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 | 286.3 | ||
Root | \(1.25038i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.286 |
Dual form | 287.3.d.c.286.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | \(-0.548663\pi\) | ||||
−0.152283 | + | 0.988337i | \(0.548663\pi\) | |||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | − | 7.47749i | − | 1.49550i | −0.663981 | − | 0.747749i | \(-0.731135\pi\) | ||
0.663981 | − | 0.747749i | \(-0.268865\pi\) | |||||||
\(6\) | 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 | \(-0.488812\pi\) | ||||
0.0351423 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(14\) | 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 | \(-0.510341\pi\) | ||||
−0.0324824 | + | 0.999472i | \(0.510341\pi\) | |||||||
\(18\) | 8.16515 | 0.453620 | ||||||||
\(19\) | 28.6265 | 1.50666 | 0.753329 | − | 0.657643i | \(-0.228447\pi\) | ||||
0.753329 | + | 0.657643i | \(0.228447\pi\) | |||||||
\(20\) | 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 | \(0.142219\pi\) | ||||
−0.901837 | + | 0.432075i | \(0.857781\pi\) | |||||||
\(32\) | −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 | \(-0.327289\pi\) | ||||
0.516353 | + | 0.856376i | \(0.327289\pi\) | |||||||
\(48\) | −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 | \(-0.947672\pi\) | ||
0.986518 | − | 0.163654i | \(-0.0523281\pi\) | |||||||
\(60\) | − | 20.4966i | − | 0.341609i | ||||||
\(61\) | − | 28.0236i | − | 0.459403i | −0.973261 | − | 0.229702i | \(-0.926225\pi\) | ||
0.973261 | − | 0.229702i | \(-0.0737750\pi\) | |||||||
\(62\) | − | 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 | \(0.0994236\pi\) | ||||
−0.951615 | + | 0.307294i | \(0.900576\pi\) | |||||||
\(74\) | 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 | \(0.183112\pi\) | ||||
−0.839049 | + | 0.544056i | \(0.816888\pi\) | |||||||
\(84\) | −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 | \(-0.651389\pi\) | ||||
−0.457875 | + | 0.889017i | \(0.651389\pi\) | |||||||
\(90\) | − | 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 | \(-0.673413\pi\) | ||||
−0.518240 | + | 0.855235i | \(0.673413\pi\) | |||||||
\(98\) | −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 | \(-0.633444\pi\) | ||||
−0.407053 | + | 0.913404i | \(0.633444\pi\) | |||||||
\(102\) | −1.00909 | −0.00989306 | ||||||||
\(103\) | − | 145.777i | − | 1.41531i | −0.706557 | − | 0.707656i | \(-0.749753\pi\) | ||
0.706557 | − | 0.707656i | \(-0.250247\pi\) | |||||||
\(104\) | 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 | \(-0.789664\pi\) | ||
0.789508 | − | 0.613741i | \(-0.210336\pi\) | |||||||
\(132\) | 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 | \(0.248504\pi\) | ||||
−0.710422 | + | 0.703776i | \(0.751496\pi\) | |||||||
\(140\) | 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 | \(-0.600207\pi\) | ||||
−0.309635 | + | 0.950856i | \(0.600207\pi\) | |||||||
\(158\) | − | 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 | \(-0.835130\pi\) | ||||
−0.868833 | + | 0.495105i | \(0.835130\pi\) | |||||||
\(168\) | 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 | \(0.0616980\pi\) | ||||
−0.981274 | + | 0.192618i | \(0.938302\pi\) | |||||||
\(174\) | 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 | \(-0.452563\pi\) | ||||
0.148478 | + | 0.988916i | \(0.452563\pi\) | |||||||
\(182\) | 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 | \(-0.536958\pi\) | ||||
−0.115845 | + | 0.993267i | \(0.536958\pi\) | |||||||
\(200\) | −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 | \(-0.926395\pi\) | ||
0.973384 | − | 0.229182i | \(-0.0736050\pi\) | |||||||
\(224\) | 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 | \(-0.340592\pi\) | ||||
0.480124 | + | 0.877200i | \(0.340592\pi\) | |||||||
\(228\) | 78.4682 | 0.344159 | ||||||||
\(229\) | −167.350 | −0.730785 | −0.365393 | − | 0.930854i | \(-0.619065\pi\) | ||||
−0.365393 | + | 0.930854i | \(0.619065\pi\) | |||||||
\(230\) | − | 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 | \(0.201213\pi\) | ||||
−0.806772 | + | 0.590863i | \(0.798787\pi\) | |||||||
\(242\) | −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 | \(-0.937549\pi\) | ||
0.980816 | − | 0.194938i | \(-0.0624505\pi\) | |||||||
\(252\) | −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 | \(-0.576426\pi\) | ||||
−0.237799 | + | 0.971314i | \(0.576426\pi\) | |||||||
\(258\) | −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 | \(-0.922965\pi\) | ||
0.970857 | − | 0.239658i | \(-0.0770352\pi\) | |||||||
\(270\) | 117.276i | 0.434354i | ||||||||
\(271\) | 354.495i | 1.30810i | 0.756451 | + | 0.654051i | \(0.226932\pi\) | ||||
−0.756451 | + | 0.654051i | \(0.773068\pi\) | |||||||
\(272\) | −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 | \(-0.792961\pi\) | ||
0.795823 | − | 0.605529i | \(-0.207039\pi\) | |||||||
\(284\) | 404.761i | 1.42521i | ||||||||
\(285\) | 195.582i | 0.686252i | ||||||||
\(286\) | − | 5.59112i | − | 0.0195494i | ||||||
\(287\) | 39.3438 | + | 284.290i | 0.137086 | + | 0.990559i | ||||
\(288\) | 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 | \(-0.502188\pi\) | ||||
−0.00687354 | + | 0.999976i | \(0.502188\pi\) | |||||||
\(294\) | 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 | \(-0.859090\pi\) | ||
0.903607 | − | 0.428363i | \(-0.140910\pi\) | |||||||
\(308\) | −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 | \(-0.887587\pi\) | ||||
−0.938286 | + | 0.345860i | \(0.887587\pi\) | |||||||
\(312\) | −5.84394 | −0.0187306 | ||||||||
\(313\) | 512.727 | 1.63810 | 0.819052 | − | 0.573719i | \(-0.194500\pi\) | ||||
0.819052 | + | 0.573719i | \(0.194500\pi\) | |||||||
\(314\) | 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 | \(0.0872282\pi\) | ||||
−0.962687 | + | 0.270618i | \(0.912772\pi\) | |||||||
\(350\) | −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 | \(-0.907960\pi\) | ||
0.958486 | − | 0.285140i | \(-0.0920401\pi\) | |||||||
\(354\) | − | 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 | \(-0.992666\pi\) | ||
0.999735 | − | 0.0230372i | \(-0.00733363\pi\) | |||||||
\(368\) | −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 | \(-0.751993\pi\) | ||||
−0.711521 | + | 0.702665i | \(0.751993\pi\) | |||||||
\(384\) | −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 | \(-0.511109\pi\) | ||||
−0.0348923 | + | 0.999391i | \(0.511109\pi\) | |||||||
\(398\) | 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 | \(0.210107\pi\) | ||||
−0.789949 | + | 0.613173i | \(0.789893\pi\) | |||||||
\(410\) | 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 | \(-0.963937\pi\) | ||
0.993589 | − | 0.113052i | \(-0.0360627\pi\) | |||||||
\(420\) | −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 | \(0.313968\pi\) | ||||
−0.551731 | + | 0.834022i | \(0.686032\pi\) | |||||||
\(434\) | −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 | \(-0.370887\pi\) | ||||
0.394590 | + | 0.918857i | \(0.370887\pi\) | |||||||
\(440\) | 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 | \(-0.671594\pi\) | ||
0.513347 | − | 0.858181i | \(-0.328406\pi\) | |||||||
\(462\) | 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 | \(0.146322\pi\) | ||||
−0.896193 | + | 0.443665i | \(0.853678\pi\) | |||||||
\(468\) | 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 | \(-0.311074\pi\) | ||||
0.559290 | + | 0.828972i | \(0.311074\pi\) | |||||||
\(480\) | − | 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 | \(-0.432293\pi\) | ||||
0.211108 | + | 0.977463i | \(0.432293\pi\) | |||||||
\(504\) | 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 | \(-0.438122\pi\) | ||||
0.193174 | + | 0.981165i | \(0.438122\pi\) | |||||||
\(510\) | 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 | \(-0.326433\pi\) | ||||
0.518656 | + | 0.854983i | \(0.326433\pi\) | |||||||
\(522\) | 428.822i | 0.821498i | ||||||||
\(523\) | 586.434i | 1.12129i | 0.828057 | + | 0.560644i | \(0.189446\pi\) | ||||
−0.828057 | + | 0.560644i | \(0.810554\pi\) | |||||||
\(524\) | 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 | \(-0.172507\pi\) | ||||
0.856705 | + | 0.515806i | \(0.172507\pi\) | |||||||
\(564\) | 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 | ||||||
\(574\) | −39.3438 | − | 284.290i | −0.0685432 | − | 0.495280i | ||||
\(575\) | 826.849 | 1.43800 | ||||||||
\(576\) | −106.147 | −0.184283 | ||||||||
\(577\) | 514.349 | 0.891419 | 0.445709 | − | 0.895178i | \(-0.352951\pi\) | ||||
0.445709 | + | 0.895178i | \(0.352951\pi\) | |||||||
\(578\) | 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 | \(-0.346761\pi\) | ||||
0.463034 | + | 0.886341i | \(0.346761\pi\) | |||||||
\(588\) | 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 | \(-0.942575\pi\) | ||||
−0.983771 | + | 0.179429i | \(0.942575\pi\) | |||||||
\(594\) | − | 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 | \(-0.724321\pi\) | ||||
−0.647824 | + | 0.761790i | \(0.724321\pi\) | |||||||
\(602\) | −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 | \(-0.772877\pi\) | ||
0.756058 | − | 0.654504i | \(-0.227123\pi\) | |||||||
\(608\) | −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 | \(-0.895747\pi\) | ||
0.946843 | − | 0.321697i | \(-0.104253\pi\) | |||||||
\(620\) | −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 | \(-0.405490\pi\) | ||||
0.292569 | + | 0.956244i | \(0.405490\pi\) | |||||||
\(644\) | −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 | \(-0.691644\pi\) | ||
0.566347 | − | 0.824167i | \(-0.308356\pi\) | |||||||
\(648\) | 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 | \(-0.913313\pi\) | ||
0.963145 | − | 0.268982i | \(-0.0866873\pi\) | |||||||
\(662\) | − | 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 | \(0.0134704\pi\) | ||||
−0.999105 | + | 0.0423058i | \(0.986530\pi\) | |||||||
\(678\) | −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 | \(-0.694329\pi\) | ||||
−0.573279 | + | 0.819360i | \(0.694329\pi\) | |||||||
\(692\) | − | 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 | \(-0.340455\pi\) | ||||
0.480502 | + | 0.876994i | \(0.340455\pi\) | |||||||
\(720\) | 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 | \(-0.550070\pi\) | ||||
−0.156653 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(728\) | −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 | \(0.0980964\pi\) | ||||
−0.952888 | + | 0.303324i | \(0.901904\pi\) | |||||||
\(734\) | 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 | \(-0.725610\pi\) | ||
0.650903 | − | 0.759161i | \(-0.274390\pi\) | |||||||
\(762\) | −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 | \(-0.937483\pi\) | ||
0.980775 | − | 0.195143i | \(-0.0625172\pi\) | |||||||
\(770\) | 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 | \(-0.764513\pi\) | ||||
−0.738600 | + | 0.674144i | \(0.764513\pi\) | |||||||
\(774\) | −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 | \(-0.855920\pi\) | ||
0.899295 | − | 0.437342i | \(-0.144080\pi\) | |||||||
\(788\) | 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 | \(-0.591594\pi\) | ||
0.283797 | − | 0.958884i | \(-0.408406\pi\) | |||||||
\(798\) | −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 | \(0.294156\pi\) | ||||
−0.602539 | + | 0.798089i | \(0.705844\pi\) | |||||||
\(812\) | −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 | \(0.0604186\pi\) | ||||
−0.982040 | + | 0.188673i | \(0.939581\pi\) | |||||||
\(830\) | −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 | \(-0.767807\pi\) | ||||
−0.745536 | + | 0.666465i | \(0.767807\pi\) | |||||||
\(840\) | 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 | \(-0.941178\pi\) | ||
0.982974 | − | 0.183746i | \(-0.0588225\pi\) | |||||||
\(854\) | 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 | \(0.0209534\pi\) | ||||
−0.997834 | + | 0.0657794i | \(0.979047\pi\) | |||||||
\(858\) | 5.10861i | 0.00595409i | ||||||||
\(859\) | 950.944i | 1.10704i | 0.832837 | + | 0.553518i | \(0.186715\pi\) | ||||
−0.832837 | + | 0.553518i | \(0.813285\pi\) | |||||||
\(860\) | − | 437.331i | − | 0.508525i | ||||||
\(861\) | −35.9484 | − | 259.756i | −0.0417520 | − | 0.301691i | ||||
\(862\) | 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 | \(-0.765982\pi\) | ||
0.741703 | − | 0.670728i | \(-0.234018\pi\) | |||||||
\(882\) | 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 | \(-0.417658\pi\) | ||||
0.255809 | + | 0.966727i | \(0.417658\pi\) | |||||||
\(888\) | 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 | \(-0.622442\pi\) | ||||
−0.375246 | + | 0.926925i | \(0.622442\pi\) | |||||||
\(930\) | 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 | \(-0.680622\pi\) | ||||
−0.537475 | + | 0.843280i | \(0.680622\pi\) | |||||||
\(938\) | −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 | \(-0.861951\pi\) | ||
0.907420 | − | 0.420225i | \(-0.138049\pi\) | |||||||
\(942\) | −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 | \(-0.253202\pi\) | ||||
0.699958 | + | 0.714184i | \(0.253202\pi\) | |||||||
\(972\) | 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 | \(0.0682575\pi\) | ||||
−0.977096 | + | 0.212798i | \(0.931743\pi\) | |||||||
\(984\) | 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 | \(-0.354079\pi\) | ||||
0.442536 | + | 0.896751i | \(0.354079\pi\) | |||||||
\(998\) | − | 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.286.3 | ✓ | 8 | |
7.6 | odd | 2 | inner | 287.3.d.c.286.6 | yes | 8 | |
41.40 | even | 2 | inner | 287.3.d.c.286.5 | yes | 8 | |
287.286 | odd | 2 | inner | 287.3.d.c.286.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.d.c.286.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
287.3.d.c.286.4 | yes | 8 | 287.286 | odd | 2 | inner | |
287.3.d.c.286.5 | yes | 8 | 41.40 | even | 2 | inner | |
287.3.d.c.286.6 | yes | 8 | 7.6 | odd | 2 | inner |