Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.19050 | −1.84204 | −0.921019 | − | 0.389517i | \(-0.872642\pi\) | ||||
−0.921019 | + | 0.389517i | \(0.872642\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.434778 | −0.194439 | −0.0972194 | − | 0.995263i | \(-0.530995\pi\) | ||||
−0.0972194 | + | 0.995263i | \(0.530995\pi\) | |||||||
\(6\) | 3.19050 | 1.30252 | ||||||||
\(7\) | 2.23469 | 0.844632 | 0.422316 | − | 0.906449i | \(-0.361217\pi\) | ||||
0.422316 | + | 0.906449i | \(0.361217\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.17932 | 2.39311 | ||||||||
\(10\) | 0.434778 | 0.137489 | ||||||||
\(11\) | −0.690985 | −0.208340 | −0.104170 | − | 0.994560i | \(-0.533219\pi\) | ||||
−0.104170 | + | 0.994560i | \(0.533219\pi\) | |||||||
\(12\) | −3.19050 | −0.921019 | ||||||||
\(13\) | 4.85100 | 1.34543 | 0.672713 | − | 0.739904i | \(-0.265129\pi\) | ||||
0.672713 | + | 0.739904i | \(0.265129\pi\) | |||||||
\(14\) | −2.23469 | −0.597245 | ||||||||
\(15\) | 1.38716 | 0.358164 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.67758 | −0.406872 | −0.203436 | − | 0.979088i | \(-0.565211\pi\) | ||||
−0.203436 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(18\) | −7.17932 | −1.69218 | ||||||||
\(19\) | −6.17918 | −1.41760 | −0.708800 | − | 0.705409i | \(-0.750763\pi\) | ||||
−0.708800 | + | 0.705409i | \(0.750763\pi\) | |||||||
\(20\) | −0.434778 | −0.0972194 | ||||||||
\(21\) | −7.12978 | −1.55585 | ||||||||
\(22\) | 0.690985 | 0.147318 | ||||||||
\(23\) | −0.601471 | −0.125415 | −0.0627077 | − | 0.998032i | \(-0.519974\pi\) | ||||
−0.0627077 | + | 0.998032i | \(0.519974\pi\) | |||||||
\(24\) | 3.19050 | 0.651259 | ||||||||
\(25\) | −4.81097 | −0.962194 | ||||||||
\(26\) | −4.85100 | −0.951359 | ||||||||
\(27\) | −13.3341 | −2.56616 | ||||||||
\(28\) | 2.23469 | 0.422316 | ||||||||
\(29\) | 0.669083 | 0.124246 | 0.0621228 | − | 0.998069i | \(-0.480213\pi\) | ||||
0.0621228 | + | 0.998069i | \(0.480213\pi\) | |||||||
\(30\) | −1.38716 | −0.253260 | ||||||||
\(31\) | 4.81141 | 0.864155 | 0.432077 | − | 0.901836i | \(-0.357781\pi\) | ||||
0.432077 | + | 0.901836i | \(0.357781\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.20459 | 0.383770 | ||||||||
\(34\) | 1.67758 | 0.287702 | ||||||||
\(35\) | −0.971594 | −0.164229 | ||||||||
\(36\) | 7.17932 | 1.19655 | ||||||||
\(37\) | −9.68724 | −1.59257 | −0.796286 | − | 0.604920i | \(-0.793205\pi\) | ||||
−0.796286 | + | 0.604920i | \(0.793205\pi\) | |||||||
\(38\) | 6.17918 | 1.00240 | ||||||||
\(39\) | −15.4771 | −2.47833 | ||||||||
\(40\) | 0.434778 | 0.0687445 | ||||||||
\(41\) | −0.204017 | −0.0318621 | −0.0159310 | − | 0.999873i | \(-0.505071\pi\) | ||||
−0.0159310 | + | 0.999873i | \(0.505071\pi\) | |||||||
\(42\) | 7.12978 | 1.10015 | ||||||||
\(43\) | 5.09994 | 0.777733 | 0.388867 | − | 0.921294i | \(-0.372867\pi\) | ||||
0.388867 | + | 0.921294i | \(0.372867\pi\) | |||||||
\(44\) | −0.690985 | −0.104170 | ||||||||
\(45\) | −3.12141 | −0.465313 | ||||||||
\(46\) | 0.601471 | 0.0886820 | ||||||||
\(47\) | 4.45461 | 0.649772 | 0.324886 | − | 0.945753i | \(-0.394674\pi\) | ||||
0.324886 | + | 0.945753i | \(0.394674\pi\) | |||||||
\(48\) | −3.19050 | −0.460510 | ||||||||
\(49\) | −2.00617 | −0.286596 | ||||||||
\(50\) | 4.81097 | 0.680374 | ||||||||
\(51\) | 5.35232 | 0.749475 | ||||||||
\(52\) | 4.85100 | 0.672713 | ||||||||
\(53\) | 11.4209 | 1.56878 | 0.784388 | − | 0.620271i | \(-0.212977\pi\) | ||||
0.784388 | + | 0.620271i | \(0.212977\pi\) | |||||||
\(54\) | 13.3341 | 1.81455 | ||||||||
\(55\) | 0.300425 | 0.0405093 | ||||||||
\(56\) | −2.23469 | −0.298623 | ||||||||
\(57\) | 19.7147 | 2.61128 | ||||||||
\(58\) | −0.669083 | −0.0878549 | ||||||||
\(59\) | 13.4068 | 1.74541 | 0.872707 | − | 0.488245i | \(-0.162363\pi\) | ||||
0.872707 | + | 0.488245i | \(0.162363\pi\) | |||||||
\(60\) | 1.38716 | 0.179082 | ||||||||
\(61\) | −2.80565 | −0.359227 | −0.179613 | − | 0.983737i | \(-0.557485\pi\) | ||||
−0.179613 | + | 0.983737i | \(0.557485\pi\) | |||||||
\(62\) | −4.81141 | −0.611050 | ||||||||
\(63\) | 16.0435 | 2.02130 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.10911 | −0.261603 | ||||||||
\(66\) | −2.20459 | −0.271366 | ||||||||
\(67\) | 6.27731 | 0.766895 | 0.383448 | − | 0.923563i | \(-0.374737\pi\) | ||||
0.383448 | + | 0.923563i | \(0.374737\pi\) | |||||||
\(68\) | −1.67758 | −0.203436 | ||||||||
\(69\) | 1.91900 | 0.231020 | ||||||||
\(70\) | 0.971594 | 0.116128 | ||||||||
\(71\) | −5.15436 | −0.611710 | −0.305855 | − | 0.952078i | \(-0.598942\pi\) | ||||
−0.305855 | + | 0.952078i | \(0.598942\pi\) | |||||||
\(72\) | −7.17932 | −0.846091 | ||||||||
\(73\) | −0.0754243 | −0.00882775 | −0.00441388 | − | 0.999990i | \(-0.501405\pi\) | ||||
−0.00441388 | + | 0.999990i | \(0.501405\pi\) | |||||||
\(74\) | 9.68724 | 1.12612 | ||||||||
\(75\) | 15.3494 | 1.77240 | ||||||||
\(76\) | −6.17918 | −0.708800 | ||||||||
\(77\) | −1.54413 | −0.175971 | ||||||||
\(78\) | 15.4771 | 1.75244 | ||||||||
\(79\) | 10.5721 | 1.18946 | 0.594728 | − | 0.803927i | \(-0.297260\pi\) | ||||
0.594728 | + | 0.803927i | \(0.297260\pi\) | |||||||
\(80\) | −0.434778 | −0.0486097 | ||||||||
\(81\) | 21.0047 | 2.33385 | ||||||||
\(82\) | 0.204017 | 0.0225299 | ||||||||
\(83\) | 8.43670 | 0.926048 | 0.463024 | − | 0.886346i | \(-0.346764\pi\) | ||||
0.463024 | + | 0.886346i | \(0.346764\pi\) | |||||||
\(84\) | −7.12978 | −0.777923 | ||||||||
\(85\) | 0.729375 | 0.0791118 | ||||||||
\(86\) | −5.09994 | −0.549941 | ||||||||
\(87\) | −2.13471 | −0.228865 | ||||||||
\(88\) | 0.690985 | 0.0736592 | ||||||||
\(89\) | −1.88869 | −0.200200 | −0.100100 | − | 0.994977i | \(-0.531916\pi\) | ||||
−0.100100 | + | 0.994977i | \(0.531916\pi\) | |||||||
\(90\) | 3.12141 | 0.329026 | ||||||||
\(91\) | 10.8405 | 1.13639 | ||||||||
\(92\) | −0.601471 | −0.0627077 | ||||||||
\(93\) | −15.3508 | −1.59181 | ||||||||
\(94\) | −4.45461 | −0.459458 | ||||||||
\(95\) | 2.68657 | 0.275637 | ||||||||
\(96\) | 3.19050 | 0.325630 | ||||||||
\(97\) | −15.3399 | −1.55753 | −0.778766 | − | 0.627315i | \(-0.784154\pi\) | ||||
−0.778766 | + | 0.627315i | \(0.784154\pi\) | |||||||
\(98\) | 2.00617 | 0.202654 | ||||||||
\(99\) | −4.96080 | −0.498579 | ||||||||
\(100\) | −4.81097 | −0.481097 | ||||||||
\(101\) | −2.51366 | −0.250118 | −0.125059 | − | 0.992149i | \(-0.539912\pi\) | ||||
−0.125059 | + | 0.992149i | \(0.539912\pi\) | |||||||
\(102\) | −5.35232 | −0.529959 | ||||||||
\(103\) | −18.1843 | −1.79176 | −0.895878 | − | 0.444299i | \(-0.853453\pi\) | ||||
−0.895878 | + | 0.444299i | \(0.853453\pi\) | |||||||
\(104\) | −4.85100 | −0.475680 | ||||||||
\(105\) | 3.09987 | 0.302517 | ||||||||
\(106\) | −11.4209 | −1.10929 | ||||||||
\(107\) | 3.01826 | 0.291786 | 0.145893 | − | 0.989300i | \(-0.453395\pi\) | ||||
0.145893 | + | 0.989300i | \(0.453395\pi\) | |||||||
\(108\) | −13.3341 | −1.28308 | ||||||||
\(109\) | −2.62418 | −0.251351 | −0.125675 | − | 0.992071i | \(-0.540110\pi\) | ||||
−0.125675 | + | 0.992071i | \(0.540110\pi\) | |||||||
\(110\) | −0.300425 | −0.0286444 | ||||||||
\(111\) | 30.9072 | 2.93358 | ||||||||
\(112\) | 2.23469 | 0.211158 | ||||||||
\(113\) | −3.89903 | −0.366790 | −0.183395 | − | 0.983039i | \(-0.558709\pi\) | ||||
−0.183395 | + | 0.983039i | \(0.558709\pi\) | |||||||
\(114\) | −19.7147 | −1.84645 | ||||||||
\(115\) | 0.261507 | 0.0243856 | ||||||||
\(116\) | 0.669083 | 0.0621228 | ||||||||
\(117\) | 34.8269 | 3.21975 | ||||||||
\(118\) | −13.4068 | −1.23419 | ||||||||
\(119\) | −3.74886 | −0.343657 | ||||||||
\(120\) | −1.38716 | −0.126630 | ||||||||
\(121\) | −10.5225 | −0.956595 | ||||||||
\(122\) | 2.80565 | 0.254012 | ||||||||
\(123\) | 0.650917 | 0.0586912 | ||||||||
\(124\) | 4.81141 | 0.432077 | ||||||||
\(125\) | 4.26560 | 0.381527 | ||||||||
\(126\) | −16.0435 | −1.42927 | ||||||||
\(127\) | −4.44903 | −0.394788 | −0.197394 | − | 0.980324i | \(-0.563248\pi\) | ||||
−0.197394 | + | 0.980324i | \(0.563248\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −16.2714 | −1.43262 | ||||||||
\(130\) | 2.10911 | 0.184981 | ||||||||
\(131\) | 12.1312 | 1.05991 | 0.529954 | − | 0.848026i | \(-0.322209\pi\) | ||||
0.529954 | + | 0.848026i | \(0.322209\pi\) | |||||||
\(132\) | 2.20459 | 0.191885 | ||||||||
\(133\) | −13.8085 | −1.19735 | ||||||||
\(134\) | −6.27731 | −0.542277 | ||||||||
\(135\) | 5.79740 | 0.498960 | ||||||||
\(136\) | 1.67758 | 0.143851 | ||||||||
\(137\) | −17.6190 | −1.50529 | −0.752644 | − | 0.658427i | \(-0.771222\pi\) | ||||
−0.752644 | + | 0.658427i | \(0.771222\pi\) | |||||||
\(138\) | −1.91900 | −0.163356 | ||||||||
\(139\) | 6.22339 | 0.527861 | 0.263931 | − | 0.964542i | \(-0.414981\pi\) | ||||
0.263931 | + | 0.964542i | \(0.414981\pi\) | |||||||
\(140\) | −0.971594 | −0.0821147 | ||||||||
\(141\) | −14.2125 | −1.19690 | ||||||||
\(142\) | 5.15436 | 0.432544 | ||||||||
\(143\) | −3.35197 | −0.280306 | ||||||||
\(144\) | 7.17932 | 0.598277 | ||||||||
\(145\) | −0.290903 | −0.0241582 | ||||||||
\(146\) | 0.0754243 | 0.00624216 | ||||||||
\(147\) | 6.40071 | 0.527922 | ||||||||
\(148\) | −9.68724 | −0.796286 | ||||||||
\(149\) | 0.801116 | 0.0656300 | 0.0328150 | − | 0.999461i | \(-0.489553\pi\) | ||||
0.0328150 | + | 0.999461i | \(0.489553\pi\) | |||||||
\(150\) | −15.3494 | −1.25327 | ||||||||
\(151\) | 7.68648 | 0.625517 | 0.312759 | − | 0.949833i | \(-0.398747\pi\) | ||||
0.312759 | + | 0.949833i | \(0.398747\pi\) | |||||||
\(152\) | 6.17918 | 0.501198 | ||||||||
\(153\) | −12.0439 | −0.973689 | ||||||||
\(154\) | 1.54413 | 0.124430 | ||||||||
\(155\) | −2.09190 | −0.168025 | ||||||||
\(156\) | −15.4771 | −1.23916 | ||||||||
\(157\) | −13.7351 | −1.09618 | −0.548090 | − | 0.836419i | \(-0.684645\pi\) | ||||
−0.548090 | + | 0.836419i | \(0.684645\pi\) | |||||||
\(158\) | −10.5721 | −0.841073 | ||||||||
\(159\) | −36.4383 | −2.88975 | ||||||||
\(160\) | 0.434778 | 0.0343723 | ||||||||
\(161\) | −1.34410 | −0.105930 | ||||||||
\(162\) | −21.0047 | −1.65028 | ||||||||
\(163\) | 8.72923 | 0.683726 | 0.341863 | − | 0.939750i | \(-0.388942\pi\) | ||||
0.341863 | + | 0.939750i | \(0.388942\pi\) | |||||||
\(164\) | −0.204017 | −0.0159310 | ||||||||
\(165\) | −0.958509 | −0.0746198 | ||||||||
\(166\) | −8.43670 | −0.654815 | ||||||||
\(167\) | 21.8834 | 1.69339 | 0.846693 | − | 0.532082i | \(-0.178590\pi\) | ||||
0.846693 | + | 0.532082i | \(0.178590\pi\) | |||||||
\(168\) | 7.12978 | 0.550074 | ||||||||
\(169\) | 10.5322 | 0.810169 | ||||||||
\(170\) | −0.729375 | −0.0559405 | ||||||||
\(171\) | −44.3623 | −3.39247 | ||||||||
\(172\) | 5.09994 | 0.388867 | ||||||||
\(173\) | 21.5724 | 1.64012 | 0.820060 | − | 0.572277i | \(-0.193940\pi\) | ||||
0.820060 | + | 0.572277i | \(0.193940\pi\) | |||||||
\(174\) | 2.13471 | 0.161832 | ||||||||
\(175\) | −10.7510 | −0.812700 | ||||||||
\(176\) | −0.690985 | −0.0520849 | ||||||||
\(177\) | −42.7744 | −3.21512 | ||||||||
\(178\) | 1.88869 | 0.141563 | ||||||||
\(179\) | 20.1156 | 1.50351 | 0.751755 | − | 0.659442i | \(-0.229207\pi\) | ||||
0.751755 | + | 0.659442i | \(0.229207\pi\) | |||||||
\(180\) | −3.12141 | −0.232656 | ||||||||
\(181\) | −6.25494 | −0.464926 | −0.232463 | − | 0.972605i | \(-0.574678\pi\) | ||||
−0.232463 | + | 0.972605i | \(0.574678\pi\) | |||||||
\(182\) | −10.8405 | −0.803549 | ||||||||
\(183\) | 8.95144 | 0.661709 | ||||||||
\(184\) | 0.601471 | 0.0443410 | ||||||||
\(185\) | 4.21180 | 0.309658 | ||||||||
\(186\) | 15.3508 | 1.12558 | ||||||||
\(187\) | 1.15918 | 0.0847677 | ||||||||
\(188\) | 4.45461 | 0.324886 | ||||||||
\(189\) | −29.7976 | −2.16746 | ||||||||
\(190\) | −2.68657 | −0.194905 | ||||||||
\(191\) | 5.72799 | 0.414463 | 0.207232 | − | 0.978292i | \(-0.433555\pi\) | ||||
0.207232 | + | 0.978292i | \(0.433555\pi\) | |||||||
\(192\) | −3.19050 | −0.230255 | ||||||||
\(193\) | 14.5513 | 1.04742 | 0.523712 | − | 0.851895i | \(-0.324547\pi\) | ||||
0.523712 | + | 0.851895i | \(0.324547\pi\) | |||||||
\(194\) | 15.3399 | 1.10134 | ||||||||
\(195\) | 6.72913 | 0.481883 | ||||||||
\(196\) | −2.00617 | −0.143298 | ||||||||
\(197\) | 4.38440 | 0.312376 | 0.156188 | − | 0.987727i | \(-0.450079\pi\) | ||||
0.156188 | + | 0.987727i | \(0.450079\pi\) | |||||||
\(198\) | 4.96080 | 0.352549 | ||||||||
\(199\) | 2.04300 | 0.144825 | 0.0724123 | − | 0.997375i | \(-0.476930\pi\) | ||||
0.0724123 | + | 0.997375i | \(0.476930\pi\) | |||||||
\(200\) | 4.81097 | 0.340187 | ||||||||
\(201\) | −20.0278 | −1.41265 | ||||||||
\(202\) | 2.51366 | 0.176860 | ||||||||
\(203\) | 1.49519 | 0.104942 | ||||||||
\(204\) | 5.35232 | 0.374737 | ||||||||
\(205\) | 0.0887021 | 0.00619523 | ||||||||
\(206\) | 18.1843 | 1.26696 | ||||||||
\(207\) | −4.31815 | −0.300132 | ||||||||
\(208\) | 4.85100 | 0.336356 | ||||||||
\(209\) | 4.26972 | 0.295343 | ||||||||
\(210\) | −3.09987 | −0.213912 | ||||||||
\(211\) | −2.47265 | −0.170224 | −0.0851120 | − | 0.996371i | \(-0.527125\pi\) | ||||
−0.0851120 | + | 0.996371i | \(0.527125\pi\) | |||||||
\(212\) | 11.4209 | 0.784388 | ||||||||
\(213\) | 16.4450 | 1.12679 | ||||||||
\(214\) | −3.01826 | −0.206324 | ||||||||
\(215\) | −2.21734 | −0.151222 | ||||||||
\(216\) | 13.3341 | 0.907273 | ||||||||
\(217\) | 10.7520 | 0.729893 | ||||||||
\(218\) | 2.62418 | 0.177732 | ||||||||
\(219\) | 0.240642 | 0.0162611 | ||||||||
\(220\) | 0.300425 | 0.0202547 | ||||||||
\(221\) | −8.13793 | −0.547416 | ||||||||
\(222\) | −30.9072 | −2.07435 | ||||||||
\(223\) | −19.9821 | −1.33810 | −0.669050 | − | 0.743218i | \(-0.733299\pi\) | ||||
−0.669050 | + | 0.743218i | \(0.733299\pi\) | |||||||
\(224\) | −2.23469 | −0.149311 | ||||||||
\(225\) | −34.5395 | −2.30263 | ||||||||
\(226\) | 3.89903 | 0.259359 | ||||||||
\(227\) | −1.66765 | −0.110686 | −0.0553428 | − | 0.998467i | \(-0.517625\pi\) | ||||
−0.0553428 | + | 0.998467i | \(0.517625\pi\) | |||||||
\(228\) | 19.7147 | 1.30564 | ||||||||
\(229\) | −18.4150 | −1.21690 | −0.608449 | − | 0.793593i | \(-0.708208\pi\) | ||||
−0.608449 | + | 0.793593i | \(0.708208\pi\) | |||||||
\(230\) | −0.261507 | −0.0172432 | ||||||||
\(231\) | 4.92657 | 0.324144 | ||||||||
\(232\) | −0.669083 | −0.0439275 | ||||||||
\(233\) | −14.5883 | −0.955714 | −0.477857 | − | 0.878438i | \(-0.658586\pi\) | ||||
−0.477857 | + | 0.878438i | \(0.658586\pi\) | |||||||
\(234\) | −34.8269 | −2.27670 | ||||||||
\(235\) | −1.93677 | −0.126341 | ||||||||
\(236\) | 13.4068 | 0.872707 | ||||||||
\(237\) | −33.7304 | −2.19103 | ||||||||
\(238\) | 3.74886 | 0.243003 | ||||||||
\(239\) | −21.6769 | −1.40216 | −0.701080 | − | 0.713083i | \(-0.747298\pi\) | ||||
−0.701080 | + | 0.713083i | \(0.747298\pi\) | |||||||
\(240\) | 1.38716 | 0.0895410 | ||||||||
\(241\) | 14.0509 | 0.905096 | 0.452548 | − | 0.891740i | \(-0.350515\pi\) | ||||
0.452548 | + | 0.891740i | \(0.350515\pi\) | |||||||
\(242\) | 10.5225 | 0.676414 | ||||||||
\(243\) | −27.0131 | −1.73289 | ||||||||
\(244\) | −2.80565 | −0.179613 | ||||||||
\(245\) | 0.872241 | 0.0557255 | ||||||||
\(246\) | −0.650917 | −0.0415009 | ||||||||
\(247\) | −29.9752 | −1.90728 | ||||||||
\(248\) | −4.81141 | −0.305525 | ||||||||
\(249\) | −26.9173 | −1.70582 | ||||||||
\(250\) | −4.26560 | −0.269780 | ||||||||
\(251\) | 19.0646 | 1.20335 | 0.601673 | − | 0.798743i | \(-0.294501\pi\) | ||||
0.601673 | + | 0.798743i | \(0.294501\pi\) | |||||||
\(252\) | 16.0435 | 1.01065 | ||||||||
\(253\) | 0.415607 | 0.0261290 | ||||||||
\(254\) | 4.44903 | 0.279157 | ||||||||
\(255\) | −2.32707 | −0.145727 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.62253 | 0.288346 | 0.144173 | − | 0.989553i | \(-0.453948\pi\) | ||||
0.144173 | + | 0.989553i | \(0.453948\pi\) | |||||||
\(258\) | 16.2714 | 1.01301 | ||||||||
\(259\) | −21.6479 | −1.34514 | ||||||||
\(260\) | −2.10911 | −0.130801 | ||||||||
\(261\) | 4.80356 | 0.297333 | ||||||||
\(262\) | −12.1312 | −0.749468 | ||||||||
\(263\) | −21.6171 | −1.33297 | −0.666484 | − | 0.745519i | \(-0.732201\pi\) | ||||
−0.666484 | + | 0.745519i | \(0.732201\pi\) | |||||||
\(264\) | −2.20459 | −0.135683 | ||||||||
\(265\) | −4.96554 | −0.305031 | ||||||||
\(266\) | 13.8085 | 0.846655 | ||||||||
\(267\) | 6.02586 | 0.368777 | ||||||||
\(268\) | 6.27731 | 0.383448 | ||||||||
\(269\) | −15.4263 | −0.940559 | −0.470280 | − | 0.882518i | \(-0.655847\pi\) | ||||
−0.470280 | + | 0.882518i | \(0.655847\pi\) | |||||||
\(270\) | −5.79740 | −0.352818 | ||||||||
\(271\) | 12.2999 | 0.747167 | 0.373584 | − | 0.927597i | \(-0.378129\pi\) | ||||
0.373584 | + | 0.927597i | \(0.378129\pi\) | |||||||
\(272\) | −1.67758 | −0.101718 | ||||||||
\(273\) | −34.5866 | −2.09327 | ||||||||
\(274\) | 17.6190 | 1.06440 | ||||||||
\(275\) | 3.32431 | 0.200463 | ||||||||
\(276\) | 1.91900 | 0.115510 | ||||||||
\(277\) | 23.9710 | 1.44028 | 0.720138 | − | 0.693831i | \(-0.244079\pi\) | ||||
0.720138 | + | 0.693831i | \(0.244079\pi\) | |||||||
\(278\) | −6.22339 | −0.373254 | ||||||||
\(279\) | 34.5427 | 2.06801 | ||||||||
\(280\) | 0.971594 | 0.0580638 | ||||||||
\(281\) | 20.8408 | 1.24326 | 0.621629 | − | 0.783312i | \(-0.286471\pi\) | ||||
0.621629 | + | 0.783312i | \(0.286471\pi\) | |||||||
\(282\) | 14.2125 | 0.846339 | ||||||||
\(283\) | −2.23312 | −0.132745 | −0.0663726 | − | 0.997795i | \(-0.521143\pi\) | ||||
−0.0663726 | + | 0.997795i | \(0.521143\pi\) | |||||||
\(284\) | −5.15436 | −0.305855 | ||||||||
\(285\) | −8.57153 | −0.507733 | ||||||||
\(286\) | 3.35197 | 0.198206 | ||||||||
\(287\) | −0.455914 | −0.0269117 | ||||||||
\(288\) | −7.17932 | −0.423045 | ||||||||
\(289\) | −14.1857 | −0.834455 | ||||||||
\(290\) | 0.290903 | 0.0170824 | ||||||||
\(291\) | 48.9420 | 2.86903 | ||||||||
\(292\) | −0.0754243 | −0.00441388 | ||||||||
\(293\) | −4.57319 | −0.267168 | −0.133584 | − | 0.991037i | \(-0.542649\pi\) | ||||
−0.133584 | + | 0.991037i | \(0.542649\pi\) | |||||||
\(294\) | −6.40071 | −0.373297 | ||||||||
\(295\) | −5.82898 | −0.339376 | ||||||||
\(296\) | 9.68724 | 0.563059 | ||||||||
\(297\) | 9.21369 | 0.534632 | ||||||||
\(298\) | −0.801116 | −0.0464074 | ||||||||
\(299\) | −2.91773 | −0.168737 | ||||||||
\(300\) | 15.3494 | 0.886199 | ||||||||
\(301\) | 11.3968 | 0.656899 | ||||||||
\(302\) | −7.68648 | −0.442307 | ||||||||
\(303\) | 8.01984 | 0.460728 | ||||||||
\(304\) | −6.17918 | −0.354400 | ||||||||
\(305\) | 1.21984 | 0.0698476 | ||||||||
\(306\) | 12.0439 | 0.688502 | ||||||||
\(307\) | 5.08758 | 0.290363 | 0.145182 | − | 0.989405i | \(-0.453623\pi\) | ||||
0.145182 | + | 0.989405i | \(0.453623\pi\) | |||||||
\(308\) | −1.54413 | −0.0879853 | ||||||||
\(309\) | 58.0172 | 3.30049 | ||||||||
\(310\) | 2.09190 | 0.118812 | ||||||||
\(311\) | 18.3559 | 1.04087 | 0.520433 | − | 0.853902i | \(-0.325770\pi\) | ||||
0.520433 | + | 0.853902i | \(0.325770\pi\) | |||||||
\(312\) | 15.4771 | 0.876220 | ||||||||
\(313\) | −11.1858 | −0.632260 | −0.316130 | − | 0.948716i | \(-0.602384\pi\) | ||||
−0.316130 | + | 0.948716i | \(0.602384\pi\) | |||||||
\(314\) | 13.7351 | 0.775117 | ||||||||
\(315\) | −6.97538 | −0.393018 | ||||||||
\(316\) | 10.5721 | 0.594728 | ||||||||
\(317\) | −33.1048 | −1.85935 | −0.929675 | − | 0.368380i | \(-0.879912\pi\) | ||||
−0.929675 | + | 0.368380i | \(0.879912\pi\) | |||||||
\(318\) | 36.4383 | 2.04336 | ||||||||
\(319\) | −0.462326 | −0.0258853 | ||||||||
\(320\) | −0.434778 | −0.0243049 | ||||||||
\(321\) | −9.62976 | −0.537481 | ||||||||
\(322\) | 1.34410 | 0.0749037 | ||||||||
\(323\) | 10.3661 | 0.576783 | ||||||||
\(324\) | 21.0047 | 1.16693 | ||||||||
\(325\) | −23.3380 | −1.29456 | ||||||||
\(326\) | −8.72923 | −0.483467 | ||||||||
\(327\) | 8.37246 | 0.462998 | ||||||||
\(328\) | 0.204017 | 0.0112649 | ||||||||
\(329\) | 9.95466 | 0.548818 | ||||||||
\(330\) | 0.958509 | 0.0527642 | ||||||||
\(331\) | −25.5319 | −1.40336 | −0.701679 | − | 0.712493i | \(-0.747566\pi\) | ||||
−0.701679 | + | 0.712493i | \(0.747566\pi\) | |||||||
\(332\) | 8.43670 | 0.463024 | ||||||||
\(333\) | −69.5478 | −3.81119 | ||||||||
\(334\) | −21.8834 | −1.19740 | ||||||||
\(335\) | −2.72924 | −0.149114 | ||||||||
\(336\) | −7.12978 | −0.388961 | ||||||||
\(337\) | 6.83133 | 0.372126 | 0.186063 | − | 0.982538i | \(-0.440427\pi\) | ||||
0.186063 | + | 0.982538i | \(0.440427\pi\) | |||||||
\(338\) | −10.5322 | −0.572876 | ||||||||
\(339\) | 12.4399 | 0.675641 | ||||||||
\(340\) | 0.729375 | 0.0395559 | ||||||||
\(341\) | −3.32461 | −0.180038 | ||||||||
\(342\) | 44.3623 | 2.39884 | ||||||||
\(343\) | −20.1260 | −1.08670 | ||||||||
\(344\) | −5.09994 | −0.274970 | ||||||||
\(345\) | −0.834338 | −0.0449192 | ||||||||
\(346\) | −21.5724 | −1.15974 | ||||||||
\(347\) | −22.3332 | −1.19891 | −0.599455 | − | 0.800408i | \(-0.704616\pi\) | ||||
−0.599455 | + | 0.800408i | \(0.704616\pi\) | |||||||
\(348\) | −2.13471 | −0.114433 | ||||||||
\(349\) | 2.52858 | 0.135352 | 0.0676758 | − | 0.997707i | \(-0.478442\pi\) | ||||
0.0676758 | + | 0.997707i | \(0.478442\pi\) | |||||||
\(350\) | 10.7510 | 0.574665 | ||||||||
\(351\) | −64.6839 | −3.45257 | ||||||||
\(352\) | 0.690985 | 0.0368296 | ||||||||
\(353\) | 26.1718 | 1.39298 | 0.696491 | − | 0.717565i | \(-0.254744\pi\) | ||||
0.696491 | + | 0.717565i | \(0.254744\pi\) | |||||||
\(354\) | 42.7744 | 2.27343 | ||||||||
\(355\) | 2.24100 | 0.118940 | ||||||||
\(356\) | −1.88869 | −0.100100 | ||||||||
\(357\) | 11.9608 | 0.633030 | ||||||||
\(358\) | −20.1156 | −1.06314 | ||||||||
\(359\) | 32.3652 | 1.70817 | 0.854084 | − | 0.520135i | \(-0.174118\pi\) | ||||
0.854084 | + | 0.520135i | \(0.174118\pi\) | |||||||
\(360\) | 3.12141 | 0.164513 | ||||||||
\(361\) | 19.1823 | 1.00959 | ||||||||
\(362\) | 6.25494 | 0.328752 | ||||||||
\(363\) | 33.5722 | 1.76208 | ||||||||
\(364\) | 10.8405 | 0.568195 | ||||||||
\(365\) | 0.0327929 | 0.00171646 | ||||||||
\(366\) | −8.95144 | −0.467899 | ||||||||
\(367\) | −22.1576 | −1.15662 | −0.578310 | − | 0.815817i | \(-0.696288\pi\) | ||||
−0.578310 | + | 0.815817i | \(0.696288\pi\) | |||||||
\(368\) | −0.601471 | −0.0313538 | ||||||||
\(369\) | −1.46470 | −0.0762493 | ||||||||
\(370\) | −4.21180 | −0.218961 | ||||||||
\(371\) | 25.5220 | 1.32504 | ||||||||
\(372\) | −15.3508 | −0.795903 | ||||||||
\(373\) | 20.6328 | 1.06833 | 0.534164 | − | 0.845381i | \(-0.320627\pi\) | ||||
0.534164 | + | 0.845381i | \(0.320627\pi\) | |||||||
\(374\) | −1.15918 | −0.0599398 | ||||||||
\(375\) | −13.6094 | −0.702787 | ||||||||
\(376\) | −4.45461 | −0.229729 | ||||||||
\(377\) | 3.24572 | 0.167163 | ||||||||
\(378\) | 29.7976 | 1.53262 | ||||||||
\(379\) | −1.71081 | −0.0878783 | −0.0439392 | − | 0.999034i | \(-0.513991\pi\) | ||||
−0.0439392 | + | 0.999034i | \(0.513991\pi\) | |||||||
\(380\) | 2.68657 | 0.137818 | ||||||||
\(381\) | 14.1947 | 0.727215 | ||||||||
\(382\) | −5.72799 | −0.293070 | ||||||||
\(383\) | −14.4585 | −0.738794 | −0.369397 | − | 0.929272i | \(-0.620436\pi\) | ||||
−0.369397 | + | 0.929272i | \(0.620436\pi\) | |||||||
\(384\) | 3.19050 | 0.162815 | ||||||||
\(385\) | 0.671357 | 0.0342155 | ||||||||
\(386\) | −14.5513 | −0.740641 | ||||||||
\(387\) | 36.6141 | 1.86120 | ||||||||
\(388\) | −15.3399 | −0.778766 | ||||||||
\(389\) | 36.0677 | 1.82870 | 0.914351 | − | 0.404922i | \(-0.132701\pi\) | ||||
0.914351 | + | 0.404922i | \(0.132701\pi\) | |||||||
\(390\) | −6.72913 | −0.340743 | ||||||||
\(391\) | 1.00901 | 0.0510280 | ||||||||
\(392\) | 2.00617 | 0.101327 | ||||||||
\(393\) | −38.7046 | −1.95239 | ||||||||
\(394\) | −4.38440 | −0.220883 | ||||||||
\(395\) | −4.59653 | −0.231277 | ||||||||
\(396\) | −4.96080 | −0.249290 | ||||||||
\(397\) | 8.48096 | 0.425647 | 0.212824 | − | 0.977091i | \(-0.431734\pi\) | ||||
0.212824 | + | 0.977091i | \(0.431734\pi\) | |||||||
\(398\) | −2.04300 | −0.102406 | ||||||||
\(399\) | 44.0562 | 2.20557 | ||||||||
\(400\) | −4.81097 | −0.240548 | ||||||||
\(401\) | 21.6468 | 1.08099 | 0.540494 | − | 0.841348i | \(-0.318237\pi\) | ||||
0.540494 | + | 0.841348i | \(0.318237\pi\) | |||||||
\(402\) | 20.0278 | 0.998895 | ||||||||
\(403\) | 23.3402 | 1.16266 | ||||||||
\(404\) | −2.51366 | −0.125059 | ||||||||
\(405\) | −9.13238 | −0.453792 | ||||||||
\(406\) | −1.49519 | −0.0742051 | ||||||||
\(407\) | 6.69373 | 0.331796 | ||||||||
\(408\) | −5.35232 | −0.264979 | ||||||||
\(409\) | 13.6209 | 0.673510 | 0.336755 | − | 0.941592i | \(-0.390671\pi\) | ||||
0.336755 | + | 0.941592i | \(0.390671\pi\) | |||||||
\(410\) | −0.0887021 | −0.00438069 | ||||||||
\(411\) | 56.2134 | 2.77280 | ||||||||
\(412\) | −18.1843 | −0.895878 | ||||||||
\(413\) | 29.9599 | 1.47423 | ||||||||
\(414\) | 4.31815 | 0.212226 | ||||||||
\(415\) | −3.66810 | −0.180060 | ||||||||
\(416\) | −4.85100 | −0.237840 | ||||||||
\(417\) | −19.8558 | −0.972341 | ||||||||
\(418\) | −4.26972 | −0.208839 | ||||||||
\(419\) | −18.6525 | −0.911233 | −0.455616 | − | 0.890176i | \(-0.650581\pi\) | ||||
−0.455616 | + | 0.890176i | \(0.650581\pi\) | |||||||
\(420\) | 3.09987 | 0.151258 | ||||||||
\(421\) | 15.6150 | 0.761028 | 0.380514 | − | 0.924775i | \(-0.375747\pi\) | ||||
0.380514 | + | 0.924775i | \(0.375747\pi\) | |||||||
\(422\) | 2.47265 | 0.120367 | ||||||||
\(423\) | 31.9811 | 1.55497 | ||||||||
\(424\) | −11.4209 | −0.554646 | ||||||||
\(425\) | 8.07077 | 0.391490 | ||||||||
\(426\) | −16.4450 | −0.796763 | ||||||||
\(427\) | −6.26975 | −0.303414 | ||||||||
\(428\) | 3.01826 | 0.145893 | ||||||||
\(429\) | 10.6945 | 0.516334 | ||||||||
\(430\) | 2.21734 | 0.106930 | ||||||||
\(431\) | 9.49407 | 0.457313 | 0.228657 | − | 0.973507i | \(-0.426567\pi\) | ||||
0.228657 | + | 0.973507i | \(0.426567\pi\) | |||||||
\(432\) | −13.3341 | −0.641539 | ||||||||
\(433\) | −23.8845 | −1.14782 | −0.573908 | − | 0.818920i | \(-0.694573\pi\) | ||||
−0.573908 | + | 0.818920i | \(0.694573\pi\) | |||||||
\(434\) | −10.7520 | −0.516112 | ||||||||
\(435\) | 0.928127 | 0.0445003 | ||||||||
\(436\) | −2.62418 | −0.125675 | ||||||||
\(437\) | 3.71660 | 0.177789 | ||||||||
\(438\) | −0.240642 | −0.0114983 | ||||||||
\(439\) | 25.0931 | 1.19763 | 0.598814 | − | 0.800888i | \(-0.295639\pi\) | ||||
0.598814 | + | 0.800888i | \(0.295639\pi\) | |||||||
\(440\) | −0.300425 | −0.0143222 | ||||||||
\(441\) | −14.4030 | −0.685856 | ||||||||
\(442\) | 8.13793 | 0.387082 | ||||||||
\(443\) | 9.65000 | 0.458485 | 0.229243 | − | 0.973369i | \(-0.426375\pi\) | ||||
0.229243 | + | 0.973369i | \(0.426375\pi\) | |||||||
\(444\) | 30.9072 | 1.46679 | ||||||||
\(445\) | 0.821160 | 0.0389267 | ||||||||
\(446\) | 19.9821 | 0.946179 | ||||||||
\(447\) | −2.55596 | −0.120893 | ||||||||
\(448\) | 2.23469 | 0.105579 | ||||||||
\(449\) | −33.6196 | −1.58661 | −0.793303 | − | 0.608827i | \(-0.791641\pi\) | ||||
−0.793303 | + | 0.608827i | \(0.791641\pi\) | |||||||
\(450\) | 34.5395 | 1.62821 | ||||||||
\(451\) | 0.140973 | 0.00663814 | ||||||||
\(452\) | −3.89903 | −0.183395 | ||||||||
\(453\) | −24.5238 | −1.15223 | ||||||||
\(454\) | 1.66765 | 0.0782665 | ||||||||
\(455\) | −4.71320 | −0.220958 | ||||||||
\(456\) | −19.7147 | −0.923225 | ||||||||
\(457\) | 27.1743 | 1.27116 | 0.635581 | − | 0.772034i | \(-0.280761\pi\) | ||||
0.635581 | + | 0.772034i | \(0.280761\pi\) | |||||||
\(458\) | 18.4150 | 0.860477 | ||||||||
\(459\) | 22.3691 | 1.04410 | ||||||||
\(460\) | 0.261507 | 0.0121928 | ||||||||
\(461\) | 37.6724 | 1.75458 | 0.877290 | − | 0.479961i | \(-0.159349\pi\) | ||||
0.877290 | + | 0.479961i | \(0.159349\pi\) | |||||||
\(462\) | −4.92657 | −0.229205 | ||||||||
\(463\) | −22.4542 | −1.04353 | −0.521767 | − | 0.853088i | \(-0.674727\pi\) | ||||
−0.521767 | + | 0.853088i | \(0.674727\pi\) | |||||||
\(464\) | 0.669083 | 0.0310614 | ||||||||
\(465\) | 6.67421 | 0.309509 | ||||||||
\(466\) | 14.5883 | 0.675792 | ||||||||
\(467\) | 13.9658 | 0.646260 | 0.323130 | − | 0.946355i | \(-0.395265\pi\) | ||||
0.323130 | + | 0.946355i | \(0.395265\pi\) | |||||||
\(468\) | 34.8269 | 1.60987 | ||||||||
\(469\) | 14.0278 | 0.647744 | ||||||||
\(470\) | 1.93677 | 0.0893365 | ||||||||
\(471\) | 43.8219 | 2.01921 | ||||||||
\(472\) | −13.4068 | −0.617097 | ||||||||
\(473\) | −3.52398 | −0.162033 | ||||||||
\(474\) | 33.7304 | 1.54929 | ||||||||
\(475\) | 29.7278 | 1.36401 | ||||||||
\(476\) | −3.74886 | −0.171829 | ||||||||
\(477\) | 81.9940 | 3.75425 | ||||||||
\(478\) | 21.6769 | 0.991476 | ||||||||
\(479\) | −19.6348 | −0.897137 | −0.448569 | − | 0.893748i | \(-0.648066\pi\) | ||||
−0.448569 | + | 0.893748i | \(0.648066\pi\) | |||||||
\(480\) | −1.38716 | −0.0633150 | ||||||||
\(481\) | −46.9928 | −2.14269 | ||||||||
\(482\) | −14.0509 | −0.640000 | ||||||||
\(483\) | 4.28835 | 0.195127 | ||||||||
\(484\) | −10.5225 | −0.478297 | ||||||||
\(485\) | 6.66946 | 0.302845 | ||||||||
\(486\) | 27.0131 | 1.22534 | ||||||||
\(487\) | −28.1435 | −1.27530 | −0.637652 | − | 0.770324i | \(-0.720094\pi\) | ||||
−0.637652 | + | 0.770324i | \(0.720094\pi\) | |||||||
\(488\) | 2.80565 | 0.127006 | ||||||||
\(489\) | −27.8506 | −1.25945 | ||||||||
\(490\) | −0.872241 | −0.0394039 | ||||||||
\(491\) | −0.558892 | −0.0252224 | −0.0126112 | − | 0.999920i | \(-0.504014\pi\) | ||||
−0.0126112 | + | 0.999920i | \(0.504014\pi\) | |||||||
\(492\) | 0.650917 | 0.0293456 | ||||||||
\(493\) | −1.12244 | −0.0505521 | ||||||||
\(494\) | 29.9752 | 1.34865 | ||||||||
\(495\) | 2.15685 | 0.0969432 | ||||||||
\(496\) | 4.81141 | 0.216039 | ||||||||
\(497\) | −11.5184 | −0.516670 | ||||||||
\(498\) | 26.9173 | 1.20619 | ||||||||
\(499\) | 6.35830 | 0.284637 | 0.142318 | − | 0.989821i | \(-0.454544\pi\) | ||||
0.142318 | + | 0.989821i | \(0.454544\pi\) | |||||||
\(500\) | 4.26560 | 0.190763 | ||||||||
\(501\) | −69.8190 | −3.11928 | ||||||||
\(502\) | −19.0646 | −0.850894 | ||||||||
\(503\) | 34.8764 | 1.55506 | 0.777531 | − | 0.628844i | \(-0.216472\pi\) | ||||
0.777531 | + | 0.628844i | \(0.216472\pi\) | |||||||
\(504\) | −16.0435 | −0.714636 | ||||||||
\(505\) | 1.09288 | 0.0486327 | ||||||||
\(506\) | −0.415607 | −0.0184760 | ||||||||
\(507\) | −33.6030 | −1.49236 | ||||||||
\(508\) | −4.44903 | −0.197394 | ||||||||
\(509\) | −16.7908 | −0.744239 | −0.372119 | − | 0.928185i | \(-0.621369\pi\) | ||||
−0.372119 | + | 0.928185i | \(0.621369\pi\) | |||||||
\(510\) | 2.32707 | 0.103045 | ||||||||
\(511\) | −0.168550 | −0.00745620 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 82.3940 | 3.63779 | ||||||||
\(514\) | −4.62253 | −0.203891 | ||||||||
\(515\) | 7.90616 | 0.348387 | ||||||||
\(516\) | −16.2714 | −0.716308 | ||||||||
\(517\) | −3.07807 | −0.135373 | ||||||||
\(518\) | 21.6479 | 0.951156 | ||||||||
\(519\) | −68.8269 | −3.02117 | ||||||||
\(520\) | 2.10911 | 0.0924906 | ||||||||
\(521\) | 3.88674 | 0.170281 | 0.0851406 | − | 0.996369i | \(-0.472866\pi\) | ||||
0.0851406 | + | 0.996369i | \(0.472866\pi\) | |||||||
\(522\) | −4.80356 | −0.210246 | ||||||||
\(523\) | −12.5600 | −0.549211 | −0.274606 | − | 0.961557i | \(-0.588547\pi\) | ||||
−0.274606 | + | 0.961557i | \(0.588547\pi\) | |||||||
\(524\) | 12.1312 | 0.529954 | ||||||||
\(525\) | 34.3011 | 1.49702 | ||||||||
\(526\) | 21.6171 | 0.942551 | ||||||||
\(527\) | −8.07152 | −0.351601 | ||||||||
\(528\) | 2.20459 | 0.0959425 | ||||||||
\(529\) | −22.6382 | −0.984271 | ||||||||
\(530\) | 4.96554 | 0.215689 | ||||||||
\(531\) | 96.2515 | 4.17696 | ||||||||
\(532\) | −13.8085 | −0.598676 | ||||||||
\(533\) | −0.989685 | −0.0428680 | ||||||||
\(534\) | −6.02586 | −0.260764 | ||||||||
\(535\) | −1.31227 | −0.0567345 | ||||||||
\(536\) | −6.27731 | −0.271138 | ||||||||
\(537\) | −64.1789 | −2.76952 | ||||||||
\(538\) | 15.4263 | 0.665076 | ||||||||
\(539\) | 1.38624 | 0.0597094 | ||||||||
\(540\) | 5.79740 | 0.249480 | ||||||||
\(541\) | 39.9823 | 1.71897 | 0.859486 | − | 0.511160i | \(-0.170784\pi\) | ||||
0.859486 | + | 0.511160i | \(0.170784\pi\) | |||||||
\(542\) | −12.2999 | −0.528327 | ||||||||
\(543\) | 19.9564 | 0.856412 | ||||||||
\(544\) | 1.67758 | 0.0719255 | ||||||||
\(545\) | 1.14094 | 0.0488724 | ||||||||
\(546\) | 34.5866 | 1.48017 | ||||||||
\(547\) | −16.1721 | −0.691470 | −0.345735 | − | 0.938332i | \(-0.612370\pi\) | ||||
−0.345735 | + | 0.938332i | \(0.612370\pi\) | |||||||
\(548\) | −17.6190 | −0.752644 | ||||||||
\(549\) | −20.1427 | −0.859668 | ||||||||
\(550\) | −3.32431 | −0.141749 | ||||||||
\(551\) | −4.13438 | −0.176131 | ||||||||
\(552\) | −1.91900 | −0.0816779 | ||||||||
\(553\) | 23.6254 | 1.00465 | ||||||||
\(554\) | −23.9710 | −1.01843 | ||||||||
\(555\) | −13.4378 | −0.570402 | ||||||||
\(556\) | 6.22339 | 0.263931 | ||||||||
\(557\) | 8.29052 | 0.351281 | 0.175640 | − | 0.984454i | \(-0.443800\pi\) | ||||
0.175640 | + | 0.984454i | \(0.443800\pi\) | |||||||
\(558\) | −34.5427 | −1.46231 | ||||||||
\(559\) | 24.7398 | 1.04638 | ||||||||
\(560\) | −0.971594 | −0.0410573 | ||||||||
\(561\) | −3.69837 | −0.156145 | ||||||||
\(562\) | −20.8408 | −0.879115 | ||||||||
\(563\) | 15.0492 | 0.634250 | 0.317125 | − | 0.948384i | \(-0.397282\pi\) | ||||
0.317125 | + | 0.948384i | \(0.397282\pi\) | |||||||
\(564\) | −14.2125 | −0.598452 | ||||||||
\(565\) | 1.69521 | 0.0713181 | ||||||||
\(566\) | 2.23312 | 0.0938651 | ||||||||
\(567\) | 46.9389 | 1.97125 | ||||||||
\(568\) | 5.15436 | 0.216272 | ||||||||
\(569\) | −19.2835 | −0.808407 | −0.404203 | − | 0.914669i | \(-0.632451\pi\) | ||||
−0.404203 | + | 0.914669i | \(0.632451\pi\) | |||||||
\(570\) | 8.57153 | 0.359022 | ||||||||
\(571\) | 9.82929 | 0.411343 | 0.205672 | − | 0.978621i | \(-0.434062\pi\) | ||||
0.205672 | + | 0.978621i | \(0.434062\pi\) | |||||||
\(572\) | −3.35197 | −0.140153 | ||||||||
\(573\) | −18.2752 | −0.763457 | ||||||||
\(574\) | 0.455914 | 0.0190295 | ||||||||
\(575\) | 2.89366 | 0.120674 | ||||||||
\(576\) | 7.17932 | 0.299138 | ||||||||
\(577\) | 35.0862 | 1.46066 | 0.730329 | − | 0.683096i | \(-0.239367\pi\) | ||||
0.730329 | + | 0.683096i | \(0.239367\pi\) | |||||||
\(578\) | 14.1857 | 0.590049 | ||||||||
\(579\) | −46.4259 | −1.92940 | ||||||||
\(580\) | −0.290903 | −0.0120791 | ||||||||
\(581\) | 18.8534 | 0.782170 | ||||||||
\(582\) | −48.9420 | −2.02871 | ||||||||
\(583\) | −7.89164 | −0.326838 | ||||||||
\(584\) | 0.0754243 | 0.00312108 | ||||||||
\(585\) | −15.1420 | −0.626044 | ||||||||
\(586\) | 4.57319 | 0.188917 | ||||||||
\(587\) | −9.47018 | −0.390876 | −0.195438 | − | 0.980716i | \(-0.562613\pi\) | ||||
−0.195438 | + | 0.980716i | \(0.562613\pi\) | |||||||
\(588\) | 6.40071 | 0.263961 | ||||||||
\(589\) | −29.7306 | −1.22503 | ||||||||
\(590\) | 5.82898 | 0.239975 | ||||||||
\(591\) | −13.9885 | −0.575408 | ||||||||
\(592\) | −9.68724 | −0.398143 | ||||||||
\(593\) | 7.68455 | 0.315567 | 0.157783 | − | 0.987474i | \(-0.449565\pi\) | ||||
0.157783 | + | 0.987474i | \(0.449565\pi\) | |||||||
\(594\) | −9.21369 | −0.378042 | ||||||||
\(595\) | 1.62992 | 0.0668204 | ||||||||
\(596\) | 0.801116 | 0.0328150 | ||||||||
\(597\) | −6.51821 | −0.266772 | ||||||||
\(598\) | 2.91773 | 0.119315 | ||||||||
\(599\) | 42.6494 | 1.74261 | 0.871303 | − | 0.490746i | \(-0.163276\pi\) | ||||
0.871303 | + | 0.490746i | \(0.163276\pi\) | |||||||
\(600\) | −15.3494 | −0.626637 | ||||||||
\(601\) | −9.36300 | −0.381925 | −0.190962 | − | 0.981597i | \(-0.561161\pi\) | ||||
−0.190962 | + | 0.981597i | \(0.561161\pi\) | |||||||
\(602\) | −11.3968 | −0.464498 | ||||||||
\(603\) | 45.0668 | 1.83526 | ||||||||
\(604\) | 7.68648 | 0.312759 | ||||||||
\(605\) | 4.57497 | 0.185999 | ||||||||
\(606\) | −8.01984 | −0.325784 | ||||||||
\(607\) | −15.5118 | −0.629603 | −0.314802 | − | 0.949158i | \(-0.601938\pi\) | ||||
−0.314802 | + | 0.949158i | \(0.601938\pi\) | |||||||
\(608\) | 6.17918 | 0.250599 | ||||||||
\(609\) | −4.77041 | −0.193307 | ||||||||
\(610\) | −1.21984 | −0.0493897 | ||||||||
\(611\) | 21.6093 | 0.874219 | ||||||||
\(612\) | −12.0439 | −0.486844 | ||||||||
\(613\) | 36.6250 | 1.47927 | 0.739634 | − | 0.673009i | \(-0.234999\pi\) | ||||
0.739634 | + | 0.673009i | \(0.234999\pi\) | |||||||
\(614\) | −5.08758 | −0.205318 | ||||||||
\(615\) | −0.283005 | −0.0114118 | ||||||||
\(616\) | 1.54413 | 0.0622150 | ||||||||
\(617\) | −31.1175 | −1.25274 | −0.626372 | − | 0.779524i | \(-0.715461\pi\) | ||||
−0.626372 | + | 0.779524i | \(0.715461\pi\) | |||||||
\(618\) | −58.0172 | −2.33380 | ||||||||
\(619\) | 21.2455 | 0.853929 | 0.426965 | − | 0.904268i | \(-0.359583\pi\) | ||||
0.426965 | + | 0.904268i | \(0.359583\pi\) | |||||||
\(620\) | −2.09190 | −0.0840126 | ||||||||
\(621\) | 8.02009 | 0.321835 | ||||||||
\(622\) | −18.3559 | −0.736004 | ||||||||
\(623\) | −4.22062 | −0.169096 | ||||||||
\(624\) | −15.4771 | −0.619581 | ||||||||
\(625\) | 22.2002 | 0.888010 | ||||||||
\(626\) | 11.1858 | 0.447075 | ||||||||
\(627\) | −13.6226 | −0.544033 | ||||||||
\(628\) | −13.7351 | −0.548090 | ||||||||
\(629\) | 16.2511 | 0.647973 | ||||||||
\(630\) | 6.97538 | 0.277906 | ||||||||
\(631\) | −22.7666 | −0.906324 | −0.453162 | − | 0.891428i | \(-0.649704\pi\) | ||||
−0.453162 | + | 0.891428i | \(0.649704\pi\) | |||||||
\(632\) | −10.5721 | −0.420536 | ||||||||
\(633\) | 7.88899 | 0.313559 | ||||||||
\(634\) | 33.1048 | 1.31476 | ||||||||
\(635\) | 1.93434 | 0.0767621 | ||||||||
\(636\) | −36.4383 | −1.44487 | ||||||||
\(637\) | −9.73195 | −0.385594 | ||||||||
\(638\) | 0.462326 | 0.0183037 | ||||||||
\(639\) | −37.0048 | −1.46389 | ||||||||
\(640\) | 0.434778 | 0.0171861 | ||||||||
\(641\) | −14.4369 | −0.570222 | −0.285111 | − | 0.958495i | \(-0.592030\pi\) | ||||
−0.285111 | + | 0.958495i | \(0.592030\pi\) | |||||||
\(642\) | 9.62976 | 0.380056 | ||||||||
\(643\) | 5.96496 | 0.235235 | 0.117617 | − | 0.993059i | \(-0.462474\pi\) | ||||
0.117617 | + | 0.993059i | \(0.462474\pi\) | |||||||
\(644\) | −1.34410 | −0.0529649 | ||||||||
\(645\) | 7.07445 | 0.278556 | ||||||||
\(646\) | −10.3661 | −0.407847 | ||||||||
\(647\) | 25.6332 | 1.00775 | 0.503873 | − | 0.863778i | \(-0.331908\pi\) | ||||
0.503873 | + | 0.863778i | \(0.331908\pi\) | |||||||
\(648\) | −21.0047 | −0.825142 | ||||||||
\(649\) | −9.26388 | −0.363639 | ||||||||
\(650\) | 23.3380 | 0.915392 | ||||||||
\(651\) | −34.3043 | −1.34449 | ||||||||
\(652\) | 8.72923 | 0.341863 | ||||||||
\(653\) | −9.64933 | −0.377607 | −0.188804 | − | 0.982015i | \(-0.560461\pi\) | ||||
−0.188804 | + | 0.982015i | \(0.560461\pi\) | |||||||
\(654\) | −8.37246 | −0.327389 | ||||||||
\(655\) | −5.27438 | −0.206087 | ||||||||
\(656\) | −0.204017 | −0.00796552 | ||||||||
\(657\) | −0.541495 | −0.0211257 | ||||||||
\(658\) | −9.95466 | −0.388073 | ||||||||
\(659\) | −1.15673 | −0.0450596 | −0.0225298 | − | 0.999746i | \(-0.507172\pi\) | ||||
−0.0225298 | + | 0.999746i | \(0.507172\pi\) | |||||||
\(660\) | −0.958509 | −0.0373099 | ||||||||
\(661\) | 20.4660 | 0.796037 | 0.398018 | − | 0.917377i | \(-0.369698\pi\) | ||||
0.398018 | + | 0.917377i | \(0.369698\pi\) | |||||||
\(662\) | 25.5319 | 0.992324 | ||||||||
\(663\) | 25.9641 | 1.00836 | ||||||||
\(664\) | −8.43670 | −0.327408 | ||||||||
\(665\) | 6.00365 | 0.232812 | ||||||||
\(666\) | 69.5478 | 2.69492 | ||||||||
\(667\) | −0.402434 | −0.0155823 | ||||||||
\(668\) | 21.8834 | 0.846693 | ||||||||
\(669\) | 63.7530 | 2.46483 | ||||||||
\(670\) | 2.72924 | 0.105440 | ||||||||
\(671\) | 1.93866 | 0.0748412 | ||||||||
\(672\) | 7.12978 | 0.275037 | ||||||||
\(673\) | −35.2819 | −1.36002 | −0.680010 | − | 0.733203i | \(-0.738024\pi\) | ||||
−0.680010 | + | 0.733203i | \(0.738024\pi\) | |||||||
\(674\) | −6.83133 | −0.263133 | ||||||||
\(675\) | 64.1501 | 2.46914 | ||||||||
\(676\) | 10.5322 | 0.405084 | ||||||||
\(677\) | 3.26115 | 0.125336 | 0.0626681 | − | 0.998034i | \(-0.480039\pi\) | ||||
0.0626681 | + | 0.998034i | \(0.480039\pi\) | |||||||
\(678\) | −12.4399 | −0.477750 | ||||||||
\(679\) | −34.2799 | −1.31554 | ||||||||
\(680\) | −0.729375 | −0.0279702 | ||||||||
\(681\) | 5.32063 | 0.203887 | ||||||||
\(682\) | 3.32461 | 0.127306 | ||||||||
\(683\) | −43.0908 | −1.64882 | −0.824412 | − | 0.565990i | \(-0.808494\pi\) | ||||
−0.824412 | + | 0.565990i | \(0.808494\pi\) | |||||||
\(684\) | −44.3623 | −1.69624 | ||||||||
\(685\) | 7.66034 | 0.292687 | ||||||||
\(686\) | 20.1260 | 0.768413 | ||||||||
\(687\) | 58.7532 | 2.24157 | ||||||||
\(688\) | 5.09994 | 0.194433 | ||||||||
\(689\) | 55.4026 | 2.11067 | ||||||||
\(690\) | 0.834338 | 0.0317627 | ||||||||
\(691\) | −11.8968 | −0.452575 | −0.226288 | − | 0.974061i | \(-0.572659\pi\) | ||||
−0.226288 | + | 0.974061i | \(0.572659\pi\) | |||||||
\(692\) | 21.5724 | 0.820060 | ||||||||
\(693\) | −11.0858 | −0.421116 | ||||||||
\(694\) | 22.3332 | 0.847758 | ||||||||
\(695\) | −2.70580 | −0.102637 | ||||||||
\(696\) | 2.13471 | 0.0809161 | ||||||||
\(697\) | 0.342254 | 0.0129638 | ||||||||
\(698\) | −2.52858 | −0.0957080 | ||||||||
\(699\) | 46.5442 | 1.76046 | ||||||||
\(700\) | −10.7510 | −0.406350 | ||||||||
\(701\) | 17.1232 | 0.646733 | 0.323366 | − | 0.946274i | \(-0.395185\pi\) | ||||
0.323366 | + | 0.946274i | \(0.395185\pi\) | |||||||
\(702\) | 64.6839 | 2.44134 | ||||||||
\(703\) | 59.8592 | 2.25763 | ||||||||
\(704\) | −0.690985 | −0.0260425 | ||||||||
\(705\) | 6.17927 | 0.232725 | ||||||||
\(706\) | −26.1718 | −0.984987 | ||||||||
\(707\) | −5.61724 | −0.211258 | ||||||||
\(708\) | −42.7744 | −1.60756 | ||||||||
\(709\) | 19.9521 | 0.749315 | 0.374658 | − | 0.927163i | \(-0.377760\pi\) | ||||
0.374658 | + | 0.927163i | \(0.377760\pi\) | |||||||
\(710\) | −2.24100 | −0.0841034 | ||||||||
\(711\) | 75.9006 | 2.84650 | ||||||||
\(712\) | 1.88869 | 0.0707815 | ||||||||
\(713\) | −2.89392 | −0.108378 | ||||||||
\(714\) | −11.9608 | −0.447620 | ||||||||
\(715\) | 1.45736 | 0.0545023 | ||||||||
\(716\) | 20.1156 | 0.751755 | ||||||||
\(717\) | 69.1601 | 2.58283 | ||||||||
\(718\) | −32.3652 | −1.20786 | ||||||||
\(719\) | 27.2122 | 1.01485 | 0.507423 | − | 0.861697i | \(-0.330598\pi\) | ||||
0.507423 | + | 0.861697i | \(0.330598\pi\) | |||||||
\(720\) | −3.12141 | −0.116328 | ||||||||
\(721\) | −40.6363 | −1.51338 | ||||||||
\(722\) | −19.1823 | −0.713890 | ||||||||
\(723\) | −44.8294 | −1.66722 | ||||||||
\(724\) | −6.25494 | −0.232463 | ||||||||
\(725\) | −3.21894 | −0.119548 | ||||||||
\(726\) | −33.5722 | −1.24598 | ||||||||
\(727\) | 40.3850 | 1.49780 | 0.748898 | − | 0.662685i | \(-0.230583\pi\) | ||||
0.748898 | + | 0.662685i | \(0.230583\pi\) | |||||||
\(728\) | −10.8405 | −0.401774 | ||||||||
\(729\) | 23.1714 | 0.858199 | ||||||||
\(730\) | −0.0327929 | −0.00121372 | ||||||||
\(731\) | −8.55554 | −0.316438 | ||||||||
\(732\) | 8.95144 | 0.330855 | ||||||||
\(733\) | −0.722953 | −0.0267029 | −0.0133514 | − | 0.999911i | \(-0.504250\pi\) | ||||
−0.0133514 | + | 0.999911i | \(0.504250\pi\) | |||||||
\(734\) | 22.1576 | 0.817854 | ||||||||
\(735\) | −2.78289 | −0.102648 | ||||||||
\(736\) | 0.601471 | 0.0221705 | ||||||||
\(737\) | −4.33752 | −0.159775 | ||||||||
\(738\) | 1.46470 | 0.0539164 | ||||||||
\(739\) | 46.4468 | 1.70857 | 0.854287 | − | 0.519802i | \(-0.173994\pi\) | ||||
0.854287 | + | 0.519802i | \(0.173994\pi\) | |||||||
\(740\) | 4.21180 | 0.154829 | ||||||||
\(741\) | 95.6360 | 3.51328 | ||||||||
\(742\) | −25.5220 | −0.936944 | ||||||||
\(743\) | 20.9873 | 0.769948 | 0.384974 | − | 0.922927i | \(-0.374210\pi\) | ||||
0.384974 | + | 0.922927i | \(0.374210\pi\) | |||||||
\(744\) | 15.3508 | 0.562789 | ||||||||
\(745\) | −0.348308 | −0.0127610 | ||||||||
\(746\) | −20.6328 | −0.755422 | ||||||||
\(747\) | 60.5698 | 2.21613 | ||||||||
\(748\) | 1.15918 | 0.0423838 | ||||||||
\(749\) | 6.74486 | 0.246452 | ||||||||
\(750\) | 13.6094 | 0.496945 | ||||||||
\(751\) | −27.5006 | −1.00351 | −0.501756 | − | 0.865009i | \(-0.667313\pi\) | ||||
−0.501756 | + | 0.865009i | \(0.667313\pi\) | |||||||
\(752\) | 4.45461 | 0.162443 | ||||||||
\(753\) | −60.8256 | −2.21661 | ||||||||
\(754\) | −3.24572 | −0.118202 | ||||||||
\(755\) | −3.34192 | −0.121625 | ||||||||
\(756\) | −29.7976 | −1.08373 | ||||||||
\(757\) | 42.3996 | 1.54104 | 0.770520 | − | 0.637416i | \(-0.219997\pi\) | ||||
0.770520 | + | 0.637416i | \(0.219997\pi\) | |||||||
\(758\) | 1.71081 | 0.0621393 | ||||||||
\(759\) | −1.32600 | −0.0481306 | ||||||||
\(760\) | −2.68657 | −0.0974523 | ||||||||
\(761\) | −52.8117 | −1.91442 | −0.957212 | − | 0.289387i | \(-0.906549\pi\) | ||||
−0.957212 | + | 0.289387i | \(0.906549\pi\) | |||||||
\(762\) | −14.1947 | −0.514218 | ||||||||
\(763\) | −5.86422 | −0.212299 | ||||||||
\(764\) | 5.72799 | 0.207232 | ||||||||
\(765\) | 5.23641 | 0.189323 | ||||||||
\(766\) | 14.4585 | 0.522406 | ||||||||
\(767\) | 65.0363 | 2.34832 | ||||||||
\(768\) | −3.19050 | −0.115127 | ||||||||
\(769\) | 27.0390 | 0.975051 | 0.487526 | − | 0.873109i | \(-0.337900\pi\) | ||||
0.487526 | + | 0.873109i | \(0.337900\pi\) | |||||||
\(770\) | −0.671357 | −0.0241940 | ||||||||
\(771\) | −14.7482 | −0.531144 | ||||||||
\(772\) | 14.5513 | 0.523712 | ||||||||
\(773\) | −15.3813 | −0.553228 | −0.276614 | − | 0.960981i | \(-0.589212\pi\) | ||||
−0.276614 | + | 0.960981i | \(0.589212\pi\) | |||||||
\(774\) | −36.6141 | −1.31607 | ||||||||
\(775\) | −23.1475 | −0.831484 | ||||||||
\(776\) | 15.3399 | 0.550671 | ||||||||
\(777\) | 69.0679 | 2.47780 | ||||||||
\(778\) | −36.0677 | −1.29309 | ||||||||
\(779\) | 1.26066 | 0.0451677 | ||||||||
\(780\) | 6.72913 | 0.240941 | ||||||||
\(781\) | 3.56158 | 0.127443 | ||||||||
\(782\) | −1.00901 | −0.0360823 | ||||||||
\(783\) | −8.92165 | −0.318834 | ||||||||
\(784\) | −2.00617 | −0.0716491 | ||||||||
\(785\) | 5.97173 | 0.213140 | ||||||||
\(786\) | 38.7046 | 1.38055 | ||||||||
\(787\) | 5.19527 | 0.185191 | 0.0925957 | − | 0.995704i | \(-0.470484\pi\) | ||||
0.0925957 | + | 0.995704i | \(0.470484\pi\) | |||||||
\(788\) | 4.38440 | 0.156188 | ||||||||
\(789\) | 68.9695 | 2.45538 | ||||||||
\(790\) | 4.59653 | 0.163537 | ||||||||
\(791\) | −8.71310 | −0.309802 | ||||||||
\(792\) | 4.96080 | 0.176274 | ||||||||
\(793\) | −13.6102 | −0.483313 | ||||||||
\(794\) | −8.48096 | −0.300978 | ||||||||
\(795\) | 15.8426 | 0.561879 | ||||||||
\(796\) | 2.04300 | 0.0724123 | ||||||||
\(797\) | −39.6371 | −1.40402 | −0.702009 | − | 0.712168i | \(-0.747713\pi\) | ||||
−0.702009 | + | 0.712168i | \(0.747713\pi\) | |||||||
\(798\) | −44.0562 | −1.55957 | ||||||||
\(799\) | −7.47296 | −0.264374 | ||||||||
\(800\) | 4.81097 | 0.170093 | ||||||||
\(801\) | −13.5595 | −0.479100 | ||||||||
\(802\) | −21.6468 | −0.764375 | ||||||||
\(803\) | 0.0521171 | 0.00183917 | ||||||||
\(804\) | −20.0278 | −0.706325 | ||||||||
\(805\) | 0.584385 | 0.0205969 | ||||||||
\(806\) | −23.3402 | −0.822122 | ||||||||
\(807\) | 49.2177 | 1.73255 | ||||||||
\(808\) | 2.51366 | 0.0884302 | ||||||||
\(809\) | 30.6616 | 1.07800 | 0.539002 | − | 0.842304i | \(-0.318801\pi\) | ||||
0.539002 | + | 0.842304i | \(0.318801\pi\) | |||||||
\(810\) | 9.13238 | 0.320879 | ||||||||
\(811\) | 28.7049 | 1.00797 | 0.503983 | − | 0.863714i | \(-0.331867\pi\) | ||||
0.503983 | + | 0.863714i | \(0.331867\pi\) | |||||||
\(812\) | 1.49519 | 0.0524709 | ||||||||
\(813\) | −39.2430 | −1.37631 | ||||||||
\(814\) | −6.69373 | −0.234615 | ||||||||
\(815\) | −3.79528 | −0.132943 | ||||||||
\(816\) | 5.35232 | 0.187369 | ||||||||
\(817\) | −31.5134 | −1.10252 | ||||||||
\(818\) | −13.6209 | −0.476243 | ||||||||
\(819\) | 77.8272 | 2.71950 | ||||||||
\(820\) | 0.0887021 | 0.00309761 | ||||||||
\(821\) | −23.3443 | −0.814722 | −0.407361 | − | 0.913267i | \(-0.633551\pi\) | ||||
−0.407361 | + | 0.913267i | \(0.633551\pi\) | |||||||
\(822\) | −56.2134 | −1.96067 | ||||||||
\(823\) | −11.5343 | −0.402060 | −0.201030 | − | 0.979585i | \(-0.564429\pi\) | ||||
−0.201030 | + | 0.979585i | \(0.564429\pi\) | |||||||
\(824\) | 18.1843 | 0.633482 | ||||||||
\(825\) | −10.6062 | −0.369261 | ||||||||
\(826\) | −29.9599 | −1.04244 | ||||||||
\(827\) | −23.5308 | −0.818245 | −0.409123 | − | 0.912479i | \(-0.634165\pi\) | ||||
−0.409123 | + | 0.912479i | \(0.634165\pi\) | |||||||
\(828\) | −4.31815 | −0.150066 | ||||||||
\(829\) | 48.3032 | 1.67764 | 0.838820 | − | 0.544409i | \(-0.183246\pi\) | ||||
0.838820 | + | 0.544409i | \(0.183246\pi\) | |||||||
\(830\) | 3.66810 | 0.127322 | ||||||||
\(831\) | −76.4795 | −2.65304 | ||||||||
\(832\) | 4.85100 | 0.168178 | ||||||||
\(833\) | 3.36551 | 0.116608 | ||||||||
\(834\) | 19.8558 | 0.687549 | ||||||||
\(835\) | −9.51442 | −0.329260 | ||||||||
\(836\) | 4.26972 | 0.147671 | ||||||||
\(837\) | −64.1560 | −2.21756 | ||||||||
\(838\) | 18.6525 | 0.644339 | ||||||||
\(839\) | 41.5932 | 1.43596 | 0.717978 | − | 0.696066i | \(-0.245068\pi\) | ||||
0.717978 | + | 0.696066i | \(0.245068\pi\) | |||||||
\(840\) | −3.09987 | −0.106956 | ||||||||
\(841\) | −28.5523 | −0.984563 | ||||||||
\(842\) | −15.6150 | −0.538128 | ||||||||
\(843\) | −66.4926 | −2.29013 | ||||||||
\(844\) | −2.47265 | −0.0851120 | ||||||||
\(845\) | −4.57917 | −0.157528 | ||||||||
\(846\) | −31.9811 | −1.09953 | ||||||||
\(847\) | −23.5146 | −0.807971 | ||||||||
\(848\) | 11.4209 | 0.392194 | ||||||||
\(849\) | 7.12478 | 0.244522 | ||||||||
\(850\) | −8.07077 | −0.276825 | ||||||||
\(851\) | 5.82659 | 0.199733 | ||||||||
\(852\) | 16.4450 | 0.563396 | ||||||||
\(853\) | 7.87204 | 0.269534 | 0.134767 | − | 0.990877i | \(-0.456971\pi\) | ||||
0.134767 | + | 0.990877i | \(0.456971\pi\) | |||||||
\(854\) | 6.26975 | 0.214546 | ||||||||
\(855\) | 19.2878 | 0.659628 | ||||||||
\(856\) | −3.01826 | −0.103162 | ||||||||
\(857\) | 48.9451 | 1.67193 | 0.835966 | − | 0.548781i | \(-0.184908\pi\) | ||||
0.835966 | + | 0.548781i | \(0.184908\pi\) | |||||||
\(858\) | −10.6945 | −0.365103 | ||||||||
\(859\) | −1.78872 | −0.0610302 | −0.0305151 | − | 0.999534i | \(-0.509715\pi\) | ||||
−0.0305151 | + | 0.999534i | \(0.509715\pi\) | |||||||
\(860\) | −2.21734 | −0.0756108 | ||||||||
\(861\) | 1.45459 | 0.0495725 | ||||||||
\(862\) | −9.49407 | −0.323369 | ||||||||
\(863\) | −12.1851 | −0.414787 | −0.207394 | − | 0.978258i | \(-0.566498\pi\) | ||||
−0.207394 | + | 0.978258i | \(0.566498\pi\) | |||||||
\(864\) | 13.3341 | 0.453637 | ||||||||
\(865\) | −9.37922 | −0.318903 | ||||||||
\(866\) | 23.8845 | 0.811629 | ||||||||
\(867\) | 45.2596 | 1.53710 | ||||||||
\(868\) | 10.7520 | 0.364947 | ||||||||
\(869\) | −7.30518 | −0.247811 | ||||||||
\(870\) | −0.928127 | −0.0314665 | ||||||||
\(871\) | 30.4512 | 1.03180 | ||||||||
\(872\) | 2.62418 | 0.0888659 | ||||||||
\(873\) | −110.130 | −3.72734 | ||||||||
\(874\) | −3.71660 | −0.125716 | ||||||||
\(875\) | 9.53228 | 0.322250 | ||||||||
\(876\) | 0.240642 | 0.00813053 | ||||||||
\(877\) | 8.80170 | 0.297212 | 0.148606 | − | 0.988896i | \(-0.452521\pi\) | ||||
0.148606 | + | 0.988896i | \(0.452521\pi\) | |||||||
\(878\) | −25.0931 | −0.846851 | ||||||||
\(879\) | 14.5908 | 0.492135 | ||||||||
\(880\) | 0.300425 | 0.0101273 | ||||||||
\(881\) | 4.14156 | 0.139533 | 0.0697664 | − | 0.997563i | \(-0.477775\pi\) | ||||
0.0697664 | + | 0.997563i | \(0.477775\pi\) | |||||||
\(882\) | 14.4030 | 0.484973 | ||||||||
\(883\) | 46.6939 | 1.57137 | 0.785687 | − | 0.618625i | \(-0.212310\pi\) | ||||
0.785687 | + | 0.618625i | \(0.212310\pi\) | |||||||
\(884\) | −8.13793 | −0.273708 | ||||||||
\(885\) | 18.5974 | 0.625144 | ||||||||
\(886\) | −9.65000 | −0.324198 | ||||||||
\(887\) | 15.0022 | 0.503724 | 0.251862 | − | 0.967763i | \(-0.418957\pi\) | ||||
0.251862 | + | 0.967763i | \(0.418957\pi\) | |||||||
\(888\) | −30.9072 | −1.03718 | ||||||||
\(889\) | −9.94220 | −0.333451 | ||||||||
\(890\) | −0.821160 | −0.0275253 | ||||||||
\(891\) | −14.5139 | −0.486234 | ||||||||
\(892\) | −19.9821 | −0.669050 | ||||||||
\(893\) | −27.5258 | −0.921117 | ||||||||
\(894\) | 2.55596 | 0.0854842 | ||||||||
\(895\) | −8.74583 | −0.292341 | ||||||||
\(896\) | −2.23469 | −0.0746556 | ||||||||
\(897\) | 9.30904 | 0.310820 | ||||||||
\(898\) | 33.6196 | 1.12190 | ||||||||
\(899\) | 3.21923 | 0.107367 | ||||||||
\(900\) | −34.5395 | −1.15132 | ||||||||
\(901\) | −19.1594 | −0.638291 | ||||||||
\(902\) | −0.140973 | −0.00469387 | ||||||||
\(903\) | −36.3614 | −1.21003 | ||||||||
\(904\) | 3.89903 | 0.129680 | ||||||||
\(905\) | 2.71951 | 0.0903997 | ||||||||
\(906\) | 24.5238 | 0.814747 | ||||||||
\(907\) | 8.73615 | 0.290079 | 0.145040 | − | 0.989426i | \(-0.453669\pi\) | ||||
0.145040 | + | 0.989426i | \(0.453669\pi\) | |||||||
\(908\) | −1.66765 | −0.0553428 | ||||||||
\(909\) | −18.0464 | −0.598560 | ||||||||
\(910\) | 4.71320 | 0.156241 | ||||||||
\(911\) | 3.39763 | 0.112568 | 0.0562842 | − | 0.998415i | \(-0.482075\pi\) | ||||
0.0562842 | + | 0.998415i | \(0.482075\pi\) | |||||||
\(912\) | 19.7147 | 0.652819 | ||||||||
\(913\) | −5.82963 | −0.192933 | ||||||||
\(914\) | −27.1743 | −0.898847 | ||||||||
\(915\) | −3.89189 | −0.128662 | ||||||||
\(916\) | −18.4150 | −0.608449 | ||||||||
\(917\) | 27.1094 | 0.895232 | ||||||||
\(918\) | −22.3691 | −0.738289 | ||||||||
\(919\) | 28.1388 | 0.928214 | 0.464107 | − | 0.885779i | \(-0.346375\pi\) | ||||
0.464107 | + | 0.885779i | \(0.346375\pi\) | |||||||
\(920\) | −0.261507 | −0.00862161 | ||||||||
\(921\) | −16.2319 | −0.534861 | ||||||||
\(922\) | −37.6724 | −1.24067 | ||||||||
\(923\) | −25.0038 | −0.823010 | ||||||||
\(924\) | 4.92657 | 0.162072 | ||||||||
\(925\) | 46.6050 | 1.53236 | ||||||||
\(926\) | 22.4542 | 0.737890 | ||||||||
\(927\) | −130.551 | −4.28787 | ||||||||
\(928\) | −0.669083 | −0.0219637 | ||||||||
\(929\) | 23.7268 | 0.778451 | 0.389225 | − | 0.921143i | \(-0.372743\pi\) | ||||
0.389225 | + | 0.921143i | \(0.372743\pi\) | |||||||
\(930\) | −6.67421 | −0.218856 | ||||||||
\(931\) | 12.3965 | 0.406279 | ||||||||
\(932\) | −14.5883 | −0.477857 | ||||||||
\(933\) | −58.5645 | −1.91732 | ||||||||
\(934\) | −13.9658 | −0.456975 | ||||||||
\(935\) | −0.503987 | −0.0164821 | ||||||||
\(936\) | −34.8269 | −1.13835 | ||||||||
\(937\) | 2.66814 | 0.0871645 | 0.0435822 | − | 0.999050i | \(-0.486123\pi\) | ||||
0.0435822 | + | 0.999050i | \(0.486123\pi\) | |||||||
\(938\) | −14.0278 | −0.458024 | ||||||||
\(939\) | 35.6884 | 1.16465 | ||||||||
\(940\) | −1.93677 | −0.0631704 | ||||||||
\(941\) | 14.1493 | 0.461254 | 0.230627 | − | 0.973042i | \(-0.425922\pi\) | ||||
0.230627 | + | 0.973042i | \(0.425922\pi\) | |||||||
\(942\) | −43.8219 | −1.42780 | ||||||||
\(943\) | 0.122710 | 0.00399599 | ||||||||
\(944\) | 13.4068 | 0.436353 | ||||||||
\(945\) | 12.9554 | 0.421438 | ||||||||
\(946\) | 3.52398 | 0.114575 | ||||||||
\(947\) | −25.2469 | −0.820413 | −0.410207 | − | 0.911993i | \(-0.634543\pi\) | ||||
−0.410207 | + | 0.911993i | \(0.634543\pi\) | |||||||
\(948\) | −33.7304 | −1.09551 | ||||||||
\(949\) | −0.365883 | −0.0118771 | ||||||||
\(950\) | −29.7278 | −0.964498 | ||||||||
\(951\) | 105.621 | 3.42500 | ||||||||
\(952\) | 3.74886 | 0.121501 | ||||||||
\(953\) | −31.4012 | −1.01718 | −0.508592 | − | 0.861008i | \(-0.669834\pi\) | ||||
−0.508592 | + | 0.861008i | \(0.669834\pi\) | |||||||
\(954\) | −81.9940 | −2.65465 | ||||||||
\(955\) | −2.49041 | −0.0805877 | ||||||||
\(956\) | −21.6769 | −0.701080 | ||||||||
\(957\) | 1.47505 | 0.0476817 | ||||||||
\(958\) | 19.6348 | 0.634372 | ||||||||
\(959\) | −39.3728 | −1.27142 | ||||||||
\(960\) | 1.38716 | 0.0447705 | ||||||||
\(961\) | −7.85032 | −0.253236 | ||||||||
\(962\) | 46.9928 | 1.51511 | ||||||||
\(963\) | 21.6690 | 0.698274 | ||||||||
\(964\) | 14.0509 | 0.452548 | ||||||||
\(965\) | −6.32658 | −0.203660 | ||||||||
\(966\) | −4.28835 | −0.137976 | ||||||||
\(967\) | −8.01967 | −0.257895 | −0.128948 | − | 0.991651i | \(-0.541160\pi\) | ||||
−0.128948 | + | 0.991651i | \(0.541160\pi\) | |||||||
\(968\) | 10.5225 | 0.338207 | ||||||||
\(969\) | −33.0729 | −1.06246 | ||||||||
\(970\) | −6.66946 | −0.214143 | ||||||||
\(971\) | −27.5999 | −0.885723 | −0.442862 | − | 0.896590i | \(-0.646037\pi\) | ||||
−0.442862 | + | 0.896590i | \(0.646037\pi\) | |||||||
\(972\) | −27.0131 | −0.866445 | ||||||||
\(973\) | 13.9073 | 0.445849 | ||||||||
\(974\) | 28.1435 | 0.901776 | ||||||||
\(975\) | 74.4600 | 2.38463 | ||||||||
\(976\) | −2.80565 | −0.0898067 | ||||||||
\(977\) | 25.1886 | 0.805853 | 0.402927 | − | 0.915232i | \(-0.367993\pi\) | ||||
0.402927 | + | 0.915232i | \(0.367993\pi\) | |||||||
\(978\) | 27.8506 | 0.890565 | ||||||||
\(979\) | 1.30505 | 0.0417097 | ||||||||
\(980\) | 0.872241 | 0.0278627 | ||||||||
\(981\) | −18.8398 | −0.601509 | ||||||||
\(982\) | 0.558892 | 0.0178349 | ||||||||
\(983\) | 32.2196 | 1.02764 | 0.513822 | − | 0.857897i | \(-0.328229\pi\) | ||||
0.513822 | + | 0.857897i | \(0.328229\pi\) | |||||||
\(984\) | −0.650917 | −0.0207505 | ||||||||
\(985\) | −1.90624 | −0.0607380 | ||||||||
\(986\) | 1.12244 | 0.0357457 | ||||||||
\(987\) | −31.7604 | −1.01094 | ||||||||
\(988\) | −29.9752 | −0.953638 | ||||||||
\(989\) | −3.06746 | −0.0975397 | ||||||||
\(990\) | −2.15685 | −0.0685492 | ||||||||
\(991\) | 26.3492 | 0.837010 | 0.418505 | − | 0.908215i | \(-0.362554\pi\) | ||||
0.418505 | + | 0.908215i | \(0.362554\pi\) | |||||||
\(992\) | −4.81141 | −0.152762 | ||||||||
\(993\) | 81.4595 | 2.58504 | ||||||||
\(994\) | 11.5184 | 0.365341 | ||||||||
\(995\) | −0.888253 | −0.0281595 | ||||||||
\(996\) | −26.9173 | −0.852909 | ||||||||
\(997\) | −43.7618 | −1.38595 | −0.692975 | − | 0.720961i | \(-0.743701\pi\) | ||||
−0.692975 | + | 0.720961i | \(0.743701\pi\) | |||||||
\(998\) | −6.35830 | −0.201268 | ||||||||
\(999\) | 129.171 | 4.08679 |
(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 | 8026.2.a.c.1.4 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.c.1.4 | ✓ | 86 | 1.1 | even | 1 | trivial |