Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(286,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.286");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82018358714\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 120x^{6} + 2874x^{4} + 16920x^{2} + 19881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 286.6 | ||
Root | \(-4.66647i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.286 |
Dual form | 287.3.d.c.286.5 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.500000 | −0.250000 | − | 0.968246i | \(-0.580431\pi\) | ||||
−0.250000 | + | 0.968246i | \(0.580431\pi\) | |||||||
\(3\) | 0.913701 | 0.304567 | 0.152283 | − | 0.988337i | \(-0.451337\pi\) | ||||
0.152283 | + | 0.988337i | \(0.451337\pi\) | |||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | 7.47749i | 1.49550i | 0.663981 | + | 0.747749i | \(0.268865\pi\) | ||||
−0.663981 | + | 0.747749i | \(0.731135\pi\) | |||||||
\(6\) | −0.913701 | −0.152283 | ||||||||
\(7\) | 6.10985 | − | 3.41609i | 0.872836 | − | 0.488013i | ||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | −8.16515 | −0.907239 | ||||||||
\(10\) | − | 7.47749i | − | 0.747749i | ||||||
\(11\) | 6.11921i | 0.556292i | 0.960539 | + | 0.278146i | \(0.0897198\pi\) | ||||
−0.960539 | + | 0.278146i | \(0.910280\pi\) | |||||||
\(12\) | −2.74110 | −0.228425 | ||||||||
\(13\) | −0.913701 | −0.0702847 | −0.0351423 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351423 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(14\) | −6.10985 | + | 3.41609i | −0.436418 | + | 0.244007i | ||||
\(15\) | 6.83219i | 0.455479i | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 1.10440 | 0.0649648 | 0.0324824 | − | 0.999472i | \(-0.489659\pi\) | ||||
0.0324824 | + | 0.999472i | \(0.489659\pi\) | |||||||
\(18\) | 8.16515 | 0.453620 | ||||||||
\(19\) | −28.6265 | −1.50666 | −0.753329 | − | 0.657643i | \(-0.771553\pi\) | ||||
−0.753329 | + | 0.657643i | \(0.771553\pi\) | |||||||
\(20\) | − | 22.4325i | − | 1.12162i | ||||||
\(21\) | 5.58258 | − | 3.12129i | 0.265837 | − | 0.148633i | ||||
\(22\) | − | 6.11921i | − | 0.278146i | ||||||
\(23\) | −26.7477 | −1.16294 | −0.581472 | − | 0.813566i | \(-0.697523\pi\) | ||||
−0.581472 | + | 0.813566i | \(0.697523\pi\) | |||||||
\(24\) | 6.39590 | 0.266496 | ||||||||
\(25\) | −30.9129 | −1.23652 | ||||||||
\(26\) | 0.913701 | 0.0351423 | ||||||||
\(27\) | −15.6838 | −0.580882 | ||||||||
\(28\) | −18.3296 | + | 10.2483i | −0.654627 | + | 0.366010i | ||||
\(29\) | 52.5186i | 1.81098i | 0.424362 | + | 0.905492i | \(0.360498\pi\) | ||||
−0.424362 | + | 0.905492i | \(0.639502\pi\) | |||||||
\(30\) | − | 6.83219i | − | 0.227740i | ||||||
\(31\) | − | 26.7887i | − | 0.864151i | −0.901837 | − | 0.432075i | \(-0.857781\pi\) | ||
0.901837 | − | 0.432075i | \(-0.142219\pi\) | |||||||
\(32\) | −33.0000 | −1.03125 | ||||||||
\(33\) | 5.59112i | 0.169428i | ||||||||
\(34\) | −1.10440 | −0.0324824 | ||||||||
\(35\) | 25.5438 | + | 45.6864i | 0.729823 | + | 1.30532i | ||||
\(36\) | 24.4955 | 0.680429 | ||||||||
\(37\) | −18.8348 | −0.509050 | −0.254525 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254525 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(38\) | 28.6265 | 0.753329 | ||||||||
\(39\) | −0.834849 | −0.0214064 | ||||||||
\(40\) | 52.3424i | 1.30856i | ||||||||
\(41\) | 24.7255 | + | 32.7055i | 0.603060 | + | 0.797696i | ||||
\(42\) | −5.58258 | + | 3.12129i | −0.132918 | + | 0.0743163i | ||||
\(43\) | −19.4955 | −0.453383 | −0.226691 | − | 0.973967i | \(-0.572791\pi\) | ||||
−0.226691 | + | 0.973967i | \(0.572791\pi\) | |||||||
\(44\) | − | 18.3576i | − | 0.417219i | ||||||
\(45\) | − | 61.0548i | − | 1.35677i | ||||||
\(46\) | 26.7477 | 0.581472 | ||||||||
\(47\) | −48.5372 | −1.03271 | −0.516353 | − | 0.856376i | \(-0.672711\pi\) | ||||
−0.516353 | + | 0.856376i | \(0.672711\pi\) | |||||||
\(48\) | 4.56850 | 0.0951771 | ||||||||
\(49\) | 25.6606 | − | 41.7437i | 0.523686 | − | 0.851911i | ||||
\(50\) | 30.9129 | 0.618258 | ||||||||
\(51\) | 1.00909 | 0.0197861 | ||||||||
\(52\) | 2.74110 | 0.0527135 | ||||||||
\(53\) | 44.2604i | 0.835102i | 0.908653 | + | 0.417551i | \(0.137112\pi\) | ||||
−0.908653 | + | 0.417551i | \(0.862888\pi\) | |||||||
\(54\) | 15.6838 | 0.290441 | ||||||||
\(55\) | −45.7563 | −0.831933 | ||||||||
\(56\) | 42.7690 | − | 23.9127i | 0.763732 | − | 0.427012i | ||||
\(57\) | −26.1561 | −0.458878 | ||||||||
\(58\) | − | 52.5186i | − | 0.905492i | ||||||
\(59\) | 19.3112i | 0.327308i | 0.986518 | + | 0.163654i | \(0.0523281\pi\) | ||||
−0.986518 | + | 0.163654i | \(0.947672\pi\) | |||||||
\(60\) | − | 20.4966i | − | 0.341609i | ||||||
\(61\) | 28.0236i | 0.459403i | 0.973261 | + | 0.229702i | \(0.0737750\pi\) | ||||
−0.973261 | + | 0.229702i | \(0.926225\pi\) | |||||||
\(62\) | 26.7887i | 0.432075i | ||||||||
\(63\) | −49.8879 | + | 27.8929i | −0.791871 | + | 0.442745i | ||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | − | 6.83219i | − | 0.105111i | ||||||
\(66\) | − | 5.59112i | − | 0.0847140i | ||||||
\(67\) | 14.3774i | 0.214587i | 0.994227 | + | 0.107294i | \(0.0342185\pi\) | ||||
−0.994227 | + | 0.107294i | \(0.965781\pi\) | |||||||
\(68\) | −3.31320 | −0.0487236 | ||||||||
\(69\) | −24.4394 | −0.354194 | ||||||||
\(70\) | −25.5438 | − | 45.6864i | −0.364912 | − | 0.652662i | ||||
\(71\) | − | 134.920i | − | 1.90028i | −0.311817 | − | 0.950142i | \(-0.600938\pi\) | ||
0.311817 | − | 0.950142i | \(-0.399062\pi\) | |||||||
\(72\) | −57.1561 | −0.793834 | ||||||||
\(73\) | − | 44.8649i | − | 0.614588i | −0.951615 | − | 0.307294i | \(-0.900576\pi\) | ||
0.951615 | − | 0.307294i | \(-0.0994236\pi\) | |||||||
\(74\) | 18.8348 | 0.254525 | ||||||||
\(75\) | −28.2451 | −0.376602 | ||||||||
\(76\) | 85.8795 | 1.12999 | ||||||||
\(77\) | 20.9038 | + | 37.3875i | 0.271478 | + | 0.485551i | ||||
\(78\) | 0.834849 | 0.0107032 | ||||||||
\(79\) | 70.8762i | 0.897167i | 0.893741 | + | 0.448583i | \(0.148071\pi\) | ||||
−0.893741 | + | 0.448583i | \(0.851929\pi\) | |||||||
\(80\) | 37.3875i | 0.467343i | ||||||||
\(81\) | 59.1561 | 0.730322 | ||||||||
\(82\) | −24.7255 | − | 32.7055i | −0.301530 | − | 0.398848i | ||||
\(83\) | − | 90.3134i | − | 1.08811i | −0.839049 | − | 0.544056i | \(-0.816888\pi\) | ||
0.839049 | − | 0.544056i | \(-0.183112\pi\) | |||||||
\(84\) | −16.7477 | + | 9.36386i | −0.199378 | + | 0.111475i | ||||
\(85\) | 8.25815i | 0.0971547i | ||||||||
\(86\) | 19.4955 | 0.226691 | ||||||||
\(87\) | 47.9862i | 0.551566i | ||||||||
\(88\) | 42.8345i | 0.486755i | ||||||||
\(89\) | 81.5017 | 0.915750 | 0.457875 | − | 0.889017i | \(-0.348611\pi\) | ||||
0.457875 | + | 0.889017i | \(0.348611\pi\) | |||||||
\(90\) | 61.0548i | 0.678387i | ||||||||
\(91\) | −5.58258 | + | 3.12129i | −0.0613470 | + | 0.0342999i | ||||
\(92\) | 80.2432 | 0.872208 | ||||||||
\(93\) | − | 24.4768i | − | 0.263192i | ||||||
\(94\) | 48.5372 | 0.516353 | ||||||||
\(95\) | − | 214.055i | − | 2.25321i | ||||||
\(96\) | −30.1521 | −0.314085 | ||||||||
\(97\) | 100.539 | 1.03648 | 0.518240 | − | 0.855235i | \(-0.326587\pi\) | ||||
0.518240 | + | 0.855235i | \(0.326587\pi\) | |||||||
\(98\) | −25.6606 | + | 41.7437i | −0.261843 | + | 0.425956i | ||||
\(99\) | − | 49.9643i | − | 0.504689i | ||||||
\(100\) | 92.7386 | 0.927386 | ||||||||
\(101\) | 82.2247 | 0.814106 | 0.407053 | − | 0.913404i | \(-0.366556\pi\) | ||||
0.407053 | + | 0.913404i | \(0.366556\pi\) | |||||||
\(102\) | −1.00909 | −0.00989306 | ||||||||
\(103\) | 145.777i | 1.41531i | 0.706557 | + | 0.707656i | \(0.250247\pi\) | ||||
−0.706557 | + | 0.707656i | \(0.749753\pi\) | |||||||
\(104\) | −6.39590 | −0.0614991 | ||||||||
\(105\) | 23.3394 | + | 41.7437i | 0.222280 | + | 0.397559i | ||||
\(106\) | − | 44.2604i | − | 0.417551i | ||||||
\(107\) | 93.6515 | 0.875248 | 0.437624 | − | 0.899158i | \(-0.355820\pi\) | ||||
0.437624 | + | 0.899158i | \(0.355820\pi\) | |||||||
\(108\) | 47.0514 | 0.435661 | ||||||||
\(109\) | 193.143i | 1.77195i | 0.463733 | + | 0.885975i | \(0.346510\pi\) | ||||
−0.463733 | + | 0.885975i | \(0.653490\pi\) | |||||||
\(110\) | 45.7563 | 0.415967 | ||||||||
\(111\) | −17.2094 | −0.155040 | ||||||||
\(112\) | 30.5493 | − | 17.0805i | 0.272761 | − | 0.152504i | ||||
\(113\) | −39.4083 | −0.348746 | −0.174373 | − | 0.984680i | \(-0.555790\pi\) | ||||
−0.174373 | + | 0.984680i | \(0.555790\pi\) | |||||||
\(114\) | 26.1561 | 0.229439 | ||||||||
\(115\) | − | 200.006i | − | 1.73918i | ||||||
\(116\) | − | 157.556i | − | 1.35824i | ||||||
\(117\) | 7.46050 | 0.0637650 | ||||||||
\(118\) | − | 19.3112i | − | 0.163654i | ||||||
\(119\) | 6.74773 | − | 3.77274i | 0.0567036 | − | 0.0317037i | ||||
\(120\) | 47.8253i | 0.398544i | ||||||||
\(121\) | 83.5553 | 0.690540 | ||||||||
\(122\) | − | 28.0236i | − | 0.229702i | ||||||
\(123\) | 22.5917 | + | 29.8831i | 0.183672 | + | 0.242952i | ||||
\(124\) | 80.3660i | 0.648113i | ||||||||
\(125\) | − | 44.2135i | − | 0.353708i | ||||||
\(126\) | 49.8879 | − | 27.8929i | 0.395936 | − | 0.221372i | ||||
\(127\) | −157.564 | −1.24066 | −0.620332 | − | 0.784339i | \(-0.713002\pi\) | ||||
−0.620332 | + | 0.784339i | \(0.713002\pi\) | |||||||
\(128\) | 119.000 | 0.929688 | ||||||||
\(129\) | −17.8130 | −0.138085 | ||||||||
\(130\) | 6.83219i | 0.0525553i | ||||||||
\(131\) | 160.800i | 1.22748i | 0.789508 | + | 0.613741i | \(0.210336\pi\) | ||||
−0.789508 | + | 0.613741i | \(0.789664\pi\) | |||||||
\(132\) | − | 16.7734i | − | 0.127071i | ||||||
\(133\) | −174.904 | + | 97.7909i | −1.31507 | + | 0.735270i | ||||
\(134\) | − | 14.3774i | − | 0.107294i | ||||||
\(135\) | − | 117.276i | − | 0.868708i | ||||||
\(136\) | 7.73081 | 0.0568442 | ||||||||
\(137\) | − | 64.0440i | − | 0.467474i | −0.972300 | − | 0.233737i | \(-0.924904\pi\) | ||
0.972300 | − | 0.233737i | \(-0.0750955\pi\) | |||||||
\(138\) | 24.4394 | 0.177097 | ||||||||
\(139\) | − | 195.650i | − | 1.40755i | −0.710422 | − | 0.703776i | \(-0.751496\pi\) | ||
0.710422 | − | 0.703776i | \(-0.248504\pi\) | |||||||
\(140\) | −76.6314 | − | 137.059i | −0.547367 | − | 0.978994i | ||||
\(141\) | −44.3485 | −0.314528 | ||||||||
\(142\) | 134.920i | 0.950142i | ||||||||
\(143\) | − | 5.59112i | − | 0.0390988i | ||||||
\(144\) | −40.8258 | −0.283512 | ||||||||
\(145\) | −392.707 | −2.70832 | ||||||||
\(146\) | 44.8649i | 0.307294i | ||||||||
\(147\) | 23.4461 | − | 38.1412i | 0.159497 | − | 0.259464i | ||||
\(148\) | 56.5045 | 0.381787 | ||||||||
\(149\) | 195.697i | 1.31340i | 0.754151 | + | 0.656701i | \(0.228049\pi\) | ||||
−0.754151 | + | 0.656701i | \(0.771951\pi\) | |||||||
\(150\) | 28.2451 | 0.188301 | ||||||||
\(151\) | 80.5603i | 0.533512i | 0.963764 | + | 0.266756i | \(0.0859518\pi\) | ||||
−0.963764 | + | 0.266756i | \(0.914048\pi\) | |||||||
\(152\) | −200.386 | −1.31833 | ||||||||
\(153\) | −9.01760 | −0.0589386 | ||||||||
\(154\) | −20.9038 | − | 37.3875i | −0.135739 | − | 0.242776i | ||||
\(155\) | 200.312 | 1.29234 | ||||||||
\(156\) | 2.50455 | 0.0160548 | ||||||||
\(157\) | 97.2253 | 0.619270 | 0.309635 | − | 0.950856i | \(-0.399793\pi\) | ||||
0.309635 | + | 0.950856i | \(0.399793\pi\) | |||||||
\(158\) | − | 70.8762i | − | 0.448583i | ||||||
\(159\) | 40.4408i | 0.254344i | ||||||||
\(160\) | − | 246.757i | − | 1.54223i | ||||||
\(161\) | −163.425 | + | 91.3727i | −1.01506 | + | 0.567533i | ||||
\(162\) | −59.1561 | −0.365161 | ||||||||
\(163\) | −111.808 | −0.685936 | −0.342968 | − | 0.939347i | \(-0.611432\pi\) | ||||
−0.342968 | + | 0.939347i | \(0.611432\pi\) | |||||||
\(164\) | −74.1764 | − | 98.1166i | −0.452295 | − | 0.598272i | ||||
\(165\) | −41.8076 | −0.253379 | ||||||||
\(166\) | 90.3134i | 0.544056i | ||||||||
\(167\) | 290.190 | 1.73767 | 0.868833 | − | 0.495105i | \(-0.164870\pi\) | ||||
0.868833 | + | 0.495105i | \(0.164870\pi\) | |||||||
\(168\) | 39.0780 | − | 21.8490i | 0.232607 | − | 0.130054i | ||||
\(169\) | −168.165 | −0.995060 | ||||||||
\(170\) | − | 8.25815i | − | 0.0485773i | ||||||
\(171\) | 233.740 | 1.36690 | ||||||||
\(172\) | 58.4864 | 0.340037 | ||||||||
\(173\) | − | 66.6460i | − | 0.385237i | −0.981274 | − | 0.192618i | \(-0.938302\pi\) | ||
0.981274 | − | 0.192618i | \(-0.0616980\pi\) | |||||||
\(174\) | − | 47.9862i | − | 0.275783i | ||||||
\(175\) | −188.873 | + | 105.601i | −1.07928 | + | 0.603436i | ||||
\(176\) | 30.5960i | 0.173841i | ||||||||
\(177\) | 17.6446i | 0.0996872i | ||||||||
\(178\) | −81.5017 | −0.457875 | ||||||||
\(179\) | 131.653i | 0.735491i | 0.929926 | + | 0.367746i | \(0.119870\pi\) | ||||
−0.929926 | + | 0.367746i | \(0.880130\pi\) | |||||||
\(180\) | 183.165i | 1.01758i | ||||||||
\(181\) | −53.7491 | −0.296956 | −0.148478 | − | 0.988916i | \(-0.547437\pi\) | ||||
−0.148478 | + | 0.988916i | \(0.547437\pi\) | |||||||
\(182\) | 5.58258 | − | 3.12129i | 0.0306735 | − | 0.0171499i | ||||
\(183\) | 25.6052i | 0.139919i | ||||||||
\(184\) | −187.234 | −1.01758 | ||||||||
\(185\) | − | 140.837i | − | 0.761283i | ||||||
\(186\) | 24.4768i | 0.131596i | ||||||||
\(187\) | 6.75806i | 0.0361393i | ||||||||
\(188\) | 145.612 | 0.774530 | ||||||||
\(189\) | −95.8258 | + | 53.5774i | −0.507015 | + | 0.283478i | ||||
\(190\) | 214.055i | 1.12660i | ||||||||
\(191\) | 142.050i | 0.743717i | 0.928289 | + | 0.371859i | \(0.121279\pi\) | ||||
−0.928289 | + | 0.371859i | \(0.878721\pi\) | |||||||
\(192\) | 11.8781 | 0.0618651 | ||||||||
\(193\) | 321.944i | 1.66810i | 0.551688 | + | 0.834051i | \(0.313984\pi\) | ||||
−0.551688 | + | 0.834051i | \(0.686016\pi\) | |||||||
\(194\) | −100.539 | −0.518240 | ||||||||
\(195\) | − | 6.24257i | − | 0.0320132i | ||||||
\(196\) | −76.9818 | + | 125.231i | −0.392764 | + | 0.638934i | ||||
\(197\) | −306.312 | −1.55488 | −0.777442 | − | 0.628955i | \(-0.783483\pi\) | ||||
−0.777442 | + | 0.628955i | \(0.783483\pi\) | |||||||
\(198\) | 49.9643i | 0.252345i | ||||||||
\(199\) | 46.1062 | 0.231690 | 0.115845 | − | 0.993267i | \(-0.463042\pi\) | ||||
0.115845 | + | 0.993267i | \(0.463042\pi\) | |||||||
\(200\) | −216.390 | −1.08195 | ||||||||
\(201\) | 13.1366i | 0.0653562i | ||||||||
\(202\) | −82.2247 | −0.407053 | ||||||||
\(203\) | 179.408 | + | 320.881i | 0.883785 | + | 1.58069i | ||||
\(204\) | −3.02727 | −0.0148396 | ||||||||
\(205\) | −244.555 | + | 184.884i | −1.19295 | + | 0.901875i | ||||
\(206\) | − | 145.777i | − | 0.707656i | ||||||
\(207\) | 218.399 | 1.05507 | ||||||||
\(208\) | −4.56850 | −0.0219640 | ||||||||
\(209\) | − | 175.172i | − | 0.838141i | ||||||
\(210\) | −23.3394 | − | 41.7437i | −0.111140 | − | 0.198779i | ||||
\(211\) | 108.304i | 0.513291i | 0.966506 | + | 0.256646i | \(0.0826173\pi\) | ||||
−0.966506 | + | 0.256646i | \(0.917383\pi\) | |||||||
\(212\) | − | 132.781i | − | 0.626327i | ||||||
\(213\) | − | 123.277i | − | 0.578764i | ||||||
\(214\) | −93.6515 | −0.437624 | ||||||||
\(215\) | − | 145.777i | − | 0.678033i | ||||||
\(216\) | −109.787 | −0.508272 | ||||||||
\(217\) | −91.5126 | − | 163.675i | −0.421717 | − | 0.754262i | ||||
\(218\) | − | 193.143i | − | 0.885975i | ||||||
\(219\) | − | 40.9931i | − | 0.187183i | ||||||
\(220\) | 137.269 | 0.623950 | ||||||||
\(221\) | −1.00909 | −0.00456603 | ||||||||
\(222\) | 17.2094 | 0.0775199 | ||||||||
\(223\) | 102.215i | 0.458363i | 0.973384 | + | 0.229182i | \(0.0736050\pi\) | ||||
−0.973384 | + | 0.229182i | \(0.926395\pi\) | |||||||
\(224\) | −201.625 | + | 112.731i | −0.900112 | + | 0.503264i | ||||
\(225\) | 252.408 | 1.12181 | ||||||||
\(226\) | 39.4083 | 0.174373 | ||||||||
\(227\) | −217.976 | −0.960248 | −0.480124 | − | 0.877200i | \(-0.659408\pi\) | ||||
−0.480124 | + | 0.877200i | \(0.659408\pi\) | |||||||
\(228\) | 78.4682 | 0.344159 | ||||||||
\(229\) | 167.350 | 0.730785 | 0.365393 | − | 0.930854i | \(-0.380935\pi\) | ||||
0.365393 | + | 0.930854i | \(0.380935\pi\) | |||||||
\(230\) | 200.006i | 0.869591i | ||||||||
\(231\) | 19.0998 | + | 34.1609i | 0.0826831 | + | 0.147883i | ||||
\(232\) | 367.630i | 1.58461i | ||||||||
\(233\) | − | 230.868i | − | 0.990852i | −0.868650 | − | 0.495426i | \(-0.835012\pi\) | ||
0.868650 | − | 0.495426i | \(-0.164988\pi\) | |||||||
\(234\) | −7.46050 | −0.0318825 | ||||||||
\(235\) | − | 362.937i | − | 1.54441i | ||||||
\(236\) | − | 57.9336i | − | 0.245481i | ||||||
\(237\) | 64.7596i | 0.273247i | ||||||||
\(238\) | −6.74773 | + | 3.77274i | −0.0283518 | + | 0.0158518i | ||||
\(239\) | − | 128.088i | − | 0.535933i | −0.963428 | − | 0.267967i | \(-0.913648\pi\) | ||
0.963428 | − | 0.267967i | \(-0.0863517\pi\) | |||||||
\(240\) | 34.1609i | 0.142337i | ||||||||
\(241\) | − | 284.796i | − | 1.18173i | −0.806772 | − | 0.590863i | \(-0.798787\pi\) | ||
0.806772 | − | 0.590863i | \(-0.201213\pi\) | |||||||
\(242\) | −83.5553 | −0.345270 | ||||||||
\(243\) | 195.205 | 0.803314 | ||||||||
\(244\) | − | 84.0708i | − | 0.344552i | ||||||
\(245\) | 312.138 | + | 191.877i | 1.27403 | + | 0.783171i | ||||
\(246\) | −22.5917 | − | 29.8831i | −0.0918360 | − | 0.121476i | ||||
\(247\) | 26.1561 | 0.105895 | ||||||||
\(248\) | − | 187.521i | − | 0.756132i | ||||||
\(249\) | − | 82.5194i | − | 0.331403i | ||||||
\(250\) | 44.2135i | 0.176854i | ||||||||
\(251\) | 97.8588i | 0.389876i | 0.980816 | + | 0.194938i | \(0.0624505\pi\) | ||||
−0.980816 | + | 0.194938i | \(0.937549\pi\) | |||||||
\(252\) | 149.664 | − | 83.6788i | 0.593903 | − | 0.332059i | ||||
\(253\) | − | 163.675i | − | 0.646936i | ||||||
\(254\) | 157.564 | 0.620332 | ||||||||
\(255\) | 7.54547i | 0.0295901i | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | 122.229 | 0.475597 | 0.237799 | − | 0.971314i | \(-0.423574\pi\) | ||||
0.237799 | + | 0.971314i | \(0.423574\pi\) | |||||||
\(258\) | 17.8130 | 0.0690427 | ||||||||
\(259\) | −115.078 | + | 64.3416i | −0.444317 | + | 0.248423i | ||||
\(260\) | 20.4966i | 0.0788329i | ||||||||
\(261\) | − | 428.822i | − | 1.64300i | ||||||
\(262\) | − | 160.800i | − | 0.613741i | ||||||
\(263\) | − | 326.221i | − | 1.24039i | −0.784449 | − | 0.620193i | \(-0.787054\pi\) | ||
0.784449 | − | 0.620193i | \(-0.212946\pi\) | |||||||
\(264\) | 39.1379i | 0.148249i | ||||||||
\(265\) | −330.957 | −1.24889 | ||||||||
\(266\) | 174.904 | − | 97.7909i | 0.657533 | − | 0.367635i | ||||
\(267\) | 74.4682 | 0.278907 | ||||||||
\(268\) | − | 43.1321i | − | 0.160941i | ||||||
\(269\) | 128.936i | 0.479315i | 0.970857 | + | 0.239658i | \(0.0770352\pi\) | ||||
−0.970857 | + | 0.239658i | \(0.922965\pi\) | |||||||
\(270\) | 117.276i | 0.434354i | ||||||||
\(271\) | − | 354.495i | − | 1.30810i | −0.756451 | − | 0.654051i | \(-0.773068\pi\) | ||
0.756451 | − | 0.654051i | \(-0.226932\pi\) | |||||||
\(272\) | 5.52200 | 0.0203015 | ||||||||
\(273\) | −5.10080 | + | 2.85192i | −0.0186843 | + | 0.0104466i | ||||
\(274\) | 64.0440i | 0.233737i | ||||||||
\(275\) | − | 189.162i | − | 0.687863i | ||||||
\(276\) | 73.3182 | 0.265646 | ||||||||
\(277\) | 353.964 | 1.27785 | 0.638924 | − | 0.769270i | \(-0.279380\pi\) | ||||
0.638924 | + | 0.769270i | \(0.279380\pi\) | |||||||
\(278\) | 195.650i | 0.703776i | ||||||||
\(279\) | 218.734i | 0.783991i | ||||||||
\(280\) | 178.807 | + | 319.805i | 0.638595 | + | 1.14216i | ||||
\(281\) | 214.352i | 0.762819i | 0.924406 | + | 0.381409i | \(0.124561\pi\) | ||||
−0.924406 | + | 0.381409i | \(0.875439\pi\) | |||||||
\(282\) | 44.3485 | 0.157264 | ||||||||
\(283\) | 342.730i | 1.21106i | 0.795823 | + | 0.605529i | \(0.207039\pi\) | ||||
−0.795823 | + | 0.605529i | \(0.792961\pi\) | |||||||
\(284\) | 404.761i | 1.42521i | ||||||||
\(285\) | − | 195.582i | − | 0.686252i | ||||||
\(286\) | 5.59112i | 0.0195494i | ||||||||
\(287\) | 262.794 | + | 115.361i | 0.915659 | + | 0.401956i | ||||
\(288\) | 269.450 | 0.935590 | ||||||||
\(289\) | −287.780 | −0.995780 | ||||||||
\(290\) | 392.707 | 1.35416 | ||||||||
\(291\) | 91.8621 | 0.315677 | ||||||||
\(292\) | 134.595i | 0.460941i | ||||||||
\(293\) | 4.02790 | 0.0137471 | 0.00687354 | − | 0.999976i | \(-0.497812\pi\) | ||||
0.00687354 | + | 0.999976i | \(0.497812\pi\) | |||||||
\(294\) | −23.4461 | + | 38.1412i | −0.0797487 | + | 0.129732i | ||||
\(295\) | −144.399 | −0.489489 | ||||||||
\(296\) | −131.844 | −0.445419 | ||||||||
\(297\) | − | 95.9725i | − | 0.323140i | ||||||
\(298\) | − | 195.697i | − | 0.656701i | ||||||
\(299\) | 24.4394 | 0.0817372 | ||||||||
\(300\) | 84.7353 | 0.282451 | ||||||||
\(301\) | −119.114 | + | 66.5983i | −0.395729 | + | 0.221257i | ||||
\(302\) | − | 80.5603i | − | 0.266756i | ||||||
\(303\) | 75.1288 | 0.247950 | ||||||||
\(304\) | −143.133 | −0.470831 | ||||||||
\(305\) | −209.546 | −0.687037 | ||||||||
\(306\) | 9.01760 | 0.0294693 | ||||||||
\(307\) | 263.015i | 0.856727i | 0.903607 | + | 0.428363i | \(0.140910\pi\) | ||||
−0.903607 | + | 0.428363i | \(0.859090\pi\) | |||||||
\(308\) | −62.7114 | − | 112.162i | −0.203608 | − | 0.364164i | ||||
\(309\) | 133.197i | 0.431057i | ||||||||
\(310\) | −200.312 | −0.646168 | ||||||||
\(311\) | 583.614 | 1.87657 | 0.938286 | − | 0.345860i | \(-0.112413\pi\) | ||||
0.938286 | + | 0.345860i | \(0.112413\pi\) | |||||||
\(312\) | −5.84394 | −0.0187306 | ||||||||
\(313\) | −512.727 | −1.63810 | −0.819052 | − | 0.573719i | \(-0.805500\pi\) | ||||
−0.819052 | + | 0.573719i | \(0.805500\pi\) | |||||||
\(314\) | −97.2253 | −0.309635 | ||||||||
\(315\) | −208.569 | − | 373.036i | −0.662124 | − | 1.18424i | ||||
\(316\) | − | 212.629i | − | 0.672875i | ||||||
\(317\) | − | 111.454i | − | 0.351590i | −0.984427 | − | 0.175795i | \(-0.943750\pi\) | ||
0.984427 | − | 0.175795i | \(-0.0562495\pi\) | |||||||
\(318\) | − | 40.4408i | − | 0.127172i | ||||||
\(319\) | −321.372 | −1.00744 | ||||||||
\(320\) | 97.2074i | 0.303773i | ||||||||
\(321\) | 85.5694 | 0.266571 | ||||||||
\(322\) | 163.425 | − | 91.3727i | 0.507530 | − | 0.283766i | ||||
\(323\) | −31.6151 | −0.0978797 | ||||||||
\(324\) | −177.468 | −0.547741 | ||||||||
\(325\) | 28.2451 | 0.0869080 | ||||||||
\(326\) | 111.808 | 0.342968 | ||||||||
\(327\) | 176.474i | 0.539677i | ||||||||
\(328\) | 173.078 | + | 228.939i | 0.527678 | + | 0.697984i | ||||
\(329\) | −296.555 | + | 165.808i | −0.901384 | + | 0.503975i | ||||
\(330\) | 41.8076 | 0.126690 | ||||||||
\(331\) | 359.074i | 1.08482i | 0.840115 | + | 0.542408i | \(0.182487\pi\) | ||||
−0.840115 | + | 0.542408i | \(0.817513\pi\) | |||||||
\(332\) | 270.940i | 0.816085i | ||||||||
\(333\) | 153.789 | 0.461830 | ||||||||
\(334\) | −290.190 | −0.868833 | ||||||||
\(335\) | −107.507 | −0.320915 | ||||||||
\(336\) | 27.9129 | − | 15.6064i | 0.0830740 | − | 0.0464477i | ||||
\(337\) | 483.982 | 1.43615 | 0.718074 | − | 0.695967i | \(-0.245024\pi\) | ||||
0.718074 | + | 0.695967i | \(0.245024\pi\) | |||||||
\(338\) | 168.165 | 0.497530 | ||||||||
\(339\) | −36.0074 | −0.106217 | ||||||||
\(340\) | − | 24.7744i | − | 0.0728660i | ||||||
\(341\) | 163.925 | 0.480720 | ||||||||
\(342\) | −233.740 | −0.683450 | ||||||||
\(343\) | 14.1823 | − | 342.707i | 0.0413477 | − | 0.999145i | ||||
\(344\) | −136.468 | −0.396710 | ||||||||
\(345\) | − | 182.745i | − | 0.529697i | ||||||
\(346\) | 66.6460i | 0.192618i | ||||||||
\(347\) | − | 269.425i | − | 0.776441i | −0.921567 | − | 0.388220i | \(-0.873090\pi\) | ||
0.921567 | − | 0.388220i | \(-0.126910\pi\) | |||||||
\(348\) | − | 143.959i | − | 0.413674i | ||||||
\(349\) | − | 188.892i | − | 0.541237i | −0.962687 | − | 0.270618i | \(-0.912772\pi\) | ||
0.962687 | − | 0.270618i | \(-0.0872282\pi\) | |||||||
\(350\) | 188.873 | − | 105.601i | 0.539638 | − | 0.301718i | ||||
\(351\) | 14.3303 | 0.0408271 | ||||||||
\(352\) | − | 201.934i | − | 0.573676i | ||||||
\(353\) | 201.309i | 0.570280i | 0.958486 | + | 0.285140i | \(0.0920401\pi\) | ||||
−0.958486 | + | 0.285140i | \(0.907960\pi\) | |||||||
\(354\) | − | 17.6446i | − | 0.0498436i | ||||||
\(355\) | 1008.86 | 2.84187 | ||||||||
\(356\) | −244.505 | −0.686812 | ||||||||
\(357\) | 6.16540 | − | 3.44715i | 0.0172700 | − | 0.00965589i | ||||
\(358\) | − | 131.653i | − | 0.367746i | ||||||
\(359\) | −1.55000 | −0.00431756 | −0.00215878 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215878 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(360\) | − | 427.384i | − | 1.18718i | ||||||
\(361\) | 458.477 | 1.27002 | ||||||||
\(362\) | 53.7491 | 0.148478 | ||||||||
\(363\) | 76.3445 | 0.210315 | ||||||||
\(364\) | 16.7477 | − | 9.36386i | 0.0460102 | − | 0.0257249i | ||||
\(365\) | 335.477 | 0.919116 | ||||||||
\(366\) | − | 25.6052i | − | 0.0699595i | ||||||
\(367\) | 16.9093i | 0.0460745i | 0.999735 | + | 0.0230372i | \(0.00733363\pi\) | ||||
−0.999735 | + | 0.0230372i | \(0.992666\pi\) | |||||||
\(368\) | −133.739 | −0.363420 | ||||||||
\(369\) | −201.887 | − | 267.046i | −0.547120 | − | 0.723701i | ||||
\(370\) | 140.837i | 0.380642i | ||||||||
\(371\) | 151.198 | + | 270.425i | 0.407541 | + | 0.728907i | ||||
\(372\) | 73.4305i | 0.197394i | ||||||||
\(373\) | −292.468 | −0.784097 | −0.392048 | − | 0.919945i | \(-0.628233\pi\) | ||||
−0.392048 | + | 0.919945i | \(0.628233\pi\) | |||||||
\(374\) | − | 6.75806i | − | 0.0180697i | ||||||
\(375\) | − | 40.3979i | − | 0.107728i | ||||||
\(376\) | −339.761 | −0.903619 | ||||||||
\(377\) | − | 47.9862i | − | 0.127284i | ||||||
\(378\) | 95.8258 | − | 53.5774i | 0.253507 | − | 0.141739i | ||||
\(379\) | 389.441 | 1.02755 | 0.513774 | − | 0.857925i | \(-0.328247\pi\) | ||||
0.513774 | + | 0.857925i | \(0.328247\pi\) | |||||||
\(380\) | 642.164i | 1.68990i | ||||||||
\(381\) | −143.967 | −0.377865 | ||||||||
\(382\) | − | 142.050i | − | 0.371859i | ||||||
\(383\) | 545.025 | 1.42304 | 0.711521 | − | 0.702665i | \(-0.248007\pi\) | ||||
0.711521 | + | 0.702665i | \(0.248007\pi\) | |||||||
\(384\) | 108.730 | 0.283152 | ||||||||
\(385\) | −279.564 | + | 156.308i | −0.726141 | + | 0.405995i | ||||
\(386\) | − | 321.944i | − | 0.834051i | ||||||
\(387\) | 159.183 | 0.411326 | ||||||||
\(388\) | −301.616 | −0.777360 | ||||||||
\(389\) | −301.964 | −0.776256 | −0.388128 | − | 0.921605i | \(-0.626878\pi\) | ||||
−0.388128 | + | 0.921605i | \(0.626878\pi\) | |||||||
\(390\) | 6.24257i | 0.0160066i | ||||||||
\(391\) | −29.5402 | −0.0755504 | ||||||||
\(392\) | 179.624 | − | 292.206i | 0.458225 | − | 0.745423i | ||||
\(393\) | 146.923i | 0.373850i | ||||||||
\(394\) | 306.312 | 0.777442 | ||||||||
\(395\) | −529.976 | −1.34171 | ||||||||
\(396\) | 149.893i | 0.378517i | ||||||||
\(397\) | 27.7045 | 0.0697846 | 0.0348923 | − | 0.999391i | \(-0.488891\pi\) | ||||
0.0348923 | + | 0.999391i | \(0.488891\pi\) | |||||||
\(398\) | −46.1062 | −0.115845 | ||||||||
\(399\) | −159.810 | + | 89.3516i | −0.400526 | + | 0.223939i | ||||
\(400\) | −154.564 | −0.386411 | ||||||||
\(401\) | 112.243 | 0.279908 | 0.139954 | − | 0.990158i | \(-0.455305\pi\) | ||||
0.139954 | + | 0.990158i | \(0.455305\pi\) | |||||||
\(402\) | − | 13.1366i | − | 0.0326781i | ||||||
\(403\) | 24.4768i | 0.0607365i | ||||||||
\(404\) | −246.674 | −0.610580 | ||||||||
\(405\) | 442.339i | 1.09219i | ||||||||
\(406\) | −179.408 | − | 320.881i | −0.441892 | − | 0.790347i | ||||
\(407\) | − | 115.254i | − | 0.283180i | ||||||
\(408\) | 7.06364 | 0.0173128 | ||||||||
\(409\) | − | 501.575i | − | 1.22635i | −0.789949 | − | 0.613173i | \(-0.789893\pi\) | ||
0.789949 | − | 0.613173i | \(-0.210107\pi\) | |||||||
\(410\) | 244.555 | − | 184.884i | 0.596476 | − | 0.450938i | ||||
\(411\) | − | 58.5170i | − | 0.142377i | ||||||
\(412\) | − | 437.331i | − | 1.06148i | ||||||
\(413\) | 65.9688 | + | 117.989i | 0.159731 | + | 0.285686i | ||||
\(414\) | −218.399 | −0.527534 | ||||||||
\(415\) | 675.317 | 1.62727 | ||||||||
\(416\) | 30.1521 | 0.0724810 | ||||||||
\(417\) | − | 178.765i | − | 0.428694i | ||||||
\(418\) | 175.172i | 0.419071i | ||||||||
\(419\) | 94.7376i | 0.226104i | 0.993589 | + | 0.113052i | \(0.0360627\pi\) | ||||
−0.993589 | + | 0.113052i | \(0.963937\pi\) | |||||||
\(420\) | −70.0182 | − | 125.231i | −0.166710 | − | 0.298169i | ||||
\(421\) | − | 36.0023i | − | 0.0855161i | −0.999085 | − | 0.0427580i | \(-0.986386\pi\) | ||
0.999085 | − | 0.0427580i | \(-0.0136145\pi\) | |||||||
\(422\) | − | 108.304i | − | 0.256646i | ||||||
\(423\) | 396.314 | 0.936912 | ||||||||
\(424\) | 309.823i | 0.730714i | ||||||||
\(425\) | −34.1402 | −0.0803299 | ||||||||
\(426\) | 123.277i | 0.289382i | ||||||||
\(427\) | 95.7312 | + | 171.220i | 0.224195 | + | 0.400984i | ||||
\(428\) | −280.955 | −0.656436 | ||||||||
\(429\) | − | 5.10861i | − | 0.0119082i | ||||||
\(430\) | 145.777i | 0.339016i | ||||||||
\(431\) | −388.592 | −0.901605 | −0.450802 | − | 0.892624i | \(-0.648862\pi\) | ||||
−0.450802 | + | 0.892624i | \(0.648862\pi\) | |||||||
\(432\) | −78.4190 | −0.181526 | ||||||||
\(433\) | − | 722.263i | − | 1.66804i | −0.551731 | − | 0.834022i | \(-0.686032\pi\) | ||
0.551731 | − | 0.834022i | \(-0.313968\pi\) | |||||||
\(434\) | 91.5126 | + | 163.675i | 0.210859 | + | 0.377131i | ||||
\(435\) | −358.817 | −0.824866 | ||||||||
\(436\) | − | 579.428i | − | 1.32896i | ||||||
\(437\) | 765.694 | 1.75216 | ||||||||
\(438\) | 40.9931i | 0.0935916i | ||||||||
\(439\) | −346.450 | −0.789180 | −0.394590 | − | 0.918857i | \(-0.629113\pi\) | ||||
−0.394590 | + | 0.918857i | \(0.629113\pi\) | |||||||
\(440\) | −320.294 | −0.727941 | ||||||||
\(441\) | −209.523 | + | 340.843i | −0.475108 | + | 0.772887i | ||||
\(442\) | 1.00909 | 0.00228301 | ||||||||
\(443\) | 416.744 | 0.940731 | 0.470366 | − | 0.882472i | \(-0.344122\pi\) | ||||
0.470366 | + | 0.882472i | \(0.344122\pi\) | |||||||
\(444\) | 51.6282 | 0.116280 | ||||||||
\(445\) | 609.429i | 1.36950i | ||||||||
\(446\) | − | 102.215i | − | 0.229182i | ||||||
\(447\) | 178.808i | 0.400019i | ||||||||
\(448\) | 79.4281 | − | 44.4092i | 0.177295 | − | 0.0991277i | ||||
\(449\) | −418.798 | −0.932736 | −0.466368 | − | 0.884591i | \(-0.654438\pi\) | ||||
−0.466368 | + | 0.884591i | \(0.654438\pi\) | |||||||
\(450\) | −252.408 | −0.560907 | ||||||||
\(451\) | −200.132 | + | 151.300i | −0.443751 | + | 0.335477i | ||||
\(452\) | 118.225 | 0.261560 | ||||||||
\(453\) | 73.6080i | 0.162490i | ||||||||
\(454\) | 217.976 | 0.480124 | ||||||||
\(455\) | −23.3394 | − | 41.7437i | −0.0512954 | − | 0.0917443i | ||||
\(456\) | −183.092 | −0.401518 | ||||||||
\(457\) | 362.106i | 0.792354i | 0.918174 | + | 0.396177i | \(0.129663\pi\) | ||||
−0.918174 | + | 0.396177i | \(0.870337\pi\) | |||||||
\(458\) | −167.350 | −0.365393 | ||||||||
\(459\) | −17.3212 | −0.0377368 | ||||||||
\(460\) | 600.018i | 1.30439i | ||||||||
\(461\) | 791.243i | 1.71636i | 0.513347 | + | 0.858181i | \(0.328406\pi\) | ||||
−0.513347 | + | 0.858181i | \(0.671594\pi\) | |||||||
\(462\) | −19.0998 | − | 34.1609i | −0.0413416 | − | 0.0739414i | ||||
\(463\) | − | 755.161i | − | 1.63102i | −0.578745 | − | 0.815509i | \(-0.696457\pi\) | ||
0.578745 | − | 0.815509i | \(-0.303543\pi\) | |||||||
\(464\) | 262.593i | 0.565933i | ||||||||
\(465\) | 183.025 | 0.393603 | ||||||||
\(466\) | 230.868i | 0.495426i | ||||||||
\(467\) | − | 414.383i | − | 0.887330i | −0.896193 | − | 0.443665i | \(-0.853678\pi\) | ||
0.896193 | − | 0.443665i | \(-0.146322\pi\) | |||||||
\(468\) | −22.3815 | −0.0478237 | ||||||||
\(469\) | 49.1144 | + | 87.8435i | 0.104722 | + | 0.187300i | ||||
\(470\) | 362.937i | 0.772206i | ||||||||
\(471\) | 88.8348 | 0.188609 | ||||||||
\(472\) | 135.178i | 0.286395i | ||||||||
\(473\) | − | 119.297i | − | 0.252213i | ||||||
\(474\) | − | 64.7596i | − | 0.136624i | ||||||
\(475\) | 884.928 | 1.86301 | ||||||||
\(476\) | −20.2432 | + | 11.3182i | −0.0425277 | + | 0.0237778i | ||||
\(477\) | − | 361.393i | − | 0.757637i | ||||||
\(478\) | 128.088i | 0.267967i | ||||||||
\(479\) | −535.800 | −1.11858 | −0.559290 | − | 0.828972i | \(-0.688926\pi\) | ||||
−0.559290 | + | 0.828972i | \(0.688926\pi\) | |||||||
\(480\) | − | 225.462i | − | 0.469713i | ||||||
\(481\) | 17.2094 | 0.0357784 | ||||||||
\(482\) | 284.796i | 0.590863i | ||||||||
\(483\) | −149.321 | + | 83.4873i | −0.309154 | + | 0.172852i | ||||
\(484\) | −250.666 | −0.517905 | ||||||||
\(485\) | 751.776i | 1.55005i | ||||||||
\(486\) | −195.205 | −0.401657 | ||||||||
\(487\) | 164.083 | 0.336927 | 0.168463 | − | 0.985708i | \(-0.446120\pi\) | ||||
0.168463 | + | 0.985708i | \(0.446120\pi\) | |||||||
\(488\) | 196.165i | 0.401978i | ||||||||
\(489\) | −102.159 | −0.208913 | ||||||||
\(490\) | −312.138 | − | 191.877i | −0.637016 | − | 0.391586i | ||||
\(491\) | 180.541 | 0.367700 | 0.183850 | − | 0.982954i | \(-0.441144\pi\) | ||||
0.183850 | + | 0.982954i | \(0.441144\pi\) | |||||||
\(492\) | −67.7750 | − | 89.6492i | −0.137754 | − | 0.182214i | ||||
\(493\) | 58.0015i | 0.117650i | ||||||||
\(494\) | −26.1561 | −0.0529475 | ||||||||
\(495\) | 373.607 | 0.754762 | ||||||||
\(496\) | − | 133.943i | − | 0.270047i | ||||||
\(497\) | −460.900 | − | 824.342i | −0.927364 | − | 1.65864i | ||||
\(498\) | 82.5194i | 0.165702i | ||||||||
\(499\) | 90.0645i | 0.180490i | 0.995920 | + | 0.0902450i | \(0.0287650\pi\) | ||||
−0.995920 | + | 0.0902450i | \(0.971235\pi\) | |||||||
\(500\) | 132.640i | 0.265281i | ||||||||
\(501\) | 265.147 | 0.529235 | ||||||||
\(502\) | − | 97.8588i | − | 0.194938i | ||||||
\(503\) | −212.375 | −0.422216 | −0.211108 | − | 0.977463i | \(-0.567707\pi\) | ||||
−0.211108 | + | 0.977463i | \(0.567707\pi\) | |||||||
\(504\) | −349.215 | + | 195.250i | −0.692887 | + | 0.387402i | ||||
\(505\) | 614.835i | 1.21749i | ||||||||
\(506\) | 163.675i | 0.323468i | ||||||||
\(507\) | −153.653 | −0.303062 | ||||||||
\(508\) | 472.693 | 0.930498 | ||||||||
\(509\) | −196.651 | −0.386348 | −0.193174 | − | 0.981165i | \(-0.561878\pi\) | ||||
−0.193174 | + | 0.981165i | \(0.561878\pi\) | |||||||
\(510\) | − | 7.54547i | − | 0.0147950i | ||||||
\(511\) | −153.263 | − | 274.118i | −0.299927 | − | 0.536435i | ||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | 448.973 | 0.875190 | ||||||||
\(514\) | −122.229 | −0.237799 | ||||||||
\(515\) | −1090.05 | −2.11660 | ||||||||
\(516\) | 53.4390 | 0.103564 | ||||||||
\(517\) | − | 297.009i | − | 0.574486i | ||||||
\(518\) | 115.078 | − | 64.3416i | 0.222159 | − | 0.124212i | ||||
\(519\) | − | 60.8945i | − | 0.117330i | ||||||
\(520\) | − | 47.8253i | − | 0.0919718i | ||||||
\(521\) | −540.440 | −1.03731 | −0.518656 | − | 0.854983i | \(-0.673567\pi\) | ||||
−0.518656 | + | 0.854983i | \(0.673567\pi\) | |||||||
\(522\) | 428.822i | 0.821498i | ||||||||
\(523\) | − | 586.434i | − | 1.12129i | −0.828057 | − | 0.560644i | \(-0.810554\pi\) | ||
0.828057 | − | 0.560644i | \(-0.189446\pi\) | |||||||
\(524\) | − | 482.400i | − | 0.920611i | ||||||
\(525\) | −172.573 | + | 96.4880i | −0.328711 | + | 0.183787i | ||||
\(526\) | 326.221i | 0.620193i | ||||||||
\(527\) | − | 29.5854i | − | 0.0561394i | ||||||
\(528\) | 27.9556i | 0.0529462i | ||||||||
\(529\) | 186.441 | 0.352440 | ||||||||
\(530\) | 330.957 | 0.624447 | ||||||||
\(531\) | − | 157.679i | − | 0.296947i | ||||||
\(532\) | 524.711 | − | 293.373i | 0.986300 | − | 0.551452i | ||||
\(533\) | −22.5917 | − | 29.8831i | −0.0423859 | − | 0.0560658i | ||||
\(534\) | −74.4682 | −0.139454 | ||||||||
\(535\) | 700.278i | 1.30893i | ||||||||
\(536\) | 100.641i | 0.187764i | ||||||||
\(537\) | 120.291i | 0.224006i | ||||||||
\(538\) | − | 128.936i | − | 0.239658i | ||||||
\(539\) | 255.438 | + | 157.023i | 0.473911 | + | 0.291322i | ||||
\(540\) | 351.827i | 0.651531i | ||||||||
\(541\) | −235.248 | −0.434840 | −0.217420 | − | 0.976078i | \(-0.569764\pi\) | ||||
−0.217420 | + | 0.976078i | \(0.569764\pi\) | |||||||
\(542\) | 354.495i | 0.654051i | ||||||||
\(543\) | −49.1106 | −0.0904431 | ||||||||
\(544\) | −36.4452 | −0.0669949 | ||||||||
\(545\) | −1444.22 | −2.64995 | ||||||||
\(546\) | 5.10080 | − | 2.85192i | 0.00934213 | − | 0.00522330i | ||||
\(547\) | − | 488.290i | − | 0.892670i | −0.894866 | − | 0.446335i | \(-0.852729\pi\) | ||
0.894866 | − | 0.446335i | \(-0.147271\pi\) | |||||||
\(548\) | 192.132i | 0.350606i | ||||||||
\(549\) | − | 228.817i | − | 0.416789i | ||||||
\(550\) | 189.162i | 0.343931i | ||||||||
\(551\) | − | 1503.42i | − | 2.72854i | ||||||
\(552\) | −171.076 | −0.309920 | ||||||||
\(553\) | 242.120 | + | 433.043i | 0.437829 | + | 0.783080i | ||||
\(554\) | −353.964 | −0.638924 | ||||||||
\(555\) | − | 128.683i | − | 0.231862i | ||||||
\(556\) | 586.949i | 1.05566i | ||||||||
\(557\) | 629.212i | 1.12964i | 0.825213 | + | 0.564822i | \(0.191055\pi\) | ||||
−0.825213 | + | 0.564822i | \(0.808945\pi\) | |||||||
\(558\) | − | 218.734i | − | 0.391996i | ||||||
\(559\) | 17.8130 | 0.0318658 | ||||||||
\(560\) | 127.719 | + | 228.432i | 0.228070 | + | 0.407914i | ||||
\(561\) | 6.17484i | 0.0110068i | ||||||||
\(562\) | − | 214.352i | − | 0.381409i | ||||||
\(563\) | −964.650 | −1.71341 | −0.856705 | − | 0.515806i | \(-0.827493\pi\) | ||||
−0.856705 | + | 0.515806i | \(0.827493\pi\) | |||||||
\(564\) | 133.045 | 0.235896 | ||||||||
\(565\) | − | 294.675i | − | 0.521550i | ||||||
\(566\) | − | 342.730i | − | 0.605529i | ||||||
\(567\) | 361.435 | − | 202.083i | 0.637451 | − | 0.356407i | ||||
\(568\) | − | 944.441i | − | 1.66275i | ||||||
\(569\) | −544.207 | −0.956427 | −0.478213 | − | 0.878244i | \(-0.658715\pi\) | ||||
−0.478213 | + | 0.878244i | \(0.658715\pi\) | |||||||
\(570\) | 195.582i | 0.343126i | ||||||||
\(571\) | − | 425.970i | − | 0.746007i | −0.927830 | − | 0.373004i | \(-0.878328\pi\) | ||
0.927830 | − | 0.373004i | \(-0.121672\pi\) | |||||||
\(572\) | 16.7734i | 0.0293241i | ||||||||
\(573\) | 129.791i | 0.226512i | ||||||||
\(574\) | −262.794 | − | 115.361i | −0.457829 | − | 0.200978i | ||||
\(575\) | 826.849 | 1.43800 | ||||||||
\(576\) | −106.147 | −0.184283 | ||||||||
\(577\) | −514.349 | −0.891419 | −0.445709 | − | 0.895178i | \(-0.647049\pi\) | ||||
−0.445709 | + | 0.895178i | \(0.647049\pi\) | |||||||
\(578\) | 287.780 | 0.497890 | ||||||||
\(579\) | 294.160i | 0.508048i | ||||||||
\(580\) | 1178.12 | 2.03124 | ||||||||
\(581\) | −308.519 | − | 551.801i | −0.531014 | − | 0.949744i | ||||
\(582\) | −91.8621 | −0.157839 | ||||||||
\(583\) | −270.839 | −0.464560 | ||||||||
\(584\) | − | 314.055i | − | 0.537765i | ||||||
\(585\) | 55.7858i | 0.0953604i | ||||||||
\(586\) | −4.02790 | −0.00687354 | ||||||||
\(587\) | −543.602 | −0.926068 | −0.463034 | − | 0.886341i | \(-0.653239\pi\) | ||||
−0.463034 | + | 0.886341i | \(0.653239\pi\) | |||||||
\(588\) | −70.3383 | + | 114.424i | −0.119623 | + | 0.194598i | ||||
\(589\) | 766.866i | 1.30198i | ||||||||
\(590\) | 144.399 | 0.244744 | ||||||||
\(591\) | −279.878 | −0.473566 | ||||||||
\(592\) | −94.1742 | −0.159078 | ||||||||
\(593\) | 1166.75 | 1.96754 | 0.983771 | − | 0.179429i | \(-0.0574251\pi\) | ||||
0.983771 | + | 0.179429i | \(0.0574251\pi\) | |||||||
\(594\) | 95.9725i | 0.161570i | ||||||||
\(595\) | 28.2106 | + | 50.4561i | 0.0474128 | + | 0.0848001i | ||||
\(596\) | − | 587.091i | − | 0.985051i | ||||||
\(597\) | 42.1273 | 0.0705650 | ||||||||
\(598\) | −24.4394 | −0.0408686 | ||||||||
\(599\) | 801.405 | 1.33790 | 0.668952 | − | 0.743306i | \(-0.266743\pi\) | ||||
0.668952 | + | 0.743306i | \(0.266743\pi\) | |||||||
\(600\) | −197.716 | −0.329526 | ||||||||
\(601\) | 778.685 | 1.29565 | 0.647824 | − | 0.761790i | \(-0.275679\pi\) | ||||
0.647824 | + | 0.761790i | \(0.275679\pi\) | |||||||
\(602\) | 119.114 | − | 66.5983i | 0.197864 | − | 0.110628i | ||||
\(603\) | − | 117.393i | − | 0.194682i | ||||||
\(604\) | − | 241.681i | − | 0.400134i | ||||||
\(605\) | 624.784i | 1.03270i | ||||||||
\(606\) | −75.1288 | −0.123975 | ||||||||
\(607\) | 794.568i | 1.30901i | 0.756058 | + | 0.654504i | \(0.227123\pi\) | ||||
−0.756058 | + | 0.654504i | \(0.772877\pi\) | |||||||
\(608\) | 944.675 | 1.55374 | ||||||||
\(609\) | 163.925 | + | 293.189i | 0.269172 | + | 0.481427i | ||||
\(610\) | 209.546 | 0.343518 | ||||||||
\(611\) | 44.3485 | 0.0725834 | ||||||||
\(612\) | 27.0528 | 0.0442039 | ||||||||
\(613\) | −743.982 | −1.21367 | −0.606837 | − | 0.794827i | \(-0.707562\pi\) | ||||
−0.606837 | + | 0.794827i | \(0.707562\pi\) | |||||||
\(614\) | − | 263.015i | − | 0.428363i | ||||||
\(615\) | −223.450 | + | 168.929i | −0.363334 | + | 0.274681i | ||||
\(616\) | 146.327 | + | 261.712i | 0.237543 | + | 0.424857i | ||||
\(617\) | −100.316 | −0.162587 | −0.0812933 | − | 0.996690i | \(-0.525905\pi\) | ||||
−0.0812933 | + | 0.996690i | \(0.525905\pi\) | |||||||
\(618\) | − | 133.197i | − | 0.215528i | ||||||
\(619\) | 398.261i | 0.643395i | 0.946843 | + | 0.321697i | \(0.104253\pi\) | ||||
−0.946843 | + | 0.321697i | \(0.895747\pi\) | |||||||
\(620\) | −600.936 | −0.969252 | ||||||||
\(621\) | 419.506 | 0.675533 | ||||||||
\(622\) | −583.614 | −0.938286 | ||||||||
\(623\) | 497.964 | − | 278.418i | 0.799300 | − | 0.446898i | ||||
\(624\) | −4.17424 | −0.00668949 | ||||||||
\(625\) | −442.216 | −0.707545 | ||||||||
\(626\) | 512.727 | 0.819052 | ||||||||
\(627\) | − | 160.054i | − | 0.255270i | ||||||
\(628\) | −291.676 | −0.464452 | ||||||||
\(629\) | −20.8012 | −0.0330703 | ||||||||
\(630\) | 208.569 | + | 373.036i | 0.331062 | + | 0.592121i | ||||
\(631\) | −285.492 | −0.452443 | −0.226222 | − | 0.974076i | \(-0.572637\pi\) | ||||
−0.226222 | + | 0.974076i | \(0.572637\pi\) | |||||||
\(632\) | 496.133i | 0.785021i | ||||||||
\(633\) | 98.9578i | 0.156331i | ||||||||
\(634\) | 111.454i | 0.175795i | ||||||||
\(635\) | − | 1178.19i | − | 1.85541i | ||||||
\(636\) | − | 121.322i | − | 0.190758i | ||||||
\(637\) | −23.4461 | + | 38.1412i | −0.0368071 | + | 0.0598763i | ||||
\(638\) | 321.372 | 0.503718 | ||||||||
\(639\) | 1101.64i | 1.72401i | ||||||||
\(640\) | 889.821i | 1.39035i | ||||||||
\(641\) | − | 54.3599i | − | 0.0848048i | −0.999101 | − | 0.0424024i | \(-0.986499\pi\) | ||
0.999101 | − | 0.0424024i | \(-0.0135012\pi\) | |||||||
\(642\) | −85.5694 | −0.133286 | ||||||||
\(643\) | −376.244 | −0.585138 | −0.292569 | − | 0.956244i | \(-0.594510\pi\) | ||||
−0.292569 | + | 0.956244i | \(0.594510\pi\) | |||||||
\(644\) | 490.274 | − | 274.118i | 0.761295 | − | 0.425649i | ||||
\(645\) | − | 133.197i | − | 0.206506i | ||||||
\(646\) | 31.6151 | 0.0489399 | ||||||||
\(647\) | 1066.47i | 1.64833i | 0.566347 | + | 0.824167i | \(0.308356\pi\) | ||||
−0.566347 | + | 0.824167i | \(0.691644\pi\) | |||||||
\(648\) | 414.092 | 0.639032 | ||||||||
\(649\) | −118.169 | −0.182079 | ||||||||
\(650\) | −28.2451 | −0.0434540 | ||||||||
\(651\) | −83.6151 | − | 149.550i | −0.128441 | − | 0.229723i | ||||
\(652\) | 335.423 | 0.514452 | ||||||||
\(653\) | − | 525.303i | − | 0.804446i | −0.915542 | − | 0.402223i | \(-0.868238\pi\) | ||
0.915542 | − | 0.402223i | \(-0.131762\pi\) | |||||||
\(654\) | − | 176.474i | − | 0.269839i | ||||||
\(655\) | −1202.38 | −1.83570 | ||||||||
\(656\) | 123.627 | + | 163.528i | 0.188456 | + | 0.249280i | ||||
\(657\) | 366.329i | 0.557579i | ||||||||
\(658\) | 296.555 | − | 165.808i | 0.450692 | − | 0.251987i | ||||
\(659\) | 995.831i | 1.51113i | 0.655076 | + | 0.755563i | \(0.272636\pi\) | ||||
−0.655076 | + | 0.755563i | \(0.727364\pi\) | |||||||
\(660\) | 125.423 | 0.190034 | ||||||||
\(661\) | 355.594i | 0.537964i | 0.963145 | + | 0.268982i | \(0.0866873\pi\) | ||||
−0.963145 | + | 0.268982i | \(0.913313\pi\) | |||||||
\(662\) | − | 359.074i | − | 0.542408i | ||||||
\(663\) | −0.922008 | −0.00139066 | ||||||||
\(664\) | − | 632.194i | − | 0.952099i | ||||||
\(665\) | −731.230 | − | 1307.84i | −1.09959 | − | 1.96668i | ||||
\(666\) | −153.789 | −0.230915 | ||||||||
\(667\) | − | 1404.75i | − | 2.10608i | ||||||
\(668\) | −870.571 | −1.30325 | ||||||||
\(669\) | 93.3939i | 0.139602i | ||||||||
\(670\) | 107.507 | 0.160458 | ||||||||
\(671\) | −171.482 | −0.255562 | ||||||||
\(672\) | −184.225 | + | 103.002i | −0.274144 | + | 0.153277i | ||||
\(673\) | 1134.02i | 1.68502i | 0.538680 | + | 0.842510i | \(0.318923\pi\) | ||||
−0.538680 | + | 0.842510i | \(0.681077\pi\) | |||||||
\(674\) | −483.982 | −0.718074 | ||||||||
\(675\) | 484.832 | 0.718269 | ||||||||
\(676\) | 504.495 | 0.746295 | ||||||||
\(677\) | − | 57.2821i | − | 0.0846117i | −0.999105 | − | 0.0423058i | \(-0.986530\pi\) | ||
0.999105 | − | 0.0423058i | \(-0.0134704\pi\) | |||||||
\(678\) | 36.0074 | 0.0531083 | ||||||||
\(679\) | 614.276 | − | 343.449i | 0.904677 | − | 0.505816i | ||||
\(680\) | 57.8070i | 0.0850104i | ||||||||
\(681\) | −199.165 | −0.292460 | ||||||||
\(682\) | −163.925 | −0.240360 | ||||||||
\(683\) | − | 207.340i | − | 0.303573i | −0.988413 | − | 0.151786i | \(-0.951497\pi\) | ||
0.988413 | − | 0.151786i | \(-0.0485025\pi\) | |||||||
\(684\) | −701.219 | −1.02517 | ||||||||
\(685\) | 478.888 | 0.699107 | ||||||||
\(686\) | −14.1823 | + | 342.707i | −0.0206738 | + | 0.499572i | ||||
\(687\) | 152.908 | 0.222573 | ||||||||
\(688\) | −97.4773 | −0.141682 | ||||||||
\(689\) | − | 40.4408i | − | 0.0586949i | ||||||
\(690\) | 182.745i | 0.264849i | ||||||||
\(691\) | 792.271 | 1.14656 | 0.573279 | − | 0.819360i | \(-0.305671\pi\) | ||||
0.573279 | + | 0.819360i | \(0.305671\pi\) | |||||||
\(692\) | 199.938i | 0.288928i | ||||||||
\(693\) | −170.683 | − | 305.274i | −0.246295 | − | 0.440511i | ||||
\(694\) | 269.425i | 0.388220i | ||||||||
\(695\) | 1462.97 | 2.10499 | ||||||||
\(696\) | 335.904i | 0.482620i | ||||||||
\(697\) | 27.3068 | + | 36.1200i | 0.0391777 | + | 0.0518221i | ||||
\(698\) | 188.892i | 0.270618i | ||||||||
\(699\) | − | 210.945i | − | 0.301781i | ||||||
\(700\) | 566.619 | − | 316.804i | 0.809456 | − | 0.452577i | ||||
\(701\) | 1100.36 | 1.56970 | 0.784850 | − | 0.619686i | \(-0.212740\pi\) | ||||
0.784850 | + | 0.619686i | \(0.212740\pi\) | |||||||
\(702\) | −14.3303 | −0.0204135 | ||||||||
\(703\) | 539.176 | 0.766965 | ||||||||
\(704\) | 79.5497i | 0.112997i | ||||||||
\(705\) | − | 331.615i | − | 0.470376i | ||||||
\(706\) | − | 201.309i | − | 0.285140i | ||||||
\(707\) | 502.381 | − | 280.887i | 0.710581 | − | 0.397295i | ||||
\(708\) | − | 52.9339i | − | 0.0747654i | ||||||
\(709\) | − | 332.638i | − | 0.469165i | −0.972096 | − | 0.234583i | \(-0.924628\pi\) | ||
0.972096 | − | 0.234583i | \(-0.0753724\pi\) | |||||||
\(710\) | −1008.86 | −1.42094 | ||||||||
\(711\) | − | 578.715i | − | 0.813945i | ||||||
\(712\) | 570.512 | 0.801281 | ||||||||
\(713\) | 716.536i | 1.00496i | ||||||||
\(714\) | −6.16540 | + | 3.44715i | −0.00863502 | + | 0.00482794i | ||||
\(715\) | 41.8076 | 0.0584721 | ||||||||
\(716\) | − | 394.959i | − | 0.551618i | ||||||
\(717\) | − | 117.034i | − | 0.163227i | ||||||
\(718\) | 1.55000 | 0.00215878 | ||||||||
\(719\) | −690.961 | −0.961003 | −0.480502 | − | 0.876994i | \(-0.659545\pi\) | ||||
−0.480502 | + | 0.876994i | \(0.659545\pi\) | |||||||
\(720\) | − | 305.274i | − | 0.423992i | ||||||
\(721\) | 497.988 | + | 890.677i | 0.690691 | + | 1.23534i | ||||
\(722\) | −458.477 | −0.635010 | ||||||||
\(723\) | − | 260.218i | − | 0.359915i | ||||||
\(724\) | 161.247 | 0.222717 | ||||||||
\(725\) | − | 1623.50i | − | 2.23931i | ||||||
\(726\) | −76.3445 | −0.105158 | ||||||||
\(727\) | 227.773 | 0.313306 | 0.156653 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156653 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(728\) | −39.0780 | + | 21.8490i | −0.0536786 | + | 0.0300124i | ||||
\(729\) | −354.045 | −0.485659 | ||||||||
\(730\) | −335.477 | −0.459558 | ||||||||
\(731\) | −21.5308 | −0.0294539 | ||||||||
\(732\) | − | 76.8155i | − | 0.104939i | ||||||
\(733\) | − | 444.673i | − | 0.606648i | −0.952888 | − | 0.303324i | \(-0.901904\pi\) | ||
0.952888 | − | 0.303324i | \(-0.0980964\pi\) | |||||||
\(734\) | − | 16.9093i | − | 0.0230372i | ||||||
\(735\) | 285.201 | + | 175.318i | 0.388028 | + | 0.238528i | ||||
\(736\) | 882.675 | 1.19929 | ||||||||
\(737\) | −87.9780 | −0.119373 | ||||||||
\(738\) | 201.887 | + | 267.046i | 0.273560 | + | 0.361850i | ||||
\(739\) | 187.670 | 0.253951 | 0.126975 | − | 0.991906i | \(-0.459473\pi\) | ||||
0.126975 | + | 0.991906i | \(0.459473\pi\) | |||||||
\(740\) | 422.512i | 0.570963i | ||||||||
\(741\) | 23.8988 | 0.0322521 | ||||||||
\(742\) | −151.198 | − | 270.425i | −0.203771 | − | 0.364454i | ||||
\(743\) | 277.339 | 0.373270 | 0.186635 | − | 0.982429i | \(-0.440242\pi\) | ||||
0.186635 | + | 0.982429i | \(0.440242\pi\) | |||||||
\(744\) | − | 171.338i | − | 0.230293i | ||||||
\(745\) | −1463.32 | −1.96419 | ||||||||
\(746\) | 292.468 | 0.392048 | ||||||||
\(747\) | 737.422i | 0.987178i | ||||||||
\(748\) | − | 20.2742i | − | 0.0271045i | ||||||
\(749\) | 572.197 | − | 319.922i | 0.763948 | − | 0.427133i | ||||
\(750\) | 40.3979i | 0.0538639i | ||||||||
\(751\) | − | 374.047i | − | 0.498065i | −0.968495 | − | 0.249032i | \(-0.919887\pi\) | ||
0.968495 | − | 0.249032i | \(-0.0801126\pi\) | |||||||
\(752\) | −242.686 | −0.322721 | ||||||||
\(753\) | 89.4137i | 0.118743i | ||||||||
\(754\) | 47.9862i | 0.0636422i | ||||||||
\(755\) | −602.389 | −0.797866 | ||||||||
\(756\) | 287.477 | − | 160.732i | 0.380261 | − | 0.212609i | ||||
\(757\) | − | 798.355i | − | 1.05463i | −0.849670 | − | 0.527315i | \(-0.823199\pi\) | ||
0.849670 | − | 0.527315i | \(-0.176801\pi\) | |||||||
\(758\) | −389.441 | −0.513774 | ||||||||
\(759\) | − | 149.550i | − | 0.197035i | ||||||
\(760\) | − | 1498.38i | − | 1.97155i | ||||||
\(761\) | 1155.44i | 1.51832i | 0.650903 | + | 0.759161i | \(0.274390\pi\) | ||||
−0.650903 | + | 0.759161i | \(0.725610\pi\) | |||||||
\(762\) | 143.967 | 0.188933 | ||||||||
\(763\) | 659.793 | + | 1180.07i | 0.864735 | + | 1.54662i | ||||
\(764\) | − | 426.150i | − | 0.557788i | ||||||
\(765\) | − | 67.4290i | − | 0.0881425i | ||||||
\(766\) | −545.025 | −0.711521 | ||||||||
\(767\) | − | 17.6446i | − | 0.0230047i | ||||||
\(768\) | −156.243 | −0.203441 | ||||||||
\(769\) | 300.131i | 0.390287i | 0.980775 | + | 0.195143i | \(0.0625172\pi\) | ||||
−0.980775 | + | 0.195143i | \(0.937483\pi\) | |||||||
\(770\) | 279.564 | − | 156.308i | 0.363071 | − | 0.202997i | ||||
\(771\) | 111.680 | 0.144851 | ||||||||
\(772\) | − | 965.831i | − | 1.25108i | ||||||
\(773\) | 1141.88 | 1.47720 | 0.738600 | − | 0.674144i | \(-0.235487\pi\) | ||||
0.738600 | + | 0.674144i | \(0.235487\pi\) | |||||||
\(774\) | −159.183 | −0.205663 | ||||||||
\(775\) | 828.115i | 1.06854i | ||||||||
\(776\) | 703.770 | 0.906920 | ||||||||
\(777\) | −105.147 | + | 58.7890i | −0.135324 | + | 0.0756615i | ||||
\(778\) | 301.964 | 0.388128 | ||||||||
\(779\) | −707.804 | − | 936.245i | −0.908606 | − | 1.20186i | ||||
\(780\) | 18.7277i | 0.0240099i | ||||||||
\(781\) | 825.605 | 1.05711 | ||||||||
\(782\) | 29.5402 | 0.0377752 | ||||||||
\(783\) | − | 823.691i | − | 1.05197i | ||||||
\(784\) | 128.303 | − | 208.718i | 0.163652 | − | 0.266222i | ||||
\(785\) | 727.002i | 0.926117i | ||||||||
\(786\) | − | 146.923i | − | 0.186925i | ||||||
\(787\) | 688.377i | 0.874685i | 0.899295 | + | 0.437342i | \(0.144080\pi\) | ||||
−0.899295 | + | 0.437342i | \(0.855920\pi\) | |||||||
\(788\) | 918.936 | 1.16616 | ||||||||
\(789\) | − | 298.069i | − | 0.377780i | ||||||
\(790\) | 529.976 | 0.670856 | ||||||||
\(791\) | −240.779 | + | 134.623i | −0.304398 | + | 0.170193i | ||||
\(792\) | − | 349.750i | − | 0.441603i | ||||||
\(793\) | − | 25.6052i | − | 0.0322890i | ||||||
\(794\) | −27.7045 | −0.0348923 | ||||||||
\(795\) | −302.395 | −0.380372 | ||||||||
\(796\) | −138.319 | −0.173767 | ||||||||
\(797\) | 1528.46i | 1.91777i | 0.283797 | + | 0.958884i | \(0.408406\pi\) | ||||
−0.283797 | + | 0.958884i | \(0.591594\pi\) | |||||||
\(798\) | 159.810 | − | 89.3516i | 0.200263 | − | 0.111969i | ||||
\(799\) | −53.6046 | −0.0670896 | ||||||||
\(800\) | 1020.12 | 1.27516 | ||||||||
\(801\) | −665.474 | −0.830804 | ||||||||
\(802\) | −112.243 | −0.139954 | ||||||||
\(803\) | 274.538 | 0.341890 | ||||||||
\(804\) | − | 39.4098i | − | 0.0490172i | ||||||
\(805\) | −683.239 | − | 1222.01i | −0.848744 | − | 1.51802i | ||||
\(806\) | − | 24.4768i | − | 0.0303683i | ||||||
\(807\) | 117.809i | 0.145983i | ||||||||
\(808\) | 575.573 | 0.712343 | ||||||||
\(809\) | 1121.48i | 1.38626i | 0.720813 | + | 0.693129i | \(0.243768\pi\) | ||||
−0.720813 | + | 0.693129i | \(0.756232\pi\) | |||||||
\(810\) | − | 442.339i | − | 0.546097i | ||||||
\(811\) | − | 1294.50i | − | 1.59618i | −0.602539 | − | 0.798089i | \(-0.705844\pi\) | ||
0.602539 | − | 0.798089i | \(-0.294156\pi\) | |||||||
\(812\) | −538.225 | − | 962.642i | −0.662839 | − | 1.18552i | ||||
\(813\) | − | 323.903i | − | 0.398404i | ||||||
\(814\) | 115.254i | 0.141590i | ||||||||
\(815\) | − | 836.040i | − | 1.02582i | ||||||
\(816\) | 5.04546 | 0.00618316 | ||||||||
\(817\) | 558.087 | 0.683093 | ||||||||
\(818\) | 501.575i | 0.613173i | ||||||||
\(819\) | 45.5826 | − | 25.4858i | 0.0556564 | − | 0.0311182i | ||||
\(820\) | 733.666 | − | 554.653i | 0.894715 | − | 0.676406i | ||||
\(821\) | −1256.57 | −1.53054 | −0.765268 | − | 0.643712i | \(-0.777393\pi\) | ||||
−0.765268 | + | 0.643712i | \(0.777393\pi\) | |||||||
\(822\) | 58.5170i | 0.0711886i | ||||||||
\(823\) | 973.556i | 1.18294i | 0.806329 | + | 0.591468i | \(0.201451\pi\) | ||||
−0.806329 | + | 0.591468i | \(0.798549\pi\) | |||||||
\(824\) | 1020.44i | 1.23840i | ||||||||
\(825\) | − | 172.838i | − | 0.209500i | ||||||
\(826\) | −65.9688 | − | 117.989i | −0.0798654 | − | 0.142843i | ||||
\(827\) | − | 550.140i | − | 0.665224i | −0.943064 | − | 0.332612i | \(-0.892070\pi\) | ||
0.943064 | − | 0.332612i | \(-0.107930\pi\) | |||||||
\(828\) | −655.198 | −0.791302 | ||||||||
\(829\) | − | 312.820i | − | 0.377346i | −0.982040 | − | 0.188673i | \(-0.939581\pi\) | ||
0.982040 | − | 0.188673i | \(-0.0604186\pi\) | |||||||
\(830\) | −675.317 | −0.813635 | ||||||||
\(831\) | 323.417 | 0.389190 | ||||||||
\(832\) | −11.8781 | −0.0142766 | ||||||||
\(833\) | 28.3396 | − | 46.1017i | 0.0340211 | − | 0.0553442i | ||||
\(834\) | 178.765i | 0.214347i | ||||||||
\(835\) | 2169.90i | 2.59868i | ||||||||
\(836\) | 525.515i | 0.628606i | ||||||||
\(837\) | 420.148i | 0.501970i | ||||||||
\(838\) | − | 94.7376i | − | 0.113052i | ||||||
\(839\) | 1251.01 | 1.49107 | 0.745536 | − | 0.666465i | \(-0.232193\pi\) | ||||
0.745536 | + | 0.666465i | \(0.232193\pi\) | |||||||
\(840\) | 163.376 | + | 292.206i | 0.194495 | + | 0.347864i | ||||
\(841\) | −1917.20 | −2.27967 | ||||||||
\(842\) | 36.0023i | 0.0427580i | ||||||||
\(843\) | 195.854i | 0.232329i | ||||||||
\(844\) | − | 324.913i | − | 0.384968i | ||||||
\(845\) | − | 1257.45i | − | 1.48811i | ||||||
\(846\) | −396.314 | −0.468456 | ||||||||
\(847\) | 510.511 | − | 285.433i | 0.602728 | − | 0.336993i | ||||
\(848\) | 221.302i | 0.260969i | ||||||||
\(849\) | 313.152i | 0.368848i | ||||||||
\(850\) | 34.1402 | 0.0401650 | ||||||||
\(851\) | 503.789 | 0.591997 | ||||||||
\(852\) | 369.830i | 0.434073i | ||||||||
\(853\) | 313.471i | 0.367493i | 0.982974 | + | 0.183746i | \(0.0588225\pi\) | ||||
−0.982974 | + | 0.183746i | \(0.941178\pi\) | |||||||
\(854\) | −95.7312 | − | 171.220i | −0.112097 | − | 0.200492i | ||||
\(855\) | 1747.79i | 2.04420i | ||||||||
\(856\) | 655.561 | 0.765842 | ||||||||
\(857\) | − | 112.746i | − | 0.131559i | −0.997834 | − | 0.0657794i | \(-0.979047\pi\) | ||
0.997834 | − | 0.0657794i | \(-0.0209534\pi\) | |||||||
\(858\) | 5.10861i | 0.00595409i | ||||||||
\(859\) | − | 950.944i | − | 1.10704i | −0.832837 | − | 0.553518i | \(-0.813285\pi\) | ||
0.832837 | − | 0.553518i | \(-0.186715\pi\) | |||||||
\(860\) | 437.331i | 0.508525i | ||||||||
\(861\) | 240.115 | + | 105.406i | 0.278879 | + | 0.122423i | ||||
\(862\) | 388.592 | 0.450802 | ||||||||
\(863\) | −661.826 | −0.766890 | −0.383445 | − | 0.923564i | \(-0.625262\pi\) | ||||
−0.383445 | + | 0.923564i | \(0.625262\pi\) | |||||||
\(864\) | 517.566 | 0.599034 | ||||||||
\(865\) | 498.345 | 0.576121 | ||||||||
\(866\) | 722.263i | 0.834022i | ||||||||
\(867\) | −262.945 | −0.303281 | ||||||||
\(868\) | 274.538 | + | 491.025i | 0.316288 | + | 0.565697i | ||||
\(869\) | −433.706 | −0.499086 | ||||||||
\(870\) | 358.817 | 0.412433 | ||||||||
\(871\) | − | 13.1366i | − | 0.0150822i | ||||||
\(872\) | 1352.00i | 1.55046i | ||||||||
\(873\) | −820.912 | −0.940335 | ||||||||
\(874\) | −765.694 | −0.876080 | ||||||||
\(875\) | −151.037 | − | 270.138i | −0.172614 | − | 0.308729i | ||||
\(876\) | 122.979i | 0.140387i | ||||||||
\(877\) | 430.203 | 0.490539 | 0.245270 | − | 0.969455i | \(-0.421123\pi\) | ||||
0.245270 | + | 0.969455i | \(0.421123\pi\) | |||||||
\(878\) | 346.450 | 0.394590 | ||||||||
\(879\) | 3.68029 | 0.00418691 | ||||||||
\(880\) | −228.782 | −0.259979 | ||||||||
\(881\) | 1181.82i | 1.34146i | 0.741703 | + | 0.670728i | \(0.234018\pi\) | ||||
−0.741703 | + | 0.670728i | \(0.765982\pi\) | |||||||
\(882\) | 209.523 | − | 340.843i | 0.237554 | − | 0.386444i | ||||
\(883\) | − | 721.775i | − | 0.817413i | −0.912666 | − | 0.408706i | \(-0.865980\pi\) | ||
0.912666 | − | 0.408706i | \(-0.134020\pi\) | |||||||
\(884\) | 3.02727 | 0.00342452 | ||||||||
\(885\) | −131.938 | −0.149082 | ||||||||
\(886\) | −416.744 | −0.470366 | ||||||||
\(887\) | −453.806 | −0.511619 | −0.255809 | − | 0.966727i | \(-0.582342\pi\) | ||||
−0.255809 | + | 0.966727i | \(0.582342\pi\) | |||||||
\(888\) | −120.466 | −0.135660 | ||||||||
\(889\) | −962.695 | + | 538.255i | −1.08290 | + | 0.605461i | ||||
\(890\) | − | 609.429i | − | 0.684751i | ||||||
\(891\) | 361.988i | 0.406272i | ||||||||
\(892\) | − | 306.645i | − | 0.343773i | ||||||
\(893\) | 1389.45 | 1.55594 | ||||||||
\(894\) | − | 178.808i | − | 0.200009i | ||||||
\(895\) | −984.433 | −1.09993 | ||||||||
\(896\) | 727.072 | − | 406.515i | 0.811465 | − | 0.453700i | ||||
\(897\) | 22.3303 | 0.0248944 | ||||||||
\(898\) | 418.798 | 0.466368 | ||||||||
\(899\) | 1406.90 | 1.56496 | ||||||||
\(900\) | −757.225 | −0.841361 | ||||||||
\(901\) | 48.8812i | 0.0542522i | ||||||||
\(902\) | 200.132 | − | 151.300i | 0.221876 | − | 0.167739i | ||||
\(903\) | −108.835 | + | 60.8509i | −0.120526 | + | 0.0673875i | ||||
\(904\) | −275.858 | −0.305153 | ||||||||
\(905\) | − | 401.909i | − | 0.444098i | ||||||
\(906\) | − | 73.6080i | − | 0.0812450i | ||||||
\(907\) | −1040.95 | −1.14769 | −0.573845 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(908\) | 653.929 | 0.720186 | ||||||||
\(909\) | −671.377 | −0.738589 | ||||||||
\(910\) | 23.3394 | + | 41.7437i | 0.0256477 | + | 0.0458722i | ||||
\(911\) | −1189.07 | −1.30524 | −0.652618 | − | 0.757687i | \(-0.726329\pi\) | ||||
−0.652618 | + | 0.757687i | \(0.726329\pi\) | |||||||
\(912\) | −130.780 | −0.143399 | ||||||||
\(913\) | 552.646 | 0.605308 | ||||||||
\(914\) | − | 362.106i | − | 0.396177i | ||||||
\(915\) | −191.462 | −0.209249 | ||||||||
\(916\) | −502.049 | −0.548089 | ||||||||
\(917\) | 549.308 | + | 982.465i | 0.599027 | + | 1.07139i | ||||
\(918\) | 17.3212 | 0.0188684 | ||||||||
\(919\) | 503.858i | 0.548268i | 0.961692 | + | 0.274134i | \(0.0883912\pi\) | ||||
−0.961692 | + | 0.274134i | \(0.911609\pi\) | |||||||
\(920\) | − | 1400.04i | − | 1.52178i | ||||||
\(921\) | 240.317i | 0.260931i | ||||||||
\(922\) | − | 791.243i | − | 0.858181i | ||||||
\(923\) | 123.277i | 0.133561i | ||||||||
\(924\) | −57.2994 | − | 102.483i | −0.0620123 | − | 0.110912i | ||||
\(925\) | 582.239 | 0.629448 | ||||||||
\(926\) | 755.161i | 0.815509i | ||||||||
\(927\) | − | 1190.29i | − | 1.28403i | ||||||
\(928\) | − | 1733.11i | − | 1.86758i | ||||||
\(929\) | 697.206 | 0.750491 | 0.375246 | − | 0.926925i | \(-0.377558\pi\) | ||||
0.375246 | + | 0.926925i | \(0.377558\pi\) | |||||||
\(930\) | −183.025 | −0.196801 | ||||||||
\(931\) | −734.574 | + | 1194.98i | −0.789016 | + | 1.28354i | ||||
\(932\) | 692.605i | 0.743139i | ||||||||
\(933\) | 533.248 | 0.571542 | ||||||||
\(934\) | 414.383i | 0.443665i | ||||||||
\(935\) | −50.5333 | −0.0540463 | ||||||||
\(936\) | 52.2235 | 0.0557944 | ||||||||
\(937\) | 1007.23 | 1.07495 | 0.537475 | − | 0.843280i | \(-0.319378\pi\) | ||||
0.537475 | + | 0.843280i | \(0.319378\pi\) | |||||||
\(938\) | −49.1144 | − | 87.8435i | −0.0523608 | − | 0.0936498i | ||||
\(939\) | −468.479 | −0.498912 | ||||||||
\(940\) | 1088.81i | 1.15831i | ||||||||
\(941\) | 790.864i | 0.840450i | 0.907420 | + | 0.420225i | \(0.138049\pi\) | ||||
−0.907420 | + | 0.420225i | \(0.861951\pi\) | |||||||
\(942\) | −88.8348 | −0.0943045 | ||||||||
\(943\) | −661.350 | − | 874.799i | −0.701325 | − | 0.927676i | ||||
\(944\) | 96.5559i | 0.102284i | ||||||||
\(945\) | −400.624 | − | 716.536i | −0.423941 | − | 0.758239i | ||||
\(946\) | 119.297i | 0.126106i | ||||||||
\(947\) | −1541.40 | −1.62767 | −0.813836 | − | 0.581095i | \(-0.802624\pi\) | ||||
−0.813836 | + | 0.581095i | \(0.802624\pi\) | |||||||
\(948\) | − | 194.279i | − | 0.204935i | ||||||
\(949\) | 40.9931i | 0.0431961i | ||||||||
\(950\) | −884.928 | −0.931503 | ||||||||
\(951\) | − | 101.836i | − | 0.107083i | ||||||
\(952\) | 47.2341 | − | 26.4092i | 0.0496156 | − | 0.0277407i | ||||
\(953\) | −54.1599 | −0.0568309 | −0.0284155 | − | 0.999596i | \(-0.509046\pi\) | ||||
−0.0284155 | + | 0.999596i | \(0.509046\pi\) | |||||||
\(954\) | 361.393i | 0.378819i | ||||||||
\(955\) | −1062.18 | −1.11223 | ||||||||
\(956\) | 384.264i | 0.401950i | ||||||||
\(957\) | −293.638 | −0.306831 | ||||||||
\(958\) | 535.800 | 0.559290 | ||||||||
\(959\) | −218.780 | − | 391.299i | −0.228134 | − | 0.408029i | ||||
\(960\) | 88.8184i | 0.0925192i | ||||||||
\(961\) | 243.367 | 0.253243 | ||||||||
\(962\) | −17.2094 | −0.0178892 | ||||||||
\(963\) | −764.679 | −0.794059 | ||||||||
\(964\) | 854.388i | 0.886295i | ||||||||
\(965\) | −2407.33 | −2.49464 | ||||||||
\(966\) | 149.321 | − | 83.4873i | 0.154577 | − | 0.0864258i | ||||
\(967\) | 197.836i | 0.204587i | 0.994754 | + | 0.102294i | \(0.0326181\pi\) | ||||
−0.994754 | + | 0.102294i | \(0.967382\pi\) | |||||||
\(968\) | 584.887 | 0.604222 | ||||||||
\(969\) | −28.8868 | −0.0298109 | ||||||||
\(970\) | − | 751.776i | − | 0.775027i | ||||||
\(971\) | −1359.32 | −1.39992 | −0.699958 | − | 0.714184i | \(-0.746798\pi\) | ||||
−0.699958 | + | 0.714184i | \(0.746798\pi\) | |||||||
\(972\) | −585.616 | −0.602485 | ||||||||
\(973\) | −668.358 | − | 1195.39i | −0.686904 | − | 1.22856i | ||||
\(974\) | −164.083 | −0.168463 | ||||||||
\(975\) | 25.8076 | 0.0264693 | ||||||||
\(976\) | 140.118i | 0.143564i | ||||||||
\(977\) | 1309.40i | 1.34022i | 0.742260 | + | 0.670112i | \(0.233754\pi\) | ||||
−0.742260 | + | 0.670112i | \(0.766246\pi\) | |||||||
\(978\) | 102.159 | 0.104457 | ||||||||
\(979\) | 498.726i | 0.509424i | ||||||||
\(980\) | −936.414 | − | 575.631i | −0.955524 | − | 0.587378i | ||||
\(981\) | − | 1577.04i | − | 1.60758i | ||||||
\(982\) | −180.541 | −0.183850 | ||||||||
\(983\) | − | 418.360i | − | 0.425595i | −0.977096 | − | 0.212798i | \(-0.931743\pi\) | ||
0.977096 | − | 0.212798i | \(-0.0682575\pi\) | |||||||
\(984\) | 158.142 | + | 209.181i | 0.160713 | + | 0.212583i | ||||
\(985\) | − | 2290.45i | − | 2.32533i | ||||||
\(986\) | − | 58.0015i | − | 0.0588251i | ||||||
\(987\) | −270.963 | + | 151.499i | −0.274532 | + | 0.153494i | ||||
\(988\) | −78.4682 | −0.0794212 | ||||||||
\(989\) | 521.459 | 0.527259 | ||||||||
\(990\) | −373.607 | −0.377381 | ||||||||
\(991\) | 661.767i | 0.667777i | 0.942613 | + | 0.333889i | \(0.108361\pi\) | ||||
−0.942613 | + | 0.333889i | \(0.891639\pi\) | |||||||
\(992\) | 884.026i | 0.891156i | ||||||||
\(993\) | 328.086i | 0.330399i | ||||||||
\(994\) | 460.900 | + | 824.342i | 0.463682 | + | 0.829318i | ||||
\(995\) | 344.759i | 0.346491i | ||||||||
\(996\) | 247.558i | 0.248552i | ||||||||
\(997\) | −882.417 | −0.885073 | −0.442536 | − | 0.896751i | \(-0.645921\pi\) | ||||
−0.442536 | + | 0.896751i | \(0.645921\pi\) | |||||||
\(998\) | − | 90.0645i | − | 0.0902450i | ||||||
\(999\) | 295.402 | 0.295698 |
(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 | 287.3.d.c.286.6 | yes | 8 | |
7.6 | odd | 2 | inner | 287.3.d.c.286.3 | ✓ | 8 | |
41.40 | even | 2 | inner | 287.3.d.c.286.4 | yes | 8 | |
287.286 | odd | 2 | inner | 287.3.d.c.286.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.d.c.286.3 | ✓ | 8 | 7.6 | odd | 2 | inner | |
287.3.d.c.286.4 | yes | 8 | 41.40 | even | 2 | inner | |
287.3.d.c.286.5 | yes | 8 | 287.286 | odd | 2 | inner | |
287.3.d.c.286.6 | yes | 8 | 1.1 | even | 1 | trivial |