Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [56,3,Mod(43,56)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(56, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("56.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.g (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: | \(1.52588948042\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 6x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Root | \(0.707107 + 1.87083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 56.43 |
Dual form | 56.3.g.a.43.3 |
$q$-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 \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 1.87083i | 0.353553 | + | 0.935414i | ||||
\(3\) | 3.41421 | 1.13807 | 0.569036 | − | 0.822313i | \(-0.307317\pi\) | ||||
0.569036 | + | 0.822313i | \(0.307317\pi\) | |||||||
\(4\) | −3.00000 | + | 2.64575i | −0.750000 | + | 0.661438i | ||||
\(5\) | − | 1.54985i | − | 0.309969i | −0.987917 | − | 0.154985i | \(-0.950467\pi\) | ||
0.987917 | − | 0.154985i | \(-0.0495328\pi\) | |||||||
\(6\) | 2.41421 | + | 6.38741i | 0.402369 | + | 1.06457i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −7.07107 | − | 3.74166i | −0.883883 | − | 0.467707i | ||||
\(9\) | 2.65685 | 0.295206 | ||||||||
\(10\) | 2.89949 | − | 1.09591i | 0.289949 | − | 0.109591i | ||||
\(11\) | −4.48528 | −0.407753 | −0.203876 | − | 0.978997i | \(-0.565354\pi\) | ||||
−0.203876 | + | 0.978997i | \(0.565354\pi\) | |||||||
\(12\) | −10.2426 | + | 9.03316i | −0.853553 | + | 0.752763i | ||||
\(13\) | 1.54985i | 0.119219i | 0.998222 | + | 0.0596094i | \(0.0189855\pi\) | ||||
−0.998222 | + | 0.0596094i | \(0.981014\pi\) | |||||||
\(14\) | 4.94975 | − | 1.87083i | 0.353553 | − | 0.133631i | ||||
\(15\) | − | 5.29150i | − | 0.352767i | ||||||
\(16\) | 2.00000 | − | 15.8745i | 0.125000 | − | 0.992157i | ||||
\(17\) | 23.6569 | 1.39158 | 0.695790 | − | 0.718245i | \(-0.255055\pi\) | ||||
0.695790 | + | 0.718245i | \(0.255055\pi\) | |||||||
\(18\) | 1.87868 | + | 4.97052i | 0.104371 | + | 0.276140i | ||||
\(19\) | −24.8701 | −1.30895 | −0.654475 | − | 0.756083i | \(-0.727110\pi\) | ||||
−0.654475 | + | 0.756083i | \(0.727110\pi\) | |||||||
\(20\) | 4.10051 | + | 4.64954i | 0.205025 | + | 0.232477i | ||||
\(21\) | − | 9.03316i | − | 0.430150i | ||||||
\(22\) | −3.17157 | − | 8.39119i | −0.144162 | − | 0.381418i | ||||
\(23\) | − | 35.2248i | − | 1.53151i | −0.643132 | − | 0.765756i | \(-0.722365\pi\) | ||
0.643132 | − | 0.765756i | \(-0.277635\pi\) | |||||||
\(24\) | −24.1421 | − | 12.7748i | −1.00592 | − | 0.532284i | ||||
\(25\) | 22.5980 | 0.903919 | ||||||||
\(26\) | −2.89949 | + | 1.09591i | −0.111519 | + | 0.0421502i | ||||
\(27\) | −21.6569 | −0.802106 | ||||||||
\(28\) | 7.00000 | + | 7.93725i | 0.250000 | + | 0.283473i | ||||
\(29\) | 22.4499i | 0.774136i | 0.922051 | + | 0.387068i | \(0.126512\pi\) | ||||
−0.922051 | + | 0.387068i | \(0.873488\pi\) | |||||||
\(30\) | 9.89949 | − | 3.74166i | 0.329983 | − | 0.124722i | ||||
\(31\) | 46.7156i | 1.50696i | 0.657473 | + | 0.753478i | \(0.271625\pi\) | ||||
−0.657473 | + | 0.753478i | \(0.728375\pi\) | |||||||
\(32\) | 31.1127 | − | 7.48331i | 0.972272 | − | 0.233854i | ||||
\(33\) | −15.3137 | −0.464052 | ||||||||
\(34\) | 16.7279 | + | 44.2579i | 0.491998 | + | 1.30170i | ||||
\(35\) | −4.10051 | −0.117157 | ||||||||
\(36\) | −7.97056 | + | 7.02938i | −0.221405 | + | 0.195260i | ||||
\(37\) | 58.5826i | 1.58331i | 0.610966 | + | 0.791657i | \(0.290781\pi\) | ||||
−0.610966 | + | 0.791657i | \(0.709219\pi\) | |||||||
\(38\) | −17.5858 | − | 46.5276i | −0.462784 | − | 1.22441i | ||||
\(39\) | 5.29150i | 0.135680i | ||||||||
\(40\) | −5.79899 | + | 10.9591i | −0.144975 | + | 0.273977i | ||||
\(41\) | −26.9706 | −0.657819 | −0.328909 | − | 0.944362i | \(-0.606681\pi\) | ||||
−0.328909 | + | 0.944362i | \(0.606681\pi\) | |||||||
\(42\) | 16.8995 | − | 6.38741i | 0.402369 | − | 0.152081i | ||||
\(43\) | −17.1716 | −0.399339 | −0.199669 | − | 0.979863i | \(-0.563987\pi\) | ||||
−0.199669 | + | 0.979863i | \(0.563987\pi\) | |||||||
\(44\) | 13.4558 | − | 11.8669i | 0.305815 | − | 0.269703i | ||||
\(45\) | − | 4.11771i | − | 0.0915047i | ||||||
\(46\) | 65.8995 | − | 24.9077i | 1.43260 | − | 0.541471i | ||||
\(47\) | 36.1326i | 0.768780i | 0.923171 | + | 0.384390i | \(0.125588\pi\) | ||||
−0.923171 | + | 0.384390i | \(0.874412\pi\) | |||||||
\(48\) | 6.82843 | − | 54.1990i | 0.142259 | − | 1.12915i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 15.9792 | + | 42.2769i | 0.319584 | + | 0.845539i | ||||
\(51\) | 80.7696 | 1.58372 | ||||||||
\(52\) | −4.10051 | − | 4.64954i | −0.0788559 | − | 0.0894141i | ||||
\(53\) | − | 97.8149i | − | 1.84556i | −0.385322 | − | 0.922782i | \(-0.625910\pi\) | ||
0.385322 | − | 0.922782i | \(-0.374090\pi\) | |||||||
\(54\) | −15.3137 | − | 40.5163i | −0.283587 | − | 0.750301i | ||||
\(55\) | 6.95149i | 0.126391i | ||||||||
\(56\) | −9.89949 | + | 18.7083i | −0.176777 | + | 0.334077i | ||||
\(57\) | −84.9117 | −1.48968 | ||||||||
\(58\) | −42.0000 | + | 15.8745i | −0.724138 | + | 0.273698i | ||||
\(59\) | 61.5563 | 1.04333 | 0.521664 | − | 0.853151i | \(-0.325311\pi\) | ||||
0.521664 | + | 0.853151i | \(0.325311\pi\) | |||||||
\(60\) | 14.0000 | + | 15.8745i | 0.233333 | + | 0.264575i | ||||
\(61\) | 37.6825i | 0.617746i | 0.951103 | + | 0.308873i | \(0.0999518\pi\) | ||||
−0.951103 | + | 0.308873i | \(0.900048\pi\) | |||||||
\(62\) | −87.3970 | + | 33.0329i | −1.40963 | + | 0.532790i | ||||
\(63\) | − | 7.02938i | − | 0.111577i | ||||||
\(64\) | 36.0000 | + | 52.9150i | 0.562500 | + | 0.826797i | ||||
\(65\) | 2.40202 | 0.0369542 | ||||||||
\(66\) | −10.8284 | − | 28.6493i | −0.164067 | − | 0.434081i | ||||
\(67\) | −33.3726 | −0.498098 | −0.249049 | − | 0.968491i | \(-0.580118\pi\) | ||||
−0.249049 | + | 0.968491i | \(0.580118\pi\) | |||||||
\(68\) | −70.9706 | + | 62.5902i | −1.04368 | + | 0.920443i | ||||
\(69\) | − | 120.265i | − | 1.74297i | ||||||
\(70\) | −2.89949 | − | 7.67134i | −0.0414214 | − | 0.109591i | ||||
\(71\) | − | 102.199i | − | 1.43942i | −0.694277 | − | 0.719708i | \(-0.744276\pi\) | ||
0.694277 | − | 0.719708i | \(-0.255724\pi\) | |||||||
\(72\) | −18.7868 | − | 9.94104i | −0.260928 | − | 0.138070i | ||||
\(73\) | 69.3137 | 0.949503 | 0.474751 | − | 0.880120i | \(-0.342538\pi\) | ||||
0.474751 | + | 0.880120i | \(0.342538\pi\) | |||||||
\(74\) | −109.598 | + | 41.4241i | −1.48105 | + | 0.559786i | ||||
\(75\) | 77.1543 | 1.02872 | ||||||||
\(76\) | 74.6102 | − | 65.8000i | 0.981713 | − | 0.865789i | ||||
\(77\) | 11.8669i | 0.154116i | ||||||||
\(78\) | −9.89949 | + | 3.74166i | −0.126917 | + | 0.0479700i | ||||
\(79\) | − | 38.7005i | − | 0.489880i | −0.969538 | − | 0.244940i | \(-0.921232\pi\) | ||
0.969538 | − | 0.244940i | \(-0.0787682\pi\) | |||||||
\(80\) | −24.6030 | − | 3.09969i | −0.307538 | − | 0.0387461i | ||||
\(81\) | −97.8528 | −1.20806 | ||||||||
\(82\) | −19.0711 | − | 50.4573i | −0.232574 | − | 0.615333i | ||||
\(83\) | 3.61522 | 0.0435569 | 0.0217785 | − | 0.999763i | \(-0.493067\pi\) | ||||
0.0217785 | + | 0.999763i | \(0.493067\pi\) | |||||||
\(84\) | 23.8995 | + | 27.0995i | 0.284518 | + | 0.322613i | ||||
\(85\) | − | 36.6645i | − | 0.431347i | ||||||
\(86\) | −12.1421 | − | 32.1251i | −0.141188 | − | 0.373547i | ||||
\(87\) | 76.6489i | 0.881022i | ||||||||
\(88\) | 31.7157 | + | 16.7824i | 0.360406 | + | 0.190709i | ||||
\(89\) | 44.0589 | 0.495044 | 0.247522 | − | 0.968882i | \(-0.420384\pi\) | ||||
0.247522 | + | 0.968882i | \(0.420384\pi\) | |||||||
\(90\) | 7.70354 | − | 2.91166i | 0.0855948 | − | 0.0323518i | ||||
\(91\) | 4.10051 | 0.0450605 | ||||||||
\(92\) | 93.1960 | + | 105.674i | 1.01300 | + | 1.14863i | ||||
\(93\) | 159.497i | 1.71502i | ||||||||
\(94\) | −67.5980 | + | 25.5496i | −0.719127 | + | 0.271805i | ||||
\(95\) | 38.5447i | 0.405734i | ||||||||
\(96\) | 106.225 | − | 25.5496i | 1.10651 | − | 0.266142i | ||||
\(97\) | 96.1076 | 0.990800 | 0.495400 | − | 0.868665i | \(-0.335021\pi\) | ||||
0.495400 | + | 0.868665i | \(0.335021\pi\) | |||||||
\(98\) | −4.94975 | − | 13.0958i | −0.0505076 | − | 0.133631i | ||||
\(99\) | −11.9167 | −0.120371 | ||||||||
\(100\) | −67.7939 | + | 59.7886i | −0.677939 | + | 0.597886i | ||||
\(101\) | − | 19.6162i | − | 0.194219i | −0.995274 | − | 0.0971097i | \(-0.969040\pi\) | ||
0.995274 | − | 0.0971097i | \(-0.0309598\pi\) | |||||||
\(102\) | 57.1127 | + | 151.106i | 0.559928 | + | 1.48143i | ||||
\(103\) | − | 43.0841i | − | 0.418293i | −0.977884 | − | 0.209146i | \(-0.932932\pi\) | ||
0.977884 | − | 0.209146i | \(-0.0670685\pi\) | |||||||
\(104\) | 5.79899 | − | 10.9591i | 0.0557595 | − | 0.105376i | ||||
\(105\) | −14.0000 | −0.133333 | ||||||||
\(106\) | 182.995 | − | 69.1656i | 1.72637 | − | 0.652506i | ||||
\(107\) | 15.5980 | 0.145776 | 0.0728878 | − | 0.997340i | \(-0.476779\pi\) | ||||
0.0728878 | + | 0.997340i | \(0.476779\pi\) | |||||||
\(108\) | 64.9706 | − | 57.2987i | 0.601579 | − | 0.530543i | ||||
\(109\) | − | 3.85180i | − | 0.0353376i | −0.999844 | − | 0.0176688i | \(-0.994376\pi\) | ||
0.999844 | − | 0.0176688i | \(-0.00562445\pi\) | |||||||
\(110\) | −13.0051 | + | 4.91545i | −0.118228 | + | 0.0446859i | ||||
\(111\) | 200.013i | 1.80192i | ||||||||
\(112\) | −42.0000 | − | 5.29150i | −0.375000 | − | 0.0472456i | ||||
\(113\) | −13.7746 | −0.121899 | −0.0609496 | − | 0.998141i | \(-0.519413\pi\) | ||||
−0.0609496 | + | 0.998141i | \(0.519413\pi\) | |||||||
\(114\) | −60.0416 | − | 158.855i | −0.526681 | − | 1.39347i | ||||
\(115\) | −54.5929 | −0.474721 | ||||||||
\(116\) | −59.3970 | − | 67.3498i | −0.512043 | − | 0.580602i | ||||
\(117\) | 4.11771i | 0.0351941i | ||||||||
\(118\) | 43.5269 | + | 115.161i | 0.368872 | + | 0.975944i | ||||
\(119\) | − | 62.5902i | − | 0.525968i | ||||||
\(120\) | −19.7990 | + | 37.4166i | −0.164992 | + | 0.311805i | ||||
\(121\) | −100.882 | −0.833738 | ||||||||
\(122\) | −70.4975 | + | 26.6455i | −0.577848 | + | 0.218406i | ||||
\(123\) | −92.0833 | −0.748644 | ||||||||
\(124\) | −123.598 | − | 140.147i | −0.996758 | − | 1.13022i | ||||
\(125\) | − | 73.7695i | − | 0.590156i | ||||||
\(126\) | 13.1508 | − | 4.97052i | 0.104371 | − | 0.0394486i | ||||
\(127\) | − | 125.025i | − | 0.984445i | −0.870469 | − | 0.492223i | \(-0.836185\pi\) | ||
0.870469 | − | 0.492223i | \(-0.163815\pi\) | |||||||
\(128\) | −73.5391 | + | 104.766i | −0.574524 | + | 0.818488i | ||||
\(129\) | −58.6274 | −0.454476 | ||||||||
\(130\) | 1.69848 | + | 4.49377i | 0.0130653 | + | 0.0345674i | ||||
\(131\) | 100.350 | 0.766033 | 0.383016 | − | 0.923742i | \(-0.374885\pi\) | ||||
0.383016 | + | 0.923742i | \(0.374885\pi\) | |||||||
\(132\) | 45.9411 | − | 40.5163i | 0.348039 | − | 0.306941i | ||||
\(133\) | 65.8000i | 0.494737i | ||||||||
\(134\) | −23.5980 | − | 62.4344i | −0.176104 | − | 0.465928i | ||||
\(135\) | 33.5648i | 0.248628i | ||||||||
\(136\) | −167.279 | − | 88.5158i | −1.22999 | − | 0.650852i | ||||
\(137\) | 57.3137 | 0.418348 | 0.209174 | − | 0.977878i | \(-0.432922\pi\) | ||||
0.209174 | + | 0.977878i | \(0.432922\pi\) | |||||||
\(138\) | 224.995 | − | 85.0401i | 1.63040 | − | 0.616233i | ||||
\(139\) | −183.664 | −1.32132 | −0.660662 | − | 0.750684i | \(-0.729724\pi\) | ||||
−0.660662 | + | 0.750684i | \(0.729724\pi\) | |||||||
\(140\) | 12.3015 | − | 10.8489i | 0.0878680 | − | 0.0774923i | ||||
\(141\) | 123.365i | 0.874926i | ||||||||
\(142\) | 191.196 | − | 72.2653i | 1.34645 | − | 0.508910i | ||||
\(143\) | − | 6.95149i | − | 0.0486118i | ||||||
\(144\) | 5.31371 | − | 42.1763i | 0.0369008 | − | 0.292891i | ||||
\(145\) | 34.7939 | 0.239958 | ||||||||
\(146\) | 49.0122 | + | 129.674i | 0.335700 | + | 0.888179i | ||||
\(147\) | −23.8995 | −0.162582 | ||||||||
\(148\) | −154.995 | − | 175.748i | −1.04726 | − | 1.18748i | ||||
\(149\) | − | 192.310i | − | 1.29067i | −0.763900 | − | 0.645335i | \(-0.776718\pi\) | ||
0.763900 | − | 0.645335i | \(-0.223282\pi\) | |||||||
\(150\) | 54.5563 | + | 144.343i | 0.363709 | + | 0.962284i | ||||
\(151\) | 114.753i | 0.759954i | 0.924996 | + | 0.379977i | \(0.124068\pi\) | ||||
−0.924996 | + | 0.379977i | \(0.875932\pi\) | |||||||
\(152\) | 175.858 | + | 93.0552i | 1.15696 | + | 0.612205i | ||||
\(153\) | 62.8528 | 0.410803 | ||||||||
\(154\) | −22.2010 | + | 8.39119i | −0.144162 | + | 0.0544883i | ||||
\(155\) | 72.4020 | 0.467110 | ||||||||
\(156\) | −14.0000 | − | 15.8745i | −0.0897436 | − | 0.101760i | ||||
\(157\) | 212.146i | 1.35125i | 0.737245 | + | 0.675625i | \(0.236126\pi\) | ||||
−0.737245 | + | 0.675625i | \(0.763874\pi\) | |||||||
\(158\) | 72.4020 | − | 27.3654i | 0.458241 | − | 0.173199i | ||||
\(159\) | − | 333.961i | − | 2.10038i | ||||||
\(160\) | −11.5980 | − | 48.2199i | −0.0724874 | − | 0.301374i | ||||
\(161\) | −93.1960 | −0.578857 | ||||||||
\(162\) | −69.1924 | − | 183.066i | −0.427114 | − | 1.13004i | ||||
\(163\) | −240.534 | −1.47567 | −0.737835 | − | 0.674982i | \(-0.764152\pi\) | ||||
−0.737835 | + | 0.674982i | \(0.764152\pi\) | |||||||
\(164\) | 80.9117 | − | 71.3574i | 0.493364 | − | 0.435106i | ||||
\(165\) | 23.7339i | 0.143842i | ||||||||
\(166\) | 2.55635 | + | 6.76346i | 0.0153997 | + | 0.0407438i | ||||
\(167\) | 212.101i | 1.27006i | 0.772486 | + | 0.635032i | \(0.219013\pi\) | ||||
−0.772486 | + | 0.635032i | \(0.780987\pi\) | |||||||
\(168\) | −33.7990 | + | 63.8741i | −0.201184 | + | 0.380203i | ||||
\(169\) | 166.598 | 0.985787 | ||||||||
\(170\) | 68.5929 | − | 25.9257i | 0.403488 | − | 0.152504i | ||||
\(171\) | −66.0761 | −0.386410 | ||||||||
\(172\) | 51.5147 | − | 45.4317i | 0.299504 | − | 0.264138i | ||||
\(173\) | 182.213i | 1.05325i | 0.850096 | + | 0.526627i | \(0.176544\pi\) | ||||
−0.850096 | + | 0.526627i | \(0.823456\pi\) | |||||||
\(174\) | −143.397 | + | 54.1990i | −0.824121 | + | 0.311488i | ||||
\(175\) | − | 59.7886i | − | 0.341649i | ||||||
\(176\) | −8.97056 | + | 71.2016i | −0.0509691 | + | 0.404555i | ||||
\(177\) | 210.167 | 1.18738 | ||||||||
\(178\) | 31.1543 | + | 82.4266i | 0.175024 | + | 0.463071i | ||||
\(179\) | 57.2061 | 0.319587 | 0.159793 | − | 0.987150i | \(-0.448917\pi\) | ||||
0.159793 | + | 0.987150i | \(0.448917\pi\) | |||||||
\(180\) | 10.8944 | + | 12.3531i | 0.0605247 | + | 0.0686285i | ||||
\(181\) | − | 326.212i | − | 1.80228i | −0.433533 | − | 0.901138i | \(-0.642733\pi\) | ||
0.433533 | − | 0.901138i | \(-0.357267\pi\) | |||||||
\(182\) | 2.89949 | + | 7.67134i | 0.0159313 | + | 0.0421502i | ||||
\(183\) | 128.656i | 0.703039i | ||||||||
\(184\) | −131.799 | + | 249.077i | −0.716299 | + | 1.35368i | ||||
\(185\) | 90.7939 | 0.490778 | ||||||||
\(186\) | −298.392 | + | 112.782i | −1.60426 | + | 0.606352i | ||||
\(187\) | −106.108 | −0.567421 | ||||||||
\(188\) | −95.5980 | − | 108.398i | −0.508500 | − | 0.576585i | ||||
\(189\) | 57.2987i | 0.303167i | ||||||||
\(190\) | −72.1106 | + | 27.2552i | −0.379530 | + | 0.143449i | ||||
\(191\) | − | 97.0628i | − | 0.508182i | −0.967180 | − | 0.254091i | \(-0.918224\pi\) | ||
0.967180 | − | 0.254091i | \(-0.0817763\pi\) | |||||||
\(192\) | 122.912 | + | 180.663i | 0.640165 | + | 0.940954i | ||||
\(193\) | 157.304 | 0.815045 | 0.407522 | − | 0.913195i | \(-0.366393\pi\) | ||||
0.407522 | + | 0.913195i | \(0.366393\pi\) | |||||||
\(194\) | 67.9584 | + | 179.801i | 0.350301 | + | 0.926809i | ||||
\(195\) | 8.20101 | 0.0420565 | ||||||||
\(196\) | 21.0000 | − | 18.5203i | 0.107143 | − | 0.0944911i | ||||
\(197\) | 124.117i | 0.630034i | 0.949086 | + | 0.315017i | \(0.102010\pi\) | ||||
−0.949086 | + | 0.315017i | \(0.897990\pi\) | |||||||
\(198\) | −8.42641 | − | 22.2942i | −0.0425576 | − | 0.112597i | ||||
\(199\) | − | 180.975i | − | 0.909421i | −0.890639 | − | 0.454710i | \(-0.849743\pi\) | ||
0.890639 | − | 0.454710i | \(-0.150257\pi\) | |||||||
\(200\) | −159.792 | − | 84.5539i | −0.798959 | − | 0.422769i | ||||
\(201\) | −113.941 | −0.566871 | ||||||||
\(202\) | 36.6985 | − | 13.8707i | 0.181676 | − | 0.0686669i | ||||
\(203\) | 59.3970 | 0.292596 | ||||||||
\(204\) | −242.309 | + | 213.696i | −1.18779 | + | 1.04753i | ||||
\(205\) | 41.8002i | 0.203903i | ||||||||
\(206\) | 80.6030 | − | 30.4651i | 0.391277 | − | 0.147889i | ||||
\(207\) | − | 93.5871i | − | 0.452111i | ||||||
\(208\) | 24.6030 | + | 3.09969i | 0.118284 | + | 0.0149024i | ||||
\(209\) | 111.549 | 0.533728 | ||||||||
\(210\) | −9.89949 | − | 26.1916i | −0.0471405 | − | 0.124722i | ||||
\(211\) | 164.049 | 0.777482 | 0.388741 | − | 0.921347i | \(-0.372910\pi\) | ||||
0.388741 | + | 0.921347i | \(0.372910\pi\) | |||||||
\(212\) | 258.794 | + | 293.445i | 1.22073 | + | 1.38417i | ||||
\(213\) | − | 348.928i | − | 1.63816i | ||||||
\(214\) | 11.0294 | + | 29.1811i | 0.0515394 | + | 0.136361i | ||||
\(215\) | 26.6133i | 0.123783i | ||||||||
\(216\) | 153.137 | + | 81.0325i | 0.708968 | + | 0.375151i | ||||
\(217\) | 123.598 | 0.569576 | ||||||||
\(218\) | 7.20606 | − | 2.72363i | 0.0330553 | − | 0.0124937i | ||||
\(219\) | 236.652 | 1.08060 | ||||||||
\(220\) | −18.3919 | − | 20.8545i | −0.0835996 | − | 0.0947931i | ||||
\(221\) | 36.6645i | 0.165903i | ||||||||
\(222\) | −374.191 | + | 141.431i | −1.68554 | + | 0.637076i | ||||
\(223\) | − | 10.5830i | − | 0.0474574i | −0.999718 | − | 0.0237287i | \(-0.992446\pi\) | ||
0.999718 | − | 0.0237287i | \(-0.00755379\pi\) | |||||||
\(224\) | −19.7990 | − | 82.3165i | −0.0883883 | − | 0.367484i | ||||
\(225\) | 60.0395 | 0.266842 | ||||||||
\(226\) | −9.74012 | − | 25.7699i | −0.0430979 | − | 0.114026i | ||||
\(227\) | 105.806 | 0.466106 | 0.233053 | − | 0.972464i | \(-0.425128\pi\) | ||||
0.233053 | + | 0.972464i | \(0.425128\pi\) | |||||||
\(228\) | 254.735 | − | 224.655i | 1.11726 | − | 0.985330i | ||||
\(229\) | − | 74.8788i | − | 0.326982i | −0.986545 | − | 0.163491i | \(-0.947725\pi\) | ||
0.986545 | − | 0.163491i | \(-0.0522754\pi\) | |||||||
\(230\) | −38.6030 | − | 102.134i | −0.167839 | − | 0.444061i | ||||
\(231\) | 40.5163i | 0.175395i | ||||||||
\(232\) | 84.0000 | − | 158.745i | 0.362069 | − | 0.684246i | ||||
\(233\) | −419.137 | −1.79887 | −0.899436 | − | 0.437053i | \(-0.856022\pi\) | ||||
−0.899436 | + | 0.437053i | \(0.856022\pi\) | |||||||
\(234\) | −7.70354 | + | 2.91166i | −0.0329211 | + | 0.0124430i | ||||
\(235\) | 56.0000 | 0.238298 | ||||||||
\(236\) | −184.669 | + | 162.863i | −0.782496 | + | 0.690097i | ||||
\(237\) | − | 132.132i | − | 0.557518i | ||||||
\(238\) | 117.095 | − | 44.2579i | 0.491998 | − | 0.185958i | ||||
\(239\) | 148.318i | 0.620577i | 0.950642 | + | 0.310288i | \(0.100426\pi\) | ||||
−0.950642 | + | 0.310288i | \(0.899574\pi\) | |||||||
\(240\) | −84.0000 | − | 10.5830i | −0.350000 | − | 0.0440959i | ||||
\(241\) | −459.872 | −1.90818 | −0.954092 | − | 0.299515i | \(-0.903175\pi\) | ||||
−0.954092 | + | 0.299515i | \(0.903175\pi\) | |||||||
\(242\) | −71.3345 | − | 188.733i | −0.294771 | − | 0.779890i | ||||
\(243\) | −139.179 | −0.572752 | ||||||||
\(244\) | −99.6985 | − | 113.047i | −0.408600 | − | 0.463309i | ||||
\(245\) | 10.8489i | 0.0442813i | ||||||||
\(246\) | −65.1127 | − | 172.272i | −0.264686 | − | 0.700293i | ||||
\(247\) | − | 38.5447i | − | 0.156052i | ||||||
\(248\) | 174.794 | − | 330.329i | 0.704814 | − | 1.33197i | ||||
\(249\) | 12.3431 | 0.0495709 | ||||||||
\(250\) | 138.010 | − | 52.1629i | 0.552040 | − | 0.208652i | ||||
\(251\) | 124.919 | 0.497685 | 0.248842 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248842 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(252\) | 18.5980 | + | 21.0881i | 0.0738015 | + | 0.0836830i | ||||
\(253\) | 157.993i | 0.624478i | ||||||||
\(254\) | 233.899 | − | 88.4057i | 0.920864 | − | 0.348054i | ||||
\(255\) | − | 125.180i | − | 0.490903i | ||||||
\(256\) | −248.000 | − | 63.4980i | −0.968750 | − | 0.248039i | ||||
\(257\) | −427.352 | −1.66285 | −0.831425 | − | 0.555637i | \(-0.812474\pi\) | ||||
−0.831425 | + | 0.555637i | \(0.812474\pi\) | |||||||
\(258\) | −41.4558 | − | 109.682i | −0.160682 | − | 0.425123i | ||||
\(259\) | 154.995 | 0.598436 | ||||||||
\(260\) | −7.20606 | + | 6.35515i | −0.0277156 | + | 0.0244429i | ||||
\(261\) | 59.6462i | 0.228530i | ||||||||
\(262\) | 70.9584 | + | 187.738i | 0.270833 | + | 0.716558i | ||||
\(263\) | 257.624i | 0.979558i | 0.871847 | + | 0.489779i | \(0.162922\pi\) | ||||
−0.871847 | + | 0.489779i | \(0.837078\pi\) | |||||||
\(264\) | 108.284 | + | 57.2987i | 0.410168 | + | 0.217040i | ||||
\(265\) | −151.598 | −0.572068 | ||||||||
\(266\) | −123.101 | + | 46.5276i | −0.462784 | + | 0.174916i | ||||
\(267\) | 150.426 | 0.563395 | ||||||||
\(268\) | 100.118 | − | 88.2956i | 0.373574 | − | 0.329461i | ||||
\(269\) | − | 215.246i | − | 0.800171i | −0.916478 | − | 0.400085i | \(-0.868980\pi\) | ||
0.916478 | − | 0.400085i | \(-0.131020\pi\) | |||||||
\(270\) | −62.7939 | + | 23.7339i | −0.232570 | + | 0.0879033i | ||||
\(271\) | 378.549i | 1.39686i | 0.715678 | + | 0.698431i | \(0.246118\pi\) | ||||
−0.715678 | + | 0.698431i | \(0.753882\pi\) | |||||||
\(272\) | 47.3137 | − | 375.541i | 0.173947 | − | 1.38067i | ||||
\(273\) | 14.0000 | 0.0512821 | ||||||||
\(274\) | 40.5269 | + | 107.224i | 0.147908 | + | 0.391329i | ||||
\(275\) | −101.358 | −0.368576 | ||||||||
\(276\) | 318.191 | + | 360.795i | 1.15287 | + | 1.30723i | ||||
\(277\) | − | 166.449i | − | 0.600898i | −0.953798 | − | 0.300449i | \(-0.902864\pi\) | ||
0.953798 | − | 0.300449i | \(-0.0971365\pi\) | |||||||
\(278\) | −129.870 | − | 343.604i | −0.467158 | − | 1.23599i | ||||
\(279\) | 124.117i | 0.444863i | ||||||||
\(280\) | 28.9949 | + | 15.3427i | 0.103553 | + | 0.0547953i | ||||
\(281\) | −421.765 | −1.50094 | −0.750471 | − | 0.660904i | \(-0.770173\pi\) | ||||
−0.750471 | + | 0.660904i | \(0.770173\pi\) | |||||||
\(282\) | −230.794 | + | 87.2319i | −0.818418 | + | 0.309333i | ||||
\(283\) | −345.439 | −1.22063 | −0.610316 | − | 0.792158i | \(-0.708957\pi\) | ||||
−0.610316 | + | 0.792158i | \(0.708957\pi\) | |||||||
\(284\) | 270.392 | + | 306.596i | 0.952084 | + | 1.07956i | ||||
\(285\) | 131.600i | 0.461754i | ||||||||
\(286\) | 13.0051 | − | 4.91545i | 0.0454722 | − | 0.0171869i | ||||
\(287\) | 71.3574i | 0.248632i | ||||||||
\(288\) | 82.6619 | − | 19.8821i | 0.287021 | − | 0.0690350i | ||||
\(289\) | 270.647 | 0.936494 | ||||||||
\(290\) | 24.6030 | + | 65.0935i | 0.0848380 | + | 0.224460i | ||||
\(291\) | 328.132 | 1.12760 | ||||||||
\(292\) | −207.941 | + | 183.387i | −0.712127 | + | 0.628037i | ||||
\(293\) | 511.038i | 1.74416i | 0.489365 | + | 0.872079i | \(0.337229\pi\) | ||||
−0.489365 | + | 0.872079i | \(0.662771\pi\) | |||||||
\(294\) | −16.8995 | − | 44.7119i | −0.0574813 | − | 0.152081i | ||||
\(295\) | − | 95.4028i | − | 0.323399i | ||||||
\(296\) | 219.196 | − | 414.241i | 0.740527 | − | 1.39946i | ||||
\(297\) | 97.1371 | 0.327061 | ||||||||
\(298\) | 359.779 | − | 135.984i | 1.20731 | − | 0.456321i | ||||
\(299\) | 54.5929 | 0.182585 | ||||||||
\(300\) | −231.463 | + | 204.131i | −0.771543 | + | 0.680437i | ||||
\(301\) | 45.4317i | 0.150936i | ||||||||
\(302\) | −214.683 | + | 81.1427i | −0.710872 | + | 0.268684i | ||||
\(303\) | − | 66.9738i | − | 0.221036i | ||||||
\(304\) | −49.7401 | + | 394.800i | −0.163619 | + | 1.29868i | ||||
\(305\) | 58.4020 | 0.191482 | ||||||||
\(306\) | 44.4437 | + | 117.587i | 0.145241 | + | 0.384271i | ||||
\(307\) | 223.331 | 0.727462 | 0.363731 | − | 0.931504i | \(-0.381503\pi\) | ||||
0.363731 | + | 0.931504i | \(0.381503\pi\) | |||||||
\(308\) | −31.3970 | − | 35.6008i | −0.101938 | − | 0.115587i | ||||
\(309\) | − | 147.098i | − | 0.476047i | ||||||
\(310\) | 51.1960 | + | 135.452i | 0.165148 | + | 0.436941i | ||||
\(311\) | − | 12.3988i | − | 0.0398674i | −0.999801 | − | 0.0199337i | \(-0.993654\pi\) | ||
0.999801 | − | 0.0199337i | \(-0.00634551\pi\) | |||||||
\(312\) | 19.7990 | − | 37.4166i | 0.0634583 | − | 0.119925i | ||||
\(313\) | 410.049 | 1.31006 | 0.655030 | − | 0.755603i | \(-0.272656\pi\) | ||||
0.655030 | + | 0.755603i | \(0.272656\pi\) | |||||||
\(314\) | −396.889 | + | 150.010i | −1.26398 | + | 0.477739i | ||||
\(315\) | −10.8944 | −0.0345855 | ||||||||
\(316\) | 102.392 | + | 116.102i | 0.324025 | + | 0.367410i | ||||
\(317\) | − | 130.316i | − | 0.411092i | −0.978647 | − | 0.205546i | \(-0.934103\pi\) | ||
0.978647 | − | 0.205546i | \(-0.0658970\pi\) | |||||||
\(318\) | 624.784 | − | 236.146i | 1.96473 | − | 0.742598i | ||||
\(319\) | − | 100.694i | − | 0.315656i | ||||||
\(320\) | 82.0101 | − | 55.7944i | 0.256282 | − | 0.174358i | ||||
\(321\) | 53.2548 | 0.165903 | ||||||||
\(322\) | −65.8995 | − | 174.354i | −0.204657 | − | 0.541471i | ||||
\(323\) | −588.347 | −1.82151 | ||||||||
\(324\) | 293.558 | − | 258.894i | 0.906045 | − | 0.799056i | ||||
\(325\) | 35.0234i | 0.107764i | ||||||||
\(326\) | −170.083 | − | 449.998i | −0.521728 | − | 1.38036i | ||||
\(327\) | − | 13.1509i | − | 0.0402167i | ||||||
\(328\) | 190.711 | + | 100.915i | 0.581435 | + | 0.307666i | ||||
\(329\) | 95.5980 | 0.290571 | ||||||||
\(330\) | −44.4020 | + | 16.7824i | −0.134552 | + | 0.0508557i | ||||
\(331\) | 214.260 | 0.647311 | 0.323655 | − | 0.946175i | \(-0.395088\pi\) | ||||
0.323655 | + | 0.946175i | \(0.395088\pi\) | |||||||
\(332\) | −10.8457 | + | 9.56498i | −0.0326677 | + | 0.0288102i | ||||
\(333\) | 155.645i | 0.467404i | ||||||||
\(334\) | −396.804 | + | 149.978i | −1.18804 | + | 0.449035i | ||||
\(335\) | 51.7223i | 0.154395i | ||||||||
\(336\) | −143.397 | − | 18.0663i | −0.426777 | − | 0.0537688i | ||||
\(337\) | 164.049 | 0.486792 | 0.243396 | − | 0.969927i | \(-0.421739\pi\) | ||||
0.243396 | + | 0.969927i | \(0.421739\pi\) | |||||||
\(338\) | 117.803 | + | 311.676i | 0.348528 | + | 0.922119i | ||||
\(339\) | −47.0294 | −0.138730 | ||||||||
\(340\) | 97.0051 | + | 109.993i | 0.285309 | + | 0.323510i | ||||
\(341\) | − | 209.533i | − | 0.614466i | ||||||
\(342\) | −46.7229 | − | 123.617i | −0.136617 | − | 0.361454i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 121.421 | + | 64.2501i | 0.352969 | + | 0.186774i | ||||
\(345\) | −186.392 | −0.540266 | ||||||||
\(346\) | −340.889 | + | 128.844i | −0.985229 | + | 0.372382i | ||||
\(347\) | −109.691 | −0.316113 | −0.158057 | − | 0.987430i | \(-0.550523\pi\) | ||||
−0.158057 | + | 0.987430i | \(0.550523\pi\) | |||||||
\(348\) | −202.794 | − | 229.947i | −0.582741 | − | 0.660766i | ||||
\(349\) | 463.479i | 1.32802i | 0.747723 | + | 0.664010i | \(0.231147\pi\) | ||||
−0.747723 | + | 0.664010i | \(0.768853\pi\) | |||||||
\(350\) | 111.854 | − | 42.2769i | 0.319584 | − | 0.120791i | ||||
\(351\) | − | 33.5648i | − | 0.0956261i | ||||||
\(352\) | −139.549 | + | 33.5648i | −0.396447 | + | 0.0953545i | ||||
\(353\) | 78.0975 | 0.221240 | 0.110620 | − | 0.993863i | \(-0.464716\pi\) | ||||
0.110620 | + | 0.993863i | \(0.464716\pi\) | |||||||
\(354\) | 148.610 | + | 393.186i | 0.419803 | + | 1.11069i | ||||
\(355\) | −158.392 | −0.446174 | ||||||||
\(356\) | −132.177 | + | 116.569i | −0.371283 | + | 0.327441i | ||||
\(357\) | − | 213.696i | − | 0.598589i | ||||||
\(358\) | 40.4508 | + | 107.023i | 0.112991 | + | 0.298946i | ||||
\(359\) | − | 365.114i | − | 1.01703i | −0.861053 | − | 0.508515i | \(-0.830195\pi\) | ||
0.861053 | − | 0.508515i | \(-0.169805\pi\) | |||||||
\(360\) | −15.4071 | + | 29.1166i | −0.0427974 | + | 0.0808795i | ||||
\(361\) | 257.520 | 0.713351 | ||||||||
\(362\) | 610.286 | − | 230.667i | 1.68587 | − | 0.637200i | ||||
\(363\) | −344.434 | −0.948853 | ||||||||
\(364\) | −12.3015 | + | 10.8489i | −0.0337954 | + | 0.0298047i | ||||
\(365\) | − | 107.426i | − | 0.294316i | ||||||
\(366\) | −240.693 | + | 90.9736i | −0.657632 | + | 0.248562i | ||||
\(367\) | 220.739i | 0.601468i | 0.953708 | + | 0.300734i | \(0.0972317\pi\) | ||||
−0.953708 | + | 0.300734i | \(0.902768\pi\) | |||||||
\(368\) | −559.176 | − | 70.4495i | −1.51950 | − | 0.191439i | ||||
\(369\) | −71.6569 | −0.194192 | ||||||||
\(370\) | 64.2010 | + | 169.860i | 0.173516 | + | 0.459081i | ||||
\(371\) | −258.794 | −0.697558 | ||||||||
\(372\) | −421.990 | − | 478.492i | −1.13438 | − | 1.28627i | ||||
\(373\) | 251.553i | 0.674406i | 0.941432 | + | 0.337203i | \(0.109481\pi\) | ||||
−0.941432 | + | 0.337203i | \(0.890519\pi\) | |||||||
\(374\) | −75.0294 | − | 198.509i | −0.200613 | − | 0.530773i | ||||
\(375\) | − | 251.865i | − | 0.671640i | ||||||
\(376\) | 135.196 | − | 255.496i | 0.359564 | − | 0.679512i | ||||
\(377\) | −34.7939 | −0.0922916 | ||||||||
\(378\) | −107.196 | + | 40.5163i | −0.283587 | + | 0.107186i | ||||
\(379\) | 286.024 | 0.754682 | 0.377341 | − | 0.926074i | \(-0.376839\pi\) | ||||
0.377341 | + | 0.926074i | \(0.376839\pi\) | |||||||
\(380\) | −101.980 | − | 115.634i | −0.268368 | − | 0.304301i | ||||
\(381\) | − | 426.860i | − | 1.12037i | ||||||
\(382\) | 181.588 | − | 68.6338i | 0.475361 | − | 0.179670i | ||||
\(383\) | − | 106.894i | − | 0.279096i | −0.990215 | − | 0.139548i | \(-0.955435\pi\) | ||
0.990215 | − | 0.139548i | \(-0.0445649\pi\) | |||||||
\(384\) | −251.078 | + | 357.695i | −0.653850 | + | 0.931497i | ||||
\(385\) | 18.3919 | 0.0477712 | ||||||||
\(386\) | 111.230 | + | 294.288i | 0.288162 | + | 0.762404i | ||||
\(387\) | −45.6224 | −0.117887 | ||||||||
\(388\) | −288.323 | + | 254.277i | −0.743100 | + | 0.655353i | ||||
\(389\) | 77.1807i | 0.198408i | 0.995067 | + | 0.0992040i | \(0.0316296\pi\) | ||||
−0.995067 | + | 0.0992040i | \(0.968370\pi\) | |||||||
\(390\) | 5.79899 | + | 15.3427i | 0.0148692 | + | 0.0393402i | ||||
\(391\) | − | 833.307i | − | 2.13122i | ||||||
\(392\) | 49.4975 | + | 26.1916i | 0.126269 | + | 0.0668153i | ||||
\(393\) | 342.617 | 0.871800 | ||||||||
\(394\) | −232.201 | + | 87.7637i | −0.589343 | + | 0.222751i | ||||
\(395\) | −59.9798 | −0.151848 | ||||||||
\(396\) | 35.7502 | − | 31.5287i | 0.0902783 | − | 0.0796180i | ||||
\(397\) | − | 657.514i | − | 1.65621i | −0.560576 | − | 0.828103i | \(-0.689420\pi\) | ||
0.560576 | − | 0.828103i | \(-0.310580\pi\) | |||||||
\(398\) | 338.573 | − | 127.968i | 0.850685 | − | 0.321529i | ||||
\(399\) | 224.655i | 0.563046i | ||||||||
\(400\) | 45.1960 | − | 358.732i | 0.112990 | − | 0.896830i | ||||
\(401\) | 318.794 | 0.794997 | 0.397499 | − | 0.917603i | \(-0.369878\pi\) | ||||
0.397499 | + | 0.917603i | \(0.369878\pi\) | |||||||
\(402\) | −80.5685 | − | 213.164i | −0.200419 | − | 0.530260i | ||||
\(403\) | −72.4020 | −0.179658 | ||||||||
\(404\) | 51.8995 | + | 58.8485i | 0.128464 | + | 0.145665i | ||||
\(405\) | 151.657i | 0.374461i | ||||||||
\(406\) | 42.0000 | + | 111.122i | 0.103448 | + | 0.273698i | ||||
\(407\) | − | 262.759i | − | 0.645600i | ||||||
\(408\) | −571.127 | − | 302.212i | −1.39982 | − | 0.740716i | ||||
\(409\) | 145.265 | 0.355171 | 0.177585 | − | 0.984105i | \(-0.443171\pi\) | ||||
0.177585 | + | 0.984105i | \(0.443171\pi\) | |||||||
\(410\) | −78.2010 | + | 29.5572i | −0.190734 | + | 0.0720907i | ||||
\(411\) | 195.681 | 0.476110 | ||||||||
\(412\) | 113.990 | + | 129.252i | 0.276675 | + | 0.313719i | ||||
\(413\) | − | 162.863i | − | 0.394341i | ||||||
\(414\) | 175.085 | − | 66.1760i | 0.422911 | − | 0.159846i | ||||
\(415\) | − | 5.60304i | − | 0.0135013i | ||||||
\(416\) | 11.5980 | + | 48.2199i | 0.0278798 | + | 0.115913i | ||||
\(417\) | −627.068 | −1.50376 | ||||||||
\(418\) | 78.8772 | + | 208.689i | 0.188701 | + | 0.499257i | ||||
\(419\) | 707.012 | 1.68738 | 0.843690 | − | 0.536831i | \(-0.180379\pi\) | ||||
0.843690 | + | 0.536831i | \(0.180379\pi\) | |||||||
\(420\) | 42.0000 | − | 37.0405i | 0.100000 | − | 0.0881917i | ||||
\(421\) | − | 121.989i | − | 0.289761i | −0.989449 | − | 0.144880i | \(-0.953720\pi\) | ||
0.989449 | − | 0.144880i | \(-0.0462798\pi\) | |||||||
\(422\) | 116.000 | + | 306.907i | 0.274882 | + | 0.727268i | ||||
\(423\) | 95.9992i | 0.226948i | ||||||||
\(424\) | −365.990 | + | 691.656i | −0.863184 | + | 1.63126i | ||||
\(425\) | 534.597 | 1.25788 | ||||||||
\(426\) | 652.784 | − | 246.729i | 1.53236 | − | 0.579176i | ||||
\(427\) | 99.6985 | 0.233486 | ||||||||
\(428\) | −46.7939 | + | 41.2684i | −0.109332 | + | 0.0964214i | ||||
\(429\) | − | 23.7339i | − | 0.0553237i | ||||||
\(430\) | −49.7889 | + | 18.8184i | −0.115788 | + | 0.0437638i | ||||
\(431\) | 588.861i | 1.36627i | 0.730294 | + | 0.683133i | \(0.239383\pi\) | ||||
−0.730294 | + | 0.683133i | \(0.760617\pi\) | |||||||
\(432\) | −43.3137 | + | 343.792i | −0.100263 | + | 0.795815i | ||||
\(433\) | 137.696 | 0.318004 | 0.159002 | − | 0.987278i | \(-0.449172\pi\) | ||||
0.159002 | + | 0.987278i | \(0.449172\pi\) | |||||||
\(434\) | 87.3970 | + | 231.231i | 0.201376 | + | 0.532790i | ||||
\(435\) | 118.794 | 0.273090 | ||||||||
\(436\) | 10.1909 | + | 11.5554i | 0.0233736 | + | 0.0265032i | ||||
\(437\) | 876.042i | 2.00467i | ||||||||
\(438\) | 167.338 | + | 442.735i | 0.382050 | + | 1.01081i | ||||
\(439\) | 440.543i | 1.00352i | 0.865008 | + | 0.501758i | \(0.167313\pi\) | ||||
−0.865008 | + | 0.501758i | \(0.832687\pi\) | |||||||
\(440\) | 26.0101 | − | 49.1545i | 0.0591139 | − | 0.111715i | ||||
\(441\) | −18.5980 | −0.0421723 | ||||||||
\(442\) | −68.5929 | + | 25.9257i | −0.155188 | + | 0.0586554i | ||||
\(443\) | −487.058 | −1.09945 | −0.549727 | − | 0.835344i | \(-0.685268\pi\) | ||||
−0.549727 | + | 0.835344i | \(0.685268\pi\) | |||||||
\(444\) | −529.186 | − | 600.040i | −1.19186 | − | 1.35144i | ||||
\(445\) | − | 68.2844i | − | 0.153448i | ||||||
\(446\) | 19.7990 | − | 7.48331i | 0.0443924 | − | 0.0167787i | ||||
\(447\) | − | 656.587i | − | 1.46887i | ||||||
\(448\) | 140.000 | − | 95.2470i | 0.312500 | − | 0.212605i | ||||
\(449\) | 264.039 | 0.588059 | 0.294030 | − | 0.955796i | \(-0.405004\pi\) | ||||
0.294030 | + | 0.955796i | \(0.405004\pi\) | |||||||
\(450\) | 42.4544 | + | 112.324i | 0.0943430 | + | 0.249608i | ||||
\(451\) | 120.971 | 0.268227 | ||||||||
\(452\) | 41.3238 | − | 36.4442i | 0.0914244 | − | 0.0806287i | ||||
\(453\) | 391.791i | 0.864882i | ||||||||
\(454\) | 74.8162 | + | 197.945i | 0.164793 | + | 0.436003i | ||||
\(455\) | − | 6.35515i | − | 0.0139674i | ||||||
\(456\) | 600.416 | + | 317.710i | 1.31670 | + | 0.696733i | ||||
\(457\) | −514.323 | −1.12543 | −0.562717 | − | 0.826650i | \(-0.690244\pi\) | ||||
−0.562717 | + | 0.826650i | \(0.690244\pi\) | |||||||
\(458\) | 140.085 | − | 52.9473i | 0.305863 | − | 0.115605i | ||||
\(459\) | −512.333 | −1.11619 | ||||||||
\(460\) | 163.779 | − | 144.439i | 0.356041 | − | 0.313999i | ||||
\(461\) | 202.224i | 0.438664i | 0.975650 | + | 0.219332i | \(0.0703878\pi\) | ||||
−0.975650 | + | 0.219332i | \(0.929612\pi\) | |||||||
\(462\) | −75.7990 | + | 28.6493i | −0.164067 | + | 0.0620115i | ||||
\(463\) | 722.653i | 1.56081i | 0.625277 | + | 0.780403i | \(0.284986\pi\) | ||||
−0.625277 | + | 0.780403i | \(0.715014\pi\) | |||||||
\(464\) | 356.382 | + | 44.8999i | 0.768064 | + | 0.0967670i | ||||
\(465\) | 247.196 | 0.531604 | ||||||||
\(466\) | −296.375 | − | 784.134i | −0.635997 | − | 1.68269i | ||||
\(467\) | −347.282 | −0.743645 | −0.371822 | − | 0.928304i | \(-0.621267\pi\) | ||||
−0.371822 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(468\) | −10.8944 | − | 12.3531i | −0.0232787 | − | 0.0263956i | ||||
\(469\) | 88.2956i | 0.188263i | ||||||||
\(470\) | 39.5980 | + | 104.766i | 0.0842510 | + | 0.222907i | ||||
\(471\) | 724.313i | 1.53782i | ||||||||
\(472\) | −435.269 | − | 230.323i | −0.922180 | − | 0.487972i | ||||
\(473\) | 77.0193 | 0.162832 | ||||||||
\(474\) | 247.196 | − | 93.4313i | 0.521510 | − | 0.197112i | ||||
\(475\) | −562.013 | −1.18319 | ||||||||
\(476\) | 165.598 | + | 187.770i | 0.347895 | + | 0.394476i | ||||
\(477\) | − | 259.880i | − | 0.544822i | ||||||
\(478\) | −277.477 | + | 104.877i | −0.580496 | + | 0.219407i | ||||
\(479\) | − | 29.1811i | − | 0.0609210i | −0.999536 | − | 0.0304605i | \(-0.990303\pi\) | ||
0.999536 | − | 0.0304605i | \(-0.00969737\pi\) | |||||||
\(480\) | −39.5980 | − | 164.633i | −0.0824958 | − | 0.342985i | ||||
\(481\) | −90.7939 | −0.188761 | ||||||||
\(482\) | −325.179 | − | 860.342i | −0.674645 | − | 1.78494i | ||||
\(483\) | −318.191 | −0.658780 | ||||||||
\(484\) | 302.647 | − | 266.909i | 0.625303 | − | 0.551466i | ||||
\(485\) | − | 148.952i | − | 0.307117i | ||||||
\(486\) | −98.4142 | − | 260.380i | −0.202498 | − | 0.535760i | ||||
\(487\) | − | 701.643i | − | 1.44074i | −0.693588 | − | 0.720372i | \(-0.743971\pi\) | ||
0.693588 | − | 0.720372i | \(-0.256029\pi\) | |||||||
\(488\) | 140.995 | − | 266.455i | 0.288924 | − | 0.546015i | ||||
\(489\) | −821.235 | −1.67942 | ||||||||
\(490\) | −20.2965 | + | 7.67134i | −0.0414214 | + | 0.0156558i | ||||
\(491\) | −59.9512 | −0.122100 | −0.0610501 | − | 0.998135i | \(-0.519445\pi\) | ||||
−0.0610501 | + | 0.998135i | \(0.519445\pi\) | |||||||
\(492\) | 276.250 | − | 243.629i | 0.561483 | − | 0.495182i | ||||
\(493\) | 531.095i | 1.07727i | ||||||||
\(494\) | 72.1106 | − | 27.2552i | 0.145973 | − | 0.0551726i | ||||
\(495\) | 18.4691i | 0.0373113i | ||||||||
\(496\) | 741.588 | + | 93.4313i | 1.49514 | + | 0.188370i | ||||
\(497\) | −270.392 | −0.544048 | ||||||||
\(498\) | 8.72792 | + | 23.0919i | 0.0175259 | + | 0.0463693i | ||||
\(499\) | −84.2843 | −0.168906 | −0.0844532 | − | 0.996427i | \(-0.526914\pi\) | ||||
−0.0844532 | + | 0.996427i | \(0.526914\pi\) | |||||||
\(500\) | 195.176 | + | 221.309i | 0.390352 | + | 0.442617i | ||||
\(501\) | 724.157i | 1.44542i | ||||||||
\(502\) | 88.3310 | + | 233.702i | 0.175958 | + | 0.465541i | ||||
\(503\) | − | 409.987i | − | 0.815083i | −0.913187 | − | 0.407542i | \(-0.866386\pi\) | ||
0.913187 | − | 0.407542i | \(-0.133614\pi\) | |||||||
\(504\) | −26.3015 | + | 49.7052i | −0.0521855 | + | 0.0986214i | ||||
\(505\) | −30.4020 | −0.0602020 | ||||||||
\(506\) | −295.578 | + | 111.718i | −0.584146 | + | 0.220786i | ||||
\(507\) | 568.801 | 1.12190 | ||||||||
\(508\) | 330.784 | + | 375.074i | 0.651149 | + | 0.738334i | ||||
\(509\) | − | 477.033i | − | 0.937196i | −0.883411 | − | 0.468598i | \(-0.844759\pi\) | ||
0.883411 | − | 0.468598i | \(-0.155241\pi\) | |||||||
\(510\) | 234.191 | − | 88.5158i | 0.459198 | − | 0.173560i | ||||
\(511\) | − | 183.387i | − | 0.358878i | ||||||
\(512\) | −56.5685 | − | 508.865i | −0.110485 | − | 0.993878i | ||||
\(513\) | 538.607 | 1.04992 | ||||||||
\(514\) | −302.184 | − | 799.503i | −0.587906 | − | 1.55545i | ||||
\(515\) | −66.7737 | −0.129658 | ||||||||
\(516\) | 175.882 | − | 155.114i | 0.340857 | − | 0.300608i | ||||
\(517\) | − | 162.065i | − | 0.313472i | ||||||
\(518\) | 109.598 | + | 289.969i | 0.211579 | + | 0.559786i | ||||
\(519\) | 622.114i | 1.19868i | ||||||||
\(520\) | −16.9848 | − | 8.98754i | −0.0326632 | − | 0.0172837i | ||||
\(521\) | 210.873 | 0.404747 | 0.202373 | − | 0.979308i | \(-0.435135\pi\) | ||||
0.202373 | + | 0.979308i | \(0.435135\pi\) | |||||||
\(522\) | −111.588 | + | 42.1763i | −0.213770 | + | 0.0807974i | ||||
\(523\) | 511.566 | 0.978139 | 0.489069 | − | 0.872245i | \(-0.337337\pi\) | ||||
0.489069 | + | 0.872245i | \(0.337337\pi\) | |||||||
\(524\) | −301.051 | + | 265.502i | −0.574525 | + | 0.506683i | ||||
\(525\) | − | 204.131i | − | 0.388821i | ||||||
\(526\) | −481.970 | + | 182.167i | −0.916292 | + | 0.346326i | ||||
\(527\) | 1105.15i | 2.09705i | ||||||||
\(528\) | −30.6274 | + | 243.098i | −0.0580065 | + | 0.460412i | ||||
\(529\) | −711.784 | −1.34553 | ||||||||
\(530\) | −107.196 | − | 283.614i | −0.202257 | − | 0.535120i | ||||
\(531\) | 163.546 | 0.307997 | ||||||||
\(532\) | −174.090 | − | 197.400i | −0.327238 | − | 0.371053i | ||||
\(533\) | − | 41.8002i | − | 0.0784244i | ||||||
\(534\) | 106.368 | + | 281.422i | 0.199190 | + | 0.527008i | ||||
\(535\) | − | 24.1745i | − | 0.0451859i | ||||||
\(536\) | 235.980 | + | 124.869i | 0.440261 | + | 0.232964i | ||||
\(537\) | 195.314 | 0.363713 | ||||||||
\(538\) | 402.688 | − | 152.202i | 0.748491 | − | 0.282903i | ||||
\(539\) | 31.3970 | 0.0582504 | ||||||||
\(540\) | −88.8040 | − | 100.694i | −0.164452 | − | 0.186471i | ||||
\(541\) | − | 342.417i | − | 0.632933i | −0.948604 | − | 0.316466i | \(-0.897504\pi\) | ||
0.948604 | − | 0.316466i | \(-0.102496\pi\) | |||||||
\(542\) | −708.201 | + | 267.675i | −1.30664 | + | 0.493865i | ||||
\(543\) | − | 1113.76i | − | 2.05112i | ||||||
\(544\) | 736.029 | − | 177.032i | 1.35299 | − | 0.325426i | ||||
\(545\) | −5.96970 | −0.0109536 | ||||||||
\(546\) | 9.89949 | + | 26.1916i | 0.0181309 | + | 0.0479700i | ||||
\(547\) | −441.976 | −0.807999 | −0.404000 | − | 0.914759i | \(-0.632380\pi\) | ||||
−0.404000 | + | 0.914759i | \(0.632380\pi\) | |||||||
\(548\) | −171.941 | + | 151.638i | −0.313761 | + | 0.276711i | ||||
\(549\) | 100.117i | 0.182362i | ||||||||
\(550\) | −71.6711 | − | 189.624i | −0.130311 | − | 0.344771i | ||||
\(551\) | − | 558.331i | − | 1.01331i | ||||||
\(552\) | −449.990 | + | 850.401i | −0.815199 | + | 1.54058i | ||||
\(553\) | −102.392 | −0.185157 | ||||||||
\(554\) | 311.397 | − | 117.697i | 0.562088 | − | 0.212449i | ||||
\(555\) | 309.990 | 0.558540 | ||||||||
\(556\) | 550.992 | − | 485.929i | 0.990993 | − | 0.873973i | ||||
\(557\) | − | 365.710i | − | 0.656571i | −0.944579 | − | 0.328285i | \(-0.893529\pi\) | ||
0.944579 | − | 0.328285i | \(-0.106471\pi\) | |||||||
\(558\) | −232.201 | + | 87.7637i | −0.416131 | + | 0.157283i | ||||
\(559\) | − | 26.6133i | − | 0.0476087i | ||||||
\(560\) | −8.20101 | + | 65.0935i | −0.0146447 | + | 0.116238i | ||||
\(561\) | −362.274 | −0.645765 | ||||||||
\(562\) | −298.233 | − | 789.049i | −0.530663 | − | 1.40400i | ||||
\(563\) | 806.389 | 1.43231 | 0.716154 | − | 0.697943i | \(-0.245901\pi\) | ||||
0.716154 | + | 0.697943i | \(0.245901\pi\) | |||||||
\(564\) | −326.392 | − | 370.094i | −0.578709 | − | 0.656194i | ||||
\(565\) | 21.3485i | 0.0377850i | ||||||||
\(566\) | −244.262 | − | 646.256i | −0.431558 | − | 1.14180i | ||||
\(567\) | 258.894i | 0.456604i | ||||||||
\(568\) | −382.392 | + | 722.653i | −0.673225 | + | 1.27228i | ||||
\(569\) | 222.891 | 0.391725 | 0.195862 | − | 0.980631i | \(-0.437249\pi\) | ||||
0.195862 | + | 0.980631i | \(0.437249\pi\) | |||||||
\(570\) | −246.201 | + | 93.0552i | −0.431932 | + | 0.163255i | ||||
\(571\) | 573.082 | 1.00365 | 0.501823 | − | 0.864970i | \(-0.332663\pi\) | ||||
0.501823 | + | 0.864970i | \(0.332663\pi\) | |||||||
\(572\) | 18.3919 | + | 20.8545i | 0.0321537 | + | 0.0364589i | ||||
\(573\) | − | 331.393i | − | 0.578348i | ||||||
\(574\) | −133.497 | + | 50.4573i | −0.232574 | + | 0.0879047i | ||||
\(575\) | − | 796.008i | − | 1.38436i | ||||||
\(576\) | 95.6468 | + | 140.588i | 0.166053 | + | 0.244076i | ||||
\(577\) | −723.901 | −1.25459 | −0.627297 | − | 0.778780i | \(-0.715839\pi\) | ||||
−0.627297 | + | 0.778780i | \(0.715839\pi\) | |||||||
\(578\) | 191.376 | + | 506.334i | 0.331101 | + | 0.876010i | ||||
\(579\) | 537.068 | 0.927579 | ||||||||
\(580\) | −104.382 | + | 92.0561i | −0.179969 | + | 0.158717i | ||||
\(581\) | − | 9.56498i | − | 0.0164630i | ||||||
\(582\) | 232.024 | + | 613.879i | 0.398667 | + | 1.05477i | ||||
\(583\) | 438.727i | 0.752534i | ||||||||
\(584\) | −490.122 | − | 259.348i | −0.839250 | − | 0.444089i | ||||
\(585\) | 6.38182 | 0.0109091 | ||||||||
\(586\) | −956.065 | + | 361.359i | −1.63151 | + | 0.616653i | ||||
\(587\) | 21.1198 | 0.0359793 | 0.0179896 | − | 0.999838i | \(-0.494273\pi\) | ||||
0.0179896 | + | 0.999838i | \(0.494273\pi\) | |||||||
\(588\) | 71.6985 | − | 63.2321i | 0.121936 | − | 0.107538i | ||||
\(589\) | − | 1161.82i | − | 1.97253i | ||||||
\(590\) | 178.482 | − | 67.4600i | 0.302512 | − | 0.114339i | ||||
\(591\) | 423.761i | 0.717023i | ||||||||
\(592\) | 929.970 | + | 117.165i | 1.57089 | + | 0.197914i | ||||
\(593\) | −128.745 | −0.217108 | −0.108554 | − | 0.994091i | \(-0.534622\pi\) | ||||
−0.108554 | + | 0.994091i | \(0.534622\pi\) | |||||||
\(594\) | 68.6863 | + | 181.727i | 0.115633 | + | 0.305937i | ||||
\(595\) | −97.0051 | −0.163034 | ||||||||
\(596\) | 508.804 | + | 576.930i | 0.853698 | + | 0.968003i | ||||
\(597\) | − | 617.886i | − | 1.03499i | ||||||
\(598\) | 38.6030 | + | 102.134i | 0.0645536 | + | 0.170793i | ||||
\(599\) | 324.130i | 0.541119i | 0.962703 | + | 0.270559i | \(0.0872086\pi\) | ||||
−0.962703 | + | 0.270559i | \(0.912791\pi\) | |||||||
\(600\) | −545.563 | − | 288.685i | −0.909272 | − | 0.481142i | ||||
\(601\) | −721.862 | −1.20110 | −0.600551 | − | 0.799587i | \(-0.705052\pi\) | ||||
−0.600551 | + | 0.799587i | \(0.705052\pi\) | |||||||
\(602\) | −84.9949 | + | 32.1251i | −0.141188 | + | 0.0533639i | ||||
\(603\) | −88.6661 | −0.147042 | ||||||||
\(604\) | −303.608 | − | 344.259i | −0.502662 | − | 0.569966i | ||||
\(605\) | 156.352i | 0.258433i | ||||||||
\(606\) | 125.296 | − | 47.3576i | 0.206760 | − | 0.0781479i | ||||
\(607\) | 705.999i | 1.16310i | 0.813512 | + | 0.581548i | \(0.197553\pi\) | ||||
−0.813512 | + | 0.581548i | \(0.802447\pi\) | |||||||
\(608\) | −773.775 | + | 186.110i | −1.27266 | + | 0.306103i | ||||
\(609\) | 202.794 | 0.332995 | ||||||||
\(610\) | 41.2965 | + | 109.260i | 0.0676991 | + | 0.179115i | ||||
\(611\) | −56.0000 | −0.0916530 | ||||||||
\(612\) | −188.558 | + | 166.293i | −0.308102 | + | 0.271720i | ||||
\(613\) | 21.8269i | 0.0356066i | 0.999842 | + | 0.0178033i | \(0.00566727\pi\) | ||||
−0.999842 | + | 0.0178033i | \(0.994333\pi\) | |||||||
\(614\) | 157.919 | + | 417.814i | 0.257197 | + | 0.680479i | ||||
\(615\) | 142.715i | 0.232057i | ||||||||
\(616\) | 44.4020 | − | 83.9119i | 0.0720812 | − | 0.136221i | ||||
\(617\) | −699.578 | −1.13384 | −0.566919 | − | 0.823774i | \(-0.691865\pi\) | ||||
−0.566919 | + | 0.823774i | \(0.691865\pi\) | |||||||
\(618\) | 275.196 | − | 104.014i | 0.445301 | − | 0.168308i | ||||
\(619\) | 96.1981 | 0.155409 | 0.0777044 | − | 0.996976i | \(-0.475241\pi\) | ||||
0.0777044 | + | 0.996976i | \(0.475241\pi\) | |||||||
\(620\) | −217.206 | + | 191.558i | −0.350332 | + | 0.308964i | ||||
\(621\) | 762.858i | 1.22843i | ||||||||
\(622\) | 23.1960 | − | 8.76725i | 0.0372925 | − | 0.0140953i | ||||
\(623\) | − | 116.569i | − | 0.187109i | ||||||
\(624\) | 84.0000 | + | 10.5830i | 0.134615 | + | 0.0169599i | ||||
\(625\) | 450.618 | 0.720989 | ||||||||
\(626\) | 289.948 | + | 767.131i | 0.463176 | + | 1.22545i | ||||
\(627\) | 380.853 | 0.607421 | ||||||||
\(628\) | −561.286 | − | 636.439i | −0.893768 | − | 1.01344i | ||||
\(629\) | 1385.88i | 2.20331i | ||||||||
\(630\) | −7.70354 | − | 20.3816i | −0.0122278 | − | 0.0323518i | ||||
\(631\) | 269.399i | 0.426940i | 0.976950 | + | 0.213470i | \(0.0684766\pi\) | ||||
−0.976950 | + | 0.213470i | \(0.931523\pi\) | |||||||
\(632\) | −144.804 | + | 273.654i | −0.229120 | + | 0.432997i | ||||
\(633\) | 560.098 | 0.884830 | ||||||||
\(634\) | 243.799 | − | 92.1474i | 0.384541 | − | 0.145343i | ||||
\(635\) | −193.769 | −0.305148 | ||||||||
\(636\) | 883.578 | + | 1001.88i | 1.38927 | + | 1.57529i | ||||
\(637\) | − | 10.8489i | − | 0.0170313i | ||||||
\(638\) | 188.382 | − | 71.2016i | 0.295269 | − | 0.111601i | ||||
\(639\) | − | 271.527i | − | 0.424924i | ||||||
\(640\) | 162.372 | + | 113.974i | 0.253706 | + | 0.178085i | ||||
\(641\) | 635.813 | 0.991908 | 0.495954 | − | 0.868349i | \(-0.334818\pi\) | ||||
0.495954 | + | 0.868349i | \(0.334818\pi\) | |||||||
\(642\) | 37.6569 | + | 99.6307i | 0.0586555 | + | 0.155188i | ||||
\(643\) | 1281.70 | 1.99332 | 0.996658 | − | 0.0816828i | \(-0.0260295\pi\) | ||||
0.996658 | + | 0.0816828i | \(0.0260295\pi\) | |||||||
\(644\) | 279.588 | − | 246.573i | 0.434143 | − | 0.382878i | ||||
\(645\) | 90.8634i | 0.140874i | ||||||||
\(646\) | −416.024 | − | 1100.70i | −0.644001 | − | 1.70387i | ||||
\(647\) | − | 260.761i | − | 0.403031i | −0.979485 | − | 0.201516i | \(-0.935413\pi\) | ||
0.979485 | − | 0.201516i | \(-0.0645867\pi\) | |||||||
\(648\) | 691.924 | + | 366.132i | 1.06778 | + | 0.565018i | ||||
\(649\) | −276.098 | −0.425420 | ||||||||
\(650\) | −65.5227 | + | 24.7653i | −0.100804 | + | 0.0381004i | ||||
\(651\) | 421.990 | 0.648218 | ||||||||
\(652\) | 721.602 | − | 636.393i | 1.10675 | − | 0.976063i | ||||
\(653\) | − | 1090.58i | − | 1.67011i | −0.550167 | − | 0.835055i | \(-0.685436\pi\) | ||
0.550167 | − | 0.835055i | \(-0.314564\pi\) | |||||||
\(654\) | 24.6030 | − | 9.29907i | 0.0376193 | − | 0.0142188i | ||||
\(655\) | − | 155.527i | − | 0.237446i | ||||||
\(656\) | −53.9411 | + | 428.144i | −0.0822273 | + | 0.652659i | ||||
\(657\) | 184.156 | 0.280299 | ||||||||
\(658\) | 67.5980 | + | 178.847i | 0.102732 | + | 0.271805i | ||||
\(659\) | −362.780 | −0.550500 | −0.275250 | − | 0.961373i | \(-0.588761\pi\) | ||||
−0.275250 | + | 0.961373i | \(0.588761\pi\) | |||||||
\(660\) | −62.7939 | − | 71.2016i | −0.0951423 | − | 0.107881i | ||||
\(661\) | 117.834i | 0.178266i | 0.996020 | + | 0.0891330i | \(0.0284096\pi\) | ||||
−0.996020 | + | 0.0891330i | \(0.971590\pi\) | |||||||
\(662\) | 151.505 | + | 400.844i | 0.228859 | + | 0.605504i | ||||
\(663\) | 125.180i | 0.188809i | ||||||||
\(664\) | −25.5635 | − | 13.5269i | −0.0384992 | − | 0.0203719i | ||||
\(665\) | 101.980 | 0.153353 | ||||||||
\(666\) | −291.186 | + | 110.058i | −0.437216 | + | 0.165252i | ||||
\(667\) | 790.794 | 1.18560 | ||||||||
\(668\) | −561.166 | − | 636.302i | −0.840068 | − | 0.952548i | ||||
\(669\) | − | 36.1326i | − | 0.0540099i | ||||||
\(670\) | −96.7636 | + | 36.5732i | −0.144423 | + | 0.0545869i | ||||
\(671\) | − | 169.017i | − | 0.251888i | ||||||
\(672\) | −67.5980 | − | 281.046i | −0.100592 | − | 0.418223i | ||||
\(673\) | −6.56854 | −0.00976009 | −0.00488005 | − | 0.999988i | \(-0.501553\pi\) | ||||
−0.00488005 | + | 0.999988i | \(0.501553\pi\) | |||||||
\(674\) | 116.000 | + | 306.907i | 0.172107 | + | 0.455352i | ||||
\(675\) | −489.401 | −0.725039 | ||||||||
\(676\) | −499.794 | + | 440.777i | −0.739340 | + | 0.652037i | ||||
\(677\) | 125.796i | 0.185813i | 0.995675 | + | 0.0929066i | \(0.0296158\pi\) | ||||
−0.995675 | + | 0.0929066i | \(0.970384\pi\) | |||||||
\(678\) | −33.2548 | − | 87.9840i | −0.0490484 | − | 0.129770i | ||||
\(679\) | − | 254.277i | − | 0.374487i | ||||||
\(680\) | −137.186 | + | 259.257i | −0.201744 | + | 0.381260i | ||||
\(681\) | 361.245 | 0.530462 | ||||||||
\(682\) | 392.000 | − | 148.162i | 0.574780 | − | 0.217246i | ||||
\(683\) | −553.775 | −0.810797 | −0.405399 | − | 0.914140i | \(-0.632867\pi\) | ||||
−0.405399 | + | 0.914140i | \(0.632867\pi\) | |||||||
\(684\) | 198.228 | − | 174.821i | 0.289808 | − | 0.255586i | ||||
\(685\) | − | 88.8274i | − | 0.129675i | ||||||
\(686\) | −34.6482 | + | 13.0958i | −0.0505076 | + | 0.0190901i | ||||
\(687\) | − | 255.652i | − | 0.372128i | ||||||
\(688\) | −34.3431 | + | 272.590i | −0.0499174 | + | 0.396207i | ||||
\(689\) | 151.598 | 0.220026 | ||||||||
\(690\) | −131.799 | − | 348.707i | −0.191013 | − | 0.505373i | ||||
\(691\) | −1046.83 | −1.51494 | −0.757471 | − | 0.652868i | \(-0.773565\pi\) | ||||
−0.757471 | + | 0.652868i | \(0.773565\pi\) | |||||||
\(692\) | −482.090 | − | 546.639i | −0.696662 | − | 0.789941i | ||||
\(693\) | 31.5287i | 0.0454960i | ||||||||
\(694\) | −77.5635 | − | 205.214i | −0.111763 | − | 0.295697i | ||||
\(695\) | 284.651i | 0.409569i | ||||||||
\(696\) | 286.794 | − | 541.990i | 0.412060 | − | 0.778721i | ||||
\(697\) | −638.039 | −0.915407 | ||||||||
\(698\) | −867.090 | + | 327.729i | −1.24225 | + | 0.469526i | ||||
\(699\) | −1431.02 | −2.04724 | ||||||||
\(700\) | 158.186 | + | 179.366i | 0.225980 | + | 0.256237i | ||||
\(701\) | − | 625.993i | − | 0.893000i | −0.894784 | − | 0.446500i | \(-0.852670\pi\) | ||
0.894784 | − | 0.446500i | \(-0.147330\pi\) | |||||||
\(702\) | 62.7939 | − | 23.7339i | 0.0894501 | − | 0.0338089i | ||||
\(703\) | − | 1456.95i | − | 2.07248i | ||||||
\(704\) | −161.470 | − | 237.339i | −0.229361 | − | 0.337129i | ||||
\(705\) | 191.196 | 0.271200 | ||||||||
\(706\) | 55.2233 | + | 146.107i | 0.0782200 | + | 0.206951i | ||||
\(707\) | −51.8995 | −0.0734081 | ||||||||
\(708\) | −630.500 | + | 556.048i | −0.890536 | + | 0.785379i | ||||
\(709\) | 593.492i | 0.837083i | 0.908198 | + | 0.418541i | \(0.137459\pi\) | ||||
−0.908198 | + | 0.418541i | \(0.862541\pi\) | |||||||
\(710\) | −112.000 | − | 296.324i | −0.157746 | − | 0.417358i | ||||
\(711\) | − | 102.822i | − | 0.144615i | ||||||
\(712\) | −311.543 | − | 164.853i | −0.437561 | − | 0.231535i | ||||
\(713\) | 1645.55 | 2.30792 | ||||||||
\(714\) | 399.789 | − | 151.106i | 0.559928 | − | 0.211633i | ||||
\(715\) | −10.7737 | −0.0150682 | ||||||||
\(716\) | −171.618 | + | 151.353i | −0.239690 | + | 0.211387i | ||||
\(717\) | 506.389i | 0.706261i | ||||||||
\(718\) | 683.065 | − | 258.174i | 0.951344 | − | 0.359574i | ||||
\(719\) | − | 611.505i | − | 0.850493i | −0.905078 | − | 0.425247i | \(-0.860187\pi\) | ||
0.905078 | − | 0.425247i | \(-0.139813\pi\) | |||||||
\(720\) | −65.3667 | − | 8.23543i | −0.0907870 | − | 0.0114381i | ||||
\(721\) | −113.990 | −0.158100 | ||||||||
\(722\) | 182.094 | + | 481.775i | 0.252208 | + | 0.667279i | ||||
\(723\) | −1570.10 | −2.17165 | ||||||||
\(724\) | 863.075 | + | 978.635i | 1.19209 | + | 1.35171i | ||||
\(725\) | 507.323i | 0.699756i | ||||||||
\(726\) | −243.551 | − | 644.376i | −0.335470 | − | 0.887570i | ||||
\(727\) | 944.144i | 1.29868i | 0.760496 | + | 0.649342i | \(0.224956\pi\) | ||||
−0.760496 | + | 0.649342i | \(0.775044\pi\) | |||||||
\(728\) | −28.9949 | − | 15.3427i | −0.0398282 | − | 0.0210751i | ||||
\(729\) | 405.489 | 0.556227 | ||||||||
\(730\) | 200.975 | − | 75.9613i | 0.275308 | − | 0.104057i | ||||
\(731\) | −406.225 | −0.555712 | ||||||||
\(732\) | −340.392 | − | 385.968i | −0.465016 | − | 0.527279i | ||||
\(733\) | − | 218.254i | − | 0.297755i | −0.988856 | − | 0.148878i | \(-0.952434\pi\) | ||
0.988856 | − | 0.148878i | \(-0.0475660\pi\) | |||||||
\(734\) | −412.965 | + | 156.086i | −0.562622 | + | 0.212651i | ||||
\(735\) | 37.0405i | 0.0503953i | ||||||||
\(736\) | −263.598 | − | 1095.94i | −0.358149 | − | 1.48905i | ||||
\(737\) | 149.685 | 0.203101 | ||||||||
\(738\) | −50.6690 | − | 134.058i | −0.0686572 | − | 0.181650i | ||||
\(739\) | −7.29942 | −0.00987743 | −0.00493872 | − | 0.999988i | \(-0.501572\pi\) | ||||
−0.00493872 | + | 0.999988i | \(0.501572\pi\) | |||||||
\(740\) | −272.382 | + | 240.218i | −0.368084 | + | 0.324619i | ||||
\(741\) | − | 131.600i | − | 0.177598i | ||||||
\(742\) | −182.995 | − | 484.159i | −0.246624 | − | 0.652506i | ||||
\(743\) | − | 106.867i | − | 0.143832i | −0.997411 | − | 0.0719159i | \(-0.977089\pi\) | ||
0.997411 | − | 0.0719159i | \(-0.0229113\pi\) | |||||||
\(744\) | 596.784 | − | 1127.82i | 0.802129 | − | 1.51588i | ||||
\(745\) | −298.051 | −0.400068 | ||||||||
\(746\) | −470.613 | + | 177.875i | −0.630849 | + | 0.238438i | ||||
\(747\) | 9.60512 | 0.0128583 | ||||||||
\(748\) | 318.323 | − | 280.734i | 0.425565 | − | 0.375313i | ||||
\(749\) | − | 41.2684i | − | 0.0550980i | ||||||
\(750\) | 471.196 | − | 178.095i | 0.628261 | − | 0.237460i | ||||
\(751\) | 127.463i | 0.169725i | 0.996393 | + | 0.0848624i | \(0.0270451\pi\) | ||||
−0.996393 | + | 0.0848624i | \(0.972955\pi\) | |||||||
\(752\) | 573.588 | + | 72.2653i | 0.762750 | + | 0.0960974i | ||||
\(753\) | 426.500 | 0.566400 | ||||||||
\(754\) | −24.6030 | − | 65.0935i | −0.0326300 | − | 0.0863309i | ||||
\(755\) | 177.849 | 0.235562 | ||||||||
\(756\) | −151.598 | − | 171.896i | −0.200526 | − | 0.227376i | ||||
\(757\) | 704.275i | 0.930350i | 0.885219 | + | 0.465175i | \(0.154009\pi\) | ||||
−0.885219 | + | 0.465175i | \(0.845991\pi\) | |||||||
\(758\) | 202.250 | + | 535.103i | 0.266820 | + | 0.705940i | ||||
\(759\) | 539.422i | 0.710701i | ||||||||
\(760\) | 144.221 | − | 272.552i | 0.189765 | − | 0.358622i | ||||
\(761\) | −1002.93 | −1.31791 | −0.658955 | − | 0.752182i | \(-0.729001\pi\) | ||||
−0.658955 | + | 0.752182i | \(0.729001\pi\) | |||||||
\(762\) | 798.583 | − | 301.836i | 1.04801 | − | 0.396110i | ||||
\(763\) | −10.1909 | −0.0133564 | ||||||||
\(764\) | 256.804 | + | 291.188i | 0.336131 | + | 0.381137i | ||||
\(765\) | − | 97.4121i | − | 0.127336i | ||||||
\(766\) | 199.980 | − | 75.5853i | 0.261070 | − | 0.0986753i | ||||
\(767\) | 95.4028i | 0.124384i | ||||||||
\(768\) | −846.725 | − | 216.796i | −1.10251 | − | 0.282286i | ||||
\(769\) | −646.950 | −0.841288 | −0.420644 | − | 0.907226i | \(-0.638196\pi\) | ||||
−0.420644 | + | 0.907226i | \(0.638196\pi\) | |||||||
\(770\) | 13.0051 | + | 34.4081i | 0.0168897 | + | 0.0446859i | ||||
\(771\) | −1459.07 | −1.89244 | ||||||||
\(772\) | −471.911 | + | 416.186i | −0.611283 | + | 0.539101i | ||||
\(773\) | − | 564.265i | − | 0.729968i | −0.931014 | − | 0.364984i | \(-0.881075\pi\) | ||
0.931014 | − | 0.364984i | \(-0.118925\pi\) | |||||||
\(774\) | −32.2599 | − | 85.3516i | −0.0416794 | − | 0.110273i | ||||
\(775\) | 1055.68i | 1.36217i | ||||||||
\(776\) | −679.584 | − | 359.602i | −0.875752 | − | 0.463404i | ||||
\(777\) | 529.186 | 0.681063 | ||||||||
\(778\) | −144.392 | + | 54.5750i | −0.185594 | + | 0.0701478i | ||||
\(779\) | 670.759 | 0.861052 | ||||||||
\(780\) | −24.6030 | + | 21.6978i | −0.0315423 | + | 0.0278177i | ||||
\(781\) | 458.389i | 0.586926i | ||||||||
\(782\) | 1558.97 | − | 589.237i | 1.99357 | − | 0.753500i | ||||
\(783\) | − | 486.195i | − | 0.620939i | ||||||
\(784\) | −14.0000 | + | 111.122i | −0.0178571 | + | 0.141737i | ||||
\(785\) | 328.794 | 0.418846 | ||||||||
\(786\) | 242.267 | + | 640.978i | 0.308228 | + | 0.815494i | ||||
\(787\) | 923.345 | 1.17325 | 0.586623 | − | 0.809860i | \(-0.300457\pi\) | ||||
0.586623 | + | 0.809860i | \(0.300457\pi\) | |||||||
\(788\) | −328.382 | − | 372.350i | −0.416728 | − | 0.472525i | ||||
\(789\) | 879.582i | 1.11481i | ||||||||
\(790\) | −42.4121 | − | 112.212i | −0.0536862 | − | 0.142040i | ||||
\(791\) | 36.4442i | 0.0460735i | ||||||||
\(792\) | 84.2641 | + | 44.5884i | 0.106394 | + | 0.0562984i | ||||
\(793\) | −58.4020 | −0.0736469 | ||||||||
\(794\) | 1230.10 | − | 464.932i | 1.54924 | − | 0.585557i | ||||
\(795\) | −517.588 | −0.651054 | ||||||||
\(796\) | 478.814 | + | 542.924i | 0.601525 | + | 0.682066i | ||||
\(797\) | − | 207.983i | − | 0.260957i | −0.991451 | − | 0.130479i | \(-0.958349\pi\) | ||
0.991451 | − | 0.130479i | \(-0.0416514\pi\) | |||||||
\(798\) | −420.291 | + | 158.855i | −0.526681 | + | 0.199067i | ||||
\(799\) | 854.785i | 1.06982i | ||||||||
\(800\) | 703.084 | − | 169.108i | 0.878855 | − | 0.211385i | ||||
\(801\) | 117.058 | 0.146140 | ||||||||
\(802\) | 225.421 | + | 596.409i | 0.281074 | + | 0.743652i | ||||
\(803\) | −310.891 | −0.387162 | ||||||||
\(804\) | 341.823 | − | 301.460i | 0.425153 | − | 0.374950i | ||||
\(805\) | 144.439i | 0.179428i | ||||||||
\(806\) | −51.1960 | − | 135.452i | −0.0635186 | − | 0.168054i | ||||
\(807\) | − | 734.896i | − | 0.910652i | ||||||
\(808\) | −73.3970 | + | 138.707i | −0.0908378 | + | 0.171667i | ||||
\(809\) | 340.540 | 0.420939 | 0.210470 | − | 0.977600i | \(-0.432501\pi\) | ||||
0.210470 | + | 0.977600i | \(0.432501\pi\) | |||||||
\(810\) | −283.724 | + | 107.237i | −0.350276 | + | 0.132392i | ||||
\(811\) | −907.380 | −1.11884 | −0.559420 | − | 0.828884i | \(-0.688976\pi\) | ||||
−0.559420 | + | 0.828884i | \(0.688976\pi\) | |||||||
\(812\) | −178.191 | + | 157.150i | −0.219447 | + | 0.193534i | ||||
\(813\) | 1292.45i | 1.58973i | ||||||||
\(814\) | 491.578 | − | 185.799i | 0.603904 | − | 0.228254i | ||||
\(815\) | 372.791i | 0.457412i | ||||||||
\(816\) | 161.539 | − | 1282.18i | 0.197965 | − | 1.57130i | ||||
\(817\) | 427.058 | 0.522715 | ||||||||
\(818\) | 102.718 | + | 271.766i | 0.125572 | + | 0.332232i | ||||
\(819\) | 10.8944 | 0.0133021 | ||||||||
\(820\) | −110.593 | − | 125.401i | −0.134869 | − | 0.152928i | ||||
\(821\) | 633.423i | 0.771526i | 0.922598 | + | 0.385763i | \(0.126062\pi\) | ||||
−0.922598 | + | 0.385763i | \(0.873938\pi\) | |||||||
\(822\) | 138.368 | + | 366.086i | 0.168330 | + | 0.445360i | ||||
\(823\) | − | 143.649i | − | 0.174544i | −0.996185 | − | 0.0872718i | \(-0.972185\pi\) | ||
0.996185 | − | 0.0872718i | \(-0.0278149\pi\) | |||||||
\(824\) | −161.206 | + | 304.651i | −0.195638 | + | 0.369722i | ||||
\(825\) | −346.059 | −0.419465 | ||||||||
\(826\) | 304.688 | − | 115.161i | 0.368872 | − | 0.139421i | ||||
\(827\) | 1545.57 | 1.86888 | 0.934442 | − | 0.356114i | \(-0.115899\pi\) | ||||
0.934442 | + | 0.356114i | \(0.115899\pi\) | |||||||
\(828\) | 247.608 | + | 280.761i | 0.299044 | + | 0.339084i | ||||
\(829\) | − | 743.956i | − | 0.897413i | −0.893679 | − | 0.448707i | \(-0.851885\pi\) | ||
0.893679 | − | 0.448707i | \(-0.148115\pi\) | |||||||
\(830\) | 10.4823 | − | 3.96195i | 0.0126293 | − | 0.00477343i | ||||
\(831\) | − | 568.291i | − | 0.683864i | ||||||
\(832\) | −82.0101 | + | 55.7944i | −0.0985698 | + | 0.0670606i | ||||
\(833\) | −165.598 | −0.198797 | ||||||||
\(834\) | −443.404 | − | 1173.14i | −0.531660 | − | 1.40664i | ||||
\(835\) | 328.723 | 0.393681 | ||||||||
\(836\) | −334.648 | + | 295.131i | −0.400296 | + | 0.353028i | ||||
\(837\) | − | 1011.71i | − | 1.20874i | ||||||
\(838\) | 499.933 | + | 1322.70i | 0.596579 | + | 1.57840i | ||||
\(839\) | 96.3107i | 0.114792i | 0.998351 | + | 0.0573961i | \(0.0182798\pi\) | ||||
−0.998351 | + | 0.0573961i | \(0.981720\pi\) | |||||||
\(840\) | 98.9949 | + | 52.3832i | 0.117851 | + | 0.0623610i | ||||
\(841\) | 337.000 | 0.400713 | ||||||||
\(842\) | 228.221 | − | 86.2595i | 0.271047 | − | 0.102446i | ||||
\(843\) | −1439.99 | −1.70818 | ||||||||
\(844\) | −492.146 | + | 434.032i | −0.583112 | + | 0.514256i | ||||
\(845\) | − | 258.201i | − | 0.305563i | ||||||
\(846\) | −179.598 | + | 67.8817i | −0.212291 | + | 0.0802384i | ||||
\(847\) | 266.909i | 0.315123i | ||||||||
\(848\) | −1552.76 | − | 195.630i | −1.83109 | − | 0.230696i | ||||
\(849\) | −1179.40 | −1.38917 | ||||||||
\(850\) | 378.017 | + | 1000.14i | 0.444726 | + | 1.17663i | ||||
\(851\) | 2063.56 | 2.42486 | ||||||||
\(852\) | 923.176 | + | 1046.78i | 1.08354 | + | 1.22862i | ||||
\(853\) | − | 904.866i | − | 1.06080i | −0.847746 | − | 0.530402i | \(-0.822041\pi\) | ||
0.847746 | − | 0.530402i | \(-0.177959\pi\) | |||||||
\(854\) | 70.4975 | + | 186.519i | 0.0825497 | + | 0.218406i | ||||
\(855\) | 102.408i | 0.119775i | ||||||||
\(856\) | −110.294 | − | 58.3623i | −0.128849 | − | 0.0681803i | ||||
\(857\) | 160.932 | 0.187785 | 0.0938926 | − | 0.995582i | \(-0.470069\pi\) | ||||
0.0938926 | + | 0.995582i | \(0.470069\pi\) | |||||||
\(858\) | 44.4020 | − | 16.7824i | 0.0517506 | − | 0.0195599i | ||||
\(859\) | 231.693 | 0.269724 | 0.134862 | − | 0.990864i | \(-0.456941\pi\) | ||||
0.134862 | + | 0.990864i | \(0.456941\pi\) | |||||||
\(860\) | −70.4121 | − | 79.8398i | −0.0818746 | − | 0.0928370i | ||||
\(861\) | 243.629i | 0.282961i | ||||||||
\(862\) | −1101.66 | + | 416.388i | −1.27803 | + | 0.483048i | ||||
\(863\) | − | 1337.35i | − | 1.54965i | −0.632176 | − | 0.774825i | \(-0.717838\pi\) | ||
0.632176 | − | 0.774825i | \(-0.282162\pi\) | |||||||
\(864\) | −673.803 | + | 162.065i | −0.779865 | + | 0.187575i | ||||
\(865\) | 282.402 | 0.326476 | ||||||||
\(866\) | 97.3654 | + | 257.605i | 0.112431 | + | 0.297465i | ||||
\(867\) | 924.046 | 1.06580 | ||||||||
\(868\) | −370.794 | + | 327.010i | −0.427182 | + | 0.376739i | ||||
\(869\) | 173.583i | 0.199750i | ||||||||
\(870\) | 84.0000 | + | 222.243i | 0.0965517 | + | 0.255452i | ||||
\(871\) | − | 51.7223i | − | 0.0593827i | ||||||
\(872\) | −14.4121 | + | 27.2363i | −0.0165277 | + | 0.0312343i | ||||
\(873\) | 255.344 | 0.292490 | ||||||||
\(874\) | −1638.92 | + | 619.455i | −1.87520 | + | 0.708759i | ||||
\(875\) | −195.176 | −0.223058 | ||||||||
\(876\) | −709.955 | + | 626.122i | −0.810451 | + | 0.714751i | ||||
\(877\) | 1436.14i | 1.63755i | 0.574111 | + | 0.818777i | \(0.305348\pi\) | ||||
−0.574111 | + | 0.818777i | \(0.694652\pi\) | |||||||
\(878\) | −824.181 | + | 311.511i | −0.938703 | + | 0.354796i | ||||
\(879\) | 1744.79i | 1.98498i | ||||||||
\(880\) | 110.352 | + | 13.9030i | 0.125399 | + | 0.0157988i | ||||
\(881\) | −186.706 | −0.211926 | −0.105963 | − | 0.994370i | \(-0.533792\pi\) | ||||
−0.105963 | + | 0.994370i | \(0.533792\pi\) | |||||||
\(882\) | −13.1508 | − | 34.7936i | −0.0149102 | − | 0.0394486i | ||||
\(883\) | 1277.99 | 1.44733 | 0.723664 | − | 0.690153i | \(-0.242457\pi\) | ||||
0.723664 | + | 0.690153i | \(0.242457\pi\) | |||||||
\(884\) | −97.0051 | − | 109.993i | −0.109734 | − | 0.124427i | ||||
\(885\) | − | 325.726i | − | 0.368052i | ||||||
\(886\) | −344.402 | − | 911.202i | −0.388716 | − | 1.02844i | ||||
\(887\) | − | 980.717i | − | 1.10566i | −0.833295 | − | 0.552828i | \(-0.813549\pi\) | ||
0.833295 | − | 0.552828i | \(-0.186451\pi\) | |||||||
\(888\) | 748.382 | − | 1414.31i | 0.842772 | − | 1.59269i | ||||
\(889\) | −330.784 | −0.372085 | ||||||||
\(890\) | 127.748 | − | 48.2844i | 0.143538 | − | 0.0542521i | ||||
\(891\) | 438.897 | 0.492590 | ||||||||
\(892\) | 28.0000 | + | 31.7490i | 0.0313901 | + | 0.0355931i | ||||
\(893\) | − | 898.621i | − | 1.00629i | ||||||
\(894\) | 1228.36 | − | 464.277i | 1.37401 | − | 0.519326i | ||||
\(895\) | − | 88.6605i | − | 0.0990621i | ||||||
\(896\) | 277.186 | + | 194.566i | 0.309359 | + | 0.217150i | ||||
\(897\) | 186.392 | 0.207795 | ||||||||
\(898\) | 186.704 | + | 493.971i | 0.207910 | + | 0.550079i | ||||
\(899\) | −1048.76 | −1.16659 | ||||||||
\(900\) | −180.119 | + | 158.850i | −0.200132 | + | 0.176500i | ||||
\(901\) | − | 2313.99i | − | 2.56825i | ||||||
\(902\) | 85.5391 | + | 226.315i | 0.0948327 | + | 0.250904i | ||||
\(903\) | 155.114i | 0.171776i | ||||||||
\(904\) | 97.4012 | + | 51.5398i | 0.107745 | + | 0.0570131i | ||||
\(905\) | −505.578 | −0.558649 | ||||||||
\(906\) | −732.975 | + | 277.038i | −0.809023 | + | 0.305782i | ||||
\(907\) | −658.372 | −0.725878 | −0.362939 | − | 0.931813i | \(-0.618227\pi\) | ||||
−0.362939 | + | 0.931813i | \(0.618227\pi\) | |||||||
\(908\) | −317.418 | + | 279.937i | −0.349580 | + | 0.308300i | ||||
\(909\) | − | 52.1173i | − | 0.0573348i | ||||||
\(910\) | 11.8894 | − | 4.49377i | 0.0130653 | − | 0.00493821i | ||||
\(911\) | − | 276.507i | − | 0.303520i | −0.988417 | − | 0.151760i | \(-0.951506\pi\) | ||
0.988417 | − | 0.151760i | \(-0.0484941\pi\) | |||||||
\(912\) | −169.823 | + | 1347.93i | −0.186210 | + | 1.47799i | ||||
\(913\) | −16.2153 | −0.0177605 | ||||||||
\(914\) | −363.681 | − | 962.210i | −0.397901 | − | 1.05275i | ||||
\(915\) | 199.397 | 0.217920 | ||||||||
\(916\) | 198.111 | + | 224.636i | 0.216278 | + | 0.245236i | ||||
\(917\) | − | 265.502i | − | 0.289533i | ||||||
\(918\) | −362.274 | − | 958.487i | −0.394634 | − | 1.04410i | ||||
\(919\) | − | 1339.73i | − | 1.45782i | −0.684611 | − | 0.728908i | \(-0.740028\pi\) | ||
0.684611 | − | 0.728908i | \(-0.259972\pi\) | |||||||
\(920\) | 386.030 | + | 204.268i | 0.419598 | + | 0.222030i | ||||
\(921\) | 762.500 | 0.827904 | ||||||||
\(922\) | −378.327 | + | 142.994i | −0.410333 | + | 0.155091i | ||||
\(923\) | 158.392 | 0.171606 | ||||||||
\(924\) | −107.196 | − | 121.549i | −0.116013 | − | 0.131546i | ||||
\(925\) | 1323.85i | 1.43119i | ||||||||
\(926\) | −1351.96 | + | 510.993i | −1.46000 | + | 0.551828i | ||||
\(927\) | − | 114.468i | − | 0.123482i | ||||||
\(928\) | 168.000 | + | 698.478i | 0.181034 | + | 0.752671i | ||||
\(929\) | 35.4012 | 0.0381067 | 0.0190534 | − | 0.999818i | \(-0.493935\pi\) | ||||
0.0190534 | + | 0.999818i | \(0.493935\pi\) | |||||||
\(930\) | 174.794 | + | 462.461i | 0.187950 | + | 0.497270i | ||||
\(931\) | 174.090 | 0.186993 | ||||||||
\(932\) | 1257.41 | − | 1108.93i | 1.34915 | − | 1.18984i | ||||
\(933\) | − | 42.3320i | − | 0.0453719i | ||||||
\(934\) | −245.566 | − | 649.705i | −0.262918 | − | 0.695616i | ||||
\(935\) | 164.450i | 0.175883i | ||||||||
\(936\) | 15.4071 | − | 29.1166i | 0.0164605 | − | 0.0311075i | ||||
\(937\) | 610.235 | 0.651265 | 0.325633 | − | 0.945496i | \(-0.394423\pi\) | ||||
0.325633 | + | 0.945496i | \(0.394423\pi\) | |||||||
\(938\) | −165.186 | + | 62.4344i | −0.176104 | + | 0.0665612i | ||||
\(939\) | 1399.99 | 1.49094 | ||||||||
\(940\) | −168.000 | + | 148.162i | −0.178723 | + | 0.157619i | ||||
\(941\) | − | 1852.90i | − | 1.96907i | −0.175175 | − | 0.984537i | \(-0.556049\pi\) | ||
0.175175 | − | 0.984537i | \(-0.443951\pi\) | |||||||
\(942\) | −1355.07 | + | 512.166i | −1.43850 | + | 0.543701i | ||||
\(943\) | 950.032i | 1.00746i | ||||||||
\(944\) | 123.113 | − | 977.177i | 0.130416 | − | 1.03514i | ||||
\(945\) | 88.8040 | 0.0939725 | ||||||||
\(946\) | 54.4609 | + | 144.090i | 0.0575697 | + | 0.152315i | ||||
\(947\) | −1832.90 | −1.93548 | −0.967738 | − | 0.251959i | \(-0.918925\pi\) | ||||
−0.967738 | + | 0.251959i | \(0.918925\pi\) | |||||||
\(948\) | 349.588 | + | 396.395i | 0.368764 | + | 0.418139i | ||||
\(949\) | 107.426i | 0.113199i | ||||||||
\(950\) | −397.403 | − | 1051.43i | −0.418319 | − | 1.10677i | ||||
\(951\) | − | 444.927i | − | 0.467852i | ||||||
\(952\) | −234.191 | + | 442.579i | −0.245999 | + | 0.464894i | ||||
\(953\) | 349.687 | 0.366933 | 0.183467 | − | 0.983026i | \(-0.441268\pi\) | ||||
0.183467 | + | 0.983026i | \(0.441268\pi\) | |||||||
\(954\) | 486.191 | − | 183.763i | 0.509634 | − | 0.192624i | ||||
\(955\) | −150.432 | −0.157521 | ||||||||
\(956\) | −392.412 | − | 444.954i | −0.410473 | − | 0.465433i | ||||
\(957\) | − | 343.792i | − | 0.359239i | ||||||
\(958\) | 54.5929 | − | 20.6342i | 0.0569864 | − | 0.0215388i | ||||
\(959\) | − | 151.638i | − | 0.158121i | ||||||
\(960\) | 280.000 | − | 190.494i | 0.291667 | − | 0.198431i | ||||
\(961\) | −1221.35 | −1.27092 | ||||||||
\(962\) | −64.2010 | − | 169.860i | −0.0667370 | − | 0.176570i | ||||
\(963\) | 41.4416 | 0.0430338 | ||||||||
\(964\) | 1379.62 | − | 1216.71i | 1.43114 | − | 1.26214i | ||||
\(965\) | − | 243.796i | − | 0.252639i | ||||||
\(966\) | −224.995 | − | 595.281i | −0.232914 | − | 0.616233i | ||||
\(967\) | − | 632.128i | − | 0.653700i | −0.945076 | − | 0.326850i | \(-0.894013\pi\) | ||
0.945076 | − | 0.326850i | \(-0.105987\pi\) | |||||||
\(968\) | 713.345 | + | 377.467i | 0.736927 | + | 0.389945i | ||||
\(969\) | −2008.74 | −2.07301 | ||||||||
\(970\) | 278.664 | − | 105.325i | 0.287282 | − | 0.108582i | ||||
\(971\) | 656.497 | 0.676104 | 0.338052 | − | 0.941128i | \(-0.390232\pi\) | ||||
0.338052 | + | 0.941128i | \(0.390232\pi\) | |||||||
\(972\) | 417.536 | − | 368.232i | 0.429564 | − | 0.378840i | ||||
\(973\) | 485.929i | 0.499413i | ||||||||
\(974\) | 1312.65 | − | 496.136i | 1.34769 | − | 0.509380i | ||||
\(975\) | 119.577i | 0.122643i | ||||||||
\(976\) | 598.191 | + | 75.3650i | 0.612901 | + | 0.0772182i | ||||
\(977\) | 169.314 | 0.173300 | 0.0866498 | − | 0.996239i | \(-0.472384\pi\) | ||||
0.0866498 | + | 0.996239i | \(0.472384\pi\) | |||||||
\(978\) | −580.701 | − | 1536.39i | −0.593763 | − | 1.57095i | ||||
\(979\) | −197.616 | −0.201855 | ||||||||
\(980\) | −28.7035 | − | 32.5467i | −0.0292893 | − | 0.0332110i | ||||
\(981\) | − | 10.2337i | − | 0.0104319i | ||||||
\(982\) | −42.3919 | − | 112.158i | −0.0431690 | − | 0.114214i | ||||
\(983\) | 698.607i | 0.710689i | 0.934735 | + | 0.355345i | \(0.115636\pi\) | ||||
−0.934735 | + | 0.355345i | \(0.884364\pi\) | |||||||
\(984\) | 651.127 | + | 344.544i | 0.661714 | + | 0.350146i | ||||
\(985\) | 192.362 | 0.195291 | ||||||||
\(986\) | −993.588 | + | 375.541i | −1.00770 | + | 0.380873i | ||||
\(987\) | 326.392 | 0.330691 | ||||||||
\(988\) | 101.980 | + | 115.634i | 0.103218 | + | 0.117039i | ||||
\(989\) | 604.865i | 0.611592i | ||||||||
\(990\) | −34.5525 | + | 13.0596i | −0.0349015 | + | 0.0131915i | ||||
\(991\) | 429.702i | 0.433605i | 0.976216 | + | 0.216802i | \(0.0695627\pi\) | ||||
−0.976216 | + | 0.216802i | \(0.930437\pi\) | |||||||
\(992\) | 349.588 | + | 1453.45i | 0.352407 | + | 1.46517i | ||||
\(993\) | 731.529 | 0.736686 | ||||||||
\(994\) | −191.196 | − | 505.857i | −0.192350 | − | 0.508910i | ||||
\(995\) | −280.483 | −0.281892 | ||||||||
\(996\) | −37.0294 | + | 32.6569i | −0.0371781 | + | 0.0327880i | ||||
\(997\) | − | 52.3910i | − | 0.0525487i | −0.999655 | − | 0.0262743i | \(-0.991636\pi\) | ||
0.999655 | − | 0.0262743i | \(-0.00836434\pi\) | |||||||
\(998\) | −59.5980 | − | 157.681i | −0.0597174 | − | 0.157997i | ||||
\(999\) | − | 1268.71i | − | 1.26998i |
(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 | 56.3.g.a.43.4 | yes | 4 | |
3.2 | odd | 2 | 504.3.g.a.379.1 | 4 | |||
4.3 | odd | 2 | 224.3.g.a.15.1 | 4 | |||
7.2 | even | 3 | 392.3.k.i.67.3 | 8 | |||
7.3 | odd | 6 | 392.3.k.j.275.1 | 8 | |||
7.4 | even | 3 | 392.3.k.i.275.1 | 8 | |||
7.5 | odd | 6 | 392.3.k.j.67.3 | 8 | |||
7.6 | odd | 2 | 392.3.g.h.99.4 | 4 | |||
8.3 | odd | 2 | inner | 56.3.g.a.43.3 | ✓ | 4 | |
8.5 | even | 2 | 224.3.g.a.15.2 | 4 | |||
12.11 | even | 2 | 2016.3.g.a.1135.3 | 4 | |||
16.3 | odd | 4 | 1792.3.d.g.1023.1 | 8 | |||
16.5 | even | 4 | 1792.3.d.g.1023.2 | 8 | |||
16.11 | odd | 4 | 1792.3.d.g.1023.8 | 8 | |||
16.13 | even | 4 | 1792.3.d.g.1023.7 | 8 | |||
24.5 | odd | 2 | 2016.3.g.a.1135.2 | 4 | |||
24.11 | even | 2 | 504.3.g.a.379.2 | 4 | |||
28.27 | even | 2 | 1568.3.g.h.687.4 | 4 | |||
56.3 | even | 6 | 392.3.k.j.275.3 | 8 | |||
56.11 | odd | 6 | 392.3.k.i.275.3 | 8 | |||
56.13 | odd | 2 | 1568.3.g.h.687.3 | 4 | |||
56.19 | even | 6 | 392.3.k.j.67.1 | 8 | |||
56.27 | even | 2 | 392.3.g.h.99.3 | 4 | |||
56.51 | odd | 6 | 392.3.k.i.67.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.a.43.3 | ✓ | 4 | 8.3 | odd | 2 | inner | |
56.3.g.a.43.4 | yes | 4 | 1.1 | even | 1 | trivial | |
224.3.g.a.15.1 | 4 | 4.3 | odd | 2 | |||
224.3.g.a.15.2 | 4 | 8.5 | even | 2 | |||
392.3.g.h.99.3 | 4 | 56.27 | even | 2 | |||
392.3.g.h.99.4 | 4 | 7.6 | odd | 2 | |||
392.3.k.i.67.1 | 8 | 56.51 | odd | 6 | |||
392.3.k.i.67.3 | 8 | 7.2 | even | 3 | |||
392.3.k.i.275.1 | 8 | 7.4 | even | 3 | |||
392.3.k.i.275.3 | 8 | 56.11 | odd | 6 | |||
392.3.k.j.67.1 | 8 | 56.19 | even | 6 | |||
392.3.k.j.67.3 | 8 | 7.5 | odd | 6 | |||
392.3.k.j.275.1 | 8 | 7.3 | odd | 6 | |||
392.3.k.j.275.3 | 8 | 56.3 | even | 6 | |||
504.3.g.a.379.1 | 4 | 3.2 | odd | 2 | |||
504.3.g.a.379.2 | 4 | 24.11 | even | 2 | |||
1568.3.g.h.687.3 | 4 | 56.13 | odd | 2 | |||
1568.3.g.h.687.4 | 4 | 28.27 | even | 2 | |||
1792.3.d.g.1023.1 | 8 | 16.3 | odd | 4 | |||
1792.3.d.g.1023.2 | 8 | 16.5 | even | 4 | |||
1792.3.d.g.1023.7 | 8 | 16.13 | even | 4 | |||
1792.3.d.g.1023.8 | 8 | 16.11 | odd | 4 | |||
2016.3.g.a.1135.2 | 4 | 24.5 | odd | 2 | |||
2016.3.g.a.1135.3 | 4 | 12.11 | even | 2 |