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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 52 x^{14} + 1743 x^{12} - 34996 x^{10} + 513409 x^{8} - 5039424 x^{6} + 36142848 x^{4} - 155271168 x^{2} + 429981696 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 319.5 | ||
Root | \(2.78422 + 1.60747i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.319 |
Dual form | 768.3.l.f.703.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(5\) | −5.27866 | − | 5.27866i | −1.05573 | − | 1.05573i | −0.998352 | − | 0.0573795i | \(-0.981726\pi\) |
−0.0573795 | − | 0.998352i | \(-0.518274\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.7431 | 1.82044 | 0.910219 | − | 0.414127i | \(-0.135913\pi\) | ||||
0.910219 | + | 0.414127i | \(0.135913\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.46515 | + | 7.46515i | −0.678650 | + | 0.678650i | −0.959695 | − | 0.281045i | \(-0.909319\pi\) |
0.281045 | + | 0.959695i | \(0.409319\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.9575 | + | 11.9575i | −0.919805 | + | 0.919805i | −0.997015 | − | 0.0772099i | \(-0.975399\pi\) |
0.0772099 | + | 0.997015i | \(0.475399\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 12.9300i | − | 0.862002i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.55732 | −0.268078 | −0.134039 | − | 0.990976i | \(-0.542795\pi\) | ||||
−0.134039 | + | 0.990976i | \(0.542795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.6216 | + | 14.6216i | 0.769560 | + | 0.769560i | 0.978029 | − | 0.208469i | \(-0.0668481\pi\) |
−0.208469 | + | 0.978029i | \(0.566848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.6070 | + | 15.6070i | 0.743191 | + | 0.743191i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 31.6675 | 1.37685 | 0.688424 | − | 0.725309i | \(-0.258303\pi\) | ||||
0.688424 | + | 0.725309i | \(0.258303\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 30.7285i | 1.22914i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38.3491 | − | 38.3491i | 1.32238 | − | 1.32238i | 0.410539 | − | 0.911843i | \(-0.365340\pi\) |
0.911843 | − | 0.410539i | \(-0.134660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.8749i | 0.447576i | 0.974638 | + | 0.223788i | \(0.0718423\pi\) | ||||
−0.974638 | + | 0.223788i | \(0.928158\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18.2858 | −0.554116 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −67.2663 | − | 67.2663i | −1.92189 | − | 1.92189i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 28.7278 | + | 28.7278i | 0.776426 | + | 0.776426i | 0.979221 | − | 0.202795i | \(-0.0650025\pi\) |
−0.202795 | + | 0.979221i | \(0.565003\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −29.2897 | −0.751018 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.98569i | 0.0972120i | 0.998818 | + | 0.0486060i | \(0.0154779\pi\) | ||||
−0.998818 | + | 0.0486060i | \(0.984522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7717 | + | 10.7717i | −0.250504 | + | 0.250504i | −0.821177 | − | 0.570673i | \(-0.806682\pi\) |
0.570673 | + | 0.821177i | \(0.306682\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.8360 | − | 15.8360i | 0.351911 | − | 0.351911i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 27.1203i | − | 0.577027i | −0.957476 | − | 0.288513i | \(-0.906839\pi\) | ||
0.957476 | − | 0.288513i | \(-0.0931610\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 113.386 | 2.31400 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.58155 | − | 5.58155i | −0.109442 | − | 0.109442i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 43.3372 | + | 43.3372i | 0.817683 | + | 0.817683i | 0.985772 | − | 0.168089i | \(-0.0537596\pi\) |
−0.168089 | + | 0.985772i | \(0.553760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 78.8120 | 1.43295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 35.8156i | 0.628343i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.84922 | − | 6.84922i | 0.116089 | − | 0.116089i | −0.646676 | − | 0.762765i | \(-0.723841\pi\) |
0.762765 | + | 0.646676i | \(0.223841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.18476 | − | 8.18476i | 0.134176 | − | 0.134176i | −0.636829 | − | 0.771005i | \(-0.719754\pi\) |
0.771005 | + | 0.636829i | \(0.219754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 38.2292i | 0.606813i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 126.239 | 1.94213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26.6785 | + | 26.6785i | 0.398187 | + | 0.398187i | 0.877593 | − | 0.479406i | \(-0.159148\pi\) |
−0.479406 | + | 0.877593i | \(0.659148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 38.7846 | + | 38.7846i | 0.562096 | + | 0.562096i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7372 | 0.235735 | 0.117868 | − | 0.993029i | \(-0.462394\pi\) | ||||
0.117868 | + | 0.993029i | \(0.462394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 50.1252i | − | 0.686646i | −0.939217 | − | 0.343323i | \(-0.888447\pi\) | ||
0.939217 | − | 0.343323i | \(-0.111553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −37.6346 | + | 37.6346i | −0.501794 | + | 0.501794i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −95.1289 | + | 95.1289i | −1.23544 | + | 1.23544i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 75.2018i | 0.951922i | 0.879466 | + | 0.475961i | \(0.157900\pi\) | ||||
−0.879466 | + | 0.475961i | \(0.842100\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.382563 | − | 0.382563i | −0.00460919 | − | 0.00460919i | 0.704798 | − | 0.709408i | \(-0.251037\pi\) |
−0.709408 | + | 0.704798i | \(0.751037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.0565 | + | 24.0565i | 0.283018 | + | 0.283018i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 93.9357 | 1.07972 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 165.167i | 1.85581i | 0.372817 | + | 0.927905i | \(0.378392\pi\) | ||||
−0.372817 | + | 0.927905i | \(0.621608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −152.375 | + | 152.375i | −1.67445 | + | 1.67445i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.9932 | + | 16.9932i | −0.182722 | + | 0.182722i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 154.365i | − | 1.62490i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −63.7481 | −0.657197 | −0.328599 | − | 0.944470i | \(-0.606576\pi\) | ||||
−0.328599 | + | 0.944470i | \(0.606576\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.3955 | − | 22.3955i | −0.226217 | − | 0.226217i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −46.0210 | − | 46.0210i | −0.455654 | − | 0.455654i | 0.441572 | − | 0.897226i | \(-0.354421\pi\) |
−0.897226 | + | 0.441572i | \(0.854421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 75.8798 | 0.736697 | 0.368348 | − | 0.929688i | \(-0.379923\pi\) | ||||
0.368348 | + | 0.929688i | \(0.379923\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 164.768i | − | 1.56922i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −37.4899 | + | 37.4899i | −0.350373 | + | 0.350373i | −0.860248 | − | 0.509875i | \(-0.829691\pi\) |
0.509875 | + | 0.860248i | \(0.329691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.75535 | + | 3.75535i | −0.0344527 | + | 0.0344527i | −0.724123 | − | 0.689671i | \(-0.757755\pi\) |
0.689671 | + | 0.724123i | \(0.257755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 70.3684i | 0.633949i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 27.2277 | 0.240953 | 0.120477 | − | 0.992716i | \(-0.461558\pi\) | ||||
0.120477 | + | 0.992716i | \(0.461558\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −167.162 | − | 167.162i | −1.45358 | − | 1.45358i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −35.8724 | − | 35.8724i | −0.306602 | − | 0.306602i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −58.0742 | −0.488019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.54301i | 0.0788679i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.88146 | + | 4.88146i | −0.0396866 | + | 0.0396866i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 30.2388 | − | 30.2388i | 0.241910 | − | 0.241910i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 154.301i | − | 1.21496i | −0.794333 | − | 0.607482i | \(-0.792180\pi\) | ||
0.794333 | − | 0.607482i | \(-0.207820\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −26.3851 | −0.204536 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −23.9299 | − | 23.9299i | −0.182671 | − | 0.182671i | 0.609848 | − | 0.792519i | \(-0.291231\pi\) |
−0.792519 | + | 0.609848i | \(0.791231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 186.325 | + | 186.325i | 1.40094 | + | 1.40094i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 38.7901 | 0.287334 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 239.640i | 1.74920i | 0.484848 | + | 0.874598i | \(0.338875\pi\) | ||||
−0.484848 | + | 0.874598i | \(0.661125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 127.817 | − | 127.817i | 0.919545 | − | 0.919545i | −0.0774514 | − | 0.996996i | \(-0.524678\pi\) |
0.996996 | + | 0.0774514i | \(0.0246783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.2154 | − | 33.2154i | 0.235570 | − | 0.235570i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 178.529i | − | 1.24845i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −404.864 | −2.79216 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 138.869 | + | 138.869i | 0.944685 | + | 0.944685i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −118.099 | − | 118.099i | −0.792613 | − | 0.792613i | 0.189305 | − | 0.981918i | \(-0.439377\pi\) |
−0.981918 | + | 0.189305i | \(0.939377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −230.413 | −1.52592 | −0.762958 | − | 0.646448i | \(-0.776254\pi\) | ||||
−0.762958 | + | 0.646448i | \(0.776254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 13.6720i | − | 0.0893592i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 73.2406 | − | 73.2406i | 0.472520 | − | 0.472520i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 159.055 | − | 159.055i | 1.01309 | − | 1.01309i | 0.0131763 | − | 0.999913i | \(-0.495806\pi\) |
0.999913 | − | 0.0131763i | \(-0.00419426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 106.154i | 0.667635i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 403.541 | 2.50647 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 83.2597 | + | 83.2597i | 0.510796 | + | 0.510796i | 0.914770 | − | 0.403974i | \(-0.132372\pi\) |
−0.403974 | + | 0.914770i | \(0.632372\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 96.5246 | + | 96.5246i | 0.584997 | + | 0.584997i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1469 | 0.0907001 | 0.0453500 | − | 0.998971i | \(-0.485560\pi\) | ||||
0.0453500 | + | 0.998971i | \(0.485560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 116.962i | − | 0.692082i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −43.8649 | + | 43.8649i | −0.256520 | + | 0.256520i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −36.4769 | + | 36.4769i | −0.210849 | + | 0.210849i | −0.804628 | − | 0.593779i | \(-0.797635\pi\) |
0.593779 | + | 0.804628i | \(0.297635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 391.575i | 2.23757i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.7771 | 0.0947859 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.5489 | + | 16.5489i | 0.0924522 | + | 0.0924522i | 0.751820 | − | 0.659368i | \(-0.229176\pi\) |
−0.659368 | + | 0.751820i | \(0.729176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −136.141 | − | 136.141i | −0.752158 | − | 0.752158i | 0.222724 | − | 0.974882i | \(-0.428505\pi\) |
−0.974882 | + | 0.222724i | \(0.928505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.0485 | 0.109555 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 303.288i | − | 1.63940i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.0211 | − | 34.0211i | 0.181931 | − | 0.181931i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −46.8210 | + | 46.8210i | −0.247730 | + | 0.247730i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 196.337i | 1.02794i | 0.857807 | + | 0.513972i | \(0.171827\pi\) | ||||
−0.857807 | + | 0.513972i | \(0.828173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 166.674 | 0.863597 | 0.431798 | − | 0.901970i | \(-0.357879\pi\) | ||||
0.431798 | + | 0.901970i | \(0.357879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 154.610 | + | 154.610i | 0.792873 | + | 0.792873i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −233.904 | − | 233.904i | −1.18733 | − | 1.18733i | −0.977803 | − | 0.209527i | \(-0.932808\pi\) |
−0.209527 | − | 0.977803i | \(-0.567192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.62043 | 0.00814286 | 0.00407143 | − | 0.999992i | \(-0.498704\pi\) | ||||
0.00407143 | + | 0.999992i | \(0.498704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 65.3487i | 0.325118i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 488.685 | − | 488.685i | 2.40732 | − | 2.40732i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.0391 | − | 21.0391i | 0.102630 | − | 0.102630i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 95.0025i | 0.458949i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −218.305 | −1.04452 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 194.766 | + | 194.766i | 0.923059 | + | 0.923059i | 0.997244 | − | 0.0741852i | \(-0.0236356\pi\) |
−0.0741852 | + | 0.997244i | \(0.523636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.4988 | + | 20.4988i | 0.0962385 | + | 0.0962385i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 113.720 | 0.528930 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 176.808i | 0.814784i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 61.3905 | − | 61.3905i | 0.280322 | − | 0.280322i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 54.4940 | − | 54.4940i | 0.246579 | − | 0.246579i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 119.867i | − | 0.537521i | −0.963207 | − | 0.268760i | \(-0.913386\pi\) | ||
0.963207 | − | 0.268760i | \(-0.0866140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −92.1855 | −0.409713 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −258.655 | − | 258.655i | −1.13945 | − | 1.13945i | −0.988549 | − | 0.150899i | \(-0.951783\pi\) |
−0.150899 | − | 0.988549i | \(-0.548217\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 143.105 | + | 143.105i | 0.624915 | + | 0.624915i | 0.946784 | − | 0.321869i | \(-0.104311\pi\) |
−0.321869 | + | 0.946784i | \(0.604311\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −233.017 | −1.00873 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 215.658i | − | 0.925569i | −0.886471 | − | 0.462785i | \(-0.846850\pi\) | ||
0.886471 | − | 0.462785i | \(-0.153150\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −143.159 | + | 143.159i | −0.609185 | + | 0.609185i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −92.1031 | + | 92.1031i | −0.388620 | + | 0.388620i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 467.706i | − | 1.95693i | −0.206411 | − | 0.978465i | \(-0.566178\pi\) | ||
0.206411 | − | 0.978465i | \(-0.433822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −243.864 | −1.01188 | −0.505941 | − | 0.862568i | \(-0.668855\pi\) | ||||
−0.505941 | + | 0.862568i | \(0.668855\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −598.525 | − | 598.525i | −2.44296 | − | 2.44296i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −349.675 | −1.41569 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 0.937084i | − | 0.00376339i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −47.8205 | + | 47.8205i | −0.190520 | + | 0.190520i | −0.795921 | − | 0.605401i | \(-0.793013\pi\) |
0.605401 | + | 0.795921i | \(0.293013\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −236.403 | + | 236.403i | −0.934398 | + | 0.934398i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 58.9262i | 0.231083i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −198.672 | −0.773043 | −0.386521 | − | 0.922280i | \(-0.626323\pi\) | ||||
−0.386521 | + | 0.922280i | \(0.626323\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 366.080 | + | 366.080i | 1.41344 | + | 1.41344i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 115.047 | + | 115.047i | 0.440794 | + | 0.440794i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −318.482 | −1.21096 | −0.605478 | − | 0.795862i | \(-0.707018\pi\) | ||||
−0.605478 | + | 0.795862i | \(0.707018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 457.524i | − | 1.72651i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −202.288 | + | 202.288i | −0.757631 | + | 0.757631i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −80.7988 | + | 80.7988i | −0.300367 | + | 0.300367i | −0.841158 | − | 0.540790i | \(-0.818125\pi\) |
0.540790 | + | 0.841158i | \(0.318125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 238.383i | − | 0.879643i | −0.898085 | − | 0.439822i | \(-0.855042\pi\) | ||
0.898085 | − | 0.439822i | \(-0.144958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −373.240 | −1.36718 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −229.393 | − | 229.393i | −0.834156 | − | 0.834156i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −158.651 | − | 158.651i | −0.572747 | − | 0.572747i | 0.360148 | − | 0.932895i | \(-0.382726\pi\) |
−0.932895 | + | 0.360148i | \(0.882726\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −41.6246 | −0.149192 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 446.105i | 1.58756i | 0.608205 | + | 0.793780i | \(0.291890\pi\) | ||||
−0.608205 | + | 0.793780i | \(0.708110\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 191.252 | − | 191.252i | 0.675801 | − | 0.675801i | −0.283246 | − | 0.959047i | \(-0.591411\pi\) |
0.959047 | + | 0.283246i | \(0.0914113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 189.058 | − | 189.058i | 0.663362 | − | 0.663362i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 50.7900i | 0.176968i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −268.231 | −0.928134 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −78.0752 | − | 78.0752i | −0.268300 | − | 0.268300i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 256.523 | + | 256.523i | 0.875503 | + | 0.875503i | 0.993066 | − | 0.117562i | \(-0.0375079\pi\) |
−0.117562 | + | 0.993066i | \(0.537508\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −72.3094 | −0.245117 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 54.8574i | − | 0.184705i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −378.663 | + | 378.663i | −1.26643 | + | 1.26643i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −137.264 | + | 137.264i | −0.456027 | + | 0.456027i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 112.728i | − | 0.372040i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −86.4091 | −0.283308 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 58.8027 | + | 58.8027i | 0.191540 | + | 0.191540i | 0.796361 | − | 0.604821i | \(-0.206756\pi\) |
−0.604821 | + | 0.796361i | \(0.706756\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 92.9333 | + | 92.9333i | 0.300755 | + | 0.300755i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −453.650 | −1.45868 | −0.729341 | − | 0.684151i | \(-0.760173\pi\) | ||||
−0.729341 | + | 0.684151i | \(0.760173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 309.389i | − | 0.988464i | −0.869330 | − | 0.494232i | \(-0.835449\pi\) | ||
0.869330 | − | 0.494232i | \(-0.164551\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 201.799 | − | 201.799i | 0.640632 | − | 0.640632i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 141.334 | − | 141.334i | 0.445848 | − | 0.445848i | −0.448124 | − | 0.893972i | \(-0.647908\pi\) |
0.893972 | + | 0.448124i | \(0.147908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 572.563i | 1.79487i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −91.8311 | −0.286078 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −66.6355 | − | 66.6355i | −0.206302 | − | 0.206302i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −367.435 | − | 367.435i | −1.13057 | − | 1.13057i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.19869 | −0.0281305 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 345.595i | − | 1.05044i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −119.102 | + | 119.102i | −0.359826 | + | 0.359826i | −0.863749 | − | 0.503923i | \(-0.831890\pi\) |
0.503923 | + | 0.863749i | \(0.331890\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −86.1833 | + | 86.1833i | −0.258809 | + | 0.258809i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 281.654i | − | 0.840757i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 270.363 | 0.802265 | 0.401133 | − | 0.916020i | \(-0.368617\pi\) | ||||
0.401133 | + | 0.916020i | \(0.368617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.3470 | + | 33.3470i | 0.0983687 | + | 0.0983687i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −103.578 | − | 103.578i | −0.303747 | − | 0.303747i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 820.473 | 2.39205 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 409.462i | − | 1.18684i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 362.402 | − | 362.402i | 1.04439 | − | 1.04439i | 0.0454174 | − | 0.998968i | \(-0.485538\pi\) |
0.998968 | − | 0.0454174i | \(-0.0144618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3277 | − | 14.3277i | 0.0410537 | − | 0.0410537i | −0.686282 | − | 0.727336i | \(-0.740758\pi\) |
0.727336 | + | 0.686282i | \(0.240758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 87.8691i | − | 0.250339i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 370.167 | 1.04863 | 0.524316 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524316 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −88.3500 | − | 88.3500i | −0.248873 | − | 0.248873i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −71.1261 | − | 71.1261i | −0.199233 | − | 0.199233i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −129.009 | −0.359356 | −0.179678 | − | 0.983725i | \(-0.557506\pi\) | ||||
−0.179678 | + | 0.983725i | \(0.557506\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 66.5846i | 0.184445i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.6878 | + | 11.6878i | −0.0321977 | + | 0.0321977i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −264.594 | + | 264.594i | −0.724914 | + | 0.724914i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 608.337i | 1.65759i | 0.559550 | + | 0.828797i | \(0.310974\pi\) | ||||
−0.559550 | + | 0.828797i | \(0.689026\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.9571 | −0.0324040 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 552.249 | + | 552.249i | 1.48854 | + | 1.48854i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 193.032 | + | 193.032i | 0.517513 | + | 0.517513i | 0.916818 | − | 0.399305i | \(-0.130748\pi\) |
−0.399305 | + | 0.916818i | \(0.630748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 74.0696 | 0.197519 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 917.116i | 2.43267i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 192.727 | − | 192.727i | 0.508515 | − | 0.508515i | −0.405555 | − | 0.914071i | \(-0.632922\pi\) |
0.914071 | + | 0.405555i | \(0.132922\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 188.979 | − | 188.979i | 0.496007 | − | 0.496007i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 144.237i | − | 0.376598i | −0.982112 | − | 0.188299i | \(-0.939703\pi\) | ||
0.982112 | − | 0.188299i | \(-0.0602974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1004.31 | 2.60859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.3150 | − | 32.3150i | −0.0835014 | − | 0.0835014i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 186.426 | + | 186.426i | 0.479244 | + | 0.479244i | 0.904890 | − | 0.425646i | \(-0.139953\pi\) |
−0.425646 | + | 0.904890i | \(0.639953\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −144.319 | −0.369102 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 58.6161i | − | 0.149150i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 396.965 | − | 396.965i | 1.00497 | − | 1.00497i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −299.949 | + | 299.949i | −0.755540 | + | 0.755540i | −0.975507 | − | 0.219968i | \(-0.929405\pi\) |
0.219968 | + | 0.975507i | \(0.429405\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 456.400i | 1.14386i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 532.680 | 1.32838 | 0.664189 | − | 0.747565i | \(-0.268777\pi\) | ||||
0.664189 | + | 0.747565i | \(0.268777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −165.908 | − | 165.908i | −0.411682 | − | 0.411682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 47.5079 | + | 47.5079i | 0.117304 | + | 0.117304i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −428.914 | −1.05384 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 373.085i | 0.912187i | 0.889932 | + | 0.456094i | \(0.150752\pi\) | ||||
−0.889932 | + | 0.456094i | \(0.849248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −293.498 | + | 293.498i | −0.714106 | + | 0.714106i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 87.2801 | − | 87.2801i | 0.211332 | − | 0.211332i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.03884i | 0.00973214i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 313.086 | 0.750805 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 91.9363 | + | 91.9363i | 0.219418 | + | 0.219418i | 0.808253 | − | 0.588835i | \(-0.200413\pi\) |
−0.588835 | + | 0.808253i | \(0.700413\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 110.915 | + | 110.915i | 0.263456 | + | 0.263456i | 0.826457 | − | 0.563001i | \(-0.190353\pi\) |
−0.563001 | + | 0.826457i | \(0.690353\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 81.3608 | 0.192342 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 140.040i | − | 0.329505i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 104.299 | − | 104.299i | 0.244260 | − | 0.244260i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 218.652 | − | 218.652i | 0.509678 | − | 0.509678i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.9392i | − | 0.0462626i | −0.999732 | − | 0.0231313i | \(-0.992636\pi\) | ||
0.999732 | − | 0.0231313i | \(-0.00736358\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −707.556 | −1.63408 | −0.817039 | − | 0.576582i | \(-0.804386\pi\) | ||||
−0.817039 | + | 0.576582i | \(0.804386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −495.854 | − | 495.854i | −1.13990 | − | 1.13990i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 463.031 | + | 463.031i | 1.05957 | + | 1.05957i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.5403 | −0.0581784 | −0.0290892 | − | 0.999577i | \(-0.509261\pi\) | ||||
−0.0290892 | + | 0.999577i | \(0.509261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 340.157i | 0.771332i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −468.137 | + | 468.137i | −1.05674 | + | 1.05674i | −0.0584533 | + | 0.998290i | \(0.518617\pi\) |
−0.998290 | + | 0.0584533i | \(0.981383\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 871.861 | − | 871.861i | 1.95924 | − | 1.95924i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 289.283i | − | 0.647166i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −724.735 | −1.61411 | −0.807055 | − | 0.590476i | \(-0.798940\pi\) | ||||
−0.807055 | + | 0.590476i | \(0.798940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.7538 | − | 29.7538i | −0.0659730 | − | 0.0659730i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −282.198 | − | 282.198i | −0.622953 | − | 0.622953i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1608.67 | 3.53554 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 100.661i | − | 0.220266i | −0.993917 | − | 0.110133i | \(-0.964872\pi\) | ||
0.993917 | − | 0.110133i | \(-0.0351276\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.7447 | − | 16.7447i | 0.0364807 | − | 0.0364807i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 376.240 | − | 376.240i | 0.816139 | − | 0.816139i | −0.169407 | − | 0.985546i | \(-0.554185\pi\) |
0.985546 | + | 0.169407i | \(0.0541852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 845.968i | − | 1.82714i | −0.406677 | − | 0.913572i | \(-0.633312\pi\) | ||
0.406677 | − | 0.913572i | \(-0.366688\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 179.402 | 0.385811 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −234.037 | − | 234.037i | −0.501150 | − | 0.501150i | 0.410646 | − | 0.911795i | \(-0.365303\pi\) |
−0.911795 | + | 0.410646i | \(0.865303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 339.966 | + | 339.966i | 0.724874 | + | 0.724874i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 389.604 | 0.827184 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 160.824i | − | 0.340009i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −449.301 | + | 449.301i | −0.945897 | + | 0.945897i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −130.012 | + | 130.012i | −0.272561 | + | 0.272561i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 161.916i | 0.338029i | 0.985614 | + | 0.169015i | \(0.0540585\pi\) | ||||
−0.985614 | + | 0.169015i | \(0.945941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −687.023 | −1.42832 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 494.235 | + | 494.235i | 1.02326 | + | 1.02326i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 336.505 | + | 336.505i | 0.693824 | + | 0.693824i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 137.720 | 0.282793 | 0.141396 | − | 0.989953i | \(-0.454841\pi\) | ||||
0.141396 | + | 0.989953i | \(0.454841\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 203.944i | 0.417063i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.5877 | + | 43.5877i | −0.0887734 | + | 0.0887734i | −0.750099 | − | 0.661326i | \(-0.769994\pi\) |
0.661326 | + | 0.750099i | \(0.269994\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −174.769 | + | 174.769i | −0.354501 | + | 0.354501i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 236.436i | 0.477648i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 213.283 | 0.429141 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −529.133 | − | 529.133i | −1.06039 | − | 1.06039i | −0.998056 | − | 0.0623308i | \(-0.980147\pi\) |
−0.0623308 | − | 0.998056i | \(-0.519853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.5511 | + | 18.5511i | 0.0370282 | + | 0.0370282i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −391.263 | −0.777859 | −0.388929 | − | 0.921268i | \(-0.627155\pi\) | ||||
−0.388929 | + | 0.921268i | \(0.627155\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 485.859i | 0.962097i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 143.249 | − | 143.249i | 0.282541 | − | 0.282541i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −605.614 | + | 605.614i | −1.18981 | + | 1.18981i | −0.212692 | + | 0.977119i | \(0.568223\pi\) |
−0.977119 | + | 0.212692i | \(0.931777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 638.748i | − | 1.25000i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −107.447 | −0.209448 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −400.543 | − | 400.543i | −0.777754 | − | 0.777754i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 202.457 | + | 202.457i | 0.391599 | + | 0.391599i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −89.3498 | −0.172158 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 288.250i | − | 0.553262i | −0.960976 | − | 0.276631i | \(-0.910782\pi\) | ||
0.960976 | − | 0.276631i | \(-0.0892180\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −641.538 | + | 641.538i | −1.22665 | + | 1.22665i | −0.261427 | + | 0.965223i | \(0.584193\pi\) |
−0.965223 | + | 0.261427i | \(0.915807\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −479.580 | + | 479.580i | −0.913485 | + | 0.913485i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 63.2321i | − | 0.119985i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 473.831 | 0.895710 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.5477 | + | 20.5477i | 0.0386962 | + | 0.0386962i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −47.6588 | − | 47.6588i | −0.0894161 | − | 0.0894161i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 395.793 | 0.739799 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.5365i | 0.0754869i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −846.442 | + | 846.442i | −1.57039 | + | 1.57039i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 539.789 | − | 539.789i | 0.997762 | − | 0.997762i | −0.00223575 | − | 0.999998i | \(-0.500712\pi\) |
0.999998 | + | 0.00223575i | \(0.000711663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 333.475i | − | 0.614134i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.6464 | 0.0727457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −404.757 | − | 404.757i | −0.739958 | − | 0.739958i | 0.232612 | − | 0.972570i | \(-0.425273\pi\) |
−0.972570 | + | 0.232612i | \(0.925273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.5543 | + | 24.5543i | 0.0447254 | + | 0.0447254i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1121.45 | 2.03530 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 958.302i | 1.73292i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 371.451 | − | 371.451i | 0.669280 | − | 0.669280i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 127.187 | − | 127.187i | 0.228343 | − | 0.228343i | −0.583657 | − | 0.812000i | \(-0.698379\pi\) |
0.812000 | + | 0.583657i | \(0.198379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 257.604i | − | 0.460830i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 83.3343 | 0.148546 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 292.853 | + | 292.853i | 0.520164 | + | 0.520164i | 0.917621 | − | 0.397457i | \(-0.130107\pi\) |
−0.397457 | + | 0.917621i | \(0.630107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −143.726 | − | 143.726i | −0.254382 | − | 0.254382i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −114.688 | −0.202271 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 414.222i | 0.727982i | 0.931403 | + | 0.363991i | \(0.118586\pi\) | ||||
−0.931403 | + | 0.363991i | \(0.881414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 203.517 | − | 203.517i | 0.356422 | − | 0.356422i | −0.506070 | − | 0.862492i | \(-0.668902\pi\) |
0.862492 | + | 0.506070i | \(0.168902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −240.463 | + | 240.463i | −0.419657 | + | 0.419657i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 973.095i | 1.69234i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 474.909 | 0.823065 | 0.411533 | − | 0.911395i | \(-0.364994\pi\) | ||||
0.411533 | + | 0.911395i | \(0.364994\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 204.133 | + | 204.133i | 0.352562 | + | 0.352562i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.87503 | − | 4.87503i | −0.00839075 | − | 0.00839075i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −647.037 | −1.10984 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 378.716i | 0.647378i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.33802 | − | 9.33802i | 0.0159080 | − | 0.0159080i | −0.699108 | − | 0.715016i | \(-0.746419\pi\) |
0.715016 | + | 0.699108i | \(0.246419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −202.873 | + | 202.873i | −0.344436 | + | 0.344436i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 572.945i | − | 0.969451i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 332.523 | 0.560748 | 0.280374 | − | 0.959891i | \(-0.409542\pi\) | ||||
0.280374 | + | 0.959891i | \(0.409542\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 306.554 | + | 306.554i | 0.515217 | + | 0.515217i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.98461 | + | 1.98461i | 0.00332431 | + | 0.00332431i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1044.75 | 1.74415 | 0.872076 | − | 0.489371i | \(-0.162773\pi\) | ||||
0.872076 | + | 0.489371i | \(0.162773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 635.025i | − | 1.05661i | −0.849053 | − | 0.528307i | \(-0.822827\pi\) | ||
0.849053 | − | 0.528307i | \(-0.177173\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −80.0355 | + | 80.0355i | −0.132729 | + | 0.132729i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 50.3743 | − | 50.3743i | 0.0832633 | − | 0.0832633i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 813.850i | − | 1.34078i | −0.742011 | − | 0.670388i | \(-0.766128\pi\) | ||
0.742011 | − | 0.670388i | \(-0.233872\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1197.03 | 1.96556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 324.289 | + | 324.289i | 0.530752 | + | 0.530752i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 429.836 | + | 429.836i | 0.701201 | + | 0.701201i | 0.964668 | − | 0.263468i | \(-0.0848662\pi\) |
−0.263468 | + | 0.964668i | \(0.584866\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 51.5351 | 0.0837969 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 333.971i | − | 0.541282i | −0.962680 | − | 0.270641i | \(-0.912764\pi\) | ||
0.962680 | − | 0.270641i | \(-0.0872357\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 114.066 | − | 114.066i | 0.184275 | − | 0.184275i | −0.608941 | − | 0.793216i | \(-0.708405\pi\) |
0.793216 | + | 0.608941i | \(0.208405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −116.354 | + | 116.354i | −0.187365 | + | 0.187365i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2104.74i | 3.37839i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 448.972 | 0.718355 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −267.369 | − | 267.369i | −0.426425 | − | 0.426425i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −130.922 | − | 130.922i | −0.208142 | − | 0.208142i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 160.396 | 0.254193 | 0.127096 | − | 0.991890i | \(-0.459434\pi\) | ||||
0.127096 | + | 0.991890i | \(0.459434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 477.076i | 0.753675i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −814.500 | + | 814.500i | −1.28268 | + | 1.28268i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1355.81 | + | 1355.81i | −2.12843 | + | 2.12843i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 50.2116i | 0.0785784i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 309.175 | 0.482333 | 0.241166 | − | 0.970484i | \(-0.422470\pi\) | ||||
0.241166 | + | 0.970484i | \(0.422470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −392.517 | − | 392.517i | −0.610446 | − | 0.610446i | 0.332616 | − | 0.943062i | \(-0.392069\pi\) |
−0.943062 | + | 0.332616i | \(0.892069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 139.278 | + | 139.278i | 0.215935 | + | 0.215935i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −199.770 | −0.308763 | −0.154381 | − | 0.988011i | \(-0.549338\pi\) | ||||
−0.154381 | + | 0.988011i | \(0.549338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 102.261i | 0.157567i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −216.545 | + | 216.545i | −0.332634 | + | 0.332634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 632.149 | − | 632.149i | 0.968068 | − | 0.968068i | −0.0314373 | − | 0.999506i | \(-0.510008\pi\) |
0.999506 | + | 0.0314373i | \(0.0100084\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 252.636i | 0.385704i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 150.375 | 0.228882 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 62.1301 | + | 62.1301i | 0.0942793 | + | 0.0942793i | 0.752673 | − | 0.658394i | \(-0.228764\pi\) |
−0.658394 | + | 0.752673i | \(0.728764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.1550 | + | 48.1550i | 0.0728517 | + | 0.0728517i | 0.742594 | − | 0.669742i | \(-0.233595\pi\) |
−0.669742 | + | 0.742594i | \(0.733595\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 133.482 | 0.201331 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1967.09i | − | 2.95803i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1214.42 | − | 1214.42i | 1.82072 | − | 1.82072i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 146.807 | − | 146.807i | 0.219442 | − | 0.219442i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 122.201i | 0.182118i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 88.3501 | 0.131278 | 0.0656390 | − | 0.997843i | \(-0.479091\pi\) | ||||
0.0656390 | + | 0.997843i | \(0.479091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −112.904 | − | 112.904i | −0.167265 | − | 0.167265i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 405.589 | + | 405.589i | 0.599097 | + | 0.599097i | 0.940072 | − | 0.340975i | \(-0.110757\pi\) |
−0.340975 | + | 0.940072i | \(0.610757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −812.347 | −1.19639 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 633.572i | − | 0.930356i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 572.903 | − | 572.903i | 0.838803 | − | 0.838803i | −0.149898 | − | 0.988701i | \(-0.547895\pi\) |
0.988701 | + | 0.149898i | \(0.0478946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1264.98 | − | 1264.98i | 1.84668 | − | 1.84668i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 350.535i | 0.510241i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1036.41 | −1.50422 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −210.640 | − | 210.640i | −0.304833 | − | 0.304833i | 0.538068 | − | 0.842901i | \(-0.319154\pi\) |
−0.842901 | + | 0.538068i | \(0.819154\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −285.387 | − | 285.387i | −0.411814 | − | 0.411814i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1349.40 | −1.94159 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18.1641i | − | 0.0260604i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 264.126 | − | 264.126i | 0.377862 | − | 0.377862i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 419.735 | − | 419.735i | 0.598766 | − | 0.598766i | −0.341218 | − | 0.939984i | \(-0.610840\pi\) |
0.939984 | + | 0.341218i | \(0.110840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 840.094i | 1.19501i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −350.665 | −0.497398 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −586.449 | − | 586.449i | −0.829490 | − | 0.829490i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 228.651 | + | 228.651i | 0.322497 | + | 0.322497i | 0.849724 | − | 0.527227i | \(-0.176768\pi\) |
−0.527227 | + | 0.849724i | \(0.676768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −225.605 | −0.317307 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 439.382i | 0.616244i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −942.392 | + | 942.392i | −1.31803 | + | 1.31803i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 572.821 | − | 572.821i | 0.798914 | − | 0.798914i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1144.39i | − | 1.59165i | −0.605528 | − | 0.795824i | \(-0.707038\pi\) | ||
0.605528 | − | 0.795824i | \(-0.292962\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 966.941 | 1.34111 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −298.671 | − | 298.671i | −0.413099 | − | 0.413099i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1178.41 | + | 1178.41i | 1.62539 | + | 1.62539i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 646.638 | 0.889461 | 0.444731 | − | 0.895664i | \(-0.353299\pi\) | ||||
0.444731 | + | 0.895664i | \(0.353299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.0900 | − | 49.0900i | 0.0671545 | − | 0.0671545i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −485.081 | + | 485.081i | −0.661775 | + | 0.661775i | −0.955798 | − | 0.294023i | \(-0.905006\pi\) |
0.294023 | + | 0.955798i | \(0.405006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1466.08i | − | 1.99467i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −398.318 | −0.540459 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.07050 | + | 7.07050i | 0.00956766 | + | 0.00956766i | 0.711874 | − | 0.702307i | \(-0.247847\pi\) |
−0.702307 | + | 0.711874i | \(0.747847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −428.263 | − | 428.263i | −0.577953 | − | 0.577953i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1272.93 | −1.71322 | −0.856612 | − | 0.515961i | \(-0.827435\pi\) | ||||
−0.856612 | + | 0.515961i | \(0.827435\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1246.81i | 1.67357i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.14769 | − | 1.14769i | 0.00153640 | − | 0.00153640i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −477.736 | + | 477.736i | −0.637832 | + | 0.637832i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 176.056i | − | 0.234428i | −0.993107 | − | 0.117214i | \(-0.962604\pi\) | ||
0.993107 | − | 0.117214i | \(-0.0373964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −117.136 | −0.155559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1216.27 | + | 1216.27i | 1.61096 | + | 1.61096i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −840.383 | − | 840.383i | −1.11015 | − | 1.11015i | −0.993130 | − | 0.117019i | \(-0.962666\pi\) |
−0.117019 | − | 0.993130i | \(-0.537334\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −579.066 | −0.762933 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 525.952i | − | 0.691132i | −0.938394 | − | 0.345566i | \(-0.887687\pi\) | ||
0.938394 | − | 0.345566i | \(-0.112313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.8547 | + | 47.8547i | −0.0627191 | + | 0.0627191i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −72.1696 | + | 72.1696i | −0.0943394 | + | 0.0943394i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 163.799i | 0.213558i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −805.196 | −1.04707 | −0.523534 | − | 0.852005i | \(-0.675387\pi\) | ||||
−0.523534 | + | 0.852005i | \(0.675387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −243.322 | − | 243.322i | −0.315593 | − | 0.315593i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 91.8885 | + | 91.8885i | 0.118873 | + | 0.118873i | 0.764041 | − | 0.645168i | \(-0.223213\pi\) |
−0.645168 | + | 0.764041i | \(0.723213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −426.353 | −0.550133 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 896.709i | 1.15407i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −58.2774 | + | 58.2774i | −0.0748105 | + | 0.0748105i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −124.946 | + | 124.946i | −0.159982 | + | 0.159982i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 281.807i | 0.359907i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1679.19 | −2.13910 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 250.015 | + | 250.015i | 0.317681 | + | 0.317681i | 0.847876 | − | 0.530195i | \(-0.177881\pi\) |
−0.530195 | + | 0.847876i | \(0.677881\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −390.059 | − | 390.059i | −0.494371 | − | 0.494371i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 346.965 | 0.438640 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 195.738i | 0.246832i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 560.351 | − | 560.351i | 0.704844 | − | 0.704844i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −428.762 | + | 428.762i | −0.537969 | + | 0.537969i | −0.922932 | − | 0.384963i | \(-0.874214\pi\) |
0.384963 | + | 0.922932i | \(0.374214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 123.596i | 0.154688i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −495.501 | −0.618603 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 374.192 | + | 374.192i | 0.465992 | + | 0.465992i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2130.16 | − | 2130.16i | −2.64616 | − | 2.64616i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −197.916 | −0.245249 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 960.576i | 1.18736i | 0.804700 | + | 0.593681i | \(0.202326\pi\) | ||||
−0.804700 | + | 0.593681i | \(0.797674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1095.66 | − | 1095.66i | 1.35100 | − | 1.35100i | 0.466451 | − | 0.884547i | \(-0.345532\pi\) |
0.884547 | − | 0.466451i | \(-0.154468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 291.959 | − | 291.959i | 0.359113 | − | 0.359113i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 878.999i | − | 1.07853i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −314.999 | −0.385556 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −457.124 | − | 457.124i | −0.558149 | − | 0.558149i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 987.644 | + | 987.644i | 1.20298 | + | 1.20298i | 0.973257 | + | 0.229721i | \(0.0737813\pi\) |
0.229721 | + | 0.973257i | \(0.426219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1265.91 | 1.53817 | 0.769083 | − | 0.639149i | \(-0.220713\pi\) | ||||
0.769083 | + | 0.639149i | \(0.220713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 561.896i | − | 0.681085i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −246.989 | + | 246.989i | −0.298657 | + | 0.298657i | −0.840488 | − | 0.541831i | \(-0.817731\pi\) |
0.541831 | + | 0.840488i | \(0.317731\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 70.0908 | − | 70.0908i | 0.0845486 | − | 0.0845486i | −0.663568 | − | 0.748116i | \(-0.730959\pi\) |
0.748116 | + | 0.663568i | \(0.230959\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 388.614i | − | 0.467646i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −516.735 | −0.620330 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −79.9554 | − | 79.9554i | −0.0957550 | − | 0.0957550i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −50.9795 | − | 50.9795i | −0.0609074 | − | 0.0609074i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 850.570 | 1.01379 | 0.506895 | − | 0.862008i | \(-0.330793\pi\) | ||||
0.506895 | + | 0.862008i | \(0.330793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2100.30i | − | 2.49739i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −546.364 | + | 546.364i | −0.648119 | + | 0.648119i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −617.402 | + | 617.402i | −0.730653 | + | 0.730653i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 121.607i | 0.143574i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 468.469 | 0.551790 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 909.737 | + | 909.737i | 1.06902 | + | 1.06902i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −958.146 | − | 958.146i | −1.12327 | − | 1.12327i | −0.991247 | − | 0.132019i | \(-0.957854\pi\) |
−0.132019 | − | 0.991247i | \(-0.542146\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 463.096 | 0.541633 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 574.307i | − | 0.670137i | −0.942194 | − | 0.335068i | \(-0.891241\pi\) | ||
0.942194 | − | 0.335068i | \(-0.108759\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 167.633 | − | 167.633i | 0.195149 | − | 0.195149i | −0.602768 | − | 0.797917i | \(-0.705935\pi\) |
0.797917 | + | 0.602768i | \(0.205935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −62.2047 | + | 62.2047i | −0.0722471 | + | 0.0722471i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1451.78i | 1.68225i | 0.540843 | + | 0.841124i | \(0.318105\pi\) | ||||
−0.540843 | + | 0.841124i | \(0.681895\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 385.098 | 0.445200 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −328.514 | − | 328.514i | −0.378909 | − | 0.378909i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −561.393 | − | 561.393i | −0.646022 | − | 0.646022i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −638.015 | −0.732508 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 191.244i | − | 0.219066i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 385.335 | − | 385.335i | 0.440383 | − | 0.440383i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −696.542 | + | 696.542i | −0.794233 | + | 0.794233i | −0.982179 | − | 0.187946i | \(-0.939817\pi\) |
0.187946 | + | 0.982179i | \(0.439817\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 628.349i | 0.714846i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −483.595 | −0.548916 | −0.274458 | − | 0.961599i | \(-0.588498\pi\) | ||||
−0.274458 | + | 0.961599i | \(0.588498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1013.54 | + | 1013.54i | 1.14784 | + | 1.14784i | 0.986977 | + | 0.160863i | \(0.0514277\pi\) |
0.160863 | + | 0.986977i | \(0.448572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −88.5606 | − | 88.5606i | −0.100068 | − | 0.100068i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1132.45 | −1.27672 | −0.638359 | − | 0.769739i | \(-0.720386\pi\) | ||||
−0.638359 | + | 0.769739i | \(0.720386\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1966.26i | − | 2.21177i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 67.1864 | − | 67.1864i | 0.0754056 | − | 0.0754056i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 396.543 | − | 396.543i | 0.444057 | − | 0.444057i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 174.712i | − | 0.195209i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −927.531 | −1.03404 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 532.088 | + | 532.088i | 0.591866 | + | 0.591866i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −197.501 | − | 197.501i | −0.219202 | − | 0.219202i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −336.227 | −0.372345 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1437.28i | 1.58815i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −213.492 | + | 213.492i | −0.235383 | + | 0.235383i | −0.814935 | − | 0.579552i | \(-0.803228\pi\) |
0.579552 | + | 0.814935i | \(0.303228\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 138.063 | − | 138.063i | 0.151885 | − | 0.151885i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1383.69i | − | 1.51887i | −0.650584 | − | 0.759435i | \(-0.725476\pi\) | ||
0.650584 | − | 0.759435i | \(-0.274524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.71178 | 0.00625606 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −105.829 | − | 105.829i | −0.115660 | − | 0.115660i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −304.941 | − | 304.941i | −0.332542 | − | 0.332542i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 841.973 | 0.916184 | 0.458092 | − | 0.888905i | \(-0.348533\pi\) | ||||
0.458092 | + | 0.888905i | \(0.348533\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 144.037i | 0.156391i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −200.134 | + | 200.134i | −0.216830 | + | 0.216830i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −882.761 | + | 882.761i | −0.954336 | + | 0.954336i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 227.639i | 0.245566i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1467.41 | −1.57956 | −0.789780 | − | 0.613390i | \(-0.789805\pi\) | ||||
−0.789780 | + | 0.613390i | \(0.789805\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1657.89 | + | 1657.89i | 1.78076 | + | 1.78076i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −555.605 | − | 555.605i | −0.595504 | − | 0.595504i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −359.171 | −0.384141 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 868.448i | 0.926839i | 0.886139 | + | 0.463419i | \(0.153378\pi\) | ||||
−0.886139 | + | 0.463419i | \(0.846622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 378.923 | − | 378.923i | 0.403539 | − | 0.403539i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 877.521 | − | 877.521i | 0.932541 | − | 0.932541i | −0.0653233 | − | 0.997864i | \(-0.520808\pi\) |
0.997864 | + | 0.0653233i | \(0.0208079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 126.217i | 0.133846i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 494.305 | 0.523074 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 588.434 | + | 588.434i | 0.621366 | + | 0.621366i | 0.945881 | − | 0.324514i | \(-0.105201\pi\) |
−0.324514 | + | 0.945881i | \(0.605201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 599.370 | + | 599.370i | 0.631580 | + | 0.631580i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 346.196 | 0.364033 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 622.721i | − | 0.653432i | −0.945122 | − | 0.326716i | \(-0.894058\pi\) | ||
0.945122 | − | 0.326716i | \(-0.105942\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1036.40 | − | 1036.40i | 1.08523 | − | 1.08523i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −701.244 | + | 701.244i | −0.732753 | + | 0.732753i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3053.75i | 3.18430i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 768.489 | 0.799676 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −112.470 | − | 112.470i | −0.116791 | − | 0.116791i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −879.816 | − | 879.816i | −0.911727 | − | 0.911727i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1405.67 | 1.45364 | 0.726820 | − | 0.686828i | \(-0.240998\pi\) | ||||
0.726820 | + | 0.686828i | \(0.240998\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 163.223i | − | 0.168445i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 400.839 | − | 400.839i | 0.412810 | − | 0.412810i | −0.469906 | − | 0.882716i | \(-0.655712\pi\) |
0.882716 | + | 0.469906i | \(0.155712\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1628.78 | − | 1628.78i | 1.67397 | − | 1.67397i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 900.028i | − | 0.923106i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 63.0363 | 0.0645203 | 0.0322601 | − | 0.999480i | \(-0.489729\pi\) | ||||
0.0322601 | + | 0.999480i | \(0.489729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1233.00 | − | 1233.00i | −1.25945 | − | 1.25945i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.2660 | − | 11.2660i | −0.0114842 | − | 0.0114842i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1179.73 | −1.20013 | −0.600064 | − | 0.799952i | \(-0.704858\pi\) | ||||
−0.600064 | + | 0.799952i | \(0.704858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2469.40i | 2.50700i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 423.266 | − | 423.266i | 0.428841 | − | 0.428841i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −341.112 | + | 341.112i | −0.344906 | + | 0.344906i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1827.60i | − | 1.84420i | −0.386952 | − | 0.922100i | \(-0.626472\pi\) | ||
0.386952 | − | 0.922100i | \(-0.373528\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −291.740 | −0.293797 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.55369 | − | 8.55369i | −0.00859668 | − | 0.00859668i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.3327 | + | 53.3327i | 0.0534932 | + | 0.0534932i | 0.733347 | − | 0.679854i | \(-0.237957\pi\) |
−0.679854 | + | 0.733347i | \(0.737957\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −211.105 | −0.211316 |
(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.f.319.5 | yes | 16 | |
4.3 | odd | 2 | inner | 768.3.l.f.319.1 | yes | 16 | |
8.3 | odd | 2 | 768.3.l.e.319.8 | yes | 16 | ||
8.5 | even | 2 | 768.3.l.e.319.4 | ✓ | 16 | ||
16.3 | odd | 4 | inner | 768.3.l.f.703.5 | yes | 16 | |
16.5 | even | 4 | 768.3.l.e.703.8 | yes | 16 | ||
16.11 | odd | 4 | 768.3.l.e.703.4 | yes | 16 | ||
16.13 | even | 4 | inner | 768.3.l.f.703.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.3.l.e.319.4 | ✓ | 16 | 8.5 | even | 2 | ||
768.3.l.e.319.8 | yes | 16 | 8.3 | odd | 2 | ||
768.3.l.e.703.4 | yes | 16 | 16.11 | odd | 4 | ||
768.3.l.e.703.8 | yes | 16 | 16.5 | even | 4 | ||
768.3.l.f.319.1 | yes | 16 | 4.3 | odd | 2 | inner | |
768.3.l.f.319.5 | yes | 16 | 1.1 | even | 1 | trivial | |
768.3.l.f.703.1 | yes | 16 | 16.13 | even | 4 | inner | |
768.3.l.f.703.5 | yes | 16 | 16.3 | odd | 4 | inner |