Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(76,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.i (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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.13 | ||
Root | \(0.0566033 - 1.17421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.76 |
Dual form | 1155.2.i.c.76.4 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.19849i | 1.55457i | 0.629150 | + | 0.777284i | \(0.283403\pi\) | ||||
−0.629150 | + | 0.777284i | \(0.716597\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −2.83337 | −1.41668 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 2.19849 | 0.897530 | ||||||||
\(7\) | −2.19849 | − | 1.47195i | −0.830952 | − | 0.556344i | ||||
\(8\) | − | 1.83215i | − | 0.647762i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.19849 | −0.695224 | ||||||||
\(11\) | −1.23607 | − | 3.07768i | −0.372689 | − | 0.927957i | ||||
\(12\) | 2.83337i | 0.817922i | ||||||||
\(13\) | 6.52171 | 1.80880 | 0.904399 | − | 0.426689i | \(-0.140320\pi\) | ||||
0.904399 | + | 0.426689i | \(0.140320\pi\) | |||||||
\(14\) | 3.23607 | − | 4.83337i | 0.864876 | − | 1.29177i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −1.63877 | −0.409693 | ||||||||
\(17\) | 3.82309 | 0.927236 | 0.463618 | − | 0.886035i | \(-0.346551\pi\) | ||||
0.463618 | + | 0.886035i | \(0.346551\pi\) | |||||||
\(18\) | − | 2.19849i | − | 0.518189i | ||||||
\(19\) | 2.33228 | 0.535061 | 0.267531 | − | 0.963549i | \(-0.413792\pi\) | ||||
0.267531 | + | 0.963549i | \(0.413792\pi\) | |||||||
\(20\) | − | 2.83337i | − | 0.633560i | ||||||
\(21\) | −1.47195 | + | 2.19849i | −0.321206 | + | 0.479750i | ||||
\(22\) | 6.76626 | − | 2.71749i | 1.44257 | − | 0.579370i | ||||
\(23\) | 3.83337 | 0.799312 | 0.399656 | − | 0.916665i | \(-0.369130\pi\) | ||||
0.399656 | + | 0.916665i | \(0.369130\pi\) | |||||||
\(24\) | −1.83215 | −0.373986 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 14.3379i | 2.81190i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 6.22913 | + | 4.17057i | 1.17720 | + | 0.788164i | ||||
\(29\) | − | 4.90983i | − | 0.911733i | −0.890048 | − | 0.455866i | \(-0.849329\pi\) | ||
0.890048 | − | 0.455866i | \(-0.150671\pi\) | |||||||
\(30\) | 2.19849i | 0.401388i | ||||||||
\(31\) | 7.93290i | 1.42479i | 0.701779 | + | 0.712395i | \(0.252390\pi\) | ||||
−0.701779 | + | 0.712395i | \(0.747610\pi\) | |||||||
\(32\) | − | 7.26712i | − | 1.28466i | ||||||
\(33\) | −3.07768 | + | 1.23607i | −0.535756 | + | 0.215172i | ||||
\(34\) | 8.40503i | 1.44145i | ||||||||
\(35\) | 1.47195 | − | 2.19849i | 0.248805 | − | 0.371613i | ||||
\(36\) | 2.83337 | 0.472228 | ||||||||
\(37\) | −7.93290 | −1.30416 | −0.652080 | − | 0.758150i | \(-0.726103\pi\) | ||||
−0.652080 | + | 0.758150i | \(0.726103\pi\) | |||||||
\(38\) | 5.12749i | 0.831789i | ||||||||
\(39\) | − | 6.52171i | − | 1.04431i | ||||||
\(40\) | 1.83215 | 0.289688 | ||||||||
\(41\) | 10.1860 | 1.59079 | 0.795393 | − | 0.606093i | \(-0.207264\pi\) | ||||
0.795393 | + | 0.606093i | \(0.207264\pi\) | |||||||
\(42\) | −4.83337 | − | 3.23607i | −0.745805 | − | 0.499336i | ||||
\(43\) | 6.37521i | 0.972210i | 0.873900 | + | 0.486105i | \(0.161583\pi\) | ||||
−0.873900 | + | 0.486105i | \(0.838417\pi\) | |||||||
\(44\) | 3.50223 | + | 8.72020i | 0.527981 | + | 1.31462i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 8.42762i | 1.24259i | ||||||||
\(47\) | − | 2.06710i | − | 0.301518i | −0.988571 | − | 0.150759i | \(-0.951828\pi\) | ||
0.988571 | − | 0.150759i | \(-0.0481718\pi\) | |||||||
\(48\) | 1.63877i | 0.236536i | ||||||||
\(49\) | 2.66673 | + | 6.47214i | 0.380962 | + | 0.924591i | ||||
\(50\) | − | 2.19849i | − | 0.310914i | ||||||
\(51\) | − | 3.82309i | − | 0.535340i | ||||||
\(52\) | −18.4784 | −2.56249 | ||||||||
\(53\) | 10.0324 | 1.37806 | 0.689030 | − | 0.724733i | \(-0.258037\pi\) | ||||
0.689030 | + | 0.724733i | \(0.258037\pi\) | |||||||
\(54\) | −2.19849 | −0.299177 | ||||||||
\(55\) | 3.07768 | − | 1.23607i | 0.414995 | − | 0.166671i | ||||
\(56\) | −2.69683 | + | 4.02796i | −0.360379 | + | 0.538259i | ||||
\(57\) | − | 2.33228i | − | 0.308918i | ||||||
\(58\) | 10.7942 | 1.41735 | ||||||||
\(59\) | − | 3.76626i | − | 0.490326i | −0.969482 | − | 0.245163i | \(-0.921159\pi\) | ||
0.969482 | − | 0.245163i | \(-0.0788414\pi\) | |||||||
\(60\) | −2.83337 | −0.365786 | ||||||||
\(61\) | 9.22033 | 1.18054 | 0.590271 | − | 0.807205i | \(-0.299021\pi\) | ||||
0.590271 | + | 0.807205i | \(0.299021\pi\) | |||||||
\(62\) | −17.4404 | −2.21493 | ||||||||
\(63\) | 2.19849 | + | 1.47195i | 0.276984 | + | 0.185448i | ||||
\(64\) | 12.6992 | 1.58739 | ||||||||
\(65\) | 6.52171i | 0.808919i | ||||||||
\(66\) | −2.71749 | − | 6.76626i | −0.334499 | − | 0.832869i | ||||
\(67\) | −2.13887 | −0.261304 | −0.130652 | − | 0.991428i | \(-0.541707\pi\) | ||||
−0.130652 | + | 0.991428i | \(0.541707\pi\) | |||||||
\(68\) | −10.8322 | −1.31360 | ||||||||
\(69\) | − | 3.83337i | − | 0.461483i | ||||||
\(70\) | 4.83337 | + | 3.23607i | 0.577698 | + | 0.386784i | ||||
\(71\) | 8.40503 | 0.997494 | 0.498747 | − | 0.866748i | \(-0.333794\pi\) | ||||
0.498747 | + | 0.866748i | \(0.333794\pi\) | |||||||
\(72\) | 1.83215i | 0.215921i | ||||||||
\(73\) | 8.34114 | 0.976257 | 0.488128 | − | 0.872772i | \(-0.337680\pi\) | ||||
0.488128 | + | 0.872772i | \(0.337680\pi\) | |||||||
\(74\) | − | 17.4404i | − | 2.02741i | ||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | −6.60819 | −0.758012 | ||||||||
\(77\) | −1.81271 | + | 8.58569i | −0.206577 | + | 0.978430i | ||||
\(78\) | 14.3379 | 1.62345 | ||||||||
\(79\) | 13.1299i | 1.47723i | 0.674128 | + | 0.738615i | \(0.264520\pi\) | ||||
−0.674128 | + | 0.738615i | \(0.735480\pi\) | |||||||
\(80\) | − | 1.63877i | − | 0.183220i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 22.3939i | 2.47299i | ||||||||
\(83\) | −15.3757 | −1.68770 | −0.843851 | − | 0.536577i | \(-0.819717\pi\) | ||||
−0.843851 | + | 0.536577i | \(0.819717\pi\) | |||||||
\(84\) | 4.17057 | − | 6.22913i | 0.455047 | − | 0.679654i | ||||
\(85\) | 3.82309i | 0.414672i | ||||||||
\(86\) | −14.0158 | −1.51137 | ||||||||
\(87\) | −4.90983 | −0.526389 | ||||||||
\(88\) | −5.63877 | + | 2.26466i | −0.601095 | + | 0.241413i | ||||
\(89\) | 0.705874i | 0.0748225i | 0.999300 | + | 0.0374113i | \(0.0119112\pi\) | ||||
−0.999300 | + | 0.0374113i | \(0.988089\pi\) | |||||||
\(90\) | 2.19849 | 0.231741 | ||||||||
\(91\) | −14.3379 | − | 9.59963i | −1.50302 | − | 1.00631i | ||||
\(92\) | −10.8613 | −1.13237 | ||||||||
\(93\) | 7.93290 | 0.822603 | ||||||||
\(94\) | 4.54451 | 0.468731 | ||||||||
\(95\) | 2.33228i | 0.239287i | ||||||||
\(96\) | −7.26712 | −0.741697 | ||||||||
\(97\) | − | 10.0995i | − | 1.02545i | −0.858552 | − | 0.512726i | \(-0.828636\pi\) | ||
0.858552 | − | 0.512726i | \(-0.171364\pi\) | |||||||
\(98\) | −14.2289 | + | 5.86279i | −1.43734 | + | 0.592231i | ||||
\(99\) | 1.23607 | + | 3.07768i | 0.124230 | + | 0.309319i | ||||
\(100\) | 2.83337 | 0.283337 | ||||||||
\(101\) | 1.45309 | 0.144587 | 0.0722937 | − | 0.997383i | \(-0.476968\pi\) | ||||
0.0722937 | + | 0.997383i | \(0.476968\pi\) | |||||||
\(102\) | 8.40503 | 0.832222 | ||||||||
\(103\) | − | 8.96086i | − | 0.882939i | −0.897276 | − | 0.441470i | \(-0.854457\pi\) | ||
0.897276 | − | 0.441470i | \(-0.145543\pi\) | |||||||
\(104\) | − | 11.9487i | − | 1.17167i | ||||||
\(105\) | −2.19849 | − | 1.47195i | −0.214551 | − | 0.143648i | ||||
\(106\) | 22.0562i | 2.14229i | ||||||||
\(107\) | − | 11.6514i | − | 1.12638i | −0.826327 | − | 0.563191i | \(-0.809574\pi\) | ||
0.826327 | − | 0.563191i | \(-0.190426\pi\) | |||||||
\(108\) | − | 2.83337i | − | 0.272641i | ||||||
\(109\) | 8.73292i | 0.836462i | 0.908341 | + | 0.418231i | \(0.137350\pi\) | ||||
−0.908341 | + | 0.418231i | \(0.862650\pi\) | |||||||
\(110\) | 2.71749 | + | 6.76626i | 0.259102 | + | 0.645138i | ||||
\(111\) | 7.93290i | 0.752957i | ||||||||
\(112\) | 3.60282 | + | 2.41219i | 0.340435 | + | 0.227930i | ||||
\(113\) | 9.36589 | 0.881069 | 0.440534 | − | 0.897736i | \(-0.354789\pi\) | ||||
0.440534 | + | 0.897736i | \(0.354789\pi\) | |||||||
\(114\) | 5.12749 | 0.480234 | ||||||||
\(115\) | 3.83337i | 0.357463i | ||||||||
\(116\) | 13.9113i | 1.29164i | ||||||||
\(117\) | −6.52171 | −0.602932 | ||||||||
\(118\) | 8.28009 | 0.762245 | ||||||||
\(119\) | −8.40503 | − | 5.62739i | −0.770488 | − | 0.515862i | ||||
\(120\) | − | 1.83215i | − | 0.167251i | ||||||
\(121\) | −7.94427 | + | 7.60845i | −0.722207 | + | 0.691677i | ||||
\(122\) | 20.2708i | 1.83523i | ||||||||
\(123\) | − | 10.1860i | − | 0.918441i | ||||||
\(124\) | − | 22.4768i | − | 2.01848i | ||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −3.23607 | + | 4.83337i | −0.288292 | + | 0.430590i | ||||
\(127\) | − | 16.1949i | − | 1.43706i | −0.695495 | − | 0.718531i | \(-0.744815\pi\) | ||
0.695495 | − | 0.718531i | \(-0.255185\pi\) | |||||||
\(128\) | 13.3848i | 1.18306i | ||||||||
\(129\) | 6.37521 | 0.561306 | ||||||||
\(130\) | −14.3379 | −1.25752 | ||||||||
\(131\) | 12.9824 | 1.13428 | 0.567138 | − | 0.823623i | \(-0.308051\pi\) | ||||
0.567138 | + | 0.823623i | \(0.308051\pi\) | |||||||
\(132\) | 8.72020 | − | 3.50223i | 0.758996 | − | 0.304830i | ||||
\(133\) | −5.12749 | − | 3.43299i | −0.444610 | − | 0.297678i | ||||
\(134\) | − | 4.70228i | − | 0.406215i | ||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | − | 7.00447i | − | 0.600628i | ||||||
\(137\) | −0.116115 | −0.00992041 | −0.00496021 | − | 0.999988i | \(-0.501579\pi\) | ||||
−0.00496021 | + | 0.999988i | \(0.501579\pi\) | |||||||
\(138\) | 8.42762 | 0.717407 | ||||||||
\(139\) | 2.18577 | 0.185395 | 0.0926974 | − | 0.995694i | \(-0.470451\pi\) | ||||
0.0926974 | + | 0.995694i | \(0.470451\pi\) | |||||||
\(140\) | −4.17057 | + | 6.22913i | −0.352478 | + | 0.526458i | ||||
\(141\) | −2.06710 | −0.174082 | ||||||||
\(142\) | 18.4784i | 1.55067i | ||||||||
\(143\) | −8.06128 | − | 20.0718i | −0.674118 | − | 1.67849i | ||||
\(144\) | 1.63877 | 0.136564 | ||||||||
\(145\) | 4.90983 | 0.407739 | ||||||||
\(146\) | 18.3379i | 1.51766i | ||||||||
\(147\) | 6.47214 | − | 2.66673i | 0.533813 | − | 0.219948i | ||||
\(148\) | 22.4768 | 1.84758 | ||||||||
\(149\) | 5.43497i | 0.445250i | 0.974904 | + | 0.222625i | \(0.0714626\pi\) | ||||
−0.974904 | + | 0.222625i | \(0.928537\pi\) | |||||||
\(150\) | −2.19849 | −0.179506 | ||||||||
\(151\) | − | 22.7176i | − | 1.84873i | −0.381506 | − | 0.924366i | \(-0.624595\pi\) | ||
0.381506 | − | 0.924366i | \(-0.375405\pi\) | |||||||
\(152\) | − | 4.27308i | − | 0.346592i | ||||||
\(153\) | −3.82309 | −0.309079 | ||||||||
\(154\) | −18.8756 | − | 3.98522i | −1.52104 | − | 0.321139i | ||||
\(155\) | −7.93290 | −0.637186 | ||||||||
\(156\) | 18.4784i | 1.47946i | ||||||||
\(157\) | − | 6.51147i | − | 0.519672i | −0.965653 | − | 0.259836i | \(-0.916331\pi\) | ||
0.965653 | − | 0.259836i | \(-0.0836685\pi\) | |||||||
\(158\) | −28.8660 | −2.29645 | ||||||||
\(159\) | − | 10.0324i | − | 0.795623i | ||||||
\(160\) | 7.26712 | 0.574516 | ||||||||
\(161\) | −8.42762 | − | 5.64252i | −0.664190 | − | 0.444693i | ||||
\(162\) | 2.19849i | 0.172730i | ||||||||
\(163\) | −10.7942 | −0.845469 | −0.422734 | − | 0.906254i | \(-0.638930\pi\) | ||||
−0.422734 | + | 0.906254i | \(0.638930\pi\) | |||||||
\(164\) | −28.8607 | −2.25364 | ||||||||
\(165\) | −1.23607 | − | 3.07768i | −0.0962278 | − | 0.239597i | ||||
\(166\) | − | 33.8033i | − | 2.62365i | ||||||
\(167\) | −17.4027 | −1.34666 | −0.673330 | − | 0.739342i | \(-0.735137\pi\) | ||||
−0.673330 | + | 0.739342i | \(0.735137\pi\) | |||||||
\(168\) | 4.02796 | + | 2.69683i | 0.310764 | + | 0.208065i | ||||
\(169\) | 29.5327 | 2.27175 | ||||||||
\(170\) | −8.40503 | −0.644637 | ||||||||
\(171\) | −2.33228 | −0.178354 | ||||||||
\(172\) | − | 18.0633i | − | 1.37731i | ||||||
\(173\) | 4.82437 | 0.366790 | 0.183395 | − | 0.983039i | \(-0.441291\pi\) | ||||
0.183395 | + | 0.983039i | \(0.441291\pi\) | |||||||
\(174\) | − | 10.7942i | − | 0.818308i | ||||||
\(175\) | 2.19849 | + | 1.47195i | 0.166190 | + | 0.111269i | ||||
\(176\) | 2.02563 | + | 5.04362i | 0.152688 | + | 0.380177i | ||||
\(177\) | −3.76626 | −0.283090 | ||||||||
\(178\) | −1.55186 | −0.116317 | ||||||||
\(179\) | −22.3267 | −1.66878 | −0.834390 | − | 0.551175i | \(-0.814180\pi\) | ||||
−0.834390 | + | 0.551175i | \(0.814180\pi\) | |||||||
\(180\) | 2.83337i | 0.211187i | ||||||||
\(181\) | 13.2775i | 0.986912i | 0.869771 | + | 0.493456i | \(0.164267\pi\) | ||||
−0.869771 | + | 0.493456i | \(0.835733\pi\) | |||||||
\(182\) | 21.1047 | − | 31.5218i | 1.56438 | − | 2.33655i | ||||
\(183\) | − | 9.22033i | − | 0.681587i | ||||||
\(184\) | − | 7.02329i | − | 0.517764i | ||||||
\(185\) | − | 7.93290i | − | 0.583238i | ||||||
\(186\) | 17.4404i | 1.27879i | ||||||||
\(187\) | −4.72560 | − | 11.7663i | −0.345570 | − | 0.860434i | ||||
\(188\) | 5.85686i | 0.427156i | ||||||||
\(189\) | 1.47195 | − | 2.19849i | 0.107069 | − | 0.159917i | ||||
\(190\) | −5.12749 | −0.371987 | ||||||||
\(191\) | −4.52806 | −0.327639 | −0.163819 | − | 0.986490i | \(-0.552381\pi\) | ||||
−0.163819 | + | 0.986490i | \(0.552381\pi\) | |||||||
\(192\) | − | 12.6992i | − | 0.916483i | ||||||
\(193\) | − | 4.39698i | − | 0.316502i | −0.987399 | − | 0.158251i | \(-0.949415\pi\) | ||
0.987399 | − | 0.158251i | \(-0.0505855\pi\) | |||||||
\(194\) | 22.2037 | 1.59414 | ||||||||
\(195\) | 6.52171 | 0.467029 | ||||||||
\(196\) | −7.55583 | − | 18.3379i | −0.539702 | − | 1.30985i | ||||
\(197\) | − | 22.8254i | − | 1.62624i | −0.582097 | − | 0.813120i | \(-0.697767\pi\) | ||
0.582097 | − | 0.813120i | \(-0.302233\pi\) | |||||||
\(198\) | −6.76626 | + | 2.71749i | −0.480857 | + | 0.193123i | ||||
\(199\) | 17.5325i | 1.24285i | 0.783475 | + | 0.621424i | \(0.213445\pi\) | ||||
−0.783475 | + | 0.621424i | \(0.786555\pi\) | |||||||
\(200\) | 1.83215i | 0.129552i | ||||||||
\(201\) | 2.13887i | 0.150864i | ||||||||
\(202\) | 3.19460i | 0.224771i | ||||||||
\(203\) | −7.22702 | + | 10.7942i | −0.507237 | + | 0.757606i | ||||
\(204\) | 10.8322i | 0.758407i | ||||||||
\(205\) | 10.1860i | 0.711422i | ||||||||
\(206\) | 19.7004 | 1.37259 | ||||||||
\(207\) | −3.83337 | −0.266437 | ||||||||
\(208\) | −10.6876 | −0.741051 | ||||||||
\(209\) | −2.88285 | − | 7.17801i | −0.199411 | − | 0.496513i | ||||
\(210\) | 3.23607 | − | 4.83337i | 0.223310 | − | 0.333534i | ||||
\(211\) | 12.9488i | 0.891433i | 0.895174 | + | 0.445717i | \(0.147051\pi\) | ||||
−0.895174 | + | 0.445717i | \(0.852949\pi\) | |||||||
\(212\) | −28.4255 | −1.95227 | ||||||||
\(213\) | − | 8.40503i | − | 0.575903i | ||||||
\(214\) | 25.6155 | 1.75104 | ||||||||
\(215\) | −6.37521 | −0.434786 | ||||||||
\(216\) | 1.83215 | 0.124662 | ||||||||
\(217\) | 11.6768 | − | 17.4404i | 0.792674 | − | 1.18393i | ||||
\(218\) | −19.1993 | −1.30034 | ||||||||
\(219\) | − | 8.34114i | − | 0.563642i | ||||||
\(220\) | −8.72020 | + | 3.50223i | −0.587916 | + | 0.236120i | ||||
\(221\) | 24.9331 | 1.67718 | ||||||||
\(222\) | −17.4404 | −1.17052 | ||||||||
\(223\) | − | 1.62739i | − | 0.108978i | −0.998514 | − | 0.0544892i | \(-0.982647\pi\) | ||
0.998514 | − | 0.0544892i | \(-0.0173530\pi\) | |||||||
\(224\) | −10.6968 | + | 15.9767i | −0.714712 | + | 1.06749i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 20.5908i | 1.36968i | ||||||||
\(227\) | 15.1336 | 1.00445 | 0.502225 | − | 0.864737i | \(-0.332515\pi\) | ||||
0.502225 | + | 0.864737i | \(0.332515\pi\) | |||||||
\(228\) | 6.60819i | 0.437638i | ||||||||
\(229\) | − | 4.85442i | − | 0.320789i | −0.987053 | − | 0.160394i | \(-0.948723\pi\) | ||
0.987053 | − | 0.160394i | \(-0.0512766\pi\) | |||||||
\(230\) | −8.42762 | −0.555701 | ||||||||
\(231\) | 8.58569 | + | 1.81271i | 0.564897 | + | 0.119267i | ||||
\(232\) | −8.99553 | −0.590586 | ||||||||
\(233\) | − | 18.9545i | − | 1.24175i | −0.783908 | − | 0.620876i | \(-0.786777\pi\) | ||
0.783908 | − | 0.620876i | \(-0.213223\pi\) | |||||||
\(234\) | − | 14.3379i | − | 0.937300i | ||||||
\(235\) | 2.06710 | 0.134843 | ||||||||
\(236\) | 10.6712i | 0.694636i | ||||||||
\(237\) | 13.1299 | 0.852879 | ||||||||
\(238\) | 12.3718 | − | 18.4784i | 0.801943 | − | 1.19778i | ||||
\(239\) | 8.61185i | 0.557055i | 0.960428 | + | 0.278527i | \(0.0898463\pi\) | ||||
−0.960428 | + | 0.278527i | \(0.910154\pi\) | |||||||
\(240\) | −1.63877 | −0.105782 | ||||||||
\(241\) | −25.0234 | −1.61190 | −0.805950 | − | 0.591983i | \(-0.798345\pi\) | ||||
−0.805950 | + | 0.591983i | \(0.798345\pi\) | |||||||
\(242\) | −16.7271 | − | 17.4654i | −1.07526 | − | 1.12272i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −26.1246 | −1.67245 | ||||||||
\(245\) | −6.47214 | + | 2.66673i | −0.413490 | + | 0.170371i | ||||
\(246\) | 22.3939 | 1.42778 | ||||||||
\(247\) | 15.2104 | 0.967817 | ||||||||
\(248\) | 14.5342 | 0.922925 | ||||||||
\(249\) | 15.3757i | 0.974395i | ||||||||
\(250\) | 2.19849 | 0.139045 | ||||||||
\(251\) | − | 1.93981i | − | 0.122440i | −0.998124 | − | 0.0612198i | \(-0.980501\pi\) | ||
0.998124 | − | 0.0612198i | \(-0.0194990\pi\) | |||||||
\(252\) | −6.22913 | − | 4.17057i | −0.392398 | − | 0.262721i | ||||
\(253\) | −4.73830 | − | 11.7979i | −0.297894 | − | 0.741727i | ||||
\(254\) | 35.6043 | 2.23401 | ||||||||
\(255\) | 3.82309 | 0.239411 | ||||||||
\(256\) | −4.02796 | −0.251748 | ||||||||
\(257\) | 27.7987i | 1.73403i | 0.498278 | + | 0.867017i | \(0.333966\pi\) | ||||
−0.498278 | + | 0.867017i | \(0.666034\pi\) | |||||||
\(258\) | 14.0158i | 0.872588i | ||||||||
\(259\) | 17.4404 | + | 11.6768i | 1.08369 | + | 0.725562i | ||||
\(260\) | − | 18.4784i | − | 1.14598i | ||||||
\(261\) | 4.90983i | 0.303911i | ||||||||
\(262\) | 28.5416i | 1.76331i | ||||||||
\(263\) | 2.96933i | 0.183097i | 0.995801 | + | 0.0915485i | \(0.0291817\pi\) | ||||
−0.995801 | + | 0.0915485i | \(0.970818\pi\) | |||||||
\(264\) | 2.26466 | + | 5.63877i | 0.139380 | + | 0.347042i | ||||
\(265\) | 10.0324i | 0.616287i | ||||||||
\(266\) | 7.54741 | − | 11.2727i | 0.462761 | − | 0.691176i | ||||
\(267\) | 0.705874 | 0.0431988 | ||||||||
\(268\) | 6.06019 | 0.370185 | ||||||||
\(269\) | − | 10.2943i | − | 0.627656i | −0.949480 | − | 0.313828i | \(-0.898389\pi\) | ||
0.949480 | − | 0.313828i | \(-0.101611\pi\) | |||||||
\(270\) | − | 2.19849i | − | 0.133796i | ||||||
\(271\) | 19.5051 | 1.18485 | 0.592426 | − | 0.805625i | \(-0.298170\pi\) | ||||
0.592426 | + | 0.805625i | \(0.298170\pi\) | |||||||
\(272\) | −6.26517 | −0.379882 | ||||||||
\(273\) | −9.59963 | + | 14.3379i | −0.580996 | + | 0.867771i | ||||
\(274\) | − | 0.255279i | − | 0.0154220i | ||||||
\(275\) | 1.23607 | + | 3.07768i | 0.0745377 | + | 0.185591i | ||||
\(276\) | 10.8613i | 0.653775i | ||||||||
\(277\) | 24.0609i | 1.44568i | 0.691016 | + | 0.722839i | \(0.257163\pi\) | ||||
−0.691016 | + | 0.722839i | \(0.742837\pi\) | |||||||
\(278\) | 4.80540i | 0.288209i | ||||||||
\(279\) | − | 7.93290i | − | 0.474930i | ||||||
\(280\) | −4.02796 | − | 2.69683i | −0.240717 | − | 0.161166i | ||||
\(281\) | 2.65089i | 0.158139i | 0.996869 | + | 0.0790695i | \(0.0251949\pi\) | ||||
−0.996869 | + | 0.0790695i | \(0.974805\pi\) | |||||||
\(282\) | − | 4.54451i | − | 0.270622i | ||||||
\(283\) | 14.1047 | 0.838439 | 0.419219 | − | 0.907885i | \(-0.362304\pi\) | ||||
0.419219 | + | 0.907885i | \(0.362304\pi\) | |||||||
\(284\) | −23.8145 | −1.41313 | ||||||||
\(285\) | 2.33228 | 0.138152 | ||||||||
\(286\) | 44.1276 | − | 17.7227i | 2.60932 | − | 1.04796i | ||||
\(287\) | −22.3939 | − | 14.9933i | −1.32187 | − | 0.885026i | ||||
\(288\) | 7.26712i | 0.428219i | ||||||||
\(289\) | −2.38398 | −0.140234 | ||||||||
\(290\) | 10.7942i | 0.633859i | ||||||||
\(291\) | −10.0995 | −0.592045 | ||||||||
\(292\) | −23.6335 | −1.38305 | ||||||||
\(293\) | −1.94262 | −0.113489 | −0.0567444 | − | 0.998389i | \(-0.518072\pi\) | ||||
−0.0567444 | + | 0.998389i | \(0.518072\pi\) | |||||||
\(294\) | 5.86279 | + | 14.2289i | 0.341925 | + | 0.829848i | ||||
\(295\) | 3.76626 | 0.219280 | ||||||||
\(296\) | 14.5342i | 0.844785i | ||||||||
\(297\) | 3.07768 | − | 1.23607i | 0.178585 | − | 0.0717239i | ||||
\(298\) | −11.9487 | −0.692172 | ||||||||
\(299\) | 25.0001 | 1.44579 | ||||||||
\(300\) | − | 2.83337i | − | 0.163584i | ||||||
\(301\) | 9.38398 | − | 14.0158i | 0.540884 | − | 0.807860i | ||||
\(302\) | 49.9445 | 2.87398 | ||||||||
\(303\) | − | 1.45309i | − | 0.0834776i | ||||||
\(304\) | −3.82207 | −0.219211 | ||||||||
\(305\) | 9.22033i | 0.527955i | ||||||||
\(306\) | − | 8.40503i | − | 0.480484i | ||||||
\(307\) | −8.03584 | −0.458630 | −0.229315 | − | 0.973352i | \(-0.573649\pi\) | ||||
−0.229315 | + | 0.973352i | \(0.573649\pi\) | |||||||
\(308\) | 5.13607 | − | 24.3264i | 0.292655 | − | 1.38613i | ||||
\(309\) | −8.96086 | −0.509765 | ||||||||
\(310\) | − | 17.4404i | − | 0.990548i | ||||||
\(311\) | 12.4949i | 0.708520i | 0.935147 | + | 0.354260i | \(0.115267\pi\) | ||||
−0.935147 | + | 0.354260i | \(0.884733\pi\) | |||||||
\(312\) | −11.9487 | −0.676464 | ||||||||
\(313\) | − | 4.68778i | − | 0.264969i | −0.991185 | − | 0.132485i | \(-0.957705\pi\) | ||
0.991185 | − | 0.132485i | \(-0.0422955\pi\) | |||||||
\(314\) | 14.3154 | 0.807866 | ||||||||
\(315\) | −1.47195 | + | 2.19849i | −0.0829349 | + | 0.123871i | ||||
\(316\) | − | 37.2018i | − | 2.09277i | ||||||
\(317\) | 17.0604 | 0.958207 | 0.479103 | − | 0.877758i | \(-0.340962\pi\) | ||||
0.479103 | + | 0.877758i | \(0.340962\pi\) | |||||||
\(318\) | 22.0562 | 1.23685 | ||||||||
\(319\) | −15.1109 | + | 6.06888i | −0.846048 | + | 0.339792i | ||||
\(320\) | 12.6992i | 0.709904i | ||||||||
\(321\) | −11.6514 | −0.650317 | ||||||||
\(322\) | 12.4050 | − | 18.5281i | 0.691305 | − | 1.03253i | ||||
\(323\) | 8.91650 | 0.496128 | ||||||||
\(324\) | −2.83337 | −0.157409 | ||||||||
\(325\) | −6.52171 | −0.361759 | ||||||||
\(326\) | − | 23.7310i | − | 1.31434i | ||||||
\(327\) | 8.73292 | 0.482932 | ||||||||
\(328\) | − | 18.6623i | − | 1.03045i | ||||||
\(329\) | −3.04267 | + | 4.54451i | −0.167748 | + | 0.250547i | ||||
\(330\) | 6.76626 | − | 2.71749i | 0.372470 | − | 0.149593i | ||||
\(331\) | 17.0507 | 0.937192 | 0.468596 | − | 0.883413i | \(-0.344760\pi\) | ||||
0.468596 | + | 0.883413i | \(0.344760\pi\) | |||||||
\(332\) | 43.5650 | 2.39094 | ||||||||
\(333\) | 7.93290 | 0.434720 | ||||||||
\(334\) | − | 38.2596i | − | 2.09347i | ||||||
\(335\) | − | 2.13887i | − | 0.116859i | ||||||
\(336\) | 2.41219 | − | 3.60282i | 0.131596 | − | 0.196550i | ||||
\(337\) | − | 7.58616i | − | 0.413244i | −0.978421 | − | 0.206622i | \(-0.933753\pi\) | ||
0.978421 | − | 0.206622i | \(-0.0662471\pi\) | |||||||
\(338\) | 64.9274i | 3.53159i | ||||||||
\(339\) | − | 9.36589i | − | 0.508685i | ||||||
\(340\) | − | 10.8322i | − | 0.587459i | ||||||
\(341\) | 24.4149 | − | 9.80560i | 1.32214 | − | 0.531003i | ||||
\(342\) | − | 5.12749i | − | 0.277263i | ||||||
\(343\) | 3.66387 | − | 18.1542i | 0.197830 | − | 0.980236i | ||||
\(344\) | 11.6803 | 0.629761 | ||||||||
\(345\) | 3.83337 | 0.206381 | ||||||||
\(346\) | 10.6063i | 0.570201i | ||||||||
\(347\) | 28.3235i | 1.52048i | 0.649640 | + | 0.760242i | \(0.274920\pi\) | ||||
−0.649640 | + | 0.760242i | \(0.725080\pi\) | |||||||
\(348\) | 13.9113 | 0.745726 | ||||||||
\(349\) | −19.9702 | −1.06898 | −0.534491 | − | 0.845174i | \(-0.679497\pi\) | ||||
−0.534491 | + | 0.845174i | \(0.679497\pi\) | |||||||
\(350\) | −3.23607 | + | 4.83337i | −0.172975 | + | 0.258354i | ||||
\(351\) | 6.52171i | 0.348103i | ||||||||
\(352\) | −22.3659 | + | 8.98265i | −1.19211 | + | 0.478777i | ||||
\(353\) | − | 15.5098i | − | 0.825502i | −0.910844 | − | 0.412751i | \(-0.864568\pi\) | ||
0.910844 | − | 0.412751i | \(-0.135432\pi\) | |||||||
\(354\) | − | 8.28009i | − | 0.440082i | ||||||
\(355\) | 8.40503i | 0.446093i | ||||||||
\(356\) | − | 2.00000i | − | 0.106000i | ||||||
\(357\) | −5.62739 | + | 8.40503i | −0.297833 | + | 0.444841i | ||||
\(358\) | − | 49.0852i | − | 2.59423i | ||||||
\(359\) | − | 25.9068i | − | 1.36731i | −0.729806 | − | 0.683654i | \(-0.760390\pi\) | ||
0.729806 | − | 0.683654i | \(-0.239610\pi\) | |||||||
\(360\) | −1.83215 | −0.0965627 | ||||||||
\(361\) | −13.5605 | −0.713710 | ||||||||
\(362\) | −29.1906 | −1.53422 | ||||||||
\(363\) | 7.60845 | + | 7.94427i | 0.399340 | + | 0.416966i | ||||
\(364\) | 40.6246 | + | 27.1993i | 2.12931 | + | 1.42563i | ||||
\(365\) | 8.34114i | 0.436595i | ||||||||
\(366\) | 20.2708 | 1.05957 | ||||||||
\(367\) | 16.2943i | 0.850557i | 0.905063 | + | 0.425278i | \(0.139824\pi\) | ||||
−0.905063 | + | 0.425278i | \(0.860176\pi\) | |||||||
\(368\) | −6.28201 | −0.327472 | ||||||||
\(369\) | −10.1860 | −0.530262 | ||||||||
\(370\) | 17.4404 | 0.906684 | ||||||||
\(371\) | −22.0562 | − | 14.7672i | −1.14510 | − | 0.766676i | ||||
\(372\) | −22.4768 | −1.16537 | ||||||||
\(373\) | − | 10.6124i | − | 0.549488i | −0.961517 | − | 0.274744i | \(-0.911407\pi\) | ||
0.961517 | − | 0.274744i | \(-0.0885931\pi\) | |||||||
\(374\) | 25.8680 | − | 10.3892i | 1.33760 | − | 0.537212i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −3.78724 | −0.195312 | ||||||||
\(377\) | − | 32.0205i | − | 1.64914i | ||||||
\(378\) | 4.83337 | + | 3.23607i | 0.248602 | + | 0.166445i | ||||
\(379\) | −26.9586 | −1.38477 | −0.692385 | − | 0.721528i | \(-0.743440\pi\) | ||||
−0.692385 | + | 0.721528i | \(0.743440\pi\) | |||||||
\(380\) | − | 6.60819i | − | 0.338993i | ||||||
\(381\) | −16.1949 | −0.829688 | ||||||||
\(382\) | − | 9.95490i | − | 0.509337i | ||||||
\(383\) | − | 10.2106i | − | 0.521739i | −0.965374 | − | 0.260869i | \(-0.915991\pi\) | ||
0.965374 | − | 0.260869i | \(-0.0840092\pi\) | |||||||
\(384\) | 13.3848 | 0.683038 | ||||||||
\(385\) | −8.58569 | − | 1.81271i | −0.437567 | − | 0.0923842i | ||||
\(386\) | 9.66673 | 0.492024 | ||||||||
\(387\) | − | 6.37521i | − | 0.324070i | ||||||
\(388\) | 28.6157i | 1.45274i | ||||||||
\(389\) | 9.57688 | 0.485567 | 0.242783 | − | 0.970081i | \(-0.421940\pi\) | ||||
0.242783 | + | 0.970081i | \(0.421940\pi\) | |||||||
\(390\) | 14.3379i | 0.726029i | ||||||||
\(391\) | 14.6553 | 0.741151 | ||||||||
\(392\) | 11.8579 | − | 4.88585i | 0.598915 | − | 0.246772i | ||||
\(393\) | − | 12.9824i | − | 0.654874i | ||||||
\(394\) | 50.1814 | 2.52810 | ||||||||
\(395\) | −13.1299 | −0.660637 | ||||||||
\(396\) | −3.50223 | − | 8.72020i | −0.175994 | − | 0.438207i | ||||
\(397\) | 29.9264i | 1.50196i | 0.660324 | + | 0.750981i | \(0.270419\pi\) | ||||
−0.660324 | + | 0.750981i | \(0.729581\pi\) | |||||||
\(398\) | −38.5451 | −1.93209 | ||||||||
\(399\) | −3.43299 | + | 5.12749i | −0.171865 | + | 0.256696i | ||||
\(400\) | 1.63877 | 0.0819385 | ||||||||
\(401\) | −27.5441 | −1.37549 | −0.687743 | − | 0.725954i | \(-0.741398\pi\) | ||||
−0.687743 | + | 0.725954i | \(0.741398\pi\) | |||||||
\(402\) | −4.70228 | −0.234529 | ||||||||
\(403\) | 51.7361i | 2.57716i | ||||||||
\(404\) | −4.11712 | −0.204834 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −23.7310 | − | 15.8885i | −1.17775 | − | 0.788535i | ||||
\(407\) | 9.80560 | + | 24.4149i | 0.486045 | + | 1.21020i | ||||
\(408\) | −7.00447 | −0.346773 | ||||||||
\(409\) | −4.16714 | −0.206052 | −0.103026 | − | 0.994679i | \(-0.532852\pi\) | ||||
−0.103026 | + | 0.994679i | \(0.532852\pi\) | |||||||
\(410\) | −22.3939 | −1.10595 | ||||||||
\(411\) | 0.116115i | 0.00572755i | ||||||||
\(412\) | 25.3894i | 1.25085i | ||||||||
\(413\) | −5.54375 | + | 8.28009i | −0.272790 | + | 0.407437i | ||||
\(414\) | − | 8.42762i | − | 0.414195i | ||||||
\(415\) | − | 15.3757i | − | 0.754763i | ||||||
\(416\) | − | 47.3940i | − | 2.32368i | ||||||
\(417\) | − | 2.18577i | − | 0.107038i | ||||||
\(418\) | 15.7808 | − | 6.33793i | 0.771864 | − | 0.309998i | ||||
\(419\) | 11.9005i | 0.581376i | 0.956818 | + | 0.290688i | \(0.0938842\pi\) | ||||
−0.956818 | + | 0.290688i | \(0.906116\pi\) | |||||||
\(420\) | 6.22913 | + | 4.17057i | 0.303950 | + | 0.203503i | ||||
\(421\) | −25.9722 | −1.26581 | −0.632905 | − | 0.774230i | \(-0.718137\pi\) | ||||
−0.632905 | + | 0.774230i | \(0.718137\pi\) | |||||||
\(422\) | −28.4679 | −1.38579 | ||||||||
\(423\) | 2.06710i | 0.100506i | ||||||||
\(424\) | − | 18.3809i | − | 0.892655i | ||||||
\(425\) | −3.82309 | −0.185447 | ||||||||
\(426\) | 18.4784 | 0.895281 | ||||||||
\(427\) | −20.2708 | − | 13.5719i | −0.980974 | − | 0.656788i | ||||
\(428\) | 33.0126i | 1.59573i | ||||||||
\(429\) | −20.0718 | + | 8.06128i | −0.969074 | + | 0.389202i | ||||
\(430\) | − | 14.0158i | − | 0.675904i | ||||||
\(431\) | 19.3963i | 0.934289i | 0.884181 | + | 0.467144i | \(0.154717\pi\) | ||||
−0.884181 | + | 0.467144i | \(0.845283\pi\) | |||||||
\(432\) | − | 1.63877i | − | 0.0788454i | ||||||
\(433\) | − | 3.16143i | − | 0.151928i | −0.997111 | − | 0.0759642i | \(-0.975797\pi\) | ||
0.997111 | − | 0.0759642i | \(-0.0242035\pi\) | |||||||
\(434\) | 38.3426 | + | 25.6714i | 1.84050 | + | 1.23227i | ||||
\(435\) | − | 4.90983i | − | 0.235408i | ||||||
\(436\) | − | 24.7436i | − | 1.18500i | ||||||
\(437\) | 8.94047 | 0.427681 | ||||||||
\(438\) | 18.3379 | 0.876220 | ||||||||
\(439\) | 28.0569 | 1.33908 | 0.669542 | − | 0.742774i | \(-0.266490\pi\) | ||||
0.669542 | + | 0.742774i | \(0.266490\pi\) | |||||||
\(440\) | −2.26466 | − | 5.63877i | −0.107963 | − | 0.268818i | ||||
\(441\) | −2.66673 | − | 6.47214i | −0.126987 | − | 0.308197i | ||||
\(442\) | 54.8152i | 2.60729i | ||||||||
\(443\) | −32.9489 | −1.56545 | −0.782725 | − | 0.622367i | \(-0.786171\pi\) | ||||
−0.782725 | + | 0.622367i | \(0.786171\pi\) | |||||||
\(444\) | − | 22.4768i | − | 1.06670i | ||||||
\(445\) | −0.705874 | −0.0334617 | ||||||||
\(446\) | 3.57781 | 0.169414 | ||||||||
\(447\) | 5.43497 | 0.257065 | ||||||||
\(448\) | −27.9190 | − | 18.6925i | −1.31905 | − | 0.883138i | ||||
\(449\) | 28.2106 | 1.33134 | 0.665671 | − | 0.746245i | \(-0.268145\pi\) | ||||
0.665671 | + | 0.746245i | \(0.268145\pi\) | |||||||
\(450\) | 2.19849i | 0.103638i | ||||||||
\(451\) | −12.5906 | − | 31.3493i | −0.592868 | − | 1.47618i | ||||
\(452\) | −26.5370 | −1.24819 | ||||||||
\(453\) | −22.7176 | −1.06737 | ||||||||
\(454\) | 33.2710i | 1.56149i | ||||||||
\(455\) | 9.59963 | − | 14.3379i | 0.450037 | − | 0.672172i | ||||
\(456\) | −4.27308 | −0.200105 | ||||||||
\(457\) | − | 4.26489i | − | 0.199503i | −0.995012 | − | 0.0997516i | \(-0.968195\pi\) | ||
0.995012 | − | 0.0997516i | \(-0.0318048\pi\) | |||||||
\(458\) | 10.6724 | 0.498688 | ||||||||
\(459\) | 3.82309i | 0.178447i | ||||||||
\(460\) | − | 10.8613i | − | 0.506412i | ||||||
\(461\) | 17.6002 | 0.819724 | 0.409862 | − | 0.912147i | \(-0.365577\pi\) | ||||
0.409862 | + | 0.912147i | \(0.365577\pi\) | |||||||
\(462\) | −3.98522 | + | 18.8756i | −0.185409 | + | 0.878171i | ||||
\(463\) | 7.41641 | 0.344670 | 0.172335 | − | 0.985038i | \(-0.444869\pi\) | ||||
0.172335 | + | 0.985038i | \(0.444869\pi\) | |||||||
\(464\) | 8.04609i | 0.373530i | ||||||||
\(465\) | 7.93290i | 0.367879i | ||||||||
\(466\) | 41.6714 | 1.93039 | ||||||||
\(467\) | − | 2.27735i | − | 0.105383i | −0.998611 | − | 0.0526915i | \(-0.983220\pi\) | ||
0.998611 | − | 0.0526915i | \(-0.0167800\pi\) | |||||||
\(468\) | 18.4784 | 0.854164 | ||||||||
\(469\) | 4.70228 | + | 3.14830i | 0.217131 | + | 0.145375i | ||||
\(470\) | 4.54451i | 0.209623i | ||||||||
\(471\) | −6.51147 | −0.300033 | ||||||||
\(472\) | −6.90035 | −0.317614 | ||||||||
\(473\) | 19.6209 | − | 7.88019i | 0.902169 | − | 0.362332i | ||||
\(474\) | 28.8660i | 1.32586i | ||||||||
\(475\) | −2.33228 | −0.107012 | ||||||||
\(476\) | 23.8145 | + | 15.9445i | 1.09154 | + | 0.730813i | ||||
\(477\) | −10.0324 | −0.459353 | ||||||||
\(478\) | −18.9331 | −0.865979 | ||||||||
\(479\) | 13.4221 | 0.613269 | 0.306635 | − | 0.951827i | \(-0.400797\pi\) | ||||
0.306635 | + | 0.951827i | \(0.400797\pi\) | |||||||
\(480\) | − | 7.26712i | − | 0.331697i | ||||||
\(481\) | −51.7361 | −2.35896 | ||||||||
\(482\) | − | 55.0138i | − | 2.50581i | ||||||
\(483\) | −5.64252 | + | 8.42762i | −0.256744 | + | 0.383470i | ||||
\(484\) | 22.5090 | − | 21.5575i | 1.02314 | − | 0.979888i | ||||
\(485\) | 10.0995 | 0.458596 | ||||||||
\(486\) | 2.19849 | 0.0997256 | ||||||||
\(487\) | −21.0272 | −0.952834 | −0.476417 | − | 0.879219i | \(-0.658065\pi\) | ||||
−0.476417 | + | 0.879219i | \(0.658065\pi\) | |||||||
\(488\) | − | 16.8930i | − | 0.764711i | ||||||
\(489\) | 10.7942i | 0.488132i | ||||||||
\(490\) | −5.86279 | − | 14.2289i | −0.264854 | − | 0.642798i | ||||
\(491\) | − | 29.1814i | − | 1.31694i | −0.752608 | − | 0.658469i | \(-0.771204\pi\) | ||
0.752608 | − | 0.658469i | \(-0.228796\pi\) | |||||||
\(492\) | 28.8607i | 1.30114i | ||||||||
\(493\) | − | 18.7707i | − | 0.845391i | ||||||
\(494\) | 33.4400i | 1.50454i | ||||||||
\(495\) | −3.07768 | + | 1.23607i | −0.138332 | + | 0.0555571i | ||||
\(496\) | − | 13.0002i | − | 0.583726i | ||||||
\(497\) | −18.4784 | − | 12.3718i | −0.828869 | − | 0.554950i | ||||
\(498\) | −33.8033 | −1.51476 | ||||||||
\(499\) | −29.1156 | −1.30339 | −0.651696 | − | 0.758480i | \(-0.725942\pi\) | ||||
−0.651696 | + | 0.758480i | \(0.725942\pi\) | |||||||
\(500\) | 2.83337i | 0.126712i | ||||||||
\(501\) | 17.4027i | 0.777494i | ||||||||
\(502\) | 4.26465 | 0.190341 | ||||||||
\(503\) | −26.8337 | −1.19646 | −0.598228 | − | 0.801326i | \(-0.704128\pi\) | ||||
−0.598228 | + | 0.801326i | \(0.704128\pi\) | |||||||
\(504\) | 2.69683 | − | 4.02796i | 0.120126 | − | 0.179420i | ||||
\(505\) | 1.45309i | 0.0646614i | ||||||||
\(506\) | 25.9376 | − | 10.4171i | 1.15306 | − | 0.463097i | ||||
\(507\) | − | 29.5327i | − | 1.31159i | ||||||
\(508\) | 45.8860i | 2.03586i | ||||||||
\(509\) | − | 9.01678i | − | 0.399662i | −0.979830 | − | 0.199831i | \(-0.935961\pi\) | ||
0.979830 | − | 0.199831i | \(-0.0640393\pi\) | |||||||
\(510\) | 8.40503i | 0.372181i | ||||||||
\(511\) | −18.3379 | − | 12.2777i | −0.811222 | − | 0.543135i | ||||
\(512\) | 17.9141i | 0.791698i | ||||||||
\(513\) | 2.33228i | 0.102973i | ||||||||
\(514\) | −61.1152 | −2.69568 | ||||||||
\(515\) | 8.96086 | 0.394863 | ||||||||
\(516\) | −18.0633 | −0.795192 | ||||||||
\(517\) | −6.36189 | + | 2.55508i | −0.279796 | + | 0.112372i | ||||
\(518\) | −25.6714 | + | 38.3426i | −1.12794 | + | 1.68468i | ||||
\(519\) | − | 4.82437i | − | 0.211766i | ||||||
\(520\) | 11.9487 | 0.523987 | ||||||||
\(521\) | 28.1829i | 1.23471i | 0.786683 | + | 0.617357i | \(0.211797\pi\) | ||||
−0.786683 | + | 0.617357i | \(0.788203\pi\) | |||||||
\(522\) | −10.7942 | −0.472450 | ||||||||
\(523\) | −32.3643 | −1.41519 | −0.707596 | − | 0.706617i | \(-0.750220\pi\) | ||||
−0.707596 | + | 0.706617i | \(0.750220\pi\) | |||||||
\(524\) | −36.7838 | −1.60691 | ||||||||
\(525\) | 1.47195 | − | 2.19849i | 0.0642411 | − | 0.0959500i | ||||
\(526\) | −6.52806 | −0.284637 | ||||||||
\(527\) | 30.3282i | 1.32112i | ||||||||
\(528\) | 5.04362 | − | 2.02563i | 0.219495 | − | 0.0881543i | ||||
\(529\) | −8.30531 | −0.361100 | ||||||||
\(530\) | −22.0562 | −0.958060 | ||||||||
\(531\) | 3.76626i | 0.163442i | ||||||||
\(532\) | 14.5281 | + | 9.72692i | 0.629871 | + | 0.421716i | ||||
\(533\) | 66.4302 | 2.87741 | ||||||||
\(534\) | 1.55186i | 0.0671555i | ||||||||
\(535\) | 11.6514 | 0.503733 | ||||||||
\(536\) | 3.91872i | 0.169263i | ||||||||
\(537\) | 22.3267i | 0.963470i | ||||||||
\(538\) | 22.6320 | 0.975734 | ||||||||
\(539\) | 16.6229 | − | 16.2074i | 0.716000 | − | 0.698100i | ||||
\(540\) | 2.83337 | 0.121929 | ||||||||
\(541\) | − | 4.01749i | − | 0.172726i | −0.996264 | − | 0.0863628i | \(-0.972476\pi\) | ||
0.996264 | − | 0.0863628i | \(-0.0275244\pi\) | |||||||
\(542\) | 42.8818i | 1.84193i | ||||||||
\(543\) | 13.2775 | 0.569794 | ||||||||
\(544\) | − | 27.7828i | − | 1.19118i | ||||||
\(545\) | −8.73292 | −0.374077 | ||||||||
\(546\) | −31.5218 | − | 21.1047i | −1.34901 | − | 0.903198i | ||||
\(547\) | − | 4.86524i | − | 0.208023i | −0.994576 | − | 0.104011i | \(-0.966832\pi\) | ||
0.994576 | − | 0.104011i | \(-0.0331679\pi\) | |||||||
\(548\) | 0.328998 | 0.0140541 | ||||||||
\(549\) | −9.22033 | −0.393514 | ||||||||
\(550\) | −6.76626 | + | 2.71749i | −0.288514 | + | 0.115874i | ||||
\(551\) | − | 11.4511i | − | 0.487833i | ||||||
\(552\) | −7.02329 | −0.298931 | ||||||||
\(553\) | 19.3266 | − | 28.8660i | 0.821849 | − | 1.22751i | ||||
\(554\) | −52.8977 | −2.24741 | ||||||||
\(555\) | −7.93290 | −0.336733 | ||||||||
\(556\) | −6.19310 | −0.262646 | ||||||||
\(557\) | 5.35951i | 0.227090i | 0.993533 | + | 0.113545i | \(0.0362206\pi\) | ||||
−0.993533 | + | 0.113545i | \(0.963779\pi\) | |||||||
\(558\) | 17.4404 | 0.738311 | ||||||||
\(559\) | 41.5773i | 1.75853i | ||||||||
\(560\) | −2.41219 | + | 3.60282i | −0.101933 | + | 0.152247i | ||||
\(561\) | −11.7663 | + | 4.72560i | −0.496772 | + | 0.199515i | ||||
\(562\) | −5.82796 | −0.245838 | ||||||||
\(563\) | −1.65063 | −0.0695659 | −0.0347829 | − | 0.999395i | \(-0.511074\pi\) | ||||
−0.0347829 | + | 0.999395i | \(0.511074\pi\) | |||||||
\(564\) | 5.85686 | 0.246618 | ||||||||
\(565\) | 9.36589i | 0.394026i | ||||||||
\(566\) | 31.0091i | 1.30341i | ||||||||
\(567\) | −2.19849 | − | 1.47195i | −0.0923280 | − | 0.0618161i | ||||
\(568\) | − | 15.3993i | − | 0.646139i | ||||||
\(569\) | 39.4976i | 1.65583i | 0.560856 | + | 0.827914i | \(0.310472\pi\) | ||||
−0.560856 | + | 0.827914i | \(0.689528\pi\) | |||||||
\(570\) | 5.12749i | 0.214767i | ||||||||
\(571\) | − | 9.97531i | − | 0.417454i | −0.977974 | − | 0.208727i | \(-0.933068\pi\) | ||
0.977974 | − | 0.208727i | \(-0.0669320\pi\) | |||||||
\(572\) | 22.8405 | + | 56.8706i | 0.955011 | + | 2.37788i | ||||
\(573\) | 4.52806i | 0.189162i | ||||||||
\(574\) | 32.9626 | − | 49.2327i | 1.37583 | − | 2.05493i | ||||
\(575\) | −3.83337 | −0.159862 | ||||||||
\(576\) | −12.6992 | −0.529132 | ||||||||
\(577\) | 42.3245i | 1.76199i | 0.473124 | + | 0.880996i | \(0.343126\pi\) | ||||
−0.473124 | + | 0.880996i | \(0.656874\pi\) | |||||||
\(578\) | − | 5.24116i | − | 0.218004i | ||||||
\(579\) | −4.39698 | −0.182732 | ||||||||
\(580\) | −13.9113 | −0.577637 | ||||||||
\(581\) | 33.8033 | + | 22.6322i | 1.40240 | + | 0.938944i | ||||
\(582\) | − | 22.2037i | − | 0.920374i | ||||||
\(583\) | −12.4008 | − | 30.8766i | −0.513587 | − | 1.27878i | ||||
\(584\) | − | 15.2822i | − | 0.632382i | ||||||
\(585\) | − | 6.52171i | − | 0.269640i | ||||||
\(586\) | − | 4.27082i | − | 0.176426i | ||||||
\(587\) | − | 0.386939i | − | 0.0159707i | −0.999968 | − | 0.00798535i | \(-0.997458\pi\) | ||
0.999968 | − | 0.00798535i | \(-0.00254184\pi\) | |||||||
\(588\) | −18.3379 | + | 7.55583i | −0.756243 | + | 0.311597i | ||||
\(589\) | 18.5017i | 0.762350i | ||||||||
\(590\) | 8.28009i | 0.340886i | ||||||||
\(591\) | −22.8254 | −0.938910 | ||||||||
\(592\) | 13.0002 | 0.534305 | ||||||||
\(593\) | −7.48636 | −0.307428 | −0.153714 | − | 0.988115i | \(-0.549123\pi\) | ||||
−0.153714 | + | 0.988115i | \(0.549123\pi\) | |||||||
\(594\) | 2.71749 | + | 6.76626i | 0.111500 | + | 0.277623i | ||||
\(595\) | 5.62739 | − | 8.40503i | 0.230701 | − | 0.344573i | ||||
\(596\) | − | 15.3993i | − | 0.630778i | ||||||
\(597\) | 17.5325 | 0.717558 | ||||||||
\(598\) | 54.9625i | 2.24758i | ||||||||
\(599\) | 24.3939 | 0.996706 | 0.498353 | − | 0.866974i | \(-0.333938\pi\) | ||||
0.498353 | + | 0.866974i | \(0.333938\pi\) | |||||||
\(600\) | 1.83215 | 0.0747971 | ||||||||
\(601\) | −17.1086 | −0.697876 | −0.348938 | − | 0.937146i | \(-0.613458\pi\) | ||||
−0.348938 | + | 0.937146i | \(0.613458\pi\) | |||||||
\(602\) | 30.8137 | + | 20.6306i | 1.25587 | + | 0.840841i | ||||
\(603\) | 2.13887 | 0.0871014 | ||||||||
\(604\) | 64.3673i | 2.61907i | ||||||||
\(605\) | −7.60845 | − | 7.94427i | −0.309328 | − | 0.322981i | ||||
\(606\) | 3.19460 | 0.129772 | ||||||||
\(607\) | −32.4398 | −1.31669 | −0.658345 | − | 0.752717i | \(-0.728743\pi\) | ||||
−0.658345 | + | 0.752717i | \(0.728743\pi\) | |||||||
\(608\) | − | 16.9489i | − | 0.687370i | ||||||
\(609\) | 10.7942 | + | 7.22702i | 0.437404 | + | 0.292854i | ||||
\(610\) | −20.2708 | −0.820742 | ||||||||
\(611\) | − | 13.4811i | − | 0.545385i | ||||||
\(612\) | 10.8322 | 0.437866 | ||||||||
\(613\) | 12.1632i | 0.491267i | 0.969363 | + | 0.245634i | \(0.0789960\pi\) | ||||
−0.969363 | + | 0.245634i | \(0.921004\pi\) | |||||||
\(614\) | − | 17.6667i | − | 0.712971i | ||||||
\(615\) | 10.1860 | 0.410739 | ||||||||
\(616\) | 15.7303 | + | 3.32115i | 0.633790 | + | 0.133813i | ||||
\(617\) | −35.0831 | −1.41239 | −0.706197 | − | 0.708015i | \(-0.749591\pi\) | ||||
−0.706197 | + | 0.708015i | \(0.749591\pi\) | |||||||
\(618\) | − | 19.7004i | − | 0.792465i | ||||||
\(619\) | 2.89877i | 0.116511i | 0.998302 | + | 0.0582557i | \(0.0185539\pi\) | ||||
−0.998302 | + | 0.0582557i | \(0.981446\pi\) | |||||||
\(620\) | 22.4768 | 0.902690 | ||||||||
\(621\) | 3.83337i | 0.153828i | ||||||||
\(622\) | −27.4699 | −1.10144 | ||||||||
\(623\) | 1.03901 | − | 1.55186i | 0.0416271 | − | 0.0621739i | ||||
\(624\) | 10.6876i | 0.427846i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.3060 | 0.411913 | ||||||||
\(627\) | −7.17801 | + | 2.88285i | −0.286662 | + | 0.115130i | ||||
\(628\) | 18.4494i | 0.736211i | ||||||||
\(629\) | −30.3282 | −1.20926 | ||||||||
\(630\) | −4.83337 | − | 3.23607i | −0.192566 | − | 0.128928i | ||||
\(631\) | 34.8050 | 1.38557 | 0.692784 | − | 0.721146i | \(-0.256384\pi\) | ||||
0.692784 | + | 0.721146i | \(0.256384\pi\) | |||||||
\(632\) | 24.0559 | 0.956893 | ||||||||
\(633\) | 12.9488 | 0.514669 | ||||||||
\(634\) | 37.5071i | 1.48960i | ||||||||
\(635\) | 16.1949 | 0.642674 | ||||||||
\(636\) | 28.4255i | 1.12715i | ||||||||
\(637\) | 17.3917 | + | 42.2094i | 0.689082 | + | 1.67240i | ||||
\(638\) | −13.3424 | − | 33.2212i | −0.528230 | − | 1.31524i | ||||
\(639\) | −8.40503 | −0.332498 | ||||||||
\(640\) | −13.3848 | −0.529079 | ||||||||
\(641\) | 20.5976 | 0.813555 | 0.406778 | − | 0.913527i | \(-0.366652\pi\) | ||||
0.406778 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(642\) | − | 25.6155i | − | 1.01096i | ||||||
\(643\) | 20.1269i | 0.793729i | 0.917877 | + | 0.396865i | \(0.129902\pi\) | ||||
−0.917877 | + | 0.396865i | \(0.870098\pi\) | |||||||
\(644\) | 23.8785 | + | 15.9873i | 0.940946 | + | 0.629989i | ||||
\(645\) | 6.37521i | 0.251024i | ||||||||
\(646\) | 19.6029i | 0.771264i | ||||||||
\(647\) | − | 5.14333i | − | 0.202205i | −0.994876 | − | 0.101103i | \(-0.967763\pi\) | ||
0.994876 | − | 0.101103i | \(-0.0322370\pi\) | |||||||
\(648\) | − | 1.83215i | − | 0.0719736i | ||||||
\(649\) | −11.5914 | + | 4.65536i | −0.455001 | + | 0.182739i | ||||
\(650\) | − | 14.3379i | − | 0.562380i | ||||||
\(651\) | −17.4404 | − | 11.6768i | −0.683543 | − | 0.457651i | ||||
\(652\) | 30.5840 | 1.19776 | ||||||||
\(653\) | −30.9118 | −1.20967 | −0.604837 | − | 0.796349i | \(-0.706762\pi\) | ||||
−0.604837 | + | 0.796349i | \(0.706762\pi\) | |||||||
\(654\) | 19.1993i | 0.750750i | ||||||||
\(655\) | 12.9824i | 0.507263i | ||||||||
\(656\) | −16.6925 | −0.651734 | ||||||||
\(657\) | −8.34114 | −0.325419 | ||||||||
\(658\) | −9.99107 | − | 6.68929i | −0.389492 | − | 0.260776i | ||||
\(659\) | 2.92161i | 0.113810i | 0.998380 | + | 0.0569048i | \(0.0181231\pi\) | ||||
−0.998380 | + | 0.0569048i | \(0.981877\pi\) | |||||||
\(660\) | 3.50223 | + | 8.72020i | 0.136324 | + | 0.339433i | ||||
\(661\) | 15.7991i | 0.614513i | 0.951627 | + | 0.307256i | \(0.0994109\pi\) | ||||
−0.951627 | + | 0.307256i | \(0.900589\pi\) | |||||||
\(662\) | 37.4859i | 1.45693i | ||||||||
\(663\) | − | 24.9331i | − | 0.968321i | ||||||
\(664\) | 28.1705i | 1.09323i | ||||||||
\(665\) | 3.43299 | − | 5.12749i | 0.133126 | − | 0.198836i | ||||
\(666\) | 17.4404i | 0.675802i | ||||||||
\(667\) | − | 18.8212i | − | 0.728759i | ||||||
\(668\) | 49.3081 | 1.90779 | ||||||||
\(669\) | −1.62739 | −0.0629187 | ||||||||
\(670\) | 4.70228 | 0.181665 | ||||||||
\(671\) | −11.3970 | − | 28.3773i | −0.439975 | − | 1.09549i | ||||
\(672\) | 15.9767 | + | 10.6968i | 0.616315 | + | 0.412639i | ||||
\(673\) | 13.1809i | 0.508088i | 0.967193 | + | 0.254044i | \(0.0817608\pi\) | ||||
−0.967193 | + | 0.254044i | \(0.918239\pi\) | |||||||
\(674\) | 16.6781 | 0.642417 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | −83.6770 | −3.21835 | ||||||||
\(677\) | −24.6857 | −0.948747 | −0.474373 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474373 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(678\) | 20.5908 | 0.790786 | ||||||||
\(679\) | −14.8660 | + | 22.2037i | −0.570505 | + | 0.852101i | ||||
\(680\) | 7.00447 | 0.268609 | ||||||||
\(681\) | − | 15.1336i | − | 0.579919i | ||||||
\(682\) | 21.5575 | + | 53.6760i | 0.825480 | + | 2.05536i | ||||
\(683\) | 36.4028 | 1.39291 | 0.696457 | − | 0.717599i | \(-0.254759\pi\) | ||||
0.696457 | + | 0.717599i | \(0.254759\pi\) | |||||||
\(684\) | 6.60819 | 0.252671 | ||||||||
\(685\) | − | 0.116115i | − | 0.00443654i | ||||||
\(686\) | 39.9119 | + | 8.05498i | 1.52384 | + | 0.307541i | ||||
\(687\) | −4.85442 | −0.185208 | ||||||||
\(688\) | − | 10.4475i | − | 0.398307i | ||||||
\(689\) | 65.4286 | 2.49263 | ||||||||
\(690\) | 8.42762i | 0.320834i | ||||||||
\(691\) | 35.8885i | 1.36526i | 0.730762 | + | 0.682632i | \(0.239165\pi\) | ||||
−0.730762 | + | 0.682632i | \(0.760835\pi\) | |||||||
\(692\) | −13.6692 | −0.519626 | ||||||||
\(693\) | 1.81271 | − | 8.58569i | 0.0688591 | − | 0.326143i | ||||
\(694\) | −62.2690 | −2.36370 | ||||||||
\(695\) | 2.18577i | 0.0829111i | ||||||||
\(696\) | 8.99553i | 0.340975i | ||||||||
\(697\) | 38.9420 | 1.47503 | ||||||||
\(698\) | − | 43.9044i | − | 1.66181i | ||||||
\(699\) | −18.9545 | −0.716926 | ||||||||
\(700\) | −6.22913 | − | 4.17057i | −0.235439 | − | 0.157633i | ||||
\(701\) | − | 10.3071i | − | 0.389293i | −0.980873 | − | 0.194646i | \(-0.937644\pi\) | ||
0.980873 | − | 0.194646i | \(-0.0623559\pi\) | |||||||
\(702\) | −14.3379 | −0.541150 | ||||||||
\(703\) | −18.5017 | −0.697805 | ||||||||
\(704\) | −15.6970 | − | 39.0840i | −0.591604 | − | 1.47303i | ||||
\(705\) | − | 2.06710i | − | 0.0778516i | ||||||
\(706\) | 34.0981 | 1.28330 | ||||||||
\(707\) | −3.19460 | − | 2.13887i | −0.120145 | − | 0.0804404i | ||||
\(708\) | 10.6712 | 0.401048 | ||||||||
\(709\) | −20.5273 | −0.770919 | −0.385460 | − | 0.922725i | \(-0.625957\pi\) | ||||
−0.385460 | + | 0.922725i | \(0.625957\pi\) | |||||||
\(710\) | −18.4784 | −0.693482 | ||||||||
\(711\) | − | 13.1299i | − | 0.492410i | ||||||
\(712\) | 1.29327 | 0.0484672 | ||||||||
\(713\) | 30.4097i | 1.13885i | ||||||||
\(714\) | −18.4784 | − | 12.3718i | −0.691536 | − | 0.463002i | ||||
\(715\) | 20.0718 | − | 8.06128i | 0.750641 | − | 0.301475i | ||||
\(716\) | 63.2598 | 2.36413 | ||||||||
\(717\) | 8.61185 | 0.321616 | ||||||||
\(718\) | 56.9558 | 2.12557 | ||||||||
\(719\) | − | 0.665030i | − | 0.0248014i | −0.999923 | − | 0.0124007i | \(-0.996053\pi\) | ||
0.999923 | − | 0.0124007i | \(-0.00394737\pi\) | |||||||
\(720\) | 1.63877i | 0.0610734i | ||||||||
\(721\) | −13.1899 | + | 19.7004i | −0.491219 | + | 0.733680i | ||||
\(722\) | − | 29.8126i | − | 1.10951i | ||||||
\(723\) | 25.0234i | 0.930631i | ||||||||
\(724\) | − | 37.6201i | − | 1.39814i | ||||||
\(725\) | 4.90983i | 0.182347i | ||||||||
\(726\) | −17.4654 | + | 16.7271i | −0.648202 | + | 0.620802i | ||||
\(727\) | − | 32.3592i | − | 1.20014i | −0.799949 | − | 0.600068i | \(-0.795140\pi\) | ||
0.799949 | − | 0.600068i | \(-0.204860\pi\) | |||||||
\(728\) | −17.5879 | + | 26.2692i | −0.651852 | + | 0.973601i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −18.3379 | −0.678717 | ||||||||
\(731\) | 24.3730i | 0.901468i | ||||||||
\(732\) | 26.1246i | 0.965592i | ||||||||
\(733\) | 37.9468 | 1.40160 | 0.700799 | − | 0.713359i | \(-0.252827\pi\) | ||||
0.700799 | + | 0.713359i | \(0.252827\pi\) | |||||||
\(734\) | −35.8229 | −1.32225 | ||||||||
\(735\) | 2.66673 | + | 6.47214i | 0.0983639 | + | 0.238728i | ||||
\(736\) | − | 27.8575i | − | 1.02684i | ||||||
\(737\) | 2.64379 | + | 6.58276i | 0.0973851 | + | 0.242479i | ||||
\(738\) | − | 22.3939i | − | 0.824329i | ||||||
\(739\) | 17.3895i | 0.639684i | 0.947471 | + | 0.319842i | \(0.103630\pi\) | ||||
−0.947471 | + | 0.319842i | \(0.896370\pi\) | |||||||
\(740\) | 22.4768i | 0.826263i | ||||||||
\(741\) | − | 15.2104i | − | 0.558769i | ||||||
\(742\) | 32.4656 | − | 48.4904i | 1.19185 | − | 1.78014i | ||||
\(743\) | − | 11.3236i | − | 0.415423i | −0.978190 | − | 0.207712i | \(-0.933398\pi\) | ||
0.978190 | − | 0.207712i | \(-0.0666016\pi\) | |||||||
\(744\) | − | 14.5342i | − | 0.532851i | ||||||
\(745\) | −5.43497 | −0.199122 | ||||||||
\(746\) | 23.3312 | 0.854216 | ||||||||
\(747\) | 15.3757 | 0.562567 | ||||||||
\(748\) | 13.3894 | + | 33.3381i | 0.489563 | + | 1.21896i | ||||
\(749\) | −17.1502 | + | 25.6155i | −0.626656 | + | 0.935969i | ||||
\(750\) | − | 2.19849i | − | 0.0802776i | ||||||
\(751\) | −43.7038 | −1.59477 | −0.797387 | − | 0.603468i | \(-0.793785\pi\) | ||||
−0.797387 | + | 0.603468i | \(0.793785\pi\) | |||||||
\(752\) | 3.38751i | 0.123530i | ||||||||
\(753\) | −1.93981 | −0.0706905 | ||||||||
\(754\) | 70.3968 | 2.56370 | ||||||||
\(755\) | 22.7176 | 0.826778 | ||||||||
\(756\) | −4.17057 | + | 6.22913i | −0.151682 | + | 0.226551i | ||||
\(757\) | −51.0654 | −1.85600 | −0.928002 | − | 0.372574i | \(-0.878475\pi\) | ||||
−0.928002 | + | 0.372574i | \(0.878475\pi\) | |||||||
\(758\) | − | 59.2683i | − | 2.15272i | ||||||
\(759\) | −11.7979 | + | 4.73830i | −0.428236 | + | 0.171989i | ||||
\(760\) | 4.27308 | 0.155001 | ||||||||
\(761\) | −43.3228 | −1.57045 | −0.785226 | − | 0.619209i | \(-0.787453\pi\) | ||||
−0.785226 | + | 0.619209i | \(0.787453\pi\) | |||||||
\(762\) | − | 35.6043i | − | 1.28981i | ||||||
\(763\) | 12.8544 | − | 19.1993i | 0.465361 | − | 0.695060i | ||||
\(764\) | 12.8296 | 0.464160 | ||||||||
\(765\) | − | 3.82309i | − | 0.138224i | ||||||
\(766\) | 22.4480 | 0.811079 | ||||||||
\(767\) | − | 24.5625i | − | 0.886899i | ||||||
\(768\) | 4.02796i | 0.145347i | ||||||||
\(769\) | 27.7894 | 1.00211 | 0.501055 | − | 0.865415i | \(-0.332945\pi\) | ||||
0.501055 | + | 0.865415i | \(0.332945\pi\) | |||||||
\(770\) | 3.98522 | − | 18.8756i | 0.143618 | − | 0.680228i | ||||
\(771\) | 27.7987 | 1.00115 | ||||||||
\(772\) | 12.4583i | 0.448383i | ||||||||
\(773\) | − | 30.3758i | − | 1.09254i | −0.837609 | − | 0.546270i | \(-0.816047\pi\) | ||
0.837609 | − | 0.546270i | \(-0.183953\pi\) | |||||||
\(774\) | 14.0158 | 0.503789 | ||||||||
\(775\) | − | 7.93290i | − | 0.284958i | ||||||
\(776\) | −18.5038 | −0.664249 | ||||||||
\(777\) | 11.6768 | − | 17.4404i | 0.418904 | − | 0.625671i | ||||
\(778\) | 21.0547i | 0.754847i | ||||||||
\(779\) | 23.7566 | 0.851168 | ||||||||
\(780\) | −18.4784 | −0.661633 | ||||||||
\(781\) | −10.3892 | − | 25.8680i | −0.371754 | − | 0.925631i | ||||
\(782\) | 32.2196i | 1.15217i | ||||||||
\(783\) | 4.90983 | 0.175463 | ||||||||
\(784\) | −4.37016 | − | 10.6063i | −0.156077 | − | 0.378798i | ||||
\(785\) | 6.51147 | 0.232404 | ||||||||
\(786\) | 28.5416 | 1.01805 | ||||||||
\(787\) | 11.5972 | 0.413395 | 0.206698 | − | 0.978405i | \(-0.433728\pi\) | ||||
0.206698 | + | 0.978405i | \(0.433728\pi\) | |||||||
\(788\) | 64.6726i | 2.30387i | ||||||||
\(789\) | 2.96933 | 0.105711 | ||||||||
\(790\) | − | 28.8660i | − | 1.02701i | ||||||
\(791\) | −20.5908 | − | 13.7861i | −0.732126 | − | 0.490178i | ||||
\(792\) | 5.63877 | − | 2.26466i | 0.200365 | − | 0.0804711i | ||||
\(793\) | 60.1323 | 2.13536 | ||||||||
\(794\) | −65.7929 | −2.33490 | ||||||||
\(795\) | 10.0324 | 0.355813 | ||||||||
\(796\) | − | 49.6760i | − | 1.76072i | ||||||
\(797\) | − | 17.6112i | − | 0.623821i | −0.950112 | − | 0.311910i | \(-0.899031\pi\) | ||
0.950112 | − | 0.311910i | \(-0.100969\pi\) | |||||||
\(798\) | −11.2727 | − | 7.54741i | −0.399051 | − | 0.267175i | ||||
\(799\) | − | 7.90273i | − | 0.279578i | ||||||
\(800\) | 7.26712i | 0.256931i | ||||||||
\(801\) | − | 0.705874i | − | 0.0249408i | ||||||
\(802\) | − | 60.5555i | − | 2.13829i | ||||||
\(803\) | −10.3102 | − | 25.6714i | −0.363840 | − | 0.905924i | ||||
\(804\) | − | 6.06019i | − | 0.213727i | ||||||
\(805\) | 5.64252 | − | 8.42762i | 0.198873 | − | 0.297035i | ||||
\(806\) | −113.741 | −4.00637 | ||||||||
\(807\) | −10.2943 | −0.362377 | ||||||||
\(808\) | − | 2.66227i | − | 0.0936582i | ||||||
\(809\) | 14.3510i | 0.504555i | 0.967655 | + | 0.252278i | \(0.0811796\pi\) | ||||
−0.967655 | + | 0.252278i | \(0.918820\pi\) | |||||||
\(810\) | −2.19849 | −0.0772471 | ||||||||
\(811\) | 6.31314 | 0.221684 | 0.110842 | − | 0.993838i | \(-0.464645\pi\) | ||||
0.110842 | + | 0.993838i | \(0.464645\pi\) | |||||||
\(812\) | 20.4768 | − | 30.5840i | 0.718595 | − | 1.07329i | ||||
\(813\) | − | 19.5051i | − | 0.684074i | ||||||
\(814\) | −53.6760 | + | 21.5575i | −1.88134 | + | 0.755591i | ||||
\(815\) | − | 10.7942i | − | 0.378105i | ||||||
\(816\) | 6.26517i | 0.219325i | ||||||||
\(817\) | 14.8687i | 0.520192i | ||||||||
\(818\) | − | 9.16143i | − | 0.320322i | ||||||
\(819\) | 14.3379 | + | 9.59963i | 0.501008 | + | 0.335438i | ||||
\(820\) | − | 28.8607i | − | 1.00786i | ||||||
\(821\) | − | 51.0311i | − | 1.78100i | −0.454986 | − | 0.890499i | \(-0.650356\pi\) | ||
0.454986 | − | 0.890499i | \(-0.349644\pi\) | |||||||
\(822\) | −0.255279 | −0.00890387 | ||||||||
\(823\) | 47.7810 | 1.66554 | 0.832770 | − | 0.553619i | \(-0.186754\pi\) | ||||
0.832770 | + | 0.553619i | \(0.186754\pi\) | |||||||
\(824\) | −16.4176 | −0.571935 | ||||||||
\(825\) | 3.07768 | − | 1.23607i | 0.107151 | − | 0.0430344i | ||||
\(826\) | −18.2037 | − | 12.1879i | −0.633388 | − | 0.424071i | ||||
\(827\) | − | 3.94416i | − | 0.137152i | −0.997646 | − | 0.0685759i | \(-0.978154\pi\) | ||
0.997646 | − | 0.0685759i | \(-0.0218455\pi\) | |||||||
\(828\) | 10.8613 | 0.377457 | ||||||||
\(829\) | 23.9638i | 0.832298i | 0.909297 | + | 0.416149i | \(0.136620\pi\) | ||||
−0.909297 | + | 0.416149i | \(0.863380\pi\) | |||||||
\(830\) | 33.8033 | 1.17333 | ||||||||
\(831\) | 24.0609 | 0.834663 | ||||||||
\(832\) | 82.8202 | 2.87128 | ||||||||
\(833\) | 10.1952 | + | 24.7436i | 0.353241 | + | 0.857314i | ||||
\(834\) | 4.80540 | 0.166398 | ||||||||
\(835\) | − | 17.4027i | − | 0.602244i | ||||||
\(836\) | 8.16818 | + | 20.3379i | 0.282502 | + | 0.703402i | ||||
\(837\) | −7.93290 | −0.274201 | ||||||||
\(838\) | −26.1631 | −0.903789 | ||||||||
\(839\) | − | 23.2339i | − | 0.802124i | −0.916051 | − | 0.401062i | \(-0.868641\pi\) | ||
0.916051 | − | 0.401062i | \(-0.131359\pi\) | |||||||
\(840\) | −2.69683 | + | 4.02796i | −0.0930494 | + | 0.138978i | ||||
\(841\) | 4.89356 | 0.168743 | ||||||||
\(842\) | − | 57.0997i | − | 1.96779i | ||||||
\(843\) | 2.65089 | 0.0913015 | ||||||||
\(844\) | − | 36.6887i | − | 1.26288i | ||||||
\(845\) | 29.5327i | 1.01596i | ||||||||
\(846\) | −4.54451 | −0.156244 | ||||||||
\(847\) | 28.6647 | − | 5.03355i | 0.984930 | − | 0.172955i | ||||
\(848\) | −16.4408 | −0.564581 | ||||||||
\(849\) | − | 14.1047i | − | 0.484073i | ||||||
\(850\) | − | 8.40503i | − | 0.288290i | ||||||
\(851\) | −30.4097 | −1.04243 | ||||||||
\(852\) | 23.8145i | 0.815872i | ||||||||
\(853\) | −27.8240 | −0.952674 | −0.476337 | − | 0.879263i | \(-0.658036\pi\) | ||||
−0.476337 | + | 0.879263i | \(0.658036\pi\) | |||||||
\(854\) | 29.8376 | − | 44.5652i | 1.02102 | − | 1.52499i | ||||
\(855\) | − | 2.33228i | − | 0.0797622i | ||||||
\(856\) | −21.3471 | −0.729627 | ||||||||
\(857\) | −3.63200 | −0.124067 | −0.0620334 | − | 0.998074i | \(-0.519759\pi\) | ||||
−0.0620334 | + | 0.998074i | \(0.519759\pi\) | |||||||
\(858\) | −17.7227 | − | 44.1276i | −0.605041 | − | 1.50649i | ||||
\(859\) | − | 23.3644i | − | 0.797182i | −0.917129 | − | 0.398591i | \(-0.869499\pi\) | ||
0.917129 | − | 0.398591i | \(-0.130501\pi\) | |||||||
\(860\) | 18.0633 | 0.615953 | ||||||||
\(861\) | −14.9933 | + | 22.3939i | −0.510970 | + | 0.763180i | ||||
\(862\) | −42.6427 | −1.45242 | ||||||||
\(863\) | 7.16683 | 0.243962 | 0.121981 | − | 0.992532i | \(-0.461075\pi\) | ||||
0.121981 | + | 0.992532i | \(0.461075\pi\) | |||||||
\(864\) | 7.26712 | 0.247232 | ||||||||
\(865\) | 4.82437i | 0.164034i | ||||||||
\(866\) | 6.95037 | 0.236183 | ||||||||
\(867\) | 2.38398i | 0.0809643i | ||||||||
\(868\) | −33.0847 | + | 49.4150i | −1.12297 | + | 1.67726i | ||||
\(869\) | 40.4097 | − | 16.2295i | 1.37080 | − | 0.550547i | ||||
\(870\) | 10.7942 | 0.365958 | ||||||||
\(871\) | −13.9491 | −0.472646 | ||||||||
\(872\) | 16.0000 | 0.541828 | ||||||||
\(873\) | 10.0995i | 0.341817i | ||||||||
\(874\) | 19.6555i | 0.664859i | ||||||||
\(875\) | −1.47195 | + | 2.19849i | −0.0497610 | + | 0.0743226i | ||||
\(876\) | 23.6335i | 0.798502i | ||||||||
\(877\) | 20.0190i | 0.675993i | 0.941147 | + | 0.337997i | \(0.109749\pi\) | ||||
−0.941147 | + | 0.337997i | \(0.890251\pi\) | |||||||
\(878\) | 61.6830i | 2.08170i | ||||||||
\(879\) | 1.94262i | 0.0655228i | ||||||||
\(880\) | −5.04362 | + | 2.02563i | −0.170020 | + | 0.0682840i | ||||
\(881\) | 14.0814i | 0.474416i | 0.971459 | + | 0.237208i | \(0.0762322\pi\) | ||||
−0.971459 | + | 0.237208i | \(0.923768\pi\) | |||||||
\(882\) | 14.2289 | − | 5.86279i | 0.479113 | − | 0.197410i | ||||
\(883\) | −12.1161 | −0.407740 | −0.203870 | − | 0.978998i | \(-0.565352\pi\) | ||||
−0.203870 | + | 0.978998i | \(0.565352\pi\) | |||||||
\(884\) | −70.6446 | −2.37603 | ||||||||
\(885\) | − | 3.76626i | − | 0.126602i | ||||||
\(886\) | − | 72.4380i | − | 2.43360i | ||||||
\(887\) | 1.96381 | 0.0659384 | 0.0329692 | − | 0.999456i | \(-0.489504\pi\) | ||||
0.0329692 | + | 0.999456i | \(0.489504\pi\) | |||||||
\(888\) | 14.5342 | 0.487737 | ||||||||
\(889\) | −23.8380 | + | 35.6043i | −0.799502 | + | 1.19413i | ||||
\(890\) | − | 1.55186i | − | 0.0520184i | ||||||
\(891\) | −1.23607 | − | 3.07768i | −0.0414098 | − | 0.103106i | ||||
\(892\) | 4.61100i | 0.154388i | ||||||||
\(893\) | − | 4.82106i | − | 0.161331i | ||||||
\(894\) | 11.9487i | 0.399626i | ||||||||
\(895\) | − | 22.3267i | − | 0.746301i | ||||||
\(896\) | 19.7017 | − | 29.4263i | 0.658187 | − | 0.983063i | ||||
\(897\) | − | 25.0001i | − | 0.834729i | ||||||
\(898\) | 62.0208i | 2.06966i | ||||||||
\(899\) | 38.9492 | 1.29903 | ||||||||
\(900\) | −2.83337 | −0.0944455 | ||||||||
\(901\) | 38.3549 | 1.27779 | ||||||||
\(902\) | 68.9212 | − | 27.6803i | 2.29482 | − | 0.921654i | ||||
\(903\) | −14.0158 | − | 9.38398i | −0.466418 | − | 0.312279i | ||||
\(904\) | − | 17.1597i | − | 0.570723i | ||||||
\(905\) | −13.2775 | −0.441360 | ||||||||
\(906\) | − | 49.9445i | − | 1.65929i | ||||||
\(907\) | 35.5032 | 1.17887 | 0.589433 | − | 0.807817i | \(-0.299351\pi\) | ||||
0.589433 | + | 0.807817i | \(0.299351\pi\) | |||||||
\(908\) | −42.8789 | −1.42299 | ||||||||
\(909\) | −1.45309 | −0.0481958 | ||||||||
\(910\) | 31.5218 | + | 21.1047i | 1.04494 | + | 0.699614i | ||||
\(911\) | −36.4032 | −1.20609 | −0.603045 | − | 0.797707i | \(-0.706046\pi\) | ||||
−0.603045 | + | 0.797707i | \(0.706046\pi\) | |||||||
\(912\) | 3.82207i | 0.126561i | ||||||||
\(913\) | 19.0054 | + | 47.3215i | 0.628987 | + | 1.56611i | ||||
\(914\) | 9.37633 | 0.310141 | ||||||||
\(915\) | 9.22033 | 0.304815 | ||||||||
\(916\) | 13.7543i | 0.454456i | ||||||||
\(917\) | −28.5416 | − | 19.1094i | −0.942528 | − | 0.631048i | ||||
\(918\) | −8.40503 | −0.277407 | ||||||||
\(919\) | 43.9423i | 1.44952i | 0.688999 | + | 0.724762i | \(0.258050\pi\) | ||||
−0.688999 | + | 0.724762i | \(0.741950\pi\) | |||||||
\(920\) | 7.02329 | 0.231551 | ||||||||
\(921\) | 8.03584i | 0.264790i | ||||||||
\(922\) | 38.6939i | 1.27432i | ||||||||
\(923\) | 54.8152 | 1.80426 | ||||||||
\(924\) | −24.3264 | − | 5.13607i | −0.800280 | − | 0.168964i | ||||
\(925\) | 7.93290 | 0.260832 | ||||||||
\(926\) | 16.3049i | 0.535813i | ||||||||
\(927\) | 8.96086i | 0.294313i | ||||||||
\(928\) | −35.6803 | −1.17126 | ||||||||
\(929\) | − | 20.4209i | − | 0.669987i | −0.942220 | − | 0.334994i | \(-0.891266\pi\) | ||
0.942220 | − | 0.334994i | \(-0.108734\pi\) | |||||||
\(930\) | −17.4404 | −0.571893 | ||||||||
\(931\) | 6.21956 | + | 15.0948i | 0.203838 | + | 0.494713i | ||||
\(932\) | 53.7051i | 1.75917i | ||||||||
\(933\) | 12.4949 | 0.409064 | ||||||||
\(934\) | 5.00673 | 0.163825 | ||||||||
\(935\) | 11.7663 | − | 4.72560i | 0.384798 | − | 0.154544i | ||||
\(936\) | 11.9487i | 0.390557i | ||||||||
\(937\) | 24.1831 | 0.790026 | 0.395013 | − | 0.918676i | \(-0.370740\pi\) | ||||
0.395013 | + | 0.918676i | \(0.370740\pi\) | |||||||
\(938\) | −6.92152 | + | 10.3379i | −0.225996 | + | 0.337545i | ||||
\(939\) | −4.68778 | −0.152980 | ||||||||
\(940\) | −5.85686 | −0.191030 | ||||||||
\(941\) | 10.6236 | 0.346321 | 0.173160 | − | 0.984894i | \(-0.444602\pi\) | ||||
0.173160 | + | 0.984894i | \(0.444602\pi\) | |||||||
\(942\) | − | 14.3154i | − | 0.466422i | ||||||
\(943\) | 39.0467 | 1.27154 | ||||||||
\(944\) | 6.17204i | 0.200883i | ||||||||
\(945\) | 2.19849 | + | 1.47195i | 0.0715169 | + | 0.0478825i | ||||
\(946\) | 17.3245 | + | 43.1363i | 0.563269 | + | 1.40248i | ||||
\(947\) | −14.1439 | −0.459614 | −0.229807 | − | 0.973236i | \(-0.573810\pi\) | ||||
−0.229807 | + | 0.973236i | \(0.573810\pi\) | |||||||
\(948\) | −37.2018 | −1.20826 | ||||||||
\(949\) | 54.3985 | 1.76585 | ||||||||
\(950\) | − | 5.12749i | − | 0.166358i | ||||||
\(951\) | − | 17.0604i | − | 0.553221i | ||||||
\(952\) | −10.3102 | + | 15.3993i | −0.334156 | + | 0.499093i | ||||
\(953\) | 27.8095i | 0.900840i | 0.892817 | + | 0.450420i | \(0.148726\pi\) | ||||
−0.892817 | + | 0.450420i | \(0.851274\pi\) | |||||||
\(954\) | − | 22.0562i | − | 0.714096i | ||||||
\(955\) | − | 4.52806i | − | 0.146525i | ||||||
\(956\) | − | 24.4005i | − | 0.789170i | ||||||
\(957\) | 6.06888 | + | 15.1109i | 0.196179 | + | 0.488466i | ||||
\(958\) | 29.5083i | 0.953369i | ||||||||
\(959\) | 0.255279 | + | 0.170916i | 0.00824338 | + | 0.00551917i | ||||
\(960\) | 12.6992 | 0.409864 | ||||||||
\(961\) | −31.9308 | −1.03003 | ||||||||
\(962\) | − | 113.741i | − | 3.66717i | ||||||
\(963\) | 11.6514i | 0.375461i | ||||||||
\(964\) | 70.9005 | 2.28355 | ||||||||
\(965\) | 4.39698 | 0.141544 | ||||||||
\(966\) | −18.5281 | − | 12.4050i | −0.596130 | − | 0.399125i | ||||
\(967\) | 11.4103i | 0.366930i | 0.983026 | + | 0.183465i | \(0.0587313\pi\) | ||||
−0.983026 | + | 0.183465i | \(0.941269\pi\) | |||||||
\(968\) | 13.9398 | + | 14.5551i | 0.448042 | + | 0.467818i | ||||
\(969\) | − | 8.91650i | − | 0.286439i | ||||||
\(970\) | 22.2037i | 0.712919i | ||||||||
\(971\) | 45.1873i | 1.45013i | 0.688680 | + | 0.725065i | \(0.258190\pi\) | ||||
−0.688680 | + | 0.725065i | \(0.741810\pi\) | |||||||
\(972\) | 2.83337i | 0.0908802i | ||||||||
\(973\) | −4.80540 | − | 3.21735i | −0.154054 | − | 0.103143i | ||||
\(974\) | − | 46.2282i | − | 1.48125i | ||||||
\(975\) | 6.52171i | 0.208862i | ||||||||
\(976\) | −15.1100 | −0.483660 | ||||||||
\(977\) | 49.5094 | 1.58395 | 0.791973 | − | 0.610556i | \(-0.209054\pi\) | ||||
0.791973 | + | 0.610556i | \(0.209054\pi\) | |||||||
\(978\) | −23.7310 | −0.758834 | ||||||||
\(979\) | 2.17246 | − | 0.872509i | 0.0694320 | − | 0.0278855i | ||||
\(980\) | 18.3379 | − | 7.55583i | 0.585784 | − | 0.241362i | ||||
\(981\) | − | 8.73292i | − | 0.278821i | ||||||
\(982\) | 64.1551 | 2.04727 | ||||||||
\(983\) | 1.65631i | 0.0528282i | 0.999651 | + | 0.0264141i | \(0.00840884\pi\) | ||||
−0.999651 | + | 0.0264141i | \(0.991591\pi\) | |||||||
\(984\) | −18.6623 | −0.594931 | ||||||||
\(985\) | 22.8254 | 0.727276 | ||||||||
\(986\) | 41.2673 | 1.31422 | ||||||||
\(987\) | 4.54451 | + | 3.04267i | 0.144653 | + | 0.0968493i | ||||
\(988\) | −43.0967 | −1.37109 | ||||||||
\(989\) | 24.4385i | 0.777099i | ||||||||
\(990\) | −2.71749 | − | 6.76626i | −0.0863673 | − | 0.215046i | ||||
\(991\) | 57.7821 | 1.83551 | 0.917754 | − | 0.397148i | \(-0.130000\pi\) | ||||
0.917754 | + | 0.397148i | \(0.130000\pi\) | |||||||
\(992\) | 57.6493 | 1.83037 | ||||||||
\(993\) | − | 17.0507i | − | 0.541088i | ||||||
\(994\) | 27.1993 | − | 40.6246i | 0.862708 | − | 1.28853i | ||||
\(995\) | −17.5325 | −0.555818 | ||||||||
\(996\) | − | 43.5650i | − | 1.38041i | ||||||
\(997\) | −49.4028 | −1.56460 | −0.782300 | − | 0.622901i | \(-0.785954\pi\) | ||||
−0.782300 | + | 0.622901i | \(0.785954\pi\) | |||||||
\(998\) | − | 64.0103i | − | 2.02621i | ||||||
\(999\) | − | 7.93290i | − | 0.250986i |
(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 | 1155.2.i.c.76.13 | yes | 16 | |
7.6 | odd | 2 | inner | 1155.2.i.c.76.14 | yes | 16 | |
11.10 | odd | 2 | inner | 1155.2.i.c.76.3 | ✓ | 16 | |
77.76 | even | 2 | inner | 1155.2.i.c.76.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.i.c.76.3 | ✓ | 16 | 11.10 | odd | 2 | inner | |
1155.2.i.c.76.4 | yes | 16 | 77.76 | even | 2 | inner | |
1155.2.i.c.76.13 | yes | 16 | 1.1 | even | 1 | trivial | |
1155.2.i.c.76.14 | yes | 16 | 7.6 | odd | 2 | inner |