Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(307,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("462.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.e (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.6679465984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 88x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 307.2 | ||
Root | \(-2.62511i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.307 |
Dual form | 462.2.e.a.307.7 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | − | 0.266088i | − | 0.118998i | −0.998228 | − | 0.0594991i | \(-0.981050\pi\) | ||
0.998228 | − | 0.0594991i | \(-0.0189504\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.34926 | − | 2.27585i | −0.509971 | − | 0.860192i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.266088 | −0.0841445 | ||||||||
\(11\) | 1.62511 | − | 2.89120i | 0.489989 | − | 0.871729i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.55171 | 0.707716 | 0.353858 | − | 0.935299i | \(-0.384870\pi\) | ||||
0.353858 | + | 0.935299i | \(0.384870\pi\) | |||||||
\(14\) | −2.27585 | + | 1.34926i | −0.608248 | + | 0.360604i | ||||
\(15\) | −0.266088 | −0.0687037 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.96460 | −1.20409 | −0.602046 | − | 0.798461i | \(-0.705648\pi\) | ||||
−0.602046 | + | 0.798461i | \(0.705648\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −8.21482 | −1.88461 | −0.942304 | − | 0.334758i | \(-0.891345\pi\) | ||||
−0.942304 | + | 0.334758i | \(0.891345\pi\) | |||||||
\(20\) | 0.266088i | 0.0594991i | ||||||||
\(21\) | −2.27585 | + | 1.34926i | −0.496632 | + | 0.294432i | ||||
\(22\) | −2.89120 | − | 1.62511i | −0.616405 | − | 0.346474i | ||||
\(23\) | −5.23069 | −1.09067 | −0.545337 | − | 0.838217i | \(-0.683598\pi\) | ||||
−0.545337 | + | 0.838217i | \(0.683598\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.92920 | 0.985839 | ||||||||
\(26\) | − | 2.55171i | − | 0.500431i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 1.34926 | + | 2.27585i | 0.254985 | + | 0.430096i | ||||
\(29\) | − | 5.25022i | − | 0.974941i | −0.873139 | − | 0.487470i | \(-0.837920\pi\) | ||
0.873139 | − | 0.487470i | \(-0.162080\pi\) | |||||||
\(30\) | 0.266088i | 0.0485808i | ||||||||
\(31\) | 4.28562i | 0.769720i | 0.922975 | + | 0.384860i | \(0.125750\pi\) | ||||
−0.922975 | + | 0.384860i | \(0.874250\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −2.89120 | − | 1.62511i | −0.503293 | − | 0.282895i | ||||
\(34\) | 4.96460i | 0.851422i | ||||||||
\(35\) | −0.605578 | + | 0.359021i | −0.102361 | + | 0.0606856i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.39702 | 1.21606 | 0.608031 | − | 0.793913i | \(-0.291959\pi\) | ||||
0.608031 | + | 0.793913i | \(0.291959\pi\) | |||||||
\(38\) | 8.21482i | 1.33262i | ||||||||
\(39\) | − | 2.55171i | − | 0.408600i | ||||||
\(40\) | 0.266088 | 0.0420722 | ||||||||
\(41\) | 6.21482 | 0.970591 | 0.485296 | − | 0.874350i | \(-0.338712\pi\) | ||||
0.485296 | + | 0.874350i | \(0.338712\pi\) | |||||||
\(42\) | 1.34926 | + | 2.27585i | 0.208195 | + | 0.351172i | ||||
\(43\) | − | 1.46782i | − | 0.223841i | −0.993717 | − | 0.111921i | \(-0.964300\pi\) | ||
0.993717 | − | 0.111921i | \(-0.0357002\pi\) | |||||||
\(44\) | −1.62511 | + | 2.89120i | −0.244994 | + | 0.435864i | ||||
\(45\) | 0.266088i | 0.0396661i | ||||||||
\(46\) | 5.23069i | 0.771223i | ||||||||
\(47\) | − | 10.0485i | − | 1.46572i | −0.680378 | − | 0.732861i | \(-0.738185\pi\) | ||
0.680378 | − | 0.732861i | \(-0.261815\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −3.35902 | + | 6.14142i | −0.479860 | + | 0.877345i | ||||
\(50\) | − | 4.92920i | − | 0.697094i | ||||||
\(51\) | 4.96460i | 0.695183i | ||||||||
\(52\) | −2.55171 | −0.353858 | ||||||||
\(53\) | −13.1989 | −1.81301 | −0.906507 | − | 0.422190i | \(-0.861261\pi\) | ||||
−0.906507 | + | 0.422190i | \(0.861261\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.769313 | − | 0.432422i | −0.103734 | − | 0.0583078i | ||||
\(56\) | 2.27585 | − | 1.34926i | 0.304124 | − | 0.180302i | ||||
\(57\) | 8.21482i | 1.08808i | ||||||||
\(58\) | −5.25022 | −0.689387 | ||||||||
\(59\) | − | 9.10342i | − | 1.18516i | −0.805510 | − | 0.592582i | \(-0.798109\pi\) | ||
0.805510 | − | 0.592582i | \(-0.201891\pi\) | |||||||
\(60\) | 0.266088 | 0.0343518 | ||||||||
\(61\) | 5.98047 | 0.765721 | 0.382860 | − | 0.923806i | \(-0.374939\pi\) | ||||
0.382860 | + | 0.923806i | \(0.374939\pi\) | |||||||
\(62\) | 4.28562 | 0.544274 | ||||||||
\(63\) | 1.34926 | + | 2.27585i | 0.169990 | + | 0.286731i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 0.678979i | − | 0.0842170i | ||||||
\(66\) | −1.62511 | + | 2.89120i | −0.200037 | + | 0.355882i | ||||
\(67\) | 12.3536 | 1.50924 | 0.754618 | − | 0.656164i | \(-0.227822\pi\) | ||||
0.754618 | + | 0.656164i | \(0.227822\pi\) | |||||||
\(68\) | 4.96460 | 0.602046 | ||||||||
\(69\) | 5.23069i | 0.629701i | ||||||||
\(70\) | 0.359021 | + | 0.605578i | 0.0429112 | + | 0.0723804i | ||||
\(71\) | 4.93708 | 0.585924 | 0.292962 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292962 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 2.96460 | 0.346980 | 0.173490 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173490 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(74\) | − | 7.39702i | − | 0.859886i | ||||||
\(75\) | − | 4.92920i | − | 0.569175i | ||||||
\(76\) | 8.21482 | 0.942304 | ||||||||
\(77\) | −8.77263 | + | 0.202452i | −0.999734 | + | 0.0230716i | ||||
\(78\) | −2.55171 | −0.288924 | ||||||||
\(79\) | 6.16633i | 0.693767i | 0.937908 | + | 0.346883i | \(0.112760\pi\) | ||||
−0.937908 | + | 0.346883i | \(0.887240\pi\) | |||||||
\(80\) | − | 0.266088i | − | 0.0297496i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 6.21482i | − | 0.686312i | ||||||
\(83\) | 10.6002 | 1.16352 | 0.581761 | − | 0.813360i | \(-0.302364\pi\) | ||||
0.581761 | + | 0.813360i | \(0.302364\pi\) | |||||||
\(84\) | 2.27585 | − | 1.34926i | 0.248316 | − | 0.147216i | ||||
\(85\) | 1.32102i | 0.143285i | ||||||||
\(86\) | −1.46782 | −0.158279 | ||||||||
\(87\) | −5.25022 | −0.562882 | ||||||||
\(88\) | 2.89120 | + | 1.62511i | 0.308203 | + | 0.173237i | ||||
\(89\) | − | 1.78239i | − | 0.188933i | −0.995528 | − | 0.0944667i | \(-0.969885\pi\) | ||
0.995528 | − | 0.0944667i | \(-0.0301146\pi\) | |||||||
\(90\) | 0.266088 | 0.0280482 | ||||||||
\(91\) | −3.44290 | − | 5.80731i | −0.360914 | − | 0.608772i | ||||
\(92\) | 5.23069 | 0.545337 | ||||||||
\(93\) | 4.28562 | 0.444398 | ||||||||
\(94\) | −10.0485 | −1.03642 | ||||||||
\(95\) | 2.18587i | 0.224265i | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 0.146803i | − | 0.0149056i | −0.999972 | − | 0.00745279i | \(-0.997628\pi\) | ||
0.999972 | − | 0.00745279i | \(-0.00237232\pi\) | |||||||
\(98\) | 6.14142 | + | 3.35902i | 0.620377 | + | 0.339312i | ||||
\(99\) | −1.62511 | + | 2.89120i | −0.163330 | + | 0.290576i | ||||
\(100\) | −4.92920 | −0.492920 | ||||||||
\(101\) | 13.7824 | 1.37140 | 0.685700 | − | 0.727885i | \(-0.259496\pi\) | ||||
0.685700 | + | 0.727885i | \(0.259496\pi\) | |||||||
\(102\) | 4.96460 | 0.491569 | ||||||||
\(103\) | − | 19.8504i | − | 1.95592i | −0.208795 | − | 0.977959i | \(-0.566954\pi\) | ||
0.208795 | − | 0.977959i | \(-0.433046\pi\) | |||||||
\(104\) | 2.55171i | 0.250216i | ||||||||
\(105\) | 0.359021 | + | 0.605578i | 0.0350368 | + | 0.0590983i | ||||
\(106\) | 13.1989i | 1.28199i | ||||||||
\(107\) | − | 13.7824i | − | 1.33239i | −0.745776 | − | 0.666197i | \(-0.767921\pi\) | ||
0.745776 | − | 0.666197i | \(-0.232079\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 0.365842i | 0.0350413i | 0.999847 | + | 0.0175207i | \(0.00557729\pi\) | ||||
−0.999847 | + | 0.0175207i | \(0.994423\pi\) | |||||||
\(110\) | −0.432422 | + | 0.769313i | −0.0412298 | + | 0.0733511i | ||||
\(111\) | − | 7.39702i | − | 0.702094i | ||||||
\(112\) | −1.34926 | − | 2.27585i | −0.127493 | − | 0.215048i | ||||
\(113\) | 12.2828 | 1.15547 | 0.577736 | − | 0.816224i | \(-0.303936\pi\) | ||||
0.577736 | + | 0.816224i | \(0.303936\pi\) | |||||||
\(114\) | 8.21482 | 0.769388 | ||||||||
\(115\) | 1.39182i | 0.129788i | ||||||||
\(116\) | 5.25022i | 0.487470i | ||||||||
\(117\) | −2.55171 | −0.235905 | ||||||||
\(118\) | −9.10342 | −0.838037 | ||||||||
\(119\) | 6.69851 | + | 11.2987i | 0.614051 | + | 1.03575i | ||||
\(120\) | − | 0.266088i | − | 0.0242904i | ||||||
\(121\) | −5.71804 | − | 9.39702i | −0.519822 | − | 0.854275i | ||||
\(122\) | − | 5.98047i | − | 0.541446i | ||||||
\(123\) | − | 6.21482i | − | 0.560371i | ||||||
\(124\) | − | 4.28562i | − | 0.384860i | ||||||
\(125\) | − | 2.64204i | − | 0.236311i | ||||||
\(126\) | 2.27585 | − | 1.34926i | 0.202749 | − | 0.120201i | ||||
\(127\) | 10.0247i | 0.889551i | 0.895642 | + | 0.444775i | \(0.146716\pi\) | ||||
−0.895642 | + | 0.444775i | \(0.853284\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.46782 | −0.129235 | ||||||||
\(130\) | −0.678979 | −0.0595504 | ||||||||
\(131\) | −20.0363 | −1.75058 | −0.875289 | − | 0.483601i | \(-0.839329\pi\) | ||||
−0.875289 | + | 0.483601i | \(0.839329\pi\) | |||||||
\(132\) | 2.89120 | + | 1.62511i | 0.251646 | + | 0.141448i | ||||
\(133\) | 11.0839 | + | 18.6957i | 0.961095 | + | 1.62112i | ||||
\(134\) | − | 12.3536i | − | 1.06719i | ||||||
\(135\) | 0.266088 | 0.0229012 | ||||||||
\(136\) | − | 4.96460i | − | 0.425711i | ||||||
\(137\) | −7.17942 | −0.613379 | −0.306689 | − | 0.951810i | \(-0.599221\pi\) | ||||
−0.306689 | + | 0.951810i | \(0.599221\pi\) | |||||||
\(138\) | 5.23069 | 0.445266 | ||||||||
\(139\) | 16.7861 | 1.42377 | 0.711887 | − | 0.702294i | \(-0.247841\pi\) | ||||
0.711887 | + | 0.702294i | \(0.247841\pi\) | |||||||
\(140\) | 0.605578 | − | 0.359021i | 0.0511807 | − | 0.0303428i | ||||
\(141\) | −10.0485 | −0.846235 | ||||||||
\(142\) | − | 4.93708i | − | 0.414311i | ||||||
\(143\) | 4.14680 | − | 7.37749i | 0.346773 | − | 0.616937i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −1.39702 | −0.116016 | ||||||||
\(146\) | − | 2.96460i | − | 0.245352i | ||||||
\(147\) | 6.14142 | + | 3.35902i | 0.506535 | + | 0.277047i | ||||
\(148\) | −7.39702 | −0.608031 | ||||||||
\(149\) | 17.5648i | 1.43896i | 0.694511 | + | 0.719482i | \(0.255621\pi\) | ||||
−0.694511 | + | 0.719482i | \(0.744379\pi\) | |||||||
\(150\) | −4.92920 | −0.402467 | ||||||||
\(151\) | 15.0131i | 1.22175i | 0.791728 | + | 0.610874i | \(0.209182\pi\) | ||||
−0.791728 | + | 0.610874i | \(0.790818\pi\) | |||||||
\(152\) | − | 8.21482i | − | 0.666310i | ||||||
\(153\) | 4.96460 | 0.401364 | ||||||||
\(154\) | 0.202452 | + | 8.77263i | 0.0163141 | + | 0.706919i | ||||
\(155\) | 1.14035 | 0.0915953 | ||||||||
\(156\) | 2.55171i | 0.204300i | ||||||||
\(157\) | − | 10.6393i | − | 0.849105i | −0.905403 | − | 0.424552i | \(-0.860431\pi\) | ||
0.905403 | − | 0.424552i | \(-0.139569\pi\) | |||||||
\(158\) | 6.16633 | 0.490567 | ||||||||
\(159\) | 13.1989i | 1.04674i | ||||||||
\(160\) | −0.266088 | −0.0210361 | ||||||||
\(161\) | 7.05753 | + | 11.9043i | 0.556211 | + | 0.938189i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 0.385373 | 0.0301848 | 0.0150924 | − | 0.999886i | \(-0.495196\pi\) | ||||
0.0150924 | + | 0.999886i | \(0.495196\pi\) | |||||||
\(164\) | −6.21482 | −0.485296 | ||||||||
\(165\) | −0.432422 | + | 0.769313i | −0.0336640 | + | 0.0598910i | ||||
\(166\) | − | 10.6002i | − | 0.822734i | ||||||
\(167\) | −0.967388 | −0.0748587 | −0.0374294 | − | 0.999299i | \(-0.511917\pi\) | ||||
−0.0374294 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(168\) | −1.34926 | − | 2.27585i | −0.104097 | − | 0.175586i | ||||
\(169\) | −6.48879 | −0.499138 | ||||||||
\(170\) | 1.32102 | 0.101318 | ||||||||
\(171\) | 8.21482 | 0.628203 | ||||||||
\(172\) | 1.46782i | 0.111921i | ||||||||
\(173\) | −0.385373 | −0.0292994 | −0.0146497 | − | 0.999893i | \(-0.504663\pi\) | ||||
−0.0146497 | + | 0.999893i | \(0.504663\pi\) | |||||||
\(174\) | 5.25022i | 0.398018i | ||||||||
\(175\) | −6.65074 | − | 11.2181i | −0.502749 | − | 0.848011i | ||||
\(176\) | 1.62511 | − | 2.89120i | 0.122497 | − | 0.217932i | ||||
\(177\) | −9.10342 | −0.684255 | ||||||||
\(178\) | −1.78239 | −0.133596 | ||||||||
\(179\) | −6.69994 | −0.500777 | −0.250389 | − | 0.968145i | \(-0.580558\pi\) | ||||
−0.250389 | + | 0.968145i | \(0.580558\pi\) | |||||||
\(180\) | − | 0.266088i | − | 0.0198330i | ||||||
\(181\) | 26.1650i | 1.94483i | 0.233263 | + | 0.972414i | \(0.425060\pi\) | ||||
−0.233263 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(182\) | −5.80731 | + | 3.44290i | −0.430467 | + | 0.255205i | ||||
\(183\) | − | 5.98047i | − | 0.442089i | ||||||
\(184\) | − | 5.23069i | − | 0.385611i | ||||||
\(185\) | − | 1.96826i | − | 0.144709i | ||||||
\(186\) | − | 4.28562i | − | 0.314237i | ||||||
\(187\) | −8.06801 | + | 14.3536i | −0.589992 | + | 1.04964i | ||||
\(188\) | 10.0485i | 0.732861i | ||||||||
\(189\) | 2.27585 | − | 1.34926i | 0.165544 | − | 0.0981439i | ||||
\(190\) | 2.18587 | 0.158579 | ||||||||
\(191\) | 10.6277 | 0.768994 | 0.384497 | − | 0.923126i | \(-0.374375\pi\) | ||||
0.384497 | + | 0.923126i | \(0.374375\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 14.4614i | − | 1.04095i | −0.853876 | − | 0.520476i | \(-0.825754\pi\) | ||
0.853876 | − | 0.520476i | \(-0.174246\pi\) | |||||||
\(194\) | −0.146803 | −0.0105398 | ||||||||
\(195\) | −0.678979 | −0.0486227 | ||||||||
\(196\) | 3.35902 | − | 6.14142i | 0.239930 | − | 0.438673i | ||||
\(197\) | 1.35276i | 0.0963802i | 0.998838 | + | 0.0481901i | \(0.0153453\pi\) | ||||
−0.998838 | + | 0.0481901i | \(0.984655\pi\) | |||||||
\(198\) | 2.89120 | + | 1.62511i | 0.205468 | + | 0.115491i | ||||
\(199\) | − | 8.52419i | − | 0.604264i | −0.953266 | − | 0.302132i | \(-0.902302\pi\) | ||
0.953266 | − | 0.302132i | \(-0.0976983\pi\) | |||||||
\(200\) | 4.92920i | 0.348547i | ||||||||
\(201\) | − | 12.3536i | − | 0.871358i | ||||||
\(202\) | − | 13.7824i | − | 0.969726i | ||||||
\(203\) | −11.9487 | + | 7.08388i | −0.838636 | + | 0.497191i | ||||
\(204\) | − | 4.96460i | − | 0.347591i | ||||||
\(205\) | − | 1.65369i | − | 0.115499i | ||||||
\(206\) | −19.8504 | −1.38304 | ||||||||
\(207\) | 5.23069 | 0.363558 | ||||||||
\(208\) | 2.55171 | 0.176929 | ||||||||
\(209\) | −13.3500 | + | 23.7507i | −0.923437 | + | 1.64287i | ||||
\(210\) | 0.605578 | − | 0.359021i | 0.0417888 | − | 0.0247748i | ||||
\(211\) | − | 10.8258i | − | 0.745278i | −0.927976 | − | 0.372639i | \(-0.878453\pi\) | ||
0.927976 | − | 0.372639i | \(-0.121547\pi\) | |||||||
\(212\) | 13.1989 | 0.906507 | ||||||||
\(213\) | − | 4.93708i | − | 0.338283i | ||||||
\(214\) | −13.7824 | −0.942145 | ||||||||
\(215\) | −0.390570 | −0.0266367 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 9.75344 | − | 5.78239i | 0.662107 | − | 0.392534i | ||||
\(218\) | 0.365842 | 0.0247780 | ||||||||
\(219\) | − | 2.96460i | − | 0.200329i | ||||||
\(220\) | 0.769313 | + | 0.432422i | 0.0518671 | + | 0.0291539i | ||||
\(221\) | −12.6682 | −0.852156 | ||||||||
\(222\) | −7.39702 | −0.496456 | ||||||||
\(223\) | − | 1.38903i | − | 0.0930166i | −0.998918 | − | 0.0465083i | \(-0.985191\pi\) | ||
0.998918 | − | 0.0465083i | \(-0.0148094\pi\) | |||||||
\(224\) | −2.27585 | + | 1.34926i | −0.152062 | + | 0.0901509i | ||||
\(225\) | −4.92920 | −0.328613 | ||||||||
\(226\) | − | 12.2828i | − | 0.817042i | ||||||
\(227\) | −4.04705 | −0.268612 | −0.134306 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134306 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(228\) | − | 8.21482i | − | 0.544040i | ||||||
\(229\) | 15.2265i | 1.00619i | 0.864230 | + | 0.503097i | \(0.167806\pi\) | ||||
−0.864230 | + | 0.503097i | \(0.832194\pi\) | |||||||
\(230\) | 1.39182 | 0.0917741 | ||||||||
\(231\) | 0.202452 | + | 8.77263i | 0.0133204 | + | 0.577197i | ||||
\(232\) | 5.25022 | 0.344694 | ||||||||
\(233\) | 10.2936i | 0.674357i | 0.941441 | + | 0.337178i | \(0.109473\pi\) | ||||
−0.941441 | + | 0.337178i | \(0.890527\pi\) | |||||||
\(234\) | 2.55171i | 0.166810i | ||||||||
\(235\) | −2.67378 | −0.174418 | ||||||||
\(236\) | 9.10342i | 0.592582i | ||||||||
\(237\) | 6.16633 | 0.400546 | ||||||||
\(238\) | 11.2987 | − | 6.69851i | 0.732386 | − | 0.434200i | ||||
\(239\) | − | 1.14248i | − | 0.0739007i | −0.999317 | − | 0.0369504i | \(-0.988236\pi\) | ||
0.999317 | − | 0.0369504i | \(-0.0117643\pi\) | |||||||
\(240\) | −0.266088 | −0.0171759 | ||||||||
\(241\) | −0.503225 | −0.0324156 | −0.0162078 | − | 0.999869i | \(-0.505159\pi\) | ||||
−0.0162078 | + | 0.999869i | \(0.505159\pi\) | |||||||
\(242\) | −9.39702 | + | 5.71804i | −0.604063 | + | 0.367570i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −5.98047 | −0.382860 | ||||||||
\(245\) | 1.63416 | + | 0.893796i | 0.104403 | + | 0.0571025i | ||||
\(246\) | −6.21482 | −0.396242 | ||||||||
\(247\) | −20.9618 | −1.33377 | ||||||||
\(248\) | −4.28562 | −0.272137 | ||||||||
\(249\) | − | 10.6002i | − | 0.671760i | ||||||
\(250\) | −2.64204 | −0.167097 | ||||||||
\(251\) | 7.03261i | 0.443895i | 0.975059 | + | 0.221947i | \(0.0712413\pi\) | ||||
−0.975059 | + | 0.221947i | \(0.928759\pi\) | |||||||
\(252\) | −1.34926 | − | 2.27585i | −0.0849951 | − | 0.143365i | ||||
\(253\) | −8.50044 | + | 15.1229i | −0.534418 | + | 0.950771i | ||||
\(254\) | 10.0247 | 0.629007 | ||||||||
\(255\) | 1.32102 | 0.0827255 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 3.85320i | − | 0.240356i | −0.992752 | − | 0.120178i | \(-0.961653\pi\) | ||
0.992752 | − | 0.120178i | \(-0.0383465\pi\) | |||||||
\(258\) | 1.46782i | 0.0913827i | ||||||||
\(259\) | −9.98047 | − | 16.8345i | −0.620156 | − | 1.04605i | ||||
\(260\) | 0.678979i | 0.0421085i | ||||||||
\(261\) | 5.25022i | 0.324980i | ||||||||
\(262\) | 20.0363i | 1.23785i | ||||||||
\(263\) | 6.48234i | 0.399718i | 0.979825 | + | 0.199859i | \(0.0640484\pi\) | ||||
−0.979825 | + | 0.199859i | \(0.935952\pi\) | |||||||
\(264\) | 1.62511 | − | 2.89120i | 0.100019 | − | 0.177941i | ||||
\(265\) | 3.51208i | 0.215746i | ||||||||
\(266\) | 18.6957 | − | 11.0839i | 1.14631 | − | 0.679597i | ||||
\(267\) | −1.78239 | −0.109081 | ||||||||
\(268\) | −12.3536 | −0.754618 | ||||||||
\(269\) | 20.7983i | 1.26809i | 0.773295 | + | 0.634046i | \(0.218607\pi\) | ||||
−0.773295 | + | 0.634046i | \(0.781393\pi\) | |||||||
\(270\) | − | 0.266088i | − | 0.0161936i | ||||||
\(271\) | −22.7955 | −1.38473 | −0.692363 | − | 0.721549i | \(-0.743430\pi\) | ||||
−0.692363 | + | 0.721549i | \(0.743430\pi\) | |||||||
\(272\) | −4.96460 | −0.301023 | ||||||||
\(273\) | −5.80731 | + | 3.44290i | −0.351475 | + | 0.208374i | ||||
\(274\) | 7.17942i | 0.433724i | ||||||||
\(275\) | 8.01048 | − | 14.2513i | 0.483050 | − | 0.859385i | ||||
\(276\) | − | 5.23069i | − | 0.314850i | ||||||
\(277\) | 17.3277i | 1.04112i | 0.853826 | + | 0.520559i | \(0.174276\pi\) | ||||
−0.853826 | + | 0.520559i | \(0.825724\pi\) | |||||||
\(278\) | − | 16.7861i | − | 1.00676i | ||||||
\(279\) | − | 4.28562i | − | 0.256573i | ||||||
\(280\) | −0.359021 | − | 0.605578i | −0.0214556 | − | 0.0361902i | ||||
\(281\) | − | 5.17942i | − | 0.308978i | −0.987995 | − | 0.154489i | \(-0.950627\pi\) | ||
0.987995 | − | 0.154489i | \(-0.0493731\pi\) | |||||||
\(282\) | 10.0485i | 0.598378i | ||||||||
\(283\) | 12.4534 | 0.740277 | 0.370139 | − | 0.928977i | \(-0.379310\pi\) | ||||
0.370139 | + | 0.928977i | \(0.379310\pi\) | |||||||
\(284\) | −4.93708 | −0.292962 | ||||||||
\(285\) | 2.18587 | 0.129479 | ||||||||
\(286\) | −7.37749 | − | 4.14680i | −0.436240 | − | 0.245206i | ||||
\(287\) | −8.38537 | − | 14.1440i | −0.494973 | − | 0.834895i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 7.64724 | 0.449838 | ||||||||
\(290\) | 1.39702i | 0.0820359i | ||||||||
\(291\) | −0.146803 | −0.00860574 | ||||||||
\(292\) | −2.96460 | −0.173490 | ||||||||
\(293\) | −11.4570 | −0.669328 | −0.334664 | − | 0.942338i | \(-0.608623\pi\) | ||||
−0.334664 | + | 0.942338i | \(0.608623\pi\) | |||||||
\(294\) | 3.35902 | − | 6.14142i | 0.195902 | − | 0.358175i | ||||
\(295\) | −2.42231 | −0.141032 | ||||||||
\(296\) | 7.39702i | 0.429943i | ||||||||
\(297\) | 2.89120 | + | 1.62511i | 0.167764 | + | 0.0942984i | ||||
\(298\) | 17.5648 | 1.01750 | ||||||||
\(299\) | −13.3472 | −0.771888 | ||||||||
\(300\) | 4.92920i | 0.284587i | ||||||||
\(301\) | −3.34055 | + | 1.98047i | −0.192546 | + | 0.114152i | ||||
\(302\) | 15.0131 | 0.863906 | ||||||||
\(303\) | − | 13.7824i | − | 0.791778i | ||||||
\(304\) | −8.21482 | −0.471152 | ||||||||
\(305\) | − | 1.59133i | − | 0.0911194i | ||||||
\(306\) | − | 4.96460i | − | 0.283807i | ||||||
\(307\) | −4.78606 | −0.273155 | −0.136577 | − | 0.990629i | \(-0.543610\pi\) | ||||
−0.136577 | + | 0.990629i | \(0.543610\pi\) | |||||||
\(308\) | 8.77263 | − | 0.202452i | 0.499867 | − | 0.0115358i | ||||
\(309\) | −19.8504 | −1.12925 | ||||||||
\(310\) | − | 1.14035i | − | 0.0647677i | ||||||
\(311\) | 15.8807i | 0.900513i | 0.892899 | + | 0.450256i | \(0.148667\pi\) | ||||
−0.892899 | + | 0.450256i | \(0.851333\pi\) | |||||||
\(312\) | 2.55171 | 0.144462 | ||||||||
\(313\) | − | 30.6524i | − | 1.73258i | −0.499543 | − | 0.866289i | \(-0.666499\pi\) | ||
0.499543 | − | 0.866289i | \(-0.333501\pi\) | |||||||
\(314\) | −10.6393 | −0.600408 | ||||||||
\(315\) | 0.605578 | − | 0.359021i | 0.0341204 | − | 0.0202285i | ||||
\(316\) | − | 6.16633i | − | 0.346883i | ||||||
\(317\) | −6.69851 | −0.376226 | −0.188113 | − | 0.982147i | \(-0.560237\pi\) | ||||
−0.188113 | + | 0.982147i | \(0.560237\pi\) | |||||||
\(318\) | 13.1989 | 0.740160 | ||||||||
\(319\) | −15.1794 | − | 8.53218i | −0.849884 | − | 0.477710i | ||||
\(320\) | 0.266088i | 0.0148748i | ||||||||
\(321\) | −13.7824 | −0.769258 | ||||||||
\(322\) | 11.9043 | − | 7.05753i | 0.663399 | − | 0.393301i | ||||
\(323\) | 40.7833 | 2.26924 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 12.5779 | 0.697695 | ||||||||
\(326\) | − | 0.385373i | − | 0.0213439i | ||||||
\(327\) | 0.365842 | 0.0202311 | ||||||||
\(328\) | 6.21482i | 0.343156i | ||||||||
\(329\) | −22.8689 | + | 13.5580i | −1.26080 | + | 0.747475i | ||||
\(330\) | 0.769313 | + | 0.432422i | 0.0423493 | + | 0.0238041i | ||||
\(331\) | 31.5330 | 1.73321 | 0.866607 | − | 0.498992i | \(-0.166296\pi\) | ||||
0.866607 | + | 0.498992i | \(0.166296\pi\) | |||||||
\(332\) | −10.6002 | −0.581761 | ||||||||
\(333\) | −7.39702 | −0.405354 | ||||||||
\(334\) | 0.967388i | 0.0529331i | ||||||||
\(335\) | − | 3.28716i | − | 0.179596i | ||||||
\(336\) | −2.27585 | + | 1.34926i | −0.124158 | + | 0.0736079i | ||||
\(337\) | − | 22.0652i | − | 1.20197i | −0.799261 | − | 0.600985i | \(-0.794775\pi\) | ||
0.799261 | − | 0.600985i | \(-0.205225\pi\) | |||||||
\(338\) | 6.48879i | 0.352944i | ||||||||
\(339\) | − | 12.2828i | − | 0.667112i | ||||||
\(340\) | − | 1.32102i | − | 0.0716424i | ||||||
\(341\) | 12.3906 | + | 6.96460i | 0.670987 | + | 0.377154i | ||||
\(342\) | − | 8.21482i | − | 0.444206i | ||||||
\(343\) | 18.5091 | − | 0.641696i | 0.999400 | − | 0.0346483i | ||||
\(344\) | 1.46782 | 0.0791397 | ||||||||
\(345\) | 1.39182 | 0.0749333 | ||||||||
\(346\) | 0.385373i | 0.0207178i | ||||||||
\(347\) | 27.9365i | 1.49971i | 0.661602 | + | 0.749855i | \(0.269877\pi\) | ||||
−0.661602 | + | 0.749855i | \(0.730123\pi\) | |||||||
\(348\) | 5.25022 | 0.281441 | ||||||||
\(349\) | 1.19375 | 0.0638999 | 0.0319500 | − | 0.999489i | \(-0.489828\pi\) | ||||
0.0319500 | + | 0.999489i | \(0.489828\pi\) | |||||||
\(350\) | −11.2181 | + | 6.65074i | −0.599634 | + | 0.355497i | ||||
\(351\) | 2.55171i | 0.136200i | ||||||||
\(352\) | −2.89120 | − | 1.62511i | −0.154101 | − | 0.0866186i | ||||
\(353\) | − | 33.4413i | − | 1.77990i | −0.456058 | − | 0.889950i | \(-0.650739\pi\) | ||
0.456058 | − | 0.889950i | \(-0.349261\pi\) | |||||||
\(354\) | 9.10342i | 0.483841i | ||||||||
\(355\) | − | 1.31370i | − | 0.0697239i | ||||||
\(356\) | 1.78239i | 0.0944667i | ||||||||
\(357\) | 11.2987 | − | 6.69851i | 0.597991 | − | 0.354523i | ||||
\(358\) | 6.69994i | 0.354103i | ||||||||
\(359\) | 8.45618i | 0.446300i | 0.974784 | + | 0.223150i | \(0.0716340\pi\) | ||||
−0.974784 | + | 0.223150i | \(0.928366\pi\) | |||||||
\(360\) | −0.266088 | −0.0140241 | ||||||||
\(361\) | 48.4832 | 2.55175 | ||||||||
\(362\) | 26.1650 | 1.37520 | ||||||||
\(363\) | −9.39702 | + | 5.71804i | −0.493216 | + | 0.300119i | ||||
\(364\) | 3.44290 | + | 5.80731i | 0.180457 | + | 0.304386i | ||||
\(365\) | − | 0.788845i | − | 0.0412900i | ||||||
\(366\) | −5.98047 | −0.312604 | ||||||||
\(367\) | − | 21.4831i | − | 1.12141i | −0.828016 | − | 0.560705i | \(-0.810530\pi\) | ||
0.828016 | − | 0.560705i | \(-0.189470\pi\) | |||||||
\(368\) | −5.23069 | −0.272668 | ||||||||
\(369\) | −6.21482 | −0.323530 | ||||||||
\(370\) | −1.96826 | −0.102325 | ||||||||
\(371\) | 17.8087 | + | 30.0389i | 0.924584 | + | 1.55954i | ||||
\(372\) | −4.28562 | −0.222199 | ||||||||
\(373\) | − | 9.94141i | − | 0.514747i | −0.966312 | − | 0.257373i | \(-0.917143\pi\) | ||
0.966312 | − | 0.257373i | \(-0.0828570\pi\) | |||||||
\(374\) | 14.3536 | + | 8.06801i | 0.742209 | + | 0.417187i | ||||
\(375\) | −2.64204 | −0.136434 | ||||||||
\(376\) | 10.0485 | 0.518211 | ||||||||
\(377\) | − | 13.3970i | − | 0.689982i | ||||||
\(378\) | −1.34926 | − | 2.27585i | −0.0693982 | − | 0.117057i | ||||
\(379\) | −21.3862 | −1.09854 | −0.549269 | − | 0.835646i | \(-0.685094\pi\) | ||||
−0.549269 | + | 0.835646i | \(0.685094\pi\) | |||||||
\(380\) | − | 2.18587i | − | 0.112133i | ||||||
\(381\) | 10.0247 | 0.513582 | ||||||||
\(382\) | − | 10.6277i | − | 0.543761i | ||||||
\(383\) | − | 0.706497i | − | 0.0361003i | −0.999837 | − | 0.0180501i | \(-0.994254\pi\) | ||
0.999837 | − | 0.0180501i | \(-0.00574585\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.0538702 | + | 2.33429i | 0.00274548 | + | 0.118967i | ||||
\(386\) | −14.4614 | −0.736065 | ||||||||
\(387\) | 1.46782i | 0.0746137i | ||||||||
\(388\) | 0.146803i | 0.00745279i | ||||||||
\(389\) | −5.30149 | −0.268796 | −0.134398 | − | 0.990927i | \(-0.542910\pi\) | ||||
−0.134398 | + | 0.990927i | \(0.542910\pi\) | |||||||
\(390\) | 0.678979i | 0.0343814i | ||||||||
\(391\) | 25.9683 | 1.31327 | ||||||||
\(392\) | −6.14142 | − | 3.35902i | −0.310188 | − | 0.169656i | ||||
\(393\) | 20.0363i | 1.01070i | ||||||||
\(394\) | 1.35276 | 0.0681511 | ||||||||
\(395\) | 1.64079 | 0.0825570 | ||||||||
\(396\) | 1.62511 | − | 2.89120i | 0.0816648 | − | 0.145288i | ||||
\(397\) | 24.9646i | 1.25294i | 0.779447 | + | 0.626469i | \(0.215500\pi\) | ||||
−0.779447 | + | 0.626469i | \(0.784500\pi\) | |||||||
\(398\) | −8.52419 | −0.427279 | ||||||||
\(399\) | 18.6957 | − | 11.0839i | 0.935957 | − | 0.554888i | ||||
\(400\) | 4.92920 | 0.246460 | ||||||||
\(401\) | −11.6146 | −0.580007 | −0.290003 | − | 0.957026i | \(-0.593656\pi\) | ||||
−0.290003 | + | 0.957026i | \(0.593656\pi\) | |||||||
\(402\) | −12.3536 | −0.616143 | ||||||||
\(403\) | 10.9356i | 0.544743i | ||||||||
\(404\) | −13.7824 | −0.685700 | ||||||||
\(405\) | − | 0.266088i | − | 0.0132220i | ||||||
\(406\) | 7.08388 | + | 11.9487i | 0.351567 | + | 0.593005i | ||||
\(407\) | 12.0210 | − | 21.3862i | 0.595857 | − | 1.06008i | ||||
\(408\) | −4.96460 | −0.245784 | ||||||||
\(409\) | 15.2032 | 0.751748 | 0.375874 | − | 0.926671i | \(-0.377342\pi\) | ||||
0.375874 | + | 0.926671i | \(0.377342\pi\) | |||||||
\(410\) | −1.65369 | −0.0816699 | ||||||||
\(411\) | 7.17942i | 0.354134i | ||||||||
\(412\) | 19.8504i | 0.977959i | ||||||||
\(413\) | −20.7180 | + | 12.2828i | −1.01947 | + | 0.604399i | ||||
\(414\) | − | 5.23069i | − | 0.257074i | ||||||
\(415\) | − | 2.82058i | − | 0.138457i | ||||||
\(416\) | − | 2.55171i | − | 0.125108i | ||||||
\(417\) | − | 16.7861i | − | 0.822017i | ||||||
\(418\) | 23.7507 | + | 13.3500i | 1.16168 | + | 0.652968i | ||||
\(419\) | − | 13.9683i | − | 0.682394i | −0.939992 | − | 0.341197i | \(-0.889168\pi\) | ||
0.939992 | − | 0.341197i | \(-0.110832\pi\) | |||||||
\(420\) | −0.359021 | − | 0.605578i | −0.0175184 | − | 0.0295492i | ||||
\(421\) | −4.53950 | −0.221242 | −0.110621 | − | 0.993863i | \(-0.535284\pi\) | ||||
−0.110621 | + | 0.993863i | \(0.535284\pi\) | |||||||
\(422\) | −10.8258 | −0.526991 | ||||||||
\(423\) | 10.0485i | 0.488574i | ||||||||
\(424\) | − | 13.1989i | − | 0.640997i | ||||||
\(425\) | −24.4715 | −1.18704 | ||||||||
\(426\) | −4.93708 | −0.239202 | ||||||||
\(427\) | −8.06918 | − | 13.6107i | −0.390495 | − | 0.658667i | ||||
\(428\) | 13.7824i | 0.666197i | ||||||||
\(429\) | −7.37749 | − | 4.14680i | −0.356189 | − | 0.200210i | ||||
\(430\) | 0.390570i | 0.0188350i | ||||||||
\(431\) | − | 11.5829i | − | 0.557928i | −0.960302 | − | 0.278964i | \(-0.910009\pi\) | ||
0.960302 | − | 0.278964i | \(-0.0899910\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 20.9227i | − | 1.00548i | −0.864437 | − | 0.502742i | \(-0.832325\pi\) | ||
0.864437 | − | 0.502742i | \(-0.167675\pi\) | |||||||
\(434\) | −5.78239 | − | 9.75344i | −0.277564 | − | 0.468180i | ||||
\(435\) | 1.39702i | 0.0669820i | ||||||||
\(436\) | − | 0.365842i | − | 0.0175207i | ||||||
\(437\) | 42.9691 | 2.05549 | ||||||||
\(438\) | −2.96460 | −0.141654 | ||||||||
\(439\) | −9.63703 | −0.459950 | −0.229975 | − | 0.973197i | \(-0.573864\pi\) | ||||
−0.229975 | + | 0.973197i | \(0.573864\pi\) | |||||||
\(440\) | 0.432422 | − | 0.769313i | 0.0206149 | − | 0.0366756i | ||||
\(441\) | 3.35902 | − | 6.14142i | 0.159953 | − | 0.292448i | ||||
\(442\) | 12.6682i | 0.602565i | ||||||||
\(443\) | 26.9935 | 1.28250 | 0.641251 | − | 0.767331i | \(-0.278416\pi\) | ||||
0.641251 | + | 0.767331i | \(0.278416\pi\) | |||||||
\(444\) | 7.39702i | 0.351047i | ||||||||
\(445\) | −0.474274 | −0.0224827 | ||||||||
\(446\) | −1.38903 | −0.0657727 | ||||||||
\(447\) | 17.5648 | 0.830786 | ||||||||
\(448\) | 1.34926 | + | 2.27585i | 0.0637463 | + | 0.107524i | ||||
\(449\) | 17.6799 | 0.834364 | 0.417182 | − | 0.908823i | \(-0.363018\pi\) | ||||
0.417182 | + | 0.908823i | \(0.363018\pi\) | |||||||
\(450\) | 4.92920i | 0.232365i | ||||||||
\(451\) | 10.0998 | − | 17.9683i | 0.475579 | − | 0.846092i | ||||
\(452\) | −12.2828 | −0.577736 | ||||||||
\(453\) | 15.0131 | 0.705376 | ||||||||
\(454\) | 4.04705i | 0.189937i | ||||||||
\(455\) | −1.54526 | + | 0.916116i | −0.0724428 | + | 0.0429482i | ||||
\(456\) | −8.21482 | −0.384694 | ||||||||
\(457\) | 35.4622i | 1.65885i | 0.558615 | + | 0.829427i | \(0.311333\pi\) | ||||
−0.558615 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(458\) | 15.2265 | 0.711486 | ||||||||
\(459\) | − | 4.96460i | − | 0.231728i | ||||||
\(460\) | − | 1.39182i | − | 0.0648941i | ||||||
\(461\) | 25.0507 | 1.16673 | 0.583364 | − | 0.812211i | \(-0.301736\pi\) | ||||
0.583364 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(462\) | 8.77263 | − | 0.202452i | 0.408140 | − | 0.00941894i | ||||
\(463\) | −7.04858 | −0.327576 | −0.163788 | − | 0.986496i | \(-0.552371\pi\) | ||||
−0.163788 | + | 0.986496i | \(0.552371\pi\) | |||||||
\(464\) | − | 5.25022i | − | 0.243735i | ||||||
\(465\) | − | 1.14035i | − | 0.0528826i | ||||||
\(466\) | 10.2936 | 0.476842 | ||||||||
\(467\) | 6.93007i | 0.320685i | 0.987061 | + | 0.160343i | \(0.0512599\pi\) | ||||
−0.987061 | + | 0.160343i | \(0.948740\pi\) | |||||||
\(468\) | 2.55171 | 0.117953 | ||||||||
\(469\) | −16.6682 | − | 28.1151i | −0.769666 | − | 1.29823i | ||||
\(470\) | 2.67378i | 0.123332i | ||||||||
\(471\) | −10.6393 | −0.490231 | ||||||||
\(472\) | 9.10342 | 0.419019 | ||||||||
\(473\) | −4.24377 | − | 2.38537i | −0.195129 | − | 0.109680i | ||||
\(474\) | − | 6.16633i | − | 0.283229i | ||||||
\(475\) | −40.4924 | −1.85792 | ||||||||
\(476\) | −6.69851 | − | 11.2987i | −0.307026 | − | 0.517875i | ||||
\(477\) | 13.1989 | 0.604338 | ||||||||
\(478\) | −1.14248 | −0.0522557 | ||||||||
\(479\) | −11.7614 | −0.537393 | −0.268697 | − | 0.963225i | \(-0.586593\pi\) | ||||
−0.268697 | + | 0.963225i | \(0.586593\pi\) | |||||||
\(480\) | 0.266088i | 0.0121452i | ||||||||
\(481\) | 18.8750 | 0.860627 | ||||||||
\(482\) | 0.503225i | 0.0229213i | ||||||||
\(483\) | 11.9043 | − | 7.05753i | 0.541663 | − | 0.321129i | ||||
\(484\) | 5.71804 | + | 9.39702i | 0.259911 | + | 0.427137i | ||||
\(485\) | −0.0390625 | −0.00177374 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 5.14248 | 0.233028 | 0.116514 | − | 0.993189i | \(-0.462828\pi\) | ||||
0.116514 | + | 0.993189i | \(0.462828\pi\) | |||||||
\(488\) | 5.98047i | 0.270723i | ||||||||
\(489\) | − | 0.385373i | − | 0.0174272i | ||||||
\(490\) | 0.893796 | − | 1.63416i | 0.0403776 | − | 0.0738237i | ||||
\(491\) | 0.424436i | 0.0191545i | 0.999954 | + | 0.00957726i | \(0.00304858\pi\) | ||||
−0.999954 | + | 0.00957726i | \(0.996951\pi\) | |||||||
\(492\) | 6.21482i | 0.280186i | ||||||||
\(493\) | 26.0652i | 1.17392i | ||||||||
\(494\) | 20.9618i | 0.943116i | ||||||||
\(495\) | 0.769313 | + | 0.432422i | 0.0345781 | + | 0.0194359i | ||||
\(496\) | 4.28562i | 0.192430i | ||||||||
\(497\) | −6.66138 | − | 11.2361i | −0.298804 | − | 0.504007i | ||||
\(498\) | −10.6002 | −0.475006 | ||||||||
\(499\) | −28.5974 | −1.28020 | −0.640098 | − | 0.768293i | \(-0.721106\pi\) | ||||
−0.640098 | + | 0.768293i | \(0.721106\pi\) | |||||||
\(500\) | 2.64204i | 0.118156i | ||||||||
\(501\) | 0.967388i | 0.0432197i | ||||||||
\(502\) | 7.03261 | 0.313881 | ||||||||
\(503\) | −3.83955 | −0.171197 | −0.0855986 | − | 0.996330i | \(-0.527280\pi\) | ||||
−0.0855986 | + | 0.996330i | \(0.527280\pi\) | |||||||
\(504\) | −2.27585 | + | 1.34926i | −0.101375 | + | 0.0601006i | ||||
\(505\) | − | 3.66733i | − | 0.163194i | ||||||
\(506\) | 15.1229 | + | 8.50044i | 0.672297 | + | 0.377890i | ||||
\(507\) | 6.48879i | 0.288177i | ||||||||
\(508\) | − | 10.0247i | − | 0.444775i | ||||||
\(509\) | − | 5.27254i | − | 0.233701i | −0.993150 | − | 0.116851i | \(-0.962720\pi\) | ||
0.993150 | − | 0.116851i | \(-0.0372799\pi\) | |||||||
\(510\) | − | 1.32102i | − | 0.0584958i | ||||||
\(511\) | −4.00000 | − | 6.74699i | −0.176950 | − | 0.298469i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 8.21482i | − | 0.362693i | ||||||
\(514\) | −3.85320 | −0.169957 | ||||||||
\(515\) | −5.28196 | −0.232751 | ||||||||
\(516\) | 1.46782 | 0.0646173 | ||||||||
\(517\) | −29.0521 | − | 16.3299i | −1.27771 | − | 0.718187i | ||||
\(518\) | −16.8345 | + | 9.98047i | −0.739667 | + | 0.438517i | ||||
\(519\) | 0.385373i | 0.0169160i | ||||||||
\(520\) | 0.678979 | 0.0297752 | ||||||||
\(521\) | − | 21.8794i | − | 0.958552i | −0.877664 | − | 0.479276i | \(-0.840899\pi\) | ||
0.877664 | − | 0.479276i | \(-0.159101\pi\) | |||||||
\(522\) | 5.25022 | 0.229796 | ||||||||
\(523\) | 36.1123 | 1.57908 | 0.789540 | − | 0.613699i | \(-0.210319\pi\) | ||||
0.789540 | + | 0.613699i | \(0.210319\pi\) | |||||||
\(524\) | 20.0363 | 0.875289 | ||||||||
\(525\) | −11.2181 | + | 6.65074i | −0.489599 | + | 0.290262i | ||||
\(526\) | 6.48234 | 0.282643 | ||||||||
\(527\) | − | 21.2764i | − | 0.926814i | ||||||
\(528\) | −2.89120 | − | 1.62511i | −0.125823 | − | 0.0707238i | ||||
\(529\) | 4.36008 | 0.189569 | ||||||||
\(530\) | 3.51208 | 0.152555 | ||||||||
\(531\) | 9.10342i | 0.395055i | ||||||||
\(532\) | −11.0839 | − | 18.6957i | −0.480547 | − | 0.810562i | ||||
\(533\) | 15.8584 | 0.686903 | ||||||||
\(534\) | 1.78239i | 0.0771317i | ||||||||
\(535\) | −3.66733 | −0.158553 | ||||||||
\(536\) | 12.3536i | 0.533596i | ||||||||
\(537\) | 6.69994i | 0.289124i | ||||||||
\(538\) | 20.7983 | 0.896677 | ||||||||
\(539\) | 12.2973 | + | 19.6921i | 0.529681 | + | 0.848197i | ||||
\(540\) | −0.266088 | −0.0114506 | ||||||||
\(541\) | 8.58345i | 0.369031i | 0.982830 | + | 0.184516i | \(0.0590716\pi\) | ||||
−0.982830 | + | 0.184516i | \(0.940928\pi\) | |||||||
\(542\) | 22.7955i | 0.979150i | ||||||||
\(543\) | 26.1650 | 1.12285 | ||||||||
\(544\) | 4.96460i | 0.212855i | ||||||||
\(545\) | 0.0973463 | 0.00416986 | ||||||||
\(546\) | 3.44290 | + | 5.80731i | 0.147343 | + | 0.248530i | ||||
\(547\) | 37.2237i | 1.59157i | 0.605580 | + | 0.795785i | \(0.292941\pi\) | ||||
−0.605580 | + | 0.795785i | \(0.707059\pi\) | |||||||
\(548\) | 7.17942 | 0.306689 | ||||||||
\(549\) | −5.98047 | −0.255240 | ||||||||
\(550\) | −14.2513 | − | 8.01048i | −0.607677 | − | 0.341568i | ||||
\(551\) | 43.1296i | 1.83738i | ||||||||
\(552\) | −5.23069 | −0.222633 | ||||||||
\(553\) | 14.0337 | − | 8.31996i | 0.596773 | − | 0.353801i | ||||
\(554\) | 17.3277 | 0.736181 | ||||||||
\(555\) | −1.96826 | −0.0835480 | ||||||||
\(556\) | −16.7861 | −0.711887 | ||||||||
\(557\) | − | 10.9018i | − | 0.461923i | −0.972963 | − | 0.230962i | \(-0.925813\pi\) | ||
0.972963 | − | 0.230962i | \(-0.0741872\pi\) | |||||||
\(558\) | −4.28562 | −0.181425 | ||||||||
\(559\) | − | 3.74546i | − | 0.158416i | ||||||
\(560\) | −0.605578 | + | 0.359021i | −0.0255903 | + | 0.0151714i | ||||
\(561\) | 14.3536 | + | 8.06801i | 0.606011 | + | 0.340632i | ||||
\(562\) | −5.17942 | −0.218480 | ||||||||
\(563\) | 15.0406 | 0.633886 | 0.316943 | − | 0.948445i | \(-0.397344\pi\) | ||||
0.316943 | + | 0.948445i | \(0.397344\pi\) | |||||||
\(564\) | 10.0485 | 0.423117 | ||||||||
\(565\) | − | 3.26832i | − | 0.137499i | ||||||
\(566\) | − | 12.4534i | − | 0.523455i | ||||||
\(567\) | −1.34926 | − | 2.27585i | −0.0566634 | − | 0.0955769i | ||||
\(568\) | 4.93708i | 0.207155i | ||||||||
\(569\) | − | 20.2986i | − | 0.850961i | −0.904967 | − | 0.425481i | \(-0.860105\pi\) | ||
0.904967 | − | 0.425481i | \(-0.139895\pi\) | |||||||
\(570\) | − | 2.18587i | − | 0.0915558i | ||||||
\(571\) | 14.1995i | 0.594231i | 0.954842 | + | 0.297115i | \(0.0960246\pi\) | ||||
−0.954842 | + | 0.297115i | \(0.903975\pi\) | |||||||
\(572\) | −4.14680 | + | 7.37749i | −0.173387 | + | 0.308468i | ||||
\(573\) | − | 10.6277i | − | 0.443979i | ||||||
\(574\) | −14.1440 | + | 8.38537i | −0.590360 | + | 0.349999i | ||||
\(575\) | −25.7831 | −1.07523 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 7.08245i | 0.294846i | 0.989074 | + | 0.147423i | \(0.0470979\pi\) | ||||
−0.989074 | + | 0.147423i | \(0.952902\pi\) | |||||||
\(578\) | − | 7.64724i | − | 0.318083i | ||||||
\(579\) | −14.4614 | −0.600994 | ||||||||
\(580\) | 1.39702 | 0.0580081 | ||||||||
\(581\) | −14.3024 | − | 24.1245i | −0.593362 | − | 1.00085i | ||||
\(582\) | 0.146803i | 0.00608517i | ||||||||
\(583\) | −21.4497 | + | 38.1608i | −0.888357 | + | 1.58046i | ||||
\(584\) | 2.96460i | 0.122676i | ||||||||
\(585\) | 0.678979i | 0.0280723i | ||||||||
\(586\) | 11.4570i | 0.473286i | ||||||||
\(587\) | 5.83223i | 0.240722i | 0.992730 | + | 0.120361i | \(0.0384052\pi\) | ||||
−0.992730 | + | 0.120361i | \(0.961595\pi\) | |||||||
\(588\) | −6.14142 | − | 3.35902i | −0.253268 | − | 0.138524i | ||||
\(589\) | − | 35.2056i | − | 1.45062i | ||||||
\(590\) | 2.42231i | 0.0997250i | ||||||||
\(591\) | 1.35276 | 0.0556452 | ||||||||
\(592\) | 7.39702 | 0.304016 | ||||||||
\(593\) | 12.4353 | 0.510656 | 0.255328 | − | 0.966854i | \(-0.417817\pi\) | ||||
0.255328 | + | 0.966854i | \(0.417817\pi\) | |||||||
\(594\) | 1.62511 | − | 2.89120i | 0.0666790 | − | 0.118627i | ||||
\(595\) | 3.00645 | − | 1.78239i | 0.123252 | − | 0.0730710i | ||||
\(596\) | − | 17.5648i | − | 0.719482i | ||||||
\(597\) | −8.52419 | −0.348872 | ||||||||
\(598\) | 13.3472i | 0.545807i | ||||||||
\(599\) | 20.1663 | 0.823974 | 0.411987 | − | 0.911190i | \(-0.364835\pi\) | ||||
0.411987 | + | 0.911190i | \(0.364835\pi\) | |||||||
\(600\) | 4.92920 | 0.201234 | ||||||||
\(601\) | −18.6075 | −0.759016 | −0.379508 | − | 0.925188i | \(-0.623907\pi\) | ||||
−0.379508 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(602\) | 1.98047 | + | 3.34055i | 0.0807179 | + | 0.136151i | ||||
\(603\) | −12.3536 | −0.503079 | ||||||||
\(604\) | − | 15.0131i | − | 0.610874i | ||||||
\(605\) | −2.50044 | + | 1.52150i | −0.101657 | + | 0.0618579i | ||||
\(606\) | −13.7824 | −0.559871 | ||||||||
\(607\) | −21.5401 | −0.874284 | −0.437142 | − | 0.899392i | \(-0.644009\pi\) | ||||
−0.437142 | + | 0.899392i | \(0.644009\pi\) | |||||||
\(608\) | 8.21482i | 0.333155i | ||||||||
\(609\) | 7.08388 | + | 11.9487i | 0.287053 | + | 0.484187i | ||||
\(610\) | −1.59133 | −0.0644311 | ||||||||
\(611\) | − | 25.6408i | − | 1.03732i | ||||||
\(612\) | −4.96460 | −0.200682 | ||||||||
\(613\) | 8.87705i | 0.358541i | 0.983800 | + | 0.179270i | \(0.0573737\pi\) | ||||
−0.983800 | + | 0.179270i | \(0.942626\pi\) | |||||||
\(614\) | 4.78606i | 0.193149i | ||||||||
\(615\) | −1.65369 | −0.0666832 | ||||||||
\(616\) | −0.202452 | − | 8.77263i | −0.00815704 | − | 0.353459i | ||||
\(617\) | 15.7716 | 0.634941 | 0.317471 | − | 0.948268i | \(-0.397166\pi\) | ||||
0.317471 | + | 0.948268i | \(0.397166\pi\) | |||||||
\(618\) | 19.8504i | 0.798501i | ||||||||
\(619\) | 25.7433i | 1.03471i | 0.855770 | + | 0.517356i | \(0.173084\pi\) | ||||
−0.855770 | + | 0.517356i | \(0.826916\pi\) | |||||||
\(620\) | −1.14035 | −0.0457977 | ||||||||
\(621\) | − | 5.23069i | − | 0.209900i | ||||||
\(622\) | 15.8807 | 0.636759 | ||||||||
\(623\) | −4.05647 | + | 2.40490i | −0.162519 | + | 0.0963505i | ||||
\(624\) | − | 2.55171i | − | 0.102150i | ||||||
\(625\) | 23.9430 | 0.957719 | ||||||||
\(626\) | −30.6524 | −1.22512 | ||||||||
\(627\) | 23.7507 | + | 13.3500i | 0.948510 | + | 0.533147i | ||||
\(628\) | 10.6393i | 0.424552i | ||||||||
\(629\) | −36.7232 | −1.46425 | ||||||||
\(630\) | −0.359021 | − | 0.605578i | −0.0143037 | − | 0.0241268i | ||||
\(631\) | −44.2330 | −1.76089 | −0.880444 | − | 0.474151i | \(-0.842755\pi\) | ||||
−0.880444 | + | 0.474151i | \(0.842755\pi\) | |||||||
\(632\) | −6.16633 | −0.245284 | ||||||||
\(633\) | −10.8258 | −0.430286 | ||||||||
\(634\) | 6.69851i | 0.266032i | ||||||||
\(635\) | 2.66746 | 0.105855 | ||||||||
\(636\) | − | 13.1989i | − | 0.523372i | ||||||
\(637\) | −8.57124 | + | 15.6711i | −0.339605 | + | 0.620911i | ||||
\(638\) | −8.53218 | + | 15.1794i | −0.337792 | + | 0.600959i | ||||
\(639\) | −4.93708 | −0.195308 | ||||||||
\(640\) | 0.266088 | 0.0105181 | ||||||||
\(641\) | −7.39702 | −0.292165 | −0.146082 | − | 0.989272i | \(-0.546666\pi\) | ||||
−0.146082 | + | 0.989272i | \(0.546666\pi\) | |||||||
\(642\) | 13.7824i | 0.543948i | ||||||||
\(643\) | − | 41.8159i | − | 1.64906i | −0.565820 | − | 0.824529i | \(-0.691440\pi\) | ||
0.565820 | − | 0.824529i | \(-0.308560\pi\) | |||||||
\(644\) | −7.05753 | − | 11.9043i | −0.278106 | − | 0.469094i | ||||
\(645\) | 0.390570i | 0.0153787i | ||||||||
\(646\) | − | 40.7833i | − | 1.60460i | ||||||
\(647\) | 5.88804i | 0.231483i | 0.993279 | + | 0.115741i | \(0.0369244\pi\) | ||||
−0.993279 | + | 0.115741i | \(0.963076\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −26.3198 | − | 14.7940i | −1.03314 | − | 0.580717i | ||||
\(650\) | − | 12.5779i | − | 0.493345i | ||||||
\(651\) | −5.78239 | − | 9.75344i | −0.226630 | − | 0.382268i | ||||
\(652\) | −0.385373 | −0.0150924 | ||||||||
\(653\) | 4.90534 | 0.191961 | 0.0959804 | − | 0.995383i | \(-0.469401\pi\) | ||||
0.0959804 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(654\) | − | 0.365842i | − | 0.0143056i | ||||||
\(655\) | 5.33141i | 0.208316i | ||||||||
\(656\) | 6.21482 | 0.242648 | ||||||||
\(657\) | −2.96460 | −0.115660 | ||||||||
\(658\) | 13.5580 | + | 22.8689i | 0.528545 | + | 0.891522i | ||||
\(659\) | − | 25.7189i | − | 1.00187i | −0.865486 | − | 0.500933i | \(-0.832990\pi\) | ||
0.865486 | − | 0.500933i | \(-0.167010\pi\) | |||||||
\(660\) | 0.432422 | − | 0.769313i | 0.0168320 | − | 0.0299455i | ||||
\(661\) | − | 2.70273i | − | 0.105124i | −0.998618 | − | 0.0525621i | \(-0.983261\pi\) | ||
0.998618 | − | 0.0525621i | \(-0.0167387\pi\) | |||||||
\(662\) | − | 31.5330i | − | 1.22557i | ||||||
\(663\) | 12.6682i | 0.491992i | ||||||||
\(664\) | 10.6002i | 0.411367i | ||||||||
\(665\) | 4.97471 | − | 2.94929i | 0.192911 | − | 0.114369i | ||||
\(666\) | 7.39702i | 0.286629i | ||||||||
\(667\) | 27.4622i | 1.06334i | ||||||||
\(668\) | 0.967388 | 0.0374294 | ||||||||
\(669\) | −1.38903 | −0.0537032 | ||||||||
\(670\) | −3.28716 | −0.126994 | ||||||||
\(671\) | 9.71891 | − | 17.2907i | 0.375194 | − | 0.667501i | ||||
\(672\) | 1.34926 | + | 2.27585i | 0.0520486 | + | 0.0877930i | ||||
\(673\) | − | 39.0166i | − | 1.50398i | −0.659174 | − | 0.751990i | \(-0.729094\pi\) | ||
0.659174 | − | 0.751990i | \(-0.270906\pi\) | |||||||
\(674\) | −22.0652 | −0.849921 | ||||||||
\(675\) | 4.92920i | 0.189725i | ||||||||
\(676\) | 6.48879 | 0.249569 | ||||||||
\(677\) | 44.7906 | 1.72144 | 0.860721 | − | 0.509077i | \(-0.170013\pi\) | ||||
0.860721 | + | 0.509077i | \(0.170013\pi\) | |||||||
\(678\) | −12.2828 | −0.471719 | ||||||||
\(679\) | −0.334102 | + | 0.198074i | −0.0128217 | + | 0.00760140i | ||||
\(680\) | −1.32102 | −0.0506588 | ||||||||
\(681\) | 4.04705i | 0.155083i | ||||||||
\(682\) | 6.96460 | − | 12.3906i | 0.266688 | − | 0.474459i | ||||
\(683\) | −4.57124 | −0.174914 | −0.0874568 | − | 0.996168i | \(-0.527874\pi\) | ||||
−0.0874568 | + | 0.996168i | \(0.527874\pi\) | |||||||
\(684\) | −8.21482 | −0.314101 | ||||||||
\(685\) | 1.91036i | 0.0729910i | ||||||||
\(686\) | −0.641696 | − | 18.5091i | −0.0245001 | − | 0.706682i | ||||
\(687\) | 15.2265 | 0.580926 | ||||||||
\(688\) | − | 1.46782i | − | 0.0559603i | ||||||
\(689\) | −33.6799 | −1.28310 | ||||||||
\(690\) | − | 1.39182i | − | 0.0529858i | ||||||
\(691\) | 29.1086i | 1.10734i | 0.832735 | + | 0.553672i | \(0.186774\pi\) | ||||
−0.832735 | + | 0.553672i | \(0.813226\pi\) | |||||||
\(692\) | 0.385373 | 0.0146497 | ||||||||
\(693\) | 8.77263 | − | 0.202452i | 0.333245 | − | 0.00769053i | ||||
\(694\) | 27.9365 | 1.06046 | ||||||||
\(695\) | − | 4.46657i | − | 0.169427i | ||||||
\(696\) | − | 5.25022i | − | 0.199009i | ||||||
\(697\) | −30.8541 | −1.16868 | ||||||||
\(698\) | − | 1.19375i | − | 0.0451841i | ||||||
\(699\) | 10.2936 | 0.389340 | ||||||||
\(700\) | 6.65074 | + | 11.2181i | 0.251375 | + | 0.424006i | ||||
\(701\) | − | 12.1678i | − | 0.459570i | −0.973241 | − | 0.229785i | \(-0.926198\pi\) | ||
0.973241 | − | 0.229785i | \(-0.0738023\pi\) | |||||||
\(702\) | 2.55171 | 0.0963080 | ||||||||
\(703\) | −60.7652 | −2.29180 | ||||||||
\(704\) | −1.62511 | + | 2.89120i | −0.0612486 | + | 0.108966i | ||||
\(705\) | 2.67378i | 0.100700i | ||||||||
\(706\) | −33.4413 | −1.25858 | ||||||||
\(707\) | −18.5960 | − | 31.3667i | −0.699373 | − | 1.17967i | ||||
\(708\) | 9.10342 | 0.342127 | ||||||||
\(709\) | 11.2945 | 0.424173 | 0.212087 | − | 0.977251i | \(-0.431974\pi\) | ||||
0.212087 | + | 0.977251i | \(0.431974\pi\) | |||||||
\(710\) | −1.31370 | −0.0493022 | ||||||||
\(711\) | − | 6.16633i | − | 0.231256i | ||||||
\(712\) | 1.78239 | 0.0667980 | ||||||||
\(713\) | − | 22.4167i | − | 0.839513i | ||||||
\(714\) | −6.69851 | − | 11.2987i | −0.250685 | − | 0.422843i | ||||
\(715\) | −1.96306 | − | 1.10342i | −0.0734144 | − | 0.0412654i | ||||
\(716\) | 6.69994 | 0.250389 | ||||||||
\(717\) | −1.14248 | −0.0426666 | ||||||||
\(718\) | 8.45618 | 0.315582 | ||||||||
\(719\) | 47.5180i | 1.77212i | 0.463567 | + | 0.886062i | \(0.346569\pi\) | ||||
−0.463567 | + | 0.886062i | \(0.653431\pi\) | |||||||
\(720\) | 0.266088i | 0.00991652i | ||||||||
\(721\) | −45.1766 | + | 26.7833i | −1.68247 | + | 0.997461i | ||||
\(722\) | − | 48.4832i | − | 1.80436i | ||||||
\(723\) | 0.503225i | 0.0187151i | ||||||||
\(724\) | − | 26.1650i | − | 0.972414i | ||||||
\(725\) | − | 25.8794i | − | 0.961135i | ||||||
\(726\) | 5.71804 | + | 9.39702i | 0.212216 | + | 0.348756i | ||||
\(727\) | − | 9.38903i | − | 0.348220i | −0.984726 | − | 0.174110i | \(-0.944295\pi\) | ||
0.984726 | − | 0.174110i | \(-0.0557048\pi\) | |||||||
\(728\) | 5.80731 | − | 3.44290i | 0.215233 | − | 0.127603i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −0.788845 | −0.0291964 | ||||||||
\(731\) | 7.28716i | 0.269525i | ||||||||
\(732\) | 5.98047i | 0.221044i | ||||||||
\(733\) | 23.1333 | 0.854449 | 0.427225 | − | 0.904145i | \(-0.359491\pi\) | ||||
0.427225 | + | 0.904145i | \(0.359491\pi\) | |||||||
\(734\) | −21.4831 | −0.792957 | ||||||||
\(735\) | 0.893796 | − | 1.63416i | 0.0329681 | − | 0.0602768i | ||||
\(736\) | 5.23069i | 0.192806i | ||||||||
\(737\) | 20.0760 | − | 35.7168i | 0.739509 | − | 1.31564i | ||||
\(738\) | 6.21482i | 0.228771i | ||||||||
\(739\) | − | 35.0978i | − | 1.29109i | −0.763720 | − | 0.645547i | \(-0.776629\pi\) | ||
0.763720 | − | 0.645547i | \(-0.223371\pi\) | |||||||
\(740\) | 1.96826i | 0.0723547i | ||||||||
\(741\) | 20.9618i | 0.770051i | ||||||||
\(742\) | 30.0389 | − | 17.8087i | 1.10276 | − | 0.653780i | ||||
\(743\) | 24.9618i | 0.915760i | 0.889014 | + | 0.457880i | \(0.151391\pi\) | ||||
−0.889014 | + | 0.457880i | \(0.848609\pi\) | |||||||
\(744\) | 4.28562i | 0.157118i | ||||||||
\(745\) | 4.67378 | 0.171234 | ||||||||
\(746\) | −9.94141 | −0.363981 | ||||||||
\(747\) | −10.6002 | −0.387841 | ||||||||
\(748\) | 8.06801 | − | 14.3536i | 0.294996 | − | 0.524821i | ||||
\(749\) | −31.3667 | + | 18.5960i | −1.14611 | + | 0.679482i | ||||
\(750\) | 2.64204i | 0.0964737i | ||||||||
\(751\) | −22.7550 | −0.830341 | −0.415170 | − | 0.909744i | \(-0.636278\pi\) | ||||
−0.415170 | + | 0.909744i | \(0.636278\pi\) | |||||||
\(752\) | − | 10.0485i | − | 0.366430i | ||||||
\(753\) | 7.03261 | 0.256283 | ||||||||
\(754\) | −13.3970 | −0.487891 | ||||||||
\(755\) | 3.99480 | 0.145386 | ||||||||
\(756\) | −2.27585 | + | 1.34926i | −0.0827720 | + | 0.0490719i | ||||
\(757\) | −27.9627 | −1.01632 | −0.508160 | − | 0.861262i | \(-0.669674\pi\) | ||||
−0.508160 | + | 0.861262i | \(0.669674\pi\) | |||||||
\(758\) | 21.3862i | 0.776783i | ||||||||
\(759\) | 15.1229 | + | 8.50044i | 0.548928 | + | 0.308546i | ||||
\(760\) | −2.18587 | −0.0792897 | ||||||||
\(761\) | 16.6654 | 0.604121 | 0.302060 | − | 0.953289i | \(-0.402326\pi\) | ||||
0.302060 | + | 0.953289i | \(0.402326\pi\) | |||||||
\(762\) | − | 10.0247i | − | 0.363158i | ||||||
\(763\) | 0.832603 | − | 0.493615i | 0.0301423 | − | 0.0178700i | ||||
\(764\) | −10.6277 | −0.384497 | ||||||||
\(765\) | − | 1.32102i | − | 0.0477616i | ||||||
\(766\) | −0.706497 | −0.0255268 | ||||||||
\(767\) | − | 23.2293i | − | 0.838760i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 21.2740 | 0.767159 | 0.383580 | − | 0.923508i | \(-0.374691\pi\) | ||||
0.383580 | + | 0.923508i | \(0.374691\pi\) | |||||||
\(770\) | 2.33429 | − | 0.0538702i | 0.0841221 | − | 0.00194135i | ||||
\(771\) | −3.85320 | −0.138770 | ||||||||
\(772\) | 14.4614i | 0.520476i | ||||||||
\(773\) | 25.0759i | 0.901917i | 0.892545 | + | 0.450959i | \(0.148918\pi\) | ||||
−0.892545 | + | 0.450959i | \(0.851082\pi\) | |||||||
\(774\) | 1.46782 | 0.0527598 | ||||||||
\(775\) | 21.1247i | 0.758820i | ||||||||
\(776\) | 0.146803 | 0.00526991 | ||||||||
\(777\) | −16.8345 | + | 9.98047i | −0.603936 | + | 0.358047i | ||||
\(778\) | 5.30149i | 0.190068i | ||||||||
\(779\) | −51.0536 | −1.82918 | ||||||||
\(780\) | 0.678979 | 0.0243114 | ||||||||
\(781\) | 8.02329 | − | 14.2741i | 0.287096 | − | 0.510767i | ||||
\(782\) | − | 25.9683i | − | 0.928623i | ||||||
\(783\) | 5.25022 | 0.187627 | ||||||||
\(784\) | −3.35902 | + | 6.14142i | −0.119965 | + | 0.219336i | ||||
\(785\) | −2.83098 | −0.101042 | ||||||||
\(786\) | 20.0363 | 0.714670 | ||||||||
\(787\) | −16.3753 | −0.583715 | −0.291858 | − | 0.956462i | \(-0.594273\pi\) | ||||
−0.291858 | + | 0.956462i | \(0.594273\pi\) | |||||||
\(788\) | − | 1.35276i | − | 0.0481901i | ||||||
\(789\) | 6.48234 | 0.230777 | ||||||||
\(790\) | − | 1.64079i | − | 0.0583766i | ||||||
\(791\) | −16.5727 | − | 27.9539i | −0.589256 | − | 0.993927i | ||||
\(792\) | −2.89120 | − | 1.62511i | −0.102734 | − | 0.0577457i | ||||
\(793\) | 15.2604 | 0.541913 | ||||||||
\(794\) | 24.9646 | 0.885960 | ||||||||
\(795\) | 3.51208 | 0.124561 | ||||||||
\(796\) | 8.52419i | 0.302132i | ||||||||
\(797\) | − | 0.250116i | − | 0.00885955i | −0.999990 | − | 0.00442977i | \(-0.998590\pi\) | ||
0.999990 | − | 0.00442977i | \(-0.00141005\pi\) | |||||||
\(798\) | −11.0839 | − | 18.6957i | −0.392365 | − | 0.661821i | ||||
\(799\) | 49.8867i | 1.76486i | ||||||||
\(800\) | − | 4.92920i | − | 0.174273i | ||||||
\(801\) | 1.78239i | 0.0629778i | ||||||||
\(802\) | 11.6146i | 0.410127i | ||||||||
\(803\) | 4.81780 | − | 8.57124i | 0.170016 | − | 0.302472i | ||||
\(804\) | 12.3536i | 0.435679i | ||||||||
\(805\) | 3.16759 | − | 1.87793i | 0.111643 | − | 0.0661882i | ||||
\(806\) | 10.9356 | 0.385192 | ||||||||
\(807\) | 20.7983 | 0.732134 | ||||||||
\(808\) | 13.7824i | 0.484863i | ||||||||
\(809\) | 7.20596i | 0.253348i | 0.991944 | + | 0.126674i | \(0.0404302\pi\) | ||||
−0.991944 | + | 0.126674i | \(0.959570\pi\) | |||||||
\(810\) | −0.266088 | −0.00934938 | ||||||||
\(811\) | 25.7479 | 0.904130 | 0.452065 | − | 0.891985i | \(-0.350688\pi\) | ||||
0.452065 | + | 0.891985i | \(0.350688\pi\) | |||||||
\(812\) | 11.9487 | − | 7.08388i | 0.419318 | − | 0.248596i | ||||
\(813\) | 22.7955i | 0.799472i | ||||||||
\(814\) | −21.3862 | − | 12.0210i | −0.749588 | − | 0.421335i | ||||
\(815\) | − | 0.102543i | − | 0.00359194i | ||||||
\(816\) | 4.96460i | 0.173796i | ||||||||
\(817\) | 12.0579i | 0.421853i | ||||||||
\(818\) | − | 15.2032i | − | 0.531566i | ||||||
\(819\) | 3.44290 | + | 5.80731i | 0.120305 | + | 0.202924i | ||||
\(820\) | 1.65369i | 0.0577493i | ||||||||
\(821\) | 11.2060i | 0.391091i | 0.980695 | + | 0.195545i | \(0.0626477\pi\) | ||||
−0.980695 | + | 0.195545i | \(0.937352\pi\) | |||||||
\(822\) | 7.17942 | 0.250411 | ||||||||
\(823\) | −19.7949 | −0.690007 | −0.345004 | − | 0.938601i | \(-0.612122\pi\) | ||||
−0.345004 | + | 0.938601i | \(0.612122\pi\) | |||||||
\(824\) | 19.8504 | 0.691522 | ||||||||
\(825\) | −14.2513 | − | 8.01048i | −0.496166 | − | 0.278889i | ||||
\(826\) | 12.2828 | + | 20.7180i | 0.427374 | + | 0.720873i | ||||
\(827\) | − | 10.9460i | − | 0.380631i | −0.981723 | − | 0.190316i | \(-0.939049\pi\) | ||
0.981723 | − | 0.190316i | \(-0.0609511\pi\) | |||||||
\(828\) | −5.23069 | −0.181779 | ||||||||
\(829\) | − | 1.51275i | − | 0.0525399i | −0.999655 | − | 0.0262699i | \(-0.991637\pi\) | ||
0.999655 | − | 0.0262699i | \(-0.00836295\pi\) | |||||||
\(830\) | −2.82058 | −0.0979039 | ||||||||
\(831\) | 17.3277 | 0.601090 | ||||||||
\(832\) | −2.55171 | −0.0884645 | ||||||||
\(833\) | 16.6762 | − | 30.4897i | 0.577796 | − | 1.05640i | ||||
\(834\) | −16.7861 | −0.581254 | ||||||||
\(835\) | 0.257410i | 0.00890806i | ||||||||
\(836\) | 13.3500 | − | 23.7507i | 0.461718 | − | 0.821434i | ||||
\(837\) | −4.28562 | −0.148133 | ||||||||
\(838\) | −13.9683 | −0.482526 | ||||||||
\(839\) | 3.94420i | 0.136169i | 0.997680 | + | 0.0680844i | \(0.0216887\pi\) | ||||
−0.997680 | + | 0.0680844i | \(0.978311\pi\) | |||||||
\(840\) | −0.605578 | + | 0.359021i | −0.0208944 | + | 0.0123874i | ||||
\(841\) | 1.43521 | 0.0494901 | ||||||||
\(842\) | 4.53950i | 0.156441i | ||||||||
\(843\) | −5.17942 | −0.178389 | ||||||||
\(844\) | 10.8258i | 0.372639i | ||||||||
\(845\) | 1.72659i | 0.0593965i | ||||||||
\(846\) | 10.0485 | 0.345474 | ||||||||
\(847\) | −13.6711 | + | 25.6924i | −0.469746 | + | 0.882802i | ||||
\(848\) | −13.1989 | −0.453254 | ||||||||
\(849\) | − | 12.4534i | − | 0.427399i | ||||||
\(850\) | 24.4715i | 0.839365i | ||||||||
\(851\) | −38.6915 | −1.32633 | ||||||||
\(852\) | 4.93708i | 0.169142i | ||||||||
\(853\) | 13.8444 | 0.474025 | 0.237012 | − | 0.971507i | \(-0.423832\pi\) | ||||
0.237012 | + | 0.971507i | \(0.423832\pi\) | |||||||
\(854\) | −13.6107 | + | 8.06918i | −0.465748 | + | 0.276122i | ||||
\(855\) | − | 2.18587i | − | 0.0747550i | ||||||
\(856\) | 13.7824 | 0.471073 | ||||||||
\(857\) | −6.07879 | −0.207647 | −0.103824 | − | 0.994596i | \(-0.533108\pi\) | ||||
−0.103824 | + | 0.994596i | \(0.533108\pi\) | |||||||
\(858\) | −4.14680 | + | 7.37749i | −0.141570 | + | 0.251863i | ||||
\(859\) | 55.6533i | 1.89887i | 0.313969 | + | 0.949433i | \(0.398341\pi\) | ||||
−0.313969 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(860\) | 0.390570 | 0.0133183 | ||||||||
\(861\) | −14.1440 | + | 8.38537i | −0.482027 | + | 0.285773i | ||||
\(862\) | −11.5829 | −0.394515 | ||||||||
\(863\) | 32.6539 | 1.11155 | 0.555775 | − | 0.831333i | \(-0.312421\pi\) | ||||
0.555775 | + | 0.831333i | \(0.312421\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0.102543i | 0.00348658i | ||||||||
\(866\) | −20.9227 | −0.710984 | ||||||||
\(867\) | − | 7.64724i | − | 0.259714i | ||||||
\(868\) | −9.75344 | + | 5.78239i | −0.331053 | + | 0.196267i | ||||
\(869\) | 17.8281 | + | 10.0210i | 0.604776 | + | 0.339938i | ||||
\(870\) | 1.39702 | 0.0473634 | ||||||||
\(871\) | 31.5229 | 1.06811 | ||||||||
\(872\) | −0.365842 | −0.0123890 | ||||||||
\(873\) | 0.146803i | 0.00496852i | ||||||||
\(874\) | − | 42.9691i | − | 1.45345i | ||||||
\(875\) | −6.01290 | + | 3.56479i | −0.203273 | + | 0.120512i | ||||
\(876\) | 2.96460i | 0.100165i | ||||||||
\(877\) | 37.9324i | 1.28089i | 0.768006 | + | 0.640443i | \(0.221249\pi\) | ||||
−0.768006 | + | 0.640443i | \(0.778751\pi\) | |||||||
\(878\) | 9.63703i | 0.325234i | ||||||||
\(879\) | 11.4570i | 0.386437i | ||||||||
\(880\) | −0.769313 | − | 0.432422i | −0.0259335 | − | 0.0145770i | ||||
\(881\) | − | 16.5820i | − | 0.558662i | −0.960195 | − | 0.279331i | \(-0.909887\pi\) | ||
0.960195 | − | 0.279331i | \(-0.0901127\pi\) | |||||||
\(882\) | −6.14142 | − | 3.35902i | −0.206792 | − | 0.113104i | ||||
\(883\) | 21.1425 | 0.711501 | 0.355751 | − | 0.934581i | \(-0.384225\pi\) | ||||
0.355751 | + | 0.934581i | \(0.384225\pi\) | |||||||
\(884\) | 12.6682 | 0.426078 | ||||||||
\(885\) | 2.42231i | 0.0814251i | ||||||||
\(886\) | − | 26.9935i | − | 0.906866i | ||||||
\(887\) | 39.9944 | 1.34288 | 0.671441 | − | 0.741058i | \(-0.265676\pi\) | ||||
0.671441 | + | 0.741058i | \(0.265676\pi\) | |||||||
\(888\) | 7.39702 | 0.248228 | ||||||||
\(889\) | 22.8148 | − | 13.5259i | 0.765184 | − | 0.453645i | ||||
\(890\) | 0.474274i | 0.0158977i | ||||||||
\(891\) | 1.62511 | − | 2.89120i | 0.0544432 | − | 0.0968587i | ||||
\(892\) | 1.38903i | 0.0465083i | ||||||||
\(893\) | 82.5464i | 2.76231i | ||||||||
\(894\) | − | 17.5648i | − | 0.587454i | ||||||
\(895\) | 1.78278i | 0.0595916i | ||||||||
\(896\) | 2.27585 | − | 1.34926i | 0.0760309 | − | 0.0450755i | ||||
\(897\) | 13.3472i | 0.445649i | ||||||||
\(898\) | − | 17.6799i | − | 0.589984i | ||||||
\(899\) | 22.5004 | 0.750432 | ||||||||
\(900\) | 4.92920 | 0.164307 | ||||||||
\(901\) | 65.5275 | 2.18304 | ||||||||
\(902\) | −17.9683 | − | 10.0998i | −0.598278 | − | 0.336285i | ||||
\(903\) | 1.98047 | + | 3.34055i | 0.0659059 | + | 0.111167i | ||||
\(904\) | 12.2828i | 0.408521i | ||||||||
\(905\) | 6.96219 | 0.231431 | ||||||||
\(906\) | − | 15.0131i | − | 0.498776i | ||||||
\(907\) | 8.01810 | 0.266237 | 0.133118 | − | 0.991100i | \(-0.457501\pi\) | ||||
0.133118 | + | 0.991100i | \(0.457501\pi\) | |||||||
\(908\) | 4.04705 | 0.134306 | ||||||||
\(909\) | −13.7824 | −0.457133 | ||||||||
\(910\) | 0.916116 | + | 1.54526i | 0.0303690 | + | 0.0512248i | ||||
\(911\) | 19.0629 | 0.631583 | 0.315791 | − | 0.948829i | \(-0.397730\pi\) | ||||
0.315791 | + | 0.948829i | \(0.397730\pi\) | |||||||
\(912\) | 8.21482i | 0.272020i | ||||||||
\(913\) | 17.2265 | − | 30.6472i | 0.570113 | − | 1.01428i | ||||
\(914\) | 35.4622 | 1.17299 | ||||||||
\(915\) | −1.59133 | −0.0526078 | ||||||||
\(916\) | − | 15.2265i | − | 0.503097i | ||||||
\(917\) | 27.0340 | + | 45.5996i | 0.892743 | + | 1.50583i | ||||
\(918\) | −4.96460 | −0.163856 | ||||||||
\(919\) | 3.51177i | 0.115843i | 0.998321 | + | 0.0579214i | \(0.0184473\pi\) | ||||
−0.998321 | + | 0.0579214i | \(0.981553\pi\) | |||||||
\(920\) | −1.39182 | −0.0458871 | ||||||||
\(921\) | 4.78606i | 0.157706i | ||||||||
\(922\) | − | 25.0507i | − | 0.825001i | ||||||
\(923\) | 12.5980 | 0.414668 | ||||||||
\(924\) | −0.202452 | − | 8.77263i | −0.00666019 | − | 0.288598i | ||||
\(925\) | 36.4614 | 1.19884 | ||||||||
\(926\) | 7.04858i | 0.231631i | ||||||||
\(927\) | 19.8504i | 0.651973i | ||||||||
\(928\) | −5.25022 | −0.172347 | ||||||||
\(929\) | − | 45.2446i | − | 1.48443i | −0.670163 | − | 0.742214i | \(-0.733776\pi\) | ||
0.670163 | − | 0.742214i | \(-0.266224\pi\) | |||||||
\(930\) | −1.14035 | −0.0373936 | ||||||||
\(931\) | 27.5937 | − | 50.4506i | 0.904348 | − | 1.65345i | ||||
\(932\) | − | 10.2936i | − | 0.337178i | ||||||
\(933\) | 15.8807 | 0.519911 | ||||||||
\(934\) | 6.93007 | 0.226759 | ||||||||
\(935\) | 3.81933 | + | 2.14680i | 0.124906 | + | 0.0702080i | ||||
\(936\) | − | 2.55171i | − | 0.0834052i | ||||||
\(937\) | 0.259076 | 0.00846364 | 0.00423182 | − | 0.999991i | \(-0.498653\pi\) | ||||
0.00423182 | + | 0.999991i | \(0.498653\pi\) | |||||||
\(938\) | −28.1151 | + | 16.6682i | −0.917989 | + | 0.544236i | ||||
\(939\) | −30.6524 | −1.00030 | ||||||||
\(940\) | 2.67378 | 0.0872092 | ||||||||
\(941\) | −53.1896 | −1.73393 | −0.866966 | − | 0.498368i | \(-0.833933\pi\) | ||||
−0.866966 | + | 0.498368i | \(0.833933\pi\) | |||||||
\(942\) | 10.6393i | 0.346646i | ||||||||
\(943\) | −32.5078 | −1.05860 | ||||||||
\(944\) | − | 9.10342i | − | 0.296291i | ||||||
\(945\) | −0.359021 | − | 0.605578i | −0.0116789 | − | 0.0196994i | ||||
\(946\) | −2.38537 | + | 4.24377i | −0.0775552 | + | 0.137977i | ||||
\(947\) | −38.6099 | −1.25465 | −0.627327 | − | 0.778756i | \(-0.715851\pi\) | ||||
−0.627327 | + | 0.778756i | \(0.715851\pi\) | |||||||
\(948\) | −6.16633 | −0.200273 | ||||||||
\(949\) | 7.56479 | 0.245563 | ||||||||
\(950\) | 40.4924i | 1.31375i | ||||||||
\(951\) | 6.69851i | 0.217214i | ||||||||
\(952\) | −11.2987 | + | 6.69851i | −0.366193 | + | 0.217100i | ||||
\(953\) | − | 7.87129i | − | 0.254976i | −0.991840 | − | 0.127488i | \(-0.959309\pi\) | ||
0.991840 | − | 0.127488i | \(-0.0406915\pi\) | |||||||
\(954\) | − | 13.1989i | − | 0.427332i | ||||||
\(955\) | − | 2.82791i | − | 0.0915089i | ||||||
\(956\) | 1.14248i | 0.0369504i | ||||||||
\(957\) | −8.53218 | + | 15.1794i | −0.275806 | + | 0.490681i | ||||
\(958\) | 11.7614i | 0.379995i | ||||||||
\(959\) | 9.68686 | + | 16.3393i | 0.312805 | + | 0.527623i | ||||
\(960\) | 0.266088 | 0.00858796 | ||||||||
\(961\) | 12.6335 | 0.407531 | ||||||||
\(962\) | − | 18.8750i | − | 0.608556i | ||||||
\(963\) | 13.7824i | 0.444131i | ||||||||
\(964\) | 0.503225 | 0.0162078 | ||||||||
\(965\) | −3.84800 | −0.123872 | ||||||||
\(966\) | −7.05753 | − | 11.9043i | −0.227072 | − | 0.383014i | ||||
\(967\) | − | 27.4977i | − | 0.884268i | −0.896949 | − | 0.442134i | \(-0.854222\pi\) | ||
0.896949 | − | 0.442134i | \(-0.145778\pi\) | |||||||
\(968\) | 9.39702 | − | 5.71804i | 0.302032 | − | 0.183785i | ||||
\(969\) | − | 40.7833i | − | 1.31015i | ||||||
\(970\) | 0.0390625i | 0.00125422i | ||||||||
\(971\) | 4.00287i | 0.128458i | 0.997935 | + | 0.0642291i | \(0.0204588\pi\) | ||||
−0.997935 | + | 0.0642291i | \(0.979541\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | −22.6487 | − | 38.2026i | −0.726083 | − | 1.22472i | ||||
\(974\) | − | 5.14248i | − | 0.164776i | ||||||
\(975\) | − | 12.5779i | − | 0.402814i | ||||||
\(976\) | 5.98047 | 0.191430 | ||||||||
\(977\) | −43.8107 | −1.40163 | −0.700814 | − | 0.713344i | \(-0.747180\pi\) | ||||
−0.700814 | + | 0.713344i | \(0.747180\pi\) | |||||||
\(978\) | −0.385373 | −0.0123229 | ||||||||
\(979\) | −5.15325 | − | 2.89658i | −0.164699 | − | 0.0925753i | ||||
\(980\) | −1.63416 | − | 0.893796i | −0.0522013 | − | 0.0285513i | ||||
\(981\) | − | 0.365842i | − | 0.0116804i | ||||||
\(982\) | 0.424436 | 0.0135443 | ||||||||
\(983\) | 56.5768i | 1.80452i | 0.431192 | + | 0.902260i | \(0.358093\pi\) | ||||
−0.431192 | + | 0.902260i | \(0.641907\pi\) | |||||||
\(984\) | 6.21482 | 0.198121 | ||||||||
\(985\) | 0.359954 | 0.0114691 | ||||||||
\(986\) | 26.0652 | 0.830086 | ||||||||
\(987\) | 13.5580 | + | 22.8689i | 0.431555 | + | 0.727924i | ||||
\(988\) | 20.9618 | 0.666884 | ||||||||
\(989\) | 7.67773i | 0.244137i | ||||||||
\(990\) | 0.432422 | − | 0.769313i | 0.0137433 | − | 0.0244504i | ||||
\(991\) | 0.731684 | 0.0232427 | 0.0116214 | − | 0.999932i | \(-0.496301\pi\) | ||||
0.0116214 | + | 0.999932i | \(0.496301\pi\) | |||||||
\(992\) | 4.28562 | 0.136069 | ||||||||
\(993\) | − | 31.5330i | − | 1.00067i | ||||||
\(994\) | −11.2361 | + | 6.66138i | −0.356387 | + | 0.211286i | ||||
\(995\) | −2.26819 | −0.0719063 | ||||||||
\(996\) | 10.6002i | 0.335880i | ||||||||
\(997\) | −23.1229 | −0.732311 | −0.366156 | − | 0.930554i | \(-0.619326\pi\) | ||||
−0.366156 | + | 0.930554i | \(0.619326\pi\) | |||||||
\(998\) | 28.5974i | 0.905235i | ||||||||
\(999\) | 7.39702i | 0.234031i |
(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 | 462.2.e.a.307.2 | ✓ | 8 | |
3.2 | odd | 2 | 1386.2.e.e.307.7 | 8 | |||
4.3 | odd | 2 | 3696.2.q.b.769.6 | 8 | |||
7.6 | odd | 2 | 462.2.e.b.307.3 | yes | 8 | ||
11.10 | odd | 2 | 462.2.e.b.307.6 | yes | 8 | ||
21.20 | even | 2 | 1386.2.e.a.307.6 | 8 | |||
28.27 | even | 2 | 3696.2.q.c.769.3 | 8 | |||
33.32 | even | 2 | 1386.2.e.a.307.3 | 8 | |||
44.43 | even | 2 | 3696.2.q.c.769.6 | 8 | |||
77.76 | even | 2 | inner | 462.2.e.a.307.7 | yes | 8 | |
231.230 | odd | 2 | 1386.2.e.e.307.2 | 8 | |||
308.307 | odd | 2 | 3696.2.q.b.769.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.e.a.307.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
462.2.e.a.307.7 | yes | 8 | 77.76 | even | 2 | inner | |
462.2.e.b.307.3 | yes | 8 | 7.6 | odd | 2 | ||
462.2.e.b.307.6 | yes | 8 | 11.10 | odd | 2 | ||
1386.2.e.a.307.3 | 8 | 33.32 | even | 2 | |||
1386.2.e.a.307.6 | 8 | 21.20 | even | 2 | |||
1386.2.e.e.307.2 | 8 | 231.230 | odd | 2 | |||
1386.2.e.e.307.7 | 8 | 3.2 | odd | 2 | |||
3696.2.q.b.769.3 | 8 | 308.307 | odd | 2 | |||
3696.2.q.b.769.6 | 8 | 4.3 | odd | 2 | |||
3696.2.q.c.769.3 | 8 | 28.27 | even | 2 | |||
3696.2.q.c.769.6 | 8 | 44.43 | even | 2 |