Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | −2.31184 | −1.33474 | −0.667370 | − | 0.744726i | \(-0.732580\pi\) | ||||
−0.667370 | + | 0.744726i | \(0.732580\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.83764 | −0.821817 | −0.410908 | − | 0.911677i | \(-0.634788\pi\) | ||||
−0.410908 | + | 0.911677i | \(0.634788\pi\) | |||||||
\(6\) | 2.31184 | 0.943803 | ||||||||
\(7\) | 0.291912 | 0.110332 | 0.0551662 | − | 0.998477i | \(-0.482431\pi\) | ||||
0.0551662 | + | 0.998477i | \(0.482431\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.34459 | 0.781530 | ||||||||
\(10\) | 1.83764 | 0.581112 | ||||||||
\(11\) | −0.391390 | −0.118009 | −0.0590043 | − | 0.998258i | \(-0.518793\pi\) | ||||
−0.0590043 | + | 0.998258i | \(0.518793\pi\) | |||||||
\(12\) | −2.31184 | −0.667370 | ||||||||
\(13\) | 0.600528 | 0.166556 | 0.0832782 | − | 0.996526i | \(-0.473461\pi\) | ||||
0.0832782 | + | 0.996526i | \(0.473461\pi\) | |||||||
\(14\) | −0.291912 | −0.0780168 | ||||||||
\(15\) | 4.24832 | 1.09691 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 8.06571 | 1.95622 | 0.978110 | − | 0.208086i | \(-0.0667235\pi\) | ||||
0.978110 | + | 0.208086i | \(0.0667235\pi\) | |||||||
\(18\) | −2.34459 | −0.552625 | ||||||||
\(19\) | −1.02842 | −0.235935 | −0.117968 | − | 0.993017i | \(-0.537638\pi\) | ||||
−0.117968 | + | 0.993017i | \(0.537638\pi\) | |||||||
\(20\) | −1.83764 | −0.410908 | ||||||||
\(21\) | −0.674854 | −0.147265 | ||||||||
\(22\) | 0.391390 | 0.0834447 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.31184 | 0.471902 | ||||||||
\(25\) | −1.62309 | −0.324617 | ||||||||
\(26\) | −0.600528 | −0.117773 | ||||||||
\(27\) | 1.51520 | 0.291600 | ||||||||
\(28\) | 0.291912 | 0.0551662 | ||||||||
\(29\) | 6.44707 | 1.19719 | 0.598596 | − | 0.801051i | \(-0.295726\pi\) | ||||
0.598596 | + | 0.801051i | \(0.295726\pi\) | |||||||
\(30\) | −4.24832 | −0.775633 | ||||||||
\(31\) | 9.49895 | 1.70606 | 0.853031 | − | 0.521861i | \(-0.174762\pi\) | ||||
0.853031 | + | 0.521861i | \(0.174762\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.904830 | 0.157511 | ||||||||
\(34\) | −8.06571 | −1.38326 | ||||||||
\(35\) | −0.536429 | −0.0906731 | ||||||||
\(36\) | 2.34459 | 0.390765 | ||||||||
\(37\) | 5.12747 | 0.842951 | 0.421476 | − | 0.906840i | \(-0.361512\pi\) | ||||
0.421476 | + | 0.906840i | \(0.361512\pi\) | |||||||
\(38\) | 1.02842 | 0.166831 | ||||||||
\(39\) | −1.38832 | −0.222309 | ||||||||
\(40\) | 1.83764 | 0.290556 | ||||||||
\(41\) | −5.09126 | −0.795122 | −0.397561 | − | 0.917576i | \(-0.630143\pi\) | ||||
−0.397561 | + | 0.917576i | \(0.630143\pi\) | |||||||
\(42\) | 0.674854 | 0.104132 | ||||||||
\(43\) | −4.74073 | −0.722954 | −0.361477 | − | 0.932381i | \(-0.617727\pi\) | ||||
−0.361477 | + | 0.932381i | \(0.617727\pi\) | |||||||
\(44\) | −0.391390 | −0.0590043 | ||||||||
\(45\) | −4.30851 | −0.642274 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −1.05671 | −0.154137 | −0.0770685 | − | 0.997026i | \(-0.524556\pi\) | ||||
−0.0770685 | + | 0.997026i | \(0.524556\pi\) | |||||||
\(48\) | −2.31184 | −0.333685 | ||||||||
\(49\) | −6.91479 | −0.987827 | ||||||||
\(50\) | 1.62309 | 0.229539 | ||||||||
\(51\) | −18.6466 | −2.61105 | ||||||||
\(52\) | 0.600528 | 0.0832782 | ||||||||
\(53\) | −4.00089 | −0.549564 | −0.274782 | − | 0.961507i | \(-0.588606\pi\) | ||||
−0.274782 | + | 0.961507i | \(0.588606\pi\) | |||||||
\(54\) | −1.51520 | −0.206193 | ||||||||
\(55\) | 0.719233 | 0.0969814 | ||||||||
\(56\) | −0.291912 | −0.0390084 | ||||||||
\(57\) | 2.37754 | 0.314912 | ||||||||
\(58\) | −6.44707 | −0.846542 | ||||||||
\(59\) | 9.67887 | 1.26008 | 0.630041 | − | 0.776562i | \(-0.283038\pi\) | ||||
0.630041 | + | 0.776562i | \(0.283038\pi\) | |||||||
\(60\) | 4.24832 | 0.548456 | ||||||||
\(61\) | 0.715006 | 0.0915471 | 0.0457736 | − | 0.998952i | \(-0.485425\pi\) | ||||
0.0457736 | + | 0.998952i | \(0.485425\pi\) | |||||||
\(62\) | −9.49895 | −1.20637 | ||||||||
\(63\) | 0.684415 | 0.0862281 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.10355 | −0.136879 | ||||||||
\(66\) | −0.904830 | −0.111377 | ||||||||
\(67\) | 13.1299 | 1.60407 | 0.802035 | − | 0.597277i | \(-0.203751\pi\) | ||||
0.802035 | + | 0.597277i | \(0.203751\pi\) | |||||||
\(68\) | 8.06571 | 0.978110 | ||||||||
\(69\) | −2.31184 | −0.278312 | ||||||||
\(70\) | 0.536429 | 0.0641155 | ||||||||
\(71\) | −5.39996 | −0.640858 | −0.320429 | − | 0.947273i | \(-0.603827\pi\) | ||||
−0.320429 | + | 0.947273i | \(0.603827\pi\) | |||||||
\(72\) | −2.34459 | −0.276313 | ||||||||
\(73\) | −5.19493 | −0.608020 | −0.304010 | − | 0.952669i | \(-0.598326\pi\) | ||||
−0.304010 | + | 0.952669i | \(0.598326\pi\) | |||||||
\(74\) | −5.12747 | −0.596056 | ||||||||
\(75\) | 3.75231 | 0.433280 | ||||||||
\(76\) | −1.02842 | −0.117968 | ||||||||
\(77\) | −0.114252 | −0.0130202 | ||||||||
\(78\) | 1.38832 | 0.157197 | ||||||||
\(79\) | 13.6192 | 1.53228 | 0.766139 | − | 0.642675i | \(-0.222176\pi\) | ||||
0.766139 | + | 0.642675i | \(0.222176\pi\) | |||||||
\(80\) | −1.83764 | −0.205454 | ||||||||
\(81\) | −10.5367 | −1.17074 | ||||||||
\(82\) | 5.09126 | 0.562236 | ||||||||
\(83\) | −15.0036 | −1.64686 | −0.823428 | − | 0.567421i | \(-0.807941\pi\) | ||||
−0.823428 | + | 0.567421i | \(0.807941\pi\) | |||||||
\(84\) | −0.674854 | −0.0736326 | ||||||||
\(85\) | −14.8218 | −1.60765 | ||||||||
\(86\) | 4.74073 | 0.511206 | ||||||||
\(87\) | −14.9046 | −1.59794 | ||||||||
\(88\) | 0.391390 | 0.0417223 | ||||||||
\(89\) | 3.64262 | 0.386117 | 0.193058 | − | 0.981187i | \(-0.438159\pi\) | ||||
0.193058 | + | 0.981187i | \(0.438159\pi\) | |||||||
\(90\) | 4.30851 | 0.454157 | ||||||||
\(91\) | 0.175301 | 0.0183766 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −21.9600 | −2.27715 | ||||||||
\(94\) | 1.05671 | 0.108991 | ||||||||
\(95\) | 1.88986 | 0.193896 | ||||||||
\(96\) | 2.31184 | 0.235951 | ||||||||
\(97\) | 5.12604 | 0.520470 | 0.260235 | − | 0.965545i | \(-0.416200\pi\) | ||||
0.260235 | + | 0.965545i | \(0.416200\pi\) | |||||||
\(98\) | 6.91479 | 0.698499 | ||||||||
\(99\) | −0.917649 | −0.0922272 | ||||||||
\(100\) | −1.62309 | −0.162309 | ||||||||
\(101\) | −9.66843 | −0.962044 | −0.481022 | − | 0.876708i | \(-0.659734\pi\) | ||||
−0.481022 | + | 0.876708i | \(0.659734\pi\) | |||||||
\(102\) | 18.6466 | 1.84629 | ||||||||
\(103\) | −10.9862 | −1.08251 | −0.541253 | − | 0.840860i | \(-0.682050\pi\) | ||||
−0.541253 | + | 0.840860i | \(0.682050\pi\) | |||||||
\(104\) | −0.600528 | −0.0588866 | ||||||||
\(105\) | 1.24014 | 0.121025 | ||||||||
\(106\) | 4.00089 | 0.388600 | ||||||||
\(107\) | 14.1778 | 1.37062 | 0.685309 | − | 0.728253i | \(-0.259667\pi\) | ||||
0.685309 | + | 0.728253i | \(0.259667\pi\) | |||||||
\(108\) | 1.51520 | 0.145800 | ||||||||
\(109\) | 19.1852 | 1.83761 | 0.918805 | − | 0.394711i | \(-0.129155\pi\) | ||||
0.918805 | + | 0.394711i | \(0.129155\pi\) | |||||||
\(110\) | −0.719233 | −0.0685762 | ||||||||
\(111\) | −11.8539 | −1.12512 | ||||||||
\(112\) | 0.291912 | 0.0275831 | ||||||||
\(113\) | −7.68528 | −0.722970 | −0.361485 | − | 0.932378i | \(-0.617730\pi\) | ||||
−0.361485 | + | 0.932378i | \(0.617730\pi\) | |||||||
\(114\) | −2.37754 | −0.222677 | ||||||||
\(115\) | −1.83764 | −0.171361 | ||||||||
\(116\) | 6.44707 | 0.598596 | ||||||||
\(117\) | 1.40799 | 0.130169 | ||||||||
\(118\) | −9.67887 | −0.891013 | ||||||||
\(119\) | 2.35448 | 0.215835 | ||||||||
\(120\) | −4.24832 | −0.387817 | ||||||||
\(121\) | −10.8468 | −0.986074 | ||||||||
\(122\) | −0.715006 | −0.0647336 | ||||||||
\(123\) | 11.7702 | 1.06128 | ||||||||
\(124\) | 9.49895 | 0.853031 | ||||||||
\(125\) | 12.1708 | 1.08859 | ||||||||
\(126\) | −0.684415 | −0.0609725 | ||||||||
\(127\) | −4.61410 | −0.409436 | −0.204718 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204718 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.9598 | 0.964956 | ||||||||
\(130\) | 1.10355 | 0.0967879 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | 0.904830 | 0.0787554 | ||||||||
\(133\) | −0.300208 | −0.0260313 | ||||||||
\(134\) | −13.1299 | −1.13425 | ||||||||
\(135\) | −2.78439 | −0.239642 | ||||||||
\(136\) | −8.06571 | −0.691629 | ||||||||
\(137\) | −6.11296 | −0.522265 | −0.261133 | − | 0.965303i | \(-0.584096\pi\) | ||||
−0.261133 | + | 0.965303i | \(0.584096\pi\) | |||||||
\(138\) | 2.31184 | 0.196797 | ||||||||
\(139\) | 14.7533 | 1.25136 | 0.625679 | − | 0.780080i | \(-0.284822\pi\) | ||||
0.625679 | + | 0.780080i | \(0.284822\pi\) | |||||||
\(140\) | −0.536429 | −0.0453365 | ||||||||
\(141\) | 2.44294 | 0.205733 | ||||||||
\(142\) | 5.39996 | 0.453155 | ||||||||
\(143\) | −0.235041 | −0.0196551 | ||||||||
\(144\) | 2.34459 | 0.195383 | ||||||||
\(145\) | −11.8474 | −0.983872 | ||||||||
\(146\) | 5.19493 | 0.429935 | ||||||||
\(147\) | 15.9859 | 1.31849 | ||||||||
\(148\) | 5.12747 | 0.421476 | ||||||||
\(149\) | −2.61721 | −0.214410 | −0.107205 | − | 0.994237i | \(-0.534190\pi\) | ||||
−0.107205 | + | 0.994237i | \(0.534190\pi\) | |||||||
\(150\) | −3.75231 | −0.306375 | ||||||||
\(151\) | −22.7375 | −1.85035 | −0.925175 | − | 0.379542i | \(-0.876082\pi\) | ||||
−0.925175 | + | 0.379542i | \(0.876082\pi\) | |||||||
\(152\) | 1.02842 | 0.0834157 | ||||||||
\(153\) | 18.9108 | 1.52885 | ||||||||
\(154\) | 0.114252 | 0.00920666 | ||||||||
\(155\) | −17.4556 | −1.40207 | ||||||||
\(156\) | −1.38832 | −0.111155 | ||||||||
\(157\) | −5.75420 | −0.459235 | −0.229618 | − | 0.973281i | \(-0.573748\pi\) | ||||
−0.229618 | + | 0.973281i | \(0.573748\pi\) | |||||||
\(158\) | −13.6192 | −1.08348 | ||||||||
\(159\) | 9.24939 | 0.733525 | ||||||||
\(160\) | 1.83764 | 0.145278 | ||||||||
\(161\) | 0.291912 | 0.0230059 | ||||||||
\(162\) | 10.5367 | 0.827839 | ||||||||
\(163\) | 17.6530 | 1.38269 | 0.691346 | − | 0.722524i | \(-0.257018\pi\) | ||||
0.691346 | + | 0.722524i | \(0.257018\pi\) | |||||||
\(164\) | −5.09126 | −0.397561 | ||||||||
\(165\) | −1.66275 | −0.129445 | ||||||||
\(166\) | 15.0036 | 1.16450 | ||||||||
\(167\) | −3.15337 | −0.244015 | −0.122008 | − | 0.992529i | \(-0.538933\pi\) | ||||
−0.122008 | + | 0.992529i | \(0.538933\pi\) | |||||||
\(168\) | 0.674854 | 0.0520661 | ||||||||
\(169\) | −12.6394 | −0.972259 | ||||||||
\(170\) | 14.8218 | 1.13678 | ||||||||
\(171\) | −2.41122 | −0.184391 | ||||||||
\(172\) | −4.74073 | −0.361477 | ||||||||
\(173\) | −0.767044 | −0.0583172 | −0.0291586 | − | 0.999575i | \(-0.509283\pi\) | ||||
−0.0291586 | + | 0.999575i | \(0.509283\pi\) | |||||||
\(174\) | 14.9046 | 1.12991 | ||||||||
\(175\) | −0.473799 | −0.0358159 | ||||||||
\(176\) | −0.391390 | −0.0295021 | ||||||||
\(177\) | −22.3760 | −1.68188 | ||||||||
\(178\) | −3.64262 | −0.273026 | ||||||||
\(179\) | −19.8829 | −1.48612 | −0.743060 | − | 0.669225i | \(-0.766626\pi\) | ||||
−0.743060 | + | 0.669225i | \(0.766626\pi\) | |||||||
\(180\) | −4.30851 | −0.321137 | ||||||||
\(181\) | 12.8264 | 0.953377 | 0.476689 | − | 0.879072i | \(-0.341837\pi\) | ||||
0.476689 | + | 0.879072i | \(0.341837\pi\) | |||||||
\(182\) | −0.175301 | −0.0129942 | ||||||||
\(183\) | −1.65298 | −0.122192 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −9.42244 | −0.692751 | ||||||||
\(186\) | 21.9600 | 1.61019 | ||||||||
\(187\) | −3.15684 | −0.230851 | ||||||||
\(188\) | −1.05671 | −0.0770685 | ||||||||
\(189\) | 0.442306 | 0.0321730 | ||||||||
\(190\) | −1.88986 | −0.137105 | ||||||||
\(191\) | 7.81875 | 0.565745 | 0.282872 | − | 0.959158i | \(-0.408713\pi\) | ||||
0.282872 | + | 0.959158i | \(0.408713\pi\) | |||||||
\(192\) | −2.31184 | −0.166842 | ||||||||
\(193\) | −21.0531 | −1.51544 | −0.757719 | − | 0.652581i | \(-0.773686\pi\) | ||||
−0.757719 | + | 0.652581i | \(0.773686\pi\) | |||||||
\(194\) | −5.12604 | −0.368028 | ||||||||
\(195\) | 2.55123 | 0.182698 | ||||||||
\(196\) | −6.91479 | −0.493913 | ||||||||
\(197\) | −10.5148 | −0.749147 | −0.374574 | − | 0.927197i | \(-0.622211\pi\) | ||||
−0.374574 | + | 0.927197i | \(0.622211\pi\) | |||||||
\(198\) | 0.917649 | 0.0652145 | ||||||||
\(199\) | 0.438705 | 0.0310990 | 0.0155495 | − | 0.999879i | \(-0.495050\pi\) | ||||
0.0155495 | + | 0.999879i | \(0.495050\pi\) | |||||||
\(200\) | 1.62309 | 0.114770 | ||||||||
\(201\) | −30.3541 | −2.14102 | ||||||||
\(202\) | 9.66843 | 0.680268 | ||||||||
\(203\) | 1.88198 | 0.132089 | ||||||||
\(204\) | −18.6466 | −1.30552 | ||||||||
\(205\) | 9.35590 | 0.653444 | ||||||||
\(206\) | 10.9862 | 0.765447 | ||||||||
\(207\) | 2.34459 | 0.162960 | ||||||||
\(208\) | 0.600528 | 0.0416391 | ||||||||
\(209\) | 0.402513 | 0.0278424 | ||||||||
\(210\) | −1.24014 | −0.0855776 | ||||||||
\(211\) | 4.87649 | 0.335712 | 0.167856 | − | 0.985812i | \(-0.446316\pi\) | ||||
0.167856 | + | 0.985812i | \(0.446316\pi\) | |||||||
\(212\) | −4.00089 | −0.274782 | ||||||||
\(213\) | 12.4838 | 0.855378 | ||||||||
\(214\) | −14.1778 | −0.969173 | ||||||||
\(215\) | 8.71174 | 0.594136 | ||||||||
\(216\) | −1.51520 | −0.103096 | ||||||||
\(217\) | 2.77286 | 0.188234 | ||||||||
\(218\) | −19.1852 | −1.29939 | ||||||||
\(219\) | 12.0098 | 0.811549 | ||||||||
\(220\) | 0.719233 | 0.0484907 | ||||||||
\(221\) | 4.84368 | 0.325821 | ||||||||
\(222\) | 11.8539 | 0.795580 | ||||||||
\(223\) | 16.8305 | 1.12705 | 0.563525 | − | 0.826099i | \(-0.309445\pi\) | ||||
0.563525 | + | 0.826099i | \(0.309445\pi\) | |||||||
\(224\) | −0.291912 | −0.0195042 | ||||||||
\(225\) | −3.80547 | −0.253698 | ||||||||
\(226\) | 7.68528 | 0.511217 | ||||||||
\(227\) | 5.58864 | 0.370931 | 0.185465 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185465 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(228\) | 2.37754 | 0.157456 | ||||||||
\(229\) | −9.85633 | −0.651324 | −0.325662 | − | 0.945486i | \(-0.605587\pi\) | ||||
−0.325662 | + | 0.945486i | \(0.605587\pi\) | |||||||
\(230\) | 1.83764 | 0.121170 | ||||||||
\(231\) | 0.264131 | 0.0173785 | ||||||||
\(232\) | −6.44707 | −0.423271 | ||||||||
\(233\) | −2.48199 | −0.162600 | −0.0813002 | − | 0.996690i | \(-0.525907\pi\) | ||||
−0.0813002 | + | 0.996690i | \(0.525907\pi\) | |||||||
\(234\) | −1.40799 | −0.0920433 | ||||||||
\(235\) | 1.94185 | 0.126672 | ||||||||
\(236\) | 9.67887 | 0.630041 | ||||||||
\(237\) | −31.4853 | −2.04519 | ||||||||
\(238\) | −2.35448 | −0.152618 | ||||||||
\(239\) | −16.0896 | −1.04075 | −0.520375 | − | 0.853938i | \(-0.674208\pi\) | ||||
−0.520375 | + | 0.853938i | \(0.674208\pi\) | |||||||
\(240\) | 4.24832 | 0.274228 | ||||||||
\(241\) | 14.8127 | 0.954170 | 0.477085 | − | 0.878857i | \(-0.341693\pi\) | ||||
0.477085 | + | 0.878857i | \(0.341693\pi\) | |||||||
\(242\) | 10.8468 | 0.697260 | ||||||||
\(243\) | 19.8135 | 1.27103 | ||||||||
\(244\) | 0.715006 | 0.0457736 | ||||||||
\(245\) | 12.7069 | 0.811812 | ||||||||
\(246\) | −11.7702 | −0.750438 | ||||||||
\(247\) | −0.617594 | −0.0392965 | ||||||||
\(248\) | −9.49895 | −0.603184 | ||||||||
\(249\) | 34.6858 | 2.19812 | ||||||||
\(250\) | −12.1708 | −0.769751 | ||||||||
\(251\) | −5.88435 | −0.371417 | −0.185708 | − | 0.982605i | \(-0.559458\pi\) | ||||
−0.185708 | + | 0.982605i | \(0.559458\pi\) | |||||||
\(252\) | 0.684415 | 0.0431141 | ||||||||
\(253\) | −0.391390 | −0.0246065 | ||||||||
\(254\) | 4.61410 | 0.289515 | ||||||||
\(255\) | 34.2657 | 2.14580 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.44280 | −0.464269 | −0.232134 | − | 0.972684i | \(-0.574571\pi\) | ||||
−0.232134 | + | 0.972684i | \(0.574571\pi\) | |||||||
\(258\) | −10.9598 | −0.682327 | ||||||||
\(259\) | 1.49677 | 0.0930049 | ||||||||
\(260\) | −1.10355 | −0.0684394 | ||||||||
\(261\) | 15.1157 | 0.935641 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 9.52011 | 0.587035 | 0.293518 | − | 0.955954i | \(-0.405174\pi\) | ||||
0.293518 | + | 0.955954i | \(0.405174\pi\) | |||||||
\(264\) | −0.904830 | −0.0556884 | ||||||||
\(265\) | 7.35218 | 0.451641 | ||||||||
\(266\) | 0.300208 | 0.0184069 | ||||||||
\(267\) | −8.42114 | −0.515365 | ||||||||
\(268\) | 13.1299 | 0.802035 | ||||||||
\(269\) | 4.97658 | 0.303428 | 0.151714 | − | 0.988424i | \(-0.451521\pi\) | ||||
0.151714 | + | 0.988424i | \(0.451521\pi\) | |||||||
\(270\) | 2.78439 | 0.169453 | ||||||||
\(271\) | 26.6826 | 1.62085 | 0.810427 | − | 0.585839i | \(-0.199235\pi\) | ||||
0.810427 | + | 0.585839i | \(0.199235\pi\) | |||||||
\(272\) | 8.06571 | 0.489055 | ||||||||
\(273\) | −0.405268 | −0.0245280 | ||||||||
\(274\) | 6.11296 | 0.369297 | ||||||||
\(275\) | 0.635260 | 0.0383076 | ||||||||
\(276\) | −2.31184 | −0.139156 | ||||||||
\(277\) | 25.2453 | 1.51685 | 0.758423 | − | 0.651763i | \(-0.225970\pi\) | ||||
0.758423 | + | 0.651763i | \(0.225970\pi\) | |||||||
\(278\) | −14.7533 | −0.884844 | ||||||||
\(279\) | 22.2711 | 1.33334 | ||||||||
\(280\) | 0.536429 | 0.0320578 | ||||||||
\(281\) | 5.15622 | 0.307595 | 0.153797 | − | 0.988102i | \(-0.450850\pi\) | ||||
0.153797 | + | 0.988102i | \(0.450850\pi\) | |||||||
\(282\) | −2.44294 | −0.145475 | ||||||||
\(283\) | 6.09035 | 0.362033 | 0.181017 | − | 0.983480i | \(-0.442061\pi\) | ||||
0.181017 | + | 0.983480i | \(0.442061\pi\) | |||||||
\(284\) | −5.39996 | −0.320429 | ||||||||
\(285\) | −4.36905 | −0.258800 | ||||||||
\(286\) | 0.235041 | 0.0138982 | ||||||||
\(287\) | −1.48620 | −0.0877277 | ||||||||
\(288\) | −2.34459 | −0.138156 | ||||||||
\(289\) | 48.0556 | 2.82680 | ||||||||
\(290\) | 11.8474 | 0.695702 | ||||||||
\(291\) | −11.8506 | −0.694692 | ||||||||
\(292\) | −5.19493 | −0.304010 | ||||||||
\(293\) | 8.93691 | 0.522100 | 0.261050 | − | 0.965325i | \(-0.415931\pi\) | ||||
0.261050 | + | 0.965325i | \(0.415931\pi\) | |||||||
\(294\) | −15.9859 | −0.932314 | ||||||||
\(295\) | −17.7863 | −1.03556 | ||||||||
\(296\) | −5.12747 | −0.298028 | ||||||||
\(297\) | −0.593034 | −0.0344114 | ||||||||
\(298\) | 2.61721 | 0.151611 | ||||||||
\(299\) | 0.600528 | 0.0347294 | ||||||||
\(300\) | 3.75231 | 0.216640 | ||||||||
\(301\) | −1.38388 | −0.0797653 | ||||||||
\(302\) | 22.7375 | 1.30839 | ||||||||
\(303\) | 22.3518 | 1.28408 | ||||||||
\(304\) | −1.02842 | −0.0589838 | ||||||||
\(305\) | −1.31392 | −0.0752350 | ||||||||
\(306\) | −18.9108 | −1.08106 | ||||||||
\(307\) | 5.29939 | 0.302452 | 0.151226 | − | 0.988499i | \(-0.451678\pi\) | ||||
0.151226 | + | 0.988499i | \(0.451678\pi\) | |||||||
\(308\) | −0.114252 | −0.00651009 | ||||||||
\(309\) | 25.3984 | 1.44486 | ||||||||
\(310\) | 17.4556 | 0.991413 | ||||||||
\(311\) | 10.2093 | 0.578917 | 0.289458 | − | 0.957191i | \(-0.406525\pi\) | ||||
0.289458 | + | 0.957191i | \(0.406525\pi\) | |||||||
\(312\) | 1.38832 | 0.0785983 | ||||||||
\(313\) | −16.6678 | −0.942122 | −0.471061 | − | 0.882101i | \(-0.656129\pi\) | ||||
−0.471061 | + | 0.882101i | \(0.656129\pi\) | |||||||
\(314\) | 5.75420 | 0.324728 | ||||||||
\(315\) | −1.25771 | −0.0708637 | ||||||||
\(316\) | 13.6192 | 0.766139 | ||||||||
\(317\) | 22.1664 | 1.24499 | 0.622493 | − | 0.782625i | \(-0.286120\pi\) | ||||
0.622493 | + | 0.782625i | \(0.286120\pi\) | |||||||
\(318\) | −9.24939 | −0.518680 | ||||||||
\(319\) | −2.52332 | −0.141279 | ||||||||
\(320\) | −1.83764 | −0.102727 | ||||||||
\(321\) | −32.7767 | −1.82942 | ||||||||
\(322\) | −0.291912 | −0.0162676 | ||||||||
\(323\) | −8.29492 | −0.461542 | ||||||||
\(324\) | −10.5367 | −0.585370 | ||||||||
\(325\) | −0.974709 | −0.0540671 | ||||||||
\(326\) | −17.6530 | −0.977711 | ||||||||
\(327\) | −44.3531 | −2.45273 | ||||||||
\(328\) | 5.09126 | 0.281118 | ||||||||
\(329\) | −0.308466 | −0.0170063 | ||||||||
\(330\) | 1.66275 | 0.0915314 | ||||||||
\(331\) | 13.0179 | 0.715529 | 0.357764 | − | 0.933812i | \(-0.383539\pi\) | ||||
0.357764 | + | 0.933812i | \(0.383539\pi\) | |||||||
\(332\) | −15.0036 | −0.823428 | ||||||||
\(333\) | 12.0218 | 0.658792 | ||||||||
\(334\) | 3.15337 | 0.172545 | ||||||||
\(335\) | −24.1280 | −1.31825 | ||||||||
\(336\) | −0.674854 | −0.0368163 | ||||||||
\(337\) | −18.7061 | −1.01898 | −0.509492 | − | 0.860475i | \(-0.670167\pi\) | ||||
−0.509492 | + | 0.860475i | \(0.670167\pi\) | |||||||
\(338\) | 12.6394 | 0.687491 | ||||||||
\(339\) | 17.7671 | 0.964977 | ||||||||
\(340\) | −14.8218 | −0.803827 | ||||||||
\(341\) | −3.71779 | −0.201330 | ||||||||
\(342\) | 2.41122 | 0.130384 | ||||||||
\(343\) | −4.06190 | −0.219322 | ||||||||
\(344\) | 4.74073 | 0.255603 | ||||||||
\(345\) | 4.24832 | 0.228722 | ||||||||
\(346\) | 0.767044 | 0.0412365 | ||||||||
\(347\) | −2.90742 | −0.156078 | −0.0780392 | − | 0.996950i | \(-0.524866\pi\) | ||||
−0.0780392 | + | 0.996950i | \(0.524866\pi\) | |||||||
\(348\) | −14.9046 | −0.798969 | ||||||||
\(349\) | 9.23019 | 0.494081 | 0.247040 | − | 0.969005i | \(-0.420542\pi\) | ||||
0.247040 | + | 0.969005i | \(0.420542\pi\) | |||||||
\(350\) | 0.473799 | 0.0253256 | ||||||||
\(351\) | 0.909920 | 0.0485679 | ||||||||
\(352\) | 0.391390 | 0.0208612 | ||||||||
\(353\) | −20.2316 | −1.07682 | −0.538411 | − | 0.842682i | \(-0.680975\pi\) | ||||
−0.538411 | + | 0.842682i | \(0.680975\pi\) | |||||||
\(354\) | 22.3760 | 1.18927 | ||||||||
\(355\) | 9.92318 | 0.526667 | ||||||||
\(356\) | 3.64262 | 0.193058 | ||||||||
\(357\) | −5.44317 | −0.288083 | ||||||||
\(358\) | 19.8829 | 1.05085 | ||||||||
\(359\) | −18.7728 | −0.990792 | −0.495396 | − | 0.868667i | \(-0.664977\pi\) | ||||
−0.495396 | + | 0.868667i | \(0.664977\pi\) | |||||||
\(360\) | 4.30851 | 0.227078 | ||||||||
\(361\) | −17.9424 | −0.944335 | ||||||||
\(362\) | −12.8264 | −0.674139 | ||||||||
\(363\) | 25.0761 | 1.31615 | ||||||||
\(364\) | 0.175301 | 0.00918829 | ||||||||
\(365\) | 9.54639 | 0.499681 | ||||||||
\(366\) | 1.65298 | 0.0864025 | ||||||||
\(367\) | 4.38357 | 0.228821 | 0.114410 | − | 0.993434i | \(-0.463502\pi\) | ||||
0.114410 | + | 0.993434i | \(0.463502\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −11.9369 | −0.621411 | ||||||||
\(370\) | 9.42244 | 0.489849 | ||||||||
\(371\) | −1.16791 | −0.0606347 | ||||||||
\(372\) | −21.9600 | −1.13857 | ||||||||
\(373\) | 18.6895 | 0.967707 | 0.483853 | − | 0.875149i | \(-0.339237\pi\) | ||||
0.483853 | + | 0.875149i | \(0.339237\pi\) | |||||||
\(374\) | 3.15684 | 0.163236 | ||||||||
\(375\) | −28.1370 | −1.45299 | ||||||||
\(376\) | 1.05671 | 0.0544956 | ||||||||
\(377\) | 3.87165 | 0.199400 | ||||||||
\(378\) | −0.442306 | −0.0227497 | ||||||||
\(379\) | −0.781344 | −0.0401350 | −0.0200675 | − | 0.999799i | \(-0.506388\pi\) | ||||
−0.0200675 | + | 0.999799i | \(0.506388\pi\) | |||||||
\(380\) | 1.88986 | 0.0969478 | ||||||||
\(381\) | 10.6671 | 0.546490 | ||||||||
\(382\) | −7.81875 | −0.400042 | ||||||||
\(383\) | −12.2150 | −0.624158 | −0.312079 | − | 0.950056i | \(-0.601025\pi\) | ||||
−0.312079 | + | 0.950056i | \(0.601025\pi\) | |||||||
\(384\) | 2.31184 | 0.117975 | ||||||||
\(385\) | 0.209953 | 0.0107002 | ||||||||
\(386\) | 21.0531 | 1.07158 | ||||||||
\(387\) | −11.1151 | −0.565011 | ||||||||
\(388\) | 5.12604 | 0.260235 | ||||||||
\(389\) | 15.2089 | 0.771122 | 0.385561 | − | 0.922682i | \(-0.374008\pi\) | ||||
0.385561 | + | 0.922682i | \(0.374008\pi\) | |||||||
\(390\) | −2.55123 | −0.129187 | ||||||||
\(391\) | 8.06571 | 0.407900 | ||||||||
\(392\) | 6.91479 | 0.349249 | ||||||||
\(393\) | 2.31184 | 0.116617 | ||||||||
\(394\) | 10.5148 | 0.529727 | ||||||||
\(395\) | −25.0271 | −1.25925 | ||||||||
\(396\) | −0.917649 | −0.0461136 | ||||||||
\(397\) | −9.52792 | −0.478193 | −0.239096 | − | 0.970996i | \(-0.576851\pi\) | ||||
−0.239096 | + | 0.970996i | \(0.576851\pi\) | |||||||
\(398\) | −0.438705 | −0.0219903 | ||||||||
\(399\) | 0.694032 | 0.0347450 | ||||||||
\(400\) | −1.62309 | −0.0811544 | ||||||||
\(401\) | −22.6444 | −1.13081 | −0.565404 | − | 0.824814i | \(-0.691280\pi\) | ||||
−0.565404 | + | 0.824814i | \(0.691280\pi\) | |||||||
\(402\) | 30.3541 | 1.51393 | ||||||||
\(403\) | 5.70438 | 0.284155 | ||||||||
\(404\) | −9.66843 | −0.481022 | ||||||||
\(405\) | 19.3626 | 0.962134 | ||||||||
\(406\) | −1.88198 | −0.0934011 | ||||||||
\(407\) | −2.00684 | −0.0994755 | ||||||||
\(408\) | 18.6466 | 0.923144 | ||||||||
\(409\) | 20.8266 | 1.02981 | 0.514905 | − | 0.857247i | \(-0.327827\pi\) | ||||
0.514905 | + | 0.857247i | \(0.327827\pi\) | |||||||
\(410\) | −9.35590 | −0.462055 | ||||||||
\(411\) | 14.1322 | 0.697088 | ||||||||
\(412\) | −10.9862 | −0.541253 | ||||||||
\(413\) | 2.82538 | 0.139028 | ||||||||
\(414\) | −2.34459 | −0.115230 | ||||||||
\(415\) | 27.5711 | 1.35341 | ||||||||
\(416\) | −0.600528 | −0.0294433 | ||||||||
\(417\) | −34.1072 | −1.67024 | ||||||||
\(418\) | −0.402513 | −0.0196875 | ||||||||
\(419\) | −2.15454 | −0.105256 | −0.0526281 | − | 0.998614i | \(-0.516760\pi\) | ||||
−0.0526281 | + | 0.998614i | \(0.516760\pi\) | |||||||
\(420\) | 1.24014 | 0.0605125 | ||||||||
\(421\) | 33.6833 | 1.64162 | 0.820812 | − | 0.571198i | \(-0.193521\pi\) | ||||
0.820812 | + | 0.571198i | \(0.193521\pi\) | |||||||
\(422\) | −4.87649 | −0.237384 | ||||||||
\(423\) | −2.47755 | −0.120463 | ||||||||
\(424\) | 4.00089 | 0.194300 | ||||||||
\(425\) | −13.0913 | −0.635024 | ||||||||
\(426\) | −12.4838 | −0.604844 | ||||||||
\(427\) | 0.208719 | 0.0101006 | ||||||||
\(428\) | 14.1778 | 0.685309 | ||||||||
\(429\) | 0.543376 | 0.0262344 | ||||||||
\(430\) | −8.71174 | −0.420117 | ||||||||
\(431\) | 12.9361 | 0.623112 | 0.311556 | − | 0.950228i | \(-0.399150\pi\) | ||||
0.311556 | + | 0.950228i | \(0.399150\pi\) | |||||||
\(432\) | 1.51520 | 0.0729001 | ||||||||
\(433\) | −12.2226 | −0.587379 | −0.293690 | − | 0.955901i | \(-0.594883\pi\) | ||||
−0.293690 | + | 0.955901i | \(0.594883\pi\) | |||||||
\(434\) | −2.77286 | −0.133102 | ||||||||
\(435\) | 27.3892 | 1.31321 | ||||||||
\(436\) | 19.1852 | 0.918805 | ||||||||
\(437\) | −1.02842 | −0.0491959 | ||||||||
\(438\) | −12.0098 | −0.573851 | ||||||||
\(439\) | 14.0286 | 0.669549 | 0.334774 | − | 0.942298i | \(-0.391340\pi\) | ||||
0.334774 | + | 0.942298i | \(0.391340\pi\) | |||||||
\(440\) | −0.719233 | −0.0342881 | ||||||||
\(441\) | −16.2123 | −0.772016 | ||||||||
\(442\) | −4.84368 | −0.230390 | ||||||||
\(443\) | 21.9918 | 1.04486 | 0.522432 | − | 0.852681i | \(-0.325025\pi\) | ||||
0.522432 | + | 0.852681i | \(0.325025\pi\) | |||||||
\(444\) | −11.8539 | −0.562560 | ||||||||
\(445\) | −6.69381 | −0.317317 | ||||||||
\(446\) | −16.8305 | −0.796945 | ||||||||
\(447\) | 6.05055 | 0.286181 | ||||||||
\(448\) | 0.291912 | 0.0137916 | ||||||||
\(449\) | 16.9033 | 0.797718 | 0.398859 | − | 0.917012i | \(-0.369406\pi\) | ||||
0.398859 | + | 0.917012i | \(0.369406\pi\) | |||||||
\(450\) | 3.80547 | 0.179392 | ||||||||
\(451\) | 1.99267 | 0.0938311 | ||||||||
\(452\) | −7.68528 | −0.361485 | ||||||||
\(453\) | 52.5653 | 2.46973 | ||||||||
\(454\) | −5.58864 | −0.262288 | ||||||||
\(455\) | −0.322140 | −0.0151022 | ||||||||
\(456\) | −2.37754 | −0.111338 | ||||||||
\(457\) | −9.49580 | −0.444195 | −0.222097 | − | 0.975024i | \(-0.571290\pi\) | ||||
−0.222097 | + | 0.975024i | \(0.571290\pi\) | |||||||
\(458\) | 9.85633 | 0.460556 | ||||||||
\(459\) | 12.2212 | 0.570435 | ||||||||
\(460\) | −1.83764 | −0.0856803 | ||||||||
\(461\) | 3.13431 | 0.145979 | 0.0729897 | − | 0.997333i | \(-0.476746\pi\) | ||||
0.0729897 | + | 0.997333i | \(0.476746\pi\) | |||||||
\(462\) | −0.264131 | −0.0122885 | ||||||||
\(463\) | 25.5419 | 1.18703 | 0.593516 | − | 0.804822i | \(-0.297739\pi\) | ||||
0.593516 | + | 0.804822i | \(0.297739\pi\) | |||||||
\(464\) | 6.44707 | 0.299298 | ||||||||
\(465\) | 40.3546 | 1.87140 | ||||||||
\(466\) | 2.48199 | 0.114976 | ||||||||
\(467\) | 11.3457 | 0.525018 | 0.262509 | − | 0.964930i | \(-0.415450\pi\) | ||||
0.262509 | + | 0.964930i | \(0.415450\pi\) | |||||||
\(468\) | 1.40799 | 0.0650844 | ||||||||
\(469\) | 3.83277 | 0.176981 | ||||||||
\(470\) | −1.94185 | −0.0895708 | ||||||||
\(471\) | 13.3028 | 0.612960 | ||||||||
\(472\) | −9.67887 | −0.445506 | ||||||||
\(473\) | 1.85547 | 0.0853148 | ||||||||
\(474\) | 31.4853 | 1.44617 | ||||||||
\(475\) | 1.66921 | 0.0765887 | ||||||||
\(476\) | 2.35448 | 0.107917 | ||||||||
\(477\) | −9.38044 | −0.429501 | ||||||||
\(478\) | 16.0896 | 0.735922 | ||||||||
\(479\) | −17.2723 | −0.789190 | −0.394595 | − | 0.918855i | \(-0.629115\pi\) | ||||
−0.394595 | + | 0.918855i | \(0.629115\pi\) | |||||||
\(480\) | −4.24832 | −0.193908 | ||||||||
\(481\) | 3.07919 | 0.140399 | ||||||||
\(482\) | −14.8127 | −0.674700 | ||||||||
\(483\) | −0.674854 | −0.0307069 | ||||||||
\(484\) | −10.8468 | −0.493037 | ||||||||
\(485\) | −9.41980 | −0.427731 | ||||||||
\(486\) | −19.8135 | −0.898757 | ||||||||
\(487\) | 5.31269 | 0.240741 | 0.120370 | − | 0.992729i | \(-0.461592\pi\) | ||||
0.120370 | + | 0.992729i | \(0.461592\pi\) | |||||||
\(488\) | −0.715006 | −0.0323668 | ||||||||
\(489\) | −40.8109 | −1.84553 | ||||||||
\(490\) | −12.7069 | −0.574038 | ||||||||
\(491\) | −3.50231 | −0.158057 | −0.0790284 | − | 0.996872i | \(-0.525182\pi\) | ||||
−0.0790284 | + | 0.996872i | \(0.525182\pi\) | |||||||
\(492\) | 11.7702 | 0.530640 | ||||||||
\(493\) | 52.0002 | 2.34197 | ||||||||
\(494\) | 0.617594 | 0.0277868 | ||||||||
\(495\) | 1.68631 | 0.0757939 | ||||||||
\(496\) | 9.49895 | 0.426515 | ||||||||
\(497\) | −1.57632 | −0.0707074 | ||||||||
\(498\) | −34.6858 | −1.55431 | ||||||||
\(499\) | 33.8963 | 1.51741 | 0.758703 | − | 0.651437i | \(-0.225833\pi\) | ||||
0.758703 | + | 0.651437i | \(0.225833\pi\) | |||||||
\(500\) | 12.1708 | 0.544296 | ||||||||
\(501\) | 7.29008 | 0.325697 | ||||||||
\(502\) | 5.88435 | 0.262631 | ||||||||
\(503\) | 21.6035 | 0.963251 | 0.481625 | − | 0.876377i | \(-0.340047\pi\) | ||||
0.481625 | + | 0.876377i | \(0.340047\pi\) | |||||||
\(504\) | −0.684415 | −0.0304863 | ||||||||
\(505\) | 17.7671 | 0.790624 | ||||||||
\(506\) | 0.391390 | 0.0173994 | ||||||||
\(507\) | 29.2202 | 1.29771 | ||||||||
\(508\) | −4.61410 | −0.204718 | ||||||||
\(509\) | −38.3094 | −1.69803 | −0.849017 | − | 0.528365i | \(-0.822805\pi\) | ||||
−0.849017 | + | 0.528365i | \(0.822805\pi\) | |||||||
\(510\) | −34.2657 | −1.51731 | ||||||||
\(511\) | −1.51646 | −0.0670844 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.55826 | −0.0687988 | ||||||||
\(514\) | 7.44280 | 0.328288 | ||||||||
\(515\) | 20.1887 | 0.889621 | ||||||||
\(516\) | 10.9598 | 0.482478 | ||||||||
\(517\) | 0.413586 | 0.0181895 | ||||||||
\(518\) | −1.49677 | −0.0657644 | ||||||||
\(519\) | 1.77328 | 0.0778383 | ||||||||
\(520\) | 1.10355 | 0.0483940 | ||||||||
\(521\) | 4.61837 | 0.202335 | 0.101167 | − | 0.994869i | \(-0.467742\pi\) | ||||
0.101167 | + | 0.994869i | \(0.467742\pi\) | |||||||
\(522\) | −15.1157 | −0.661598 | ||||||||
\(523\) | 1.47740 | 0.0646021 | 0.0323010 | − | 0.999478i | \(-0.489716\pi\) | ||||
0.0323010 | + | 0.999478i | \(0.489716\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 1.09535 | 0.0478048 | ||||||||
\(526\) | −9.52011 | −0.415096 | ||||||||
\(527\) | 76.6157 | 3.33743 | ||||||||
\(528\) | 0.904830 | 0.0393777 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −7.35218 | −0.319358 | ||||||||
\(531\) | 22.6930 | 0.984792 | ||||||||
\(532\) | −0.300208 | −0.0130157 | ||||||||
\(533\) | −3.05744 | −0.132433 | ||||||||
\(534\) | 8.42114 | 0.364418 | ||||||||
\(535\) | −26.0536 | −1.12640 | ||||||||
\(536\) | −13.1299 | −0.567125 | ||||||||
\(537\) | 45.9661 | 1.98358 | ||||||||
\(538\) | −4.97658 | −0.214556 | ||||||||
\(539\) | 2.70638 | 0.116572 | ||||||||
\(540\) | −2.78439 | −0.119821 | ||||||||
\(541\) | 37.6086 | 1.61692 | 0.808461 | − | 0.588550i | \(-0.200301\pi\) | ||||
0.808461 | + | 0.588550i | \(0.200301\pi\) | |||||||
\(542\) | −26.6826 | −1.14612 | ||||||||
\(543\) | −29.6525 | −1.27251 | ||||||||
\(544\) | −8.06571 | −0.345814 | ||||||||
\(545\) | −35.2555 | −1.51018 | ||||||||
\(546\) | 0.405268 | 0.0173439 | ||||||||
\(547\) | 11.6975 | 0.500150 | 0.250075 | − | 0.968226i | \(-0.419545\pi\) | ||||
0.250075 | + | 0.968226i | \(0.419545\pi\) | |||||||
\(548\) | −6.11296 | −0.261133 | ||||||||
\(549\) | 1.67640 | 0.0715468 | ||||||||
\(550\) | −0.635260 | −0.0270876 | ||||||||
\(551\) | −6.63029 | −0.282460 | ||||||||
\(552\) | 2.31184 | 0.0983983 | ||||||||
\(553\) | 3.97561 | 0.169060 | ||||||||
\(554\) | −25.2453 | −1.07257 | ||||||||
\(555\) | 21.7831 | 0.924643 | ||||||||
\(556\) | 14.7533 | 0.625679 | ||||||||
\(557\) | −40.8947 | −1.73276 | −0.866382 | − | 0.499382i | \(-0.833560\pi\) | ||||
−0.866382 | + | 0.499382i | \(0.833560\pi\) | |||||||
\(558\) | −22.2711 | −0.942813 | ||||||||
\(559\) | −2.84694 | −0.120413 | ||||||||
\(560\) | −0.536429 | −0.0226683 | ||||||||
\(561\) | 7.29809 | 0.308126 | ||||||||
\(562\) | −5.15622 | −0.217502 | ||||||||
\(563\) | −25.1196 | −1.05866 | −0.529332 | − | 0.848415i | \(-0.677557\pi\) | ||||
−0.529332 | + | 0.848415i | \(0.677557\pi\) | |||||||
\(564\) | 2.44294 | 0.102866 | ||||||||
\(565\) | 14.1228 | 0.594149 | ||||||||
\(566\) | −6.09035 | −0.255996 | ||||||||
\(567\) | −3.07578 | −0.129171 | ||||||||
\(568\) | 5.39996 | 0.226577 | ||||||||
\(569\) | 40.4073 | 1.69396 | 0.846981 | − | 0.531623i | \(-0.178418\pi\) | ||||
0.846981 | + | 0.531623i | \(0.178418\pi\) | |||||||
\(570\) | 4.36905 | 0.182999 | ||||||||
\(571\) | 13.6070 | 0.569435 | 0.284718 | − | 0.958611i | \(-0.408100\pi\) | ||||
0.284718 | + | 0.958611i | \(0.408100\pi\) | |||||||
\(572\) | −0.235041 | −0.00982754 | ||||||||
\(573\) | −18.0757 | −0.755122 | ||||||||
\(574\) | 1.48620 | 0.0620329 | ||||||||
\(575\) | −1.62309 | −0.0676874 | ||||||||
\(576\) | 2.34459 | 0.0976913 | ||||||||
\(577\) | −6.04962 | −0.251849 | −0.125924 | − | 0.992040i | \(-0.540190\pi\) | ||||
−0.125924 | + | 0.992040i | \(0.540190\pi\) | |||||||
\(578\) | −48.0556 | −1.99885 | ||||||||
\(579\) | 48.6714 | 2.02272 | ||||||||
\(580\) | −11.8474 | −0.491936 | ||||||||
\(581\) | −4.37973 | −0.181702 | ||||||||
\(582\) | 11.8506 | 0.491222 | ||||||||
\(583\) | 1.56591 | 0.0648532 | ||||||||
\(584\) | 5.19493 | 0.214968 | ||||||||
\(585\) | −2.58738 | −0.106975 | ||||||||
\(586\) | −8.93691 | −0.369180 | ||||||||
\(587\) | −27.0011 | −1.11445 | −0.557227 | − | 0.830360i | \(-0.688135\pi\) | ||||
−0.557227 | + | 0.830360i | \(0.688135\pi\) | |||||||
\(588\) | 15.9859 | 0.659246 | ||||||||
\(589\) | −9.76889 | −0.402520 | ||||||||
\(590\) | 17.7863 | 0.732249 | ||||||||
\(591\) | 24.3085 | 0.999917 | ||||||||
\(592\) | 5.12747 | 0.210738 | ||||||||
\(593\) | 35.7759 | 1.46914 | 0.734569 | − | 0.678534i | \(-0.237384\pi\) | ||||
0.734569 | + | 0.678534i | \(0.237384\pi\) | |||||||
\(594\) | 0.593034 | 0.0243325 | ||||||||
\(595\) | −4.32668 | −0.177377 | ||||||||
\(596\) | −2.61721 | −0.107205 | ||||||||
\(597\) | −1.01421 | −0.0415090 | ||||||||
\(598\) | −0.600528 | −0.0245574 | ||||||||
\(599\) | 31.1303 | 1.27195 | 0.635975 | − | 0.771710i | \(-0.280598\pi\) | ||||
0.635975 | + | 0.771710i | \(0.280598\pi\) | |||||||
\(600\) | −3.75231 | −0.153188 | ||||||||
\(601\) | 2.77336 | 0.113128 | 0.0565639 | − | 0.998399i | \(-0.481986\pi\) | ||||
0.0565639 | + | 0.998399i | \(0.481986\pi\) | |||||||
\(602\) | 1.38388 | 0.0564026 | ||||||||
\(603\) | 30.7842 | 1.25363 | ||||||||
\(604\) | −22.7375 | −0.925175 | ||||||||
\(605\) | 19.9325 | 0.810372 | ||||||||
\(606\) | −22.3518 | −0.907981 | ||||||||
\(607\) | 40.2172 | 1.63236 | 0.816182 | − | 0.577795i | \(-0.196087\pi\) | ||||
0.816182 | + | 0.577795i | \(0.196087\pi\) | |||||||
\(608\) | 1.02842 | 0.0417079 | ||||||||
\(609\) | −4.35083 | −0.176305 | ||||||||
\(610\) | 1.31392 | 0.0531991 | ||||||||
\(611\) | −0.634583 | −0.0256725 | ||||||||
\(612\) | 18.9108 | 0.764423 | ||||||||
\(613\) | 6.97330 | 0.281649 | 0.140824 | − | 0.990035i | \(-0.455025\pi\) | ||||
0.140824 | + | 0.990035i | \(0.455025\pi\) | |||||||
\(614\) | −5.29939 | −0.213866 | ||||||||
\(615\) | −21.6293 | −0.872178 | ||||||||
\(616\) | 0.114252 | 0.00460333 | ||||||||
\(617\) | −21.0336 | −0.846781 | −0.423390 | − | 0.905947i | \(-0.639160\pi\) | ||||
−0.423390 | + | 0.905947i | \(0.639160\pi\) | |||||||
\(618\) | −25.3984 | −1.02167 | ||||||||
\(619\) | 9.93695 | 0.399400 | 0.199700 | − | 0.979857i | \(-0.436003\pi\) | ||||
0.199700 | + | 0.979857i | \(0.436003\pi\) | |||||||
\(620\) | −17.4556 | −0.701035 | ||||||||
\(621\) | 1.51520 | 0.0608029 | ||||||||
\(622\) | −10.2093 | −0.409356 | ||||||||
\(623\) | 1.06333 | 0.0426012 | ||||||||
\(624\) | −1.38832 | −0.0555774 | ||||||||
\(625\) | −14.2502 | −0.570006 | ||||||||
\(626\) | 16.6678 | 0.666181 | ||||||||
\(627\) | −0.930544 | −0.0371623 | ||||||||
\(628\) | −5.75420 | −0.229618 | ||||||||
\(629\) | 41.3567 | 1.64900 | ||||||||
\(630\) | 1.25771 | 0.0501082 | ||||||||
\(631\) | 37.3336 | 1.48623 | 0.743113 | − | 0.669166i | \(-0.233348\pi\) | ||||
0.743113 | + | 0.669166i | \(0.233348\pi\) | |||||||
\(632\) | −13.6192 | −0.541742 | ||||||||
\(633\) | −11.2737 | −0.448088 | ||||||||
\(634\) | −22.1664 | −0.880338 | ||||||||
\(635\) | 8.47905 | 0.336481 | ||||||||
\(636\) | 9.24939 | 0.366762 | ||||||||
\(637\) | −4.15252 | −0.164529 | ||||||||
\(638\) | 2.52332 | 0.0998992 | ||||||||
\(639\) | −12.6607 | −0.500850 | ||||||||
\(640\) | 1.83764 | 0.0726390 | ||||||||
\(641\) | 45.1693 | 1.78408 | 0.892040 | − | 0.451957i | \(-0.149274\pi\) | ||||
0.892040 | + | 0.451957i | \(0.149274\pi\) | |||||||
\(642\) | 32.7767 | 1.29359 | ||||||||
\(643\) | −36.1403 | −1.42523 | −0.712617 | − | 0.701554i | \(-0.752490\pi\) | ||||
−0.712617 | + | 0.701554i | \(0.752490\pi\) | |||||||
\(644\) | 0.291912 | 0.0115030 | ||||||||
\(645\) | −20.1401 | −0.793017 | ||||||||
\(646\) | 8.29492 | 0.326359 | ||||||||
\(647\) | −19.5308 | −0.767837 | −0.383918 | − | 0.923367i | \(-0.625426\pi\) | ||||
−0.383918 | + | 0.923367i | \(0.625426\pi\) | |||||||
\(648\) | 10.5367 | 0.413919 | ||||||||
\(649\) | −3.78822 | −0.148700 | ||||||||
\(650\) | 0.974709 | 0.0382312 | ||||||||
\(651\) | −6.41040 | −0.251243 | ||||||||
\(652\) | 17.6530 | 0.691346 | ||||||||
\(653\) | −8.93254 | −0.349557 | −0.174779 | − | 0.984608i | \(-0.555921\pi\) | ||||
−0.174779 | + | 0.984608i | \(0.555921\pi\) | |||||||
\(654\) | 44.3531 | 1.73434 | ||||||||
\(655\) | 1.83764 | 0.0718024 | ||||||||
\(656\) | −5.09126 | −0.198780 | ||||||||
\(657\) | −12.1800 | −0.475186 | ||||||||
\(658\) | 0.308466 | 0.0120253 | ||||||||
\(659\) | 33.5200 | 1.30576 | 0.652878 | − | 0.757463i | \(-0.273562\pi\) | ||||
0.652878 | + | 0.757463i | \(0.273562\pi\) | |||||||
\(660\) | −1.66275 | −0.0647225 | ||||||||
\(661\) | 0.510953 | 0.0198738 | 0.00993688 | − | 0.999951i | \(-0.496837\pi\) | ||||
0.00993688 | + | 0.999951i | \(0.496837\pi\) | |||||||
\(662\) | −13.0179 | −0.505955 | ||||||||
\(663\) | −11.1978 | −0.434886 | ||||||||
\(664\) | 15.0036 | 0.582251 | ||||||||
\(665\) | 0.551673 | 0.0213930 | ||||||||
\(666\) | −12.0218 | −0.465836 | ||||||||
\(667\) | 6.44707 | 0.249632 | ||||||||
\(668\) | −3.15337 | −0.122008 | ||||||||
\(669\) | −38.9093 | −1.50432 | ||||||||
\(670\) | 24.1280 | 0.932145 | ||||||||
\(671\) | −0.279846 | −0.0108033 | ||||||||
\(672\) | 0.674854 | 0.0260330 | ||||||||
\(673\) | −2.79126 | −0.107595 | −0.0537976 | − | 0.998552i | \(-0.517133\pi\) | ||||
−0.0537976 | + | 0.998552i | \(0.517133\pi\) | |||||||
\(674\) | 18.7061 | 0.720531 | ||||||||
\(675\) | −2.45930 | −0.0946586 | ||||||||
\(676\) | −12.6394 | −0.486129 | ||||||||
\(677\) | 2.47139 | 0.0949832 | 0.0474916 | − | 0.998872i | \(-0.484877\pi\) | ||||
0.0474916 | + | 0.998872i | \(0.484877\pi\) | |||||||
\(678\) | −17.7671 | −0.682342 | ||||||||
\(679\) | 1.49635 | 0.0574248 | ||||||||
\(680\) | 14.8218 | 0.568392 | ||||||||
\(681\) | −12.9200 | −0.495096 | ||||||||
\(682\) | 3.71779 | 0.142362 | ||||||||
\(683\) | −42.9761 | −1.64443 | −0.822217 | − | 0.569174i | \(-0.807263\pi\) | ||||
−0.822217 | + | 0.569174i | \(0.807263\pi\) | |||||||
\(684\) | −2.41122 | −0.0921953 | ||||||||
\(685\) | 11.2334 | 0.429206 | ||||||||
\(686\) | 4.06190 | 0.155084 | ||||||||
\(687\) | 22.7862 | 0.869349 | ||||||||
\(688\) | −4.74073 | −0.180739 | ||||||||
\(689\) | −2.40264 | −0.0915334 | ||||||||
\(690\) | −4.24832 | −0.161731 | ||||||||
\(691\) | −6.68098 | −0.254157 | −0.127078 | − | 0.991893i | \(-0.540560\pi\) | ||||
−0.127078 | + | 0.991893i | \(0.540560\pi\) | |||||||
\(692\) | −0.767044 | −0.0291586 | ||||||||
\(693\) | −0.267873 | −0.0101757 | ||||||||
\(694\) | 2.90742 | 0.110364 | ||||||||
\(695\) | −27.1112 | −1.02839 | ||||||||
\(696\) | 14.9046 | 0.564957 | ||||||||
\(697\) | −41.0646 | −1.55543 | ||||||||
\(698\) | −9.23019 | −0.349368 | ||||||||
\(699\) | 5.73795 | 0.217029 | ||||||||
\(700\) | −0.473799 | −0.0179079 | ||||||||
\(701\) | −15.7800 | −0.596001 | −0.298000 | − | 0.954566i | \(-0.596320\pi\) | ||||
−0.298000 | + | 0.954566i | \(0.596320\pi\) | |||||||
\(702\) | −0.909920 | −0.0343427 | ||||||||
\(703\) | −5.27319 | −0.198882 | ||||||||
\(704\) | −0.391390 | −0.0147511 | ||||||||
\(705\) | −4.48924 | −0.169075 | ||||||||
\(706\) | 20.2316 | 0.761428 | ||||||||
\(707\) | −2.82233 | −0.106145 | ||||||||
\(708\) | −22.3760 | −0.840941 | ||||||||
\(709\) | −10.9250 | −0.410297 | −0.205148 | − | 0.978731i | \(-0.565768\pi\) | ||||
−0.205148 | + | 0.978731i | \(0.565768\pi\) | |||||||
\(710\) | −9.92318 | −0.372410 | ||||||||
\(711\) | 31.9314 | 1.19752 | ||||||||
\(712\) | −3.64262 | −0.136513 | ||||||||
\(713\) | 9.49895 | 0.355738 | ||||||||
\(714\) | 5.44317 | 0.203706 | ||||||||
\(715\) | 0.431919 | 0.0161529 | ||||||||
\(716\) | −19.8829 | −0.743060 | ||||||||
\(717\) | 37.1966 | 1.38913 | ||||||||
\(718\) | 18.7728 | 0.700596 | ||||||||
\(719\) | 7.16778 | 0.267313 | 0.133657 | − | 0.991028i | \(-0.457328\pi\) | ||||
0.133657 | + | 0.991028i | \(0.457328\pi\) | |||||||
\(720\) | −4.30851 | −0.160569 | ||||||||
\(721\) | −3.20701 | −0.119435 | ||||||||
\(722\) | 17.9424 | 0.667745 | ||||||||
\(723\) | −34.2445 | −1.27357 | ||||||||
\(724\) | 12.8264 | 0.476689 | ||||||||
\(725\) | −10.4642 | −0.388629 | ||||||||
\(726\) | −25.0761 | −0.930660 | ||||||||
\(727\) | 11.0765 | 0.410806 | 0.205403 | − | 0.978677i | \(-0.434149\pi\) | ||||
0.205403 | + | 0.978677i | \(0.434149\pi\) | |||||||
\(728\) | −0.175301 | −0.00649710 | ||||||||
\(729\) | −14.1955 | −0.525758 | ||||||||
\(730\) | −9.54639 | −0.353328 | ||||||||
\(731\) | −38.2373 | −1.41426 | ||||||||
\(732\) | −1.65298 | −0.0610958 | ||||||||
\(733\) | −22.0414 | −0.814116 | −0.407058 | − | 0.913402i | \(-0.633445\pi\) | ||||
−0.407058 | + | 0.913402i | \(0.633445\pi\) | |||||||
\(734\) | −4.38357 | −0.161801 | ||||||||
\(735\) | −29.3762 | −1.08356 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −5.13891 | −0.189294 | ||||||||
\(738\) | 11.9369 | 0.439404 | ||||||||
\(739\) | −2.11263 | −0.0777143 | −0.0388572 | − | 0.999245i | \(-0.512372\pi\) | ||||
−0.0388572 | + | 0.999245i | \(0.512372\pi\) | |||||||
\(740\) | −9.42244 | −0.346376 | ||||||||
\(741\) | 1.42778 | 0.0524507 | ||||||||
\(742\) | 1.16791 | 0.0428752 | ||||||||
\(743\) | −44.9082 | −1.64752 | −0.823761 | − | 0.566937i | \(-0.808128\pi\) | ||||
−0.823761 | + | 0.566937i | \(0.808128\pi\) | |||||||
\(744\) | 21.9600 | 0.805093 | ||||||||
\(745\) | 4.80948 | 0.176206 | ||||||||
\(746\) | −18.6895 | −0.684272 | ||||||||
\(747\) | −35.1772 | −1.28707 | ||||||||
\(748\) | −3.15684 | −0.115425 | ||||||||
\(749\) | 4.13867 | 0.151224 | ||||||||
\(750\) | 28.1370 | 1.02742 | ||||||||
\(751\) | 28.6291 | 1.04469 | 0.522345 | − | 0.852734i | \(-0.325057\pi\) | ||||
0.522345 | + | 0.852734i | \(0.325057\pi\) | |||||||
\(752\) | −1.05671 | −0.0385342 | ||||||||
\(753\) | 13.6037 | 0.495745 | ||||||||
\(754\) | −3.87165 | −0.140997 | ||||||||
\(755\) | 41.7832 | 1.52065 | ||||||||
\(756\) | 0.442306 | 0.0160865 | ||||||||
\(757\) | −12.1385 | −0.441183 | −0.220591 | − | 0.975366i | \(-0.570799\pi\) | ||||
−0.220591 | + | 0.975366i | \(0.570799\pi\) | |||||||
\(758\) | 0.781344 | 0.0283797 | ||||||||
\(759\) | 0.904830 | 0.0328433 | ||||||||
\(760\) | −1.88986 | −0.0685524 | ||||||||
\(761\) | 46.0156 | 1.66807 | 0.834033 | − | 0.551715i | \(-0.186026\pi\) | ||||
0.834033 | + | 0.551715i | \(0.186026\pi\) | |||||||
\(762\) | −10.6671 | −0.386427 | ||||||||
\(763\) | 5.60040 | 0.202748 | ||||||||
\(764\) | 7.81875 | 0.282872 | ||||||||
\(765\) | −34.7512 | −1.25643 | ||||||||
\(766\) | 12.2150 | 0.441346 | ||||||||
\(767\) | 5.81243 | 0.209875 | ||||||||
\(768\) | −2.31184 | −0.0834212 | ||||||||
\(769\) | 22.2253 | 0.801466 | 0.400733 | − | 0.916195i | \(-0.368755\pi\) | ||||
0.400733 | + | 0.916195i | \(0.368755\pi\) | |||||||
\(770\) | −0.209953 | −0.00756618 | ||||||||
\(771\) | 17.2065 | 0.619678 | ||||||||
\(772\) | −21.0531 | −0.757719 | ||||||||
\(773\) | −3.83845 | −0.138059 | −0.0690297 | − | 0.997615i | \(-0.521990\pi\) | ||||
−0.0690297 | + | 0.997615i | \(0.521990\pi\) | |||||||
\(774\) | 11.1151 | 0.399523 | ||||||||
\(775\) | −15.4176 | −0.553817 | ||||||||
\(776\) | −5.12604 | −0.184014 | ||||||||
\(777\) | −3.46029 | −0.124137 | ||||||||
\(778\) | −15.2089 | −0.545266 | ||||||||
\(779\) | 5.23595 | 0.187597 | ||||||||
\(780\) | 2.55123 | 0.0913488 | ||||||||
\(781\) | 2.11349 | 0.0756267 | ||||||||
\(782\) | −8.06571 | −0.288429 | ||||||||
\(783\) | 9.76861 | 0.349102 | ||||||||
\(784\) | −6.91479 | −0.246957 | ||||||||
\(785\) | 10.5741 | 0.377407 | ||||||||
\(786\) | −2.31184 | −0.0824605 | ||||||||
\(787\) | 52.5794 | 1.87425 | 0.937127 | − | 0.348988i | \(-0.113475\pi\) | ||||
0.937127 | + | 0.348988i | \(0.113475\pi\) | |||||||
\(788\) | −10.5148 | −0.374574 | ||||||||
\(789\) | −22.0089 | −0.783539 | ||||||||
\(790\) | 25.0271 | 0.890425 | ||||||||
\(791\) | −2.24343 | −0.0797671 | ||||||||
\(792\) | 0.917649 | 0.0326073 | ||||||||
\(793\) | 0.429381 | 0.0152478 | ||||||||
\(794\) | 9.52792 | 0.338133 | ||||||||
\(795\) | −16.9970 | −0.602823 | ||||||||
\(796\) | 0.438705 | 0.0155495 | ||||||||
\(797\) | 36.5466 | 1.29455 | 0.647274 | − | 0.762258i | \(-0.275909\pi\) | ||||
0.647274 | + | 0.762258i | \(0.275909\pi\) | |||||||
\(798\) | −0.694032 | −0.0245685 | ||||||||
\(799\) | −8.52311 | −0.301526 | ||||||||
\(800\) | 1.62309 | 0.0573848 | ||||||||
\(801\) | 8.54045 | 0.301762 | ||||||||
\(802\) | 22.6444 | 0.799602 | ||||||||
\(803\) | 2.03324 | 0.0717516 | ||||||||
\(804\) | −30.3541 | −1.07051 | ||||||||
\(805\) | −0.536429 | −0.0189066 | ||||||||
\(806\) | −5.70438 | −0.200928 | ||||||||
\(807\) | −11.5050 | −0.404997 | ||||||||
\(808\) | 9.66843 | 0.340134 | ||||||||
\(809\) | −5.97613 | −0.210110 | −0.105055 | − | 0.994466i | \(-0.533502\pi\) | ||||
−0.105055 | + | 0.994466i | \(0.533502\pi\) | |||||||
\(810\) | −19.3626 | −0.680332 | ||||||||
\(811\) | 1.09223 | 0.0383535 | 0.0191767 | − | 0.999816i | \(-0.493895\pi\) | ||||
0.0191767 | + | 0.999816i | \(0.493895\pi\) | |||||||
\(812\) | 1.88198 | 0.0660445 | ||||||||
\(813\) | −61.6859 | −2.16342 | ||||||||
\(814\) | 2.00684 | 0.0703398 | ||||||||
\(815\) | −32.4399 | −1.13632 | ||||||||
\(816\) | −18.6466 | −0.652761 | ||||||||
\(817\) | 4.87545 | 0.170570 | ||||||||
\(818\) | −20.8266 | −0.728185 | ||||||||
\(819\) | 0.411010 | 0.0143619 | ||||||||
\(820\) | 9.35590 | 0.326722 | ||||||||
\(821\) | −43.3201 | −1.51188 | −0.755941 | − | 0.654640i | \(-0.772820\pi\) | ||||
−0.755941 | + | 0.654640i | \(0.772820\pi\) | |||||||
\(822\) | −14.1322 | −0.492916 | ||||||||
\(823\) | −36.4413 | −1.27026 | −0.635132 | − | 0.772403i | \(-0.719054\pi\) | ||||
−0.635132 | + | 0.772403i | \(0.719054\pi\) | |||||||
\(824\) | 10.9862 | 0.382723 | ||||||||
\(825\) | −1.46862 | −0.0511307 | ||||||||
\(826\) | −2.82538 | −0.0983076 | ||||||||
\(827\) | 52.9344 | 1.84071 | 0.920355 | − | 0.391084i | \(-0.127900\pi\) | ||||
0.920355 | + | 0.391084i | \(0.127900\pi\) | |||||||
\(828\) | 2.34459 | 0.0814801 | ||||||||
\(829\) | −25.8646 | −0.898314 | −0.449157 | − | 0.893453i | \(-0.648276\pi\) | ||||
−0.449157 | + | 0.893453i | \(0.648276\pi\) | |||||||
\(830\) | −27.5711 | −0.957008 | ||||||||
\(831\) | −58.3631 | −2.02459 | ||||||||
\(832\) | 0.600528 | 0.0208196 | ||||||||
\(833\) | −55.7726 | −1.93241 | ||||||||
\(834\) | 34.1072 | 1.18104 | ||||||||
\(835\) | 5.79476 | 0.200536 | ||||||||
\(836\) | 0.402513 | 0.0139212 | ||||||||
\(837\) | 14.3928 | 0.497488 | ||||||||
\(838\) | 2.15454 | 0.0744274 | ||||||||
\(839\) | 26.3222 | 0.908742 | 0.454371 | − | 0.890813i | \(-0.349864\pi\) | ||||
0.454371 | + | 0.890813i | \(0.349864\pi\) | |||||||
\(840\) | −1.24014 | −0.0427888 | ||||||||
\(841\) | 12.5648 | 0.433267 | ||||||||
\(842\) | −33.6833 | −1.16080 | ||||||||
\(843\) | −11.9203 | −0.410559 | ||||||||
\(844\) | 4.87649 | 0.167856 | ||||||||
\(845\) | 23.2266 | 0.799019 | ||||||||
\(846\) | 2.47755 | 0.0851799 | ||||||||
\(847\) | −3.16632 | −0.108796 | ||||||||
\(848\) | −4.00089 | −0.137391 | ||||||||
\(849\) | −14.0799 | −0.483220 | ||||||||
\(850\) | 13.0913 | 0.449029 | ||||||||
\(851\) | 5.12747 | 0.175767 | ||||||||
\(852\) | 12.4838 | 0.427689 | ||||||||
\(853\) | −41.5731 | −1.42344 | −0.711719 | − | 0.702465i | \(-0.752083\pi\) | ||||
−0.711719 | + | 0.702465i | \(0.752083\pi\) | |||||||
\(854\) | −0.208719 | −0.00714222 | ||||||||
\(855\) | 4.43095 | 0.151535 | ||||||||
\(856\) | −14.1778 | −0.484586 | ||||||||
\(857\) | −1.93308 | −0.0660327 | −0.0330164 | − | 0.999455i | \(-0.510511\pi\) | ||||
−0.0330164 | + | 0.999455i | \(0.510511\pi\) | |||||||
\(858\) | −0.543376 | −0.0185505 | ||||||||
\(859\) | 37.2019 | 1.26931 | 0.634657 | − | 0.772794i | \(-0.281142\pi\) | ||||
0.634657 | + | 0.772794i | \(0.281142\pi\) | |||||||
\(860\) | 8.71174 | 0.297068 | ||||||||
\(861\) | 3.43586 | 0.117094 | ||||||||
\(862\) | −12.9361 | −0.440607 | ||||||||
\(863\) | 33.3017 | 1.13360 | 0.566801 | − | 0.823855i | \(-0.308181\pi\) | ||||
0.566801 | + | 0.823855i | \(0.308181\pi\) | |||||||
\(864\) | −1.51520 | −0.0515482 | ||||||||
\(865\) | 1.40955 | 0.0479261 | ||||||||
\(866\) | 12.2226 | 0.415340 | ||||||||
\(867\) | −111.097 | −3.77304 | ||||||||
\(868\) | 2.77286 | 0.0941170 | ||||||||
\(869\) | −5.33041 | −0.180822 | ||||||||
\(870\) | −27.3892 | −0.928582 | ||||||||
\(871\) | 7.88486 | 0.267168 | ||||||||
\(872\) | −19.1852 | −0.649694 | ||||||||
\(873\) | 12.0185 | 0.406763 | ||||||||
\(874\) | 1.02842 | 0.0347868 | ||||||||
\(875\) | 3.55282 | 0.120107 | ||||||||
\(876\) | 12.0098 | 0.405774 | ||||||||
\(877\) | 26.7970 | 0.904871 | 0.452435 | − | 0.891797i | \(-0.350555\pi\) | ||||
0.452435 | + | 0.891797i | \(0.350555\pi\) | |||||||
\(878\) | −14.0286 | −0.473442 | ||||||||
\(879\) | −20.6607 | −0.696867 | ||||||||
\(880\) | 0.719233 | 0.0242453 | ||||||||
\(881\) | 49.3912 | 1.66403 | 0.832016 | − | 0.554751i | \(-0.187187\pi\) | ||||
0.832016 | + | 0.554751i | \(0.187187\pi\) | |||||||
\(882\) | 16.2123 | 0.545898 | ||||||||
\(883\) | −32.3332 | −1.08810 | −0.544050 | − | 0.839053i | \(-0.683110\pi\) | ||||
−0.544050 | + | 0.839053i | \(0.683110\pi\) | |||||||
\(884\) | 4.84368 | 0.162911 | ||||||||
\(885\) | 41.1189 | 1.38220 | ||||||||
\(886\) | −21.9918 | −0.738831 | ||||||||
\(887\) | −48.5609 | −1.63052 | −0.815258 | − | 0.579098i | \(-0.803405\pi\) | ||||
−0.815258 | + | 0.579098i | \(0.803405\pi\) | |||||||
\(888\) | 11.8539 | 0.397790 | ||||||||
\(889\) | −1.34691 | −0.0451740 | ||||||||
\(890\) | 6.69381 | 0.224377 | ||||||||
\(891\) | 4.12395 | 0.138157 | ||||||||
\(892\) | 16.8305 | 0.563525 | ||||||||
\(893\) | 1.08674 | 0.0363663 | ||||||||
\(894\) | −6.05055 | −0.202361 | ||||||||
\(895\) | 36.5376 | 1.22132 | ||||||||
\(896\) | −0.291912 | −0.00975211 | ||||||||
\(897\) | −1.38832 | −0.0463547 | ||||||||
\(898\) | −16.9033 | −0.564072 | ||||||||
\(899\) | 61.2404 | 2.04248 | ||||||||
\(900\) | −3.80547 | −0.126849 | ||||||||
\(901\) | −32.2700 | −1.07507 | ||||||||
\(902\) | −1.99267 | −0.0663486 | ||||||||
\(903\) | 3.19930 | 0.106466 | ||||||||
\(904\) | 7.68528 | 0.255608 | ||||||||
\(905\) | −23.5702 | −0.783501 | ||||||||
\(906\) | −52.5653 | −1.74637 | ||||||||
\(907\) | 13.7691 | 0.457196 | 0.228598 | − | 0.973521i | \(-0.426586\pi\) | ||||
0.228598 | + | 0.973521i | \(0.426586\pi\) | |||||||
\(908\) | 5.58864 | 0.185465 | ||||||||
\(909\) | −22.6685 | −0.751867 | ||||||||
\(910\) | 0.322140 | 0.0106789 | ||||||||
\(911\) | 35.3910 | 1.17256 | 0.586279 | − | 0.810110i | \(-0.300592\pi\) | ||||
0.586279 | + | 0.810110i | \(0.300592\pi\) | |||||||
\(912\) | 2.37754 | 0.0787281 | ||||||||
\(913\) | 5.87225 | 0.194343 | ||||||||
\(914\) | 9.49580 | 0.314093 | ||||||||
\(915\) | 3.03757 | 0.100419 | ||||||||
\(916\) | −9.85633 | −0.325662 | ||||||||
\(917\) | −0.291912 | −0.00963979 | ||||||||
\(918\) | −12.2212 | −0.403358 | ||||||||
\(919\) | −17.4031 | −0.574074 | −0.287037 | − | 0.957920i | \(-0.592670\pi\) | ||||
−0.287037 | + | 0.957920i | \(0.592670\pi\) | |||||||
\(920\) | 1.83764 | 0.0605851 | ||||||||
\(921\) | −12.2513 | −0.403695 | ||||||||
\(922\) | −3.13431 | −0.103223 | ||||||||
\(923\) | −3.24283 | −0.106739 | ||||||||
\(924\) | 0.264131 | 0.00868927 | ||||||||
\(925\) | −8.32233 | −0.273637 | ||||||||
\(926\) | −25.5419 | −0.839359 | ||||||||
\(927\) | −25.7582 | −0.846010 | ||||||||
\(928\) | −6.44707 | −0.211636 | ||||||||
\(929\) | −41.9984 | −1.37792 | −0.688962 | − | 0.724797i | \(-0.741933\pi\) | ||||
−0.688962 | + | 0.724797i | \(0.741933\pi\) | |||||||
\(930\) | −40.3546 | −1.32328 | ||||||||
\(931\) | 7.11129 | 0.233063 | ||||||||
\(932\) | −2.48199 | −0.0813002 | ||||||||
\(933\) | −23.6023 | −0.772703 | ||||||||
\(934\) | −11.3457 | −0.371244 | ||||||||
\(935\) | 5.80112 | 0.189717 | ||||||||
\(936\) | −1.40799 | −0.0460216 | ||||||||
\(937\) | −9.45234 | −0.308795 | −0.154397 | − | 0.988009i | \(-0.549344\pi\) | ||||
−0.154397 | + | 0.988009i | \(0.549344\pi\) | |||||||
\(938\) | −3.83277 | −0.125145 | ||||||||
\(939\) | 38.5333 | 1.25749 | ||||||||
\(940\) | 1.94185 | 0.0633361 | ||||||||
\(941\) | −49.2484 | −1.60545 | −0.802726 | − | 0.596348i | \(-0.796618\pi\) | ||||
−0.802726 | + | 0.596348i | \(0.796618\pi\) | |||||||
\(942\) | −13.3028 | −0.433428 | ||||||||
\(943\) | −5.09126 | −0.165794 | ||||||||
\(944\) | 9.67887 | 0.315021 | ||||||||
\(945\) | −0.812798 | −0.0264403 | ||||||||
\(946\) | −1.85547 | −0.0603267 | ||||||||
\(947\) | −19.8431 | −0.644815 | −0.322408 | − | 0.946601i | \(-0.604492\pi\) | ||||
−0.322408 | + | 0.946601i | \(0.604492\pi\) | |||||||
\(948\) | −31.4853 | −1.02260 | ||||||||
\(949\) | −3.11970 | −0.101270 | ||||||||
\(950\) | −1.66921 | −0.0541564 | ||||||||
\(951\) | −51.2450 | −1.66173 | ||||||||
\(952\) | −2.35448 | −0.0763091 | ||||||||
\(953\) | −22.0569 | −0.714493 | −0.357247 | − | 0.934010i | \(-0.616284\pi\) | ||||
−0.357247 | + | 0.934010i | \(0.616284\pi\) | |||||||
\(954\) | 9.38044 | 0.303703 | ||||||||
\(955\) | −14.3680 | −0.464939 | ||||||||
\(956\) | −16.0896 | −0.520375 | ||||||||
\(957\) | 5.83351 | 0.188570 | ||||||||
\(958\) | 17.2723 | 0.558041 | ||||||||
\(959\) | −1.78445 | −0.0576228 | ||||||||
\(960\) | 4.24832 | 0.137114 | ||||||||
\(961\) | 59.2300 | 1.91065 | ||||||||
\(962\) | −3.07919 | −0.0992770 | ||||||||
\(963\) | 33.2411 | 1.07118 | ||||||||
\(964\) | 14.8127 | 0.477085 | ||||||||
\(965\) | 38.6881 | 1.24541 | ||||||||
\(966\) | 0.674854 | 0.0217131 | ||||||||
\(967\) | 2.55272 | 0.0820900 | 0.0410450 | − | 0.999157i | \(-0.486931\pi\) | ||||
0.0410450 | + | 0.999157i | \(0.486931\pi\) | |||||||
\(968\) | 10.8468 | 0.348630 | ||||||||
\(969\) | 19.1765 | 0.616038 | ||||||||
\(970\) | 9.41980 | 0.302452 | ||||||||
\(971\) | −22.1532 | −0.710929 | −0.355464 | − | 0.934690i | \(-0.615677\pi\) | ||||
−0.355464 | + | 0.934690i | \(0.615677\pi\) | |||||||
\(972\) | 19.8135 | 0.635517 | ||||||||
\(973\) | 4.30667 | 0.138066 | ||||||||
\(974\) | −5.31269 | −0.170229 | ||||||||
\(975\) | 2.25337 | 0.0721655 | ||||||||
\(976\) | 0.715006 | 0.0228868 | ||||||||
\(977\) | −58.3425 | −1.86654 | −0.933271 | − | 0.359172i | \(-0.883059\pi\) | ||||
−0.933271 | + | 0.359172i | \(0.883059\pi\) | |||||||
\(978\) | 40.8109 | 1.30499 | ||||||||
\(979\) | −1.42568 | −0.0455651 | ||||||||
\(980\) | 12.7069 | 0.405906 | ||||||||
\(981\) | 44.9815 | 1.43615 | ||||||||
\(982\) | 3.50231 | 0.111763 | ||||||||
\(983\) | −43.5128 | −1.38784 | −0.693922 | − | 0.720051i | \(-0.744119\pi\) | ||||
−0.693922 | + | 0.720051i | \(0.744119\pi\) | |||||||
\(984\) | −11.7702 | −0.375219 | ||||||||
\(985\) | 19.3224 | 0.615662 | ||||||||
\(986\) | −52.0002 | −1.65602 | ||||||||
\(987\) | 0.713124 | 0.0226990 | ||||||||
\(988\) | −0.617594 | −0.0196483 | ||||||||
\(989\) | −4.74073 | −0.150746 | ||||||||
\(990\) | −1.68631 | −0.0535944 | ||||||||
\(991\) | −13.6453 | −0.433457 | −0.216729 | − | 0.976232i | \(-0.569539\pi\) | ||||
−0.216729 | + | 0.976232i | \(0.569539\pi\) | |||||||
\(992\) | −9.49895 | −0.301592 | ||||||||
\(993\) | −30.0953 | −0.955045 | ||||||||
\(994\) | 1.57632 | 0.0499977 | ||||||||
\(995\) | −0.806181 | −0.0255576 | ||||||||
\(996\) | 34.6858 | 1.09906 | ||||||||
\(997\) | −18.2018 | −0.576455 | −0.288228 | − | 0.957562i | \(-0.593066\pi\) | ||||
−0.288228 | + | 0.957562i | \(0.593066\pi\) | |||||||
\(998\) | −33.8963 | −1.07297 | ||||||||
\(999\) | 7.76915 | 0.245805 |
(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 | 6026.2.a.j.1.6 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.j.1.6 | ✓ | 33 | 1.1 | even | 1 | trivial |