Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(319,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("768.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.l (of order \(4\), degree \(2\), 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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 703.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.703 |
Dual form | 768.3.l.d.319.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | − | 2.00000i | 0.400000 | − | 0.400000i | −0.478233 | − | 0.878233i | \(-0.658723\pi\) |
0.878233 | + | 0.478233i | \(0.158723\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.378937 | 0.0541339 | 0.0270670 | − | 0.999634i | \(-0.491383\pi\) | ||||
0.0270670 | + | 0.999634i | \(0.491383\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.5558 | + | 10.5558i | 0.959621 | + | 0.959621i | 0.999216 | − | 0.0395946i | \(-0.0126066\pi\) |
−0.0395946 | + | 0.999216i | \(0.512607\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.46410 | − | 6.46410i | −0.497239 | − | 0.497239i | 0.413339 | − | 0.910577i | \(-0.364363\pi\) |
−0.910577 | + | 0.413339i | \(0.864363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.89898i | 0.326599i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.8564 | −0.697436 | −0.348718 | − | 0.937228i | \(-0.613383\pi\) | ||||
−0.348718 | + | 0.937228i | \(0.613383\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.6622 | − | 18.6622i | 0.982220 | − | 0.982220i | −0.0176248 | − | 0.999845i | \(-0.505610\pi\) |
0.999845 | + | 0.0176248i | \(0.00561044\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.464102 | + | 0.464102i | −0.0221001 | + | 0.0221001i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.0716 | 0.524851 | 0.262426 | − | 0.964952i | \(-0.415478\pi\) | ||||
0.262426 | + | 0.964952i | \(0.415478\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.0000i | 0.680000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.07180 | − | 1.07180i | −0.0369585 | − | 0.0369585i | 0.688386 | − | 0.725345i | \(-0.258320\pi\) |
−0.725345 | + | 0.688386i | \(0.758320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.38752i | 0.206049i | 0.994679 | + | 0.103025i | \(0.0328520\pi\) | ||||
−0.994679 | + | 0.103025i | \(0.967148\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −25.8564 | −0.783527 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.757875 | − | 0.757875i | 0.0216536 | − | 0.0216536i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35.3923 | − | 35.3923i | 0.956549 | − | 0.956549i | −0.0425457 | − | 0.999095i | \(-0.513547\pi\) |
0.999095 | + | 0.0425457i | \(0.0135468\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.8338 | 0.405994 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.56922i | − | 0.0870541i | −0.999052 | − | 0.0435271i | \(-0.986141\pi\) | ||
0.999052 | − | 0.0435271i | \(-0.0138595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.9759 | + | 29.9759i | 0.697114 | + | 0.697114i | 0.963787 | − | 0.266673i | \(-0.0859245\pi\) |
−0.266673 | + | 0.963787i | \(0.585924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | − | 6.00000i | −0.133333 | − | 0.133333i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 31.6675i | − | 0.673777i | −0.941545 | − | 0.336888i | \(-0.890626\pi\) | ||
0.941545 | − | 0.336888i | \(-0.109374\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.8564 | −0.997070 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.5211 | − | 14.5211i | 0.284727 | − | 0.284727i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 68.7846 | − | 68.7846i | 1.29782 | − | 1.29782i | 0.367995 | − | 0.929828i | \(-0.380044\pi\) |
0.929828 | − | 0.367995i | \(-0.119956\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 42.2233 | 0.767697 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 45.7128i | 0.801979i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27.8781 | + | 27.8781i | 0.472511 | + | 0.472511i | 0.902726 | − | 0.430216i | \(-0.141562\pi\) |
−0.430216 | + | 0.902726i | \(0.641562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 62.8179 | + | 62.8179i | 1.02980 | + | 1.02980i | 0.999542 | + | 0.0302601i | \(0.00963355\pi\) |
0.0302601 | + | 0.999542i | \(0.490366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.13681i | − | 0.0180446i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −25.8564 | −0.397791 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30.5579 | − | 30.5579i | 0.456088 | − | 0.456088i | −0.441281 | − | 0.897369i | \(-0.645476\pi\) |
0.897369 | + | 0.441281i | \(0.145476\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.7846 | + | 14.7846i | −0.214270 | + | 0.214270i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 131.975 | 1.85880 | 0.929402 | − | 0.369068i | \(-0.120323\pi\) | ||||
0.929402 | + | 0.369068i | \(0.120323\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 50.1436i | 0.686899i | 0.939171 | + | 0.343449i | \(0.111595\pi\) | ||||
−0.939171 | + | 0.343449i | \(0.888405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −20.8207 | − | 20.8207i | −0.277609 | − | 0.277609i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 4.00000i | 0.0519481 | + | 0.0519481i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 114.219i | 1.44582i | 0.690944 | + | 0.722908i | \(0.257195\pi\) | ||||
−0.690944 | + | 0.722908i | \(0.742805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.92189 | − | 1.92189i | 0.0231553 | − | 0.0231553i | −0.695434 | − | 0.718590i | \(-0.744788\pi\) |
0.718590 | + | 0.695434i | \(0.244788\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.7128 | + | 23.7128i | −0.278974 | + | 0.278974i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.62536 | 0.0301765 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 74.0000i | 0.831461i | 0.909488 | + | 0.415730i | \(0.136474\pi\) | ||||
−0.909488 | + | 0.415730i | \(0.863526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.44949 | − | 2.44949i | −0.0269175 | − | 0.0269175i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.82309 | − | 7.82309i | −0.0841192 | − | 0.0841192i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 74.6487i | − | 0.785776i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −89.2820 | −0.920433 | −0.460217 | − | 0.887807i | \(-0.652228\pi\) | ||||
−0.460217 | + | 0.887807i | \(0.652228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.6675 | − | 31.6675i | 0.319874 | − | 0.319874i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 123.923 | − | 123.923i | 1.22696 | − | 1.22696i | 0.261853 | − | 0.965108i | \(-0.415666\pi\) |
0.965108 | − | 0.261853i | \(-0.0843336\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 96.1393 | 0.933391 | 0.466696 | − | 0.884418i | \(-0.345444\pi\) | ||||
0.466696 | + | 0.884418i | \(0.345444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.85641i | 0.0176801i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 115.708 | + | 115.708i | 1.08138 | + | 1.08138i | 0.996381 | + | 0.0850027i | \(0.0270899\pi\) |
0.0850027 | + | 0.996381i | \(0.472910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −81.2487 | − | 81.2487i | −0.745401 | − | 0.745401i | 0.228211 | − | 0.973612i | \(-0.426712\pi\) |
−0.973612 | + | 0.228211i | \(0.926712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86.6931i | 0.781019i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 164.851 | 1.45886 | 0.729430 | − | 0.684055i | \(-0.239785\pi\) | ||||
0.729430 | + | 0.684055i | \(0.239785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.1432 | − | 24.1432i | 0.209941 | − | 0.209941i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.3923 | + | 19.3923i | −0.165746 | + | 0.165746i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.49284 | −0.0377549 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 101.851i | 0.841746i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.37138 | + | 4.37138i | 0.0355397 | + | 0.0355397i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 84.0000 | + | 84.0000i | 0.672000 | + | 0.672000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 66.7454i | − | 0.525555i | −0.964857 | − | 0.262777i | \(-0.915362\pi\) | ||
0.964857 | − | 0.262777i | \(-0.0846385\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −73.4256 | −0.569191 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −136.116 | + | 136.116i | −1.03906 | + | 1.03906i | −0.0398495 | + | 0.999206i | \(0.512688\pi\) |
−0.999206 | + | 0.0398495i | \(0.987312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.07180 | − | 7.07180i | 0.0531714 | − | 0.0531714i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.6969 | 0.108866 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 225.559i | − | 1.64642i | −0.567740 | − | 0.823208i | \(-0.692182\pi\) | ||
0.567740 | − | 0.823208i | \(-0.307818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −41.0593 | − | 41.0593i | −0.295391 | − | 0.295391i | 0.543815 | − | 0.839205i | \(-0.316979\pi\) |
−0.839205 | + | 0.543815i | \(0.816979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 38.7846 | + | 38.7846i | 0.275068 | + | 0.275068i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 136.468i | − | 0.954321i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.28719 | −0.0295668 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 59.8366 | − | 59.8366i | 0.407052 | − | 0.407052i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −31.8564 | + | 31.8564i | −0.213801 | + | 0.213801i | −0.805880 | − | 0.592079i | \(-0.798307\pi\) |
0.592079 | + | 0.805880i | \(0.298307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −27.5536 | −0.182474 | −0.0912371 | − | 0.995829i | \(-0.529082\pi\) | ||||
−0.0912371 | + | 0.995829i | \(0.529082\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 35.5692i | 0.232479i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.7750 | + | 12.7750i | 0.0824196 | + | 0.0824196i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −65.5359 | − | 65.5359i | −0.417426 | − | 0.417426i | 0.466890 | − | 0.884316i | \(-0.345375\pi\) |
−0.884316 | + | 0.466890i | \(0.845375\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 168.487i | 1.05967i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.57437 | 0.0284123 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 80.8332 | − | 80.8332i | 0.495909 | − | 0.495909i | −0.414253 | − | 0.910162i | \(-0.635957\pi\) |
0.910162 | + | 0.414253i | \(0.135957\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −51.7128 | + | 51.7128i | −0.313411 | + | 0.313411i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −252.528 | −1.51214 | −0.756071 | − | 0.654490i | \(-0.772884\pi\) | ||||
−0.756071 | + | 0.654490i | \(0.772884\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 85.4308i | − | 0.505508i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −55.9865 | − | 55.9865i | −0.327407 | − | 0.327407i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −90.4205 | − | 90.4205i | −0.522662 | − | 0.522662i | 0.395713 | − | 0.918374i | \(-0.370498\pi\) |
−0.918374 | + | 0.395713i | \(0.870498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.44194i | 0.0368111i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −68.2872 | −0.385803 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.09450 | + | 9.09450i | −0.0508072 | + | 0.0508072i | −0.732054 | − | 0.681247i | \(-0.761438\pi\) |
0.681247 | + | 0.732054i | \(0.261438\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −214.310 | + | 214.310i | −1.18403 | + | 1.18403i | −0.205344 | + | 0.978690i | \(0.565831\pi\) |
−0.978690 | + | 0.205344i | \(0.934169\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −153.872 | −0.840830 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 141.569i | − | 0.765239i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −125.154 | − | 125.154i | −0.669274 | − | 0.669274i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.39230 | + | 1.39230i | 0.00736669 | + | 0.00736669i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 91.1043i | − | 0.476986i | −0.971144 | − | 0.238493i | \(-0.923347\pi\) | ||
0.971144 | − | 0.238493i | \(-0.0766534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −191.990 | −0.994765 | −0.497383 | − | 0.867531i | \(-0.665705\pi\) | ||||
−0.497383 | + | 0.867531i | \(0.665705\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 31.6675 | − | 31.6675i | 0.162397 | − | 0.162397i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 252.631 | − | 252.631i | 1.28239 | − | 1.28239i | 0.343085 | − | 0.939304i | \(-0.388528\pi\) |
0.939304 | − | 0.343085i | \(-0.111472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −268.876 | −1.35114 | −0.675569 | − | 0.737297i | \(-0.736102\pi\) | ||||
−0.675569 | + | 0.737297i | \(0.736102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 74.8513i | 0.372394i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.406144 | − | 0.406144i | −0.00200071 | − | 0.00200071i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.13844 | − | 7.13844i | −0.0348217 | − | 0.0348217i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 36.2147i | − | 0.174950i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 393.990 | 1.88512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −140.663 | + | 140.663i | −0.666652 | + | 0.666652i | −0.956939 | − | 0.290288i | \(-0.906249\pi\) |
0.290288 | + | 0.956939i | \(0.406249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −161.636 | + | 161.636i | −0.758854 | + | 0.758854i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 119.904 | 0.557691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.42047i | 0.0111542i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −61.4131 | − | 61.4131i | −0.280425 | − | 0.280425i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 76.6410 | + | 76.6410i | 0.346792 | + | 0.346792i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 135.331i | 0.606866i | 0.952853 | + | 0.303433i | \(0.0981329\pi\) | ||||
−0.952853 | + | 0.303433i | \(0.901867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.0000 | 0.226667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −219.102 | + | 219.102i | −0.965205 | + | 0.965205i | −0.999415 | − | 0.0342095i | \(-0.989109\pi\) |
0.0342095 | + | 0.999415i | \(0.489109\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −160.895 | + | 160.895i | −0.702598 | + | 0.702598i | −0.964967 | − | 0.262370i | \(-0.915496\pi\) |
0.262370 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.79796 | −0.0424154 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 231.990i | − | 0.995664i | −0.867274 | − | 0.497832i | \(-0.834130\pi\) | ||
0.867274 | − | 0.497832i | \(-0.165870\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −63.3350 | − | 63.3350i | −0.269511 | − | 0.269511i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −139.890 | − | 139.890i | −0.590252 | − | 0.590252i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 454.550i | − | 1.90188i | −0.309372 | − | 0.950941i | \(-0.600119\pi\) | ||
0.309372 | − | 0.950941i | \(-0.399881\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 330.554 | 1.37159 | 0.685796 | − | 0.727794i | \(-0.259454\pi\) | ||||
0.685796 | + | 0.727794i | \(0.259454\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −97.7128 | + | 97.7128i | −0.398828 | + | 0.398828i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −241.268 | −0.976795 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.70766i | 0.0189063i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9010 | − | 24.9010i | −0.0992073 | − | 0.0992073i | 0.655761 | − | 0.754968i | \(-0.272348\pi\) |
−0.754968 | + | 0.655761i | \(0.772348\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 127.426 | + | 127.426i | 0.503659 | + | 0.503659i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 58.0843i | − | 0.227782i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 277.138 | 1.07836 | 0.539180 | − | 0.842191i | \(-0.318734\pi\) | ||||
0.539180 | + | 0.842191i | \(0.318734\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.4115 | − | 13.4115i | 0.0517817 | − | 0.0517817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.21539 | + | 3.21539i | −0.0123195 | + | 0.0123195i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −119.200 | −0.453232 | −0.226616 | − | 0.973984i | \(-0.572766\pi\) | ||||
−0.226616 | + | 0.973984i | \(0.572766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 275.138i | − | 1.03826i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −90.6311 | − | 90.6311i | −0.339442 | − | 0.339442i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −151.061 | − | 151.061i | −0.561567 | − | 0.561567i | 0.368185 | − | 0.929752i | \(-0.379979\pi\) |
−0.929752 | + | 0.368185i | \(0.879979\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 430.137i | 1.58722i | 0.608427 | + | 0.793610i | \(0.291801\pi\) | ||||
−0.608427 | + | 0.793610i | \(0.708199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | 0.0219780 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −179.449 | + | 179.449i | −0.652542 | + | 0.652542i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −213.249 | + | 213.249i | −0.769851 | + | 0.769851i | −0.978080 | − | 0.208229i | \(-0.933230\pi\) |
0.208229 | + | 0.978080i | \(0.433230\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.1626 | 0.0686830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 78.0000i | − | 0.277580i | −0.990322 | − | 0.138790i | \(-0.955679\pi\) | ||
0.990322 | − | 0.138790i | \(-0.0443213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −41.7628 | − | 41.7628i | −0.147572 | − | 0.147572i | 0.629461 | − | 0.777032i | \(-0.283276\pi\) |
−0.777032 | + | 0.629461i | \(0.783276\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 91.4256 | + | 91.4256i | 0.320792 | + | 0.320792i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.35251i | − | 0.00471258i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −148.426 | −0.513583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 109.348 | − | 109.348i | 0.375765 | − | 0.375765i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −141.933 | + | 141.933i | −0.484414 | + | 0.484414i | −0.906538 | − | 0.422124i | \(-0.861285\pi\) |
0.422124 | + | 0.906538i | \(0.361285\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 111.513 | 0.378009 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 77.5692i | 0.261176i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −78.0319 | − | 78.0319i | −0.260976 | − | 0.260976i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.3590 | + | 11.3590i | 0.0377375 | + | 0.0377375i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 303.548i | 1.00181i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 251.272 | 0.823842 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3215 | + | 16.3215i | −0.0531645 | + | 0.0531645i | −0.733189 | − | 0.680025i | \(-0.761969\pi\) |
0.680025 | + | 0.733189i | \(0.261969\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −117.746 | + | 117.746i | −0.381055 | + | 0.381055i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −111.404 | −0.358211 | −0.179106 | − | 0.983830i | \(-0.557320\pi\) | ||||
−0.179106 | + | 0.983830i | \(0.557320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 502.267i | 1.60469i | 0.596864 | + | 0.802343i | \(0.296413\pi\) | ||||
−0.596864 | + | 0.802343i | \(0.703587\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.27362 | − | 2.27362i | −0.00721785 | − | 0.00721785i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 140.785 | + | 140.785i | 0.444115 | + | 0.444115i | 0.893393 | − | 0.449277i | \(-0.148318\pi\) |
−0.449277 | + | 0.893393i | \(0.648318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 22.6274i | − | 0.0709323i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −283.426 | −0.882946 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −221.266 | + | 221.266i | −0.685035 | + | 0.685035i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 109.890 | − | 109.890i | 0.338122 | − | 0.338122i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 199.018 | 0.608617 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.0000i | − | 0.0364742i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −302.682 | − | 302.682i | −0.914446 | − | 0.914446i | 0.0821724 | − | 0.996618i | \(-0.473814\pi\) |
−0.996618 | + | 0.0821724i | \(0.973814\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −106.177 | − | 106.177i | −0.318850 | − | 0.318850i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 122.232i | − | 0.364870i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 435.559 | 1.29246 | 0.646230 | − | 0.763143i | \(-0.276345\pi\) | ||||
0.646230 | + | 0.763143i | \(0.276345\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −201.901 | + | 201.901i | −0.595577 | + | 0.595577i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −67.4256 | + | 67.4256i | −0.197729 | + | 0.197729i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −37.0815 | −0.108109 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 59.1384i | 0.171416i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 59.7885 | + | 59.7885i | 0.172301 | + | 0.172301i | 0.787990 | − | 0.615688i | \(-0.211122\pi\) |
−0.615688 | + | 0.787990i | \(0.711122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 56.4538 | + | 56.4538i | 0.161759 | + | 0.161759i | 0.783345 | − | 0.621587i | \(-0.213512\pi\) |
−0.621587 | + | 0.783345i | \(0.713512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 47.5013i | − | 0.135331i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −87.9897 | −0.249263 | −0.124631 | − | 0.992203i | \(-0.539775\pi\) | ||||
−0.124631 | + | 0.992203i | \(0.539775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 263.950 | − | 263.950i | 0.743522 | − | 0.743522i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.50258 | − | 5.50258i | 0.0154134 | − | 0.0154134i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −213.499 | −0.594705 | −0.297353 | − | 0.954768i | \(-0.596104\pi\) | ||||
−0.297353 | + | 0.954768i | \(0.596104\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 335.554i | − | 0.929512i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −124.742 | − | 124.742i | −0.343641 | − | 0.343641i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 100.287 | + | 100.287i | 0.274759 | + | 0.274759i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 537.102i | − | 1.46349i | −0.681577 | − | 0.731746i | \(-0.738706\pi\) | ||
0.681577 | − | 0.731746i | \(-0.261294\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.7077 | −0.0290180 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.0651 | − | 26.0651i | 0.0702562 | − | 0.0702562i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 120.895 | − | 120.895i | 0.324115 | − | 0.324115i | −0.526228 | − | 0.850343i | \(-0.676394\pi\) |
0.850343 | + | 0.526228i | \(0.176394\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −205.757 | −0.548686 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8564i | 0.0367544i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 178.922 | + | 178.922i | 0.472089 | + | 0.472089i | 0.902590 | − | 0.430501i | \(-0.141663\pi\) |
−0.430501 | + | 0.902590i | \(0.641663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 81.7461 | + | 81.7461i | 0.214557 | + | 0.214557i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 61.1158i | 0.159571i | 0.996812 | + | 0.0797856i | \(0.0254236\pi\) | ||||
−0.996812 | + | 0.0797856i | \(0.974576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.0415584 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 89.9277 | − | 89.9277i | 0.232371 | − | 0.232371i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 399.569 | − | 399.569i | 1.02717 | − | 1.02717i | 0.0275498 | − | 0.999620i | \(-0.491230\pi\) |
0.999620 | − | 0.0275498i | \(-0.00877048\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −143.126 | −0.366050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 333.415i | − | 0.848385i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 228.439 | + | 228.439i | 0.578327 | + | 0.578327i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −310.597 | − | 310.597i | −0.782361 | − | 0.782361i | 0.197868 | − | 0.980229i | \(-0.436598\pi\) |
−0.980229 | + | 0.197868i | \(0.936598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.3223i | 0.0434143i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −447.856 | −1.11685 | −0.558424 | − | 0.829555i | \(-0.688594\pi\) | ||||
−0.558424 | + | 0.829555i | \(0.688594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.2896 | − | 41.2896i | 0.102456 | − | 0.102456i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0000 | + | 18.0000i | −0.0444444 | + | 0.0444444i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 747.191 | 1.83585 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 208.133i | 0.508883i | 0.967088 | + | 0.254442i | \(0.0818917\pi\) | ||||
−0.967088 | + | 0.254442i | \(0.918108\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 276.252 | + | 276.252i | 0.672146 | + | 0.672146i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.5641 | + | 10.5641i | 0.0255788 | + | 0.0255788i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.68757i | − | 0.0185243i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 100.574 | 0.241186 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 169.191 | − | 169.191i | 0.403796 | − | 0.403796i | −0.475772 | − | 0.879569i | \(-0.657831\pi\) |
0.879569 | + | 0.475772i | \(0.157831\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 64.9615 | − | 64.9615i | 0.154303 | − | 0.154303i | −0.625734 | − | 0.780037i | \(-0.715200\pi\) |
0.780037 | + | 0.625734i | \(0.215200\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −95.0025 | −0.224592 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 201.559i | − | 0.474256i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.8041 | + | 23.8041i | 0.0557472 | + | 0.0557472i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 167.138 | + | 167.138i | 0.389600 | + | 0.389600i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 104.206i | − | 0.241777i | −0.992666 | − | 0.120888i | \(-0.961426\pi\) | ||
0.992666 | − | 0.120888i | \(-0.0385743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −533.549 | −1.23221 | −0.616107 | − | 0.787663i | \(-0.711291\pi\) | ||||
−0.616107 | + | 0.787663i | \(0.711291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.25071 | − | 5.25071i | 0.0120706 | − | 0.0120706i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 225.282 | − | 225.282i | 0.515520 | − | 0.515520i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 163.318 | 0.372023 | 0.186012 | − | 0.982548i | \(-0.440444\pi\) | ||||
0.186012 | + | 0.982548i | \(0.440444\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 146.569i | 0.332357i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −238.589 | − | 238.589i | −0.538575 | − | 0.538575i | 0.384535 | − | 0.923110i | \(-0.374362\pi\) |
−0.923110 | + | 0.384535i | \(0.874362\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 148.000 | + | 148.000i | 0.332584 | + | 0.332584i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 78.0319i | − | 0.174568i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −333.559 | −0.742893 | −0.371446 | − | 0.928454i | \(-0.621138\pi\) | ||||
−0.371446 | + | 0.928454i | \(0.621138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.6761 | − | 37.6761i | 0.0835390 | − | 0.0835390i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.7461 | − | 33.7461i | 0.0744948 | − | 0.0744948i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.79796 | −0.0215340 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 431.292i | 0.943747i | 0.881666 | + | 0.471873i | \(0.156422\pi\) | ||||
−0.881666 | + | 0.471873i | \(0.843578\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −43.5632 | − | 43.5632i | −0.0949090 | − | 0.0949090i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −232.277 | − | 232.277i | −0.503854 | − | 0.503854i | 0.408779 | − | 0.912633i | \(-0.365955\pi\) |
−0.912633 | + | 0.408779i | \(0.865955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 470.681i | 1.01659i | 0.861183 | + | 0.508295i | \(0.169724\pi\) | ||||
−0.861183 | + | 0.508295i | \(0.830276\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.2923 | −0.0672954 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 412.950 | − | 412.950i | 0.884262 | − | 0.884262i | −0.109702 | − | 0.993964i | \(-0.534990\pi\) |
0.993964 | + | 0.109702i | \(0.0349898\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.5795 | − | 11.5795i | 0.0246898 | − | 0.0246898i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 160.530 | 0.340827 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 632.841i | 1.33793i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 317.257 | + | 317.257i | 0.667910 | + | 0.667910i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −206.354 | − | 206.354i | −0.432608 | − | 0.432608i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 802.784i | 1.67596i | 0.545703 | + | 0.837979i | \(0.316263\pi\) | ||||
−0.545703 | + | 0.837979i | \(0.683737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −457.559 | −0.951266 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.60244 | + | 5.60244i | −0.0115993 | + | 0.0115993i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −178.564 | + | 178.564i | −0.368173 | + | 0.368173i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 317.326 | 0.651593 | 0.325797 | − | 0.945440i | \(-0.394367\pi\) | ||||
0.325797 | + | 0.945440i | \(0.394367\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 198.000i | 0.404908i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 651.648 | + | 651.648i | 1.32719 | + | 1.32719i | 0.907816 | + | 0.419369i | \(0.137749\pi\) |
0.419369 | + | 0.907816i | \(0.362251\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7077 | + | 12.7077i | 0.0257762 | + | 0.0257762i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 126.670i | − | 0.255899i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 50.0103 | 0.100624 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.9489 | − | 38.9489i | 0.0780540 | − | 0.0780540i | −0.667002 | − | 0.745056i | \(-0.732423\pi\) |
0.745056 | + | 0.667002i | \(0.232423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 309.282 | − | 309.282i | 0.617329 | − | 0.617329i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −205.594 | −0.408735 | −0.204368 | − | 0.978894i | \(-0.565514\pi\) | ||||
−0.204368 | + | 0.978894i | \(0.565514\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 495.692i | − | 0.981569i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 104.631 | + | 104.631i | 0.206373 | + | 0.206373i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −91.6565 | − | 91.6565i | −0.180072 | − | 0.180072i | 0.611315 | − | 0.791387i | \(-0.290641\pi\) |
−0.791387 | + | 0.611315i | \(0.790641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.0013i | 0.0371845i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 137.138 | 0.267326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 192.279 | − | 192.279i | 0.373357 | − | 0.373357i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 334.277 | − | 334.277i | 0.646570 | − | 0.646570i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 221.484 | 0.426751 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 155.282i | − | 0.298046i | −0.988834 | − | 0.149023i | \(-0.952387\pi\) | ||
0.988834 | − | 0.149023i | \(-0.0476129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 501.090 | + | 501.090i | 0.958107 | + | 0.958107i | 0.999157 | − | 0.0410496i | \(-0.0130702\pi\) |
−0.0410496 | + | 0.999157i | \(0.513070\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.88973 | − | 7.88973i | −0.0150281 | − | 0.0150281i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 75.7331i | − | 0.143706i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −383.277 | −0.724531 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 83.6344 | − | 83.6344i | 0.157504 | − | 0.157504i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.0718 | + | 23.0718i | −0.0432867 | + | 0.0432867i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 462.832 | 0.865107 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 22.2769i | − | 0.0414839i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −515.720 | − | 515.720i | −0.956809 | − | 0.956809i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.53590 | − | 1.53590i | −0.00283900 | − | 0.00283900i | 0.705686 | − | 0.708525i | \(-0.250639\pi\) |
−0.708525 | + | 0.705686i | \(0.750639\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 524.951i | − | 0.966760i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −324.995 | −0.596321 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −456.891 | + | 456.891i | −0.835266 | + | 0.835266i | −0.988232 | − | 0.152965i | \(-0.951118\pi\) |
0.152965 | + | 0.988232i | \(0.451118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 188.454 | − | 188.454i | 0.343267 | − | 0.343267i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.0041 | −0.0726028 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.2820i | 0.0782677i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 173.386 | + | 173.386i | 0.312408 | + | 0.312408i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.86672 | − | 9.86672i | −0.0177140 | − | 0.0177140i | 0.698194 | − | 0.715908i | \(-0.253987\pi\) |
−0.715908 | + | 0.698194i | \(0.753987\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 387.534i | − | 0.693264i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 306.564 | 0.546460 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 533.909 | − | 533.909i | 0.948329 | − | 0.948329i | −0.0504003 | − | 0.998729i | \(-0.516050\pi\) |
0.998729 | + | 0.0504003i | \(0.0160497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 329.703 | − | 329.703i | 0.583544 | − | 0.583544i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.41044 | −0.00601488 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 673.846i | 1.18426i | 0.805841 | + | 0.592132i | \(0.201714\pi\) | ||||
−0.805841 | + | 0.592132i | \(0.798286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 490.467 | + | 490.467i | 0.858962 | + | 0.858962i | 0.991216 | − | 0.132254i | \(-0.0422214\pi\) |
−0.132254 | + | 0.991216i | \(0.542221\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 111.580 | + | 111.580i | 0.194729 | + | 0.194729i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 205.217i | 0.356899i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 403.005 | 0.698449 | 0.349225 | − | 0.937039i | \(-0.386445\pi\) | ||||
0.349225 | + | 0.937039i | \(0.386445\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 235.138 | − | 235.138i | 0.406111 | − | 0.406111i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.728277 | − | 0.728277i | 0.00125349 | − | 0.00125349i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1452.16 | 2.49084 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 77.5692i | 0.132597i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 157.688 | + | 157.688i | 0.268635 | + | 0.268635i | 0.828550 | − | 0.559915i | \(-0.189166\pi\) |
−0.559915 | + | 0.828550i | \(0.689166\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 119.205 | + | 119.205i | 0.202386 | + | 0.202386i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 618.816i | 1.04707i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.0000 | 0.0505902 | 0.0252951 | − | 0.999680i | \(-0.491947\pi\) | ||||
0.0252951 | + | 0.999680i | \(0.491947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.98567 | + | 8.98567i | −0.0151020 | + | 0.0151020i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 329.305 | − | 329.305i | 0.551600 | − | 0.551600i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1139.76 | 1.90277 | 0.951384 | − | 0.308007i | \(-0.0996622\pi\) | ||||
0.951384 | + | 0.308007i | \(0.0996622\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 327.559i | − | 0.545023i | −0.962153 | − | 0.272512i | \(-0.912146\pi\) | ||
0.962153 | − | 0.272512i | \(-0.0878543\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −91.6737 | − | 91.6737i | −0.152029 | − | 0.152029i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 203.703 | + | 203.703i | 0.336698 | + | 0.336698i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 484.540i | − | 0.798254i | −0.916896 | − | 0.399127i | \(-0.869313\pi\) | ||
0.916896 | − | 0.399127i | \(-0.130687\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.994845 | 0.00163357 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −204.702 | + | 204.702i | −0.335028 | + | 0.335028i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 463.105 | − | 463.105i | 0.755473 | − | 0.755473i | −0.220022 | − | 0.975495i | \(-0.570613\pi\) |
0.975495 | + | 0.220022i | \(0.0706128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.4855 | 0.0284318 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1115.39i | 1.80777i | 0.427774 | + | 0.903885i | \(0.359298\pi\) | ||||
−0.427774 | + | 0.903885i | \(0.640702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −590.884 | − | 590.884i | −0.954578 | − | 0.954578i | 0.0444343 | − | 0.999012i | \(-0.485851\pi\) |
−0.999012 | + | 0.0444343i | \(0.985851\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.3538 | + | 44.3538i | 0.0714232 | + | 0.0714232i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.0414i | 0.0450102i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −89.0000 | −0.142400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −482.537 | + | 482.537i | −0.769596 | + | 0.769596i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −419.626 | + | 419.626i | −0.667131 | + | 0.667131i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1221.55 | −1.93590 | −0.967949 | − | 0.251145i | \(-0.919193\pi\) | ||||
−0.967949 | + | 0.251145i | \(0.919193\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 344.554i | − | 0.544319i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −133.491 | − | 133.491i | −0.210222 | − | 0.210222i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 315.813 | + | 315.813i | 0.495781 | + | 0.495781i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 395.925i | − | 0.619602i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1152.41 | −1.79783 | −0.898916 | − | 0.438121i | \(-0.855644\pi\) | ||||
−0.898916 | + | 0.438121i | \(0.855644\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 177.649 | − | 177.649i | 0.276281 | − | 0.276281i | −0.555341 | − | 0.831622i | \(-0.687412\pi\) |
0.831622 | + | 0.555341i | \(0.187412\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −146.851 | + | 146.851i | −0.227676 | + | 0.227676i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −390.892 | −0.604161 | −0.302081 | − | 0.953282i | \(-0.597681\pi\) | ||||
−0.302081 | + | 0.953282i | \(0.597681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 588.554i | 0.906862i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.96446 | − | 2.96446i | −0.00455370 | − | 0.00455370i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 441.538 | + | 441.538i | 0.676169 | + | 0.676169i | 0.959131 | − | 0.282962i | \(-0.0913171\pi\) |
−0.282962 | + | 0.959131i | \(0.591317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 544.465i | 0.831244i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 150.431 | 0.228966 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 671.947 | − | 671.947i | 1.01965 | − | 1.01965i | 0.0198437 | − | 0.999803i | \(-0.493683\pi\) |
0.999803 | − | 0.0198437i | \(-0.00631685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0333 | + | 16.0333i | −0.0242562 | + | 0.0242562i | −0.719131 | − | 0.694875i | \(-0.755460\pi\) |
0.694875 | + | 0.719131i | \(0.255460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −187.731 | −0.283154 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 28.2872i | − | 0.0425371i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.9383 | − | 12.9383i | −0.0193977 | − | 0.0193977i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −165.746 | − | 165.746i | −0.247752 | − | 0.247752i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1326.19i | 1.97644i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 512.954 | 0.762190 | 0.381095 | − | 0.924536i | \(-0.375547\pi\) | ||||
0.381095 | + | 0.924536i | \(0.375547\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −62.4620 | + | 62.4620i | −0.0925363 | + | 0.0925363i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −282.000 | + | 282.000i | −0.416544 | + | 0.416544i | −0.884011 | − | 0.467467i | \(-0.845167\pi\) |
0.467467 | + | 0.884011i | \(0.345167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.8323 | −0.0498267 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 536.687i | − | 0.788087i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −307.660 | − | 307.660i | −0.450454 | − | 0.450454i | 0.445051 | − | 0.895505i | \(-0.353186\pi\) |
−0.895505 | + | 0.445051i | \(0.853186\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −451.118 | − | 451.118i | −0.658566 | − | 0.658566i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 394.110i | − | 0.573669i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −889.261 | −1.29066 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −599.422 | + | 599.422i | −0.867470 | + | 0.867470i | −0.992192 | − | 0.124722i | \(-0.960196\pi\) |
0.124722 | + | 0.992192i | \(0.460196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0000 | − | 12.0000i | 0.0173160 | − | 0.0173160i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −164.237 | −0.236313 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.3181i | 0.0607147i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 284.128 | + | 284.128i | 0.406478 | + | 0.406478i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −63.3487 | − | 63.3487i | −0.0903690 | − | 0.0903690i | 0.660477 | − | 0.750846i | \(-0.270354\pi\) |
−0.750846 | + | 0.660477i | \(0.770354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1320.99i | − | 1.87908i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 155.138 | 0.220055 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 46.9591 | − | 46.9591i | 0.0664202 | − | 0.0664202i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −247.259 | + | 247.259i | −0.348743 | + | 0.348743i | −0.859641 | − | 0.510898i | \(-0.829313\pi\) |
0.510898 | + | 0.859641i | \(0.329313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 342.658 | 0.481939 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 77.1075i | 0.108145i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −272.936 | − | 272.936i | −0.381729 | − | 0.381729i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 556.708 | + | 556.708i | 0.776440 | + | 0.776440i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 794.987i | 1.10568i | 0.833286 | + | 0.552842i | \(0.186457\pi\) | ||||
−0.833286 | + | 0.552842i | \(0.813543\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.4308 | 0.0505281 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −404.844 | + | 404.844i | −0.559950 | + | 0.559950i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.2205 | − | 18.2205i | 0.0251318 | − | 0.0251318i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 395.706 | 0.544300 | 0.272150 | − | 0.962255i | \(-0.412265\pi\) | ||||
0.272150 | + | 0.962255i | \(0.412265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −355.406 | − | 355.406i | −0.486192 | − | 0.486192i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −486.443 | − | 486.443i | −0.663634 | − | 0.663634i | 0.292601 | − | 0.956235i | \(-0.405479\pi\) |
−0.956235 | + | 0.292601i | \(0.905479\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 239.347i | − | 0.325642i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 645.128 | 0.875343 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 503.079 | − | 503.079i | 0.680757 | − | 0.680757i | −0.279414 | − | 0.960171i | \(-0.590140\pi\) |
0.960171 | + | 0.279414i | \(0.0901402\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 295.492 | − | 295.492i | 0.398775 | − | 0.398775i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −270.934 | −0.364649 | −0.182325 | − | 0.983238i | \(-0.558362\pi\) | ||||
−0.182325 | + | 0.983238i | \(0.558362\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 127.426i | 0.171041i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.76568 | − | 5.76568i | −0.00771845 | − | 0.00771845i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.8461 | + | 43.8461i | 0.0585395 | + | 0.0585395i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 348.232i | − | 0.463691i | −0.972753 | − | 0.231845i | \(-0.925524\pi\) | ||
0.972753 | − | 0.231845i | \(-0.0744763\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.9948 | 0.0810025 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −55.1072 | + | 55.1072i | −0.0729897 | + | 0.0729897i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 231.792 | − | 231.792i | 0.306198 | − | 0.306198i | −0.537235 | − | 0.843433i | \(-0.680531\pi\) |
0.843433 | + | 0.537235i | \(0.180531\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −312.128 | −0.411236 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1038.99i | − | 1.36530i | −0.730745 | − | 0.682651i | \(-0.760827\pi\) | ||
0.730745 | − | 0.682651i | \(-0.239173\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.7882 | − | 30.7882i | −0.0403515 | − | 0.0403515i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 71.1384 | + | 71.1384i | 0.0929914 | + | 0.0929914i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 360.414i | − | 0.469901i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1047.42 | 1.36205 | 0.681024 | − | 0.732261i | \(-0.261535\pi\) | ||||
0.681024 | + | 0.732261i | \(0.261535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −339.424 | + | 339.424i | −0.440238 | + | 0.440238i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −863.041 | + | 863.041i | −1.11648 | + | 1.11648i | −0.124229 | + | 0.992254i | \(0.539646\pi\) |
−0.992254 | + | 0.124229i | \(0.960354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −108.588 | −0.140113 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.8513i | 0.0422796i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −66.6094 | − | 66.6094i | −0.0855063 | − | 0.0855063i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1393.11 | + | 1393.11i | 1.78375 | + | 1.78375i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 7.87607i | − | 0.0100588i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −262.144 | −0.333941 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 61.6142 | − | 61.6142i | 0.0782900 | − | 0.0782900i | −0.666877 | − | 0.745167i | \(-0.732370\pi\) |
0.745167 | + | 0.666877i | \(0.232370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 145.990 | − | 145.990i | 0.185031 | − | 0.185031i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62.4683 | 0.0789738 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 812.123i | − | 1.02411i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 336.974 | + | 336.974i | 0.423867 | + | 0.423867i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −998.379 | − | 998.379i | −1.25267 | − | 1.25267i | −0.954518 | − | 0.298154i | \(-0.903629\pi\) |
−0.298154 | − | 0.954518i | \(-0.596371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 375.463i | 0.469916i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 222.000 | 0.277154 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −529.307 | + | 529.307i | −0.659162 | + | 0.659162i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.14875 | − | 9.14875i | 0.0113649 | − | 0.0113649i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 370.024 | 0.458517 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 400.390i | 0.494919i | 0.968898 | + | 0.247460i | \(0.0795957\pi\) | ||||
−0.968898 | + | 0.247460i | \(0.920404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 504.096 | + | 504.096i | 0.621574 | + | 0.621574i | 0.945934 | − | 0.324360i | \(-0.105149\pi\) |
−0.324360 | + | 0.945934i | \(0.605149\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −526.808 | − | 526.808i | −0.647980 | − | 0.647980i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 323.333i | − | 0.396727i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1118.83 | 1.36944 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.34847 | + | 7.34847i | −0.00897249 | + | 0.00897249i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −596.477 | + | 596.477i | −0.726525 | + | 0.726525i | −0.969926 | − | 0.243401i | \(-0.921737\pi\) |
0.243401 | + | 0.969926i | \(0.421737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1615.20 | −1.96258 | −0.981290 | − | 0.192534i | \(-0.938329\pi\) | ||||
−0.981290 | + | 0.192534i | \(0.938329\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 439.559i | − | 0.532799i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1010.90 | − | 1010.90i | −1.22237 | − | 1.22237i | −0.966788 | − | 0.255579i | \(-0.917734\pi\) |
−0.255579 | − | 0.966788i | \(-0.582266\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −933.561 | − | 933.561i | −1.12613 | − | 1.12613i | −0.990801 | − | 0.135329i | \(-0.956791\pi\) |
−0.135329 | − | 0.990801i | \(-0.543209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 522.351i | − | 0.628581i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 579.261 | 0.695392 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −505.055 | + | 505.055i | −0.604857 | + | 0.604857i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.4693 | + | 23.4693i | −0.0280397 | + | 0.0280397i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1408.20 | −1.67843 | −0.839216 | − | 0.543798i | \(-0.816986\pi\) | ||||
−0.839216 | + | 0.543798i | \(0.816986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 838.703i | − | 0.997268i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 95.5301 | + | 95.5301i | 0.113322 | + | 0.113322i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −170.862 | − | 170.862i | −0.202203 | − | 0.202203i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.5952i | 0.0455670i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 102.297 | 0.120492 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 427.241 | − | 427.241i | 0.502046 | − | 0.502046i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.8691 | − | 41.8691i | 0.0490845 | − | 0.0490845i | −0.682138 | − | 0.731223i | \(-0.738950\pi\) |
0.731223 | + | 0.682138i | \(0.238950\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −223.946 | −0.261925 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 418.441i | − | 0.488263i | −0.969742 | − | 0.244131i | \(-0.921497\pi\) | ||
0.969742 | − | 0.244131i | \(-0.0785028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 272.814 | + | 272.814i | 0.317595 | + | 0.317595i | 0.847843 | − | 0.530247i | \(-0.177901\pi\) |
−0.530247 | + | 0.847843i | \(0.677901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.65648 | + | 1.65648i | 0.00192390 | + | 0.00192390i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 988.405i | 1.14531i | 0.819796 | + | 0.572656i | \(0.194087\pi\) | ||||
−0.819796 | + | 0.572656i | \(0.805913\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −361.682 | −0.418129 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 181.784 | − | 181.784i | 0.209670 | − | 0.209670i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1205.68 | + | 1205.68i | −1.38744 | + | 1.38744i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −395.059 | −0.453569 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 267.846i | 0.306811i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.8307 | + | 31.8307i | 0.0363780 | + | 0.0363780i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −116.254 | − | 116.254i | −0.132559 | − | 0.132559i | 0.637714 | − | 0.770273i | \(-0.279880\pi\) |
−0.770273 | + | 0.637714i | \(0.779880\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 347.664i | − | 0.395523i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −727.395 | −0.825647 | −0.412823 | − | 0.910811i | \(-0.635457\pi\) | ||||
−0.412823 | + | 0.910811i | \(0.635457\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.6981 | − | 44.6981i | 0.0506207 | − | 0.0506207i | −0.681343 | − | 0.731964i | \(-0.738604\pi\) |
0.731964 | + | 0.681343i | \(0.238604\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −136.574 | + | 136.574i | −0.154321 | + | 0.154321i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −566.766 | −0.638969 | −0.319485 | − | 0.947591i | \(-0.603510\pi\) | ||||
−0.319485 | + | 0.947591i | \(0.603510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 25.2923i | − | 0.0284503i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −95.0025 | − | 95.0025i | −0.106625 | − | 0.106625i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −590.985 | − | 590.985i | −0.661797 | − | 0.661797i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.3780i | 0.0406458i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 191.138 | 0.213086 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.84613 | − | 6.84613i | 0.00761527 | − | 0.00761527i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −815.538 | + | 815.538i | −0.905148 | + | 0.905148i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.8237 | −0.0308125 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 857.241i | 0.947227i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −259.499 | − | 259.499i | −0.286107 | − | 0.286107i | 0.549432 | − | 0.835539i | \(-0.314844\pi\) |
−0.835539 | + | 0.549432i | \(0.814844\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −371.769 | − | 371.769i | −0.408987 | − | 0.408987i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1020.02i | 1.11967i | 0.828605 | + | 0.559834i | \(0.189135\pi\) | ||||
−0.828605 | + | 0.559834i | \(0.810865\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.5744 | 0.0444407 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −307.744 | + | 307.744i | −0.336332 | + | 0.336332i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −51.5795 | + | 51.5795i | −0.0562481 | + | 0.0562481i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −398.632 | −0.433768 | −0.216884 | − | 0.976197i | \(-0.569589\pi\) | ||||
−0.216884 | + | 0.976197i | \(0.569589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 39.9794i | − | 0.0434087i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −853.101 | − | 853.101i | −0.924269 | − | 0.924269i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 601.669 | + | 601.669i | 0.650453 | + | 0.650453i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 288.418i | − | 0.311130i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 645.251 | 0.694565 | 0.347283 | − | 0.937761i | \(-0.387104\pi\) | ||||
0.347283 | + | 0.937761i | \(0.387104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −911.767 | + | 911.767i | −0.979342 | + | 0.979342i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 136.441 | − | 136.441i | 0.146239 | − | 0.146239i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −500.617 | −0.535419 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1279.72i | − | 1.36577i | −0.730528 | − | 0.682883i | \(-0.760726\pi\) | ||
0.730528 | − | 0.682883i | \(-0.239274\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −615.148 | − | 615.148i | −0.655110 | − | 0.655110i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 796.144 | + | 796.144i | 0.846061 | + | 0.846061i | 0.989639 | − | 0.143578i | \(-0.0458607\pi\) |
−0.143578 | + | 0.989639i | \(0.545861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 43.0861i | − | 0.0456905i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.56922 | 0.00589335 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 903.254 | − | 903.254i | 0.953806 | − | 0.953806i | −0.0451730 | − | 0.998979i | \(-0.514384\pi\) |
0.998979 | + | 0.0451730i | \(0.0143839\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 324.133 | − | 324.133i | 0.341552 | − | 0.341552i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −344.850 | −0.362619 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 286.687i | 0.300826i | 0.988623 | + | 0.150413i | \(0.0480603\pi\) | ||||
−0.988623 | + | 0.150413i | \(0.951940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −182.209 | − | 182.209i | −0.190794 | − | 0.190794i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.7128 | + | 27.7128i | 0.0289580 | + | 0.0289580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 85.4727i | − | 0.0891269i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 920.200 | 0.957544 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 347.124 | − | 347.124i | 0.360461 | − | 0.360461i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −383.979 | + | 383.979i | −0.397906 | + | 0.397906i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −153.089 | −0.158313 | −0.0791565 | − | 0.996862i | \(-0.525223\pi\) | ||||
−0.0791565 | + | 0.996862i | \(0.525223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 541.990i | − | 0.559329i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 704.184 | + | 704.184i | 0.725215 | + | 0.725215i | 0.969663 | − | 0.244447i | \(-0.0786065\pi\) |
−0.244447 | + | 0.969663i | \(0.578606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.5589 | − | 15.5589i | −0.0159907 | − | 0.0159907i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 269.174i | 0.276076i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −521.230 | −0.533501 | −0.266751 | − | 0.963766i | \(-0.585950\pi\) | ||||
−0.266751 | + | 0.963766i | \(0.585950\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −781.132 | + | 781.132i | −0.797887 | + | 0.797887i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −243.746 | + | 243.746i | −0.248467 | + | 0.248467i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 952.730 | 0.969207 | 0.484603 | − | 0.874734i | \(-0.338964\pi\) | ||||
0.484603 | + | 0.874734i | \(0.338964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1010.52i | − | 1.02591i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.6969 | + | 14.6969i | 0.0148905 | + | 0.0148905i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 361.856 | + | 361.856i | 0.365881 | + | 0.365881i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 788.654i | 0.795816i | 0.917425 | + | 0.397908i | \(0.130264\pi\) | ||||
−0.917425 | + | 0.397908i | \(0.869736\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 741.415 | 0.746642 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −537.753 | + | 537.753i | −0.540455 | + | 0.540455i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −370.177 | + | 370.177i | −0.371291 | + | 0.371291i | −0.867947 | − | 0.496656i | \(-0.834561\pi\) |
0.496656 | + | 0.867947i | \(0.334561\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 260.079 | 0.260340 |
(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 | 768.3.l.d.703.2 | yes | 8 | |
4.3 | odd | 2 | inner | 768.3.l.d.703.3 | yes | 8 | |
8.3 | odd | 2 | 768.3.l.a.703.1 | yes | 8 | ||
8.5 | even | 2 | 768.3.l.a.703.4 | yes | 8 | ||
16.3 | odd | 4 | 768.3.l.a.319.4 | yes | 8 | ||
16.5 | even | 4 | inner | 768.3.l.d.319.3 | yes | 8 | |
16.11 | odd | 4 | inner | 768.3.l.d.319.2 | yes | 8 | |
16.13 | even | 4 | 768.3.l.a.319.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.3.l.a.319.1 | ✓ | 8 | 16.13 | even | 4 | ||
768.3.l.a.319.4 | yes | 8 | 16.3 | odd | 4 | ||
768.3.l.a.703.1 | yes | 8 | 8.3 | odd | 2 | ||
768.3.l.a.703.4 | yes | 8 | 8.5 | even | 2 | ||
768.3.l.d.319.2 | yes | 8 | 16.11 | odd | 4 | inner | |
768.3.l.d.319.3 | yes | 8 | 16.5 | even | 4 | inner | |
768.3.l.d.703.2 | yes | 8 | 1.1 | even | 1 | trivial | |
768.3.l.d.703.3 | yes | 8 | 4.3 | odd | 2 | inner |