Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(449,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1050.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.c (of order \(2\), degree \(1\), not 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(-1.28897 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.449 |
Dual form | 1050.3.c.a.449.7 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −1.41421 | − | 2.64575i | −0.471405 | − | 0.881917i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.00000 | − | 3.74166i | −0.333333 | − | 0.623610i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −5.00000 | + | 7.48331i | −0.555556 | + | 0.831479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.5544i | 1.32313i | 0.749890 | + | 0.661563i | \(0.230107\pi\) | ||||
−0.749890 | + | 0.661563i | \(0.769893\pi\) | |||||||
\(12\) | −2.82843 | − | 5.29150i | −0.235702 | − | 0.440959i | ||||
\(13\) | 0.583005i | 0.0448466i | 0.999749 | + | 0.0224233i | \(0.00713815\pi\) | ||||
−0.999749 | + | 0.0224233i | \(0.992862\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −21.5367 | −1.26687 | −0.633433 | − | 0.773798i | \(-0.718355\pi\) | ||||
−0.633433 | + | 0.773798i | \(0.718355\pi\) | |||||||
\(18\) | −7.07107 | + | 10.5830i | −0.392837 | + | 0.587945i | ||||
\(19\) | 16.0000 | 0.842105 | 0.421053 | − | 0.907036i | \(-0.361661\pi\) | ||||
0.421053 | + | 0.907036i | \(0.361661\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.00000 | + | 3.74166i | −0.333333 | + | 0.178174i | ||||
\(22\) | 20.5830i | 0.935591i | ||||||||
\(23\) | −38.8308 | −1.68830 | −0.844148 | − | 0.536111i | \(-0.819893\pi\) | ||||
−0.844148 | + | 0.536111i | \(0.819893\pi\) | |||||||
\(24\) | −4.00000 | − | 7.48331i | −0.166667 | − | 0.311805i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.824494i | 0.0317113i | ||||||||
\(27\) | 26.8701 | + | 2.64575i | 0.995187 | + | 0.0979908i | ||||
\(28\) | − | 5.29150i | − | 0.188982i | ||||||
\(29\) | 35.7676i | 1.23337i | 0.787212 | + | 0.616683i | \(0.211524\pi\) | ||||
−0.787212 | + | 0.616683i | \(0.788476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −58.4575 | −1.88573 | −0.942863 | − | 0.333180i | \(-0.891878\pi\) | ||||
−0.942863 | + | 0.333180i | \(0.891878\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 38.5073 | − | 20.5830i | 1.16689 | − | 0.623727i | ||||
\(34\) | −30.4575 | −0.895809 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.0000 | + | 14.9666i | −0.277778 | + | 0.415740i | ||||
\(37\) | 20.0000i | 0.540541i | 0.962784 | + | 0.270270i | \(0.0871131\pi\) | ||||
−0.962784 | + | 0.270270i | \(0.912887\pi\) | |||||||
\(38\) | 22.6274 | 0.595458 | ||||||||
\(39\) | 1.54249 | − | 0.824494i | 0.0395509 | − | 0.0211409i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.75149i | 0.213451i | 0.994289 | + | 0.106725i | \(0.0340366\pi\) | ||||
−0.994289 | + | 0.106725i | \(0.965963\pi\) | |||||||
\(42\) | −9.89949 | + | 5.29150i | −0.235702 | + | 0.125988i | ||||
\(43\) | 11.7490i | 0.273233i | 0.990624 | + | 0.136616i | \(0.0436228\pi\) | ||||
−0.990624 | + | 0.136616i | \(0.956377\pi\) | |||||||
\(44\) | 29.1088i | 0.661563i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −54.9150 | −1.19380 | ||||||||
\(47\) | −8.48528 | −0.180538 | −0.0902690 | − | 0.995917i | \(-0.528773\pi\) | ||||
−0.0902690 | + | 0.995917i | \(0.528773\pi\) | |||||||
\(48\) | −5.65685 | − | 10.5830i | −0.117851 | − | 0.220479i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 30.4575 | + | 56.9808i | 0.597206 | + | 1.11727i | ||||
\(52\) | 1.16601i | 0.0224233i | ||||||||
\(53\) | 50.9117 | 0.960598 | 0.480299 | − | 0.877105i | \(-0.340528\pi\) | ||||
0.480299 | + | 0.877105i | \(0.340528\pi\) | |||||||
\(54\) | 38.0000 | + | 3.74166i | 0.703704 | + | 0.0692900i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | −22.6274 | − | 42.3320i | −0.396972 | − | 0.742667i | ||||
\(58\) | 50.5830i | 0.872121i | ||||||||
\(59\) | 58.2175i | 0.986738i | 0.869820 | + | 0.493369i | \(0.164235\pi\) | ||||
−0.869820 | + | 0.493369i | \(0.835765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.9150 | 0.637951 | 0.318976 | − | 0.947763i | \(-0.396661\pi\) | ||||
0.318976 | + | 0.947763i | \(0.396661\pi\) | |||||||
\(62\) | −82.6714 | −1.33341 | ||||||||
\(63\) | 19.7990 | + | 13.2288i | 0.314270 | + | 0.209980i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 54.4575 | − | 29.1088i | 0.825114 | − | 0.441042i | ||||
\(67\) | 70.5830i | 1.05348i | 0.850027 | + | 0.526739i | \(0.176585\pi\) | ||||
−0.850027 | + | 0.526739i | \(0.823415\pi\) | |||||||
\(68\) | −43.0734 | −0.633433 | ||||||||
\(69\) | 54.9150 | + | 102.737i | 0.795870 | + | 1.48894i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17.0279i | 0.239829i | 0.992784 | + | 0.119915i | \(0.0382621\pi\) | ||||
−0.992784 | + | 0.119915i | \(0.961738\pi\) | |||||||
\(72\) | −14.1421 | + | 21.1660i | −0.196419 | + | 0.293972i | ||||
\(73\) | − | 72.3320i | − | 0.990850i | −0.868651 | − | 0.495425i | \(-0.835012\pi\) | ||
0.868651 | − | 0.495425i | \(-0.164988\pi\) | |||||||
\(74\) | 28.2843i | 0.382220i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 32.0000 | 0.421053 | ||||||||
\(77\) | 38.5073 | 0.500095 | ||||||||
\(78\) | 2.18141 | − | 1.16601i | 0.0279667 | − | 0.0149489i | ||||
\(79\) | −20.9150 | −0.264747 | −0.132374 | − | 0.991200i | \(-0.542260\pi\) | ||||
−0.132374 | + | 0.991200i | \(0.542260\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −31.0000 | − | 74.8331i | −0.382716 | − | 0.923866i | ||||
\(82\) | 12.3765i | 0.150933i | ||||||||
\(83\) | 145.544 | 1.75354 | 0.876770 | − | 0.480910i | \(-0.159694\pi\) | ||||
0.876770 | + | 0.480910i | \(0.159694\pi\) | |||||||
\(84\) | −14.0000 | + | 7.48331i | −0.166667 | + | 0.0890871i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 16.6156i | 0.193205i | ||||||||
\(87\) | 94.6321 | − | 50.5830i | 1.08773 | − | 0.581414i | ||||
\(88\) | 41.1660i | 0.467796i | ||||||||
\(89\) | 53.6514i | 0.602824i | 0.953494 | + | 0.301412i | \(0.0974580\pi\) | ||||
−0.953494 | + | 0.301412i | \(0.902542\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.54249 | 0.0169504 | ||||||||
\(92\) | −77.6616 | −0.844148 | ||||||||
\(93\) | 82.6714 | + | 154.664i | 0.888940 | + | 1.66305i | ||||
\(94\) | −12.0000 | −0.127660 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.00000 | − | 14.9666i | −0.0833333 | − | 0.155902i | ||||
\(97\) | − | 111.166i | − | 1.14604i | −0.819541 | − | 0.573021i | \(-0.805771\pi\) | ||
0.819541 | − | 0.573021i | \(-0.194229\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | −108.915 | − | 72.7719i | −1.10015 | − | 0.735070i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 57.8367i | 0.572641i | 0.958134 | + | 0.286320i | \(0.0924322\pi\) | ||||
−0.958134 | + | 0.286320i | \(0.907568\pi\) | |||||||
\(102\) | 43.0734 | + | 80.5830i | 0.422289 | + | 0.790029i | ||||
\(103\) | 119.373i | 1.15896i | 0.814988 | + | 0.579478i | \(0.196744\pi\) | ||||
−0.814988 | + | 0.579478i | \(0.803256\pi\) | |||||||
\(104\) | 1.64899i | 0.0158557i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 72.0000 | 0.679245 | ||||||||
\(107\) | −116.492 | −1.08871 | −0.544357 | − | 0.838854i | \(-0.683226\pi\) | ||||
−0.544357 | + | 0.838854i | \(0.683226\pi\) | |||||||
\(108\) | 53.7401 | + | 5.29150i | 0.497594 | + | 0.0489954i | ||||
\(109\) | −87.8301 | −0.805780 | −0.402890 | − | 0.915248i | \(-0.631994\pi\) | ||||
−0.402890 | + | 0.915248i | \(0.631994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 52.9150 | − | 28.2843i | 0.476712 | − | 0.254813i | ||||
\(112\) | − | 10.5830i | − | 0.0944911i | ||||||
\(113\) | −69.1763 | −0.612180 | −0.306090 | − | 0.952003i | \(-0.599021\pi\) | ||||
−0.306090 | + | 0.952003i | \(0.599021\pi\) | |||||||
\(114\) | −32.0000 | − | 59.8665i | −0.280702 | − | 0.525145i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 71.5352i | 0.616683i | ||||||||
\(117\) | −4.36281 | − | 2.91503i | −0.0372890 | − | 0.0249148i | ||||
\(118\) | 82.3320i | 0.697729i | ||||||||
\(119\) | 56.9808i | 0.478830i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −90.8301 | −0.750662 | ||||||||
\(122\) | 55.0342 | 0.451100 | ||||||||
\(123\) | 23.1543 | − | 12.3765i | 0.188246 | − | 0.100622i | ||||
\(124\) | −116.915 | −0.942863 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 28.0000 | + | 18.7083i | 0.222222 | + | 0.148478i | ||||
\(127\) | − | 27.0850i | − | 0.213268i | −0.994298 | − | 0.106634i | \(-0.965993\pi\) | ||
0.994298 | − | 0.106634i | \(-0.0340072\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 31.0850 | − | 16.6156i | 0.240969 | − | 0.128803i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 145.544i | − | 1.11102i | −0.831509 | − | 0.555511i | \(-0.812523\pi\) | ||
0.831509 | − | 0.555511i | \(-0.187477\pi\) | |||||||
\(132\) | 77.0146 | − | 41.1660i | 0.583444 | − | 0.311864i | ||||
\(133\) | − | 42.3320i | − | 0.318286i | ||||||
\(134\) | 99.8194i | 0.744921i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −60.9150 | −0.447905 | ||||||||
\(137\) | 24.8088 | 0.181086 | 0.0905431 | − | 0.995893i | \(-0.471140\pi\) | ||||
0.0905431 | + | 0.995893i | \(0.471140\pi\) | |||||||
\(138\) | 77.6616 | + | 145.292i | 0.562765 | + | 1.05284i | ||||
\(139\) | −146.458 | −1.05365 | −0.526826 | − | 0.849973i | \(-0.676618\pi\) | ||||
−0.526826 | + | 0.849973i | \(0.676618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | + | 22.4499i | 0.0851064 | + | 0.159219i | ||||
\(142\) | 24.0810i | 0.169585i | ||||||||
\(143\) | −8.48528 | −0.0593376 | ||||||||
\(144\) | −20.0000 | + | 29.9333i | −0.138889 | + | 0.207870i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 102.293i | − | 0.700636i | ||||||
\(147\) | 9.89949 | + | 18.5203i | 0.0673435 | + | 0.125988i | ||||
\(148\) | 40.0000i | 0.270270i | ||||||||
\(149\) | 219.552i | 1.47351i | 0.676162 | + | 0.736753i | \(0.263642\pi\) | ||||
−0.676162 | + | 0.736753i | \(0.736358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −211.660 | −1.40172 | −0.700861 | − | 0.713298i | \(-0.747201\pi\) | ||||
−0.700861 | + | 0.713298i | \(0.747201\pi\) | |||||||
\(152\) | 45.2548 | 0.297729 | ||||||||
\(153\) | 107.684 | − | 161.166i | 0.703814 | − | 1.05337i | ||||
\(154\) | 54.4575 | 0.353620 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.08497 | − | 1.64899i | 0.0197755 | − | 0.0105704i | ||||
\(157\) | 208.745i | 1.32959i | 0.747027 | + | 0.664793i | \(0.231480\pi\) | ||||
−0.747027 | + | 0.664793i | \(0.768520\pi\) | |||||||
\(158\) | −29.5783 | −0.187205 | ||||||||
\(159\) | −72.0000 | − | 134.700i | −0.452830 | − | 0.847168i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 102.737i | 0.638116i | ||||||||
\(162\) | −43.8406 | − | 105.830i | −0.270621 | − | 0.653272i | ||||
\(163\) | − | 266.996i | − | 1.63801i | −0.573784 | − | 0.819006i | \(-0.694525\pi\) | ||
0.573784 | − | 0.819006i | \(-0.305475\pi\) | |||||||
\(164\) | 17.5030i | 0.106725i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 205.830 | 1.23994 | ||||||||
\(167\) | −7.19124 | −0.0430613 | −0.0215307 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215307 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(168\) | −19.7990 | + | 10.5830i | −0.117851 | + | 0.0629941i | ||||
\(169\) | 168.660 | 0.997989 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −80.0000 | + | 119.733i | −0.467836 | + | 0.700193i | ||||
\(172\) | 23.4980i | 0.136616i | ||||||||
\(173\) | 192.536 | 1.11293 | 0.556464 | − | 0.830872i | \(-0.312158\pi\) | ||||
0.556464 | + | 0.830872i | \(0.312158\pi\) | |||||||
\(174\) | 133.830 | − | 71.5352i | 0.769138 | − | 0.411122i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 58.2175i | 0.330781i | ||||||||
\(177\) | 154.029 | − | 82.3320i | 0.870221 | − | 0.465153i | ||||
\(178\) | 75.8745i | 0.426261i | ||||||||
\(179\) | − | 43.6631i | − | 0.243928i | −0.992535 | − | 0.121964i | \(-0.961081\pi\) | ||
0.992535 | − | 0.121964i | \(-0.0389193\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −81.0850 | −0.447983 | −0.223992 | − | 0.974591i | \(-0.571909\pi\) | ||||
−0.223992 | + | 0.974591i | \(0.571909\pi\) | |||||||
\(182\) | 2.18141 | 0.0119857 | ||||||||
\(183\) | −55.0342 | − | 102.959i | −0.300733 | − | 0.562620i | ||||
\(184\) | −109.830 | −0.596902 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 116.915 | + | 218.728i | 0.628575 | + | 1.17596i | ||||
\(187\) | − | 313.454i | − | 1.67622i | ||||||
\(188\) | −16.9706 | −0.0902690 | ||||||||
\(189\) | 7.00000 | − | 71.0915i | 0.0370370 | − | 0.376145i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 53.5571i | − | 0.280404i | −0.990123 | − | 0.140202i | \(-0.955225\pi\) | ||
0.990123 | − | 0.140202i | \(-0.0447751\pi\) | |||||||
\(192\) | −11.3137 | − | 21.1660i | −0.0589256 | − | 0.110240i | ||||
\(193\) | 110.494i | 0.572508i | 0.958154 | + | 0.286254i | \(0.0924102\pi\) | ||||
−0.958154 | + | 0.286254i | \(0.907590\pi\) | |||||||
\(194\) | − | 157.212i | − | 0.810374i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −86.1469 | −0.437294 | −0.218647 | − | 0.975804i | \(-0.570164\pi\) | ||||
−0.218647 | + | 0.975804i | \(0.570164\pi\) | |||||||
\(198\) | −154.029 | − | 102.915i | −0.777925 | − | 0.519773i | ||||
\(199\) | 88.0000 | 0.442211 | 0.221106 | − | 0.975250i | \(-0.429033\pi\) | ||||
0.221106 | + | 0.975250i | \(0.429033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 186.745 | − | 99.8194i | 0.929080 | − | 0.496614i | ||||
\(202\) | 81.7935i | 0.404918i | ||||||||
\(203\) | 94.6321 | 0.466168 | ||||||||
\(204\) | 60.9150 | + | 113.962i | 0.298603 | + | 0.558635i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 168.818i | 0.819506i | ||||||||
\(207\) | 194.154 | − | 290.583i | 0.937942 | − | 1.40378i | ||||
\(208\) | 2.33202i | 0.0112116i | ||||||||
\(209\) | 232.870i | 1.11421i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −61.2549 | −0.290308 | −0.145154 | − | 0.989409i | \(-0.546368\pi\) | ||||
−0.145154 | + | 0.989409i | \(0.546368\pi\) | |||||||
\(212\) | 101.823 | 0.480299 | ||||||||
\(213\) | 45.0515 | − | 24.0810i | 0.211509 | − | 0.113057i | ||||
\(214\) | −164.745 | −0.769837 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 76.0000 | + | 7.48331i | 0.351852 | + | 0.0346450i | ||||
\(217\) | 154.664i | 0.712738i | ||||||||
\(218\) | −124.210 | −0.569773 | ||||||||
\(219\) | −191.373 | + | 102.293i | −0.873847 | + | 0.467091i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.5560i | − | 0.0568146i | ||||||
\(222\) | 74.8331 | − | 40.0000i | 0.337086 | − | 0.180180i | ||||
\(223\) | − | 150.494i | − | 0.674861i | −0.941350 | − | 0.337431i | \(-0.890442\pi\) | ||
0.941350 | − | 0.337431i | \(-0.109558\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −97.8301 | −0.432876 | ||||||||
\(227\) | −190.558 | −0.839464 | −0.419732 | − | 0.907648i | \(-0.637876\pi\) | ||||
−0.419732 | + | 0.907648i | \(0.637876\pi\) | |||||||
\(228\) | −45.2548 | − | 84.6640i | −0.198486 | − | 0.371334i | ||||
\(229\) | 142.915 | 0.624083 | 0.312042 | − | 0.950068i | \(-0.398987\pi\) | ||||
0.312042 | + | 0.950068i | \(0.398987\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −54.4575 | − | 101.881i | −0.235747 | − | 0.441042i | ||||
\(232\) | 101.166i | 0.436060i | ||||||||
\(233\) | 7.83826 | 0.0336406 | 0.0168203 | − | 0.999859i | \(-0.494646\pi\) | ||||
0.0168203 | + | 0.999859i | \(0.494646\pi\) | |||||||
\(234\) | −6.16995 | − | 4.12247i | −0.0263673 | − | 0.0176174i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 116.435i | 0.493369i | ||||||||
\(237\) | 29.5783 | + | 55.3360i | 0.124803 | + | 0.233485i | ||||
\(238\) | 80.5830i | 0.338584i | ||||||||
\(239\) | − | 213.369i | − | 0.892756i | −0.894844 | − | 0.446378i | \(-0.852714\pi\) | ||
0.894844 | − | 0.446378i | \(-0.147286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −130.000 | −0.539419 | −0.269710 | − | 0.962942i | \(-0.586928\pi\) | ||||
−0.269710 | + | 0.962942i | \(0.586928\pi\) | |||||||
\(242\) | −128.453 | −0.530798 | ||||||||
\(243\) | −154.149 | + | 187.848i | −0.634359 | + | 0.773038i | ||||
\(244\) | 77.8301 | 0.318976 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 32.7451 | − | 17.5030i | 0.133110 | − | 0.0711503i | ||||
\(247\) | 9.32808i | 0.0377655i | ||||||||
\(248\) | −165.343 | −0.666705 | ||||||||
\(249\) | −205.830 | − | 385.073i | −0.826627 | − | 1.54648i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 389.258i | − | 1.55083i | −0.631453 | − | 0.775415i | \(-0.717541\pi\) | ||
0.631453 | − | 0.775415i | \(-0.282459\pi\) | |||||||
\(252\) | 39.5980 | + | 26.4575i | 0.157135 | + | 0.104990i | ||||
\(253\) | − | 565.158i | − | 2.23383i | ||||||
\(254\) | − | 38.3039i | − | 0.150803i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −336.139 | −1.30793 | −0.653967 | − | 0.756523i | \(-0.726897\pi\) | ||||
−0.653967 | + | 0.756523i | \(0.726897\pi\) | |||||||
\(258\) | 43.9608 | − | 23.4980i | 0.170391 | − | 0.0910776i | ||||
\(259\) | 52.9150 | 0.204305 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −267.660 | − | 178.838i | −1.02552 | − | 0.685203i | ||||
\(262\) | − | 205.830i | − | 0.785611i | ||||||
\(263\) | −438.933 | −1.66895 | −0.834473 | − | 0.551048i | \(-0.814228\pi\) | ||||
−0.834473 | + | 0.551048i | \(0.814228\pi\) | |||||||
\(264\) | 108.915 | − | 58.2175i | 0.412557 | − | 0.220521i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 59.8665i | − | 0.225062i | ||||||
\(267\) | 141.948 | − | 75.8745i | 0.531641 | − | 0.284174i | ||||
\(268\) | 141.166i | 0.526739i | ||||||||
\(269\) | 14.4601i | 0.0537549i | 0.999639 | + | 0.0268775i | \(0.00855639\pi\) | ||||
−0.999639 | + | 0.0268775i | \(0.991444\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 61.5425 | 0.227094 | 0.113547 | − | 0.993533i | \(-0.463779\pi\) | ||||
0.113547 | + | 0.993533i | \(0.463779\pi\) | |||||||
\(272\) | −86.1469 | −0.316716 | ||||||||
\(273\) | −2.18141 | − | 4.08104i | −0.00799050 | − | 0.0149489i | ||||
\(274\) | 35.0850 | 0.128047 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 109.830 | + | 205.473i | 0.397935 | + | 0.744468i | ||||
\(277\) | 150.494i | 0.543300i | 0.962396 | + | 0.271650i | \(0.0875693\pi\) | ||||
−0.962396 | + | 0.271650i | \(0.912431\pi\) | |||||||
\(278\) | −207.122 | −0.745044 | ||||||||
\(279\) | 292.288 | − | 437.456i | 1.04763 | − | 1.56794i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 300.220i | 1.06840i | 0.845359 | + | 0.534199i | \(0.179387\pi\) | ||||
−0.845359 | + | 0.534199i | \(0.820613\pi\) | |||||||
\(282\) | 16.9706 | + | 31.7490i | 0.0601793 | + | 0.112585i | ||||
\(283\) | − | 98.8340i | − | 0.349237i | −0.984636 | − | 0.174618i | \(-0.944131\pi\) | ||
0.984636 | − | 0.174618i | \(-0.0558692\pi\) | |||||||
\(284\) | 34.0557i | 0.119915i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.0419580 | ||||||||
\(287\) | 23.1543 | 0.0806769 | ||||||||
\(288\) | −28.2843 | + | 42.3320i | −0.0982093 | + | 0.146986i | ||||
\(289\) | 174.830 | 0.604948 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −294.118 | + | 157.212i | −1.01071 | + | 0.540249i | ||||
\(292\) | − | 144.664i | − | 0.495425i | ||||||
\(293\) | 7.15424 | 0.0244172 | 0.0122086 | − | 0.999925i | \(-0.496114\pi\) | ||||
0.0122086 | + | 0.999925i | \(0.496114\pi\) | |||||||
\(294\) | 14.0000 | + | 26.1916i | 0.0476190 | + | 0.0890871i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 56.5685i | 0.191110i | ||||||||
\(297\) | −38.5073 | + | 391.077i | −0.129654 | + | 1.31676i | ||||
\(298\) | 310.494i | 1.04193i | ||||||||
\(299\) | − | 22.6386i | − | 0.0757142i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.0850 | 0.103272 | ||||||||
\(302\) | −299.333 | −0.991168 | ||||||||
\(303\) | 153.022 | − | 81.7935i | 0.505022 | − | 0.269945i | ||||
\(304\) | 64.0000 | 0.210526 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 152.288 | − | 227.923i | 0.497672 | − | 0.744847i | ||||
\(307\) | 105.830i | 0.344723i | 0.985034 | + | 0.172362i | \(0.0551398\pi\) | ||||
−0.985034 | + | 0.172362i | \(0.944860\pi\) | |||||||
\(308\) | 77.0146 | 0.250047 | ||||||||
\(309\) | 315.830 | − | 168.818i | 1.02210 | − | 0.546337i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 265.403i | − | 0.853385i | −0.904397 | − | 0.426692i | \(-0.859679\pi\) | ||
0.904397 | − | 0.426692i | \(-0.140321\pi\) | |||||||
\(312\) | 4.36281 | − | 2.33202i | 0.0139834 | − | 0.00747443i | ||||
\(313\) | − | 259.328i | − | 0.828524i | −0.910158 | − | 0.414262i | \(-0.864040\pi\) | ||
0.910158 | − | 0.414262i | \(-0.135960\pi\) | |||||||
\(314\) | 295.210i | 0.940160i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −41.8301 | −0.132374 | ||||||||
\(317\) | −37.8233 | −0.119316 | −0.0596581 | − | 0.998219i | \(-0.519001\pi\) | ||||
−0.0596581 | + | 0.998219i | \(0.519001\pi\) | |||||||
\(318\) | −101.823 | − | 190.494i | −0.320199 | − | 0.599038i | ||||
\(319\) | −520.575 | −1.63190 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 164.745 | + | 308.210i | 0.513225 | + | 0.960155i | ||||
\(322\) | 145.292i | 0.451216i | ||||||||
\(323\) | −344.587 | −1.06683 | ||||||||
\(324\) | −62.0000 | − | 149.666i | −0.191358 | − | 0.461933i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 377.589i | − | 1.15825i | ||||||
\(327\) | 124.210 | + | 232.376i | 0.379848 | + | 0.710631i | ||||
\(328\) | 24.7530i | 0.0754663i | ||||||||
\(329\) | 22.4499i | 0.0682369i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 145.490 | 0.439547 | 0.219774 | − | 0.975551i | \(-0.429468\pi\) | ||||
0.219774 | + | 0.975551i | \(0.429468\pi\) | |||||||
\(332\) | 291.088 | 0.876770 | ||||||||
\(333\) | −149.666 | − | 100.000i | −0.449448 | − | 0.300300i | ||||
\(334\) | −10.1699 | −0.0304489 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −28.0000 | + | 14.9666i | −0.0833333 | + | 0.0445435i | ||||
\(337\) | − | 600.316i | − | 1.78135i | −0.454637 | − | 0.890677i | \(-0.650231\pi\) | ||
0.454637 | − | 0.890677i | \(-0.349769\pi\) | |||||||
\(338\) | 238.521 | 0.705685 | ||||||||
\(339\) | 97.8301 | + | 183.023i | 0.288584 | + | 0.539892i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 850.813i | − | 2.49505i | ||||||
\(342\) | −113.137 | + | 169.328i | −0.330810 | + | 0.495111i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 33.2312i | 0.0966024i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 272.288 | 0.786958 | ||||||||
\(347\) | −31.6395 | −0.0911803 | −0.0455901 | − | 0.998960i | \(-0.514517\pi\) | ||||
−0.0455901 | + | 0.998960i | \(0.514517\pi\) | |||||||
\(348\) | 189.264 | − | 101.166i | 0.543863 | − | 0.290707i | ||||
\(349\) | 592.405 | 1.69744 | 0.848718 | − | 0.528846i | \(-0.177375\pi\) | ||||
0.848718 | + | 0.528846i | \(0.177375\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.54249 | + | 15.6654i | −0.00439455 | + | 0.0446307i | ||||
\(352\) | 82.3320i | 0.233898i | ||||||||
\(353\) | −621.977 | −1.76197 | −0.880987 | − | 0.473141i | \(-0.843120\pi\) | ||||
−0.880987 | + | 0.473141i | \(0.843120\pi\) | |||||||
\(354\) | 217.830 | − | 116.435i | 0.615339 | − | 0.328913i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 107.303i | 0.301412i | ||||||||
\(357\) | 150.757 | − | 80.5830i | 0.422289 | − | 0.225723i | ||||
\(358\) | − | 61.7490i | − | 0.172483i | ||||||
\(359\) | − | 499.509i | − | 1.39139i | −0.718337 | − | 0.695696i | \(-0.755096\pi\) | ||
0.718337 | − | 0.695696i | \(-0.244904\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −105.000 | −0.290859 | ||||||||
\(362\) | −114.671 | −0.316772 | ||||||||
\(363\) | 128.453 | + | 240.314i | 0.353865 | + | 0.662021i | ||||
\(364\) | 3.08497 | 0.00847520 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −77.8301 | − | 145.607i | −0.212650 | − | 0.397833i | ||||
\(367\) | 73.0039i | 0.198921i | 0.995042 | + | 0.0994604i | \(0.0317117\pi\) | ||||
−0.995042 | + | 0.0994604i | \(0.968288\pi\) | |||||||
\(368\) | −155.323 | −0.422074 | ||||||||
\(369\) | −65.4902 | − | 43.7575i | −0.177480 | − | 0.118584i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 134.700i | − | 0.363072i | ||||||
\(372\) | 165.343 | + | 309.328i | 0.444470 | + | 0.831527i | ||||
\(373\) | 474.664i | 1.27256i | 0.771459 | + | 0.636279i | \(0.219527\pi\) | ||||
−0.771459 | + | 0.636279i | \(0.780473\pi\) | |||||||
\(374\) | − | 443.290i | − | 1.18527i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | −0.0638298 | ||||||||
\(377\) | −20.8527 | −0.0553122 | ||||||||
\(378\) | 9.89949 | − | 100.539i | 0.0261891 | − | 0.265975i | ||||
\(379\) | 223.660 | 0.590132 | 0.295066 | − | 0.955477i | \(-0.404658\pi\) | ||||
0.295066 | + | 0.955477i | \(0.404658\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −71.6601 | + | 38.3039i | −0.188084 | + | 0.100535i | ||||
\(382\) | − | 75.7411i | − | 0.198275i | ||||||
\(383\) | 518.175 | 1.35294 | 0.676469 | − | 0.736471i | \(-0.263509\pi\) | ||||
0.676469 | + | 0.736471i | \(0.263509\pi\) | |||||||
\(384\) | −16.0000 | − | 29.9333i | −0.0416667 | − | 0.0779512i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 156.262i | 0.404824i | ||||||||
\(387\) | −87.9216 | − | 58.7451i | −0.227188 | − | 0.151796i | ||||
\(388\) | − | 222.332i | − | 0.573021i | ||||||
\(389\) | − | 44.1383i | − | 0.113466i | −0.998389 | − | 0.0567330i | \(-0.981932\pi\) | ||
0.998389 | − | 0.0567330i | \(-0.0180684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 836.288 | 2.13884 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | −385.073 | + | 205.830i | −0.979829 | + | 0.523741i | ||||
\(394\) | −121.830 | −0.309213 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −217.830 | − | 145.544i | −0.550076 | − | 0.367535i | ||||
\(397\) | 299.417i | 0.754199i | 0.926173 | + | 0.377099i | \(0.123079\pi\) | ||||
−0.926173 | + | 0.377099i | \(0.876921\pi\) | |||||||
\(398\) | 124.451 | 0.312690 | ||||||||
\(399\) | −112.000 | + | 59.8665i | −0.280702 | + | 0.150041i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 277.008i | 0.690794i | 0.938457 | + | 0.345397i | \(0.112256\pi\) | ||||
−0.938457 | + | 0.345397i | \(0.887744\pi\) | |||||||
\(402\) | 264.097 | − | 141.166i | 0.656959 | − | 0.351159i | ||||
\(403\) | − | 34.0810i | − | 0.0845683i | ||||||
\(404\) | 115.673i | 0.286320i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 133.830 | 0.329631 | ||||||||
\(407\) | −291.088 | −0.715203 | ||||||||
\(408\) | 86.1469 | + | 161.166i | 0.211144 | + | 0.395015i | ||||
\(409\) | 740.980 | 1.81169 | 0.905844 | − | 0.423612i | \(-0.139238\pi\) | ||||
0.905844 | + | 0.423612i | \(0.139238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35.0850 | − | 65.6380i | −0.0853649 | − | 0.159703i | ||||
\(412\) | 238.745i | 0.579478i | ||||||||
\(413\) | 154.029 | 0.372952 | ||||||||
\(414\) | 274.575 | − | 410.946i | 0.663225 | − | 0.992624i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.29798i | 0.00792783i | ||||||||
\(417\) | 207.122 | + | 387.490i | 0.496696 | + | 0.929233i | ||||
\(418\) | 329.328i | 0.787866i | ||||||||
\(419\) | − | 89.7998i | − | 0.214319i | −0.994242 | − | 0.107160i | \(-0.965824\pi\) | ||
0.994242 | − | 0.107160i | \(-0.0341756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 281.150 | 0.667815 | 0.333908 | − | 0.942606i | \(-0.391633\pi\) | ||||
0.333908 | + | 0.942606i | \(0.391633\pi\) | |||||||
\(422\) | −86.6275 | −0.205279 | ||||||||
\(423\) | 42.4264 | − | 63.4980i | 0.100299 | − | 0.150114i | ||||
\(424\) | 144.000 | 0.339623 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 63.7124 | − | 34.0557i | 0.149560 | − | 0.0799430i | ||||
\(427\) | − | 102.959i | − | 0.241123i | ||||||
\(428\) | −232.985 | −0.544357 | ||||||||
\(429\) | 12.0000 | + | 22.4499i | 0.0279720 | + | 0.0523309i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 560.200i | 1.29977i | 0.760033 | + | 0.649885i | \(0.225183\pi\) | ||||
−0.760033 | + | 0.649885i | \(0.774817\pi\) | |||||||
\(432\) | 107.480 | + | 10.5830i | 0.248797 | + | 0.0244977i | ||||
\(433\) | 543.004i | 1.25405i | 0.778999 | + | 0.627025i | \(0.215728\pi\) | ||||
−0.778999 | + | 0.627025i | \(0.784272\pi\) | |||||||
\(434\) | 218.728i | 0.503982i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −175.660 | −0.402890 | ||||||||
\(437\) | −621.293 | −1.42172 | ||||||||
\(438\) | −270.642 | + | 144.664i | −0.617903 | + | 0.330283i | ||||
\(439\) | −342.170 | −0.779430 | −0.389715 | − | 0.920935i | \(-0.627427\pi\) | ||||
−0.389715 | + | 0.920935i | \(0.627427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 35.0000 | − | 52.3832i | 0.0793651 | − | 0.118783i | ||||
\(442\) | − | 17.7569i | − | 0.0401740i | ||||||
\(443\) | −399.816 | −0.902519 | −0.451259 | − | 0.892393i | \(-0.649025\pi\) | ||||
−0.451259 | + | 0.892393i | \(0.649025\pi\) | |||||||
\(444\) | 105.830 | − | 56.5685i | 0.238356 | − | 0.127407i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 212.831i | − | 0.477199i | ||||||
\(447\) | 580.881 | − | 310.494i | 1.29951 | − | 0.694618i | ||||
\(448\) | − | 21.1660i | − | 0.0472456i | ||||||
\(449\) | 737.040i | 1.64151i | 0.571277 | + | 0.820757i | \(0.306448\pi\) | ||||
−0.571277 | + | 0.820757i | \(0.693552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −127.373 | −0.282422 | ||||||||
\(452\) | −138.353 | −0.306090 | ||||||||
\(453\) | 299.333 | + | 560.000i | 0.660778 | + | 1.23620i | ||||
\(454\) | −269.490 | −0.593591 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −64.0000 | − | 119.733i | −0.140351 | − | 0.262572i | ||||
\(457\) | 665.336i | 1.45588i | 0.685642 | + | 0.727939i | \(0.259521\pi\) | ||||
−0.685642 | + | 0.727939i | \(0.740479\pi\) | |||||||
\(458\) | 202.112 | 0.441293 | ||||||||
\(459\) | −578.693 | − | 56.9808i | −1.26077 | − | 0.124141i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 318.865i | − | 0.691682i | −0.938293 | − | 0.345841i | \(-0.887594\pi\) | ||
0.938293 | − | 0.345841i | \(-0.112406\pi\) | |||||||
\(462\) | −77.0146 | − | 144.081i | −0.166698 | − | 0.311864i | ||||
\(463\) | − | 402.332i | − | 0.868968i | −0.900680 | − | 0.434484i | \(-0.856931\pi\) | ||
0.900680 | − | 0.434484i | \(-0.143069\pi\) | |||||||
\(464\) | 143.070i | 0.308341i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.0850 | 0.0237875 | ||||||||
\(467\) | 697.087 | 1.49269 | 0.746346 | − | 0.665558i | \(-0.231806\pi\) | ||||
0.746346 | + | 0.665558i | \(0.231806\pi\) | |||||||
\(468\) | −8.72562 | − | 5.83005i | −0.0186445 | − | 0.0124574i | ||||
\(469\) | 186.745 | 0.398177 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 552.288 | − | 295.210i | 1.17259 | − | 0.626773i | ||||
\(472\) | 164.664i | 0.348864i | ||||||||
\(473\) | −171.000 | −0.361522 | ||||||||
\(474\) | 41.8301 | + | 78.2569i | 0.0882491 | + | 0.165099i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 113.962i | 0.239415i | ||||||||
\(477\) | −254.558 | + | 380.988i | −0.533665 | + | 0.798717i | ||||
\(478\) | − | 301.749i | − | 0.631274i | ||||||
\(479\) | 163.808i | 0.341980i | 0.985273 | + | 0.170990i | \(0.0546966\pi\) | ||||
−0.985273 | + | 0.170990i | \(0.945303\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.6601 | −0.0242414 | ||||||||
\(482\) | −183.848 | −0.381427 | ||||||||
\(483\) | 271.816 | − | 145.292i | 0.562765 | − | 0.300811i | ||||
\(484\) | −181.660 | −0.375331 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −218.000 | + | 265.658i | −0.448560 | + | 0.546621i | ||||
\(487\) | − | 103.498i | − | 0.212522i | −0.994338 | − | 0.106261i | \(-0.966112\pi\) | ||
0.994338 | − | 0.106261i | \(-0.0338878\pi\) | |||||||
\(488\) | 110.068 | 0.225550 | ||||||||
\(489\) | −706.405 | + | 377.589i | −1.44459 | + | 0.772167i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 570.094i | 1.16109i | 0.814229 | + | 0.580544i | \(0.197160\pi\) | ||||
−0.814229 | + | 0.580544i | \(0.802840\pi\) | |||||||
\(492\) | 46.3085 | − | 24.7530i | 0.0941230 | − | 0.0503109i | ||||
\(493\) | − | 770.316i | − | 1.56251i | ||||||
\(494\) | 13.1919i | 0.0267043i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −233.830 | −0.471432 | ||||||||
\(497\) | 45.0515 | 0.0906469 | ||||||||
\(498\) | −291.088 | − | 544.575i | −0.584513 | − | 1.09352i | ||||
\(499\) | 487.660 | 0.977275 | 0.488637 | − | 0.872487i | \(-0.337494\pi\) | ||||
0.488637 | + | 0.872487i | \(0.337494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1699 | + | 19.0262i | 0.0202993 | + | 0.0379765i | ||||
\(502\) | − | 550.494i | − | 1.09660i | ||||||
\(503\) | 97.9412 | 0.194714 | 0.0973571 | − | 0.995250i | \(-0.468961\pi\) | ||||
0.0973571 | + | 0.995250i | \(0.468961\pi\) | |||||||
\(504\) | 56.0000 | + | 37.4166i | 0.111111 | + | 0.0742392i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 799.254i | − | 1.57955i | ||||||
\(507\) | −238.521 | − | 446.233i | −0.470456 | − | 0.880143i | ||||
\(508\) | − | 54.1699i | − | 0.106634i | ||||||
\(509\) | − | 318.104i | − | 0.624958i | −0.949925 | − | 0.312479i | \(-0.898841\pi\) | ||
0.949925 | − | 0.312479i | \(-0.101159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −191.373 | −0.374506 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 429.921 | + | 42.3320i | 0.838052 | + | 0.0825186i | ||||
\(514\) | −475.373 | −0.924849 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 62.1699 | − | 33.2312i | 0.120484 | − | 0.0644016i | ||||
\(517\) | − | 123.498i | − | 0.238874i | ||||||
\(518\) | 74.8331 | 0.144466 | ||||||||
\(519\) | −272.288 | − | 509.403i | −0.524639 | − | 0.981509i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 727.150i | 1.39568i | 0.716253 | + | 0.697840i | \(0.245856\pi\) | ||||
−0.716253 | + | 0.697840i | \(0.754144\pi\) | |||||||
\(522\) | −378.529 | − | 252.915i | −0.725150 | − | 0.484512i | ||||
\(523\) | 207.624i | 0.396986i | 0.980102 | + | 0.198493i | \(0.0636047\pi\) | ||||
−0.980102 | + | 0.198493i | \(0.936395\pi\) | |||||||
\(524\) | − | 291.088i | − | 0.555511i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −620.745 | −1.18012 | ||||||||
\(527\) | 1258.98 | 2.38896 | ||||||||
\(528\) | 154.029 | − | 82.3320i | 0.291722 | − | 0.155932i | ||||
\(529\) | 978.830 | 1.85034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −435.660 | − | 291.088i | −0.820452 | − | 0.548188i | ||||
\(532\) | − | 84.6640i | − | 0.159143i | ||||||
\(533\) | −5.10216 | −0.00957254 | ||||||||
\(534\) | 200.745 | − | 107.303i | 0.375927 | − | 0.200941i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 199.639i | 0.372461i | ||||||||
\(537\) | −115.522 | + | 61.7490i | −0.215124 | + | 0.114989i | ||||
\(538\) | 20.4496i | 0.0380105i | ||||||||
\(539\) | − | 101.881i | − | 0.189018i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1025.15 | 1.89492 | 0.947459 | − | 0.319878i | \(-0.103642\pi\) | ||||
0.947459 | + | 0.319878i | \(0.103642\pi\) | |||||||
\(542\) | 87.0342 | 0.160580 | ||||||||
\(543\) | 114.671 | + | 214.531i | 0.211181 | + | 0.395084i | ||||
\(544\) | −121.830 | −0.223952 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.08497 | − | 5.77146i | −0.00565014 | − | 0.0105704i | ||||
\(547\) | − | 560.089i | − | 1.02393i | −0.859007 | − | 0.511964i | \(-0.828918\pi\) | ||
0.859007 | − | 0.511964i | \(-0.171082\pi\) | |||||||
\(548\) | 49.6176 | 0.0905431 | ||||||||
\(549\) | −194.575 | + | 291.213i | −0.354417 | + | 0.530443i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 572.281i | 1.03862i | ||||||||
\(552\) | 155.323 | + | 290.583i | 0.281383 | + | 0.526418i | ||||
\(553\) | 55.3360i | 0.100065i | ||||||||
\(554\) | 212.831i | 0.384171i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −292.915 | −0.526826 | ||||||||
\(557\) | −575.705 | −1.03358 | −0.516791 | − | 0.856112i | \(-0.672874\pi\) | ||||
−0.516791 | + | 0.856112i | \(0.672874\pi\) | |||||||
\(558\) | 413.357 | − | 618.656i | 0.740783 | − | 1.10870i | ||||
\(559\) | −6.84974 | −0.0122536 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −829.320 | + | 443.290i | −1.47829 | + | 0.790179i | ||||
\(562\) | 424.575i | 0.755472i | ||||||||
\(563\) | −468.558 | −0.832251 | −0.416126 | − | 0.909307i | \(-0.636612\pi\) | ||||
−0.416126 | + | 0.909307i | \(0.636612\pi\) | |||||||
\(564\) | 24.0000 | + | 44.8999i | 0.0425532 | + | 0.0796097i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 139.772i | − | 0.246948i | ||||||
\(567\) | −197.990 | + | 82.0183i | −0.349189 | + | 0.144653i | ||||
\(568\) | 48.1621i | 0.0847924i | ||||||||
\(569\) | 506.455i | 0.890079i | 0.895511 | + | 0.445039i | \(0.146810\pi\) | ||||
−0.895511 | + | 0.445039i | \(0.853190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.9150 | 0.0576445 | 0.0288223 | − | 0.999585i | \(-0.490824\pi\) | ||||
0.0288223 | + | 0.999585i | \(0.490824\pi\) | |||||||
\(572\) | −16.9706 | −0.0296688 | ||||||||
\(573\) | −141.699 | + | 75.7411i | −0.247293 | + | 0.132183i | ||||
\(574\) | 32.7451 | 0.0570472 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −40.0000 | + | 59.8665i | −0.0694444 | + | 0.103935i | ||||
\(577\) | − | 252.154i | − | 0.437009i | −0.975836 | − | 0.218505i | \(-0.929882\pi\) | ||
0.975836 | − | 0.218505i | \(-0.0701178\pi\) | |||||||
\(578\) | 247.247 | 0.427763 | ||||||||
\(579\) | 292.340 | − | 156.262i | 0.504905 | − | 0.269883i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 385.073i | − | 0.662776i | ||||||
\(582\) | −415.945 | + | 222.332i | −0.714682 | + | 0.382014i | ||||
\(583\) | 740.988i | 1.27099i | ||||||||
\(584\) | − | 204.586i | − | 0.350318i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.1176 | 0.0172656 | ||||||||
\(587\) | −366.882 | −0.625012 | −0.312506 | − | 0.949916i | \(-0.601168\pi\) | ||||
−0.312506 | + | 0.949916i | \(0.601168\pi\) | |||||||
\(588\) | 19.7990 | + | 37.0405i | 0.0336718 | + | 0.0629941i | ||||
\(589\) | −935.320 | −1.58798 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 121.830 | + | 227.923i | 0.206142 | + | 0.385657i | ||||
\(592\) | 80.0000i | 0.135135i | ||||||||
\(593\) | −620.757 | −1.04681 | −0.523404 | − | 0.852085i | \(-0.675338\pi\) | ||||
−0.523404 | + | 0.852085i | \(0.675338\pi\) | |||||||
\(594\) | −54.4575 | + | 553.067i | −0.0916793 | + | 0.931088i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 439.105i | 0.736753i | ||||||||
\(597\) | −124.451 | − | 232.826i | −0.208460 | − | 0.389993i | ||||
\(598\) | − | 32.0157i | − | 0.0535380i | ||||||
\(599\) | 26.3488i | 0.0439879i | 0.999758 | + | 0.0219940i | \(0.00700146\pi\) | ||||
−0.999758 | + | 0.0219940i | \(0.992999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 930.470 | 1.54820 | 0.774102 | − | 0.633061i | \(-0.218202\pi\) | ||||
0.774102 | + | 0.633061i | \(0.218202\pi\) | |||||||
\(602\) | 43.9608 | 0.0730246 | ||||||||
\(603\) | −528.195 | − | 352.915i | −0.875945 | − | 0.585265i | ||||
\(604\) | −423.320 | −0.700861 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 216.405 | − | 115.673i | 0.357104 | − | 0.190880i | ||||
\(607\) | 216.146i | 0.356089i | 0.984022 | + | 0.178045i | \(0.0569772\pi\) | ||||
−0.984022 | + | 0.178045i | \(0.943023\pi\) | |||||||
\(608\) | 90.5097 | 0.148865 | ||||||||
\(609\) | −133.830 | − | 250.373i | −0.219754 | − | 0.411122i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.94696i | − | 0.00809650i | ||||||
\(612\) | 215.367 | − | 322.332i | 0.351907 | − | 0.526686i | ||||
\(613\) | 268.834i | 0.438555i | 0.975663 | + | 0.219277i | \(0.0703699\pi\) | ||||
−0.975663 | + | 0.219277i | \(0.929630\pi\) | |||||||
\(614\) | 149.666i | 0.243756i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 108.915 | 0.176810 | ||||||||
\(617\) | 531.338 | 0.861163 | 0.430582 | − | 0.902552i | \(-0.358308\pi\) | ||||
0.430582 | + | 0.902552i | \(0.358308\pi\) | |||||||
\(618\) | 446.651 | − | 238.745i | 0.722736 | − | 0.386319i | ||||
\(619\) | −425.203 | −0.686919 | −0.343459 | − | 0.939168i | \(-0.611599\pi\) | ||||
−0.343459 | + | 0.939168i | \(0.611599\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1043.39 | − | 102.737i | −1.68017 | − | 0.165437i | ||||
\(622\) | − | 375.336i | − | 0.603434i | ||||||
\(623\) | 141.948 | 0.227846 | ||||||||
\(624\) | 6.16995 | − | 3.29798i | 0.00988774 | − | 0.00528522i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 366.745i | − | 0.585855i | ||||||
\(627\) | 616.116 | − | 329.328i | 0.982642 | − | 0.525244i | ||||
\(628\) | 417.490i | 0.664793i | ||||||||
\(629\) | − | 430.734i | − | 0.684792i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −453.490 | −0.718685 | −0.359342 | − | 0.933206i | \(-0.616999\pi\) | ||||
−0.359342 | + | 0.933206i | \(0.616999\pi\) | |||||||
\(632\) | −59.1566 | −0.0936023 | ||||||||
\(633\) | 86.6275 | + | 162.065i | 0.136852 | + | 0.256027i | ||||
\(634\) | −53.4902 | −0.0843693 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −144.000 | − | 269.399i | −0.226415 | − | 0.423584i | ||||
\(637\) | − | 4.08104i | − | 0.00640665i | ||||||
\(638\) | −736.204 | −1.15393 | ||||||||
\(639\) | −127.425 | − | 85.1393i | −0.199413 | − | 0.133238i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 463.455i | − | 0.723019i | −0.932368 | − | 0.361510i | \(-0.882261\pi\) | ||
0.932368 | − | 0.361510i | \(-0.117739\pi\) | |||||||
\(642\) | 232.985 | + | 435.875i | 0.362905 | + | 0.678932i | ||||
\(643\) | − | 820.988i | − | 1.27681i | −0.769701 | − | 0.638405i | \(-0.779595\pi\) | ||
0.769701 | − | 0.638405i | \(-0.220405\pi\) | |||||||
\(644\) | 205.473i | 0.319058i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −487.320 | −0.754366 | ||||||||
\(647\) | −996.660 | −1.54043 | −0.770216 | − | 0.637783i | \(-0.779852\pi\) | ||||
−0.770216 | + | 0.637783i | \(0.779852\pi\) | |||||||
\(648\) | −87.6812 | − | 211.660i | −0.135311 | − | 0.326636i | ||||
\(649\) | −847.320 | −1.30558 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 409.203 | − | 218.728i | 0.628575 | − | 0.335988i | ||||
\(652\) | − | 533.992i | − | 0.819006i | ||||||
\(653\) | 357.602 | 0.547629 | 0.273815 | − | 0.961782i | \(-0.411715\pi\) | ||||
0.273815 | + | 0.961782i | \(0.411715\pi\) | |||||||
\(654\) | 175.660 | + | 328.630i | 0.268593 | + | 0.502492i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 35.0060i | 0.0533627i | ||||||||
\(657\) | 541.283 | + | 361.660i | 0.823871 | + | 0.550472i | ||||
\(658\) | 31.7490i | 0.0482508i | ||||||||
\(659\) | − | 131.562i | − | 0.199640i | −0.995006 | − | 0.0998198i | \(-0.968173\pi\) | ||
0.995006 | − | 0.0998198i | \(-0.0318266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −250.915 | −0.379599 | −0.189800 | − | 0.981823i | \(-0.560784\pi\) | ||||
−0.189800 | + | 0.981823i | \(0.560784\pi\) | |||||||
\(662\) | 205.754 | 0.310807 | ||||||||
\(663\) | −33.2201 | + | 17.7569i | −0.0501057 | + | 0.0267826i | ||||
\(664\) | 411.660 | 0.619970 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −211.660 | − | 141.421i | −0.317808 | − | 0.212344i | ||||
\(667\) | − | 1388.88i | − | 2.08228i | ||||||
\(668\) | −14.3825 | −0.0215307 | ||||||||
\(669\) | −398.170 | + | 212.831i | −0.595172 | + | 0.318133i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 566.384i | 0.844090i | ||||||||
\(672\) | −39.5980 | + | 21.1660i | −0.0589256 | + | 0.0314970i | ||||
\(673\) | − | 196.502i | − | 0.291979i | −0.989286 | − | 0.145990i | \(-0.953363\pi\) | ||
0.989286 | − | 0.145990i | \(-0.0466366\pi\) | |||||||
\(674\) | − | 848.975i | − | 1.25961i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 337.320 | 0.498994 | ||||||||
\(677\) | 54.1838 | 0.0800352 | 0.0400176 | − | 0.999199i | \(-0.487259\pi\) | ||||
0.0400176 | + | 0.999199i | \(0.487259\pi\) | |||||||
\(678\) | 138.353 | + | 258.834i | 0.204060 | + | 0.381761i | ||||
\(679\) | −294.118 | −0.433163 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 269.490 | + | 504.170i | 0.395727 | + | 0.740338i | ||||
\(682\) | − | 1203.23i | − | 1.76427i | ||||||
\(683\) | 749.006 | 1.09664 | 0.548321 | − | 0.836268i | \(-0.315267\pi\) | ||||
0.548321 | + | 0.836268i | \(0.315267\pi\) | |||||||
\(684\) | −160.000 | + | 239.466i | −0.233918 | + | 0.350097i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | −202.112 | − | 378.118i | −0.294196 | − | 0.550390i | ||||
\(688\) | 46.9961i | 0.0683082i | ||||||||
\(689\) | 29.6818i | 0.0430795i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 475.137 | 0.687608 | 0.343804 | − | 0.939041i | \(-0.388284\pi\) | ||||
0.343804 | + | 0.939041i | \(0.388284\pi\) | |||||||
\(692\) | 385.073 | 0.556464 | ||||||||
\(693\) | −192.536 | + | 288.162i | −0.277830 | + | 0.415818i | ||||
\(694\) | −44.7451 | −0.0644742 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 267.660 | − | 143.070i | 0.384569 | − | 0.205561i | ||||
\(697\) | − | 188.478i | − | 0.270414i | ||||||
\(698\) | 837.787 | 1.20027 | ||||||||
\(699\) | −11.0850 | − | 20.7381i | −0.0158583 | − | 0.0296682i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1251.49i | 1.78529i | 0.450760 | + | 0.892645i | \(0.351153\pi\) | ||||
−0.450760 | + | 0.892645i | \(0.648847\pi\) | |||||||
\(702\) | −2.18141 | + | 22.1542i | −0.00310742 | + | 0.0315587i | ||||
\(703\) | 320.000i | 0.455192i | ||||||||
\(704\) | 116.435i | 0.165391i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −879.608 | −1.24590 | ||||||||
\(707\) | 153.022 | 0.216438 | ||||||||
\(708\) | 308.058 | − | 164.664i | 0.435110 | − | 0.232576i | ||||
\(709\) | 16.5098 | 0.0232861 | 0.0116430 | − | 0.999932i | \(-0.496294\pi\) | ||||
0.0116430 | + | 0.999932i | \(0.496294\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 104.575 | − | 156.514i | 0.147082 | − | 0.220132i | ||||
\(712\) | 151.749i | 0.213131i | ||||||||
\(713\) | 2269.95 | 3.18366 | ||||||||
\(714\) | 213.203 | − | 113.962i | 0.298603 | − | 0.159610i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 87.3263i | − | 0.121964i | ||||||
\(717\) | −564.521 | + | 301.749i | −0.787337 | + | 0.420849i | ||||
\(718\) | − | 706.413i | − | 0.983862i | ||||||
\(719\) | 1327.59i | 1.84643i | 0.384279 | + | 0.923217i | \(0.374450\pi\) | ||||
−0.384279 | + | 0.923217i | \(0.625550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 315.830 | 0.438044 | ||||||||
\(722\) | −148.492 | −0.205668 | ||||||||
\(723\) | 183.848 | + | 343.948i | 0.254285 | + | 0.475723i | ||||
\(724\) | −162.170 | −0.223992 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 181.660 | + | 339.855i | 0.250221 | + | 0.468120i | ||||
\(727\) | − | 202.782i | − | 0.278929i | −0.990227 | − | 0.139465i | \(-0.955462\pi\) | ||
0.990227 | − | 0.139465i | \(-0.0445382\pi\) | |||||||
\(728\) | 4.36281 | 0.00599287 | ||||||||
\(729\) | 715.000 | + | 142.183i | 0.980796 | + | 0.195038i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 253.035i | − | 0.346149i | ||||||
\(732\) | −110.068 | − | 205.919i | −0.150367 | − | 0.281310i | ||||
\(733\) | 582.559i | 0.794760i | 0.917654 | + | 0.397380i | \(0.130081\pi\) | ||||
−0.917654 | + | 0.397380i | \(0.869919\pi\) | |||||||
\(734\) | 103.243i | 0.140658i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −219.660 | −0.298451 | ||||||||
\(737\) | −1027.29 | −1.39388 | ||||||||
\(738\) | −92.6171 | − | 61.8824i | −0.125497 | − | 0.0838515i | ||||
\(739\) | 256.810 | 0.347511 | 0.173755 | − | 0.984789i | \(-0.444410\pi\) | ||||
0.173755 | + | 0.984789i | \(0.444410\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.6798 | − | 13.1919i | 0.0333061 | − | 0.0178028i | ||||
\(742\) | − | 190.494i | − | 0.256731i | ||||||
\(743\) | −573.256 | −0.771542 | −0.385771 | − | 0.922595i | \(-0.626064\pi\) | ||||
−0.385771 | + | 0.922595i | \(0.626064\pi\) | |||||||
\(744\) | 233.830 | + | 437.456i | 0.314288 | + | 0.587978i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 671.276i | 0.899834i | ||||||||
\(747\) | −727.719 | + | 1089.15i | −0.974189 | + | 1.45803i | ||||
\(748\) | − | 626.907i | − | 0.838111i | ||||||
\(749\) | 308.210i | 0.411495i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −579.085 | −0.771085 | −0.385543 | − | 0.922690i | \(-0.625986\pi\) | ||||
−0.385543 | + | 0.922690i | \(0.625986\pi\) | |||||||
\(752\) | −33.9411 | −0.0451345 | ||||||||
\(753\) | −1029.88 | + | 550.494i | −1.36770 | + | 0.731068i | ||||
\(754\) | −29.4902 | −0.0391116 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.0000 | − | 142.183i | 0.0185185 | − | 0.188073i | ||||
\(757\) | 1167.13i | 1.54179i | 0.636963 | + | 0.770895i | \(0.280191\pi\) | ||||
−0.636963 | + | 0.770895i | \(0.719809\pi\) | |||||||
\(758\) | 316.303 | 0.417286 | ||||||||
\(759\) | −1495.27 | + | 799.254i | −1.97005 | + | 1.05304i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 800.970i | − | 1.05252i | −0.850323 | − | 0.526261i | \(-0.823593\pi\) | ||
0.850323 | − | 0.526261i | \(-0.176407\pi\) | |||||||
\(762\) | −101.343 | + | 54.1699i | −0.132996 | + | 0.0710892i | ||||
\(763\) | 232.376i | 0.304556i | ||||||||
\(764\) | − | 107.114i | − | 0.140202i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 732.810 | 0.956671 | ||||||||
\(767\) | −33.9411 | −0.0442518 | ||||||||
\(768\) | −22.6274 | − | 42.3320i | −0.0294628 | − | 0.0551198i | ||||
\(769\) | 242.680 | 0.315578 | 0.157789 | − | 0.987473i | \(-0.449563\pi\) | ||||
0.157789 | + | 0.987473i | \(0.449563\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 475.373 | + | 889.341i | 0.616566 | + | 1.15349i | ||||
\(772\) | 220.988i | 0.286254i | ||||||||
\(773\) | −1262.83 | −1.63367 | −0.816836 | − | 0.576870i | \(-0.804274\pi\) | ||||
−0.816836 | + | 0.576870i | \(0.804274\pi\) | |||||||
\(774\) | −124.340 | − | 83.0781i | −0.160646 | − | 0.107336i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 314.425i | − | 0.405187i | ||||||
\(777\) | −74.8331 | − | 140.000i | −0.0963104 | − | 0.180180i | ||||
\(778\) | − | 62.4209i | − | 0.0802326i | ||||||
\(779\) | 140.024i | 0.179748i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −247.830 | −0.317324 | ||||||||
\(782\) | 1182.69 | 1.51239 | ||||||||
\(783\) | −94.6321 | + | 961.077i | −0.120858 | + | 1.22743i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −544.575 | + | 291.088i | −0.692844 | + | 0.370341i | ||||
\(787\) | 1347.00i | 1.71156i | 0.517336 | + | 0.855782i | \(0.326924\pi\) | ||||
−0.517336 | + | 0.855782i | \(0.673076\pi\) | |||||||
\(788\) | −172.294 | −0.218647 | ||||||||
\(789\) | 620.745 | + | 1161.31i | 0.786749 | + | 1.47187i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 183.023i | 0.231382i | ||||||||
\(792\) | −308.058 | − | 205.830i | −0.388962 | − | 0.259886i | ||||
\(793\) | 22.6877i | 0.0286099i | ||||||||
\(794\) | 423.440i | 0.533299i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 176.000 | 0.221106 | ||||||||
\(797\) | 1210.62 | 1.51897 | 0.759487 | − | 0.650523i | \(-0.225450\pi\) | ||||
0.759487 | + | 0.650523i | \(0.225450\pi\) | |||||||
\(798\) | −158.392 | + | 84.6640i | −0.198486 | + | 0.106095i | ||||
\(799\) | 182.745 | 0.228717 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −401.490 | − | 268.257i | −0.501236 | − | 0.334902i | ||||
\(802\) | 391.749i | 0.488465i | ||||||||
\(803\) | 1052.75 | 1.31102 | ||||||||
\(804\) | 373.490 | − | 199.639i | 0.464540 | − | 0.248307i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 48.1979i | − | 0.0597988i | ||||||
\(807\) | 38.2578 | − | 20.4496i | 0.0474074 | − | 0.0253403i | ||||
\(808\) | 163.587i | 0.202459i | ||||||||
\(809\) | − | 310.876i | − | 0.384271i | −0.981368 | − | 0.192136i | \(-0.938459\pi\) | ||
0.981368 | − | 0.192136i | \(-0.0615414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −65.7777 | −0.0811069 | −0.0405535 | − | 0.999177i | \(-0.512912\pi\) | ||||
−0.0405535 | + | 0.999177i | \(0.512912\pi\) | |||||||
\(812\) | 189.264 | 0.233084 | ||||||||
\(813\) | −87.0342 | − | 162.826i | −0.107053 | − | 0.200278i | ||||
\(814\) | −411.660 | −0.505725 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 121.830 | + | 227.923i | 0.149302 | + | 0.279318i | ||||
\(817\) | 187.984i | 0.230091i | ||||||||
\(818\) | 1047.90 | 1.28106 | ||||||||
\(819\) | −7.71243 | + | 11.5429i | −0.00941689 | + | 0.0140939i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 370.994i | − | 0.451880i | −0.974141 | − | 0.225940i | \(-0.927455\pi\) | ||
0.974141 | − | 0.225940i | \(-0.0725453\pi\) | |||||||
\(822\) | −49.6176 | − | 92.8261i | −0.0603621 | − | 0.112927i | ||||
\(823\) | − | 441.077i | − | 0.535938i | −0.963428 | − | 0.267969i | \(-0.913647\pi\) | ||
0.963428 | − | 0.267969i | \(-0.0863525\pi\) | |||||||
\(824\) | 337.637i | 0.409753i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 217.830 | 0.263717 | ||||||||
\(827\) | 116.492 | 0.140861 | 0.0704307 | − | 0.997517i | \(-0.477563\pi\) | ||||
0.0704307 | + | 0.997517i | \(0.477563\pi\) | |||||||
\(828\) | 388.308 | − | 581.166i | 0.468971 | − | 0.701891i | ||||
\(829\) | 881.425 | 1.06324 | 0.531619 | − | 0.846983i | \(-0.321584\pi\) | ||||
0.531619 | + | 0.846983i | \(0.321584\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 398.170 | − | 212.831i | 0.479146 | − | 0.256114i | ||||
\(832\) | 4.66404i | 0.00560582i | ||||||||
\(833\) | 150.757 | 0.180981 | ||||||||
\(834\) | 292.915 | + | 547.994i | 0.351217 | + | 0.657067i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 465.740i | 0.557106i | ||||||||
\(837\) | −1570.76 | − | 154.664i | −1.87665 | − | 0.184784i | ||||
\(838\) | − | 126.996i | − | 0.151547i | ||||||
\(839\) | 1346.42i | 1.60480i | 0.596789 | + | 0.802398i | \(0.296443\pi\) | ||||
−0.596789 | + | 0.802398i | \(0.703557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −438.320 | −0.521189 | ||||||||
\(842\) | 397.607 | 0.472217 | ||||||||
\(843\) | 794.307 | − | 424.575i | 0.942239 | − | 0.503648i | ||||
\(844\) | −122.510 | −0.145154 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 60.0000 | − | 89.7998i | 0.0709220 | − | 0.106146i | ||||
\(847\) | 240.314i | 0.283723i | ||||||||
\(848\) | 203.647 | 0.240149 | ||||||||
\(849\) | −261.490 | + | 139.772i | −0.307998 | + | 0.164632i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 776.616i | − | 0.912592i | ||||||
\(852\) | 90.1030 | − | 48.1621i | 0.105755 | − | 0.0565283i | ||||
\(853\) | 966.235i | 1.13275i | 0.824148 | + | 0.566375i | \(0.191654\pi\) | ||||
−0.824148 | + | 0.566375i | \(0.808346\pi\) | |||||||
\(854\) | − | 145.607i | − | 0.170500i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −329.490 | −0.384918 | ||||||||
\(857\) | 982.241 | 1.14614 | 0.573069 | − | 0.819507i | \(-0.305753\pi\) | ||||
0.573069 | + | 0.819507i | \(0.305753\pi\) | |||||||
\(858\) | 16.9706 | + | 31.7490i | 0.0197792 | + | 0.0370035i | ||||
\(859\) | −1309.49 | −1.52444 | −0.762218 | − | 0.647321i | \(-0.775889\pi\) | ||||
−0.762218 | + | 0.647321i | \(0.775889\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.7451 | − | 61.2604i | −0.0380315 | − | 0.0711503i | ||||
\(862\) | 792.243i | 0.919076i | ||||||||
\(863\) | 1001.55 | 1.16054 | 0.580272 | − | 0.814423i | \(-0.302946\pi\) | ||||
0.580272 | + | 0.814423i | \(0.302946\pi\) | |||||||
\(864\) | 152.000 | + | 14.9666i | 0.175926 | + | 0.0173225i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 767.924i | 0.886748i | ||||||||
\(867\) | −247.247 | − | 462.557i | −0.285175 | − | 0.533514i | ||||
\(868\) | 309.328i | 0.356369i | ||||||||
\(869\) | − | 304.405i | − | 0.350294i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.1503 | −0.0472448 | ||||||||
\(872\) | −248.421 | −0.284886 | ||||||||
\(873\) | 831.890 | + | 555.830i | 0.952910 | + | 0.636690i | ||||
\(874\) | −878.640 | −1.00531 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −382.745 | + | 204.586i | −0.436924 | + | 0.233545i | ||||
\(877\) | − | 33.1424i | − | 0.0377906i | −0.999821 | − | 0.0188953i | \(-0.993985\pi\) | ||
0.999821 | − | 0.0188953i | \(-0.00601492\pi\) | |||||||
\(878\) | −483.901 | −0.551141 | ||||||||
\(879\) | −10.1176 | − | 18.9283i | −0.0115104 | − | 0.0215339i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 944.040i | − | 1.07156i | −0.844359 | − | 0.535778i | \(-0.820019\pi\) | ||
0.844359 | − | 0.535778i | \(-0.179981\pi\) | |||||||
\(882\) | 49.4975 | − | 74.0810i | 0.0561196 | − | 0.0839921i | ||||
\(883\) | − | 55.5138i | − | 0.0628695i | −0.999506 | − | 0.0314348i | \(-0.989992\pi\) | ||
0.999506 | − | 0.0314348i | \(-0.0100076\pi\) | |||||||
\(884\) | − | 25.1120i | − | 0.0284073i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −565.425 | −0.638177 | ||||||||
\(887\) | 20.1317 | 0.0226964 | 0.0113482 | − | 0.999936i | \(-0.496388\pi\) | ||||
0.0113482 | + | 0.999936i | \(0.496388\pi\) | |||||||
\(888\) | 149.666 | − | 80.0000i | 0.168543 | − | 0.0900901i | ||||
\(889\) | −71.6601 | −0.0806075 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1089.15 | − | 451.186i | 1.22239 | − | 0.506381i | ||||
\(892\) | − | 300.988i | − | 0.337431i | ||||||
\(893\) | −135.765 | −0.152032 | ||||||||
\(894\) | 821.490 | − | 439.105i | 0.918893 | − | 0.491169i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | −59.8960 | + | 32.0157i | −0.0667737 | + | 0.0356920i | ||||
\(898\) | 1042.33i | 1.16073i | ||||||||
\(899\) | − | 2090.88i | − | 2.32579i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1096.47 | −1.21695 | ||||||||
\(902\) | −180.132 | −0.199703 | ||||||||
\(903\) | −43.9608 | − | 82.2431i | −0.0486830 | − | 0.0910776i | ||||
\(904\) | −195.660 | −0.216438 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 423.320 | + | 791.960i | 0.467241 | + | 0.874128i | ||||
\(907\) | 219.644i | 0.242166i | 0.992642 | + | 0.121083i | \(0.0386367\pi\) | ||||
−0.992642 | + | 0.121083i | \(0.961363\pi\) | |||||||
\(908\) | −381.117 | −0.419732 | ||||||||
\(909\) | −432.810 | − | 289.184i | −0.476139 | − | 0.318134i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 827.126i | 0.907932i | 0.891019 | + | 0.453966i | \(0.149991\pi\) | ||||
−0.891019 | + | 0.453966i | \(0.850009\pi\) | |||||||
\(912\) | −90.5097 | − | 169.328i | −0.0992431 | − | 0.185667i | ||||
\(913\) | 2118.30i | 2.32015i | ||||||||
\(914\) | 940.927i | 1.02946i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 285.830 | 0.312042 | ||||||||
\(917\) | −385.073 | −0.419927 | ||||||||
\(918\) | −818.395 | − | 80.5830i | −0.891498 | − | 0.0877811i | ||||
\(919\) | 1029.39 | 1.12011 | 0.560057 | − | 0.828454i | \(-0.310779\pi\) | ||||
0.560057 | + | 0.828454i | \(0.310779\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 280.000 | − | 149.666i | 0.304017 | − | 0.162504i | ||||
\(922\) | − | 450.944i | − | 0.489093i | ||||||
\(923\) | −9.92733 | −0.0107555 | ||||||||
\(924\) | −108.915 | − | 203.761i | −0.117873 | − | 0.220521i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 568.983i | − | 0.614453i | ||||||
\(927\) | −893.302 | − | 596.863i | −0.963649 | − | 0.643865i | ||||
\(928\) | 202.332i | 0.218030i | ||||||||
\(929\) | − | 1440.98i | − | 1.55111i | −0.631282 | − | 0.775553i | \(-0.717471\pi\) | ||
0.631282 | − | 0.775553i | \(-0.282529\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −112.000 | −0.120301 | ||||||||
\(932\) | 15.6765 | 0.0168203 | ||||||||
\(933\) | −702.189 | + | 375.336i | −0.752614 | + | 0.402289i | ||||
\(934\) | 985.830 | 1.05549 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.3399 | − | 8.24494i | −0.0131836 | − | 0.00880870i | ||||
\(937\) | 1010.00i | 1.07791i | 0.842335 | + | 0.538954i | \(0.181180\pi\) | ||||
−0.842335 | + | 0.538954i | \(0.818820\pi\) | |||||||
\(938\) | 264.097 | 0.281554 | ||||||||
\(939\) | −686.118 | + | 366.745i | −0.730690 | + | 0.390570i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 191.775i | − | 0.203799i | −0.994795 | − | 0.101899i | \(-0.967508\pi\) | ||
0.994795 | − | 0.101899i | \(-0.0324920\pi\) | |||||||
\(942\) | 781.053 | − | 417.490i | 0.829143 | − | 0.443195i | ||||
\(943\) | − | 339.827i | − | 0.360368i | ||||||
\(944\) | 232.870i | 0.246684i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −241.830 | −0.255634 | ||||||||
\(947\) | 893.108 | 0.943092 | 0.471546 | − | 0.881841i | \(-0.343696\pi\) | ||||
0.471546 | + | 0.881841i | \(0.343696\pi\) | |||||||
\(948\) | 59.1566 | + | 110.672i | 0.0624015 | + | 0.116743i | ||||
\(949\) | 42.1699 | 0.0444362 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 53.4902 | + | 100.071i | 0.0562462 | + | 0.105227i | ||||
\(952\) | 161.166i | 0.169292i | ||||||||
\(953\) | −1300.12 | −1.36423 | −0.682117 | − | 0.731243i | \(-0.738941\pi\) | ||||
−0.682117 | + | 0.731243i | \(0.738941\pi\) | |||||||
\(954\) | −360.000 | + | 538.799i | −0.377358 | + | 0.564778i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 426.738i | − | 0.446378i | ||||||
\(957\) | 736.204 | + | 1377.31i | 0.769284 | + | 1.43920i | ||||
\(958\) | 231.660i | 0.241816i | ||||||||
\(959\) | − | 65.6380i | − | 0.0684442i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2456.28 | 2.55596 | ||||||||
\(962\) | −16.4899 | −0.0171412 | ||||||||
\(963\) | 582.462 | − | 871.749i | 0.604841 | − | 0.905243i | ||||
\(964\) | −260.000 | −0.269710 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 384.405 | − | 205.473i | 0.397935 | − | 0.212705i | ||||
\(967\) | − | 375.247i | − | 0.388053i | −0.980996 | − | 0.194026i | \(-0.937845\pi\) | ||
0.980996 | − | 0.194026i | \(-0.0621547\pi\) | |||||||
\(968\) | −256.906 | −0.265399 | ||||||||
\(969\) | 487.320 | + | 911.693i | 0.502910 | + | 0.940859i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1045.06i | 1.07628i | 0.842856 | + | 0.538138i | \(0.180872\pi\) | ||||
−0.842856 | + | 0.538138i | \(0.819128\pi\) | |||||||
\(972\) | −308.299 | + | 375.697i | −0.317180 | + | 0.386519i | ||||
\(973\) | 387.490i | 0.398243i | ||||||||
\(974\) | − | 146.368i | − | 0.150275i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 155.660 | 0.159488 | ||||||||
\(977\) | −459.425 | −0.470241 | −0.235120 | − | 0.971966i | \(-0.575548\pi\) | ||||
−0.235120 | + | 0.971966i | \(0.575548\pi\) | |||||||
\(978\) | −999.008 | + | 533.992i | −1.02148 | + | 0.546004i | ||||
\(979\) | −780.863 | −0.797613 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 439.150 | − | 657.260i | 0.447656 | − | 0.669990i | ||||
\(982\) | 806.235i | 0.821013i | ||||||||
\(983\) | −103.265 | −0.105051 | −0.0525257 | − | 0.998620i | \(-0.516727\pi\) | ||||
−0.0525257 | + | 0.998620i | \(0.516727\pi\) | |||||||
\(984\) | 65.4902 | − | 35.0060i | 0.0665550 | − | 0.0355752i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1089.39i | − | 1.10486i | ||||||
\(987\) | 59.3970 | − | 31.7490i | 0.0601793 | − | 0.0321672i | ||||
\(988\) | 18.6562i | 0.0188828i | ||||||||
\(989\) | − | 456.224i | − | 0.461298i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1329.73 | 1.34180 | 0.670901 | − | 0.741547i | \(-0.265908\pi\) | ||||
0.670901 | + | 0.741547i | \(0.265908\pi\) | |||||||
\(992\) | −330.686 | −0.333352 | ||||||||
\(993\) | −205.754 | − | 384.931i | −0.207205 | − | 0.387644i | ||||
\(994\) | 63.7124 | 0.0640970 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −411.660 | − | 770.146i | −0.413313 | − | 0.773238i | ||||
\(997\) | 664.259i | 0.666258i | 0.942881 | + | 0.333129i | \(0.108104\pi\) | ||||
−0.942881 | + | 0.333129i | \(0.891896\pi\) | |||||||
\(998\) | 689.656 | 0.691038 | ||||||||
\(999\) | −52.9150 | + | 537.401i | −0.0529680 | + | 0.537939i |
(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 | 1050.3.c.a.449.6 | 8 | ||
3.2 | odd | 2 | inner | 1050.3.c.a.449.1 | 8 | ||
5.2 | odd | 4 | 1050.3.e.a.701.3 | 4 | |||
5.3 | odd | 4 | 42.3.b.a.29.2 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1050.3.c.a.449.4 | 8 | ||
15.2 | even | 4 | 1050.3.e.a.701.1 | 4 | |||
15.8 | even | 4 | 42.3.b.a.29.4 | yes | 4 | ||
15.14 | odd | 2 | inner | 1050.3.c.a.449.7 | 8 | ||
20.3 | even | 4 | 336.3.d.b.113.2 | 4 | |||
35.3 | even | 12 | 294.3.h.g.275.4 | 8 | |||
35.13 | even | 4 | 294.3.b.h.197.1 | 4 | |||
35.18 | odd | 12 | 294.3.h.d.275.3 | 8 | |||
35.23 | odd | 12 | 294.3.h.d.263.1 | 8 | |||
35.33 | even | 12 | 294.3.h.g.263.2 | 8 | |||
40.3 | even | 4 | 1344.3.d.e.449.3 | 4 | |||
40.13 | odd | 4 | 1344.3.d.c.449.2 | 4 | |||
45.13 | odd | 12 | 1134.3.q.a.1079.4 | 8 | |||
45.23 | even | 12 | 1134.3.q.a.1079.1 | 8 | |||
45.38 | even | 12 | 1134.3.q.a.701.4 | 8 | |||
45.43 | odd | 12 | 1134.3.q.a.701.1 | 8 | |||
60.23 | odd | 4 | 336.3.d.b.113.1 | 4 | |||
105.23 | even | 12 | 294.3.h.d.263.3 | 8 | |||
105.38 | odd | 12 | 294.3.h.g.275.2 | 8 | |||
105.53 | even | 12 | 294.3.h.d.275.1 | 8 | |||
105.68 | odd | 12 | 294.3.h.g.263.4 | 8 | |||
105.83 | odd | 4 | 294.3.b.h.197.3 | 4 | |||
120.53 | even | 4 | 1344.3.d.c.449.1 | 4 | |||
120.83 | odd | 4 | 1344.3.d.e.449.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.b.a.29.2 | ✓ | 4 | 5.3 | odd | 4 | ||
42.3.b.a.29.4 | yes | 4 | 15.8 | even | 4 | ||
294.3.b.h.197.1 | 4 | 35.13 | even | 4 | |||
294.3.b.h.197.3 | 4 | 105.83 | odd | 4 | |||
294.3.h.d.263.1 | 8 | 35.23 | odd | 12 | |||
294.3.h.d.263.3 | 8 | 105.23 | even | 12 | |||
294.3.h.d.275.1 | 8 | 105.53 | even | 12 | |||
294.3.h.d.275.3 | 8 | 35.18 | odd | 12 | |||
294.3.h.g.263.2 | 8 | 35.33 | even | 12 | |||
294.3.h.g.263.4 | 8 | 105.68 | odd | 12 | |||
294.3.h.g.275.2 | 8 | 105.38 | odd | 12 | |||
294.3.h.g.275.4 | 8 | 35.3 | even | 12 | |||
336.3.d.b.113.1 | 4 | 60.23 | odd | 4 | |||
336.3.d.b.113.2 | 4 | 20.3 | even | 4 | |||
1050.3.c.a.449.1 | 8 | 3.2 | odd | 2 | inner | ||
1050.3.c.a.449.4 | 8 | 5.4 | even | 2 | inner | ||
1050.3.c.a.449.6 | 8 | 1.1 | even | 1 | trivial | ||
1050.3.c.a.449.7 | 8 | 15.14 | odd | 2 | inner | ||
1050.3.e.a.701.1 | 4 | 15.2 | even | 4 | |||
1050.3.e.a.701.3 | 4 | 5.2 | odd | 4 | |||
1134.3.q.a.701.1 | 8 | 45.43 | odd | 12 | |||
1134.3.q.a.701.4 | 8 | 45.38 | even | 12 | |||
1134.3.q.a.1079.1 | 8 | 45.23 | even | 12 | |||
1134.3.q.a.1079.4 | 8 | 45.13 | odd | 12 | |||
1344.3.d.c.449.1 | 4 | 120.53 | even | 4 | |||
1344.3.d.c.449.2 | 4 | 40.13 | odd | 4 | |||
1344.3.d.e.449.3 | 4 | 40.3 | even | 4 | |||
1344.3.d.e.449.4 | 4 | 120.83 | odd | 4 |