Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(889,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.57815240704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 89x^{4} - 170x^{3} + 162x^{2} - 72x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 889.6 | ||
Root | \(-2.15569 - 2.15569i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.889 |
Dual form | 1110.2.d.j.889.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.594137 | − | 2.15569i | −0.265706 | − | 0.964054i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − | 1.17795i | − | 0.445223i | −0.974907 | − | 0.222611i | \(-0.928542\pi\) | ||
0.974907 | − | 0.222611i | \(-0.0714581\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.15569 | − | 0.594137i | 0.681689 | − | 0.187883i | ||||
\(11\) | −0.822051 | −0.247858 | −0.123929 | − | 0.992291i | \(-0.539549\pi\) | ||||
−0.123929 | + | 0.992291i | \(0.539549\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 1.74983i | 0.485315i | 0.970112 | + | 0.242657i | \(0.0780191\pi\) | ||||
−0.970112 | + | 0.242657i | \(0.921981\pi\) | |||||||
\(14\) | 1.17795 | 0.314820 | ||||||||
\(15\) | 2.15569 | − | 0.594137i | 0.556597 | − | 0.153406i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.94516i | 0.956841i | 0.878131 | + | 0.478420i | \(0.158791\pi\) | ||||
−0.878131 | + | 0.478420i | \(0.841209\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −1.29400 | −0.296864 | −0.148432 | − | 0.988923i | \(-0.547423\pi\) | ||||
−0.148432 | + | 0.988923i | \(0.547423\pi\) | |||||||
\(20\) | 0.594137 | + | 2.15569i | 0.132853 | + | 0.482027i | ||||
\(21\) | 1.17795 | 0.257050 | ||||||||
\(22\) | − | 0.822051i | − | 0.175262i | ||||||
\(23\) | 7.68466i | 1.60236i | 0.598422 | + | 0.801181i | \(0.295795\pi\) | ||||
−0.598422 | + | 0.801181i | \(0.704205\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.29400 | + | 2.56155i | −0.858800 | + | 0.512311i | ||||
\(26\) | −1.74983 | −0.343169 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.17795i | 0.222611i | ||||||||
\(29\) | −9.23916 | −1.71567 | −0.857834 | − | 0.513926i | \(-0.828190\pi\) | ||||
−0.857834 | + | 0.513926i | \(0.828190\pi\) | |||||||
\(30\) | 0.594137 | + | 2.15569i | 0.108474 | + | 0.393573i | ||||
\(31\) | −9.30433 | −1.67111 | −0.835553 | − | 0.549410i | \(-0.814853\pi\) | ||||
−0.835553 | + | 0.549410i | \(0.814853\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 0.822051i | − | 0.143101i | ||||||
\(34\) | −3.94516 | −0.676589 | ||||||||
\(35\) | −2.53929 | + | 0.699864i | −0.429219 | + | 0.118299i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − | 1.00000i | − | 0.164399i | ||||||
\(38\) | − | 1.29400i | − | 0.209915i | ||||||
\(39\) | −1.74983 | −0.280197 | ||||||||
\(40\) | −2.15569 | + | 0.594137i | −0.340845 | + | 0.0939414i | ||||
\(41\) | −2.50671 | −0.391482 | −0.195741 | − | 0.980656i | \(-0.562711\pi\) | ||||
−0.195741 | + | 0.980656i | \(0.562711\pi\) | |||||||
\(42\) | 1.17795i | 0.181762i | ||||||||
\(43\) | − | 2.92778i | − | 0.446482i | −0.974763 | − | 0.223241i | \(-0.928336\pi\) | ||
0.974763 | − | 0.223241i | \(-0.0716637\pi\) | |||||||
\(44\) | 0.822051 | 0.123929 | ||||||||
\(45\) | 0.594137 | + | 2.15569i | 0.0885688 | + | 0.321351i | ||||
\(46\) | −7.68466 | −1.13304 | ||||||||
\(47\) | − | 7.18827i | − | 1.04852i | −0.851559 | − | 0.524259i | \(-0.824342\pi\) | ||
0.851559 | − | 0.524259i | \(-0.175658\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 5.61244 | 0.801776 | ||||||||
\(50\) | −2.56155 | − | 4.29400i | −0.362258 | − | 0.607263i | ||||
\(51\) | −3.94516 | −0.552432 | ||||||||
\(52\) | − | 1.74983i | − | 0.242657i | ||||||
\(53\) | 13.8659i | 1.90463i | 0.305124 | + | 0.952313i | \(0.401302\pi\) | ||||
−0.305124 | + | 0.952313i | \(0.598698\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.488411 | + | 1.77209i | 0.0658573 | + | 0.238948i | ||||
\(56\) | −1.17795 | −0.157410 | ||||||||
\(57\) | − | 1.29400i | − | 0.171395i | ||||||
\(58\) | − | 9.23916i | − | 1.21316i | ||||||
\(59\) | −3.18827 | −0.415078 | −0.207539 | − | 0.978227i | \(-0.566545\pi\) | ||||
−0.207539 | + | 0.978227i | \(0.566545\pi\) | |||||||
\(60\) | −2.15569 | + | 0.594137i | −0.278298 | + | 0.0767028i | ||||
\(61\) | 8.78333 | 1.12459 | 0.562295 | − | 0.826937i | \(-0.309918\pi\) | ||||
0.562295 | + | 0.826937i | \(0.309918\pi\) | |||||||
\(62\) | − | 9.30433i | − | 1.18165i | ||||||
\(63\) | 1.17795i | 0.148408i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.77209 | − | 1.03964i | 0.467870 | − | 0.128951i | ||||
\(66\) | 0.822051 | 0.101187 | ||||||||
\(67\) | 15.2108i | 1.85829i | 0.369715 | + | 0.929145i | \(0.379455\pi\) | ||||
−0.369715 | + | 0.929145i | \(0.620545\pi\) | |||||||
\(68\) | − | 3.94516i | − | 0.478420i | ||||||
\(69\) | −7.68466 | −0.925124 | ||||||||
\(70\) | −0.699864 | − | 2.53929i | −0.0836497 | − | 0.303504i | ||||
\(71\) | −6.65317 | −0.789586 | −0.394793 | − | 0.918770i | \(-0.629184\pi\) | ||||
−0.394793 | + | 0.918770i | \(0.629184\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − | 11.9168i | − | 1.39475i | −0.716706 | − | 0.697376i | \(-0.754351\pi\) | ||
0.716706 | − | 0.697376i | \(-0.245649\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | −2.56155 | − | 4.29400i | −0.295783 | − | 0.495829i | ||||
\(76\) | 1.29400 | 0.148432 | ||||||||
\(77\) | 0.968334i | 0.110352i | ||||||||
\(78\) | − | 1.74983i | − | 0.198129i | ||||||
\(79\) | 0.797618 | 0.0897390 | 0.0448695 | − | 0.998993i | \(-0.485713\pi\) | ||||
0.0448695 | + | 0.998993i | \(0.485713\pi\) | |||||||
\(80\) | −0.594137 | − | 2.15569i | −0.0664266 | − | 0.241014i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 2.50671i | − | 0.276820i | ||||||
\(83\) | 7.72918i | 0.848387i | 0.905571 | + | 0.424194i | \(0.139442\pi\) | ||||
−0.905571 | + | 0.424194i | \(0.860558\pi\) | |||||||
\(84\) | −1.17795 | −0.128525 | ||||||||
\(85\) | 8.50454 | − | 2.34397i | 0.922446 | − | 0.254239i | ||||
\(86\) | 2.92778 | 0.315710 | ||||||||
\(87\) | − | 9.23916i | − | 0.990542i | ||||||
\(88\) | 0.822051i | 0.0876309i | ||||||||
\(89\) | −14.8729 | −1.57653 | −0.788264 | − | 0.615337i | \(-0.789020\pi\) | ||||
−0.788264 | + | 0.615337i | \(0.789020\pi\) | |||||||
\(90\) | −2.15569 | + | 0.594137i | −0.227230 | + | 0.0626276i | ||||
\(91\) | 2.06121 | 0.216073 | ||||||||
\(92\) | − | 7.68466i | − | 0.801181i | ||||||
\(93\) | − | 9.30433i | − | 0.964814i | ||||||
\(94\) | 7.18827 | 0.741414 | ||||||||
\(95\) | 0.768815 | + | 2.78947i | 0.0788787 | + | 0.286193i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 13.0947i | − | 1.32957i | −0.747036 | − | 0.664783i | \(-0.768524\pi\) | ||
0.747036 | − | 0.664783i | \(-0.231476\pi\) | |||||||
\(98\) | 5.61244i | 0.566942i | ||||||||
\(99\) | 0.822051 | 0.0826192 | ||||||||
\(100\) | 4.29400 | − | 2.56155i | 0.429400 | − | 0.256155i | ||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | − | 3.94516i | − | 0.390629i | ||||||
\(103\) | 19.6666i | 1.93781i | 0.247439 | + | 0.968903i | \(0.420411\pi\) | ||||
−0.247439 | + | 0.968903i | \(0.579589\pi\) | |||||||
\(104\) | 1.74983 | 0.171585 | ||||||||
\(105\) | −0.699864 | − | 2.53929i | −0.0682997 | − | 0.247810i | ||||
\(106\) | −13.8659 | −1.34677 | ||||||||
\(107\) | − | 10.4964i | − | 1.01472i | −0.861733 | − | 0.507362i | \(-0.830621\pi\) | ||
0.861733 | − | 0.507362i | \(-0.169379\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 16.0328 | 1.53567 | 0.767833 | − | 0.640651i | \(-0.221335\pi\) | ||||
0.767833 | + | 0.640651i | \(0.221335\pi\) | |||||||
\(110\) | −1.77209 | + | 0.488411i | −0.168962 | + | 0.0465682i | ||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | − | 1.17795i | − | 0.111306i | ||||||
\(113\) | 3.46288i | 0.325760i | 0.986646 | + | 0.162880i | \(0.0520784\pi\) | ||||
−0.986646 | + | 0.162880i | \(0.947922\pi\) | |||||||
\(114\) | 1.29400 | 0.121194 | ||||||||
\(115\) | 16.5657 | − | 4.56574i | 1.54476 | − | 0.425758i | ||||
\(116\) | 9.23916 | 0.857834 | ||||||||
\(117\) | − | 1.74983i | − | 0.161772i | ||||||
\(118\) | − | 3.18827i | − | 0.293505i | ||||||
\(119\) | 4.64719 | 0.426008 | ||||||||
\(120\) | −0.594137 | − | 2.15569i | −0.0542371 | − | 0.196787i | ||||
\(121\) | −10.3242 | −0.938567 | ||||||||
\(122\) | 8.78333i | 0.795205i | ||||||||
\(123\) | − | 2.50671i | − | 0.226022i | ||||||
\(124\) | 9.30433 | 0.835553 | ||||||||
\(125\) | 8.07314 | + | 7.73462i | 0.722084 | + | 0.691806i | ||||
\(126\) | −1.17795 | −0.104940 | ||||||||
\(127\) | − | 17.7498i | − | 1.57504i | −0.616287 | − | 0.787521i | \(-0.711364\pi\) | ||
0.616287 | − | 0.787521i | \(-0.288636\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 2.92778 | 0.257776 | ||||||||
\(130\) | 1.03964 | + | 3.77209i | 0.0911823 | + | 0.330834i | ||||
\(131\) | −17.3248 | −1.51367 | −0.756837 | − | 0.653603i | \(-0.773257\pi\) | ||||
−0.756837 | + | 0.653603i | \(0.773257\pi\) | |||||||
\(132\) | 0.822051i | 0.0715503i | ||||||||
\(133\) | 1.52427i | 0.132171i | ||||||||
\(134\) | −15.2108 | −1.31401 | ||||||||
\(135\) | −2.15569 | + | 0.594137i | −0.185532 | + | 0.0511352i | ||||
\(136\) | 3.94516 | 0.338294 | ||||||||
\(137\) | 1.59958i | 0.136662i | 0.997663 | + | 0.0683308i | \(0.0217673\pi\) | ||||
−0.997663 | + | 0.0683308i | \(0.978233\pi\) | |||||||
\(138\) | − | 7.68466i | − | 0.654162i | ||||||
\(139\) | −13.5364 | −1.14815 | −0.574073 | − | 0.818804i | \(-0.694637\pi\) | ||||
−0.574073 | + | 0.818804i | \(0.694637\pi\) | |||||||
\(140\) | 2.53929 | − | 0.699864i | 0.214609 | − | 0.0591493i | ||||
\(141\) | 7.18827 | 0.605362 | ||||||||
\(142\) | − | 6.65317i | − | 0.558322i | ||||||
\(143\) | − | 1.43845i | − | 0.120289i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 5.48933 | + | 19.9168i | 0.455864 | + | 1.65400i | ||||
\(146\) | 11.9168 | 0.986238 | ||||||||
\(147\) | 5.61244i | 0.462906i | ||||||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | 5.82080 | 0.476858 | 0.238429 | − | 0.971160i | \(-0.423368\pi\) | ||||
0.238429 | + | 0.971160i | \(0.423368\pi\) | |||||||
\(150\) | 4.29400 | − | 2.56155i | 0.350604 | − | 0.209150i | ||||
\(151\) | −6.62672 | −0.539275 | −0.269638 | − | 0.962962i | \(-0.586904\pi\) | ||||
−0.269638 | + | 0.962962i | \(0.586904\pi\) | |||||||
\(152\) | 1.29400i | 0.104957i | ||||||||
\(153\) | − | 3.94516i | − | 0.318947i | ||||||
\(154\) | −0.968334 | −0.0780306 | ||||||||
\(155\) | 5.52805 | + | 20.0572i | 0.444024 | + | 1.61104i | ||||
\(156\) | 1.74983 | 0.140098 | ||||||||
\(157\) | − | 13.5505i | − | 1.08145i | −0.841199 | − | 0.540725i | \(-0.818150\pi\) | ||
0.841199 | − | 0.540725i | \(-0.181850\pi\) | |||||||
\(158\) | 0.797618i | 0.0634551i | ||||||||
\(159\) | −13.8659 | −1.09964 | ||||||||
\(160\) | 2.15569 | − | 0.594137i | 0.170422 | − | 0.0469707i | ||||
\(161\) | 9.05214 | 0.713408 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − | 3.45457i | − | 0.270583i | −0.990806 | − | 0.135291i | \(-0.956803\pi\) | ||
0.990806 | − | 0.135291i | \(-0.0431971\pi\) | |||||||
\(164\) | 2.50671 | 0.195741 | ||||||||
\(165\) | −1.77209 | + | 0.488411i | −0.137957 | + | 0.0380228i | ||||
\(166\) | −7.72918 | −0.599900 | ||||||||
\(167\) | − | 0.294690i | − | 0.0228038i | −0.999935 | − | 0.0114019i | \(-0.996371\pi\) | ||
0.999935 | − | 0.0114019i | \(-0.00362942\pi\) | |||||||
\(168\) | − | 1.17795i | − | 0.0908808i | ||||||
\(169\) | 9.93810 | 0.764469 | ||||||||
\(170\) | 2.34397 | + | 8.50454i | 0.179774 | + | 0.652268i | ||||
\(171\) | 1.29400 | 0.0989548 | ||||||||
\(172\) | 2.92778i | 0.223241i | ||||||||
\(173\) | 12.9542i | 0.984892i | 0.870343 | + | 0.492446i | \(0.163897\pi\) | ||||
−0.870343 | + | 0.492446i | \(0.836103\pi\) | |||||||
\(174\) | 9.23916 | 0.700419 | ||||||||
\(175\) | 3.01738 | + | 5.05812i | 0.228092 | + | 0.382358i | ||||
\(176\) | −0.822051 | −0.0619644 | ||||||||
\(177\) | − | 3.18827i | − | 0.239645i | ||||||
\(178\) | − | 14.8729i | − | 1.11477i | ||||||
\(179\) | −20.4990 | −1.53216 | −0.766082 | − | 0.642742i | \(-0.777797\pi\) | ||||
−0.766082 | + | 0.642742i | \(0.777797\pi\) | |||||||
\(180\) | −0.594137 | − | 2.15569i | −0.0442844 | − | 0.160676i | ||||
\(181\) | 20.1449 | 1.49736 | 0.748680 | − | 0.662932i | \(-0.230688\pi\) | ||||
0.748680 | + | 0.662932i | \(0.230688\pi\) | |||||||
\(182\) | 2.06121i | 0.152787i | ||||||||
\(183\) | 8.78333i | 0.649283i | ||||||||
\(184\) | 7.68466 | 0.566521 | ||||||||
\(185\) | −2.15569 | + | 0.594137i | −0.158490 | + | 0.0436819i | ||||
\(186\) | 9.30433 | 0.682226 | ||||||||
\(187\) | − | 3.24312i | − | 0.237160i | ||||||
\(188\) | 7.18827i | 0.524259i | ||||||||
\(189\) | −1.17795 | −0.0856832 | ||||||||
\(190\) | −2.78947 | + | 0.768815i | −0.202369 | + | 0.0557757i | ||||
\(191\) | −1.59902 | −0.115701 | −0.0578504 | − | 0.998325i | \(-0.518425\pi\) | ||||
−0.0578504 | + | 0.998325i | \(0.518425\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | − | 4.53510i | − | 0.326444i | −0.986589 | − | 0.163222i | \(-0.947811\pi\) | ||
0.986589 | − | 0.163222i | \(-0.0521887\pi\) | |||||||
\(194\) | 13.0947 | 0.940146 | ||||||||
\(195\) | 1.03964 | + | 3.77209i | 0.0744500 | + | 0.270125i | ||||
\(196\) | −5.61244 | −0.400888 | ||||||||
\(197\) | 3.14956i | 0.224397i | 0.993686 | + | 0.112198i | \(0.0357892\pi\) | ||||
−0.993686 | + | 0.112198i | \(0.964211\pi\) | |||||||
\(198\) | 0.822051i | 0.0584206i | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 2.56155 | + | 4.29400i | 0.181129 | + | 0.303632i | ||||
\(201\) | −15.2108 | −1.07288 | ||||||||
\(202\) | 2.00000i | 0.140720i | ||||||||
\(203\) | 10.8833i | 0.763855i | ||||||||
\(204\) | 3.94516 | 0.276216 | ||||||||
\(205\) | 1.48933 | + | 5.40369i | 0.104019 | + | 0.377410i | ||||
\(206\) | −19.6666 | −1.37024 | ||||||||
\(207\) | − | 7.68466i | − | 0.534121i | ||||||
\(208\) | 1.74983i | 0.121329i | ||||||||
\(209\) | 1.06373 | 0.0735801 | ||||||||
\(210\) | 2.53929 | − | 0.699864i | 0.175228 | − | 0.0482952i | ||||
\(211\) | 0.0954006 | 0.00656765 | 0.00328383 | − | 0.999995i | \(-0.498955\pi\) | ||||
0.00328383 | + | 0.999995i | \(0.498955\pi\) | |||||||
\(212\) | − | 13.8659i | − | 0.952313i | ||||||
\(213\) | − | 6.65317i | − | 0.455868i | ||||||
\(214\) | 10.4964 | 0.717518 | ||||||||
\(215\) | −6.31138 | + | 1.73950i | −0.430433 | + | 0.118633i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.9600i | 0.744015i | ||||||||
\(218\) | 16.0328i | 1.08588i | ||||||||
\(219\) | 11.9168 | 0.805260 | ||||||||
\(220\) | −0.488411 | − | 1.77209i | −0.0329287 | − | 0.119474i | ||||
\(221\) | −6.90334 | −0.464369 | ||||||||
\(222\) | 1.00000i | 0.0671156i | ||||||||
\(223\) | 10.5512i | 0.706562i | 0.935517 | + | 0.353281i | \(0.114934\pi\) | ||||
−0.935517 | + | 0.353281i | \(0.885066\pi\) | |||||||
\(224\) | 1.17795 | 0.0787050 | ||||||||
\(225\) | 4.29400 | − | 2.56155i | 0.286267 | − | 0.170770i | ||||
\(226\) | −3.46288 | −0.230347 | ||||||||
\(227\) | 10.1063i | 0.670778i | 0.942080 | + | 0.335389i | \(0.108868\pi\) | ||||
−0.942080 | + | 0.335389i | \(0.891132\pi\) | |||||||
\(228\) | 1.29400i | 0.0856973i | ||||||||
\(229\) | −4.81173 | −0.317968 | −0.158984 | − | 0.987281i | \(-0.550822\pi\) | ||||
−0.158984 | + | 0.987281i | \(0.550822\pi\) | |||||||
\(230\) | 4.56574 | + | 16.5657i | 0.301056 | + | 1.09231i | ||||
\(231\) | −0.968334 | −0.0637117 | ||||||||
\(232\) | 9.23916i | 0.606580i | ||||||||
\(233\) | − | 11.6014i | − | 0.760034i | −0.924979 | − | 0.380017i | \(-0.875918\pi\) | ||
0.924979 | − | 0.380017i | \(-0.124082\pi\) | |||||||
\(234\) | 1.74983 | 0.114390 | ||||||||
\(235\) | −15.4957 | + | 4.27082i | −1.01083 | + | 0.278598i | ||||
\(236\) | 3.18827 | 0.207539 | ||||||||
\(237\) | 0.797618i | 0.0518108i | ||||||||
\(238\) | 4.64719i | 0.301233i | ||||||||
\(239\) | 23.1599 | 1.49809 | 0.749044 | − | 0.662520i | \(-0.230513\pi\) | ||||
0.749044 | + | 0.662520i | \(0.230513\pi\) | |||||||
\(240\) | 2.15569 | − | 0.594137i | 0.139149 | − | 0.0383514i | ||||
\(241\) | −12.7020 | −0.818210 | −0.409105 | − | 0.912487i | \(-0.634159\pi\) | ||||
−0.409105 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(242\) | − | 10.3242i | − | 0.663667i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −8.78333 | −0.562295 | ||||||||
\(245\) | −3.33456 | − | 12.0987i | −0.213037 | − | 0.772956i | ||||
\(246\) | 2.50671 | 0.159822 | ||||||||
\(247\) | − | 2.26428i | − | 0.144073i | ||||||
\(248\) | 9.30433i | 0.590825i | ||||||||
\(249\) | −7.72918 | −0.489817 | ||||||||
\(250\) | −7.73462 | + | 8.07314i | −0.489180 | + | 0.510590i | ||||
\(251\) | −13.5203 | −0.853394 | −0.426697 | − | 0.904395i | \(-0.640323\pi\) | ||||
−0.426697 | + | 0.904395i | \(0.640323\pi\) | |||||||
\(252\) | − | 1.17795i | − | 0.0742038i | ||||||
\(253\) | − | 6.31718i | − | 0.397158i | ||||||
\(254\) | 17.7498 | 1.11372 | ||||||||
\(255\) | 2.34397 | + | 8.50454i | 0.146785 | + | 0.532575i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.07097i | 0.378697i | 0.981910 | + | 0.189348i | \(0.0606375\pi\) | ||||
−0.981910 | + | 0.189348i | \(0.939362\pi\) | |||||||
\(258\) | 2.92778i | 0.182275i | ||||||||
\(259\) | −1.17795 | −0.0731942 | ||||||||
\(260\) | −3.77209 | + | 1.03964i | −0.233935 | + | 0.0644756i | ||||
\(261\) | 9.23916 | 0.571890 | ||||||||
\(262\) | − | 17.3248i | − | 1.07033i | ||||||
\(263\) | 18.0064i | 1.11032i | 0.831744 | + | 0.555160i | \(0.187343\pi\) | ||||
−0.831744 | + | 0.555160i | \(0.812657\pi\) | |||||||
\(264\) | −0.822051 | −0.0505937 | ||||||||
\(265\) | 29.8905 | − | 8.23824i | 1.83616 | − | 0.506071i | ||||
\(266\) | −1.52427 | −0.0934589 | ||||||||
\(267\) | − | 14.8729i | − | 0.910209i | ||||||
\(268\) | − | 15.2108i | − | 0.929145i | ||||||
\(269\) | −6.54745 | −0.399205 | −0.199602 | − | 0.979877i | \(-0.563965\pi\) | ||||
−0.199602 | + | 0.979877i | \(0.563965\pi\) | |||||||
\(270\) | −0.594137 | − | 2.15569i | −0.0361581 | − | 0.131191i | ||||
\(271\) | 25.4776 | 1.54766 | 0.773828 | − | 0.633396i | \(-0.218340\pi\) | ||||
0.773828 | + | 0.633396i | \(0.218340\pi\) | |||||||
\(272\) | 3.94516i | 0.239210i | ||||||||
\(273\) | 2.06121i | 0.124750i | ||||||||
\(274\) | −1.59958 | −0.0966344 | ||||||||
\(275\) | 3.52989 | − | 2.10573i | 0.212860 | − | 0.126980i | ||||
\(276\) | 7.68466 | 0.462562 | ||||||||
\(277\) | 1.74983i | 0.105137i | 0.998617 | + | 0.0525685i | \(0.0167408\pi\) | ||||
−0.998617 | + | 0.0525685i | \(0.983259\pi\) | |||||||
\(278\) | − | 13.5364i | − | 0.811861i | ||||||
\(279\) | 9.30433 | 0.557035 | ||||||||
\(280\) | 0.699864 | + | 2.53929i | 0.0418249 | + | 0.151752i | ||||
\(281\) | 21.1927 | 1.26425 | 0.632125 | − | 0.774866i | \(-0.282183\pi\) | ||||
0.632125 | + | 0.774866i | \(0.282183\pi\) | |||||||
\(282\) | 7.18827i | 0.428056i | ||||||||
\(283\) | 29.6420i | 1.76203i | 0.473086 | + | 0.881016i | \(0.343140\pi\) | ||||
−0.473086 | + | 0.881016i | \(0.656860\pi\) | |||||||
\(284\) | 6.65317 | 0.394793 | ||||||||
\(285\) | −2.78947 | + | 0.768815i | −0.165234 | + | 0.0455407i | ||||
\(286\) | 1.43845 | 0.0850572 | ||||||||
\(287\) | 2.95278i | 0.174297i | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 1.43574 | 0.0844554 | ||||||||
\(290\) | −19.9168 | + | 5.48933i | −1.16955 | + | 0.322345i | ||||
\(291\) | 13.0947 | 0.767626 | ||||||||
\(292\) | 11.9168i | 0.697376i | ||||||||
\(293\) | 20.7555i | 1.21255i | 0.795255 | + | 0.606275i | \(0.207337\pi\) | ||||
−0.795255 | + | 0.606275i | \(0.792663\pi\) | |||||||
\(294\) | −5.61244 | −0.327324 | ||||||||
\(295\) | 1.89427 | + | 6.87293i | 0.110289 | + | 0.400158i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0.822051i | 0.0477002i | ||||||||
\(298\) | 5.82080i | 0.337190i | ||||||||
\(299\) | −13.4468 | −0.777650 | ||||||||
\(300\) | 2.56155 | + | 4.29400i | 0.147891 | + | 0.247914i | ||||
\(301\) | −3.44877 | −0.198784 | ||||||||
\(302\) | − | 6.62672i | − | 0.381325i | ||||||
\(303\) | 2.00000i | 0.114897i | ||||||||
\(304\) | −1.29400 | −0.0742161 | ||||||||
\(305\) | −5.21851 | − | 18.9341i | −0.298811 | − | 1.08417i | ||||
\(306\) | 3.94516 | 0.225530 | ||||||||
\(307\) | − | 17.1315i | − | 0.977746i | −0.872355 | − | 0.488873i | \(-0.837408\pi\) | ||
0.872355 | − | 0.488873i | \(-0.162592\pi\) | |||||||
\(308\) | − | 0.968334i | − | 0.0551760i | ||||||
\(309\) | −19.6666 | −1.11879 | ||||||||
\(310\) | −20.0572 | + | 5.52805i | −1.13918 | + | 0.313972i | ||||
\(311\) | 29.1740 | 1.65431 | 0.827153 | − | 0.561977i | \(-0.189959\pi\) | ||||
0.827153 | + | 0.561977i | \(0.189959\pi\) | |||||||
\(312\) | 1.74983i | 0.0990645i | ||||||||
\(313\) | − | 20.0714i | − | 1.13450i | −0.823546 | − | 0.567250i | \(-0.808007\pi\) | ||
0.823546 | − | 0.567250i | \(-0.191993\pi\) | |||||||
\(314\) | 13.5505 | 0.764701 | ||||||||
\(315\) | 2.53929 | − | 0.699864i | 0.143073 | − | 0.0394329i | ||||
\(316\) | −0.797618 | −0.0448695 | ||||||||
\(317\) | − | 20.7084i | − | 1.16310i | −0.813511 | − | 0.581550i | \(-0.802447\pi\) | ||
0.813511 | − | 0.581550i | \(-0.197553\pi\) | |||||||
\(318\) | − | 13.8659i | − | 0.777560i | ||||||
\(319\) | 7.59506 | 0.425242 | ||||||||
\(320\) | 0.594137 | + | 2.15569i | 0.0332133 | + | 0.120507i | ||||
\(321\) | 10.4964 | 0.585851 | ||||||||
\(322\) | 9.05214i | 0.504456i | ||||||||
\(323\) | − | 5.10504i | − | 0.284052i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −4.48228 | − | 7.51376i | −0.248632 | − | 0.416789i | ||||
\(326\) | 3.45457 | 0.191331 | ||||||||
\(327\) | 16.0328i | 0.886617i | ||||||||
\(328\) | 2.50671i | 0.138410i | ||||||||
\(329\) | −8.46742 | −0.466824 | ||||||||
\(330\) | −0.488411 | − | 1.77209i | −0.0268861 | − | 0.0975502i | ||||
\(331\) | −18.3339 | −1.00772 | −0.503860 | − | 0.863785i | \(-0.668087\pi\) | ||||
−0.503860 | + | 0.863785i | \(0.668087\pi\) | |||||||
\(332\) | − | 7.72918i | − | 0.424194i | ||||||
\(333\) | 1.00000i | 0.0547997i | ||||||||
\(334\) | 0.294690 | 0.0161247 | ||||||||
\(335\) | 32.7897 | − | 9.03728i | 1.79149 | − | 0.493760i | ||||
\(336\) | 1.17795 | 0.0642624 | ||||||||
\(337\) | − | 32.8607i | − | 1.79003i | −0.446032 | − | 0.895017i | \(-0.647163\pi\) | ||
0.446032 | − | 0.895017i | \(-0.352837\pi\) | |||||||
\(338\) | 9.93810i | 0.540562i | ||||||||
\(339\) | −3.46288 | −0.188078 | ||||||||
\(340\) | −8.50454 | + | 2.34397i | −0.461223 | + | 0.127119i | ||||
\(341\) | 7.64863 | 0.414196 | ||||||||
\(342\) | 1.29400i | 0.0699716i | ||||||||
\(343\) | − | 14.8568i | − | 0.802192i | ||||||
\(344\) | −2.92778 | −0.157855 | ||||||||
\(345\) | 4.56574 | + | 16.5657i | 0.245811 | + | 0.891870i | ||||
\(346\) | −12.9542 | −0.696424 | ||||||||
\(347\) | 20.5369i | 1.10248i | 0.834346 | + | 0.551240i | \(0.185845\pi\) | ||||
−0.834346 | + | 0.551240i | \(0.814155\pi\) | |||||||
\(348\) | 9.23916i | 0.495271i | ||||||||
\(349\) | 3.99024 | 0.213593 | 0.106796 | − | 0.994281i | \(-0.465941\pi\) | ||||
0.106796 | + | 0.994281i | \(0.465941\pi\) | |||||||
\(350\) | −5.05812 | + | 3.01738i | −0.270368 | + | 0.161286i | ||||
\(351\) | 1.74983 | 0.0933989 | ||||||||
\(352\) | − | 0.822051i | − | 0.0438155i | ||||||
\(353\) | − | 19.2964i | − | 1.02704i | −0.858076 | − | 0.513522i | \(-0.828340\pi\) | ||
0.858076 | − | 0.513522i | \(-0.171660\pi\) | |||||||
\(354\) | 3.18827 | 0.169455 | ||||||||
\(355\) | 3.95290 | + | 14.3422i | 0.209798 | + | 0.761204i | ||||
\(356\) | 14.8729 | 0.788264 | ||||||||
\(357\) | 4.64719i | 0.245956i | ||||||||
\(358\) | − | 20.4990i | − | 1.08340i | ||||||
\(359\) | 8.39904 | 0.443284 | 0.221642 | − | 0.975128i | \(-0.428858\pi\) | ||||
0.221642 | + | 0.975128i | \(0.428858\pi\) | |||||||
\(360\) | 2.15569 | − | 0.594137i | 0.113615 | − | 0.0313138i | ||||
\(361\) | −17.3256 | −0.911872 | ||||||||
\(362\) | 20.1449i | 1.05879i | ||||||||
\(363\) | − | 10.3242i | − | 0.541882i | ||||||
\(364\) | −2.06121 | −0.108037 | ||||||||
\(365\) | −25.6888 | + | 7.08020i | −1.34462 | + | 0.370594i | ||||
\(366\) | −8.78333 | −0.459112 | ||||||||
\(367\) | 17.5325i | 0.915187i | 0.889161 | + | 0.457594i | \(0.151289\pi\) | ||||
−0.889161 | + | 0.457594i | \(0.848711\pi\) | |||||||
\(368\) | 7.68466i | 0.400591i | ||||||||
\(369\) | 2.50671 | 0.130494 | ||||||||
\(370\) | −0.594137 | − | 2.15569i | −0.0308877 | − | 0.112069i | ||||
\(371\) | 16.3333 | 0.847983 | ||||||||
\(372\) | 9.30433i | 0.482407i | ||||||||
\(373\) | 26.4479i | 1.36942i | 0.728815 | + | 0.684710i | \(0.240071\pi\) | ||||
−0.728815 | + | 0.684710i | \(0.759929\pi\) | |||||||
\(374\) | 3.24312 | 0.167698 | ||||||||
\(375\) | −7.73462 | + | 8.07314i | −0.399414 | + | 0.416895i | ||||
\(376\) | −7.18827 | −0.370707 | ||||||||
\(377\) | − | 16.1669i | − | 0.832639i | ||||||
\(378\) | − | 1.17795i | − | 0.0605872i | ||||||
\(379\) | −21.3596 | −1.09717 | −0.548583 | − | 0.836096i | \(-0.684833\pi\) | ||||
−0.548583 | + | 0.836096i | \(0.684833\pi\) | |||||||
\(380\) | −0.768815 | − | 2.78947i | −0.0394394 | − | 0.143097i | ||||
\(381\) | 17.7498 | 0.909351 | ||||||||
\(382\) | − | 1.59902i | − | 0.0818128i | ||||||
\(383\) | − | 27.0258i | − | 1.38095i | −0.723355 | − | 0.690476i | \(-0.757401\pi\) | ||
0.723355 | − | 0.690476i | \(-0.242599\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.08743 | − | 0.575324i | 0.106385 | − | 0.0293212i | ||||
\(386\) | 4.53510 | 0.230831 | ||||||||
\(387\) | 2.92778i | 0.148827i | ||||||||
\(388\) | 13.0947i | 0.664783i | ||||||||
\(389\) | 14.3786 | 0.729022 | 0.364511 | − | 0.931199i | \(-0.381236\pi\) | ||||
0.364511 | + | 0.931199i | \(0.381236\pi\) | |||||||
\(390\) | −3.77209 | + | 1.03964i | −0.191007 | + | 0.0526441i | ||||
\(391\) | −30.3172 | −1.53321 | ||||||||
\(392\) | − | 5.61244i | − | 0.283471i | ||||||
\(393\) | − | 17.3248i | − | 0.873921i | ||||||
\(394\) | −3.14956 | −0.158672 | ||||||||
\(395\) | −0.473895 | − | 1.71942i | −0.0238442 | − | 0.0865133i | ||||
\(396\) | −0.822051 | −0.0413096 | ||||||||
\(397\) | − | 28.2383i | − | 1.41724i | −0.705591 | − | 0.708620i | \(-0.749318\pi\) | ||
0.705591 | − | 0.708620i | \(-0.250682\pi\) | |||||||
\(398\) | 8.00000i | 0.401004i | ||||||||
\(399\) | −1.52427 | −0.0763088 | ||||||||
\(400\) | −4.29400 | + | 2.56155i | −0.214700 | + | 0.128078i | ||||
\(401\) | 9.70096 | 0.484443 | 0.242221 | − | 0.970221i | \(-0.422124\pi\) | ||||
0.242221 | + | 0.970221i | \(0.422124\pi\) | |||||||
\(402\) | − | 15.2108i | − | 0.758644i | ||||||
\(403\) | − | 16.2810i | − | 0.811013i | ||||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | −0.594137 | − | 2.15569i | −0.0295229 | − | 0.107117i | ||||
\(406\) | −10.8833 | −0.540127 | ||||||||
\(407\) | 0.822051i | 0.0407475i | ||||||||
\(408\) | 3.94516i | 0.195314i | ||||||||
\(409\) | 26.8103 | 1.32569 | 0.662843 | − | 0.748758i | \(-0.269350\pi\) | ||||
0.662843 | + | 0.748758i | \(0.269350\pi\) | |||||||
\(410\) | −5.40369 | + | 1.48933i | −0.266869 | + | 0.0735528i | ||||
\(411\) | −1.59958 | −0.0789016 | ||||||||
\(412\) | − | 19.6666i | − | 0.968903i | ||||||
\(413\) | 3.75563i | 0.184802i | ||||||||
\(414\) | 7.68466 | 0.377680 | ||||||||
\(415\) | 16.6617 | − | 4.59219i | 0.817891 | − | 0.225422i | ||||
\(416\) | −1.74983 | −0.0857924 | ||||||||
\(417\) | − | 13.5364i | − | 0.662882i | ||||||
\(418\) | 1.06373i | 0.0520290i | ||||||||
\(419\) | 21.2275 | 1.03703 | 0.518514 | − | 0.855069i | \(-0.326485\pi\) | ||||
0.518514 | + | 0.855069i | \(0.326485\pi\) | |||||||
\(420\) | 0.699864 | + | 2.53929i | 0.0341499 | + | 0.123905i | ||||
\(421\) | 6.40880 | 0.312346 | 0.156173 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156173 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(422\) | 0.0954006i | 0.00464403i | ||||||||
\(423\) | 7.18827i | 0.349506i | ||||||||
\(424\) | 13.8659 | 0.673387 | ||||||||
\(425\) | −10.1057 | − | 16.9405i | −0.490200 | − | 0.821735i | ||||
\(426\) | 6.65317 | 0.322347 | ||||||||
\(427\) | − | 10.3463i | − | 0.500693i | ||||||
\(428\) | 10.4964i | 0.507362i | ||||||||
\(429\) | 1.43845 | 0.0694489 | ||||||||
\(430\) | −1.73950 | − | 6.31138i | −0.0838862 | − | 0.304362i | ||||
\(431\) | 1.41981 | 0.0683900 | 0.0341950 | − | 0.999415i | \(-0.489113\pi\) | ||||
0.0341950 | + | 0.999415i | \(0.489113\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 6.06121i | 0.291283i | 0.989337 | + | 0.145642i | \(0.0465246\pi\) | ||||
−0.989337 | + | 0.145642i | \(0.953475\pi\) | |||||||
\(434\) | −10.9600 | −0.526098 | ||||||||
\(435\) | −19.9168 | + | 5.48933i | −0.954936 | + | 0.263193i | ||||
\(436\) | −16.0328 | −0.767833 | ||||||||
\(437\) | − | 9.94396i | − | 0.475684i | ||||||
\(438\) | 11.9168i | 0.569405i | ||||||||
\(439\) | −6.54147 | −0.312207 | −0.156104 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156104 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(440\) | 1.77209 | − | 0.488411i | 0.0844809 | − | 0.0232841i | ||||
\(441\) | −5.61244 | −0.267259 | ||||||||
\(442\) | − | 6.90334i | − | 0.328359i | ||||||
\(443\) | − | 4.04887i | − | 0.192367i | −0.995364 | − | 0.0961837i | \(-0.969336\pi\) | ||
0.995364 | − | 0.0961837i | \(-0.0306636\pi\) | |||||||
\(444\) | −1.00000 | −0.0474579 | ||||||||
\(445\) | 8.83657 | + | 32.0614i | 0.418893 | + | 1.51986i | ||||
\(446\) | −10.5512 | −0.499615 | ||||||||
\(447\) | 5.82080i | 0.275314i | ||||||||
\(448\) | 1.17795i | 0.0556529i | ||||||||
\(449\) | 2.45148 | 0.115692 | 0.0578462 | − | 0.998326i | \(-0.481577\pi\) | ||||
0.0578462 | + | 0.998326i | \(0.481577\pi\) | |||||||
\(450\) | 2.56155 | + | 4.29400i | 0.120753 | + | 0.202421i | ||||
\(451\) | 2.06064 | 0.0970318 | ||||||||
\(452\) | − | 3.46288i | − | 0.162880i | ||||||
\(453\) | − | 6.62672i | − | 0.311351i | ||||||
\(454\) | −10.1063 | −0.474312 | ||||||||
\(455\) | −1.22464 | − | 4.44333i | −0.0574121 | − | 0.208306i | ||||
\(456\) | −1.29400 | −0.0605972 | ||||||||
\(457\) | 6.87237i | 0.321476i | 0.986997 | + | 0.160738i | \(0.0513874\pi\) | ||||
−0.986997 | + | 0.160738i | \(0.948613\pi\) | |||||||
\(458\) | − | 4.81173i | − | 0.224837i | ||||||
\(459\) | 3.94516 | 0.184144 | ||||||||
\(460\) | −16.5657 | + | 4.56574i | −0.772382 | + | 0.212879i | ||||
\(461\) | −1.07222 | −0.0499384 | −0.0249692 | − | 0.999688i | \(-0.507949\pi\) | ||||
−0.0249692 | + | 0.999688i | \(0.507949\pi\) | |||||||
\(462\) | − | 0.968334i | − | 0.0450510i | ||||||
\(463\) | 29.3791i | 1.36536i | 0.730717 | + | 0.682681i | \(0.239186\pi\) | ||||
−0.730717 | + | 0.682681i | \(0.760814\pi\) | |||||||
\(464\) | −9.23916 | −0.428917 | ||||||||
\(465\) | −20.0572 | + | 5.52805i | −0.930133 | + | 0.256357i | ||||
\(466\) | 11.6014 | 0.537425 | ||||||||
\(467\) | 6.56099i | 0.303606i | 0.988411 | + | 0.151803i | \(0.0485080\pi\) | ||||
−0.988411 | + | 0.151803i | \(0.951492\pi\) | |||||||
\(468\) | 1.74983i | 0.0808858i | ||||||||
\(469\) | 17.9175 | 0.827354 | ||||||||
\(470\) | −4.27082 | − | 15.4957i | −0.196998 | − | 0.714763i | ||||
\(471\) | 13.5505 | 0.624376 | ||||||||
\(472\) | 3.18827i | 0.146752i | ||||||||
\(473\) | 2.40678i | 0.110664i | ||||||||
\(474\) | −0.797618 | −0.0366358 | ||||||||
\(475\) | 5.55644 | − | 3.31465i | 0.254947 | − | 0.152087i | ||||
\(476\) | −4.64719 | −0.213004 | ||||||||
\(477\) | − | 13.8659i | − | 0.634875i | ||||||
\(478\) | 23.1599i | 1.05931i | ||||||||
\(479\) | −2.93948 | −0.134308 | −0.0671541 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671541 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(480\) | 0.594137 | + | 2.15569i | 0.0271185 | + | 0.0983934i | ||||
\(481\) | 1.74983 | 0.0797853 | ||||||||
\(482\) | − | 12.7020i | − | 0.578562i | ||||||
\(483\) | 9.05214i | 0.411887i | ||||||||
\(484\) | 10.3242 | 0.469283 | ||||||||
\(485\) | −28.2281 | + | 7.78006i | −1.28177 | + | 0.353274i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 31.1217i | 1.41026i | 0.709078 | + | 0.705130i | \(0.249111\pi\) | ||||
−0.709078 | + | 0.705130i | \(0.750889\pi\) | |||||||
\(488\) | − | 8.78333i | − | 0.397603i | ||||||
\(489\) | 3.45457 | 0.156221 | ||||||||
\(490\) | 12.0987 | − | 3.33456i | 0.546562 | − | 0.150640i | ||||
\(491\) | −4.69373 | −0.211825 | −0.105913 | − | 0.994375i | \(-0.533776\pi\) | ||||
−0.105913 | + | 0.994375i | \(0.533776\pi\) | |||||||
\(492\) | 2.50671i | 0.113011i | ||||||||
\(493\) | − | 36.4499i | − | 1.64162i | ||||||
\(494\) | 2.26428 | 0.101875 | ||||||||
\(495\) | −0.488411 | − | 1.77209i | −0.0219524 | − | 0.0796494i | ||||
\(496\) | −9.30433 | −0.417777 | ||||||||
\(497\) | 7.83710i | 0.351542i | ||||||||
\(498\) | − | 7.72918i | − | 0.346353i | ||||||
\(499\) | −8.72527 | −0.390597 | −0.195298 | − | 0.980744i | \(-0.562568\pi\) | ||||
−0.195298 | + | 0.980744i | \(0.562568\pi\) | |||||||
\(500\) | −8.07314 | − | 7.73462i | −0.361042 | − | 0.345903i | ||||
\(501\) | 0.294690 | 0.0131658 | ||||||||
\(502\) | − | 13.5203i | − | 0.603441i | ||||||
\(503\) | 1.77444i | 0.0791184i | 0.999217 | + | 0.0395592i | \(0.0125954\pi\) | ||||
−0.999217 | + | 0.0395592i | \(0.987405\pi\) | |||||||
\(504\) | 1.17795 | 0.0524700 | ||||||||
\(505\) | −1.18827 | − | 4.31138i | −0.0528775 | − | 0.191854i | ||||
\(506\) | 6.31718 | 0.280833 | ||||||||
\(507\) | 9.93810i | 0.441367i | ||||||||
\(508\) | 17.7498i | 0.787521i | ||||||||
\(509\) | −31.1134 | −1.37908 | −0.689539 | − | 0.724249i | \(-0.742187\pi\) | ||||
−0.689539 | + | 0.724249i | \(0.742187\pi\) | |||||||
\(510\) | −8.50454 | + | 2.34397i | −0.376587 | + | 0.103793i | ||||
\(511\) | −14.0373 | −0.620975 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.29400i | 0.0571316i | ||||||||
\(514\) | −6.07097 | −0.267779 | ||||||||
\(515\) | 42.3951 | − | 11.6847i | 1.86815 | − | 0.514888i | ||||
\(516\) | −2.92778 | −0.128888 | ||||||||
\(517\) | 5.90913i | 0.259883i | ||||||||
\(518\) | − | 1.17795i | − | 0.0517561i | ||||||
\(519\) | −12.9542 | −0.568627 | ||||||||
\(520\) | −1.03964 | − | 3.77209i | −0.0455912 | − | 0.165417i | ||||
\(521\) | −12.6961 | −0.556228 | −0.278114 | − | 0.960548i | \(-0.589709\pi\) | ||||
−0.278114 | + | 0.960548i | \(0.589709\pi\) | |||||||
\(522\) | 9.23916i | 0.404387i | ||||||||
\(523\) | − | 38.1210i | − | 1.66692i | −0.552582 | − | 0.833458i | \(-0.686358\pi\) | ||
0.552582 | − | 0.833458i | \(-0.313642\pi\) | |||||||
\(524\) | 17.3248 | 0.756837 | ||||||||
\(525\) | −5.05812 | + | 3.01738i | −0.220754 | + | 0.131689i | ||||
\(526\) | −18.0064 | −0.785115 | ||||||||
\(527\) | − | 36.7070i | − | 1.59898i | ||||||
\(528\) | − | 0.822051i | − | 0.0357752i | ||||||
\(529\) | −36.0540 | −1.56756 | ||||||||
\(530\) | 8.23824 | + | 29.8905i | 0.357846 | + | 1.29836i | ||||
\(531\) | 3.18827 | 0.138359 | ||||||||
\(532\) | − | 1.52427i | − | 0.0660854i | ||||||
\(533\) | − | 4.38631i | − | 0.189992i | ||||||
\(534\) | 14.8729 | 0.643615 | ||||||||
\(535\) | −22.6270 | + | 6.23629i | −0.978248 | + | 0.269619i | ||||
\(536\) | 15.2108 | 0.657005 | ||||||||
\(537\) | − | 20.4990i | − | 0.884596i | ||||||
\(538\) | − | 6.54745i | − | 0.282280i | ||||||
\(539\) | −4.61371 | −0.198726 | ||||||||
\(540\) | 2.15569 | − | 0.594137i | 0.0927661 | − | 0.0255676i | ||||
\(541\) | −26.2770 | −1.12974 | −0.564868 | − | 0.825181i | \(-0.691073\pi\) | ||||
−0.564868 | + | 0.825181i | \(0.691073\pi\) | |||||||
\(542\) | 25.4776i | 1.09436i | ||||||||
\(543\) | 20.1449i | 0.864501i | ||||||||
\(544\) | −3.94516 | −0.169147 | ||||||||
\(545\) | −9.52570 | − | 34.5618i | −0.408036 | − | 1.48046i | ||||
\(546\) | −2.06121 | −0.0882116 | ||||||||
\(547\) | 6.61244i | 0.282727i | 0.989958 | + | 0.141364i | \(0.0451487\pi\) | ||||
−0.989958 | + | 0.141364i | \(0.954851\pi\) | |||||||
\(548\) | − | 1.59958i | − | 0.0683308i | ||||||
\(549\) | −8.78333 | −0.374863 | ||||||||
\(550\) | 2.10573 | + | 3.52989i | 0.0897885 | + | 0.150515i | ||||
\(551\) | 11.9555 | 0.509321 | ||||||||
\(552\) | 7.68466i | 0.327081i | ||||||||
\(553\) | − | 0.939553i | − | 0.0399539i | ||||||
\(554\) | −1.74983 | −0.0743431 | ||||||||
\(555\) | −0.594137 | − | 2.15569i | −0.0252197 | − | 0.0915040i | ||||
\(556\) | 13.5364 | 0.574073 | ||||||||
\(557\) | 3.57893i | 0.151644i | 0.997121 | + | 0.0758221i | \(0.0241581\pi\) | ||||
−0.997121 | + | 0.0758221i | \(0.975842\pi\) | |||||||
\(558\) | 9.30433i | 0.393884i | ||||||||
\(559\) | 5.12311 | 0.216684 | ||||||||
\(560\) | −2.53929 | + | 0.699864i | −0.107305 | + | 0.0295746i | ||||
\(561\) | 3.24312 | 0.136925 | ||||||||
\(562\) | 21.1927i | 0.893960i | ||||||||
\(563\) | − | 1.07544i | − | 0.0453243i | −0.999743 | − | 0.0226622i | \(-0.992786\pi\) | ||
0.999743 | − | 0.0226622i | \(-0.00721421\pi\) | |||||||
\(564\) | −7.18827 | −0.302681 | ||||||||
\(565\) | 7.46490 | − | 2.05743i | 0.314051 | − | 0.0865566i | ||||
\(566\) | −29.6420 | −1.24595 | ||||||||
\(567\) | − | 1.17795i | − | 0.0494692i | ||||||
\(568\) | 6.65317i | 0.279161i | ||||||||
\(569\) | −31.8864 | −1.33675 | −0.668373 | − | 0.743827i | \(-0.733009\pi\) | ||||
−0.668373 | + | 0.743827i | \(0.733009\pi\) | |||||||
\(570\) | −0.768815 | − | 2.78947i | −0.0322021 | − | 0.116838i | ||||
\(571\) | −2.21163 | −0.0925539 | −0.0462770 | − | 0.998929i | \(-0.514736\pi\) | ||||
−0.0462770 | + | 0.998929i | \(0.514736\pi\) | |||||||
\(572\) | 1.43845i | 0.0601445i | ||||||||
\(573\) | − | 1.59902i | − | 0.0667999i | ||||||
\(574\) | −2.95278 | −0.123246 | ||||||||
\(575\) | −19.6847 | − | 32.9979i | −0.820907 | − | 1.37611i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.66475i | 0.152566i | 0.997086 | + | 0.0762828i | \(0.0243052\pi\) | ||||
−0.997086 | + | 0.0762828i | \(0.975695\pi\) | |||||||
\(578\) | 1.43574i | 0.0597190i | ||||||||
\(579\) | 4.53510 | 0.188472 | ||||||||
\(580\) | −5.48933 | − | 19.9168i | −0.227932 | − | 0.826999i | ||||
\(581\) | 9.10458 | 0.377722 | ||||||||
\(582\) | 13.0947i | 0.542793i | ||||||||
\(583\) | − | 11.3985i | − | 0.472076i | ||||||
\(584\) | −11.9168 | −0.493119 | ||||||||
\(585\) | −3.77209 | + | 1.03964i | −0.155957 | + | 0.0429838i | ||||
\(586\) | −20.7555 | −0.857402 | ||||||||
\(587\) | − | 20.1244i | − | 0.830624i | −0.909679 | − | 0.415312i | \(-0.863672\pi\) | ||
0.909679 | − | 0.415312i | \(-0.136328\pi\) | |||||||
\(588\) | − | 5.61244i | − | 0.231453i | ||||||
\(589\) | 12.0398 | 0.496092 | ||||||||
\(590\) | −6.87293 | + | 1.89427i | −0.282954 | + | 0.0779860i | ||||
\(591\) | −3.14956 | −0.129555 | ||||||||
\(592\) | − | 1.00000i | − | 0.0410997i | ||||||
\(593\) | − | 29.7097i | − | 1.22003i | −0.792389 | − | 0.610016i | \(-0.791163\pi\) | ||
0.792389 | − | 0.610016i | \(-0.208837\pi\) | |||||||
\(594\) | −0.822051 | −0.0337291 | ||||||||
\(595\) | −2.76107 | − | 10.0179i | −0.113193 | − | 0.410694i | ||||
\(596\) | −5.82080 | −0.238429 | ||||||||
\(597\) | 8.00000i | 0.327418i | ||||||||
\(598\) | − | 13.4468i | − | 0.549882i | ||||||
\(599\) | −35.0077 | −1.43038 | −0.715188 | − | 0.698932i | \(-0.753659\pi\) | ||||
−0.715188 | + | 0.698932i | \(0.753659\pi\) | |||||||
\(600\) | −4.29400 | + | 2.56155i | −0.175302 | + | 0.104575i | ||||
\(601\) | 25.1541 | 1.02606 | 0.513028 | − | 0.858372i | \(-0.328524\pi\) | ||||
0.513028 | + | 0.858372i | \(0.328524\pi\) | |||||||
\(602\) | − | 3.44877i | − | 0.140561i | ||||||
\(603\) | − | 15.2108i | − | 0.619430i | ||||||
\(604\) | 6.62672 | 0.269638 | ||||||||
\(605\) | 6.13401 | + | 22.2558i | 0.249383 | + | 0.904829i | ||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | 26.6289i | 1.08084i | 0.841397 | + | 0.540418i | \(0.181734\pi\) | ||||
−0.841397 | + | 0.540418i | \(0.818266\pi\) | |||||||
\(608\) | − | 1.29400i | − | 0.0524787i | ||||||
\(609\) | −10.8833 | −0.441012 | ||||||||
\(610\) | 18.9341 | − | 5.21851i | 0.766621 | − | 0.211291i | ||||
\(611\) | 12.5782 | 0.508861 | ||||||||
\(612\) | 3.94516i | 0.159473i | ||||||||
\(613\) | − | 3.71564i | − | 0.150073i | −0.997181 | − | 0.0750366i | \(-0.976093\pi\) | ||
0.997181 | − | 0.0750366i | \(-0.0239073\pi\) | |||||||
\(614\) | 17.1315 | 0.691371 | ||||||||
\(615\) | −5.40369 | + | 1.48933i | −0.217898 | + | 0.0600556i | ||||
\(616\) | 0.968334 | 0.0390153 | ||||||||
\(617\) | − | 19.6872i | − | 0.792579i | −0.918126 | − | 0.396289i | \(-0.870298\pi\) | ||
0.918126 | − | 0.396289i | \(-0.129702\pi\) | |||||||
\(618\) | − | 19.6666i | − | 0.791106i | ||||||
\(619\) | 13.1708 | 0.529378 | 0.264689 | − | 0.964334i | \(-0.414731\pi\) | ||||
0.264689 | + | 0.964334i | \(0.414731\pi\) | |||||||
\(620\) | −5.52805 | − | 20.0572i | −0.222012 | − | 0.805518i | ||||
\(621\) | 7.68466 | 0.308375 | ||||||||
\(622\) | 29.1740i | 1.16977i | ||||||||
\(623\) | 17.5196i | 0.701906i | ||||||||
\(624\) | −1.74983 | −0.0700492 | ||||||||
\(625\) | 11.8769 | − | 21.9986i | 0.475076 | − | 0.879945i | ||||
\(626\) | 20.0714 | 0.802213 | ||||||||
\(627\) | 1.06373i | 0.0424815i | ||||||||
\(628\) | 13.5505i | 0.540725i | ||||||||
\(629\) | 3.94516 | 0.157304 | ||||||||
\(630\) | 0.699864 | + | 2.53929i | 0.0278832 | + | 0.101168i | ||||
\(631\) | −12.3398 | −0.491239 | −0.245619 | − | 0.969366i | \(-0.578991\pi\) | ||||
−0.245619 | + | 0.969366i | \(0.578991\pi\) | |||||||
\(632\) | − | 0.797618i | − | 0.0317275i | ||||||
\(633\) | 0.0954006i | 0.00379184i | ||||||||
\(634\) | 20.7084 | 0.822436 | ||||||||
\(635\) | −38.2631 | + | 10.5458i | −1.51843 | + | 0.418499i | ||||
\(636\) | 13.8659 | 0.549818 | ||||||||
\(637\) | 9.82080i | 0.389114i | ||||||||
\(638\) | 7.59506i | 0.300691i | ||||||||
\(639\) | 6.65317 | 0.263195 | ||||||||
\(640\) | −2.15569 | + | 0.594137i | −0.0852111 | + | 0.0234853i | ||||
\(641\) | 22.0715 | 0.871773 | 0.435887 | − | 0.900002i | \(-0.356435\pi\) | ||||
0.435887 | + | 0.900002i | \(0.356435\pi\) | |||||||
\(642\) | 10.4964i | 0.414259i | ||||||||
\(643\) | 22.8858i | 0.902530i | 0.892390 | + | 0.451265i | \(0.149027\pi\) | ||||
−0.892390 | + | 0.451265i | \(0.850973\pi\) | |||||||
\(644\) | −9.05214 | −0.356704 | ||||||||
\(645\) | −1.73950 | − | 6.31138i | −0.0684928 | − | 0.248510i | ||||
\(646\) | 5.10504 | 0.200855 | ||||||||
\(647\) | − | 17.5402i | − | 0.689577i | −0.938680 | − | 0.344788i | \(-0.887951\pi\) | ||
0.938680 | − | 0.344788i | \(-0.112049\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 2.62092 | 0.102880 | ||||||||
\(650\) | 7.51376 | − | 4.48228i | 0.294714 | − | 0.175809i | ||||
\(651\) | −10.9600 | −0.429557 | ||||||||
\(652\) | 3.45457i | 0.135291i | ||||||||
\(653\) | 20.7466i | 0.811875i | 0.913901 | + | 0.405938i | \(0.133055\pi\) | ||||
−0.913901 | + | 0.405938i | \(0.866945\pi\) | |||||||
\(654\) | −16.0328 | −0.626933 | ||||||||
\(655\) | 10.2933 | + | 37.3469i | 0.402193 | + | 1.45926i | ||||
\(656\) | −2.50671 | −0.0978705 | ||||||||
\(657\) | 11.9168i | 0.464917i | ||||||||
\(658\) | − | 8.46742i | − | 0.330095i | ||||||
\(659\) | −41.8965 | −1.63206 | −0.816028 | − | 0.578012i | \(-0.803828\pi\) | ||||
−0.816028 | + | 0.578012i | \(0.803828\pi\) | |||||||
\(660\) | 1.77209 | − | 0.488411i | 0.0689784 | − | 0.0190114i | ||||
\(661\) | −9.30691 | −0.361997 | −0.180998 | − | 0.983483i | \(-0.557933\pi\) | ||||
−0.180998 | + | 0.983483i | \(0.557933\pi\) | |||||||
\(662\) | − | 18.3339i | − | 0.712566i | ||||||
\(663\) | − | 6.90334i | − | 0.268104i | ||||||
\(664\) | 7.72918 | 0.299950 | ||||||||
\(665\) | 3.28585 | − | 0.905625i | 0.127420 | − | 0.0351186i | ||||
\(666\) | −1.00000 | −0.0387492 | ||||||||
\(667\) | − | 70.9998i | − | 2.74912i | ||||||
\(668\) | 0.294690i | 0.0114019i | ||||||||
\(669\) | −10.5512 | −0.407934 | ||||||||
\(670\) | 9.03728 | + | 32.7897i | 0.349141 | + | 1.26678i | ||||
\(671\) | −7.22034 | −0.278738 | ||||||||
\(672\) | 1.17795i | 0.0454404i | ||||||||
\(673\) | 8.73825i | 0.336835i | 0.985716 | + | 0.168417i | \(0.0538656\pi\) | ||||
−0.985716 | + | 0.168417i | \(0.946134\pi\) | |||||||
\(674\) | 32.8607 | 1.26575 | ||||||||
\(675\) | 2.56155 | + | 4.29400i | 0.0985942 | + | 0.165276i | ||||
\(676\) | −9.93810 | −0.382235 | ||||||||
\(677\) | − | 16.8064i | − | 0.645922i | −0.946412 | − | 0.322961i | \(-0.895322\pi\) | ||
0.946412 | − | 0.322961i | \(-0.104678\pi\) | |||||||
\(678\) | − | 3.46288i | − | 0.132991i | ||||||
\(679\) | −15.4249 | −0.591954 | ||||||||
\(680\) | −2.34397 | − | 8.50454i | −0.0898870 | − | 0.326134i | ||||
\(681\) | −10.1063 | −0.387274 | ||||||||
\(682\) | 7.64863i | 0.292881i | ||||||||
\(683\) | 30.8058i | 1.17875i | 0.807859 | + | 0.589376i | \(0.200626\pi\) | ||||
−0.807859 | + | 0.589376i | \(0.799374\pi\) | |||||||
\(684\) | −1.29400 | −0.0494774 | ||||||||
\(685\) | 3.44821 | − | 0.950373i | 0.131749 | − | 0.0363119i | ||||
\(686\) | 14.8568 | 0.567236 | ||||||||
\(687\) | − | 4.81173i | − | 0.183579i | ||||||
\(688\) | − | 2.92778i | − | 0.111620i | ||||||
\(689\) | −24.2629 | −0.924343 | ||||||||
\(690\) | −16.5657 | + | 4.56574i | −0.630647 | + | 0.173815i | ||||
\(691\) | 1.80146 | 0.0685306 | 0.0342653 | − | 0.999413i | \(-0.489091\pi\) | ||||
0.0342653 | + | 0.999413i | \(0.489091\pi\) | |||||||
\(692\) | − | 12.9542i | − | 0.492446i | ||||||
\(693\) | − | 0.968334i | − | 0.0367840i | ||||||
\(694\) | −20.5369 | −0.779572 | ||||||||
\(695\) | 8.04250 | + | 29.1804i | 0.305069 | + | 1.10687i | ||||
\(696\) | −9.23916 | −0.350209 | ||||||||
\(697\) | − | 9.88936i | − | 0.374586i | ||||||
\(698\) | 3.99024i | 0.151033i | ||||||||
\(699\) | 11.6014 | 0.438806 | ||||||||
\(700\) | −3.01738 | − | 5.05812i | −0.114046 | − | 0.191179i | ||||
\(701\) | 30.6087 | 1.15607 | 0.578036 | − | 0.816011i | \(-0.303819\pi\) | ||||
0.578036 | + | 0.816011i | \(0.303819\pi\) | |||||||
\(702\) | 1.74983i | 0.0660430i | ||||||||
\(703\) | 1.29400i | 0.0488042i | ||||||||
\(704\) | 0.822051 | 0.0309822 | ||||||||
\(705\) | −4.27082 | − | 15.4957i | −0.160849 | − | 0.583602i | ||||
\(706\) | 19.2964 | 0.726230 | ||||||||
\(707\) | − | 2.35590i | − | 0.0886027i | ||||||
\(708\) | 3.18827i | 0.119823i | ||||||||
\(709\) | −17.1845 | −0.645377 | −0.322689 | − | 0.946505i | \(-0.604587\pi\) | ||||
−0.322689 | + | 0.946505i | \(0.604587\pi\) | |||||||
\(710\) | −14.3422 | + | 3.95290i | −0.538252 | + | 0.148350i | ||||
\(711\) | −0.797618 | −0.0299130 | ||||||||
\(712\) | 14.8729i | 0.557387i | ||||||||
\(713\) | − | 71.5006i | − | 2.67772i | ||||||
\(714\) | −4.64719 | −0.173917 | ||||||||
\(715\) | −3.10085 | + | 0.854635i | −0.115965 | + | 0.0319616i | ||||
\(716\) | 20.4990 | 0.766082 | ||||||||
\(717\) | 23.1599i | 0.864922i | ||||||||
\(718\) | 8.39904i | 0.313449i | ||||||||
\(719\) | −8.89535 | −0.331741 | −0.165870 | − | 0.986148i | \(-0.553043\pi\) | ||||
−0.165870 | + | 0.986148i | \(0.553043\pi\) | |||||||
\(720\) | 0.594137 | + | 2.15569i | 0.0221422 | + | 0.0803378i | ||||
\(721\) | 23.1662 | 0.862756 | ||||||||
\(722\) | − | 17.3256i | − | 0.644791i | ||||||
\(723\) | − | 12.7020i | − | 0.472394i | ||||||
\(724\) | −20.1449 | −0.748680 | ||||||||
\(725\) | 39.6730 | − | 23.6666i | 1.47342 | − | 0.878955i | ||||
\(726\) | 10.3242 | 0.383168 | ||||||||
\(727\) | 8.44034i | 0.313035i | 0.987675 | + | 0.156517i | \(0.0500268\pi\) | ||||
−0.987675 | + | 0.156517i | \(0.949973\pi\) | |||||||
\(728\) | − | 2.06121i | − | 0.0763935i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −7.08020 | − | 25.6888i | −0.262050 | − | 0.950787i | ||||
\(731\) | 11.5505 | 0.427212 | ||||||||
\(732\) | − | 8.78333i | − | 0.324641i | ||||||
\(733\) | 36.7740i | 1.35828i | 0.734009 | + | 0.679140i | \(0.237647\pi\) | ||||
−0.734009 | + | 0.679140i | \(0.762353\pi\) | |||||||
\(734\) | −17.5325 | −0.647135 | ||||||||
\(735\) | 12.0987 | − | 3.33456i | 0.446266 | − | 0.122997i | ||||
\(736\) | −7.68466 | −0.283260 | ||||||||
\(737\) | − | 12.5040i | − | 0.460591i | ||||||
\(738\) | 2.50671i | 0.0922732i | ||||||||
\(739\) | −14.4481 | −0.531481 | −0.265741 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265741 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(740\) | 2.15569 | − | 0.594137i | 0.0792448 | − | 0.0218409i | ||||
\(741\) | 2.26428 | 0.0831804 | ||||||||
\(742\) | 16.3333i | 0.599614i | ||||||||
\(743\) | − | 5.29344i | − | 0.194197i | −0.995275 | − | 0.0970986i | \(-0.969044\pi\) | ||
0.995275 | − | 0.0970986i | \(-0.0309562\pi\) | |||||||
\(744\) | −9.30433 | −0.341113 | ||||||||
\(745\) | −3.45835 | − | 12.5478i | −0.126704 | − | 0.459717i | ||||
\(746\) | −26.4479 | −0.968327 | ||||||||
\(747\) | − | 7.72918i | − | 0.282796i | ||||||
\(748\) | 3.24312i | 0.118580i | ||||||||
\(749\) | −12.3642 | −0.451778 | ||||||||
\(750\) | −8.07314 | − | 7.73462i | −0.294789 | − | 0.282428i | ||||
\(751\) | −2.79946 | −0.102154 | −0.0510768 | − | 0.998695i | \(-0.516265\pi\) | ||||
−0.0510768 | + | 0.998695i | \(0.516265\pi\) | |||||||
\(752\) | − | 7.18827i | − | 0.262129i | ||||||
\(753\) | − | 13.5203i | − | 0.492707i | ||||||
\(754\) | 16.1669 | 0.588765 | ||||||||
\(755\) | 3.93718 | + | 14.2852i | 0.143289 | + | 0.519890i | ||||
\(756\) | 1.17795 | 0.0428416 | ||||||||
\(757\) | 46.2538i | 1.68112i | 0.541715 | + | 0.840562i | \(0.317775\pi\) | ||||
−0.541715 | + | 0.840562i | \(0.682225\pi\) | |||||||
\(758\) | − | 21.3596i | − | 0.775814i | ||||||
\(759\) | 6.31718 | 0.229299 | ||||||||
\(760\) | 2.78947 | − | 0.768815i | 0.101185 | − | 0.0278878i | ||||
\(761\) | −9.49764 | −0.344289 | −0.172145 | − | 0.985072i | \(-0.555070\pi\) | ||||
−0.172145 | + | 0.985072i | \(0.555070\pi\) | |||||||
\(762\) | 17.7498i | 0.643008i | ||||||||
\(763\) | − | 18.8858i | − | 0.683713i | ||||||
\(764\) | 1.59902 | 0.0578504 | ||||||||
\(765\) | −8.50454 | + | 2.34397i | −0.307482 | + | 0.0847462i | ||||
\(766\) | 27.0258 | 0.976480 | ||||||||
\(767\) | − | 5.57893i | − | 0.201444i | ||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −31.5996 | −1.13951 | −0.569755 | − | 0.821815i | \(-0.692962\pi\) | ||||
−0.569755 | + | 0.821815i | \(0.692962\pi\) | |||||||
\(770\) | 0.575324 | + | 2.08743i | 0.0207332 | + | 0.0752257i | ||||
\(771\) | −6.07097 | −0.218641 | ||||||||
\(772\) | 4.53510i | 0.163222i | ||||||||
\(773\) | − | 50.6640i | − | 1.82226i | −0.412124 | − | 0.911128i | \(-0.635213\pi\) | ||
0.412124 | − | 0.911128i | \(-0.364787\pi\) | |||||||
\(774\) | −2.92778 | −0.105237 | ||||||||
\(775\) | 39.9528 | − | 23.8335i | 1.43515 | − | 0.856125i | ||||
\(776\) | −13.0947 | −0.470073 | ||||||||
\(777\) | − | 1.17795i | − | 0.0422587i | ||||||
\(778\) | 14.3786i | 0.515497i | ||||||||
\(779\) | 3.24368 | 0.116217 | ||||||||
\(780\) | −1.03964 | − | 3.77209i | −0.0372250 | − | 0.135062i | ||||
\(781\) | 5.46924 | 0.195705 | ||||||||
\(782\) | − | 30.3172i | − | 1.08414i | ||||||
\(783\) | 9.23916i | 0.330181i | ||||||||
\(784\) | 5.61244 | 0.200444 | ||||||||
\(785\) | −29.2108 | + | 8.05088i | −1.04258 | + | 0.287348i | ||||
\(786\) | 17.3248 | 0.617955 | ||||||||
\(787\) | 11.8208i | 0.421366i | 0.977554 | + | 0.210683i | \(0.0675688\pi\) | ||||
−0.977554 | + | 0.210683i | \(0.932431\pi\) | |||||||
\(788\) | − | 3.14956i | − | 0.112198i | ||||||
\(789\) | −18.0064 | −0.641044 | ||||||||
\(790\) | 1.71942 | − | 0.473895i | 0.0611741 | − | 0.0168604i | ||||
\(791\) | 4.07910 | 0.145036 | ||||||||
\(792\) | − | 0.822051i | − | 0.0292103i | ||||||
\(793\) | 15.3693i | 0.545780i | ||||||||
\(794\) | 28.2383 | 1.00214 | ||||||||
\(795\) | 8.23824 | + | 29.8905i | 0.292180 | + | 1.06011i | ||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | 29.0645i | 1.02952i | 0.857335 | + | 0.514758i | \(0.172118\pi\) | ||||
−0.857335 | + | 0.514758i | \(0.827882\pi\) | |||||||
\(798\) | − | 1.52427i | − | 0.0539585i | ||||||
\(799\) | 28.3589 | 1.00326 | ||||||||
\(800\) | −2.56155 | − | 4.29400i | −0.0905646 | − | 0.151816i | ||||
\(801\) | 14.8729 | 0.525509 | ||||||||
\(802\) | 9.70096i | 0.342553i | ||||||||
\(803\) | 9.79618i | 0.345700i | ||||||||
\(804\) | 15.2108 | 0.536442 | ||||||||
\(805\) | −5.37821 | − | 19.5136i | −0.189557 | − | 0.687764i | ||||
\(806\) | 16.2810 | 0.573473 | ||||||||
\(807\) | − | 6.54745i | − | 0.230481i | ||||||
\(808\) | − | 2.00000i | − | 0.0703598i | ||||||
\(809\) | −26.4255 | −0.929071 | −0.464535 | − | 0.885555i | \(-0.653779\pi\) | ||||
−0.464535 | + | 0.885555i | \(0.653779\pi\) | |||||||
\(810\) | 2.15569 | − | 0.594137i | 0.0757432 | − | 0.0208759i | ||||
\(811\) | −32.7118 | −1.14867 | −0.574333 | − | 0.818622i | \(-0.694739\pi\) | ||||
−0.574333 | + | 0.818622i | \(0.694739\pi\) | |||||||
\(812\) | − | 10.8833i | − | 0.381928i | ||||||
\(813\) | 25.4776i | 0.893539i | ||||||||
\(814\) | −0.822051 | −0.0288129 | ||||||||
\(815\) | −7.44699 | + | 2.05249i | −0.260857 | + | 0.0718956i | ||||
\(816\) | −3.94516 | −0.138108 | ||||||||
\(817\) | 3.78855i | 0.132544i | ||||||||
\(818\) | 26.8103i | 0.937402i | ||||||||
\(819\) | −2.06121 | −0.0720244 | ||||||||
\(820\) | −1.48933 | − | 5.40369i | −0.0520097 | − | 0.188705i | ||||
\(821\) | −41.7992 | −1.45880 | −0.729400 | − | 0.684087i | \(-0.760201\pi\) | ||||
−0.729400 | + | 0.684087i | \(0.760201\pi\) | |||||||
\(822\) | − | 1.59958i | − | 0.0557919i | ||||||
\(823\) | − | 24.8303i | − | 0.865528i | −0.901507 | − | 0.432764i | \(-0.857538\pi\) | ||
0.901507 | − | 0.432764i | \(-0.142462\pi\) | |||||||
\(824\) | 19.6666 | 0.685118 | ||||||||
\(825\) | 2.10573 | + | 3.52989i | 0.0733120 | + | 0.122895i | ||||
\(826\) | −3.75563 | −0.130675 | ||||||||
\(827\) | 25.6338i | 0.891376i | 0.895188 | + | 0.445688i | \(0.147041\pi\) | ||||
−0.895188 | + | 0.445688i | \(0.852959\pi\) | |||||||
\(828\) | 7.68466i | 0.267060i | ||||||||
\(829\) | 24.5535 | 0.852777 | 0.426388 | − | 0.904540i | \(-0.359786\pi\) | ||||
0.426388 | + | 0.904540i | \(0.359786\pi\) | |||||||
\(830\) | 4.59219 | + | 16.6617i | 0.159397 | + | 0.578336i | ||||
\(831\) | −1.74983 | −0.0607009 | ||||||||
\(832\) | − | 1.74983i | − | 0.0606644i | ||||||
\(833\) | 22.1419i | 0.767173i | ||||||||
\(834\) | 13.5364 | 0.468728 | ||||||||
\(835\) | −0.635261 | + | 0.175086i | −0.0219841 | + | 0.00605912i | ||||
\(836\) | −1.06373 | −0.0367900 | ||||||||
\(837\) | 9.30433i | 0.321605i | ||||||||
\(838\) | 21.2275i | 0.733290i | ||||||||
\(839\) | 4.60646 | 0.159033 | 0.0795163 | − | 0.996834i | \(-0.474662\pi\) | ||||
0.0795163 | + | 0.996834i | \(0.474662\pi\) | |||||||
\(840\) | −2.53929 | + | 0.699864i | −0.0876140 | + | 0.0241476i | ||||
\(841\) | 56.3620 | 1.94352 | ||||||||
\(842\) | 6.40880i | 0.220862i | ||||||||
\(843\) | 21.1927i | 0.729915i | ||||||||
\(844\) | −0.0954006 | −0.00328383 | ||||||||
\(845\) | −5.90460 | − | 21.4235i | −0.203124 | − | 0.736990i | ||||
\(846\) | −7.18827 | −0.247138 | ||||||||
\(847\) | 12.1614i | 0.417871i | ||||||||
\(848\) | 13.8659i | 0.476156i | ||||||||
\(849\) | −29.6420 | −1.01731 | ||||||||
\(850\) | 16.9405 | − | 10.1057i | 0.581055 | − | 0.346624i | ||||
\(851\) | 7.68466 | 0.263427 | ||||||||
\(852\) | 6.65317i | 0.227934i | ||||||||
\(853\) | − | 12.5452i | − | 0.429541i | −0.976665 | − | 0.214771i | \(-0.931100\pi\) | ||
0.976665 | − | 0.214771i | \(-0.0689004\pi\) | |||||||
\(854\) | 10.3463 | 0.354044 | ||||||||
\(855\) | −0.768815 | − | 2.78947i | −0.0262929 | − | 0.0953977i | ||||
\(856\) | −10.4964 | −0.358759 | ||||||||
\(857\) | 29.1700i | 0.996429i | 0.867054 | + | 0.498215i | \(0.166011\pi\) | ||||
−0.867054 | + | 0.498215i | \(0.833989\pi\) | |||||||
\(858\) | 1.43845i | 0.0491078i | ||||||||
\(859\) | 12.5127 | 0.426927 | 0.213464 | − | 0.976951i | \(-0.431525\pi\) | ||||
0.213464 | + | 0.976951i | \(0.431525\pi\) | |||||||
\(860\) | 6.31138 | − | 1.73950i | 0.215216 | − | 0.0593165i | ||||
\(861\) | −2.95278 | −0.100630 | ||||||||
\(862\) | 1.41981i | 0.0483590i | ||||||||
\(863\) | 7.92274i | 0.269693i | 0.990866 | + | 0.134847i | \(0.0430542\pi\) | ||||
−0.990866 | + | 0.134847i | \(0.956946\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 27.9253 | − | 7.69659i | 0.949489 | − | 0.261692i | ||||
\(866\) | −6.06121 | −0.205968 | ||||||||
\(867\) | 1.43574i | 0.0487603i | ||||||||
\(868\) | − | 10.9600i | − | 0.372007i | ||||||
\(869\) | −0.655682 | −0.0222425 | ||||||||
\(870\) | −5.48933 | − | 19.9168i | −0.186106 | − | 0.675241i | ||||
\(871\) | −26.6162 | −0.901856 | ||||||||
\(872\) | − | 16.0328i | − | 0.542940i | ||||||
\(873\) | 13.0947i | 0.443189i | ||||||||
\(874\) | 9.94396 | 0.336359 | ||||||||
\(875\) | 9.11099 | − | 9.50975i | 0.308008 | − | 0.321488i | ||||
\(876\) | −11.9168 | −0.402630 | ||||||||
\(877\) | 16.0256i | 0.541147i | 0.962699 | + | 0.270574i | \(0.0872134\pi\) | ||||
−0.962699 | + | 0.270574i | \(0.912787\pi\) | |||||||
\(878\) | − | 6.54147i | − | 0.220764i | ||||||
\(879\) | −20.7555 | −0.700066 | ||||||||
\(880\) | 0.488411 | + | 1.77209i | 0.0164643 | + | 0.0597370i | ||||
\(881\) | 45.6110 | 1.53667 | 0.768337 | − | 0.640046i | \(-0.221085\pi\) | ||||
0.768337 | + | 0.640046i | \(0.221085\pi\) | |||||||
\(882\) | − | 5.61244i | − | 0.188981i | ||||||
\(883\) | 54.1737i | 1.82309i | 0.411201 | + | 0.911545i | \(0.365110\pi\) | ||||
−0.411201 | + | 0.911545i | \(0.634890\pi\) | |||||||
\(884\) | 6.90334 | 0.232185 | ||||||||
\(885\) | −6.87293 | + | 1.89427i | −0.231031 | + | 0.0636753i | ||||
\(886\) | 4.04887 | 0.136024 | ||||||||
\(887\) | 57.1933i | 1.92036i | 0.279379 | + | 0.960181i | \(0.409871\pi\) | ||||
−0.279379 | + | 0.960181i | \(0.590129\pi\) | |||||||
\(888\) | − | 1.00000i | − | 0.0335578i | ||||||
\(889\) | −20.9084 | −0.701245 | ||||||||
\(890\) | −32.0614 | + | 8.83657i | −1.07470 | + | 0.296202i | ||||
\(891\) | −0.822051 | −0.0275397 | ||||||||
\(892\) | − | 10.5512i | − | 0.353281i | ||||||
\(893\) | 9.30164i | 0.311267i | ||||||||
\(894\) | −5.82080 | −0.194677 | ||||||||
\(895\) | 12.1792 | + | 44.1894i | 0.407106 | + | 1.47709i | ||||
\(896\) | −1.17795 | −0.0393525 | ||||||||
\(897\) | − | 13.4468i | − | 0.448977i | ||||||
\(898\) | 2.45148i | 0.0818069i | ||||||||
\(899\) | 85.9641 | 2.86706 | ||||||||
\(900\) | −4.29400 | + | 2.56155i | −0.143133 | + | 0.0853851i | ||||
\(901\) | −54.7031 | −1.82242 | ||||||||
\(902\) | 2.06064i | 0.0686119i | ||||||||
\(903\) | − | 3.44877i | − | 0.114768i | ||||||
\(904\) | 3.46288 | 0.115174 | ||||||||
\(905\) | −11.9688 | − | 43.4262i | −0.397858 | − | 1.44353i | ||||
\(906\) | 6.62672 | 0.220158 | ||||||||
\(907\) | − | 15.0011i | − | 0.498103i | −0.968490 | − | 0.249051i | \(-0.919881\pi\) | ||
0.968490 | − | 0.249051i | \(-0.0801188\pi\) | |||||||
\(908\) | − | 10.1063i | − | 0.335389i | ||||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 4.44333 | − | 1.22464i | 0.147295 | − | 0.0405965i | ||||
\(911\) | 1.75379 | 0.0581056 | 0.0290528 | − | 0.999578i | \(-0.490751\pi\) | ||||
0.0290528 | + | 0.999578i | \(0.490751\pi\) | |||||||
\(912\) | − | 1.29400i | − | 0.0428487i | ||||||
\(913\) | − | 6.35378i | − | 0.210279i | ||||||
\(914\) | −6.87237 | −0.227318 | ||||||||
\(915\) | 18.9341 | − | 5.21851i | 0.625943 | − | 0.172518i | ||||
\(916\) | 4.81173 | 0.158984 | ||||||||
\(917\) | 20.4077i | 0.673923i | ||||||||
\(918\) | 3.94516i | 0.130210i | ||||||||
\(919\) | −14.1735 | −0.467540 | −0.233770 | − | 0.972292i | \(-0.575106\pi\) | ||||
−0.233770 | + | 0.972292i | \(0.575106\pi\) | |||||||
\(920\) | −4.56574 | − | 16.5657i | −0.150528 | − | 0.546156i | ||||
\(921\) | 17.1315 | 0.564502 | ||||||||
\(922\) | − | 1.07222i | − | 0.0353118i | ||||||
\(923\) | − | 11.6419i | − | 0.383198i | ||||||
\(924\) | 0.968334 | 0.0318559 | ||||||||
\(925\) | 2.56155 | + | 4.29400i | 0.0842233 | + | 0.141186i | ||||
\(926\) | −29.3791 | −0.965456 | ||||||||
\(927\) | − | 19.6666i | − | 0.645936i | ||||||
\(928\) | − | 9.23916i | − | 0.303290i | ||||||
\(929\) | 26.9057 | 0.882749 | 0.441374 | − | 0.897323i | \(-0.354491\pi\) | ||||
0.441374 | + | 0.897323i | \(0.354491\pi\) | |||||||
\(930\) | −5.52805 | − | 20.0572i | −0.181272 | − | 0.657703i | ||||
\(931\) | −7.26250 | −0.238019 | ||||||||
\(932\) | 11.6014i | 0.380017i | ||||||||
\(933\) | 29.1740i | 0.955113i | ||||||||
\(934\) | −6.56099 | −0.214682 | ||||||||
\(935\) | −6.99116 | + | 1.92686i | −0.228635 | + | 0.0630150i | ||||
\(936\) | −1.74983 | −0.0571949 | ||||||||
\(937\) | 43.4635i | 1.41989i | 0.704256 | + | 0.709946i | \(0.251281\pi\) | ||||
−0.704256 | + | 0.709946i | \(0.748719\pi\) | |||||||
\(938\) | 17.9175i | 0.585027i | ||||||||
\(939\) | 20.0714 | 0.655004 | ||||||||
\(940\) | 15.4957 | − | 4.27082i | 0.505414 | − | 0.139299i | ||||
\(941\) | 54.0784 | 1.76290 | 0.881452 | − | 0.472274i | \(-0.156567\pi\) | ||||
0.881452 | + | 0.472274i | \(0.156567\pi\) | |||||||
\(942\) | 13.5505i | 0.441500i | ||||||||
\(943\) | − | 19.2632i | − | 0.627296i | ||||||
\(944\) | −3.18827 | −0.103770 | ||||||||
\(945\) | 0.699864 | + | 2.53929i | 0.0227666 | + | 0.0826032i | ||||
\(946\) | −2.40678 | −0.0782512 | ||||||||
\(947\) | 43.8801i | 1.42591i | 0.701210 | + | 0.712955i | \(0.252644\pi\) | ||||
−0.701210 | + | 0.712955i | \(0.747356\pi\) | |||||||
\(948\) | − | 0.797618i | − | 0.0259054i | ||||||
\(949\) | 20.8523 | 0.676894 | ||||||||
\(950\) | 3.31465 | + | 5.55644i | 0.107542 | + | 0.180275i | ||||
\(951\) | 20.7084 | 0.671516 | ||||||||
\(952\) | − | 4.64719i | − | 0.150616i | ||||||
\(953\) | 55.7604i | 1.80626i | 0.429370 | + | 0.903129i | \(0.358736\pi\) | ||||
−0.429370 | + | 0.903129i | \(0.641264\pi\) | |||||||
\(954\) | 13.8659 | 0.448924 | ||||||||
\(955\) | 0.950036 | + | 3.44699i | 0.0307424 | + | 0.111542i | ||||
\(956\) | −23.1599 | −0.749044 | ||||||||
\(957\) | 7.59506i | 0.245513i | ||||||||
\(958\) | − | 2.93948i | − | 0.0949703i | ||||||
\(959\) | 1.88423 | 0.0608449 | ||||||||
\(960\) | −2.15569 | + | 0.594137i | −0.0695746 | + | 0.0191757i | ||||
\(961\) | 55.5705 | 1.79260 | ||||||||
\(962\) | 1.74983i | 0.0564167i | ||||||||
\(963\) | 10.4964i | 0.338241i | ||||||||
\(964\) | 12.7020 | 0.409105 | ||||||||
\(965\) | −9.77628 | + | 2.69447i | −0.314710 | + | 0.0867382i | ||||
\(966\) | −9.05214 | −0.291248 | ||||||||
\(967\) | − | 50.3281i | − | 1.61844i | −0.587503 | − | 0.809222i | \(-0.699889\pi\) | ||
0.587503 | − | 0.809222i | \(-0.300111\pi\) | |||||||
\(968\) | 10.3242i | 0.331833i | ||||||||
\(969\) | 5.10504 | 0.163997 | ||||||||
\(970\) | −7.78006 | − | 28.2281i | −0.249803 | − | 0.906351i | ||||
\(971\) | −15.1468 | −0.486084 | −0.243042 | − | 0.970016i | \(-0.578145\pi\) | ||||
−0.243042 | + | 0.970016i | \(0.578145\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 15.9452i | 0.511181i | ||||||||
\(974\) | −31.1217 | −0.997204 | ||||||||
\(975\) | 7.51376 | − | 4.48228i | 0.240633 | − | 0.143548i | ||||
\(976\) | 8.78333 | 0.281148 | ||||||||
\(977\) | 29.4991i | 0.943759i | 0.881663 | + | 0.471880i | \(0.156424\pi\) | ||||
−0.881663 | + | 0.471880i | \(0.843576\pi\) | |||||||
\(978\) | 3.45457i | 0.110465i | ||||||||
\(979\) | 12.2263 | 0.390754 | ||||||||
\(980\) | 3.33456 | + | 12.0987i | 0.106519 | + | 0.386478i | ||||
\(981\) | −16.0328 | −0.511888 | ||||||||
\(982\) | − | 4.69373i | − | 0.149783i | ||||||
\(983\) | − | 45.4318i | − | 1.44905i | −0.689249 | − | 0.724525i | \(-0.742059\pi\) | ||
0.689249 | − | 0.724525i | \(-0.257941\pi\) | |||||||
\(984\) | −2.50671 | −0.0799110 | ||||||||
\(985\) | 6.78947 | − | 1.87127i | 0.216330 | − | 0.0596236i | ||||
\(986\) | 36.4499 | 1.16080 | ||||||||
\(987\) | − | 8.46742i | − | 0.269521i | ||||||
\(988\) | 2.26428i | 0.0720363i | ||||||||
\(989\) | 22.4990 | 0.715426 | ||||||||
\(990\) | 1.77209 | − | 0.488411i | 0.0563206 | − | 0.0155227i | ||||
\(991\) | −17.3250 | −0.550346 | −0.275173 | − | 0.961395i | \(-0.588735\pi\) | ||||
−0.275173 | + | 0.961395i | \(0.588735\pi\) | |||||||
\(992\) | − | 9.30433i | − | 0.295413i | ||||||
\(993\) | − | 18.3339i | − | 0.581808i | ||||||
\(994\) | −7.83710 | −0.248578 | ||||||||
\(995\) | −4.75310 | − | 17.2455i | −0.150683 | − | 0.546720i | ||||
\(996\) | 7.72918 | 0.244908 | ||||||||
\(997\) | 20.9077i | 0.662153i | 0.943604 | + | 0.331077i | \(0.107412\pi\) | ||||
−0.943604 | + | 0.331077i | \(0.892588\pi\) | |||||||
\(998\) | − | 8.72527i | − | 0.276194i | ||||||
\(999\) | −1.00000 | −0.0316386 |
(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 | 1110.2.d.j.889.6 | yes | 8 | |
3.2 | odd | 2 | 3330.2.d.o.1999.3 | 8 | |||
5.2 | odd | 4 | 5550.2.a.cl.1.2 | 4 | |||
5.3 | odd | 4 | 5550.2.a.cm.1.3 | 4 | |||
5.4 | even | 2 | inner | 1110.2.d.j.889.2 | ✓ | 8 | |
15.14 | odd | 2 | 3330.2.d.o.1999.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.d.j.889.2 | ✓ | 8 | 5.4 | even | 2 | inner | |
1110.2.d.j.889.6 | yes | 8 | 1.1 | even | 1 | trivial | |
3330.2.d.o.1999.3 | 8 | 3.2 | odd | 2 | |||
3330.2.d.o.1999.7 | 8 | 15.14 | odd | 2 | |||
5550.2.a.cl.1.2 | 4 | 5.2 | odd | 4 | |||
5550.2.a.cm.1.3 | 4 | 5.3 | odd | 4 |