||
\(774\) | −13.7989 | −0.495991 | ||||||||
\(775\) | 27.0755 | 0.972579 | ||||||||
\(776\) | 3.42085 | 0.122801 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −51.4614 | −1.84498 | ||||||||
\(779\) | 7.23455 | 0.259205 | ||||||||
\(780\) | 15.9267 | 0.570267 | ||||||||
\(781\) | 6.17294 | 0.220885 | ||||||||
\(782\) | 23.6303 | 0.845018 | ||||||||
\(783\) | 9.11879 | 0.325879 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −59.6948 | −2.13060 | ||||||||
\(786\) | 3.60209 | 0.128482 | ||||||||
\(787\) | 21.1978 | 0.755621 | 0.377810 | − | 0.925883i | \(-0.376677\pi\) | ||||
0.377810 | + | 0.925883i | \(0.376677\pi\) | |||||||
\(788\) | 27.7687 | 0.989218 | ||||||||
\(789\) | 0.758785 | 0.0270135 | ||||||||
\(790\) | 96.9956 | 3.45095 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.74714 | 0.0620821 | ||||||||
\(793\) | −12.3261 | −0.437712 | ||||||||
\(794\) | 36.2337 | 1.28589 | ||||||||
\(795\) | 10.9222 | 0.387369 | ||||||||
\(796\) | 46.8234 | 1.65961 | ||||||||
\(797\) | 39.5421 | 1.40065 | 0.700326 | − | 0.713823i | \(-0.253038\pi\) | ||||
0.700326 | + | 0.713823i | \(0.253038\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.54962 | −0.125576 | ||||||||
\(800\) | 27.5212 | 0.973020 | ||||||||
\(801\) | 10.2933 | 0.363697 | ||||||||
\(802\) | −35.9858 | −1.27070 | ||||||||
\(803\) | 4.17767 | 0.147427 | ||||||||
\(804\) | 33.2980 | 1.17433 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −35.5498 | −1.25219 | ||||||||
\(807\) | −9.21857 | −0.324509 | ||||||||
\(808\) | −11.4795 | −0.403849 | ||||||||
\(809\) | 19.2888 | 0.678159 | 0.339080 | − | 0.940758i | \(-0.389884\pi\) | ||||
0.339080 | + | 0.940758i | \(0.389884\pi\) | |||||||
\(810\) | 6.21144 | 0.218248 | ||||||||
\(811\) | −29.6499 | −1.04115 | −0.520574 | − | 0.853817i | \(-0.674282\pi\) | ||||
−0.520574 | + | 0.853817i | \(0.674282\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9651 | 0.770350 | ||||||||
\(814\) | 5.65485 | 0.198202 | ||||||||
\(815\) | −33.4182 | −1.17059 | ||||||||
\(816\) | −6.43548 | −0.225287 | ||||||||
\(817\) | 46.8206 | 1.63805 | ||||||||
\(818\) | −49.8354 | −1.74245 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.41731 | −0.259024 | ||||||||
\(821\) | 8.05452 | 0.281105 | 0.140552 | − | 0.990073i | \(-0.455112\pi\) | ||||
0.140552 | + | 0.990073i | \(0.455112\pi\) | |||||||
\(822\) | −40.0758 | −1.39780 | ||||||||
\(823\) | −5.13488 | −0.178991 | −0.0894953 | − | 0.995987i | \(-0.528525\pi\) | ||||
−0.0894953 | + | 0.995987i | \(0.528525\pi\) | |||||||
\(824\) | 6.50906 | 0.226754 | ||||||||
\(825\) | 5.23224 | 0.182163 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.1238 | 1.32570 | 0.662848 | − | 0.748754i | \(-0.269348\pi\) | ||||
0.662848 | + | 0.748754i | \(0.269348\pi\) | |||||||
\(828\) | 11.4425 | 0.397654 | ||||||||
\(829\) | −1.89733 | −0.0658970 | −0.0329485 | − | 0.999457i | \(-0.510490\pi\) | ||||
−0.0329485 | + | 0.999457i | \(0.510490\pi\) | |||||||
\(830\) | 7.70009 | 0.267274 | ||||||||
\(831\) | −17.9529 | −0.622779 | ||||||||
\(832\) | −24.9281 | −0.864227 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.38672 | −0.255781 | ||||||||
\(835\) | 3.53760 | 0.122424 | ||||||||
\(836\) | −27.6399 | −0.955944 | ||||||||
\(837\) | −7.76497 | −0.268397 | ||||||||
\(838\) | 1.36120 | 0.0470220 | ||||||||
\(839\) | 42.5450 | 1.46882 | 0.734408 | − | 0.678708i | \(-0.237460\pi\) | ||||
0.734408 | + | 0.678708i | \(0.237460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.1524 | 1.86732 | ||||||||
\(842\) | 72.8223 | 2.50962 | ||||||||
\(843\) | 22.5886 | 0.777992 | ||||||||
\(844\) | 61.7580 | 2.12580 | ||||||||
\(845\) | 24.4402 | 0.840767 | ||||||||
\(846\) | −3.06901 | −0.105515 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.78393 | −0.335981 | ||||||||
\(849\) | 13.7918 | 0.473332 | ||||||||
\(850\) | 18.3340 | 0.628850 | ||||||||
\(851\) | 7.94326 | 0.272292 | ||||||||
\(852\) | 10.4740 | 0.358833 | ||||||||
\(853\) | −17.4335 | −0.596913 | −0.298457 | − | 0.954423i | \(-0.596472\pi\) | ||||
−0.298457 | + | 0.954423i | \(0.596472\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.0759 | −0.720779 | ||||||||
\(856\) | −15.9959 | −0.546727 | ||||||||
\(857\) | 26.1027 | 0.891653 | 0.445826 | − | 0.895119i | \(-0.352910\pi\) | ||||
0.445826 | + | 0.895119i | \(0.352910\pi\) | |||||||
\(858\) | −6.86989 | −0.234534 | ||||||||
\(859\) | 36.5305 | 1.24641 | 0.623203 | − | 0.782060i | \(-0.285831\pi\) | ||||
0.623203 | + | 0.782060i | \(0.285831\pi\) | |||||||
\(860\) | −48.0034 | −1.63690 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.9823 | 1.29368 | ||||||||
\(863\) | −9.24397 | −0.314669 | −0.157334 | − | 0.987545i | \(-0.550290\pi\) | ||||
−0.157334 | + | 0.987545i | \(0.550290\pi\) | |||||||
\(864\) | −7.89280 | −0.268518 | ||||||||
\(865\) | 53.3598 | 1.81429 | ||||||||
\(866\) | −39.6811 | −1.34842 | ||||||||
\(867\) | 10.9186 | 0.370815 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.4321 | −0.794879 | ||||||||
\(870\) | 56.6409 | 1.92031 | ||||||||
\(871\) | −28.0818 | −0.951515 | ||||||||
\(872\) | 19.6763 | 0.666322 | ||||||||
\(873\) | −2.93804 | −0.0994375 | ||||||||
\(874\) | −69.3232 | −2.34489 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.08851 | 0.239499 | ||||||||
\(877\) | −46.5927 | −1.57332 | −0.786662 | − | 0.617384i | \(-0.788193\pi\) | ||||
−0.786662 | + | 0.617384i | \(0.788193\pi\) | |||||||
\(878\) | 64.0311 | 2.16094 | ||||||||
\(879\) | −7.85590 | −0.264973 | ||||||||
\(880\) | −11.4079 | −0.384559 | ||||||||
\(881\) | 17.0942 | 0.575918 | 0.287959 | − | 0.957643i | \(-0.407023\pi\) | ||||
0.287959 | + | 0.957643i | \(0.407023\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.33116 | −0.246713 | −0.123357 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123357 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(884\) | −13.4820 | −0.453448 | ||||||||
\(885\) | 22.4299 | 0.753974 | ||||||||
\(886\) | −22.7852 | −0.765485 | ||||||||
\(887\) | −9.21041 | −0.309255 | −0.154628 | − | 0.987973i | \(-0.549418\pi\) | ||||
−0.154628 | + | 0.987973i | \(0.549418\pi\) | |||||||
\(888\) | 2.05792 | 0.0690592 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 63.9365 | 2.14316 | ||||||||
\(891\) | −1.50055 | −0.0502704 | ||||||||
\(892\) | 25.5939 | 0.856946 | ||||||||
\(893\) | 10.4134 | 0.348470 | ||||||||
\(894\) | −47.9988 | −1.60532 | ||||||||
\(895\) | −22.7252 | −0.759619 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.65001 | −0.322204 | ||||||||
\(898\) | 21.4449 | 0.715626 | ||||||||
\(899\) | −70.8071 | −2.36155 | ||||||||
\(900\) | 8.87786 | 0.295929 | ||||||||
\(901\) | −9.24564 | −0.308017 | ||||||||
\(902\) | 3.19941 | 0.106529 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.2909 | 0.475308 | ||||||||
\(905\) | 6.16821 | 0.205038 | ||||||||
\(906\) | −33.1333 | −1.10078 | ||||||||
\(907\) | −1.42495 | −0.0473147 | −0.0236574 | − | 0.999720i | \(-0.507531\pi\) | ||||
−0.0236574 | + | 0.999720i | \(0.507531\pi\) | |||||||
\(908\) | 9.44167 | 0.313333 | ||||||||
\(909\) | 9.85932 | 0.327013 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0834139 | 0.00276362 | 0.00138181 | − | 0.999999i | \(-0.499560\pi\) | ||||
0.00138181 | + | 0.999999i | \(0.499560\pi\) | |||||||
\(912\) | 18.8795 | 0.625162 | ||||||||
\(913\) | −1.86018 | −0.0615630 | ||||||||
\(914\) | −60.9253 | −2.01523 | ||||||||
\(915\) | −16.7232 | −0.552853 | ||||||||
\(916\) | 1.59820 | 0.0528059 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.25800 | −0.173540 | ||||||||
\(919\) | 17.4891 | 0.576911 | 0.288456 | − | 0.957493i | \(-0.406858\pi\) | ||||
0.288456 | + | 0.957493i | \(0.406858\pi\) | |||||||
\(920\) | 15.2440 | 0.502580 | ||||||||
\(921\) | −12.8613 | −0.423795 | ||||||||
\(922\) | −20.2948 | −0.668374 | ||||||||
\(923\) | −8.83323 | −0.290749 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.16292 | 0.202636 | ||||||||
\(926\) | −66.2252 | −2.17629 | ||||||||
\(927\) | −5.59038 | −0.183612 | ||||||||
\(928\) | −71.9728 | −2.36262 | ||||||||
\(929\) | −37.0853 | −1.21673 | −0.608364 | − | 0.793658i | \(-0.708174\pi\) | ||||
−0.608364 | + | 0.793658i | \(0.708174\pi\) | |||||||
\(930\) | −48.2317 | −1.58158 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.4935 | −0.474751 | ||||||||
\(933\) | 15.5497 | 0.509074 | ||||||||
\(934\) | −48.5944 | −1.59006 | ||||||||
\(935\) | −10.7802 | −0.352551 | ||||||||
\(936\) | −2.50010 | −0.0817182 | ||||||||
\(937\) | −51.2474 | −1.67418 | −0.837090 | − | 0.547065i | \(-0.815745\pi\) | ||||
−0.837090 | + | 0.547065i | \(0.815745\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.1677 | −0.886584 | ||||||||
\(940\) | −10.6764 | −0.348226 | ||||||||
\(941\) | −9.65205 | −0.314648 | −0.157324 | − | 0.987547i | \(-0.550287\pi\) | ||||
−0.157324 | + | 0.987547i | \(0.550287\pi\) | |||||||
\(942\) | 43.6900 | 1.42350 | ||||||||
\(943\) | 4.49416 | 0.146350 | ||||||||
\(944\) | −20.0924 | −0.653953 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.7060 | 0.673209 | ||||||||
\(947\) | −16.2966 | −0.529570 | −0.264785 | − | 0.964307i | \(-0.585301\pi\) | ||||
−0.264785 | + | 0.964307i | \(0.585301\pi\) | |||||||
\(948\) | −39.7587 | −1.29130 | ||||||||
\(949\) | −5.97808 | −0.194057 | ||||||||
\(950\) | −53.7856 | −1.74504 | ||||||||
\(951\) | −2.98972 | −0.0969484 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.4806 | 0.436680 | 0.218340 | − | 0.975873i | \(-0.429936\pi\) | ||||
0.218340 | + | 0.975873i | \(0.429936\pi\) | |||||||
\(954\) | −7.99380 | −0.258809 | ||||||||
\(955\) | 58.3999 | 1.88978 | ||||||||
\(956\) | −5.82508 | −0.188397 | ||||||||
\(957\) | −13.6832 | −0.442316 | ||||||||
\(958\) | −73.0268 | −2.35939 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −33.8208 | −1.09156 | ||||||||
\(961\) | 29.2947 | 0.944992 | ||||||||
\(962\) | −8.09186 | −0.260892 | ||||||||
\(963\) | 13.7382 | 0.442708 | ||||||||
\(964\) | −23.4885 | −0.756515 | ||||||||
\(965\) | 25.2389 | 0.812470 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.2230 | 1.55075 | 0.775373 | − | 0.631503i | \(-0.217562\pi\) | ||||
0.775373 | + | 0.631503i | \(0.217562\pi\) | |||||||
\(968\) | 10.1860 | 0.327390 | ||||||||
\(969\) | 17.8408 | 0.573128 | ||||||||
\(970\) | −18.2494 | −0.585954 | ||||||||
\(971\) | −0.494306 | −0.0158630 | −0.00793152 | − | 0.999969i | \(-0.502525\pi\) | ||||
−0.00793152 | + | 0.999969i | \(0.502525\pi\) | |||||||
\(972\) | −2.54608 | −0.0816656 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.5781 | 0.627324 | ||||||||
\(975\) | −7.48713 | −0.239780 | ||||||||
\(976\) | 14.9804 | 0.479512 | ||||||||
\(977\) | 4.09452 | 0.130995 | 0.0654976 | − | 0.997853i | \(-0.479137\pi\) | ||||
0.0654976 | + | 0.997853i | \(0.479137\pi\) | |||||||
\(978\) | 24.4584 | 0.782093 | ||||||||
\(979\) | −15.4457 | −0.493647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8992 | −0.539549 | ||||||||
\(982\) | 38.1238 | 1.21658 | ||||||||
\(983\) | 20.4954 | 0.653703 | 0.326851 | − | 0.945076i | \(-0.394012\pi\) | ||||
0.326851 | + | 0.945076i | \(0.394012\pi\) | |||||||
\(984\) | 1.16433 | 0.0371176 | ||||||||
\(985\) | −31.7729 | −1.01237 | ||||||||
\(986\) | −47.9466 | −1.52693 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 39.5515 | 1.25830 | ||||||||
\(989\) | 29.0853 | 0.924859 | ||||||||
\(990\) | −9.32061 | −0.296228 | ||||||||
\(991\) | 0.869374 | 0.0276166 | 0.0138083 | − | 0.999905i | \(-0.495605\pi\) | ||||
0.0138083 | + | 0.999905i | \(0.495605\pi\) | |||||||
\(992\) | 61.2873 | 1.94587 | ||||||||
\(993\) | −11.4220 | −0.362466 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.5752 | −1.69845 | ||||||||
\(996\) | −3.15628 | −0.100011 | ||||||||
\(997\) | 36.6918 | 1.16204 | 0.581020 | − | 0.813889i | \(-0.302654\pi\) | ||||
0.581020 | + | 0.813889i | \(0.302654\pi\) | |||||||
\(998\) | 50.3835 | 1.59486 | ||||||||
\(999\) | −1.76746 | −0.0559201 |
(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 | 6027.2.a.bj.1.3 | 14 | ||
7.2 | even | 3 | 861.2.i.g.739.12 | yes | 28 | ||
7.4 | even | 3 | 861.2.i.g.247.12 | ✓ | 28 | ||
7.6 | odd | 2 | 6027.2.a.bk.1.3 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.g.247.12 | ✓ | 28 | 7.4 | even | 3 | ||
861.2.i.g.739.12 | yes | 28 | 7.2 | even | 3 | ||
6027.2.a.bj.1.3 | 14 | 1.1 | even | 1 | trivial | ||
6027.2.a.bk.1.3 | 14 | 7.6 | odd | 2 |