Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(71,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.n (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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.1 | ||
Character | \(\chi\) | \(=\) | 420.71 |
Dual form | 420.2.n.b.71.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41258 | − | 0.0678578i | −0.998848 | − | 0.0479827i | ||||
\(3\) | 1.66901 | − | 0.463024i | 0.963606 | − | 0.267327i | ||||
\(4\) | 1.99079 | + | 0.191710i | 0.995395 | + | 0.0958550i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −2.38904 | + | 0.540805i | −0.975323 | + | 0.220783i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.79915 | − | 0.405897i | −0.989649 | − | 0.143506i | ||||
\(9\) | 2.57122 | − | 1.54559i | 0.857072 | − | 0.515196i | ||||
\(10\) | 0.0678578 | − | 1.41258i | 0.0214585 | − | 0.446698i | ||||
\(11\) | −0.648120 | −0.195415 | −0.0977077 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977077 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(12\) | 3.41142 | − | 0.601817i | 0.984793 | − | 0.173730i | ||||
\(13\) | 4.96381 | 1.37671 | 0.688356 | − | 0.725373i | \(-0.258333\pi\) | ||||
0.688356 | + | 0.725373i | \(0.258333\pi\) | |||||||
\(14\) | 0.0678578 | − | 1.41258i | 0.0181358 | − | 0.377529i | ||||
\(15\) | 0.463024 | + | 1.66901i | 0.119552 | + | 0.430938i | ||||
\(16\) | 3.92649 | + | 0.763309i | 0.981624 | + | 0.190827i | ||||
\(17\) | 6.88118i | 1.66893i | 0.551060 | + | 0.834466i | \(0.314224\pi\) | ||||
−0.551060 | + | 0.834466i | \(0.685776\pi\) | |||||||
\(18\) | −3.73694 | + | 2.00880i | −0.880806 | + | 0.473478i | ||||
\(19\) | − | 4.22288i | − | 0.968796i | −0.874848 | − | 0.484398i | \(-0.839039\pi\) | ||
0.874848 | − | 0.484398i | \(-0.160961\pi\) | |||||||
\(20\) | −0.191710 | + | 1.99079i | −0.0428676 | + | 0.445154i | ||||
\(21\) | 0.463024 | + | 1.66901i | 0.101040 | + | 0.364209i | ||||
\(22\) | 0.915524 | + | 0.0439800i | 0.195190 | + | 0.00937657i | ||||
\(23\) | 1.33148 | 0.277632 | 0.138816 | − | 0.990318i | \(-0.455670\pi\) | ||||
0.138816 | + | 0.990318i | \(0.455670\pi\) | |||||||
\(24\) | −4.85976 | + | 0.618626i | −0.991995 | + | 0.126277i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −7.01180 | − | 0.336833i | −1.37513 | − | 0.0660584i | ||||
\(27\) | 3.57575 | − | 3.77014i | 0.688154 | − | 0.725564i | ||||
\(28\) | −0.191710 | + | 1.99079i | −0.0362298 | + | 0.376224i | ||||
\(29\) | − | 4.10451i | − | 0.762189i | −0.924536 | − | 0.381095i | \(-0.875547\pi\) | ||
0.924536 | − | 0.381095i | \(-0.124453\pi\) | |||||||
\(30\) | −0.540805 | − | 2.38904i | −0.0987370 | − | 0.436178i | ||||
\(31\) | 7.63684i | 1.37162i | 0.727782 | + | 0.685808i | \(0.240551\pi\) | ||||
−0.727782 | + | 0.685808i | \(0.759449\pi\) | |||||||
\(32\) | −5.49471 | − | 1.34468i | −0.971337 | − | 0.237708i | ||||
\(33\) | −1.08172 | + | 0.300095i | −0.188304 | + | 0.0522398i | ||||
\(34\) | 0.466942 | − | 9.72025i | 0.0800799 | − | 1.66701i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 5.41506 | − | 2.58401i | 0.902510 | − | 0.430669i | ||||
\(37\) | −2.29722 | −0.377660 | −0.188830 | − | 0.982010i | \(-0.560469\pi\) | ||||
−0.188830 | + | 0.982010i | \(0.560469\pi\) | |||||||
\(38\) | −0.286556 | + | 5.96518i | −0.0464855 | + | 0.967680i | ||||
\(39\) | 8.28466 | − | 2.29836i | 1.32661 | − | 0.368032i | ||||
\(40\) | 0.405897 | − | 2.79915i | 0.0641780 | − | 0.442585i | ||||
\(41\) | − | 10.9561i | − | 1.71106i | −0.517754 | − | 0.855529i | \(-0.673232\pi\) | ||
0.517754 | − | 0.855529i | \(-0.326768\pi\) | |||||||
\(42\) | −0.540805 | − | 2.38904i | −0.0834480 | − | 0.368637i | ||||
\(43\) | 5.13687i | 0.783365i | 0.920100 | + | 0.391682i | \(0.128107\pi\) | ||||
−0.920100 | + | 0.391682i | \(0.871893\pi\) | |||||||
\(44\) | −1.29027 | − | 0.124251i | −0.194516 | − | 0.0187315i | ||||
\(45\) | 1.54559 | + | 2.57122i | 0.230403 | + | 0.383294i | ||||
\(46\) | −1.88082 | − | 0.0903511i | −0.277312 | − | 0.0133215i | ||||
\(47\) | 9.62134 | 1.40342 | 0.701708 | − | 0.712464i | \(-0.252421\pi\) | ||||
0.701708 | + | 0.712464i | \(0.252421\pi\) | |||||||
\(48\) | 6.90681 | − | 0.544089i | 0.996912 | − | 0.0785324i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.41258 | + | 0.0678578i | 0.199770 | + | 0.00959655i | ||||
\(51\) | 3.18615 | + | 11.4848i | 0.446151 | + | 1.60819i | ||||
\(52\) | 9.88190 | + | 0.951611i | 1.37037 | + | 0.131965i | ||||
\(53\) | 5.56316i | 0.764158i | 0.924130 | + | 0.382079i | \(0.124792\pi\) | ||||
−0.924130 | + | 0.382079i | \(0.875208\pi\) | |||||||
\(54\) | −5.30689 | + | 5.08300i | −0.722176 | + | 0.691709i | ||||
\(55\) | − | 0.648120i | − | 0.0873925i | ||||||
\(56\) | 0.405897 | − | 2.79915i | 0.0542403 | − | 0.374052i | ||||
\(57\) | −1.95530 | − | 7.04805i | −0.258985 | − | 0.933537i | ||||
\(58\) | −0.278524 | + | 5.79797i | −0.0365719 | + | 0.761311i | ||||
\(59\) | 0.421507 | 0.0548755 | 0.0274378 | − | 0.999624i | \(-0.491265\pi\) | ||||
0.0274378 | + | 0.999624i | \(0.491265\pi\) | |||||||
\(60\) | 0.601817 | + | 3.41142i | 0.0776943 | + | 0.440413i | ||||
\(61\) | 0.179252 | 0.0229509 | 0.0114754 | − | 0.999934i | \(-0.496347\pi\) | ||||
0.0114754 | + | 0.999934i | \(0.496347\pi\) | |||||||
\(62\) | 0.518219 | − | 10.7877i | 0.0658139 | − | 1.37004i | ||||
\(63\) | 1.54559 | + | 2.57122i | 0.194726 | + | 0.323943i | ||||
\(64\) | 7.67049 | + | 2.27234i | 0.958812 | + | 0.284042i | ||||
\(65\) | 4.96381i | 0.615684i | ||||||||
\(66\) | 1.54839 | − | 0.350506i | 0.190593 | − | 0.0431444i | ||||
\(67\) | − | 10.4894i | − | 1.28149i | −0.767754 | − | 0.640745i | \(-0.778626\pi\) | ||
0.767754 | − | 0.640745i | \(-0.221374\pi\) | |||||||
\(68\) | −1.31919 | + | 13.6990i | −0.159975 | + | 1.66125i | ||||
\(69\) | 2.22225 | − | 0.616506i | 0.267528 | − | 0.0742186i | ||||
\(70\) | 1.41258 | + | 0.0678578i | 0.168836 | + | 0.00811056i | ||||
\(71\) | −2.09646 | −0.248804 | −0.124402 | − | 0.992232i | \(-0.539701\pi\) | ||||
−0.124402 | + | 0.992232i | \(0.539701\pi\) | |||||||
\(72\) | −7.82458 | + | 3.28268i | −0.922135 | + | 0.386868i | ||||
\(73\) | −16.6256 | −1.94588 | −0.972941 | − | 0.231055i | \(-0.925782\pi\) | ||||
−0.972941 | + | 0.231055i | \(0.925782\pi\) | |||||||
\(74\) | 3.24501 | + | 0.155884i | 0.377225 | + | 0.0181212i | ||||
\(75\) | −1.66901 | + | 0.463024i | −0.192721 | + | 0.0534654i | ||||
\(76\) | 0.809569 | − | 8.40688i | 0.0928639 | − | 0.964335i | ||||
\(77\) | − | 0.648120i | − | 0.0738601i | ||||||
\(78\) | −11.8588 | + | 2.68445i | −1.34274 | + | 0.303954i | ||||
\(79\) | − | 7.10256i | − | 0.799100i | −0.916711 | − | 0.399550i | \(-0.869166\pi\) | ||
0.916711 | − | 0.399550i | \(-0.130834\pi\) | |||||||
\(80\) | −0.763309 | + | 3.92649i | −0.0853405 | + | 0.438995i | ||||
\(81\) | 4.22232 | − | 7.94808i | 0.469146 | − | 0.883120i | ||||
\(82\) | −0.743459 | + | 15.4764i | −0.0821013 | + | 1.70909i | ||||
\(83\) | −0.766970 | −0.0841859 | −0.0420930 | − | 0.999114i | \(-0.513403\pi\) | ||||
−0.0420930 | + | 0.999114i | \(0.513403\pi\) | |||||||
\(84\) | 0.601817 | + | 3.41142i | 0.0656637 | + | 0.372217i | ||||
\(85\) | −6.88118 | −0.746369 | ||||||||
\(86\) | 0.348577 | − | 7.25626i | 0.0375880 | − | 0.782463i | ||||
\(87\) | −1.90049 | − | 6.85049i | −0.203754 | − | 0.734450i | ||||
\(88\) | 1.81419 | + | 0.263070i | 0.193393 | + | 0.0280434i | ||||
\(89\) | − | 11.5147i | − | 1.22056i | −0.792186 | − | 0.610280i | \(-0.791057\pi\) | ||
0.792186 | − | 0.610280i | \(-0.208943\pi\) | |||||||
\(90\) | −2.00880 | − | 3.73694i | −0.211746 | − | 0.393908i | ||||
\(91\) | 4.96381i | 0.520348i | ||||||||
\(92\) | 2.65069 | + | 0.255257i | 0.276354 | + | 0.0266124i | ||||
\(93\) | 3.53604 | + | 12.7460i | 0.366670 | + | 1.32170i | ||||
\(94\) | −13.5910 | − | 0.652884i | −1.40180 | − | 0.0673398i | ||||
\(95\) | 4.22288 | 0.433259 | ||||||||
\(96\) | −9.79337 | + | 0.299890i | −0.999531 | + | 0.0306074i | ||||
\(97\) | −14.8262 | −1.50537 | −0.752685 | − | 0.658380i | \(-0.771242\pi\) | ||||
−0.752685 | + | 0.658380i | \(0.771242\pi\) | |||||||
\(98\) | 1.41258 | + | 0.0678578i | 0.142693 | + | 0.00685468i | ||||
\(99\) | −1.66646 | + | 1.00173i | −0.167485 | + | 0.100677i | ||||
\(100\) | −1.99079 | − | 0.191710i | −0.199079 | − | 0.0191710i | ||||
\(101\) | 3.56719i | 0.354948i | 0.984125 | + | 0.177474i | \(0.0567926\pi\) | ||||
−0.984125 | + | 0.177474i | \(0.943207\pi\) | |||||||
\(102\) | −3.72138 | − | 16.4394i | −0.368471 | − | 1.62775i | ||||
\(103\) | 9.56713i | 0.942678i | 0.881952 | + | 0.471339i | \(0.156229\pi\) | ||||
−0.881952 | + | 0.471339i | \(0.843771\pi\) | |||||||
\(104\) | −13.8944 | − | 2.01480i | −1.36246 | − | 0.197567i | ||||
\(105\) | −1.66901 | + | 0.463024i | −0.162879 | + | 0.0451865i | ||||
\(106\) | 0.377504 | − | 7.85843i | 0.0366664 | − | 0.763278i | ||||
\(107\) | −11.2400 | −1.08661 | −0.543305 | − | 0.839535i | \(-0.682827\pi\) | ||||
−0.543305 | + | 0.839535i | \(0.682827\pi\) | |||||||
\(108\) | 7.84135 | − | 6.82006i | 0.754534 | − | 0.656260i | ||||
\(109\) | −9.16851 | −0.878184 | −0.439092 | − | 0.898442i | \(-0.644700\pi\) | ||||
−0.439092 | + | 0.898442i | \(0.644700\pi\) | |||||||
\(110\) | −0.0439800 | + | 0.915524i | −0.00419333 | + | 0.0872918i | ||||
\(111\) | −3.83409 | + | 1.06367i | −0.363915 | + | 0.100959i | ||||
\(112\) | −0.763309 | + | 3.92649i | −0.0721259 | + | 0.371019i | ||||
\(113\) | − | 3.10716i | − | 0.292297i | −0.989263 | − | 0.146149i | \(-0.953312\pi\) | ||
0.989263 | − | 0.146149i | \(-0.0466877\pi\) | |||||||
\(114\) | 2.28376 | + | 10.0887i | 0.213893 | + | 0.944889i | ||||
\(115\) | 1.33148i | 0.124161i | ||||||||
\(116\) | 0.786876 | − | 8.17123i | 0.0730596 | − | 0.758680i | ||||
\(117\) | 12.7630 | − | 7.67200i | 1.17994 | − | 0.709276i | ||||
\(118\) | −0.595414 | − | 0.0286025i | −0.0548123 | − | 0.00263308i | ||||
\(119\) | −6.88118 | −0.630797 | ||||||||
\(120\) | −0.618626 | − | 4.85976i | −0.0564726 | − | 0.443634i | ||||
\(121\) | −10.5799 | −0.961813 | ||||||||
\(122\) | −0.253209 | − | 0.0121637i | −0.0229245 | − | 0.00110125i | ||||
\(123\) | −5.07295 | − | 18.2859i | −0.457412 | − | 1.64879i | ||||
\(124\) | −1.46406 | + | 15.2033i | −0.131476 | + | 1.36530i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −2.00880 | − | 3.73694i | −0.178958 | − | 0.332913i | ||||
\(127\) | 5.01119i | 0.444671i | 0.974970 | + | 0.222335i | \(0.0713680\pi\) | ||||
−0.974970 | + | 0.222335i | \(0.928632\pi\) | |||||||
\(128\) | −10.6810 | − | 3.73037i | −0.944078 | − | 0.329721i | ||||
\(129\) | 2.37849 | + | 8.57350i | 0.209415 | + | 0.754855i | ||||
\(130\) | 0.336833 | − | 7.01180i | 0.0295422 | − | 0.614975i | ||||
\(131\) | −18.0995 | −1.58136 | −0.790681 | − | 0.612228i | \(-0.790274\pi\) | ||||
−0.790681 | + | 0.612228i | \(0.790274\pi\) | |||||||
\(132\) | −2.21101 | + | 0.390050i | −0.192444 | + | 0.0339495i | ||||
\(133\) | 4.22288 | 0.366170 | ||||||||
\(134\) | −0.711791 | + | 14.8172i | −0.0614894 | + | 1.28001i | ||||
\(135\) | 3.77014 | + | 3.57575i | 0.324482 | + | 0.307752i | ||||
\(136\) | 2.79305 | − | 19.2615i | 0.239502 | − | 1.65166i | ||||
\(137\) | 12.2502i | 1.04661i | 0.852146 | + | 0.523304i | \(0.175301\pi\) | ||||
−0.852146 | + | 0.523304i | \(0.824699\pi\) | |||||||
\(138\) | −3.18096 | + | 0.720069i | −0.270781 | + | 0.0612964i | ||||
\(139\) | − | 12.5062i | − | 1.06076i | −0.847760 | − | 0.530380i | \(-0.822049\pi\) | ||
0.847760 | − | 0.530380i | \(-0.177951\pi\) | |||||||
\(140\) | −1.99079 | − | 0.191710i | −0.168253 | − | 0.0162024i | ||||
\(141\) | 16.0582 | − | 4.45491i | 1.35234 | − | 0.375171i | ||||
\(142\) | 2.96143 | + | 0.142261i | 0.248517 | + | 0.0119383i | ||||
\(143\) | −3.21714 | −0.269031 | ||||||||
\(144\) | 11.2756 | − | 4.10611i | 0.939636 | − | 0.342176i | ||||
\(145\) | 4.10451 | 0.340861 | ||||||||
\(146\) | 23.4851 | + | 1.12818i | 1.94364 | + | 0.0933687i | ||||
\(147\) | −1.66901 | + | 0.463024i | −0.137658 | + | 0.0381896i | ||||
\(148\) | −4.57327 | − | 0.440399i | −0.375921 | − | 0.0362006i | ||||
\(149\) | 7.75155i | 0.635031i | 0.948253 | + | 0.317516i | \(0.102849\pi\) | ||||
−0.948253 | + | 0.317516i | \(0.897151\pi\) | |||||||
\(150\) | 2.38904 | − | 0.540805i | 0.195065 | − | 0.0441565i | ||||
\(151\) | − | 1.99824i | − | 0.162614i | −0.996689 | − | 0.0813072i | \(-0.974090\pi\) | ||
0.996689 | − | 0.0813072i | \(-0.0259095\pi\) | |||||||
\(152\) | −1.71406 | + | 11.8205i | −0.139028 | + | 0.958768i | ||||
\(153\) | 10.6355 | + | 17.6930i | 0.859827 | + | 1.43040i | ||||
\(154\) | −0.0439800 | + | 0.915524i | −0.00354401 | + | 0.0737750i | ||||
\(155\) | −7.63684 | −0.613406 | ||||||||
\(156\) | 16.9337 | − | 2.98731i | 1.35578 | − | 0.239176i | ||||
\(157\) | 12.8513 | 1.02565 | 0.512824 | − | 0.858494i | \(-0.328599\pi\) | ||||
0.512824 | + | 0.858494i | \(0.328599\pi\) | |||||||
\(158\) | −0.481964 | + | 10.0330i | −0.0383430 | + | 0.798180i | ||||
\(159\) | 2.57588 | + | 9.28499i | 0.204280 | + | 0.736347i | ||||
\(160\) | 1.34468 | − | 5.49471i | 0.106306 | − | 0.434395i | ||||
\(161\) | 1.33148i | 0.104935i | ||||||||
\(162\) | −6.50372 | + | 10.9408i | −0.510981 | + | 0.859592i | ||||
\(163\) | 3.76566i | 0.294949i | 0.989066 | + | 0.147474i | \(0.0471144\pi\) | ||||
−0.989066 | + | 0.147474i | \(0.952886\pi\) | |||||||
\(164\) | 2.10040 | − | 21.8113i | 0.164013 | − | 1.70318i | ||||
\(165\) | −0.300095 | − | 1.08172i | −0.0233624 | − | 0.0842119i | ||||
\(166\) | 1.08341 | + | 0.0520449i | 0.0840889 | + | 0.00403947i | ||||
\(167\) | −12.3052 | −0.952203 | −0.476101 | − | 0.879390i | \(-0.657950\pi\) | ||||
−0.476101 | + | 0.879390i | \(0.657950\pi\) | |||||||
\(168\) | −0.618626 | − | 4.85976i | −0.0477280 | − | 0.374939i | ||||
\(169\) | 11.6394 | 0.895337 | ||||||||
\(170\) | 9.72025 | + | 0.466942i | 0.745509 | + | 0.0358128i | ||||
\(171\) | −6.52684 | − | 10.8580i | −0.499120 | − | 0.830328i | ||||
\(172\) | −0.984788 | + | 10.2264i | −0.0750894 | + | 0.779758i | ||||
\(173\) | − | 18.5642i | − | 1.41141i | −0.708506 | − | 0.705705i | \(-0.750630\pi\) | ||
0.708506 | − | 0.705705i | \(-0.249370\pi\) | |||||||
\(174\) | 2.21974 | + | 9.80586i | 0.168278 | + | 0.743381i | ||||
\(175\) | − | 1.00000i | − | 0.0755929i | ||||||
\(176\) | −2.54484 | − | 0.494715i | −0.191824 | − | 0.0372906i | ||||
\(177\) | 0.703501 | − | 0.195168i | 0.0528784 | − | 0.0146697i | ||||
\(178\) | −0.781366 | + | 16.2655i | −0.0585658 | + | 1.21915i | ||||
\(179\) | 12.1268 | 0.906401 | 0.453201 | − | 0.891408i | \(-0.350282\pi\) | ||||
0.453201 | + | 0.891408i | \(0.350282\pi\) | |||||||
\(180\) | 2.58401 | + | 5.41506i | 0.192601 | + | 0.403615i | ||||
\(181\) | −0.0867806 | −0.00645035 | −0.00322517 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322517 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(182\) | 0.336833 | − | 7.01180i | 0.0249677 | − | 0.519749i | ||||
\(183\) | 0.299175 | − | 0.0829981i | 0.0221156 | − | 0.00613540i | ||||
\(184\) | −3.72700 | − | 0.540443i | −0.274758 | − | 0.0398420i | ||||
\(185\) | − | 2.29722i | − | 0.168895i | ||||||
\(186\) | −4.13004 | − | 18.2447i | −0.302829 | − | 1.33777i | ||||
\(187\) | − | 4.45983i | − | 0.326135i | ||||||
\(188\) | 19.1541 | + | 1.84451i | 1.39695 | + | 0.134524i | ||||
\(189\) | 3.77014 | + | 3.57575i | 0.274238 | + | 0.260098i | ||||
\(190\) | −5.96518 | − | 0.286556i | −0.432760 | − | 0.0207889i | ||||
\(191\) | 17.7041 | 1.28102 | 0.640512 | − | 0.767948i | \(-0.278722\pi\) | ||||
0.640512 | + | 0.767948i | \(0.278722\pi\) | |||||||
\(192\) | 13.8543 | + | 0.240937i | 0.999849 | + | 0.0173881i | ||||
\(193\) | −14.0241 | −1.00947 | −0.504737 | − | 0.863273i | \(-0.668410\pi\) | ||||
−0.504737 | + | 0.863273i | \(0.668410\pi\) | |||||||
\(194\) | 20.9432 | + | 1.00607i | 1.50364 | + | 0.0722318i | ||||
\(195\) | 2.29836 | + | 8.28466i | 0.164589 | + | 0.593277i | ||||
\(196\) | −1.99079 | − | 0.191710i | −0.142199 | − | 0.0136936i | ||||
\(197\) | − | 6.66618i | − | 0.474946i | −0.971394 | − | 0.237473i | \(-0.923681\pi\) | ||
0.971394 | − | 0.237473i | \(-0.0763191\pi\) | |||||||
\(198\) | 2.42199 | − | 1.30194i | 0.172123 | − | 0.0925249i | ||||
\(199\) | − | 0.390542i | − | 0.0276848i | −0.999904 | − | 0.0138424i | \(-0.995594\pi\) | ||
0.999904 | − | 0.0138424i | \(-0.00440631\pi\) | |||||||
\(200\) | 2.79915 | + | 0.405897i | 0.197930 | + | 0.0287013i | ||||
\(201\) | −4.85687 | − | 17.5070i | −0.342577 | − | 1.23485i | ||||
\(202\) | 0.242062 | − | 5.03895i | 0.0170314 | − | 0.354539i | ||||
\(203\) | 4.10451 | 0.288080 | ||||||||
\(204\) | 4.14121 | + | 23.4746i | 0.289943 | + | 1.64355i | ||||
\(205\) | 10.9561 | 0.765209 | ||||||||
\(206\) | 0.649205 | − | 13.5144i | 0.0452323 | − | 0.941592i | ||||
\(207\) | 3.42352 | − | 2.05791i | 0.237951 | − | 0.143035i | ||||
\(208\) | 19.4904 | + | 3.78892i | 1.35141 | + | 0.262714i | ||||
\(209\) | 2.73693i | 0.189318i | ||||||||
\(210\) | 2.38904 | − | 0.540805i | 0.164860 | − | 0.0373191i | ||||
\(211\) | 28.5906i | 1.96826i | 0.177461 | + | 0.984128i | \(0.443212\pi\) | ||||
−0.177461 | + | 0.984128i | \(0.556788\pi\) | |||||||
\(212\) | −1.06651 | + | 11.0751i | −0.0732484 | + | 0.760640i | ||||
\(213\) | −3.49902 | + | 0.970711i | −0.239749 | + | 0.0665120i | ||||
\(214\) | 15.8774 | + | 0.762721i | 1.08536 | + | 0.0521385i | ||||
\(215\) | −5.13687 | −0.350331 | ||||||||
\(216\) | −11.5394 | + | 9.10181i | −0.785155 | + | 0.619300i | ||||
\(217\) | −7.63684 | −0.518422 | ||||||||
\(218\) | 12.9513 | + | 0.622155i | 0.877172 | + | 0.0421377i | ||||
\(219\) | −27.7484 | + | 7.69806i | −1.87506 | + | 0.520187i | ||||
\(220\) | 0.124251 | − | 1.29027i | 0.00837700 | − | 0.0869900i | ||||
\(221\) | 34.1569i | 2.29764i | ||||||||
\(222\) | 5.48815 | − | 1.24235i | 0.368340 | − | 0.0833808i | ||||
\(223\) | − | 29.4239i | − | 1.97037i | −0.171489 | − | 0.985186i | \(-0.554858\pi\) | ||
0.171489 | − | 0.985186i | \(-0.445142\pi\) | |||||||
\(224\) | 1.34468 | − | 5.49471i | 0.0898453 | − | 0.367131i | ||||
\(225\) | −2.57122 | + | 1.54559i | −0.171414 | + | 0.103039i | ||||
\(226\) | −0.210845 | + | 4.38913i | −0.0140252 | + | 0.291960i | ||||
\(227\) | 20.6406 | 1.36997 | 0.684983 | − | 0.728559i | \(-0.259809\pi\) | ||||
0.684983 | + | 0.728559i | \(0.259809\pi\) | |||||||
\(228\) | −2.54140 | − | 14.4060i | −0.168309 | − | 0.954064i | ||||
\(229\) | −1.01566 | −0.0671167 | −0.0335583 | − | 0.999437i | \(-0.510684\pi\) | ||||
−0.0335583 | + | 0.999437i | \(0.510684\pi\) | |||||||
\(230\) | 0.0903511 | − | 1.88082i | 0.00595758 | − | 0.124018i | ||||
\(231\) | −0.300095 | − | 1.08172i | −0.0197448 | − | 0.0711720i | ||||
\(232\) | −1.66601 | + | 11.4892i | −0.109379 | + | 0.754300i | ||||
\(233\) | 5.71810i | 0.374605i | 0.982302 | + | 0.187302i | \(0.0599744\pi\) | ||||
−0.982302 | + | 0.187302i | \(0.940026\pi\) | |||||||
\(234\) | −18.5495 | + | 9.97127i | −1.21262 | + | 0.651843i | ||||
\(235\) | 9.62134i | 0.627627i | ||||||||
\(236\) | 0.839132 | + | 0.0808070i | 0.0546228 | + | 0.00526009i | ||||
\(237\) | −3.28866 | − | 11.8543i | −0.213621 | − | 0.770018i | ||||
\(238\) | 9.72025 | + | 0.466942i | 0.630070 | + | 0.0302674i | ||||
\(239\) | −18.4859 | −1.19575 | −0.597876 | − | 0.801589i | \(-0.703988\pi\) | ||||
−0.597876 | + | 0.801589i | \(0.703988\pi\) | |||||||
\(240\) | 0.544089 | + | 6.90681i | 0.0351208 | + | 0.445832i | ||||
\(241\) | 11.7580 | 0.757400 | 0.378700 | − | 0.925519i | \(-0.376371\pi\) | ||||
0.378700 | + | 0.925519i | \(0.376371\pi\) | |||||||
\(242\) | 14.9451 | + | 0.717932i | 0.960705 | + | 0.0461504i | ||||
\(243\) | 3.36696 | − | 15.2205i | 0.215990 | − | 0.976396i | ||||
\(244\) | 0.356854 | + | 0.0343644i | 0.0228452 | + | 0.00219996i | ||||
\(245\) | − | 1.00000i | − | 0.0638877i | ||||||
\(246\) | 5.92512 | + | 26.1747i | 0.377772 | + | 1.66883i | ||||
\(247\) | − | 20.9616i | − | 1.33375i | ||||||
\(248\) | 3.09977 | − | 21.3767i | 0.196836 | − | 1.35742i | ||||
\(249\) | −1.28008 | + | 0.355126i | −0.0811220 | + | 0.0225052i | ||||
\(250\) | −0.0678578 | + | 1.41258i | −0.00429171 | + | 0.0893397i | ||||
\(251\) | 11.5446 | 0.728691 | 0.364345 | − | 0.931264i | \(-0.381293\pi\) | ||||
0.364345 | + | 0.931264i | \(0.381293\pi\) | |||||||
\(252\) | 2.58401 | + | 5.41506i | 0.162778 | + | 0.341117i | ||||
\(253\) | −0.862956 | −0.0542536 | ||||||||
\(254\) | 0.340048 | − | 7.07872i | 0.0213365 | − | 0.444159i | ||||
\(255\) | −11.4848 | + | 3.18615i | −0.719205 | + | 0.199525i | ||||
\(256\) | 14.8347 | + | 5.99425i | 0.927170 | + | 0.374641i | ||||
\(257\) | − | 8.63514i | − | 0.538645i | −0.963050 | − | 0.269323i | \(-0.913200\pi\) | ||
0.963050 | − | 0.269323i | \(-0.0867998\pi\) | |||||||
\(258\) | −2.77804 | − | 12.2722i | −0.172953 | − | 0.764034i | ||||
\(259\) | − | 2.29722i | − | 0.142742i | ||||||
\(260\) | −0.951611 | + | 9.88190i | −0.0590164 | + | 0.612849i | ||||
\(261\) | −6.34389 | − | 10.5536i | −0.392677 | − | 0.653251i | ||||
\(262\) | 25.5671 | + | 1.22819i | 1.57954 | + | 0.0758781i | ||||
\(263\) | −16.2106 | −0.999591 | −0.499795 | − | 0.866144i | \(-0.666591\pi\) | ||||
−0.499795 | + | 0.866144i | \(0.666591\pi\) | |||||||
\(264\) | 3.14971 | − | 0.400944i | 0.193851 | − | 0.0246764i | ||||
\(265\) | −5.56316 | −0.341742 | ||||||||
\(266\) | −5.96518 | − | 0.286556i | −0.365749 | − | 0.0175699i | ||||
\(267\) | −5.33160 | − | 19.2183i | −0.326289 | − | 1.17614i | ||||
\(268\) | 2.01093 | − | 20.8823i | 0.122837 | − | 1.27559i | ||||
\(269\) | − | 12.9285i | − | 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(270\) | −5.08300 | − | 5.30689i | −0.309342 | − | 0.322967i | ||||
\(271\) | 7.98971i | 0.485340i | 0.970109 | + | 0.242670i | \(0.0780233\pi\) | ||||
−0.970109 | + | 0.242670i | \(0.921977\pi\) | |||||||
\(272\) | −5.25246 | + | 27.0189i | −0.318477 | + | 1.63826i | ||||
\(273\) | 2.29836 | + | 8.28466i | 0.139103 | + | 0.501411i | ||||
\(274\) | 0.831275 | − | 17.3045i | 0.0502192 | − | 1.04540i | ||||
\(275\) | 0.648120 | 0.0390831 | ||||||||
\(276\) | 4.54223 | − | 0.801306i | 0.273410 | − | 0.0482329i | ||||
\(277\) | 23.8395 | 1.43238 | 0.716188 | − | 0.697908i | \(-0.245885\pi\) | ||||
0.716188 | + | 0.697908i | \(0.245885\pi\) | |||||||
\(278\) | −0.848641 | + | 17.6660i | −0.0508981 | + | 1.05954i | ||||
\(279\) | 11.8034 | + | 19.6360i | 0.706651 | + | 1.17557i | ||||
\(280\) | 2.79915 | + | 0.405897i | 0.167281 | + | 0.0242570i | ||||
\(281\) | 1.52045i | 0.0907025i | 0.998971 | + | 0.0453513i | \(0.0144407\pi\) | ||||
−0.998971 | + | 0.0453513i | \(0.985559\pi\) | |||||||
\(282\) | −22.9858 | + | 5.20327i | −1.36878 | + | 0.309850i | ||||
\(283\) | 6.56172i | 0.390054i | 0.980798 | + | 0.195027i | \(0.0624794\pi\) | ||||
−0.980798 | + | 0.195027i | \(0.937521\pi\) | |||||||
\(284\) | −4.17361 | − | 0.401912i | −0.247658 | − | 0.0238491i | ||||
\(285\) | 7.04805 | − | 1.95530i | 0.417491 | − | 0.115822i | ||||
\(286\) | 4.54448 | + | 0.218308i | 0.268721 | + | 0.0129088i | ||||
\(287\) | 10.9561 | 0.646719 | ||||||||
\(288\) | −16.2064 | + | 5.03509i | −0.954972 | + | 0.296695i | ||||
\(289\) | −30.3507 | −1.78533 | ||||||||
\(290\) | −5.79797 | − | 0.278524i | −0.340469 | − | 0.0163555i | ||||
\(291\) | −24.7451 | + | 6.86488i | −1.45058 | + | 0.402426i | ||||
\(292\) | −33.0981 | − | 3.18730i | −1.93692 | − | 0.186522i | ||||
\(293\) | − | 21.0744i | − | 1.23118i | −0.788066 | − | 0.615591i | \(-0.788917\pi\) | ||
0.788066 | − | 0.615591i | \(-0.211083\pi\) | |||||||
\(294\) | 2.38904 | − | 0.540805i | 0.139332 | − | 0.0315404i | ||||
\(295\) | 0.421507i | 0.0245411i | ||||||||
\(296\) | 6.43025 | + | 0.932433i | 0.373751 | + | 0.0541966i | ||||
\(297\) | −2.31752 | + | 2.44350i | −0.134476 | + | 0.141787i | ||||
\(298\) | 0.526003 | − | 10.9497i | 0.0304705 | − | 0.634300i | ||||
\(299\) | 6.60919 | 0.382219 | ||||||||
\(300\) | −3.41142 | + | 0.601817i | −0.196959 | + | 0.0347459i | ||||
\(301\) | −5.13687 | −0.296084 | ||||||||
\(302\) | −0.135596 | + | 2.82268i | −0.00780269 | + | 0.162427i | ||||
\(303\) | 1.65169 | + | 5.95368i | 0.0948873 | + | 0.342030i | ||||
\(304\) | 3.22336 | − | 16.5811i | 0.184873 | − | 0.950993i | ||||
\(305\) | 0.179252i | 0.0102640i | ||||||||
\(306\) | −13.8229 | − | 25.7146i | −0.790202 | − | 1.47000i | ||||
\(307\) | − | 25.3127i | − | 1.44467i | −0.691542 | − | 0.722336i | \(-0.743068\pi\) | ||
0.691542 | − | 0.722336i | \(-0.256932\pi\) | |||||||
\(308\) | 0.124251 | − | 1.29027i | 0.00707986 | − | 0.0735200i | ||||
\(309\) | 4.42981 | + | 15.9677i | 0.252003 | + | 0.908370i | ||||
\(310\) | 10.7877 | + | 0.518219i | 0.612699 | + | 0.0294329i | ||||
\(311\) | −18.2961 | −1.03748 | −0.518739 | − | 0.854933i | \(-0.673598\pi\) | ||||
−0.518739 | + | 0.854933i | \(0.673598\pi\) | |||||||
\(312\) | −24.1229 | + | 3.07074i | −1.36569 | + | 0.173846i | ||||
\(313\) | 20.8802 | 1.18022 | 0.590110 | − | 0.807323i | \(-0.299084\pi\) | ||||
0.590110 | + | 0.807323i | \(0.299084\pi\) | |||||||
\(314\) | −18.1536 | − | 0.872064i | −1.02447 | − | 0.0492134i | ||||
\(315\) | −2.57122 | + | 1.54559i | −0.144872 | + | 0.0870840i | ||||
\(316\) | 1.36163 | − | 14.1397i | 0.0765977 | − | 0.795421i | ||||
\(317\) | 25.7694i | 1.44735i | 0.690140 | + | 0.723676i | \(0.257549\pi\) | ||||
−0.690140 | + | 0.723676i | \(0.742451\pi\) | |||||||
\(318\) | −3.00858 | − | 13.2906i | −0.168713 | − | 0.745301i | ||||
\(319\) | 2.66022i | 0.148944i | ||||||||
\(320\) | −2.27234 | + | 7.67049i | −0.127027 | + | 0.428794i | ||||
\(321\) | −18.7597 | + | 5.20438i | −1.04706 | + | 0.290480i | ||||
\(322\) | 0.0903511 | − | 1.88082i | 0.00503507 | − | 0.104814i | ||||
\(323\) | 29.0584 | 1.61685 | ||||||||
\(324\) | 9.92948 | − | 15.0135i | 0.551638 | − | 0.834084i | ||||
\(325\) | −4.96381 | −0.275342 | ||||||||
\(326\) | 0.255529 | − | 5.31931i | 0.0141525 | − | 0.294609i | ||||
\(327\) | −15.3024 | + | 4.24524i | −0.846223 | + | 0.234762i | ||||
\(328\) | −4.44706 | + | 30.6678i | −0.245548 | + | 1.69335i | ||||
\(329\) | 9.62134i | 0.530442i | ||||||||
\(330\) | 0.350506 | + | 1.54839i | 0.0192947 | + | 0.0852359i | ||||
\(331\) | 21.4801i | 1.18065i | 0.807164 | + | 0.590327i | \(0.201001\pi\) | ||||
−0.807164 | + | 0.590327i | \(0.798999\pi\) | |||||||
\(332\) | −1.52688 | − | 0.147036i | −0.0837983 | − | 0.00806964i | ||||
\(333\) | −5.90664 | + | 3.55055i | −0.323682 | + | 0.194569i | ||||
\(334\) | 17.3821 | + | 0.835002i | 0.951106 | + | 0.0456893i | ||||
\(335\) | 10.4894 | 0.573100 | ||||||||
\(336\) | 0.544089 | + | 6.90681i | 0.0296825 | + | 0.376797i | ||||
\(337\) | −10.7117 | −0.583504 | −0.291752 | − | 0.956494i | \(-0.594238\pi\) | ||||
−0.291752 | + | 0.956494i | \(0.594238\pi\) | |||||||
\(338\) | −16.4416 | − | 0.789823i | −0.894305 | − | 0.0429607i | ||||
\(339\) | −1.43869 | − | 5.18590i | −0.0781389 | − | 0.281659i | ||||
\(340\) | −13.6990 | − | 1.31919i | −0.742932 | − | 0.0715432i | ||||
\(341\) | − | 4.94959i | − | 0.268035i | ||||||
\(342\) | 8.48291 | + | 15.7807i | 0.458703 | + | 0.853321i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 2.08504 | − | 14.3789i | 0.112418 | − | 0.775257i | ||||
\(345\) | 0.616506 | + | 2.22225i | 0.0331915 | + | 0.119642i | ||||
\(346\) | −1.25973 | + | 26.2235i | −0.0677233 | + | 1.40978i | ||||
\(347\) | 10.5606 | 0.566923 | 0.283462 | − | 0.958984i | \(-0.408517\pi\) | ||||
0.283462 | + | 0.958984i | \(0.408517\pi\) | |||||||
\(348\) | −2.47017 | − | 14.0022i | −0.132415 | − | 0.750599i | ||||
\(349\) | 21.7269 | 1.16301 | 0.581507 | − | 0.813541i | \(-0.302463\pi\) | ||||
0.581507 | + | 0.813541i | \(0.302463\pi\) | |||||||
\(350\) | −0.0678578 | + | 1.41258i | −0.00362715 | + | 0.0755058i | ||||
\(351\) | 17.7494 | − | 18.7143i | 0.947390 | − | 0.998893i | ||||
\(352\) | 3.56123 | + | 0.871515i | 0.189814 | + | 0.0464519i | ||||
\(353\) | − | 21.0359i | − | 1.11963i | −0.828618 | − | 0.559814i | \(-0.810872\pi\) | ||
0.828618 | − | 0.559814i | \(-0.189128\pi\) | |||||||
\(354\) | −1.00700 | + | 0.227953i | −0.0535214 | + | 0.0121156i | ||||
\(355\) | − | 2.09646i | − | 0.111269i | ||||||
\(356\) | 2.20749 | − | 22.9234i | 0.116997 | − | 1.21494i | ||||
\(357\) | −11.4848 | + | 3.18615i | −0.607840 | + | 0.168629i | ||||
\(358\) | −17.1302 | − | 0.822900i | −0.905357 | − | 0.0434916i | ||||
\(359\) | 1.14792 | 0.0605850 | 0.0302925 | − | 0.999541i | \(-0.490356\pi\) | ||||
0.0302925 | + | 0.999541i | \(0.490356\pi\) | |||||||
\(360\) | −3.28268 | − | 7.82458i | −0.173013 | − | 0.412391i | ||||
\(361\) | 1.16725 | 0.0614344 | ||||||||
\(362\) | 0.122585 | + | 0.00588874i | 0.00644292 | + | 0.000309505i | ||||
\(363\) | −17.6581 | + | 4.89877i | −0.926808 | + | 0.257119i | ||||
\(364\) | −0.951611 | + | 9.88190i | −0.0498780 | + | 0.517952i | ||||
\(365\) | − | 16.6256i | − | 0.870225i | ||||||
\(366\) | −0.428241 | + | 0.0969405i | −0.0223845 | + | 0.00506716i | ||||
\(367\) | 4.83851i | 0.252568i | 0.991994 | + | 0.126284i | \(0.0403051\pi\) | ||||
−0.991994 | + | 0.126284i | \(0.959695\pi\) | |||||||
\(368\) | 5.22804 | + | 1.01633i | 0.272530 | + | 0.0529797i | ||||
\(369\) | −16.9336 | − | 28.1706i | −0.881530 | − | 1.46650i | ||||
\(370\) | −0.155884 | + | 3.24501i | −0.00810403 | + | 0.168700i | ||||
\(371\) | −5.56316 | −0.288825 | ||||||||
\(372\) | 4.59598 | + | 26.0525i | 0.238291 | + | 1.35076i | ||||
\(373\) | 12.1232 | 0.627716 | 0.313858 | − | 0.949470i | \(-0.398378\pi\) | ||||
0.313858 | + | 0.949470i | \(0.398378\pi\) | |||||||
\(374\) | −0.302634 | + | 6.29989i | −0.0156489 | + | 0.325759i | ||||
\(375\) | −0.463024 | − | 1.66901i | −0.0239105 | − | 0.0861875i | ||||
\(376\) | −26.9316 | − | 3.90528i | −1.38889 | − | 0.201399i | ||||
\(377\) | − | 20.3740i | − | 1.04932i | ||||||
\(378\) | −5.08300 | − | 5.30689i | −0.261441 | − | 0.272957i | ||||
\(379\) | − | 23.0839i | − | 1.18574i | −0.805299 | − | 0.592869i | \(-0.797995\pi\) | ||
0.805299 | − | 0.592869i | \(-0.202005\pi\) | |||||||
\(380\) | 8.40688 | + | 0.809569i | 0.431264 | + | 0.0415300i | ||||
\(381\) | 2.32030 | + | 8.36374i | 0.118873 | + | 0.428487i | ||||
\(382\) | −25.0086 | − | 1.20136i | −1.27955 | − | 0.0614671i | ||||
\(383\) | 1.63222 | 0.0834028 | 0.0417014 | − | 0.999130i | \(-0.486722\pi\) | ||||
0.0417014 | + | 0.999130i | \(0.486722\pi\) | |||||||
\(384\) | −19.5540 | − | 1.28047i | −0.997863 | − | 0.0653436i | ||||
\(385\) | 0.648120 | 0.0330312 | ||||||||
\(386\) | 19.8102 | + | 0.951642i | 1.00831 | + | 0.0484373i | ||||
\(387\) | 7.93948 | + | 13.2080i | 0.403586 | + | 0.671400i | ||||
\(388\) | −29.5158 | − | 2.84233i | −1.49844 | − | 0.144297i | ||||
\(389\) | 26.6447i | 1.35094i | 0.737388 | + | 0.675470i | \(0.236059\pi\) | ||||
−0.737388 | + | 0.675470i | \(0.763941\pi\) | |||||||
\(390\) | −2.68445 | − | 11.8588i | −0.135932 | − | 0.600491i | ||||
\(391\) | 9.16213i | 0.463349i | ||||||||
\(392\) | 2.79915 | + | 0.405897i | 0.141378 | + | 0.0205009i | ||||
\(393\) | −30.2084 | + | 8.38052i | −1.52381 | + | 0.422741i | ||||
\(394\) | −0.452353 | + | 9.41654i | −0.0227892 | + | 0.474399i | ||||
\(395\) | 7.10256 | 0.357369 | ||||||||
\(396\) | −3.50961 | + | 1.67475i | −0.176364 | + | 0.0841594i | ||||
\(397\) | −7.86336 | −0.394651 | −0.197325 | − | 0.980338i | \(-0.563226\pi\) | ||||
−0.197325 | + | 0.980338i | \(0.563226\pi\) | |||||||
\(398\) | −0.0265013 | + | 0.551674i | −0.00132839 | + | 0.0276529i | ||||
\(399\) | 7.04805 | − | 1.95530i | 0.352844 | − | 0.0978873i | ||||
\(400\) | −3.92649 | − | 0.763309i | −0.196325 | − | 0.0381654i | ||||
\(401\) | 11.3925i | 0.568913i | 0.958689 | + | 0.284457i | \(0.0918132\pi\) | ||||
−0.958689 | + | 0.284457i | \(0.908187\pi\) | |||||||
\(402\) | 5.67274 | + | 25.0597i | 0.282931 | + | 1.24987i | ||||
\(403\) | 37.9078i | 1.88832i | ||||||||
\(404\) | −0.683865 | + | 7.10152i | −0.0340236 | + | 0.353314i | ||||
\(405\) | 7.94808 | + | 4.22232i | 0.394943 | + | 0.209809i | ||||
\(406\) | −5.79797 | − | 0.278524i | −0.287749 | − | 0.0138229i | ||||
\(407\) | 1.48887 | 0.0738006 | ||||||||
\(408\) | −4.25688 | − | 33.4409i | −0.210747 | − | 1.65557i | ||||
\(409\) | −8.80374 | −0.435317 | −0.217658 | − | 0.976025i | \(-0.569842\pi\) | ||||
−0.217658 | + | 0.976025i | \(0.569842\pi\) | |||||||
\(410\) | −15.4764 | − | 0.743459i | −0.764327 | − | 0.0367168i | ||||
\(411\) | 5.67216 | + | 20.4458i | 0.279787 | + | 1.00852i | ||||
\(412\) | −1.83411 | + | 19.0462i | −0.0903603 | + | 0.938337i | ||||
\(413\) | 0.421507i | 0.0207410i | ||||||||
\(414\) | −4.97565 | + | 2.67466i | −0.244540 | + | 0.131453i | ||||
\(415\) | − | 0.766970i | − | 0.0376491i | ||||||
\(416\) | −27.2747 | − | 6.67474i | −1.33725 | − | 0.327256i | ||||
\(417\) | −5.79066 | − | 20.8730i | −0.283570 | − | 1.02215i | ||||
\(418\) | 0.185723 | − | 3.86615i | 0.00908398 | − | 0.189100i | ||||
\(419\) | 26.0781 | 1.27400 | 0.637000 | − | 0.770864i | \(-0.280175\pi\) | ||||
0.637000 | + | 0.770864i | \(0.280175\pi\) | |||||||
\(420\) | −3.41142 | + | 0.601817i | −0.166460 | + | 0.0293657i | ||||
\(421\) | 16.4876 | 0.803556 | 0.401778 | − | 0.915737i | \(-0.368392\pi\) | ||||
0.401778 | + | 0.915737i | \(0.368392\pi\) | |||||||
\(422\) | 1.94009 | − | 40.3866i | 0.0944423 | − | 1.96599i | ||||
\(423\) | 24.7386 | − | 14.8706i | 1.20283 | − | 0.723035i | ||||
\(424\) | 2.25807 | − | 15.5721i | 0.109662 | − | 0.756249i | ||||
\(425\) | − | 6.88118i | − | 0.333786i | ||||||
\(426\) | 5.00853 | − | 1.13378i | 0.242664 | − | 0.0549316i | ||||
\(427\) | 0.179252i | 0.00867462i | ||||||||
\(428\) | −22.3764 | − | 2.15482i | −1.08161 | − | 0.104157i | ||||
\(429\) | −5.36946 | + | 1.48961i | −0.259240 | + | 0.0719192i | ||||
\(430\) | 7.25626 | + | 0.348577i | 0.349928 | + | 0.0168099i | ||||
\(431\) | −5.09236 | −0.245290 | −0.122645 | − | 0.992451i | \(-0.539138\pi\) | ||||
−0.122645 | + | 0.992451i | \(0.539138\pi\) | |||||||
\(432\) | 16.9180 | − | 12.0740i | 0.813966 | − | 0.580913i | ||||
\(433\) | 1.38310 | 0.0664673 | 0.0332337 | − | 0.999448i | \(-0.489419\pi\) | ||||
0.0332337 | + | 0.999448i | \(0.489419\pi\) | |||||||
\(434\) | 10.7877 | + | 0.518219i | 0.517825 | + | 0.0248753i | ||||
\(435\) | 6.85049 | − | 1.90049i | 0.328456 | − | 0.0911215i | ||||
\(436\) | −18.2526 | − | 1.75769i | −0.874140 | − | 0.0841783i | ||||
\(437\) | − | 5.62267i | − | 0.268969i | ||||||
\(438\) | 39.7193 | − | 8.99122i | 1.89786 | − | 0.429617i | ||||
\(439\) | − | 18.7957i | − | 0.897069i | −0.893765 | − | 0.448535i | \(-0.851946\pi\) | ||
0.893765 | − | 0.448535i | \(-0.148054\pi\) | |||||||
\(440\) | −0.263070 | + | 1.81419i | −0.0125414 | + | 0.0864879i | ||||
\(441\) | −2.57122 | + | 1.54559i | −0.122439 | + | 0.0735994i | ||||
\(442\) | 2.31781 | − | 48.2494i | 0.110247 | − | 2.29499i | ||||
\(443\) | 8.85852 | 0.420881 | 0.210441 | − | 0.977607i | \(-0.432510\pi\) | ||||
0.210441 | + | 0.977607i | \(0.432510\pi\) | |||||||
\(444\) | −7.83678 | + | 1.38250i | −0.371917 | + | 0.0656107i | ||||
\(445\) | 11.5147 | 0.545851 | ||||||||
\(446\) | −1.99664 | + | 41.5638i | −0.0945439 | + | 1.96810i | ||||
\(447\) | 3.58915 | + | 12.9374i | 0.169761 | + | 0.611920i | ||||
\(448\) | −2.27234 | + | 7.67049i | −0.107358 | + | 0.362397i | ||||
\(449\) | 1.38236i | 0.0652376i | 0.999468 | + | 0.0326188i | \(0.0103847\pi\) | ||||
−0.999468 | + | 0.0326188i | \(0.989615\pi\) | |||||||
\(450\) | 3.73694 | − | 2.00880i | 0.176161 | − | 0.0946955i | ||||
\(451\) | 7.10088i | 0.334367i | ||||||||
\(452\) | 0.595673 | − | 6.18571i | 0.0280181 | − | 0.290951i | ||||
\(453\) | −0.925233 | − | 3.33509i | −0.0434713 | − | 0.156696i | ||||
\(454\) | −29.1566 | − | 1.40063i | −1.36839 | − | 0.0657348i | ||||
\(455\) | −4.96381 | −0.232707 | ||||||||
\(456\) | 2.61239 | + | 20.5222i | 0.122336 | + | 0.961041i | ||||
\(457\) | 31.0264 | 1.45135 | 0.725676 | − | 0.688036i | \(-0.241527\pi\) | ||||
0.725676 | + | 0.688036i | \(0.241527\pi\) | |||||||
\(458\) | 1.43470 | + | 0.0689205i | 0.0670394 | + | 0.00322044i | ||||
\(459\) | 25.9430 | + | 24.6054i | 1.21092 | + | 1.14848i | ||||
\(460\) | −0.255257 | + | 2.65069i | −0.0119014 | + | 0.123589i | ||||
\(461\) | 28.1673i | 1.31188i | 0.754812 | + | 0.655941i | \(0.227728\pi\) | ||||
−0.754812 | + | 0.655941i | \(0.772272\pi\) | |||||||
\(462\) | 0.350506 | + | 1.54839i | 0.0163070 | + | 0.0720375i | ||||
\(463\) | 26.2326i | 1.21913i | 0.792735 | + | 0.609566i | \(0.208656\pi\) | ||||
−0.792735 | + | 0.609566i | \(0.791344\pi\) | |||||||
\(464\) | 3.13301 | − | 16.1164i | 0.145446 | − | 0.748183i | ||||
\(465\) | −12.7460 | + | 3.53604i | −0.591081 | + | 0.163980i | ||||
\(466\) | 0.388018 | − | 8.07729i | 0.0179746 | − | 0.374173i | ||||
\(467\) | 35.8633 | 1.65956 | 0.829778 | − | 0.558094i | \(-0.188467\pi\) | ||||
0.829778 | + | 0.558094i | \(0.188467\pi\) | |||||||
\(468\) | 26.8793 | − | 12.8265i | 1.24250 | − | 0.592907i | ||||
\(469\) | 10.4894 | 0.484358 | ||||||||
\(470\) | 0.652884 | − | 13.5910i | 0.0301153 | − | 0.626904i | ||||
\(471\) | 21.4491 | − | 5.95047i | 0.988320 | − | 0.274183i | ||||
\(472\) | −1.17986 | − | 0.171088i | −0.0543075 | − | 0.00787498i | ||||
\(473\) | − | 3.32931i | − | 0.153082i | ||||||
\(474\) | 3.84110 | + | 16.9683i | 0.176428 | + | 0.779381i | ||||
\(475\) | 4.22288i | 0.193759i | ||||||||
\(476\) | −13.6990 | − | 1.31919i | −0.627892 | − | 0.0604650i | ||||
\(477\) | 8.59835 | + | 14.3041i | 0.393691 | + | 0.654939i | ||||
\(478\) | 26.1128 | + | 1.25441i | 1.19437 | + | 0.0573754i | ||||
\(479\) | 33.1353 | 1.51399 | 0.756995 | − | 0.653421i | \(-0.226667\pi\) | ||||
0.756995 | + | 0.653421i | \(0.226667\pi\) | |||||||
\(480\) | −0.299890 | − | 9.79337i | −0.0136880 | − | 0.447004i | ||||
\(481\) | −11.4029 | −0.519929 | ||||||||
\(482\) | −16.6092 | − | 0.797873i | −0.756528 | − | 0.0363421i | ||||
\(483\) | 0.616506 | + | 2.22225i | 0.0280520 | + | 0.101116i | ||||
\(484\) | −21.0624 | − | 2.02828i | −0.957384 | − | 0.0921945i | ||||
\(485\) | − | 14.8262i | − | 0.673222i | ||||||
\(486\) | −5.78894 | + | 21.2718i | −0.262592 | + | 0.964907i | ||||
\(487\) | 25.5792i | 1.15910i | 0.814935 | + | 0.579552i | \(0.196772\pi\) | ||||
−0.814935 | + | 0.579552i | \(0.803228\pi\) | |||||||
\(488\) | −0.501754 | − | 0.0727580i | −0.0227133 | − | 0.00329360i | ||||
\(489\) | 1.74359 | + | 6.28493i | 0.0788478 | + | 0.284215i | ||||
\(490\) | −0.0678578 | + | 1.41258i | −0.00306551 | + | 0.0638141i | ||||
\(491\) | 22.5226 | 1.01643 | 0.508216 | − | 0.861229i | \(-0.330305\pi\) | ||||
0.508216 | + | 0.861229i | \(0.330305\pi\) | |||||||
\(492\) | −6.59358 | − | 37.3760i | −0.297262 | − | 1.68504i | ||||
\(493\) | 28.2439 | 1.27204 | ||||||||
\(494\) | −1.42241 | + | 29.6100i | −0.0639971 | + | 1.33222i | ||||
\(495\) | −1.00173 | − | 1.66646i | −0.0450242 | − | 0.0749017i | ||||
\(496\) | −5.82926 | + | 29.9860i | −0.261742 | + | 1.34641i | ||||
\(497\) | − | 2.09646i | − | 0.0940391i | ||||||
\(498\) | 1.83233 | − | 0.414781i | 0.0821085 | − | 0.0185868i | ||||
\(499\) | − | 37.4978i | − | 1.67863i | −0.543643 | − | 0.839316i | \(-0.682956\pi\) | ||
0.543643 | − | 0.839316i | \(-0.317044\pi\) | |||||||
\(500\) | 0.191710 | − | 1.99079i | 0.00857353 | − | 0.0890309i | ||||
\(501\) | −20.5375 | + | 5.69759i | −0.917548 | + | 0.254550i | ||||
\(502\) | −16.3078 | − | 0.783394i | −0.727851 | − | 0.0349646i | ||||
\(503\) | −24.6073 | −1.09718 | −0.548592 | − | 0.836090i | \(-0.684836\pi\) | ||||
−0.548592 | + | 0.836090i | \(0.684836\pi\) | |||||||
\(504\) | −3.28268 | − | 7.82458i | −0.146222 | − | 0.348534i | ||||
\(505\) | −3.56719 | −0.158738 | ||||||||
\(506\) | 1.21900 | + | 0.0585584i | 0.0541911 | + | 0.00260324i | ||||
\(507\) | 19.4263 | − | 5.38931i | 0.862752 | − | 0.239348i | ||||
\(508\) | −0.960694 | + | 9.97622i | −0.0426239 | + | 0.442623i | ||||
\(509\) | 20.0506i | 0.888728i | 0.895846 | + | 0.444364i | \(0.146570\pi\) | ||||
−0.895846 | + | 0.444364i | \(0.853430\pi\) | |||||||
\(510\) | 16.4394 | − | 3.72138i | 0.727951 | − | 0.164785i | ||||
\(511\) | − | 16.6256i | − | 0.735474i | ||||||
\(512\) | −20.5485 | − | 9.47404i | −0.908126 | − | 0.418698i | ||||
\(513\) | −15.9209 | − | 15.1000i | −0.702924 | − | 0.666681i | ||||
\(514\) | −0.585962 | + | 12.1979i | −0.0258457 | + | 0.538025i | ||||
\(515\) | −9.56713 | −0.421578 | ||||||||
\(516\) | 3.09146 | + | 17.5240i | 0.136094 | + | 0.771453i | ||||
\(517\) | −6.23578 | −0.274249 | ||||||||
\(518\) | −0.155884 | + | 3.24501i | −0.00684915 | + | 0.142578i | ||||
\(519\) | −8.59567 | − | 30.9839i | −0.377308 | − | 1.36004i | ||||
\(520\) | 2.01480 | − | 13.8944i | 0.0883546 | − | 0.609312i | ||||
\(521\) | 23.9103i | 1.04753i | 0.851863 | + | 0.523765i | \(0.175473\pi\) | ||||
−0.851863 | + | 0.523765i | \(0.824527\pi\) | |||||||
\(522\) | 8.24513 | + | 15.3383i | 0.360880 | + | 0.671341i | ||||
\(523\) | − | 19.7289i | − | 0.862683i | −0.902189 | − | 0.431342i | \(-0.858040\pi\) | ||
0.902189 | − | 0.431342i | \(-0.141960\pi\) | |||||||
\(524\) | −36.0324 | − | 3.46986i | −1.57408 | − | 0.151581i | ||||
\(525\) | −0.463024 | − | 1.66901i | −0.0202080 | − | 0.0728418i | ||||
\(526\) | 22.8989 | + | 1.10002i | 0.998439 | + | 0.0479631i | ||||
\(527\) | −52.5505 | −2.28913 | ||||||||
\(528\) | −4.47644 | + | 0.352635i | −0.194812 | + | 0.0153464i | ||||
\(529\) | −21.2272 | −0.922920 | ||||||||
\(530\) | 7.85843 | + | 0.377504i | 0.341348 | + | 0.0163977i | ||||
\(531\) | 1.08379 | − | 0.651476i | 0.0470323 | − | 0.0282716i | ||||
\(532\) | 8.40688 | + | 0.809569i | 0.364484 | + | 0.0350993i | ||||
\(533\) | − | 54.3841i | − | 2.35564i | ||||||
\(534\) | 6.22723 | + | 27.5092i | 0.269479 | + | 1.19044i | ||||
\(535\) | − | 11.2400i | − | 0.485947i | ||||||
\(536\) | −4.25764 | + | 29.3615i | −0.183902 | + | 1.26823i | ||||
\(537\) | 20.2398 | − | 5.61501i | 0.873414 | − | 0.242306i | ||||
\(538\) | −0.877299 | + | 18.2626i | −0.0378230 | + | 0.787356i | ||||
\(539\) | 0.648120 | 0.0279165 | ||||||||
\(540\) | 6.82006 | + | 7.84135i | 0.293489 | + | 0.337438i | ||||
\(541\) | 0.669466 | 0.0287826 | 0.0143913 | − | 0.999896i | \(-0.495419\pi\) | ||||
0.0143913 | + | 0.999896i | \(0.495419\pi\) | |||||||
\(542\) | 0.542165 | − | 11.2861i | 0.0232880 | − | 0.484781i | ||||
\(543\) | −0.144838 | + | 0.0401815i | −0.00621559 | + | 0.00172435i | ||||
\(544\) | 9.25300 | − | 37.8101i | 0.396719 | − | 1.62109i | ||||
\(545\) | − | 9.16851i | − | 0.392736i | ||||||
\(546\) | −2.68445 | − | 11.8588i | −0.114884 | − | 0.507508i | ||||
\(547\) | 9.39985i | 0.401909i | 0.979601 | + | 0.200954i | \(0.0644043\pi\) | ||||
−0.979601 | + | 0.200954i | \(0.935596\pi\) | |||||||
\(548\) | −2.34849 | + | 24.3877i | −0.100323 | + | 1.04179i | ||||
\(549\) | 0.460897 | − | 0.277050i | 0.0196706 | − | 0.0118242i | ||||
\(550\) | −0.915524 | − | 0.0439800i | −0.0390381 | − | 0.00187531i | ||||
\(551\) | −17.3329 | −0.738406 | ||||||||
\(552\) | −6.47066 | + | 0.823686i | −0.275410 | + | 0.0350584i | ||||
\(553\) | 7.10256 | 0.302032 | ||||||||
\(554\) | −33.6753 | − | 1.61770i | −1.43073 | − | 0.0687293i | ||||
\(555\) | −1.06367 | − | 3.83409i | −0.0451501 | − | 0.162748i | ||||
\(556\) | 2.39756 | − | 24.8972i | 0.101679 | − | 1.05587i | ||||
\(557\) | 39.5568i | 1.67608i | 0.545612 | + | 0.838038i | \(0.316297\pi\) | ||||
−0.545612 | + | 0.838038i | \(0.683703\pi\) | |||||||
\(558\) | −15.3408 | − | 28.5384i | −0.649430 | − | 1.20813i | ||||
\(559\) | 25.4984i | 1.07847i | ||||||||
\(560\) | −3.92649 | − | 0.763309i | −0.165925 | − | 0.0322557i | ||||
\(561\) | −2.06501 | − | 7.44352i | −0.0871847 | − | 0.314266i | ||||
\(562\) | 0.103175 | − | 2.14777i | 0.00435216 | − | 0.0905980i | ||||
\(563\) | −38.2888 | −1.61368 | −0.806840 | − | 0.590770i | \(-0.798824\pi\) | ||||
−0.806840 | + | 0.590770i | \(0.798824\pi\) | |||||||
\(564\) | 32.8225 | − | 5.79029i | 1.38208 | − | 0.243815i | ||||
\(565\) | 3.10716 | 0.130719 | ||||||||
\(566\) | 0.445264 | − | 9.26899i | 0.0187159 | − | 0.389605i | ||||
\(567\) | 7.94808 | + | 4.22232i | 0.333788 | + | 0.177321i | ||||
\(568\) | 5.86831 | + | 0.850947i | 0.246229 | + | 0.0357050i | ||||
\(569\) | − | 8.99657i | − | 0.377156i | −0.982058 | − | 0.188578i | \(-0.939612\pi\) | ||
0.982058 | − | 0.188578i | \(-0.0603878\pi\) | |||||||
\(570\) | −10.0887 | + | 2.28376i | −0.422567 | + | 0.0956560i | ||||
\(571\) | − | 4.98330i | − | 0.208545i | −0.994549 | − | 0.104272i | \(-0.966749\pi\) | ||
0.994549 | − | 0.104272i | \(-0.0332514\pi\) | |||||||
\(572\) | −6.40466 | − | 0.616758i | −0.267792 | − | 0.0257879i | ||||
\(573\) | 29.5484 | − | 8.19743i | 1.23440 | − | 0.342453i | ||||
\(574\) | −15.4764 | − | 0.743459i | −0.645974 | − | 0.0310314i | ||||
\(575\) | −1.33148 | −0.0555264 | ||||||||
\(576\) | 23.2346 | − | 6.01275i | 0.968108 | − | 0.250531i | ||||
\(577\) | −35.7825 | −1.48964 | −0.744822 | − | 0.667264i | \(-0.767465\pi\) | ||||
−0.744822 | + | 0.667264i | \(0.767465\pi\) | |||||||
\(578\) | 42.8729 | + | 2.05953i | 1.78328 | + | 0.0856652i | ||||
\(579\) | −23.4063 | + | 6.49348i | −0.972735 | + | 0.269860i | ||||
\(580\) | 8.17123 | + | 0.786876i | 0.339292 | + | 0.0326732i | ||||
\(581\) | − | 0.766970i | − | 0.0318193i | ||||||
\(582\) | 35.4204 | − | 8.01807i | 1.46822 | − | 0.332360i | ||||
\(583\) | − | 3.60559i | − | 0.149328i | ||||||
\(584\) | 46.5376 | + | 6.74829i | 1.92574 | + | 0.279246i | ||||
\(585\) | 7.67200 | + | 12.7630i | 0.317198 | + | 0.527686i | ||||
\(586\) | −1.43007 | + | 29.7694i | −0.0590755 | + | 1.22976i | ||||
\(587\) | −28.7200 | −1.18540 | −0.592700 | − | 0.805423i | \(-0.701938\pi\) | ||||
−0.592700 | + | 0.805423i | \(0.701938\pi\) | |||||||
\(588\) | −3.41142 | + | 0.601817i | −0.140685 | + | 0.0248185i | ||||
\(589\) | 32.2495 | 1.32882 | ||||||||
\(590\) | 0.0286025 | − | 0.595414i | 0.00117755 | − | 0.0245128i | ||||
\(591\) | −3.08660 | − | 11.1259i | −0.126966 | − | 0.457660i | ||||
\(592\) | −9.02000 | − | 1.75348i | −0.370720 | − | 0.0720678i | ||||
\(593\) | 1.56786i | 0.0643843i | 0.999482 | + | 0.0321921i | \(0.0102488\pi\) | ||||
−0.999482 | + | 0.0321921i | \(0.989751\pi\) | |||||||
\(594\) | 3.43950 | − | 3.29440i | 0.141124 | − | 0.135171i | ||||
\(595\) | − | 6.88118i | − | 0.282101i | ||||||
\(596\) | −1.48605 | + | 15.4317i | −0.0608709 | + | 0.632107i | ||||
\(597\) | −0.180830 | − | 0.651820i | −0.00740089 | − | 0.0266772i | ||||
\(598\) | −9.33604 | − | 0.448486i | −0.381779 | − | 0.0183399i | ||||
\(599\) | −31.8120 | −1.29980 | −0.649902 | − | 0.760018i | \(-0.725190\pi\) | ||||
−0.649902 | + | 0.760018i | \(0.725190\pi\) | |||||||
\(600\) | 4.85976 | − | 0.618626i | 0.198399 | − | 0.0252553i | ||||
\(601\) | 15.8470 | 0.646413 | 0.323206 | − | 0.946329i | \(-0.395239\pi\) | ||||
0.323206 | + | 0.946329i | \(0.395239\pi\) | |||||||
\(602\) | 7.25626 | + | 0.348577i | 0.295743 | + | 0.0142069i | ||||
\(603\) | −16.2124 | − | 26.9706i | −0.660218 | − | 1.09833i | ||||
\(604\) | 0.383082 | − | 3.97808i | 0.0155874 | − | 0.161866i | ||||
\(605\) | − | 10.5799i | − | 0.430136i | ||||||
\(606\) | −1.92915 | − | 8.52216i | −0.0783664 | − | 0.346189i | ||||
\(607\) | 9.71499i | 0.394319i | 0.980371 | + | 0.197160i | \(0.0631717\pi\) | ||||
−0.980371 | + | 0.197160i | \(0.936828\pi\) | |||||||
\(608\) | −5.67843 | + | 23.2035i | −0.230291 | + | 0.941027i | ||||
\(609\) | 6.85049 | − | 1.90049i | 0.277596 | − | 0.0770117i | ||||
\(610\) | 0.0121637 | − | 0.253209i | 0.000492493 | − | 0.0102521i | ||||
\(611\) | 47.7585 | 1.93210 | ||||||||
\(612\) | 17.7811 | + | 37.2620i | 0.718757 | + | 1.50623i | ||||
\(613\) | −33.8272 | −1.36627 | −0.683134 | − | 0.730293i | \(-0.739384\pi\) | ||||
−0.683134 | + | 0.730293i | \(0.739384\pi\) | |||||||
\(614\) | −1.71767 | + | 35.7563i | −0.0693194 | + | 1.44301i | ||||
\(615\) | 18.2859 | − | 5.07295i | 0.737360 | − | 0.204561i | ||||
\(616\) | −0.263070 | + | 1.81419i | −0.0105994 | + | 0.0730956i | ||||
\(617\) | − | 6.52428i | − | 0.262658i | −0.991339 | − | 0.131329i | \(-0.958076\pi\) | ||
0.991339 | − | 0.131329i | \(-0.0419243\pi\) | |||||||
\(618\) | −5.17395 | − | 22.8563i | −0.208127 | − | 0.919415i | ||||
\(619\) | 22.4852i | 0.903757i | 0.892080 | + | 0.451878i | \(0.149246\pi\) | ||||
−0.892080 | + | 0.451878i | \(0.850754\pi\) | |||||||
\(620\) | −15.2033 | − | 1.46406i | −0.610581 | − | 0.0587980i | ||||
\(621\) | 4.76103 | − | 5.01986i | 0.191054 | − | 0.201440i | ||||
\(622\) | 25.8448 | + | 1.24154i | 1.03628 | + | 0.0497810i | ||||
\(623\) | 11.5147 | 0.461328 | ||||||||
\(624\) | 34.2840 | − | 2.70075i | 1.37246 | − | 0.108117i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −29.4951 | − | 1.41689i | −1.17886 | − | 0.0566302i | ||||
\(627\) | 1.26727 | + | 4.56798i | 0.0506098 | + | 0.182428i | ||||
\(628\) | 25.5843 | + | 2.46373i | 1.02092 | + | 0.0983134i | ||||
\(629\) | − | 15.8076i | − | 0.630288i | ||||||
\(630\) | 3.73694 | − | 2.00880i | 0.148883 | − | 0.0800323i | ||||
\(631\) | − | 9.46183i | − | 0.376669i | −0.982105 | − | 0.188335i | \(-0.939691\pi\) | ||
0.982105 | − | 0.188335i | \(-0.0603090\pi\) | |||||||
\(632\) | −2.88291 | + | 19.8811i | −0.114676 | + | 0.790829i | ||||
\(633\) | 13.2381 | + | 47.7181i | 0.526168 | + | 1.89662i | ||||
\(634\) | 1.74865 | − | 36.4014i | 0.0694479 | − | 1.44568i | ||||
\(635\) | −5.01119 | −0.198863 | ||||||||
\(636\) | 3.34800 | + | 18.9783i | 0.132757 | + | 0.752538i | ||||
\(637\) | −4.96381 | −0.196673 | ||||||||
\(638\) | 0.180517 | − | 3.75778i | 0.00714672 | − | 0.148772i | ||||
\(639\) | −5.39045 | + | 3.24026i | −0.213243 | + | 0.128183i | ||||
\(640\) | 3.73037 | − | 10.6810i | 0.147456 | − | 0.422205i | ||||
\(641\) | − | 20.1292i | − | 0.795056i | −0.917590 | − | 0.397528i | \(-0.869868\pi\) | ||
0.917590 | − | 0.397528i | \(-0.130132\pi\) | |||||||
\(642\) | 26.8528 | − | 6.07864i | 1.05980 | − | 0.239905i | ||||
\(643\) | 23.2477i | 0.916799i | 0.888746 | + | 0.458399i | \(0.151577\pi\) | ||||
−0.888746 | + | 0.458399i | \(0.848423\pi\) | |||||||
\(644\) | −0.255257 | + | 2.65069i | −0.0100585 | + | 0.104452i | ||||
\(645\) | −8.57350 | + | 2.37849i | −0.337581 | + | 0.0936531i | ||||
\(646\) | −41.0475 | − | 1.97184i | −1.61499 | − | 0.0775811i | ||||
\(647\) | −11.4212 | −0.449013 | −0.224507 | − | 0.974473i | \(-0.572077\pi\) | ||||
−0.224507 | + | 0.974473i | \(0.572077\pi\) | |||||||
\(648\) | −15.0450 | + | 20.5341i | −0.591024 | + | 0.806654i | ||||
\(649\) | −0.273187 | −0.0107235 | ||||||||
\(650\) | 7.01180 | + | 0.336833i | 0.275025 | + | 0.0132117i | ||||
\(651\) | −12.7460 | + | 3.53604i | −0.499555 | + | 0.138588i | ||||
\(652\) | −0.721914 | + | 7.49663i | −0.0282723 | + | 0.293591i | ||||
\(653\) | − | 26.0879i | − | 1.02090i | −0.859907 | − | 0.510450i | \(-0.829479\pi\) | ||
0.859907 | − | 0.510450i | \(-0.170521\pi\) | |||||||
\(654\) | 21.9040 | − | 4.95838i | 0.856513 | − | 0.193888i | ||||
\(655\) | − | 18.0995i | − | 0.707207i | ||||||
\(656\) | 8.36290 | − | 43.0192i | 0.326516 | − | 1.67962i | ||||
\(657\) | −42.7481 | + | 25.6963i | −1.66776 | + | 1.00251i | ||||
\(658\) | 0.652884 | − | 13.5910i | 0.0254521 | − | 0.529831i | ||||
\(659\) | −11.6383 | −0.453363 | −0.226682 | − | 0.973969i | \(-0.572788\pi\) | ||||
−0.226682 | + | 0.973969i | \(0.572788\pi\) | |||||||
\(660\) | −0.390050 | − | 2.21101i | −0.0151827 | − | 0.0860635i | ||||
\(661\) | 3.03792 | 0.118161 | 0.0590807 | − | 0.998253i | \(-0.481183\pi\) | ||||
0.0590807 | + | 0.998253i | \(0.481183\pi\) | |||||||
\(662\) | 1.45759 | − | 30.3425i | 0.0566510 | − | 1.17929i | ||||
\(663\) | 15.8154 | + | 57.0083i | 0.614221 | + | 2.21402i | ||||
\(664\) | 2.14687 | + | 0.311311i | 0.0833145 | + | 0.0120812i | ||||
\(665\) | 4.22288i | 0.163756i | ||||||||
\(666\) | 8.58456 | − | 4.61464i | 0.332645 | − | 0.178814i | ||||
\(667\) | − | 5.46506i | − | 0.211608i | ||||||
\(668\) | −24.4970 | − | 2.35902i | −0.947818 | − | 0.0912733i | ||||
\(669\) | −13.6240 | − | 49.1090i | −0.526734 | − | 1.89866i | ||||
\(670\) | −14.8172 | − | 0.711791i | −0.572440 | − | 0.0274989i | ||||
\(671\) | −0.116177 | −0.00448496 | ||||||||
\(672\) | −0.299890 | − | 9.79337i | −0.0115685 | − | 0.377787i | ||||
\(673\) | −4.54733 | −0.175287 | −0.0876433 | − | 0.996152i | \(-0.527934\pi\) | ||||
−0.0876433 | + | 0.996152i | \(0.527934\pi\) | |||||||
\(674\) | 15.1312 | + | 0.726874i | 0.582832 | + | 0.0279981i | ||||
\(675\) | −3.57575 | + | 3.77014i | −0.137631 | + | 0.145113i | ||||
\(676\) | 23.1716 | + | 2.23138i | 0.891214 | + | 0.0858225i | ||||
\(677\) | 27.6263i | 1.06177i | 0.847445 | + | 0.530883i | \(0.178140\pi\) | ||||
−0.847445 | + | 0.530883i | \(0.821860\pi\) | |||||||
\(678\) | 1.68037 | + | 7.42314i | 0.0645341 | + | 0.285084i | ||||
\(679\) | − | 14.8262i | − | 0.568977i | ||||||
\(680\) | 19.2615 | + | 2.79305i | 0.738643 | + | 0.107109i | ||||
\(681\) | 34.4495 | − | 9.55711i | 1.32011 | − | 0.366229i | ||||
\(682\) | −0.335868 | + | 6.99171i | −0.0128611 | + | 0.267726i | ||||
\(683\) | 25.8932 | 0.990776 | 0.495388 | − | 0.868672i | \(-0.335026\pi\) | ||||
0.495388 | + | 0.868672i | \(0.335026\pi\) | |||||||
\(684\) | −10.9120 | − | 22.8672i | −0.417230 | − | 0.874348i | ||||
\(685\) | −12.2502 | −0.468058 | ||||||||
\(686\) | −0.0678578 | + | 1.41258i | −0.00259082 | + | 0.0539327i | ||||
\(687\) | −1.69515 | + | 0.470275i | −0.0646740 | + | 0.0179421i | ||||
\(688\) | −3.92101 | + | 20.1699i | −0.149487 | + | 0.768969i | ||||
\(689\) | 27.6144i | 1.05203i | ||||||||
\(690\) | −0.720069 | − | 3.18096i | −0.0274126 | − | 0.121097i | ||||
\(691\) | − | 51.4334i | − | 1.95662i | −0.207149 | − | 0.978309i | \(-0.566418\pi\) | ||
0.207149 | − | 0.978309i | \(-0.433582\pi\) | |||||||
\(692\) | 3.55894 | − | 36.9574i | 0.135291 | − | 1.40491i | ||||
\(693\) | −1.00173 | − | 1.66646i | −0.0380524 | − | 0.0633035i | ||||
\(694\) | −14.9178 | − | 0.716621i | −0.566270 | − | 0.0272025i | ||||
\(695\) | 12.5062 | 0.474386 | ||||||||
\(696\) | 2.53916 | + | 19.9470i | 0.0962466 | + | 0.756088i | ||||
\(697\) | 75.3911 | 2.85564 | ||||||||
\(698\) | −30.6911 | − | 1.47434i | −1.16167 | − | 0.0558046i | ||||
\(699\) | 2.64762 | + | 9.54358i | 0.100142 | + | 0.360972i | ||||
\(700\) | 0.191710 | − | 1.99079i | 0.00724595 | − | 0.0752448i | ||||
\(701\) | 17.1426i | 0.647465i | 0.946149 | + | 0.323733i | \(0.104938\pi\) | ||||
−0.946149 | + | 0.323733i | \(0.895062\pi\) | |||||||
\(702\) | −26.3424 | + | 25.2310i | −0.994229 | + | 0.952284i | ||||
\(703\) | 9.70087i | 0.365875i | ||||||||
\(704\) | −4.97140 | − | 1.47275i | −0.187367 | − | 0.0555062i | ||||
\(705\) | 4.45491 | + | 16.0582i | 0.167782 | + | 0.604785i | ||||
\(706\) | −1.42745 | + | 29.7150i | −0.0537229 | + | 1.11834i | ||||
\(707\) | −3.56719 | −0.134158 | ||||||||
\(708\) | 1.43794 | − | 0.253670i | 0.0540410 | − | 0.00953351i | ||||
\(709\) | 7.68687 | 0.288686 | 0.144343 | − | 0.989528i | \(-0.453893\pi\) | ||||
0.144343 | + | 0.989528i | \(0.453893\pi\) | |||||||
\(710\) | −0.142261 | + | 2.96143i | −0.00533897 | + | 0.111140i | ||||
\(711\) | −10.9776 | − | 18.2622i | −0.411693 | − | 0.684887i | ||||
\(712\) | −4.67380 | + | 32.2315i | −0.175158 | + | 1.20793i | ||||
\(713\) | 10.1683i | 0.380805i | ||||||||
\(714\) | 16.4394 | − | 3.72138i | 0.615231 | − | 0.139269i | ||||
\(715\) | − | 3.21714i | − | 0.120314i | ||||||
\(716\) | 24.1420 | + | 2.32483i | 0.902228 | + | 0.0868831i | ||||
\(717\) | −30.8532 | + | 8.55940i | −1.15223 | + | 0.319657i | ||||
\(718\) | −1.62154 | − | 0.0778955i | −0.0605152 | − | 0.00290703i | ||||
\(719\) | −18.4627 | −0.688541 | −0.344271 | − | 0.938870i | \(-0.611874\pi\) | ||||
−0.344271 | + | 0.938870i | \(0.611874\pi\) | |||||||
\(720\) | 4.10611 | + | 11.2756i | 0.153026 | + | 0.420218i | ||||
\(721\) | −9.56713 | −0.356299 | ||||||||
\(722\) | −1.64884 | − | 0.0792073i | −0.0613636 | − | 0.00294779i | ||||
\(723\) | 19.6243 | − | 5.44424i | 0.729835 | − | 0.202474i | ||||
\(724\) | −0.172762 | − | 0.0166367i | −0.00642065 | − | 0.000618298i | ||||
\(725\) | 4.10451i | 0.152438i | ||||||||
\(726\) | 25.2759 | − | 5.72168i | 0.938078 | − | 0.212352i | ||||
\(727\) | 37.2227i | 1.38052i | 0.723564 | + | 0.690258i | \(0.242503\pi\) | ||||
−0.723564 | + | 0.690258i | \(0.757497\pi\) | |||||||
\(728\) | 2.01480 | − | 13.8944i | 0.0746733 | − | 0.514962i | ||||
\(729\) | −1.42796 | − | 26.9622i | −0.0528874 | − | 0.998600i | ||||
\(730\) | −1.12818 | + | 23.4851i | −0.0417558 | + | 0.869222i | ||||
\(731\) | −35.3477 | −1.30738 | ||||||||
\(732\) | 0.611505 | − | 0.107877i | 0.0226019 | − | 0.00398725i | ||||
\(733\) | 24.9461 | 0.921404 | 0.460702 | − | 0.887555i | \(-0.347598\pi\) | ||||
0.460702 | + | 0.887555i | \(0.347598\pi\) | |||||||
\(734\) | 0.328331 | − | 6.83480i | 0.0121189 | − | 0.252277i | ||||
\(735\) | −0.463024 | − | 1.66901i | −0.0170789 | − | 0.0615625i | ||||
\(736\) | −7.31608 | − | 1.79041i | −0.269674 | − | 0.0659955i | ||||
\(737\) | 6.79842i | 0.250423i | ||||||||
\(738\) | 22.0086 | + | 40.9424i | 0.810148 | + | 1.50711i | ||||
\(739\) | 25.3947i | 0.934159i | 0.884215 | + | 0.467079i | \(0.154694\pi\) | ||||
−0.884215 | + | 0.467079i | \(0.845306\pi\) | |||||||
\(740\) | 0.440399 | − | 4.57327i | 0.0161894 | − | 0.168117i | ||||
\(741\) | −9.70572 | − | 34.9852i | −0.356548 | − | 1.28521i | ||||
\(742\) | 7.85843 | + | 0.377504i | 0.288492 | + | 0.0138586i | ||||
\(743\) | −23.2422 | −0.852674 | −0.426337 | − | 0.904564i | \(-0.640196\pi\) | ||||
−0.426337 | + | 0.904564i | \(0.640196\pi\) | |||||||
\(744\) | −4.72435 | − | 37.1132i | −0.173203 | − | 1.36064i | ||||
\(745\) | −7.75155 | −0.283995 | ||||||||
\(746\) | −17.1251 | − | 0.822655i | −0.626993 | − | 0.0301195i | ||||
\(747\) | −1.97205 | + | 1.18542i | −0.0721534 | + | 0.0433722i | ||||
\(748\) | 0.854994 | − | 8.87859i | 0.0312617 | − | 0.324633i | ||||
\(749\) | − | 11.2400i | − | 0.410700i | ||||||
\(750\) | 0.540805 | + | 2.38904i | 0.0197474 | + | 0.0872355i | ||||
\(751\) | − | 33.3902i | − | 1.21842i | −0.793007 | − | 0.609212i | \(-0.791486\pi\) | ||
0.793007 | − | 0.609212i | \(-0.208514\pi\) | |||||||
\(752\) | 37.7781 | + | 7.34405i | 1.37763 | + | 0.267810i | ||||
\(753\) | 19.2682 | − | 5.34544i | 0.702171 | − | 0.194799i | ||||
\(754\) | −1.38254 | + | 28.7800i | −0.0503490 | + | 1.04811i | ||||
\(755\) | 1.99824 | 0.0727234 | ||||||||
\(756\) | 6.82006 | + | 7.84135i | 0.248043 | + | 0.285187i | ||||
\(757\) | −36.3015 | −1.31940 | −0.659700 | − | 0.751529i | \(-0.729317\pi\) | ||||
−0.659700 | + | 0.751529i | \(0.729317\pi\) | |||||||
\(758\) | −1.56642 | + | 32.6079i | −0.0568950 | + | 1.18437i | ||||
\(759\) | −1.44029 | + | 0.399570i | −0.0522791 | + | 0.0145035i | ||||
\(760\) | −11.8205 | − | 1.71406i | −0.428774 | − | 0.0621754i | ||||
\(761\) | 18.6295i | 0.675320i | 0.941268 | + | 0.337660i | \(0.109635\pi\) | ||||
−0.941268 | + | 0.337660i | \(0.890365\pi\) | |||||||
\(762\) | −2.71007 | − | 11.9719i | −0.0981756 | − | 0.433698i | ||||
\(763\) | − | 9.16851i | − | 0.331922i | ||||||
\(764\) | 35.2452 | + | 3.39405i | 1.27513 | + | 0.122793i | ||||
\(765\) | −17.6930 | + | 10.6355i | −0.639692 | + | 0.384526i | ||||
\(766\) | −2.30566 | − | 0.110759i | −0.0833067 | − | 0.00400189i | ||||
\(767\) | 2.09228 | 0.0755478 | ||||||||
\(768\) | 27.5348 | + | 3.13566i | 0.993578 | + | 0.113149i | ||||
\(769\) | 45.9947 | 1.65861 | 0.829305 | − | 0.558796i | \(-0.188736\pi\) | ||||
0.829305 | + | 0.558796i | \(0.188736\pi\) | |||||||
\(770\) | −0.915524 | − | 0.0439800i | −0.0329932 | − | 0.00158493i | ||||
\(771\) | −3.99828 | − | 14.4122i | −0.143994 | − | 0.519042i | ||||
\(772\) | −27.9190 | − | 2.68855i | −1.00483 | − | 0.0967630i | ||||
\(773\) | 8.85871i | 0.318626i | 0.987228 | + | 0.159313i | \(0.0509278\pi\) | ||||
−0.987228 | + | 0.159313i | \(0.949072\pi\) | |||||||
\(774\) | −10.3189 | − | 19.1962i | −0.370906 | − | 0.689992i | ||||
\(775\) | − | 7.63684i | − | 0.274323i | ||||||
\(776\) | 41.5007 | + | 6.01791i | 1.48979 | + | 0.216030i | ||||
\(777\) | −1.06367 | − | 3.83409i | −0.0381588 | − | 0.137547i | ||||
\(778\) | 1.80805 | − | 37.6379i | 0.0648218 | − | 1.34938i | ||||
\(779\) | −46.2664 | −1.65767 | ||||||||
\(780\) | 2.98731 | + | 16.9337i | 0.106963 | + | 0.606322i | ||||
\(781\) | 1.35876 | 0.0486202 | ||||||||
\(782\) | 0.621723 | − | 12.9423i | 0.0222328 | − | 0.462815i | ||||
\(783\) | −15.4746 | − | 14.6767i | −0.553017 | − | 0.524504i | ||||
\(784\) | −3.92649 | − | 0.763309i | −0.140232 | − | 0.0272610i | ||||
\(785\) | 12.8513i | 0.458684i | ||||||||
\(786\) | 43.2406 | − | 9.78831i | 1.54234 | − | 0.349138i | ||||
\(787\) | 40.2027i | 1.43307i | 0.697550 | + | 0.716536i | \(0.254273\pi\) | ||||
−0.697550 | + | 0.716536i | \(0.745727\pi\) | |||||||
\(788\) | 1.27797 | − | 13.2710i | 0.0455259 | − | 0.472759i | ||||
\(789\) | −27.0558 | + | 7.50591i | −0.963211 | + | 0.267218i | ||||
\(790\) | −10.0330 | − | 0.481964i | −0.356957 | − | 0.0171475i | ||||
\(791\) | 3.10716 | 0.110478 | ||||||||
\(792\) | 5.07126 | − | 2.12757i | 0.180199 | − | 0.0756000i | ||||
\(793\) | 0.889774 | 0.0315968 | ||||||||
\(794\) | 11.1077 | + | 0.533591i | 0.394196 | + | 0.0189364i | ||||
\(795\) | −9.28499 | + | 2.57588i | −0.329305 | + | 0.0913569i | ||||
\(796\) | 0.0748708 | − | 0.777487i | 0.00265372 | − | 0.0275573i | ||||
\(797\) | 15.6352i | 0.553828i | 0.960895 | + | 0.276914i | \(0.0893116\pi\) | ||||
−0.960895 | + | 0.276914i | \(0.910688\pi\) | |||||||
\(798\) | −10.0887 | + | 2.28376i | −0.357134 | + | 0.0808441i | ||||
\(799\) | 66.2062i | 2.34221i | ||||||||
\(800\) | 5.49471 | + | 1.34468i | 0.194267 | + | 0.0475417i | ||||
\(801\) | −17.7970 | − | 29.6069i | −0.628828 | − | 1.04611i | ||||
\(802\) | 0.773069 | − | 16.0928i | 0.0272980 | − | 0.568258i | ||||
\(803\) | 10.7754 | 0.380255 | ||||||||
\(804\) | −6.31273 | − | 35.7840i | −0.222633 | − | 1.26200i | ||||
\(805\) | −1.33148 | −0.0469284 | ||||||||
\(806\) | 2.57234 | − | 53.5480i | 0.0906068 | − | 1.88615i | ||||
\(807\) | −5.98620 | − | 21.5778i | −0.210724 | − | 0.759575i | ||||
\(808\) | 1.44791 | − | 9.98509i | 0.0509373 | − | 0.351274i | ||||
\(809\) | − | 25.0407i | − | 0.880383i | −0.897904 | − | 0.440191i | \(-0.854911\pi\) | ||
0.897904 | − | 0.440191i | \(-0.145089\pi\) | |||||||
\(810\) | −10.9408 | − | 6.50372i | −0.384421 | − | 0.228517i | ||||
\(811\) | − | 27.3047i | − | 0.958798i | −0.877597 | − | 0.479399i | \(-0.840855\pi\) | ||
0.877597 | − | 0.479399i | \(-0.159145\pi\) | |||||||
\(812\) | 8.17123 | + | 0.786876i | 0.286754 | + | 0.0276139i | ||||
\(813\) | 3.69943 | + | 13.3349i | 0.129745 | + | 0.467677i | ||||
\(814\) | −2.10316 | − | 0.101032i | −0.0737156 | − | 0.00354115i | ||||
\(815\) | −3.76566 | −0.131905 | ||||||||
\(816\) | 3.74397 | + | 47.5270i | 0.131065 | + | 1.66378i | ||||
\(817\) | 21.6924 | 0.758921 | ||||||||
\(818\) | 12.4360 | + | 0.597403i | 0.434816 | + | 0.0208877i | ||||
\(819\) | 7.67200 | + | 12.7630i | 0.268081 | + | 0.445976i | ||||
\(820\) | 21.8113 | + | 2.10040i | 0.761685 | + | 0.0733490i | ||||
\(821\) | 47.2633i | 1.64950i | 0.565497 | + | 0.824751i | \(0.308685\pi\) | ||||
−0.565497 | + | 0.824751i | \(0.691315\pi\) | |||||||
\(822\) | −6.62499 | − | 29.2664i | −0.231073 | − | 1.02078i | ||||
\(823\) | − | 54.9448i | − | 1.91526i | −0.288008 | − | 0.957628i | \(-0.592993\pi\) | ||
0.288008 | − | 0.957628i | \(-0.407007\pi\) | |||||||
\(824\) | 3.88327 | − | 26.7799i | 0.135280 | − | 0.932920i | ||||
\(825\) | 1.08172 | − | 0.300095i | 0.0376607 | − | 0.0104480i | ||||
\(826\) | 0.0286025 | − | 0.595414i | 0.000995210 | − | 0.0207171i | ||||
\(827\) | −5.81055 | −0.202053 | −0.101026 | − | 0.994884i | \(-0.532213\pi\) | ||||
−0.101026 | + | 0.994884i | \(0.532213\pi\) | |||||||
\(828\) | 7.21003 | − | 3.44055i | 0.250566 | − | 0.119567i | ||||
\(829\) | 47.1522 | 1.63766 | 0.818832 | − | 0.574033i | \(-0.194622\pi\) | ||||
0.818832 | + | 0.574033i | \(0.194622\pi\) | |||||||
\(830\) | −0.0520449 | + | 1.08341i | −0.00180651 | + | 0.0376057i | ||||
\(831\) | 39.7884 | − | 11.0383i | 1.38025 | − | 0.382913i | ||||
\(832\) | 38.0749 | + | 11.2794i | 1.32001 | + | 0.391044i | ||||
\(833\) | − | 6.88118i | − | 0.238419i | ||||||
\(834\) | 6.76340 | + | 29.8778i | 0.234197 | + | 1.03458i | ||||
\(835\) | − | 12.3052i | − | 0.425838i | ||||||
\(836\) | −0.524698 | + | 5.44866i | −0.0181470 | + | 0.188446i | ||||
\(837\) | 28.7920 | + | 27.3075i | 0.995196 | + | 0.943884i | ||||
\(838\) | −36.8375 | − | 1.76960i | −1.27253 | − | 0.0611300i | ||||
\(839\) | −8.94935 | −0.308966 | −0.154483 | − | 0.987995i | \(-0.549371\pi\) | ||||
−0.154483 | + | 0.987995i | \(0.549371\pi\) | |||||||
\(840\) | 4.85976 | − | 0.618626i | 0.167678 | − | 0.0213446i | ||||
\(841\) | 12.1530 | 0.419068 | ||||||||
\(842\) | −23.2901 | − | 1.11881i | −0.802631 | − | 0.0385568i | ||||
\(843\) | 0.704005 | + | 2.53765i | 0.0242472 | + | 0.0874015i | ||||
\(844\) | −5.48109 | + | 56.9178i | −0.188667 | + | 1.95919i | ||||
\(845\) | 11.6394i | 0.400407i | ||||||||
\(846\) | −35.9544 | + | 19.3273i | −1.23614 | + | 0.664487i | ||||
\(847\) | − | 10.5799i | − | 0.363531i | ||||||
\(848\) | −4.24641 | + | 21.8437i | −0.145822 | + | 0.750116i | ||||
\(849\) | 3.03823 | + | 10.9516i | 0.104272 | + | 0.375858i | ||||
\(850\) | −0.466942 | + | 9.72025i | −0.0160160 | + | 0.333402i | ||||
\(851\) | −3.05869 | −0.104850 | ||||||||
\(852\) | −7.15191 | + | 1.26169i | −0.245021 | + | 0.0432246i | ||||
\(853\) | −24.8720 | −0.851600 | −0.425800 | − | 0.904817i | \(-0.640007\pi\) | ||||
−0.425800 | + | 0.904817i | \(0.640007\pi\) | |||||||
\(854\) | 0.0121637 | − | 0.253209i | 0.000416232 | − | 0.00866463i | ||||
\(855\) | 10.8580 | − | 6.52684i | 0.371334 | − | 0.223213i | ||||
\(856\) | 31.4624 | + | 4.56228i | 1.07536 | + | 0.155935i | ||||
\(857\) | − | 31.9912i | − | 1.09280i | −0.837524 | − | 0.546400i | \(-0.815998\pi\) | ||
0.837524 | − | 0.546400i | \(-0.184002\pi\) | |||||||
\(858\) | 7.68589 | − | 1.73985i | 0.262392 | − | 0.0593974i | ||||
\(859\) | − | 19.8605i | − | 0.677631i | −0.940853 | − | 0.338815i | \(-0.889974\pi\) | ||
0.940853 | − | 0.338815i | \(-0.110026\pi\) | |||||||
\(860\) | −10.2264 | − | 0.984788i | −0.348718 | − | 0.0335810i | ||||
\(861\) | 18.2859 | − | 5.07295i | 0.623183 | − | 0.172886i | ||||
\(862\) | 7.19339 | + | 0.345557i | 0.245008 | + | 0.0117697i | ||||
\(863\) | −11.6750 | −0.397422 | −0.198711 | − | 0.980058i | \(-0.563676\pi\) | ||||
−0.198711 | + | 0.980058i | \(0.563676\pi\) | |||||||
\(864\) | −24.7174 | + | 15.9076i | −0.840902 | + | 0.541187i | ||||
\(865\) | 18.5642 | 0.631202 | ||||||||
\(866\) | −1.95374 | − | 0.0938539i | −0.0663908 | − | 0.00318928i | ||||
\(867\) | −50.6557 | + | 14.0531i | −1.72036 | + | 0.477268i | ||||
\(868\) | −15.2033 | − | 1.46406i | −0.516035 | − | 0.0496933i | ||||
\(869\) | 4.60331i | 0.156157i | ||||||||
\(870\) | −9.80586 | + | 2.21974i | −0.332450 | + | 0.0752563i | ||||
\(871\) | − | 52.0676i | − | 1.76424i | ||||||
\(872\) | 25.6640 | + | 3.72147i | 0.869094 | + | 0.126025i | ||||
\(873\) | −38.1213 | + | 22.9152i | −1.29021 | + | 0.775561i | ||||
\(874\) | −0.381542 | + | 7.94250i | −0.0129059 | + | 0.268659i | ||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −56.7170 | + | 10.0056i | −1.91629 | + | 0.338057i | ||||
\(877\) | −30.3924 | −1.02628 | −0.513139 | − | 0.858306i | \(-0.671517\pi\) | ||||
−0.513139 | + | 0.858306i | \(0.671517\pi\) | |||||||
\(878\) | −1.27543 | + | 26.5505i | −0.0430438 | + | 0.896036i | ||||
\(879\) | −9.75798 | − | 35.1736i | −0.329128 | − | 1.18637i | ||||
\(880\) | 0.494715 | − | 2.54484i | 0.0166769 | − | 0.0857865i | ||||
\(881\) | − | 25.6017i | − | 0.862543i | −0.902222 | − | 0.431272i | \(-0.858065\pi\) | ||
0.902222 | − | 0.431272i | \(-0.141935\pi\) | |||||||
\(882\) | 3.73694 | − | 2.00880i | 0.125829 | − | 0.0676397i | ||||
\(883\) | − | 4.94104i | − | 0.166279i | −0.996538 | − | 0.0831397i | \(-0.973505\pi\) | ||
0.996538 | − | 0.0831397i | \(-0.0264948\pi\) | |||||||
\(884\) | −6.54821 | + | 67.9991i | −0.220240 | + | 2.28706i | ||||
\(885\) | 0.195168 | + | 0.703501i | 0.00656049 | + | 0.0236479i | ||||
\(886\) | −12.5134 | − | 0.601120i | −0.420396 | − | 0.0201950i | ||||
\(887\) | −7.24181 | −0.243156 | −0.121578 | − | 0.992582i | \(-0.538796\pi\) | ||||
−0.121578 | + | 0.992582i | \(0.538796\pi\) | |||||||
\(888\) | 11.1639 | − | 1.42112i | 0.374637 | − | 0.0476896i | ||||
\(889\) | −5.01119 | −0.168070 | ||||||||
\(890\) | −16.2655 | − | 0.781366i | −0.545222 | − | 0.0261914i | ||||
\(891\) | −2.73657 | + | 5.15131i | −0.0916785 | + | 0.172575i | ||||
\(892\) | 5.64086 | − | 58.5769i | 0.188870 | − | 1.96130i | ||||
\(893\) | − | 40.6298i | − | 1.35962i | ||||||
\(894\) | −4.19207 | − | 18.5188i | −0.140204 | − | 0.619361i | ||||
\(895\) | 12.1268i | 0.405355i | ||||||||
\(896\) | 3.73037 | − | 10.6810i | 0.124623 | − | 0.356828i | ||||
\(897\) | 11.0308 | − | 3.06022i | 0.368309 | − | 0.102178i | ||||
\(898\) | 0.0938039 | − | 1.95270i | 0.00313028 | − | 0.0651624i | ||||
\(899\) | 31.3455 | 1.04543 | ||||||||
\(900\) | −5.41506 | + | 2.58401i | −0.180502 | + | 0.0861338i | ||||
\(901\) | −38.2811 | −1.27533 | ||||||||
\(902\) | 0.481850 | − | 10.0306i | 0.0160439 | − | 0.333982i | ||||
\(903\) | −8.57350 | + | 2.37849i | −0.285308 | + | 0.0791513i | ||||
\(904\) | −1.26119 | + | 8.69741i | −0.0419465 | + | 0.289272i | ||||
\(905\) | − | 0.0867806i | − | 0.00288468i | ||||||
\(906\) | 1.08066 | + | 4.77388i | 0.0359025 | + | 0.158602i | ||||
\(907\) | 16.4936i | 0.547662i | 0.961778 | + | 0.273831i | \(0.0882909\pi\) | ||||
−0.961778 | + | 0.273831i | \(0.911709\pi\) | |||||||
\(908\) | 41.0912 | + | 3.95701i | 1.36366 | + | 0.131318i | ||||
\(909\) | 5.51340 | + | 9.17201i | 0.182868 | + | 0.304216i | ||||
\(910\) | 7.01180 | + | 0.336833i | 0.232439 | + | 0.0111659i | ||||
\(911\) | −4.20368 | −0.139274 | −0.0696371 | − | 0.997572i | \(-0.522184\pi\) | ||||
−0.0696371 | + | 0.997572i | \(0.522184\pi\) | |||||||
\(912\) | −2.29762 | − | 29.1666i | −0.0760819 | − | 0.965804i | ||||
\(913\) | 0.497089 | 0.0164512 | ||||||||
\(914\) | −43.8274 | − | 2.10538i | −1.44968 | − | 0.0696399i | ||||
\(915\) | 0.0829981 | + | 0.299175i | 0.00274383 | + | 0.00989041i | ||||
\(916\) | −2.02197 | − | 0.194712i | −0.0668076 | − | 0.00643347i | ||||
\(917\) | − | 18.0995i | − | 0.597699i | ||||||
\(918\) | −34.9771 | − | 36.5177i | −1.15442 | − | 1.20526i | ||||
\(919\) | 24.4559i | 0.806727i | 0.915040 | + | 0.403363i | \(0.132159\pi\) | ||||
−0.915040 | + | 0.403363i | \(0.867841\pi\) | |||||||
\(920\) | 0.540443 | − | 3.72700i | 0.0178179 | − | 0.122876i | ||||
\(921\) | −11.7204 | − | 42.2473i | −0.386200 | − | 1.39210i | ||||
\(922\) | 1.91137 | − | 39.7887i | 0.0629477 | − | 1.31037i | ||||
\(923\) | −10.4064 | −0.342532 | ||||||||
\(924\) | −0.390050 | − | 2.21101i | −0.0128317 | − | 0.0727369i | ||||
\(925\) | 2.29722 | 0.0755320 | ||||||||
\(926\) | 1.78009 | − | 37.0558i | 0.0584973 | − | 1.21773i | ||||
\(927\) | 14.7868 | + | 24.5992i | 0.485664 | + | 0.807943i | ||||
\(928\) | −5.51926 | + | 22.5531i | −0.181179 | + | 0.740342i | ||||
\(929\) | − | 19.5942i | − | 0.642864i | −0.946933 | − | 0.321432i | \(-0.895836\pi\) | ||
0.946933 | − | 0.321432i | \(-0.104164\pi\) | |||||||
\(930\) | 18.2447 | − | 4.13004i | 0.598269 | − | 0.135429i | ||||
\(931\) | 4.22288i | 0.138399i | ||||||||
\(932\) | −1.09622 | + | 11.3835i | −0.0359077 | + | 0.372880i | ||||
\(933\) | −30.5365 | + | 8.47154i | −0.999720 | + | 0.277346i | ||||
\(934\) | −50.6600 | − | 2.43361i | −1.65764 | − | 0.0796300i | ||||
\(935\) | 4.45983 | 0.145852 | ||||||||
\(936\) | −38.8397 | + | 16.2946i | −1.26951 | + | 0.532606i | ||||
\(937\) | −18.7661 | −0.613061 | −0.306531 | − | 0.951861i | \(-0.599168\pi\) | ||||
−0.306531 | + | 0.951861i | \(0.599168\pi\) | |||||||
\(938\) | −14.8172 | − | 0.711791i | −0.483800 | − | 0.0232408i | ||||
\(939\) | 34.8494 | − | 9.66805i | 1.13727 | − | 0.315505i | ||||
\(940\) | −1.84451 | + | 19.1541i | −0.0601612 | + | 0.624737i | ||||
\(941\) | − | 18.7595i | − | 0.611543i | −0.952105 | − | 0.305772i | \(-0.901086\pi\) | ||
0.952105 | − | 0.305772i | \(-0.0989144\pi\) | |||||||
\(942\) | −30.7024 | + | 6.95006i | −1.00034 | + | 0.226445i | ||||
\(943\) | − | 14.5878i | − | 0.475045i | ||||||
\(944\) | 1.65504 | + | 0.321740i | 0.0538671 | + | 0.0104717i | ||||
\(945\) | −3.57575 | + | 3.77014i | −0.116319 | + | 0.122643i | ||||
\(946\) | −0.225919 | + | 4.70293i | −0.00734528 | + | 0.152905i | ||||
\(947\) | −4.70695 | −0.152955 | −0.0764776 | − | 0.997071i | \(-0.524367\pi\) | ||||
−0.0764776 | + | 0.997071i | \(0.524367\pi\) | |||||||
\(948\) | −4.27444 | − | 24.2298i | −0.138827 | − | 0.786949i | ||||
\(949\) | −82.5263 | −2.67892 | ||||||||
\(950\) | 0.286556 | − | 5.96518i | 0.00929710 | − | 0.193536i | ||||
\(951\) | 11.9318 | + | 43.0094i | 0.386916 | + | 1.39468i | ||||
\(952\) | 19.2615 | + | 2.79305i | 0.624268 | + | 0.0905233i | ||||
\(953\) | 51.9232i | 1.68196i | 0.541068 | + | 0.840979i | \(0.318020\pi\) | ||||
−0.541068 | + | 0.840979i | \(0.681980\pi\) | |||||||
\(954\) | −11.1752 | − | 20.7892i | −0.361812 | − | 0.673075i | ||||
\(955\) | 17.7041i | 0.572892i | ||||||||
\(956\) | −36.8015 | − | 3.54392i | −1.19025 | − | 0.114619i | ||||
\(957\) | 1.23174 | + | 4.43994i | 0.0398166 | + | 0.143523i | ||||
\(958\) | −46.8064 | − | 2.24849i | −1.51225 | − | 0.0726454i | ||||
\(959\) | −12.2502 | −0.395581 | ||||||||
\(960\) | −0.240937 | + | 13.8543i | −0.00777620 | + | 0.447146i | ||||
\(961\) | −27.3213 | −0.881332 | ||||||||
\(962\) | 16.1076 | + | 0.773779i | 0.519330 | + | 0.0249476i | ||||
\(963\) | −28.9004 | + | 17.3724i | −0.931303 | + | 0.559817i | ||||
\(964\) | 23.4077 | + | 2.25413i | 0.753913 | + | 0.0726006i | ||||
\(965\) | − | 14.0241i | − | 0.451450i | ||||||
\(966\) | −0.720069 | − | 3.18096i | −0.0231678 | − | 0.102346i | ||||
\(967\) | 20.9108i | 0.672445i | 0.941783 | + | 0.336222i | \(0.109149\pi\) | ||||
−0.941783 | + | 0.336222i | \(0.890851\pi\) | |||||||
\(968\) | 29.6149 | + | 4.29437i | 0.951857 | + | 0.138026i | ||||
\(969\) | 48.4989 | − | 13.4548i | 1.55801 | − | 0.432229i | ||||
\(970\) | −1.00607 | + | 20.9432i | −0.0323031 | + | 0.672447i | ||||
\(971\) | −28.9974 | −0.930572 | −0.465286 | − | 0.885160i | \(-0.654049\pi\) | ||||
−0.465286 | + | 0.885160i | \(0.654049\pi\) | |||||||
\(972\) | 9.62083 | − | 29.6553i | 0.308588 | − | 0.951196i | ||||
\(973\) | 12.5062 | 0.400929 | ||||||||
\(974\) | 1.73575 | − | 36.1328i | 0.0556170 | − | 1.15777i | ||||
\(975\) | −8.28466 | + | 2.29836i | −0.265322 | + | 0.0736065i | ||||
\(976\) | 0.703833 | + | 0.136825i | 0.0225291 | + | 0.00437965i | ||||
\(977\) | − | 22.2874i | − | 0.713038i | −0.934288 | − | 0.356519i | \(-0.883964\pi\) | ||
0.934288 | − | 0.356519i | \(-0.116036\pi\) | |||||||
\(978\) | −2.03649 | − | 8.99632i | −0.0651196 | − | 0.287671i | ||||
\(979\) | 7.46293i | 0.238516i | ||||||||
\(980\) | 0.191710 | − | 1.99079i | 0.00612395 | − | 0.0635935i | ||||
\(981\) | −23.5742 | + | 14.1707i | −0.752667 | + | 0.452437i | ||||
\(982\) | −31.8151 | − | 1.52834i | −1.01526 | − | 0.0487712i | ||||
\(983\) | −12.6173 | −0.402430 | −0.201215 | − | 0.979547i | \(-0.564489\pi\) | ||||
−0.201215 | + | 0.979547i | \(0.564489\pi\) | |||||||
\(984\) | 6.77774 | + | 53.2442i | 0.216067 | + | 1.69736i | ||||
\(985\) | 6.66618 | 0.212402 | ||||||||
\(986\) | −39.8969 | − | 1.91657i | −1.27058 | − | 0.0610360i | ||||
\(987\) | 4.45491 | + | 16.0582i | 0.141801 | + | 0.511137i | ||||
\(988\) | 4.01854 | − | 41.7301i | 0.127847 | − | 1.32761i | ||||
\(989\) | 6.83962i | 0.217487i | ||||||||
\(990\) | 1.30194 | + | 2.42199i | 0.0413784 | + | 0.0769758i | ||||
\(991\) | 6.83164i | 0.217014i | 0.994096 | + | 0.108507i | \(0.0346070\pi\) | ||||
−0.994096 | + | 0.108507i | \(0.965393\pi\) | |||||||
\(992\) | 10.2691 | − | 41.9622i | 0.326045 | − | 1.33230i | ||||
\(993\) | 9.94581 | + | 35.8506i | 0.315621 | + | 1.13769i | ||||
\(994\) | −0.142261 | + | 2.96143i | −0.00451225 | + | 0.0939308i | ||||
\(995\) | 0.390542 | 0.0123810 | ||||||||
\(996\) | −2.61646 | + | 0.461576i | −0.0829057 | + | 0.0146256i | ||||
\(997\) | −33.6015 | −1.06417 | −0.532084 | − | 0.846691i | \(-0.678591\pi\) | ||||
−0.532084 | + | 0.846691i | \(0.678591\pi\) | |||||||
\(998\) | −2.54452 | + | 52.9688i | −0.0805454 | + | 1.67670i | ||||
\(999\) | −8.21428 | + | 8.66083i | −0.259888 | + | 0.274017i |
(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 | 420.2.n.b.71.1 | yes | 24 | |
3.2 | odd | 2 | 420.2.n.a.71.24 | yes | 24 | ||
4.3 | odd | 2 | 420.2.n.a.71.23 | ✓ | 24 | ||
12.11 | even | 2 | inner | 420.2.n.b.71.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.n.a.71.23 | ✓ | 24 | 4.3 | odd | 2 | ||
420.2.n.a.71.24 | yes | 24 | 3.2 | odd | 2 | ||
420.2.n.b.71.1 | yes | 24 | 1.1 | even | 1 | trivial | |
420.2.n.b.71.2 | yes | 24 | 12.11 | even | 2 | inner |