Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(83,287)]
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, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.b (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: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 83.11 | ||
Character | \(\chi\) | \(=\) | 287.83 |
Dual form | 287.3.b.a.83.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44013 | −1.22007 | −0.610033 | − | 0.792376i | \(-0.708844\pi\) | ||||
−0.610033 | + | 0.792376i | \(0.708844\pi\) | |||||||
\(3\) | − | 4.97182i | − | 1.65727i | −0.559786 | − | 0.828637i | \(-0.689117\pi\) | ||
0.559786 | − | 0.828637i | \(-0.310883\pi\) | |||||||
\(4\) | 1.95424 | 0.488561 | ||||||||
\(5\) | − | 3.83331i | − | 0.766662i | −0.923611 | − | 0.383331i | \(-0.874777\pi\) | ||
0.923611 | − | 0.383331i | \(-0.125223\pi\) | |||||||
\(6\) | 12.1319i | 2.02198i | ||||||||
\(7\) | −6.90407 | − | 1.15493i | −0.986295 | − | 0.164990i | ||||
\(8\) | 4.99192 | 0.623990 | ||||||||
\(9\) | −15.7190 | −1.74656 | ||||||||
\(10\) | 9.35378i | 0.935378i | ||||||||
\(11\) | −8.46862 | −0.769874 | −0.384937 | − | 0.922943i | \(-0.625777\pi\) | ||||
−0.384937 | + | 0.922943i | \(0.625777\pi\) | |||||||
\(12\) | − | 9.71615i | − | 0.809679i | ||||||
\(13\) | 9.27142i | 0.713186i | 0.934260 | + | 0.356593i | \(0.116062\pi\) | ||||
−0.934260 | + | 0.356593i | \(0.883938\pi\) | |||||||
\(14\) | 16.8468 | + | 2.81818i | 1.20335 | + | 0.201299i | ||||
\(15\) | −19.0585 | −1.27057 | ||||||||
\(16\) | −19.9979 | −1.24987 | ||||||||
\(17\) | − | 1.99229i | − | 0.117193i | −0.998282 | − | 0.0585967i | \(-0.981337\pi\) | ||
0.998282 | − | 0.0585967i | \(-0.0186626\pi\) | |||||||
\(18\) | 38.3565 | 2.13092 | ||||||||
\(19\) | − | 24.3633i | − | 1.28228i | −0.767423 | − | 0.641141i | \(-0.778461\pi\) | ||
0.767423 | − | 0.641141i | \(-0.221539\pi\) | |||||||
\(20\) | − | 7.49122i | − | 0.374561i | ||||||
\(21\) | −5.74211 | + | 34.3258i | −0.273434 | + | 1.63456i | ||||
\(22\) | 20.6645 | 0.939298 | ||||||||
\(23\) | −22.4925 | −0.977934 | −0.488967 | − | 0.872302i | \(-0.662626\pi\) | ||||
−0.488967 | + | 0.872302i | \(0.662626\pi\) | |||||||
\(24\) | − | 24.8189i | − | 1.03412i | ||||||
\(25\) | 10.3057 | 0.412229 | ||||||||
\(26\) | − | 22.6235i | − | 0.870134i | ||||||
\(27\) | 33.4059i | 1.23725i | ||||||||
\(28\) | −13.4922 | − | 2.25701i | −0.481865 | − | 0.0806077i | ||||
\(29\) | 56.5997 | 1.95171 | 0.975856 | − | 0.218414i | \(-0.0700883\pi\) | ||||
0.975856 | + | 0.218414i | \(0.0700883\pi\) | |||||||
\(30\) | 46.5054 | 1.55018 | ||||||||
\(31\) | 20.4692i | 0.660297i | 0.943929 | + | 0.330149i | \(0.107099\pi\) | ||||
−0.943929 | + | 0.330149i | \(0.892901\pi\) | |||||||
\(32\) | 28.8298 | 0.900933 | ||||||||
\(33\) | 42.1045i | 1.27589i | ||||||||
\(34\) | 4.86145i | 0.142984i | ||||||||
\(35\) | −4.42721 | + | 26.4654i | −0.126492 | + | 0.756155i | ||||
\(36\) | −30.7188 | −0.853300 | ||||||||
\(37\) | −5.78701 | −0.156406 | −0.0782028 | − | 0.996937i | \(-0.524918\pi\) | ||||
−0.0782028 | + | 0.996937i | \(0.524918\pi\) | |||||||
\(38\) | 59.4498i | 1.56447i | ||||||||
\(39\) | 46.0959 | 1.18195 | ||||||||
\(40\) | − | 19.1356i | − | 0.478389i | ||||||
\(41\) | − | 6.40312i | − | 0.156174i | ||||||
\(42\) | 14.0115 | − | 83.7595i | 0.333607 | − | 1.99427i | ||||
\(43\) | −63.2121 | −1.47005 | −0.735025 | − | 0.678040i | \(-0.762829\pi\) | ||||
−0.735025 | + | 0.678040i | \(0.762829\pi\) | |||||||
\(44\) | −16.5497 | −0.376130 | ||||||||
\(45\) | 60.2560i | 1.33902i | ||||||||
\(46\) | 54.8846 | 1.19314 | ||||||||
\(47\) | 62.1216i | 1.32174i | 0.750502 | + | 0.660868i | \(0.229812\pi\) | ||||
−0.750502 | + | 0.660868i | \(0.770188\pi\) | |||||||
\(48\) | 99.4261i | 2.07138i | ||||||||
\(49\) | 46.3323 | + | 15.9474i | 0.945557 | + | 0.325458i | ||||
\(50\) | −25.1473 | −0.502947 | ||||||||
\(51\) | −9.90531 | −0.194222 | ||||||||
\(52\) | 18.1186i | 0.348435i | ||||||||
\(53\) | −4.33948 | −0.0818770 | −0.0409385 | − | 0.999162i | \(-0.513035\pi\) | ||||
−0.0409385 | + | 0.999162i | \(0.513035\pi\) | |||||||
\(54\) | − | 81.5147i | − | 1.50953i | ||||||
\(55\) | 32.4629i | 0.590234i | ||||||||
\(56\) | −34.4645 | − | 5.76532i | −0.615438 | − | 0.102952i | ||||
\(57\) | −121.130 | −2.12509 | ||||||||
\(58\) | −138.111 | −2.38122 | ||||||||
\(59\) | 53.7227i | 0.910554i | 0.890350 | + | 0.455277i | \(0.150460\pi\) | ||||
−0.890350 | + | 0.455277i | \(0.849540\pi\) | |||||||
\(60\) | −37.2450 | −0.620750 | ||||||||
\(61\) | − | 74.6441i | − | 1.22367i | −0.790984 | − | 0.611837i | \(-0.790431\pi\) | ||
0.790984 | − | 0.611837i | \(-0.209569\pi\) | |||||||
\(62\) | − | 49.9476i | − | 0.805606i | ||||||
\(63\) | 108.525 | + | 18.1544i | 1.72262 | + | 0.288165i | ||||
\(64\) | 9.64300 | 0.150672 | ||||||||
\(65\) | 35.5402 | 0.546773 | ||||||||
\(66\) | − | 102.740i | − | 1.55667i | ||||||
\(67\) | 13.6686 | 0.204009 | 0.102004 | − | 0.994784i | \(-0.467474\pi\) | ||||
0.102004 | + | 0.994784i | \(0.467474\pi\) | |||||||
\(68\) | − | 3.89341i | − | 0.0572561i | ||||||
\(69\) | 111.829i | 1.62071i | ||||||||
\(70\) | 10.8030 | − | 64.5791i | 0.154328 | − | 0.922559i | ||||
\(71\) | −21.0182 | −0.296032 | −0.148016 | − | 0.988985i | \(-0.547289\pi\) | ||||
−0.148016 | + | 0.988985i | \(0.547289\pi\) | |||||||
\(72\) | −78.4681 | −1.08984 | ||||||||
\(73\) | − | 82.5094i | − | 1.13027i | −0.825000 | − | 0.565133i | \(-0.808825\pi\) | ||
0.825000 | − | 0.565133i | \(-0.191175\pi\) | |||||||
\(74\) | 14.1211 | 0.190825 | ||||||||
\(75\) | − | 51.2383i | − | 0.683177i | ||||||
\(76\) | − | 47.6119i | − | 0.626472i | ||||||
\(77\) | 58.4679 | + | 9.78067i | 0.759324 | + | 0.127022i | ||||
\(78\) | −112.480 | −1.44205 | ||||||||
\(79\) | 15.4332 | 0.195357 | 0.0976787 | − | 0.995218i | \(-0.468858\pi\) | ||||
0.0976787 | + | 0.995218i | \(0.468858\pi\) | |||||||
\(80\) | 76.6582i | 0.958227i | ||||||||
\(81\) | 24.6168 | 0.303911 | ||||||||
\(82\) | 15.6245i | 0.190542i | ||||||||
\(83\) | 138.469i | 1.66830i | 0.551541 | + | 0.834148i | \(0.314040\pi\) | ||||
−0.551541 | + | 0.834148i | \(0.685960\pi\) | |||||||
\(84\) | −11.2215 | + | 67.0809i | −0.133589 | + | 0.798583i | ||||
\(85\) | −7.63706 | −0.0898478 | ||||||||
\(86\) | 154.246 | 1.79356 | ||||||||
\(87\) | − | 281.404i | − | 3.23452i | ||||||
\(88\) | −42.2747 | −0.480394 | ||||||||
\(89\) | 11.0966i | 0.124681i | 0.998055 | + | 0.0623406i | \(0.0198565\pi\) | ||||
−0.998055 | + | 0.0623406i | \(0.980143\pi\) | |||||||
\(90\) | − | 147.032i | − | 1.63369i | ||||||
\(91\) | 10.7078 | − | 64.0105i | 0.117669 | − | 0.703412i | ||||
\(92\) | −43.9558 | −0.477780 | ||||||||
\(93\) | 101.769 | 1.09429 | ||||||||
\(94\) | − | 151.585i | − | 1.61260i | ||||||
\(95\) | −93.3923 | −0.983077 | ||||||||
\(96\) | − | 143.337i | − | 1.49309i | ||||||
\(97\) | − | 111.867i | − | 1.15327i | −0.817002 | − | 0.576634i | \(-0.804366\pi\) | ||
0.817002 | − | 0.576634i | \(-0.195634\pi\) | |||||||
\(98\) | −113.057 | − | 38.9138i | −1.15364 | − | 0.397080i | ||||
\(99\) | 133.119 | 1.34463 | ||||||||
\(100\) | 20.1399 | 0.201399 | ||||||||
\(101\) | 91.6530i | 0.907456i | 0.891140 | + | 0.453728i | \(0.149906\pi\) | ||||
−0.891140 | + | 0.453728i | \(0.850094\pi\) | |||||||
\(102\) | 24.1703 | 0.236963 | ||||||||
\(103\) | − | 147.844i | − | 1.43538i | −0.696363 | − | 0.717690i | \(-0.745199\pi\) | ||
0.696363 | − | 0.717690i | \(-0.254801\pi\) | |||||||
\(104\) | 46.2822i | 0.445021i | ||||||||
\(105\) | 131.581 | + | 22.0113i | 1.25316 | + | 0.209631i | ||||
\(106\) | 10.5889 | 0.0998953 | ||||||||
\(107\) | −147.881 | −1.38206 | −0.691031 | − | 0.722826i | \(-0.742843\pi\) | ||||
−0.691031 | + | 0.722826i | \(0.742843\pi\) | |||||||
\(108\) | 65.2832i | 0.604474i | ||||||||
\(109\) | −138.665 | −1.27216 | −0.636079 | − | 0.771624i | \(-0.719445\pi\) | ||||
−0.636079 | + | 0.771624i | \(0.719445\pi\) | |||||||
\(110\) | − | 79.2136i | − | 0.720124i | ||||||
\(111\) | 28.7720i | 0.259207i | ||||||||
\(112\) | 138.067 | + | 23.0962i | 1.23274 | + | 0.206216i | ||||
\(113\) | −32.3708 | −0.286467 | −0.143233 | − | 0.989689i | \(-0.545750\pi\) | ||||
−0.143233 | + | 0.989689i | \(0.545750\pi\) | |||||||
\(114\) | 295.574 | 2.59275 | ||||||||
\(115\) | 86.2207i | 0.749745i | ||||||||
\(116\) | 110.609 | 0.953530 | ||||||||
\(117\) | − | 145.738i | − | 1.24562i | ||||||
\(118\) | − | 131.090i | − | 1.11094i | ||||||
\(119\) | −2.30095 | + | 13.7549i | −0.0193358 | + | 0.115587i | ||||
\(120\) | −95.1387 | −0.792823 | ||||||||
\(121\) | −49.2825 | −0.407293 | ||||||||
\(122\) | 182.141i | 1.49296i | ||||||||
\(123\) | −31.8352 | −0.258823 | ||||||||
\(124\) | 40.0018i | 0.322595i | ||||||||
\(125\) | − | 135.338i | − | 1.08270i | ||||||
\(126\) | −264.816 | − | 44.2991i | −2.10171 | − | 0.351580i | ||||
\(127\) | −57.0852 | −0.449490 | −0.224745 | − | 0.974418i | \(-0.572155\pi\) | ||||
−0.224745 | + | 0.974418i | \(0.572155\pi\) | |||||||
\(128\) | −138.850 | −1.08476 | ||||||||
\(129\) | 314.280i | 2.43628i | ||||||||
\(130\) | −86.7228 | −0.667099 | ||||||||
\(131\) | 134.584i | 1.02736i | 0.857981 | + | 0.513681i | \(0.171718\pi\) | ||||
−0.857981 | + | 0.513681i | \(0.828282\pi\) | |||||||
\(132\) | 82.2824i | 0.623351i | ||||||||
\(133\) | −28.1380 | + | 168.206i | −0.211564 | + | 1.26471i | ||||
\(134\) | −33.3531 | −0.248904 | ||||||||
\(135\) | 128.055 | 0.948556 | ||||||||
\(136\) | − | 9.94534i | − | 0.0731275i | ||||||
\(137\) | −109.644 | −0.800321 | −0.400160 | − | 0.916445i | \(-0.631046\pi\) | ||||
−0.400160 | + | 0.916445i | \(0.631046\pi\) | |||||||
\(138\) | − | 272.877i | − | 1.97737i | ||||||
\(139\) | 80.3222i | 0.577858i | 0.957351 | + | 0.288929i | \(0.0932991\pi\) | ||||
−0.957351 | + | 0.288929i | \(0.906701\pi\) | |||||||
\(140\) | −8.65184 | + | 51.7199i | −0.0617988 | + | 0.369428i | ||||
\(141\) | 308.858 | 2.19048 | ||||||||
\(142\) | 51.2873 | 0.361178 | ||||||||
\(143\) | − | 78.5161i | − | 0.549064i | ||||||
\(144\) | 314.348 | 2.18297 | ||||||||
\(145\) | − | 216.964i | − | 1.49630i | ||||||
\(146\) | 201.334i | 1.37900i | ||||||||
\(147\) | 79.2879 | − | 230.356i | 0.539373 | − | 1.56705i | ||||
\(148\) | −11.3092 | −0.0764136 | ||||||||
\(149\) | 18.1575 | 0.121863 | 0.0609313 | − | 0.998142i | \(-0.480593\pi\) | ||||
0.0609313 | + | 0.998142i | \(0.480593\pi\) | |||||||
\(150\) | 125.028i | 0.833521i | ||||||||
\(151\) | −173.035 | −1.14593 | −0.572963 | − | 0.819581i | \(-0.694206\pi\) | ||||
−0.572963 | + | 0.819581i | \(0.694206\pi\) | |||||||
\(152\) | − | 121.620i | − | 0.800131i | ||||||
\(153\) | 31.3169i | 0.204685i | ||||||||
\(154\) | −142.669 | − | 23.8661i | −0.926425 | − | 0.154975i | ||||
\(155\) | 78.4649 | 0.506225 | ||||||||
\(156\) | 90.0825 | 0.577452 | ||||||||
\(157\) | 288.870i | 1.83994i | 0.391994 | + | 0.919968i | \(0.371785\pi\) | ||||
−0.391994 | + | 0.919968i | \(0.628215\pi\) | |||||||
\(158\) | −37.6591 | −0.238349 | ||||||||
\(159\) | 21.5751i | 0.135693i | ||||||||
\(160\) | − | 110.514i | − | 0.690711i | ||||||
\(161\) | 155.290 | + | 25.9773i | 0.964532 | + | 0.161349i | ||||
\(162\) | −60.0682 | −0.370792 | ||||||||
\(163\) | −140.066 | −0.859301 | −0.429651 | − | 0.902995i | \(-0.641363\pi\) | ||||
−0.429651 | + | 0.902995i | \(0.641363\pi\) | |||||||
\(164\) | − | 12.5133i | − | 0.0763003i | ||||||
\(165\) | 161.400 | 0.978179 | ||||||||
\(166\) | − | 337.881i | − | 2.03543i | ||||||
\(167\) | − | 56.0903i | − | 0.335870i | −0.985798 | − | 0.167935i | \(-0.946290\pi\) | ||
0.985798 | − | 0.167935i | \(-0.0537099\pi\) | |||||||
\(168\) | −28.6642 | + | 171.352i | −0.170620 | + | 1.01995i | ||||
\(169\) | 83.0408 | 0.491366 | ||||||||
\(170\) | 18.6354 | 0.109620 | ||||||||
\(171\) | 382.968i | 2.23958i | ||||||||
\(172\) | −123.532 | −0.718208 | ||||||||
\(173\) | 200.251i | 1.15752i | 0.815497 | + | 0.578761i | \(0.196464\pi\) | ||||
−0.815497 | + | 0.578761i | \(0.803536\pi\) | |||||||
\(174\) | 686.662i | 3.94633i | ||||||||
\(175\) | −71.1514 | − | 11.9024i | −0.406580 | − | 0.0680137i | ||||
\(176\) | 169.355 | 0.962242 | ||||||||
\(177\) | 267.100 | 1.50904 | ||||||||
\(178\) | − | 27.0772i | − | 0.152119i | ||||||
\(179\) | −304.473 | −1.70097 | −0.850484 | − | 0.526001i | \(-0.823691\pi\) | ||||
−0.850484 | + | 0.526001i | \(0.823691\pi\) | |||||||
\(180\) | 117.755i | 0.654193i | ||||||||
\(181\) | 116.912i | 0.645923i | 0.946412 | + | 0.322962i | \(0.104678\pi\) | ||||
−0.946412 | + | 0.322962i | \(0.895322\pi\) | |||||||
\(182\) | −26.1286 | + | 156.194i | −0.143563 | + | 0.858209i | ||||
\(183\) | −371.117 | −2.02796 | ||||||||
\(184\) | −112.281 | −0.610221 | ||||||||
\(185\) | 22.1834i | 0.119910i | ||||||||
\(186\) | −248.331 | −1.33511 | ||||||||
\(187\) | 16.8719i | 0.0902242i | ||||||||
\(188\) | 121.401i | 0.645748i | ||||||||
\(189\) | 38.5815 | − | 230.636i | 0.204135 | − | 1.22030i | ||||
\(190\) | 227.889 | 1.19942 | ||||||||
\(191\) | 173.646 | 0.909144 | 0.454572 | − | 0.890710i | \(-0.349792\pi\) | ||||
0.454572 | + | 0.890710i | \(0.349792\pi\) | |||||||
\(192\) | − | 47.9433i | − | 0.249705i | ||||||
\(193\) | −315.318 | −1.63377 | −0.816886 | − | 0.576799i | \(-0.804302\pi\) | ||||
−0.816886 | + | 0.576799i | \(0.804302\pi\) | |||||||
\(194\) | 272.970i | 1.40706i | ||||||||
\(195\) | − | 176.700i | − | 0.906153i | ||||||
\(196\) | 90.5445 | + | 31.1652i | 0.461962 | + | 0.159006i | ||||
\(197\) | 121.390 | 0.616195 | 0.308097 | − | 0.951355i | \(-0.400308\pi\) | ||||
0.308097 | + | 0.951355i | \(0.400308\pi\) | |||||||
\(198\) | −324.827 | −1.64054 | ||||||||
\(199\) | − | 278.090i | − | 1.39744i | −0.715396 | − | 0.698719i | \(-0.753754\pi\) | ||
0.715396 | − | 0.698719i | \(-0.246246\pi\) | |||||||
\(200\) | 51.4453 | 0.257227 | ||||||||
\(201\) | − | 67.9578i | − | 0.338099i | ||||||
\(202\) | − | 223.645i | − | 1.10716i | ||||||
\(203\) | −390.768 | − | 65.3687i | −1.92496 | − | 0.322013i | ||||
\(204\) | −19.3574 | −0.0948891 | ||||||||
\(205\) | −24.5452 | −0.119733 | ||||||||
\(206\) | 360.759i | 1.75126i | ||||||||
\(207\) | 353.560 | 1.70802 | ||||||||
\(208\) | − | 185.409i | − | 0.891389i | ||||||
\(209\) | 206.324i | 0.987196i | ||||||||
\(210\) | −321.076 | − | 53.7105i | −1.52893 | − | 0.255764i | ||||
\(211\) | 66.0953 | 0.313248 | 0.156624 | − | 0.987658i | \(-0.449939\pi\) | ||||
0.156624 | + | 0.987658i | \(0.449939\pi\) | |||||||
\(212\) | −8.48039 | −0.0400019 | ||||||||
\(213\) | 104.499i | 0.490606i | ||||||||
\(214\) | 360.848 | 1.68621 | ||||||||
\(215\) | 242.312i | 1.12703i | ||||||||
\(216\) | 166.759i | 0.772034i | ||||||||
\(217\) | 23.6405 | − | 141.321i | 0.108943 | − | 0.651248i | ||||
\(218\) | 338.361 | 1.55212 | ||||||||
\(219\) | −410.222 | −1.87316 | ||||||||
\(220\) | 63.4403i | 0.288365i | ||||||||
\(221\) | 18.4713 | 0.0835807 | ||||||||
\(222\) | − | 70.2074i | − | 0.316250i | ||||||
\(223\) | 223.904i | 1.00405i | 0.864852 | + | 0.502026i | \(0.167412\pi\) | ||||
−0.864852 | + | 0.502026i | \(0.832588\pi\) | |||||||
\(224\) | −199.043 | − | 33.2965i | −0.888586 | − | 0.148645i | ||||
\(225\) | −161.996 | −0.719983 | ||||||||
\(226\) | 78.9889 | 0.349509 | ||||||||
\(227\) | − | 271.467i | − | 1.19589i | −0.801537 | − | 0.597945i | \(-0.795984\pi\) | ||
0.801537 | − | 0.597945i | \(-0.204016\pi\) | |||||||
\(228\) | −236.718 | −1.03824 | ||||||||
\(229\) | 127.958i | 0.558767i | 0.960180 | + | 0.279383i | \(0.0901300\pi\) | ||||
−0.960180 | + | 0.279383i | \(0.909870\pi\) | |||||||
\(230\) | − | 210.390i | − | 0.914738i | ||||||
\(231\) | 48.6278 | − | 290.692i | 0.210510 | − | 1.25841i | ||||
\(232\) | 282.541 | 1.21785 | ||||||||
\(233\) | 121.853 | 0.522973 | 0.261486 | − | 0.965207i | \(-0.415787\pi\) | ||||
0.261486 | + | 0.965207i | \(0.415787\pi\) | |||||||
\(234\) | 355.619i | 1.51974i | ||||||||
\(235\) | 238.131 | 1.01332 | ||||||||
\(236\) | 104.987i | 0.444861i | ||||||||
\(237\) | − | 76.7313i | − | 0.323761i | ||||||
\(238\) | 5.61463 | − | 33.5637i | 0.0235909 | − | 0.141024i | ||||
\(239\) | −16.1630 | −0.0676275 | −0.0338137 | − | 0.999428i | \(-0.510765\pi\) | ||||
−0.0338137 | + | 0.999428i | \(0.510765\pi\) | |||||||
\(240\) | 381.131 | 1.58805 | ||||||||
\(241\) | 30.1028i | 0.124908i | 0.998048 | + | 0.0624539i | \(0.0198926\pi\) | ||||
−0.998048 | + | 0.0624539i | \(0.980107\pi\) | |||||||
\(242\) | 120.256 | 0.496925 | ||||||||
\(243\) | 178.262i | 0.733590i | ||||||||
\(244\) | − | 145.873i | − | 0.597839i | ||||||
\(245\) | 61.1315 | − | 177.606i | 0.249516 | − | 0.724922i | ||||
\(246\) | 77.6821 | 0.315781 | ||||||||
\(247\) | 225.883 | 0.914505 | ||||||||
\(248\) | 102.181i | 0.412019i | ||||||||
\(249\) | 688.441 | 2.76482 | ||||||||
\(250\) | 330.242i | 1.32097i | ||||||||
\(251\) | − | 294.126i | − | 1.17182i | −0.810377 | − | 0.585909i | \(-0.800738\pi\) | ||
0.810377 | − | 0.585909i | \(-0.199262\pi\) | |||||||
\(252\) | 212.085 | + | 35.4781i | 0.841606 | + | 0.140786i | ||||
\(253\) | 190.480 | 0.752887 | ||||||||
\(254\) | 139.295 | 0.548407 | ||||||||
\(255\) | 37.9701i | 0.148902i | ||||||||
\(256\) | 300.239 | 1.17281 | ||||||||
\(257\) | − | 405.263i | − | 1.57690i | −0.615099 | − | 0.788450i | \(-0.710884\pi\) | ||
0.615099 | − | 0.788450i | \(-0.289116\pi\) | |||||||
\(258\) | − | 766.883i | − | 2.97242i | ||||||
\(259\) | 39.9539 | + | 6.68359i | 0.154262 | + | 0.0258054i | ||||
\(260\) | 69.4542 | 0.267132 | ||||||||
\(261\) | −889.692 | −3.40878 | ||||||||
\(262\) | − | 328.404i | − | 1.25345i | ||||||
\(263\) | 191.524 | 0.728229 | 0.364115 | − | 0.931354i | \(-0.381372\pi\) | ||||
0.364115 | + | 0.931354i | \(0.381372\pi\) | |||||||
\(264\) | 210.182i | 0.796145i | ||||||||
\(265\) | 16.6346i | 0.0627720i | ||||||||
\(266\) | 68.6604 | − | 410.445i | 0.258122 | − | 1.54303i | ||||
\(267\) | 55.1705 | 0.206631 | ||||||||
\(268\) | 26.7117 | 0.0996706 | ||||||||
\(269\) | − | 302.274i | − | 1.12369i | −0.827241 | − | 0.561847i | \(-0.810091\pi\) | ||
0.827241 | − | 0.561847i | \(-0.189909\pi\) | |||||||
\(270\) | −312.471 | −1.15730 | ||||||||
\(271\) | − | 75.7443i | − | 0.279499i | −0.990187 | − | 0.139750i | \(-0.955370\pi\) | ||
0.990187 | − | 0.139750i | \(-0.0446298\pi\) | |||||||
\(272\) | 39.8416i | 0.146476i | ||||||||
\(273\) | −318.249 | − | 53.2375i | −1.16575 | − | 0.195009i | ||||
\(274\) | 267.546 | 0.976444 | ||||||||
\(275\) | −87.2753 | −0.317365 | ||||||||
\(276\) | 218.540i | 0.791813i | ||||||||
\(277\) | −330.683 | −1.19380 | −0.596901 | − | 0.802315i | \(-0.703601\pi\) | ||||
−0.596901 | + | 0.802315i | \(0.703601\pi\) | |||||||
\(278\) | − | 195.997i | − | 0.705024i | ||||||
\(279\) | − | 321.756i | − | 1.15325i | ||||||
\(280\) | −22.1003 | + | 132.113i | −0.0789295 | + | 0.471833i | ||||
\(281\) | 437.606 | 1.55732 | 0.778658 | − | 0.627448i | \(-0.215901\pi\) | ||||
0.778658 | + | 0.627448i | \(0.215901\pi\) | |||||||
\(282\) | −753.653 | −2.67253 | ||||||||
\(283\) | − | 328.197i | − | 1.15971i | −0.814721 | − | 0.579853i | \(-0.803110\pi\) | ||
0.814721 | − | 0.579853i | \(-0.196890\pi\) | |||||||
\(284\) | −41.0747 | −0.144629 | ||||||||
\(285\) | 464.330i | 1.62923i | ||||||||
\(286\) | 191.590i | 0.669894i | ||||||||
\(287\) | −7.39516 | + | 44.2076i | −0.0257671 | + | 0.154033i | ||||
\(288\) | −453.177 | −1.57353 | ||||||||
\(289\) | 285.031 | 0.986266 | ||||||||
\(290\) | 529.421i | 1.82559i | ||||||||
\(291\) | −556.183 | −1.91128 | ||||||||
\(292\) | − | 161.243i | − | 0.552203i | ||||||
\(293\) | 55.5669i | 0.189648i | 0.995494 | + | 0.0948241i | \(0.0302289\pi\) | ||||
−0.995494 | + | 0.0948241i | \(0.969771\pi\) | |||||||
\(294\) | −193.473 | + | 562.099i | −0.658071 | + | 1.91190i | ||||
\(295\) | 205.936 | 0.698088 | ||||||||
\(296\) | −28.8883 | −0.0975955 | ||||||||
\(297\) | − | 282.902i | − | 0.952531i | ||||||
\(298\) | −44.3067 | −0.148680 | ||||||||
\(299\) | − | 208.537i | − | 0.697449i | ||||||
\(300\) | − | 100.132i | − | 0.333773i | ||||||
\(301\) | 436.421 | + | 73.0056i | 1.44990 | + | 0.242544i | ||||
\(302\) | 422.228 | 1.39811 | ||||||||
\(303\) | 455.683 | 1.50390 | ||||||||
\(304\) | 487.216i | 1.60268i | ||||||||
\(305\) | −286.134 | −0.938145 | ||||||||
\(306\) | − | 76.4172i | − | 0.249730i | ||||||
\(307\) | − | 135.678i | − | 0.441948i | −0.975280 | − | 0.220974i | \(-0.929076\pi\) | ||
0.975280 | − | 0.220974i | \(-0.0709235\pi\) | |||||||
\(308\) | 114.260 | + | 19.1138i | 0.370976 | + | 0.0620578i | ||||
\(309\) | −735.055 | −2.37882 | ||||||||
\(310\) | −191.465 | −0.617628 | ||||||||
\(311\) | − | 125.987i | − | 0.405102i | −0.979272 | − | 0.202551i | \(-0.935077\pi\) | ||
0.979272 | − | 0.202551i | \(-0.0649232\pi\) | |||||||
\(312\) | 230.107 | 0.737522 | ||||||||
\(313\) | 402.228i | 1.28507i | 0.766255 | + | 0.642536i | \(0.222118\pi\) | ||||
−0.766255 | + | 0.642536i | \(0.777882\pi\) | |||||||
\(314\) | − | 704.881i | − | 2.24484i | ||||||
\(315\) | 69.5915 | − | 416.011i | 0.220925 | − | 1.32067i | ||||
\(316\) | 30.1603 | 0.0954439 | ||||||||
\(317\) | −462.669 | −1.45952 | −0.729762 | − | 0.683701i | \(-0.760369\pi\) | ||||
−0.729762 | + | 0.683701i | \(0.760369\pi\) | |||||||
\(318\) | − | 52.6462i | − | 0.165554i | ||||||
\(319\) | −479.321 | −1.50257 | ||||||||
\(320\) | − | 36.9646i | − | 0.115514i | ||||||
\(321\) | 735.236i | 2.29046i | ||||||||
\(322\) | −378.927 | − | 63.3879i | −1.17679 | − | 0.196857i | ||||
\(323\) | −48.5388 | −0.150275 | ||||||||
\(324\) | 48.1072 | 0.148479 | ||||||||
\(325\) | 95.5487i | 0.293996i | ||||||||
\(326\) | 341.780 | 1.04840 | ||||||||
\(327\) | 689.419i | 2.10831i | ||||||||
\(328\) | − | 31.9639i | − | 0.0974508i | ||||||
\(329\) | 71.7461 | − | 428.892i | 0.218073 | − | 1.30362i | ||||
\(330\) | −393.836 | −1.19344 | ||||||||
\(331\) | −48.7701 | −0.147342 | −0.0736709 | − | 0.997283i | \(-0.523471\pi\) | ||||
−0.0736709 | + | 0.997283i | \(0.523471\pi\) | |||||||
\(332\) | 270.601i | 0.815063i | ||||||||
\(333\) | 90.9662 | 0.273172 | ||||||||
\(334\) | 136.868i | 0.409784i | ||||||||
\(335\) | − | 52.3959i | − | 0.156406i | ||||||
\(336\) | 114.830 | − | 686.444i | 0.341757 | − | 2.04299i | ||||
\(337\) | −556.064 | −1.65004 | −0.825020 | − | 0.565103i | \(-0.808836\pi\) | ||||
−0.825020 | + | 0.565103i | \(0.808836\pi\) | |||||||
\(338\) | −202.630 | −0.599498 | ||||||||
\(339\) | 160.942i | 0.474755i | ||||||||
\(340\) | −14.9247 | −0.0438961 | ||||||||
\(341\) | − | 173.346i | − | 0.508346i | ||||||
\(342\) | − | 934.493i | − | 2.73244i | ||||||
\(343\) | −301.463 | − | 163.613i | −0.878901 | − | 0.477005i | ||||
\(344\) | −315.550 | −0.917296 | ||||||||
\(345\) | 428.674 | 1.24253 | ||||||||
\(346\) | − | 488.640i | − | 1.41225i | ||||||
\(347\) | −290.822 | −0.838105 | −0.419052 | − | 0.907962i | \(-0.637638\pi\) | ||||
−0.419052 | + | 0.907962i | \(0.637638\pi\) | |||||||
\(348\) | − | 549.931i | − | 1.58026i | ||||||
\(349\) | 75.2343i | 0.215571i | 0.994174 | + | 0.107786i | \(0.0343760\pi\) | ||||
−0.994174 | + | 0.107786i | \(0.965624\pi\) | |||||||
\(350\) | 173.619 | + | 29.0434i | 0.496054 | + | 0.0829812i | ||||
\(351\) | −309.720 | −0.882393 | ||||||||
\(352\) | −244.149 | −0.693605 | ||||||||
\(353\) | 214.961i | 0.608956i | 0.952519 | + | 0.304478i | \(0.0984820\pi\) | ||||
−0.952519 | + | 0.304478i | \(0.901518\pi\) | |||||||
\(354\) | −651.759 | −1.84113 | ||||||||
\(355\) | 80.5695i | 0.226956i | ||||||||
\(356\) | 21.6855i | 0.0609143i | ||||||||
\(357\) | 68.3869 | + | 11.4399i | 0.191560 | + | 0.0320447i | ||||
\(358\) | 742.955 | 2.07529 | ||||||||
\(359\) | −86.3984 | −0.240664 | −0.120332 | − | 0.992734i | \(-0.538396\pi\) | ||||
−0.120332 | + | 0.992734i | \(0.538396\pi\) | |||||||
\(360\) | 300.793i | 0.835536i | ||||||||
\(361\) | −232.573 | −0.644246 | ||||||||
\(362\) | − | 285.281i | − | 0.788069i | ||||||
\(363\) | 245.024i | 0.674997i | ||||||||
\(364\) | 20.9257 | − | 125.092i | 0.0574883 | − | 0.343659i | ||||
\(365\) | −316.284 | −0.866532 | ||||||||
\(366\) | 905.575 | 2.47425 | ||||||||
\(367\) | − | 526.143i | − | 1.43363i | −0.697262 | − | 0.716817i | \(-0.745598\pi\) | ||
0.697262 | − | 0.716817i | \(-0.254402\pi\) | |||||||
\(368\) | 449.803 | 1.22229 | ||||||||
\(369\) | 100.651i | 0.272767i | ||||||||
\(370\) | − | 54.1304i | − | 0.146298i | ||||||
\(371\) | 29.9601 | + | 5.01180i | 0.0807549 | + | 0.0135089i | ||||
\(372\) | 198.882 | 0.534629 | ||||||||
\(373\) | 376.321 | 1.00890 | 0.504451 | − | 0.863440i | \(-0.331695\pi\) | ||||
0.504451 | + | 0.863440i | \(0.331695\pi\) | |||||||
\(374\) | − | 41.1697i | − | 0.110079i | ||||||
\(375\) | −672.876 | −1.79434 | ||||||||
\(376\) | 310.106i | 0.824750i | ||||||||
\(377\) | 524.759i | 1.39193i | ||||||||
\(378\) | −94.1439 | + | 562.783i | −0.249058 | + | 1.48884i | ||||
\(379\) | 306.860 | 0.809657 | 0.404828 | − | 0.914393i | \(-0.367331\pi\) | ||||
0.404828 | + | 0.914393i | \(0.367331\pi\) | |||||||
\(380\) | −182.511 | −0.480293 | ||||||||
\(381\) | 283.818i | 0.744928i | ||||||||
\(382\) | −423.720 | −1.10922 | ||||||||
\(383\) | 371.209i | 0.969213i | 0.874732 | + | 0.484606i | \(0.161037\pi\) | ||||
−0.874732 | + | 0.484606i | \(0.838963\pi\) | |||||||
\(384\) | 690.336i | 1.79775i | ||||||||
\(385\) | 37.4923 | − | 224.126i | 0.0973827 | − | 0.582145i | ||||
\(386\) | 769.418 | 1.99331 | ||||||||
\(387\) | 993.634 | 2.56753 | ||||||||
\(388\) | − | 218.615i | − | 0.563442i | ||||||
\(389\) | 656.450 | 1.68753 | 0.843766 | − | 0.536711i | \(-0.180334\pi\) | ||||
0.843766 | + | 0.536711i | \(0.180334\pi\) | |||||||
\(390\) | 431.171i | 1.10557i | ||||||||
\(391\) | 44.8115i | 0.114607i | ||||||||
\(392\) | 231.287 | + | 79.6083i | 0.590018 | + | 0.203082i | ||||
\(393\) | 669.130 | 1.70262 | ||||||||
\(394\) | −296.208 | −0.751798 | ||||||||
\(395\) | − | 59.1604i | − | 0.149773i | ||||||
\(396\) | 260.146 | 0.656934 | ||||||||
\(397\) | − | 666.464i | − | 1.67875i | −0.543552 | − | 0.839376i | \(-0.682921\pi\) | ||
0.543552 | − | 0.839376i | \(-0.317079\pi\) | |||||||
\(398\) | 678.577i | 1.70497i | ||||||||
\(399\) | 836.292 | + | 139.897i | 2.09597 | + | 0.350619i | ||||
\(400\) | −206.093 | −0.515232 | ||||||||
\(401\) | −83.9875 | −0.209445 | −0.104723 | − | 0.994501i | \(-0.533395\pi\) | ||||
−0.104723 | + | 0.994501i | \(0.533395\pi\) | |||||||
\(402\) | 165.826i | 0.412502i | ||||||||
\(403\) | −189.779 | −0.470915 | ||||||||
\(404\) | 179.112i | 0.443347i | ||||||||
\(405\) | − | 94.3638i | − | 0.232997i | ||||||
\(406\) | 953.525 | + | 159.508i | 2.34858 | + | 0.392877i | ||||
\(407\) | 49.0080 | 0.120413 | ||||||||
\(408\) | −49.4465 | −0.121192 | ||||||||
\(409\) | − | 238.056i | − | 0.582044i | −0.956716 | − | 0.291022i | \(-0.906005\pi\) | ||
0.956716 | − | 0.291022i | \(-0.0939952\pi\) | |||||||
\(410\) | 59.8934 | 0.146082 | ||||||||
\(411\) | 545.130i | 1.32635i | ||||||||
\(412\) | − | 288.923i | − | 0.701270i | ||||||
\(413\) | 62.0460 | − | 370.905i | 0.150232 | − | 0.898076i | ||||
\(414\) | −862.733 | −2.08390 | ||||||||
\(415\) | 530.793 | 1.27902 | ||||||||
\(416\) | 267.294i | 0.642533i | ||||||||
\(417\) | 399.348 | 0.957669 | ||||||||
\(418\) | − | 503.458i | − | 1.20444i | ||||||
\(419\) | 225.067i | 0.537152i | 0.963258 | + | 0.268576i | \(0.0865531\pi\) | ||||
−0.963258 | + | 0.268576i | \(0.913447\pi\) | |||||||
\(420\) | 257.142 | + | 43.0154i | 0.612243 | + | 0.102418i | ||||
\(421\) | −350.787 | −0.833224 | −0.416612 | − | 0.909084i | \(-0.636783\pi\) | ||||
−0.416612 | + | 0.909084i | \(0.636783\pi\) | |||||||
\(422\) | −161.281 | −0.382183 | ||||||||
\(423\) | − | 976.492i | − | 2.30849i | ||||||
\(424\) | −21.6623 | −0.0510904 | ||||||||
\(425\) | − | 20.5320i | − | 0.0483105i | ||||||
\(426\) | − | 254.991i | − | 0.598571i | ||||||
\(427\) | −86.2088 | + | 515.348i | −0.201894 | + | 1.20690i | ||||
\(428\) | −288.994 | −0.675221 | ||||||||
\(429\) | −390.368 | −0.909950 | ||||||||
\(430\) | − | 591.272i | − | 1.37505i | ||||||
\(431\) | 219.772 | 0.509912 | 0.254956 | − | 0.966953i | \(-0.417939\pi\) | ||||
0.254956 | + | 0.966953i | \(0.417939\pi\) | |||||||
\(432\) | − | 668.048i | − | 1.54641i | ||||||
\(433\) | − | 441.969i | − | 1.02071i | −0.859963 | − | 0.510356i | \(-0.829513\pi\) | ||
0.859963 | − | 0.510356i | \(-0.170487\pi\) | |||||||
\(434\) | −57.6860 | + | 344.841i | −0.132917 | + | 0.794566i | ||||
\(435\) | −1078.71 | −2.47979 | ||||||||
\(436\) | −270.985 | −0.621526 | ||||||||
\(437\) | 547.992i | 1.25399i | ||||||||
\(438\) | 1001.00 | 2.28538 | ||||||||
\(439\) | 375.505i | 0.855365i | 0.903929 | + | 0.427682i | \(0.140670\pi\) | ||||
−0.903929 | + | 0.427682i | \(0.859330\pi\) | |||||||
\(440\) | 162.052i | 0.368300i | ||||||||
\(441\) | −728.299 | − | 250.678i | −1.65147 | − | 0.568432i | ||||
\(442\) | −45.0725 | −0.101974 | ||||||||
\(443\) | 774.902 | 1.74922 | 0.874608 | − | 0.484831i | \(-0.161119\pi\) | ||||
0.874608 | + | 0.484831i | \(0.161119\pi\) | |||||||
\(444\) | 56.2274i | 0.126638i | ||||||||
\(445\) | 42.5368 | 0.0955884 | ||||||||
\(446\) | − | 546.354i | − | 1.22501i | ||||||
\(447\) | − | 90.2760i | − | 0.201960i | ||||||
\(448\) | −66.5759 | − | 11.1370i | −0.148607 | − | 0.0248594i | ||||
\(449\) | 204.717 | 0.455940 | 0.227970 | − | 0.973668i | \(-0.426791\pi\) | ||||
0.227970 | + | 0.973668i | \(0.426791\pi\) | |||||||
\(450\) | 395.292 | 0.878426 | ||||||||
\(451\) | 54.2256i | 0.120234i | ||||||||
\(452\) | −63.2603 | −0.139956 | ||||||||
\(453\) | 860.299i | 1.89912i | ||||||||
\(454\) | 662.415i | 1.45906i | ||||||||
\(455\) | −245.372 | − | 41.0465i | −0.539279 | − | 0.0902121i | ||||
\(456\) | −604.673 | −1.32604 | ||||||||
\(457\) | −510.934 | −1.11802 | −0.559008 | − | 0.829162i | \(-0.688818\pi\) | ||||
−0.559008 | + | 0.829162i | \(0.688818\pi\) | |||||||
\(458\) | − | 312.233i | − | 0.681732i | ||||||
\(459\) | 66.5541 | 0.144998 | ||||||||
\(460\) | 168.496i | 0.366296i | ||||||||
\(461\) | − | 250.302i | − | 0.542955i | −0.962445 | − | 0.271478i | \(-0.912488\pi\) | ||
0.962445 | − | 0.271478i | \(-0.0875123\pi\) | |||||||
\(462\) | −118.658 | + | 709.327i | −0.256836 | + | 1.53534i | ||||
\(463\) | −632.010 | −1.36503 | −0.682516 | − | 0.730870i | \(-0.739114\pi\) | ||||
−0.682516 | + | 0.730870i | \(0.739114\pi\) | |||||||
\(464\) | −1131.87 | −2.43939 | ||||||||
\(465\) | − | 390.114i | − | 0.838954i | ||||||
\(466\) | −297.336 | −0.638061 | ||||||||
\(467\) | − | 785.192i | − | 1.68135i | −0.541538 | − | 0.840677i | \(-0.682158\pi\) | ||
0.541538 | − | 0.840677i | \(-0.317842\pi\) | |||||||
\(468\) | − | 284.807i | − | 0.608562i | ||||||
\(469\) | −94.3688 | − | 15.7863i | −0.201213 | − | 0.0336594i | ||||
\(470\) | −581.072 | −1.23632 | ||||||||
\(471\) | 1436.21 | 3.04928 | ||||||||
\(472\) | 268.179i | 0.568177i | ||||||||
\(473\) | 535.319 | 1.13175 | ||||||||
\(474\) | 187.234i | 0.395009i | ||||||||
\(475\) | − | 251.082i | − | 0.528594i | ||||||
\(476\) | −4.49662 | + | 26.8804i | −0.00944669 | + | 0.0564714i | ||||
\(477\) | 68.2124 | 0.143003 | ||||||||
\(478\) | 39.4398 | 0.0825100 | ||||||||
\(479\) | − | 211.815i | − | 0.442202i | −0.975251 | − | 0.221101i | \(-0.929035\pi\) | ||
0.975251 | − | 0.221101i | \(-0.0709650\pi\) | |||||||
\(480\) | −549.455 | −1.14470 | ||||||||
\(481\) | − | 53.6538i | − | 0.111546i | ||||||
\(482\) | − | 73.4548i | − | 0.152396i | ||||||
\(483\) | 129.154 | − | 772.073i | 0.267400 | − | 1.59849i | ||||
\(484\) | −96.3099 | −0.198987 | ||||||||
\(485\) | −428.821 | −0.884168 | ||||||||
\(486\) | − | 434.984i | − | 0.895029i | ||||||
\(487\) | 509.269 | 1.04573 | 0.522863 | − | 0.852416i | \(-0.324864\pi\) | ||||
0.522863 | + | 0.852416i | \(0.324864\pi\) | |||||||
\(488\) | − | 372.617i | − | 0.763560i | ||||||
\(489\) | 696.384i | 1.42410i | ||||||||
\(490\) | −149.169 | + | 433.382i | −0.304426 | + | 0.884453i | ||||
\(491\) | −128.327 | −0.261359 | −0.130679 | − | 0.991425i | \(-0.541716\pi\) | ||||
−0.130679 | + | 0.991425i | \(0.541716\pi\) | |||||||
\(492\) | −62.2137 | −0.126451 | ||||||||
\(493\) | − | 112.763i | − | 0.228728i | ||||||
\(494\) | −551.184 | −1.11576 | ||||||||
\(495\) | − | 510.285i | − | 1.03088i | ||||||
\(496\) | − | 409.341i | − | 0.825285i | ||||||
\(497\) | 145.111 | + | 24.2746i | 0.291975 | + | 0.0488423i | ||||
\(498\) | −1679.89 | −3.37327 | ||||||||
\(499\) | 236.891 | 0.474732 | 0.237366 | − | 0.971420i | \(-0.423716\pi\) | ||||
0.237366 | + | 0.971420i | \(0.423716\pi\) | |||||||
\(500\) | − | 264.483i | − | 0.528966i | ||||||
\(501\) | −278.871 | −0.556629 | ||||||||
\(502\) | 717.707i | 1.42969i | ||||||||
\(503\) | − | 740.385i | − | 1.47194i | −0.677015 | − | 0.735969i | \(-0.736727\pi\) | ||
0.677015 | − | 0.735969i | \(-0.263273\pi\) | |||||||
\(504\) | 541.749 | + | 90.6253i | 1.07490 | + | 0.179812i | ||||
\(505\) | 351.335 | 0.695712 | ||||||||
\(506\) | −464.797 | −0.918571 | ||||||||
\(507\) | − | 412.864i | − | 0.814328i | ||||||
\(508\) | −111.558 | −0.219603 | ||||||||
\(509\) | 431.033i | 0.846824i | 0.905937 | + | 0.423412i | \(0.139168\pi\) | ||||
−0.905937 | + | 0.423412i | \(0.860832\pi\) | |||||||
\(510\) | − | 92.6521i | − | 0.181671i | ||||||
\(511\) | −95.2926 | + | 569.650i | −0.186483 | + | 1.11478i | ||||
\(512\) | −177.225 | −0.346143 | ||||||||
\(513\) | 813.879 | 1.58651 | ||||||||
\(514\) | 988.896i | 1.92392i | ||||||||
\(515\) | −566.733 | −1.10045 | ||||||||
\(516\) | 614.178i | 1.19027i | ||||||||
\(517\) | − | 526.084i | − | 1.01757i | ||||||
\(518\) | −97.4927 | − | 16.3088i | −0.188210 | − | 0.0314843i | ||||
\(519\) | 995.615 | 1.91833 | ||||||||
\(520\) | 177.414 | 0.341181 | ||||||||
\(521\) | 593.563i | 1.13928i | 0.821896 | + | 0.569638i | \(0.192917\pi\) | ||||
−0.821896 | + | 0.569638i | \(0.807083\pi\) | |||||||
\(522\) | 2170.97 | 4.15894 | ||||||||
\(523\) | 145.052i | 0.277346i | 0.990338 | + | 0.138673i | \(0.0442837\pi\) | ||||
−0.990338 | + | 0.138673i | \(0.955716\pi\) | |||||||
\(524\) | 263.010i | 0.501928i | ||||||||
\(525\) | −59.1766 | + | 353.752i | −0.112717 | + | 0.673814i | ||||
\(526\) | −467.345 | −0.888488 | ||||||||
\(527\) | 40.7806 | 0.0773825 | ||||||||
\(528\) | − | 842.002i | − | 1.59470i | ||||||
\(529\) | −23.0882 | −0.0436449 | ||||||||
\(530\) | − | 40.5906i | − | 0.0765859i | ||||||
\(531\) | − | 844.469i | − | 1.59034i | ||||||
\(532\) | −54.9884 | + | 328.716i | −0.103362 | + | 0.617887i | ||||
\(533\) | 59.3660 | 0.111381 | ||||||||
\(534\) | −134.623 | −0.252103 | ||||||||
\(535\) | 566.872i | 1.05957i | ||||||||
\(536\) | 68.2325 | 0.127299 | ||||||||
\(537\) | 1513.79i | 2.81897i | ||||||||
\(538\) | 737.588i | 1.37098i | ||||||||
\(539\) | −392.370 | − | 135.053i | −0.727960 | − | 0.250562i | ||||
\(540\) | 250.251 | 0.463427 | ||||||||
\(541\) | −669.919 | −1.23830 | −0.619149 | − | 0.785274i | \(-0.712522\pi\) | ||||
−0.619149 | + | 0.785274i | \(0.712522\pi\) | |||||||
\(542\) | 184.826i | 0.341008i | ||||||||
\(543\) | 581.266 | 1.07047 | ||||||||
\(544\) | − | 57.4374i | − | 0.105583i | ||||||
\(545\) | 531.547i | 0.975315i | ||||||||
\(546\) | 776.569 | + | 129.907i | 1.42229 | + | 0.237924i | ||||
\(547\) | −50.3870 | −0.0921152 | −0.0460576 | − | 0.998939i | \(-0.514666\pi\) | ||||
−0.0460576 | + | 0.998939i | \(0.514666\pi\) | |||||||
\(548\) | −214.271 | −0.391005 | ||||||||
\(549\) | 1173.33i | 2.13722i | ||||||||
\(550\) | 212.963 | 0.387206 | ||||||||
\(551\) | − | 1378.96i | − | 2.50264i | ||||||
\(552\) | 558.240i | 1.01130i | ||||||||
\(553\) | −106.552 | − | 17.8243i | −0.192680 | − | 0.0322320i | ||||
\(554\) | 806.910 | 1.45652 | ||||||||
\(555\) | 110.292 | 0.198724 | ||||||||
\(556\) | 156.969i | 0.282318i | ||||||||
\(557\) | 142.761 | 0.256303 | 0.128152 | − | 0.991755i | \(-0.459096\pi\) | ||||
0.128152 | + | 0.991755i | \(0.459096\pi\) | |||||||
\(558\) | 785.128i | 1.40704i | ||||||||
\(559\) | − | 586.066i | − | 1.04842i | ||||||
\(560\) | 88.5349 | − | 529.253i | 0.158098 | − | 0.945095i | ||||
\(561\) | 83.8843 | 0.149526 | ||||||||
\(562\) | −1067.82 | −1.90003 | ||||||||
\(563\) | 401.378i | 0.712927i | 0.934309 | + | 0.356464i | \(0.116018\pi\) | ||||
−0.934309 | + | 0.356464i | \(0.883982\pi\) | |||||||
\(564\) | 603.583 | 1.07018 | ||||||||
\(565\) | 124.087i | 0.219623i | ||||||||
\(566\) | 800.843i | 1.41492i | ||||||||
\(567\) | −169.956 | − | 28.4307i | −0.299746 | − | 0.0501423i | ||||
\(568\) | −104.921 | −0.184721 | ||||||||
\(569\) | −569.373 | −1.00065 | −0.500327 | − | 0.865836i | \(-0.666787\pi\) | ||||
−0.500327 | + | 0.865836i | \(0.666787\pi\) | |||||||
\(570\) | − | 1133.03i | − | 1.98777i | ||||||
\(571\) | 522.826 | 0.915632 | 0.457816 | − | 0.889047i | \(-0.348632\pi\) | ||||
0.457816 | + | 0.889047i | \(0.348632\pi\) | |||||||
\(572\) | − | 153.440i | − | 0.268251i | ||||||
\(573\) | − | 863.340i | − | 1.50670i | ||||||
\(574\) | 18.0452 | − | 107.872i | 0.0314376 | − | 0.187931i | ||||
\(575\) | −231.801 | −0.403133 | ||||||||
\(576\) | −151.579 | −0.263157 | ||||||||
\(577\) | 927.796i | 1.60796i | 0.594653 | + | 0.803982i | \(0.297289\pi\) | ||||
−0.594653 | + | 0.803982i | \(0.702711\pi\) | |||||||
\(578\) | −695.513 | −1.20331 | ||||||||
\(579\) | 1567.71i | 2.70761i | ||||||||
\(580\) | − | 424.000i | − | 0.731035i | ||||||
\(581\) | 159.922 | − | 955.996i | 0.275252 | − | 1.64543i | ||||
\(582\) | 1357.16 | 2.33189 | ||||||||
\(583\) | 36.7494 | 0.0630350 | ||||||||
\(584\) | − | 411.880i | − | 0.705274i | ||||||
\(585\) | −558.658 | −0.954971 | ||||||||
\(586\) | − | 135.591i | − | 0.231383i | ||||||
\(587\) | 87.3727i | 0.148846i | 0.997227 | + | 0.0744231i | \(0.0237115\pi\) | ||||
−0.997227 | + | 0.0744231i | \(0.976288\pi\) | |||||||
\(588\) | 154.948 | − | 450.171i | 0.263516 | − | 0.765597i | ||||
\(589\) | 498.699 | 0.846687 | ||||||||
\(590\) | −502.511 | −0.851713 | ||||||||
\(591\) | − | 603.532i | − | 1.02120i | ||||||
\(592\) | 115.728 | 0.195487 | ||||||||
\(593\) | 1003.89i | 1.69290i | 0.532472 | + | 0.846448i | \(0.321263\pi\) | ||||
−0.532472 | + | 0.846448i | \(0.678737\pi\) | |||||||
\(594\) | 690.317i | 1.16215i | ||||||||
\(595\) | 52.7268 | + | 8.82027i | 0.0886164 | + | 0.0148240i | ||||
\(596\) | 35.4842 | 0.0595372 | ||||||||
\(597\) | −1382.62 | −2.31594 | ||||||||
\(598\) | 508.858i | 0.850934i | ||||||||
\(599\) | 784.057 | 1.30894 | 0.654472 | − | 0.756087i | \(-0.272891\pi\) | ||||
0.654472 | + | 0.756087i | \(0.272891\pi\) | |||||||
\(600\) | − | 255.777i | − | 0.426295i | ||||||
\(601\) | − | 879.714i | − | 1.46375i | −0.681439 | − | 0.731875i | \(-0.738645\pi\) | ||
0.681439 | − | 0.731875i | \(-0.261355\pi\) | |||||||
\(602\) | −1064.92 | − | 178.143i | −1.76898 | − | 0.295919i | ||||
\(603\) | −214.857 | −0.356313 | ||||||||
\(604\) | −338.152 | −0.559855 | ||||||||
\(605\) | 188.915i | 0.312256i | ||||||||
\(606\) | −1111.93 | −1.83486 | ||||||||
\(607\) | − | 662.906i | − | 1.09210i | −0.837752 | − | 0.546051i | \(-0.816130\pi\) | ||
0.837752 | − | 0.546051i | \(-0.183870\pi\) | |||||||
\(608\) | − | 702.392i | − | 1.15525i | ||||||
\(609\) | −325.002 | + | 1942.83i | −0.533664 | + | 3.19020i | ||||
\(610\) | 698.205 | 1.14460 | ||||||||
\(611\) | −575.955 | −0.942644 | ||||||||
\(612\) | 61.2007i | 0.100001i | ||||||||
\(613\) | −819.459 | −1.33680 | −0.668401 | − | 0.743802i | \(-0.733021\pi\) | ||||
−0.668401 | + | 0.743802i | \(0.733021\pi\) | |||||||
\(614\) | 331.072i | 0.539205i | ||||||||
\(615\) | 122.034i | 0.198430i | ||||||||
\(616\) | 291.867 | + | 48.8243i | 0.473810 | + | 0.0792602i | ||||
\(617\) | −742.529 | −1.20345 | −0.601725 | − | 0.798703i | \(-0.705520\pi\) | ||||
−0.601725 | + | 0.798703i | \(0.705520\pi\) | |||||||
\(618\) | 1793.63 | 2.90232 | ||||||||
\(619\) | − | 1195.27i | − | 1.93097i | −0.260467 | − | 0.965483i | \(-0.583877\pi\) | ||
0.260467 | − | 0.965483i | \(-0.416123\pi\) | |||||||
\(620\) | 153.339 | 0.247322 | ||||||||
\(621\) | − | 751.381i | − | 1.20995i | ||||||
\(622\) | 307.424i | 0.494252i | ||||||||
\(623\) | 12.8158 | − | 76.6118i | 0.0205712 | − | 0.122972i | ||||
\(624\) | −921.821 | −1.47728 | ||||||||
\(625\) | −261.149 | −0.417838 | ||||||||
\(626\) | − | 981.488i | − | 1.56787i | ||||||
\(627\) | 1025.81 | 1.63605 | ||||||||
\(628\) | 564.522i | 0.898920i | ||||||||
\(629\) | 11.5294i | 0.0183297i | ||||||||
\(630\) | −169.812 | + | 1015.12i | −0.269543 | + | 1.61130i | ||||
\(631\) | 383.855 | 0.608329 | 0.304164 | − | 0.952620i | \(-0.401623\pi\) | ||||
0.304164 | + | 0.952620i | \(0.401623\pi\) | |||||||
\(632\) | 77.0414 | 0.121901 | ||||||||
\(633\) | − | 328.614i | − | 0.519138i | ||||||
\(634\) | 1128.97 | 1.78072 | ||||||||
\(635\) | 218.825i | 0.344607i | ||||||||
\(636\) | 42.1630i | 0.0662941i | ||||||||
\(637\) | −147.855 | + | 429.566i | −0.232112 | + | 0.674358i | ||||
\(638\) | 1169.61 | 1.83324 | ||||||||
\(639\) | 330.387 | 0.517037 | ||||||||
\(640\) | 532.254i | 0.831646i | ||||||||
\(641\) | −1166.29 | −1.81949 | −0.909745 | − | 0.415168i | \(-0.863723\pi\) | ||||
−0.909745 | + | 0.415168i | \(0.863723\pi\) | |||||||
\(642\) | − | 1794.07i | − | 2.79451i | ||||||
\(643\) | 739.745i | 1.15046i | 0.817992 | + | 0.575229i | \(0.195087\pi\) | ||||
−0.817992 | + | 0.575229i | \(0.804913\pi\) | |||||||
\(644\) | 303.474 | + | 50.7659i | 0.471232 | + | 0.0788290i | ||||
\(645\) | 1204.73 | 1.86780 | ||||||||
\(646\) | 118.441 | 0.183345 | ||||||||
\(647\) | − | 387.812i | − | 0.599400i | −0.954034 | − | 0.299700i | \(-0.903113\pi\) | ||
0.954034 | − | 0.299700i | \(-0.0968865\pi\) | |||||||
\(648\) | 122.885 | 0.189637 | ||||||||
\(649\) | − | 454.957i | − | 0.701013i | ||||||
\(650\) | − | 233.151i | − | 0.358695i | ||||||
\(651\) | −702.622 | − | 117.537i | −1.07930 | − | 0.180548i | ||||
\(652\) | −273.723 | −0.419821 | ||||||||
\(653\) | 300.399 | 0.460029 | 0.230015 | − | 0.973187i | \(-0.426123\pi\) | ||||
0.230015 | + | 0.973187i | \(0.426123\pi\) | |||||||
\(654\) | − | 1682.27i | − | 2.57228i | ||||||
\(655\) | 515.904 | 0.787639 | ||||||||
\(656\) | 128.049i | 0.195197i | ||||||||
\(657\) | 1296.97i | 1.97408i | ||||||||
\(658\) | −175.070 | + | 1046.55i | −0.266064 | + | 1.59050i | ||||
\(659\) | −579.322 | −0.879093 | −0.439546 | − | 0.898220i | \(-0.644861\pi\) | ||||
−0.439546 | + | 0.898220i | \(0.644861\pi\) | |||||||
\(660\) | 315.414 | 0.477900 | ||||||||
\(661\) | − | 1259.79i | − | 1.90588i | −0.303163 | − | 0.952939i | \(-0.598043\pi\) | ||
0.303163 | − | 0.952939i | \(-0.401957\pi\) | |||||||
\(662\) | 119.006 | 0.179767 | ||||||||
\(663\) | − | 91.8362i | − | 0.138516i | ||||||
\(664\) | 691.224i | 1.04100i | ||||||||
\(665\) | 644.787 | + | 107.862i | 0.969604 | + | 0.162198i | ||||
\(666\) | −221.969 | −0.333287 | ||||||||
\(667\) | −1273.07 | −1.90865 | ||||||||
\(668\) | − | 109.614i | − | 0.164093i | ||||||
\(669\) | 1113.21 | 1.66399 | ||||||||
\(670\) | 127.853i | 0.190825i | ||||||||
\(671\) | 632.133i | 0.942075i | ||||||||
\(672\) | −165.544 | + | 989.608i | −0.246346 | + | 1.47263i | ||||
\(673\) | 288.739 | 0.429033 | 0.214516 | − | 0.976720i | \(-0.431182\pi\) | ||||
0.214516 | + | 0.976720i | \(0.431182\pi\) | |||||||
\(674\) | 1356.87 | 2.01316 | ||||||||
\(675\) | 344.272i | 0.510032i | ||||||||
\(676\) | 162.282 | 0.240062 | ||||||||
\(677\) | − | 865.508i | − | 1.27845i | −0.769021 | − | 0.639223i | \(-0.779256\pi\) | ||
0.769021 | − | 0.639223i | \(-0.220744\pi\) | |||||||
\(678\) | − | 392.719i | − | 0.579232i | ||||||
\(679\) | −129.199 | + | 772.338i | −0.190278 | + | 1.13746i | ||||
\(680\) | −38.1236 | −0.0560641 | ||||||||
\(681\) | −1349.69 | −1.98192 | ||||||||
\(682\) | 422.987i | 0.620216i | ||||||||
\(683\) | −766.924 | −1.12287 | −0.561437 | − | 0.827519i | \(-0.689751\pi\) | ||||
−0.561437 | + | 0.827519i | \(0.689751\pi\) | |||||||
\(684\) | 748.413i | 1.09417i | ||||||||
\(685\) | 420.299i | 0.613576i | ||||||||
\(686\) | 735.609 | + | 399.237i | 1.07232 | + | 0.581978i | ||||
\(687\) | 636.182 | 0.926030 | ||||||||
\(688\) | 1264.11 | 1.83737 | ||||||||
\(689\) | − | 40.2331i | − | 0.0583935i | ||||||
\(690\) | −1046.02 | −1.51597 | ||||||||
\(691\) | 1092.86i | 1.58156i | 0.612099 | + | 0.790781i | \(0.290325\pi\) | ||||
−0.612099 | + | 0.790781i | \(0.709675\pi\) | |||||||
\(692\) | 391.340i | 0.565520i | ||||||||
\(693\) | −919.059 | − | 153.743i | −1.32620 | − | 0.221851i | ||||
\(694\) | 709.645 | 1.02254 | ||||||||
\(695\) | 307.900 | 0.443022 | ||||||||
\(696\) | − | 1404.74i | − | 2.01831i | ||||||
\(697\) | −12.7569 | −0.0183025 | ||||||||
\(698\) | − | 183.582i | − | 0.263011i | ||||||
\(699\) | − | 605.830i | − | 0.866709i | ||||||
\(700\) | −139.047 | − | 23.2602i | −0.198639 | − | 0.0332288i | ||||
\(701\) | −900.508 | −1.28460 | −0.642302 | − | 0.766452i | \(-0.722021\pi\) | ||||
−0.642302 | + | 0.766452i | \(0.722021\pi\) | |||||||
\(702\) | 755.757 | 1.07658 | ||||||||
\(703\) | 140.991i | 0.200556i | ||||||||
\(704\) | −81.6629 | −0.115998 | ||||||||
\(705\) | − | 1183.95i | − | 1.67936i | ||||||
\(706\) | − | 524.534i | − | 0.742966i | ||||||
\(707\) | 105.853 | − | 632.779i | 0.149721 | − | 0.895019i | ||||
\(708\) | 521.978 | 0.737257 | ||||||||
\(709\) | 212.814 | 0.300161 | 0.150080 | − | 0.988674i | \(-0.452047\pi\) | ||||
0.150080 | + | 0.988674i | \(0.452047\pi\) | |||||||
\(710\) | − | 196.600i | − | 0.276902i | ||||||
\(711\) | −242.595 | −0.341203 | ||||||||
\(712\) | 55.3935i | 0.0777998i | ||||||||
\(713\) | − | 460.404i | − | 0.645727i | ||||||
\(714\) | −166.873 | − | 27.9150i | −0.233716 | − | 0.0390966i | ||||
\(715\) | −300.977 | −0.420946 | ||||||||
\(716\) | −595.014 | −0.831026 | ||||||||
\(717\) | 80.3594i | 0.112077i | ||||||||
\(718\) | 210.823 | 0.293626 | ||||||||
\(719\) | − | 449.020i | − | 0.624506i | −0.949999 | − | 0.312253i | \(-0.898916\pi\) | ||
0.949999 | − | 0.312253i | \(-0.101084\pi\) | |||||||
\(720\) | − | 1204.99i | − | 1.67360i | ||||||
\(721\) | −170.750 | + | 1020.73i | −0.236824 | + | 1.41571i | ||||
\(722\) | 567.508 | 0.786022 | ||||||||
\(723\) | 149.666 | 0.207007 | ||||||||
\(724\) | 228.475i | 0.315573i | ||||||||
\(725\) | 583.301 | 0.804553 | ||||||||
\(726\) | − | 597.890i | − | 0.823541i | ||||||
\(727\) | − | 508.187i | − | 0.699019i | −0.936933 | − | 0.349509i | \(-0.886348\pi\) | ||
0.936933 | − | 0.349509i | \(-0.113652\pi\) | |||||||
\(728\) | 53.4527 | − | 319.535i | 0.0734240 | − | 0.438922i | ||||
\(729\) | 1107.84 | 1.51967 | ||||||||
\(730\) | 771.775 | 1.05723 | ||||||||
\(731\) | 125.937i | 0.172280i | ||||||||
\(732\) | −725.253 | −0.990783 | ||||||||
\(733\) | − | 213.294i | − | 0.290987i | −0.989359 | − | 0.145494i | \(-0.953523\pi\) | ||
0.989359 | − | 0.145494i | \(-0.0464770\pi\) | |||||||
\(734\) | 1283.86i | 1.74913i | ||||||||
\(735\) | −883.026 | − | 303.935i | −1.20140 | − | 0.413517i | ||||
\(736\) | −648.455 | −0.881053 | ||||||||
\(737\) | −115.754 | −0.157061 | ||||||||
\(738\) | − | 245.602i | − | 0.332793i | ||||||
\(739\) | −810.600 | −1.09689 | −0.548444 | − | 0.836188i | \(-0.684779\pi\) | ||||
−0.548444 | + | 0.836188i | \(0.684779\pi\) | |||||||
\(740\) | 43.3517i | 0.0585834i | ||||||||
\(741\) | − | 1123.05i | − | 1.51559i | ||||||
\(742\) | −73.1065 | − | 12.2294i | −0.0985263 | − | 0.0164817i | ||||
\(743\) | −728.164 | −0.980033 | −0.490016 | − | 0.871713i | \(-0.663009\pi\) | ||||
−0.490016 | + | 0.871713i | \(0.663009\pi\) | |||||||
\(744\) | 508.024 | 0.682828 | ||||||||
\(745\) | − | 69.6034i | − | 0.0934274i | ||||||
\(746\) | −918.272 | −1.23093 | ||||||||
\(747\) | − | 2176.59i | − | 2.91378i | ||||||
\(748\) | 32.9718i | 0.0440800i | ||||||||
\(749\) | 1020.98 | + | 170.792i | 1.36312 | + | 0.228026i | ||||
\(750\) | 1641.91 | 2.18921 | ||||||||
\(751\) | 1370.62 | 1.82506 | 0.912531 | − | 0.409008i | \(-0.134125\pi\) | ||||
0.912531 | + | 0.409008i | \(0.134125\pi\) | |||||||
\(752\) | − | 1242.30i | − | 1.65200i | ||||||
\(753\) | −1462.34 | −1.94202 | ||||||||
\(754\) | − | 1280.48i | − | 1.69825i | ||||||
\(755\) | 663.297i | 0.878539i | ||||||||
\(756\) | 75.3975 | − | 450.719i | 0.0997322 | − | 0.596190i | ||||
\(757\) | 413.568 | 0.546325 | 0.273162 | − | 0.961968i | \(-0.411930\pi\) | ||||
0.273162 | + | 0.961968i | \(0.411930\pi\) | |||||||
\(758\) | −748.779 | −0.987835 | ||||||||
\(759\) | − | 947.035i | − | 1.24774i | ||||||
\(760\) | −466.207 | −0.613430 | ||||||||
\(761\) | 1059.96i | 1.39285i | 0.717631 | + | 0.696424i | \(0.245227\pi\) | ||||
−0.717631 | + | 0.696424i | \(0.754773\pi\) | |||||||
\(762\) | − | 692.552i | − | 0.908861i | ||||||
\(763\) | 957.353 | + | 160.149i | 1.25472 | + | 0.209893i | ||||
\(764\) | 339.347 | 0.444172 | ||||||||
\(765\) | 120.047 | 0.156924 | ||||||||
\(766\) | − | 905.798i | − | 1.18250i | ||||||
\(767\) | −498.086 | −0.649395 | ||||||||
\(768\) | − | 1492.74i | − | 1.94367i | ||||||
\(769\) | − | 677.987i | − | 0.881647i | −0.897594 | − | 0.440824i | \(-0.854686\pi\) | ||
0.897594 | − | 0.440824i | \(-0.145314\pi\) | |||||||
\(770\) | −91.4862 | + | 546.896i | −0.118813 | + | 0.710255i | ||||
\(771\) | −2014.90 | −2.61336 | ||||||||
\(772\) | −616.208 | −0.798197 | ||||||||
\(773\) | − | 88.7708i | − | 0.114839i | −0.998350 | − | 0.0574197i | \(-0.981713\pi\) | ||
0.998350 | − | 0.0574197i | \(-0.0182873\pi\) | |||||||
\(774\) | −2424.60 | −3.13255 | ||||||||
\(775\) | 210.950i | 0.272194i | ||||||||
\(776\) | − | 558.431i | − | 0.719628i | ||||||
\(777\) | 33.2296 | − | 198.644i | 0.0427666 | − | 0.255655i | ||||
\(778\) | −1601.82 | −2.05890 | ||||||||
\(779\) | −156.002 | −0.200259 | ||||||||
\(780\) | − | 345.314i | − | 0.442711i | ||||||
\(781\) | 177.996 | 0.227907 | ||||||||
\(782\) | − | 109.346i | − | 0.139829i | ||||||
\(783\) | 1890.76i | 2.41477i | ||||||||
\(784\) | −926.548 | − | 318.915i | −1.18182 | − | 0.406780i | ||||
\(785\) | 1107.33 | 1.41061 | ||||||||
\(786\) | −1632.77 | −2.07731 | ||||||||
\(787\) | 1104.27i | 1.40314i | 0.712599 | + | 0.701572i | \(0.247518\pi\) | ||||
−0.712599 | + | 0.701572i | \(0.752482\pi\) | |||||||
\(788\) | 237.226 | 0.301048 | ||||||||
\(789\) | − | 952.225i | − | 1.20688i | ||||||
\(790\) | 144.359i | 0.182733i | ||||||||
\(791\) | 223.490 | + | 37.3860i | 0.282541 | + | 0.0472642i | ||||
\(792\) | 664.517 | 0.839036 | ||||||||
\(793\) | 692.057 | 0.872707 | ||||||||
\(794\) | 1626.26i | 2.04819i | ||||||||
\(795\) | 82.7042 | 0.104030 | ||||||||
\(796\) | − | 543.456i | − | 0.682733i | ||||||
\(797\) | − | 408.281i | − | 0.512273i | −0.966641 | − | 0.256136i | \(-0.917550\pi\) | ||
0.966641 | − | 0.256136i | \(-0.0824496\pi\) | |||||||
\(798\) | −2040.66 | − | 341.367i | −2.55722 | − | 0.427779i | ||||
\(799\) | 123.764 | 0.154899 | ||||||||
\(800\) | 297.113 | 0.371391 | ||||||||
\(801\) | − | 174.428i | − | 0.217763i | ||||||
\(802\) | 204.941 | 0.255537 | ||||||||
\(803\) | 698.740i | 0.870162i | ||||||||
\(804\) | − | 132.806i | − | 0.165182i | ||||||
\(805\) | 99.5789 | − | 595.273i | 0.123701 | − | 0.739470i | ||||
\(806\) | 463.085 | 0.574547 | ||||||||
\(807\) | −1502.85 | −1.86227 | ||||||||
\(808\) | 457.524i | 0.566243i | ||||||||
\(809\) | 140.712 | 0.173934 | 0.0869669 | − | 0.996211i | \(-0.472283\pi\) | ||||
0.0869669 | + | 0.996211i | \(0.472283\pi\) | |||||||
\(810\) | 230.260i | 0.284272i | ||||||||
\(811\) | − | 665.442i | − | 0.820520i | −0.911969 | − | 0.410260i | \(-0.865438\pi\) | ||
0.911969 | − | 0.410260i | \(-0.134562\pi\) | |||||||
\(812\) | −763.655 | − | 127.746i | −0.940462 | − | 0.157323i | ||||
\(813\) | −376.587 | −0.463207 | ||||||||
\(814\) | −119.586 | −0.146911 | ||||||||
\(815\) | 536.917i | 0.658794i | ||||||||
\(816\) | 198.085 | 0.242752 | ||||||||
\(817\) | 1540.06i | 1.88502i | ||||||||
\(818\) | 580.888i | 0.710131i | ||||||||
\(819\) | −168.317 | + | 1006.18i | −0.205515 | + | 1.22855i | ||||
\(820\) | −47.9672 | −0.0584966 | ||||||||
\(821\) | −30.8103 | −0.0375278 | −0.0187639 | − | 0.999824i | \(-0.505973\pi\) | ||||
−0.0187639 | + | 0.999824i | \(0.505973\pi\) | |||||||
\(822\) | − | 1330.19i | − | 1.61824i | ||||||
\(823\) | 100.490 | 0.122102 | 0.0610512 | − | 0.998135i | \(-0.480555\pi\) | ||||
0.0610512 | + | 0.998135i | \(0.480555\pi\) | |||||||
\(824\) | − | 738.026i | − | 0.895663i | ||||||
\(825\) | 433.917i | 0.525960i | ||||||||
\(826\) | −151.400 | + | 905.057i | −0.183293 | + | 1.09571i | ||||
\(827\) | 659.624 | 0.797610 | 0.398805 | − | 0.917036i | \(-0.369425\pi\) | ||||
0.398805 | + | 0.917036i | \(0.369425\pi\) | |||||||
\(828\) | 690.942 | 0.834471 | ||||||||
\(829\) | − | 331.134i | − | 0.399438i | −0.979853 | − | 0.199719i | \(-0.935997\pi\) | ||
0.979853 | − | 0.199719i | \(-0.0640029\pi\) | |||||||
\(830\) | −1295.20 | −1.56049 | ||||||||
\(831\) | 1644.10i | 1.97846i | ||||||||
\(832\) | 89.4043i | 0.107457i | ||||||||
\(833\) | 31.7719 | − | 92.3072i | 0.0381415 | − | 0.110813i | ||||
\(834\) | −974.461 | −1.16842 | ||||||||
\(835\) | −215.012 | −0.257499 | ||||||||
\(836\) | 403.207i | 0.482305i | ||||||||
\(837\) | −683.792 | −0.816956 | ||||||||
\(838\) | − | 549.193i | − | 0.655361i | ||||||
\(839\) | 1138.98i | 1.35754i | 0.734351 | + | 0.678770i | \(0.237487\pi\) | ||||
−0.734351 | + | 0.678770i | \(0.762513\pi\) | |||||||
\(840\) | 656.844 | + | 109.879i | 0.781957 | + | 0.130808i | ||||
\(841\) | 2362.52 | 2.80918 | ||||||||
\(842\) | 855.967 | 1.01659 | ||||||||
\(843\) | − | 2175.70i | − | 2.58090i | ||||||
\(844\) | 129.166 | 0.153041 | ||||||||
\(845\) | − | 318.321i | − | 0.376711i | ||||||
\(846\) | 2382.77i | 2.81651i | ||||||||
\(847\) | 340.250 | + | 56.9179i | 0.401711 | + | 0.0671994i | ||||
\(848\) | 86.7805 | 0.102336 | ||||||||
\(849\) | −1631.74 | −1.92195 | ||||||||
\(850\) | 50.1007i | 0.0589420i | ||||||||
\(851\) | 130.164 | 0.152954 | ||||||||
\(852\) | 204.216i | 0.239691i | ||||||||
\(853\) | − | 295.096i | − | 0.345951i | −0.984926 | − | 0.172976i | \(-0.944662\pi\) | ||
0.984926 | − | 0.172976i | \(-0.0553382\pi\) | |||||||
\(854\) | 210.361 | − | 1257.52i | 0.246324 | − | 1.47250i | ||||
\(855\) | 1468.04 | 1.71700 | ||||||||
\(856\) | −738.208 | −0.862392 | ||||||||
\(857\) | 412.027i | 0.480778i | 0.970677 | + | 0.240389i | \(0.0772751\pi\) | ||||
−0.970677 | + | 0.240389i | \(0.922725\pi\) | |||||||
\(858\) | 952.550 | 1.11020 | ||||||||
\(859\) | 947.029i | 1.10248i | 0.834347 | + | 0.551239i | \(0.185845\pi\) | ||||
−0.834347 | + | 0.551239i | \(0.814155\pi\) | |||||||
\(860\) | 473.536i | 0.550623i | ||||||||
\(861\) | 219.792 | + | 36.7675i | 0.255276 | + | 0.0427032i | ||||
\(862\) | −536.273 | −0.622126 | ||||||||
\(863\) | 918.071 | 1.06381 | 0.531907 | − | 0.846803i | \(-0.321476\pi\) | ||||
0.531907 | + | 0.846803i | \(0.321476\pi\) | |||||||
\(864\) | 963.086i | 1.11468i | ||||||||
\(865\) | 767.626 | 0.887429 | ||||||||
\(866\) | 1078.46i | 1.24534i | ||||||||
\(867\) | − | 1417.12i | − | 1.63451i | ||||||
\(868\) | 46.1993 | − | 276.175i | 0.0532250 | − | 0.318174i | ||||
\(869\) | −130.698 | −0.150401 | ||||||||
\(870\) | 2632.19 | 3.02550 | ||||||||
\(871\) | 126.727i | 0.145496i | ||||||||
\(872\) | −692.205 | −0.793813 | ||||||||
\(873\) | 1758.44i | 2.01425i | ||||||||
\(874\) | − | 1337.17i | − | 1.52995i | ||||||
\(875\) | −156.306 | + | 934.381i | −0.178635 | + | 1.06786i | ||||
\(876\) | −801.673 | −0.915152 | ||||||||
\(877\) | −1000.81 | −1.14117 | −0.570585 | − | 0.821238i | \(-0.693284\pi\) | ||||
−0.570585 | + | 0.821238i | \(0.693284\pi\) | |||||||
\(878\) | − | 916.282i | − | 1.04360i | ||||||
\(879\) | 276.269 | 0.314299 | ||||||||
\(880\) | − | 649.189i | − | 0.737715i | ||||||
\(881\) | 546.821i | 0.620682i | 0.950625 | + | 0.310341i | \(0.100443\pi\) | ||||
−0.950625 | + | 0.310341i | \(0.899557\pi\) | |||||||
\(882\) | 1777.14 | + | 611.688i | 2.01490 | + | 0.693524i | ||||
\(883\) | −288.367 | −0.326576 | −0.163288 | − | 0.986578i | \(-0.552210\pi\) | ||||
−0.163288 | + | 0.986578i | \(0.552210\pi\) | |||||||
\(884\) | 36.0975 | 0.0408342 | ||||||||
\(885\) | − | 1023.88i | − | 1.15692i | ||||||
\(886\) | −1890.86 | −2.13416 | ||||||||
\(887\) | − | 1516.47i | − | 1.70966i | −0.518907 | − | 0.854831i | \(-0.673661\pi\) | ||
0.518907 | − | 0.854831i | \(-0.326339\pi\) | |||||||
\(888\) | 143.627i | 0.161743i | ||||||||
\(889\) | 394.120 | + | 65.9294i | 0.443330 | + | 0.0741613i | ||||
\(890\) | −103.795 | −0.116624 | ||||||||
\(891\) | −208.470 | −0.233973 | ||||||||
\(892\) | 437.562i | 0.490540i | ||||||||
\(893\) | 1513.49 | 1.69484 | ||||||||
\(894\) | 220.285i | 0.246404i | ||||||||
\(895\) | 1167.14i | 1.30407i | ||||||||
\(896\) | 958.627 | + | 160.362i | 1.06990 | + | 0.178975i | ||||
\(897\) | −1036.81 | −1.15586 | ||||||||
\(898\) | −499.537 | −0.556277 | ||||||||
\(899\) | 1158.55i | 1.28871i | ||||||||
\(900\) | −316.580 | −0.351755 | ||||||||
\(901\) | 8.64549i | 0.00959544i | ||||||||
\(902\) | − | 132.318i | − | 0.146694i | ||||||
\(903\) | 362.971 | − | 2169.81i | 0.401961 | − | 2.40289i | ||||
\(904\) | −161.592 | −0.178752 | ||||||||
\(905\) | 448.160 | 0.495205 | ||||||||
\(906\) | − | 2099.24i | − | 2.31705i | ||||||
\(907\) | −458.880 | −0.505932 | −0.252966 | − | 0.967475i | \(-0.581406\pi\) | ||||
−0.252966 | + | 0.967475i | \(0.581406\pi\) | |||||||
\(908\) | − | 530.512i | − | 0.584264i | ||||||
\(909\) | − | 1440.70i | − | 1.58493i | ||||||
\(910\) | 598.740 | + | 100.159i | 0.657956 | + | 0.110065i | ||||
\(911\) | 1470.54 | 1.61420 | 0.807100 | − | 0.590415i | \(-0.201036\pi\) | ||||
0.807100 | + | 0.590415i | \(0.201036\pi\) | |||||||
\(912\) | 2422.35 | 2.65609 | ||||||||
\(913\) | − | 1172.64i | − | 1.28438i | ||||||
\(914\) | 1246.75 | 1.36405 | ||||||||
\(915\) | 1422.61i | 1.55476i | ||||||||
\(916\) | 250.060i | 0.272991i | ||||||||
\(917\) | 155.436 | − | 929.180i | 0.169505 | − | 1.01328i | ||||
\(918\) | −162.401 | −0.176907 | ||||||||
\(919\) | −182.597 | −0.198691 | −0.0993453 | − | 0.995053i | \(-0.531675\pi\) | ||||
−0.0993453 | + | 0.995053i | \(0.531675\pi\) | |||||||
\(920\) | 430.407i | 0.467833i | ||||||||
\(921\) | −674.567 | −0.732429 | ||||||||
\(922\) | 610.771i | 0.662441i | ||||||||
\(923\) | − | 194.869i | − | 0.211126i | ||||||
\(924\) | 95.0304 | − | 568.083i | 0.102847 | − | 0.614808i | ||||
\(925\) | −59.6393 | −0.0644749 | ||||||||
\(926\) | 1542.19 | 1.66543 | ||||||||
\(927\) | 2323.97i | 2.50698i | ||||||||
\(928\) | 1631.76 | 1.75836 | ||||||||
\(929\) | 311.412i | 0.335212i | 0.985854 | + | 0.167606i | \(0.0536036\pi\) | ||||
−0.985854 | + | 0.167606i | \(0.946396\pi\) | |||||||
\(930\) | 951.928i | 1.02358i | ||||||||
\(931\) | 388.533 | − | 1128.81i | 0.417329 | − | 1.21247i | ||||
\(932\) | 238.130 | 0.255504 | ||||||||
\(933\) | −626.384 | −0.671366 | ||||||||
\(934\) | 1915.97i | 2.05136i | ||||||||
\(935\) | 64.6754 | 0.0691715 | ||||||||
\(936\) | − | 727.511i | − | 0.777255i | ||||||
\(937\) | − | 970.690i | − | 1.03596i | −0.855394 | − | 0.517978i | \(-0.826685\pi\) | ||
0.855394 | − | 0.517978i | \(-0.173315\pi\) | |||||||
\(938\) | 230.272 | + | 38.5206i | 0.245493 | + | 0.0410667i | ||||
\(939\) | 1999.81 | 2.12972 | ||||||||
\(940\) | 465.366 | 0.495071 | ||||||||
\(941\) | − | 291.860i | − | 0.310159i | −0.987902 | − | 0.155079i | \(-0.950437\pi\) | ||
0.987902 | − | 0.155079i | \(-0.0495634\pi\) | |||||||
\(942\) | −3504.54 | −3.72032 | ||||||||
\(943\) | 144.022i | 0.152728i | ||||||||
\(944\) | − | 1074.34i | − | 1.13807i | ||||||
\(945\) | −884.101 | − | 147.895i | −0.935557 | − | 0.156502i | ||||
\(946\) | −1306.25 | −1.38081 | ||||||||
\(947\) | −1701.82 | −1.79706 | −0.898532 | − | 0.438907i | \(-0.855366\pi\) | ||||
−0.898532 | + | 0.438907i | \(0.855366\pi\) | |||||||
\(948\) | − | 149.952i | − | 0.158177i | ||||||
\(949\) | 764.979 | 0.806089 | ||||||||
\(950\) | 612.673i | 0.644919i | ||||||||
\(951\) | 2300.31i | 2.41883i | ||||||||
\(952\) | −11.4862 | + | 68.6633i | −0.0120653 | + | 0.0721253i | ||||
\(953\) | −588.366 | −0.617383 | −0.308691 | − | 0.951162i | \(-0.599891\pi\) | ||||
−0.308691 | + | 0.951162i | \(0.599891\pi\) | |||||||
\(954\) | −166.447 | −0.174473 | ||||||||
\(955\) | − | 665.641i | − | 0.697006i | ||||||
\(956\) | −31.5864 | −0.0330401 | ||||||||
\(957\) | 2383.10i | 2.49018i | ||||||||
\(958\) | 516.856i | 0.539515i | ||||||||
\(959\) | 756.989 | + | 126.631i | 0.789352 | + | 0.132045i | ||||
\(960\) | −183.782 | −0.191439 | ||||||||
\(961\) | 542.011 | 0.564007 | ||||||||
\(962\) | 130.922i | 0.136094i | ||||||||
\(963\) | 2324.54 | 2.41385 | ||||||||
\(964\) | 58.8281i | 0.0610250i | ||||||||
\(965\) | 1208.71i | 1.25255i | ||||||||
\(966\) | −315.154 | + | 1883.96i | −0.326246 | + | 1.95027i | ||||
\(967\) | −1195.93 | −1.23674 | −0.618372 | − | 0.785886i | \(-0.712207\pi\) | ||||
−0.618372 | + | 0.785886i | \(0.712207\pi\) | |||||||
\(968\) | −246.014 | −0.254147 | ||||||||
\(969\) | 241.326i | 0.249047i | ||||||||
\(970\) | 1046.38 | 1.07874 | ||||||||
\(971\) | 461.355i | 0.475133i | 0.971371 | + | 0.237567i | \(0.0763498\pi\) | ||||
−0.971371 | + | 0.237567i | \(0.923650\pi\) | |||||||
\(972\) | 348.368i | 0.358403i | ||||||||
\(973\) | 92.7666 | − | 554.550i | 0.0953408 | − | 0.569938i | ||||
\(974\) | −1242.68 | −1.27586 | ||||||||
\(975\) | 475.051 | 0.487232 | ||||||||
\(976\) | 1492.73i | 1.52943i | ||||||||
\(977\) | 1341.19 | 1.37276 | 0.686381 | − | 0.727242i | \(-0.259198\pi\) | ||||
0.686381 | + | 0.727242i | \(0.259198\pi\) | |||||||
\(978\) | − | 1699.27i | − | 1.73749i | ||||||
\(979\) | − | 93.9731i | − | 0.0959889i | ||||||
\(980\) | 119.466 | − | 347.085i | 0.121904 | − | 0.354169i | ||||
\(981\) | 2179.68 | 2.22190 | ||||||||
\(982\) | 313.135 | 0.318875 | ||||||||
\(983\) | 159.110i | 0.161861i | 0.996720 | + | 0.0809307i | \(0.0257892\pi\) | ||||
−0.996720 | + | 0.0809307i | \(0.974211\pi\) | |||||||
\(984\) | −158.919 | −0.161503 | ||||||||
\(985\) | − | 465.327i | − | 0.472413i | ||||||
\(986\) | 275.156i | 0.279063i | ||||||||
\(987\) | −2132.37 | − | 356.709i | −2.16046 | − | 0.361407i | ||||
\(988\) | 441.430 | 0.446791 | ||||||||
\(989\) | 1421.80 | 1.43761 | ||||||||
\(990\) | 1245.16i | 1.25774i | ||||||||
\(991\) | −404.558 | −0.408232 | −0.204116 | − | 0.978947i | \(-0.565432\pi\) | ||||
−0.204116 | + | 0.978947i | \(0.565432\pi\) | |||||||
\(992\) | 590.124i | 0.594884i | ||||||||
\(993\) | 242.477i | 0.244186i | ||||||||
\(994\) | −354.091 | − | 59.2333i | −0.356228 | − | 0.0595908i | ||||
\(995\) | −1066.01 | −1.07136 | ||||||||
\(996\) | 1345.38 | 1.35078 | ||||||||
\(997\) | 1186.56i | 1.19013i | 0.803678 | + | 0.595065i | \(0.202874\pi\) | ||||
−0.803678 | + | 0.595065i | \(0.797126\pi\) | |||||||
\(998\) | −578.046 | −0.579204 | ||||||||
\(999\) | − | 193.320i | − | 0.193514i |
(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.b.a.83.11 | ✓ | 52 | |
7.6 | odd | 2 | inner | 287.3.b.a.83.12 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.b.a.83.11 | ✓ | 52 | 1.1 | even | 1 | trivial | |
287.3.b.a.83.12 | yes | 52 | 7.6 | odd | 2 | inner |