Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (of order \(6\), degree \(2\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 749.3 | ||
Character | \(\chi\) | \(=\) | 900.749 |
Dual form | 900.3.u.c.149.3 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.39478 | − | 2.65605i | −0.464927 | − | 0.885349i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.45229 | + | 1.41583i | 0.350327 | + | 0.202262i | 0.664829 | − | 0.746995i | \(-0.268504\pi\) |
−0.314502 | + | 0.949257i | \(0.601838\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.10917 | + | 7.40921i | −0.567686 | + | 0.823245i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.949152 | − | 0.547993i | −0.0862865 | − | 0.0498175i | 0.456236 | − | 0.889859i | \(-0.349197\pi\) |
−0.542522 | + | 0.840041i | \(0.682531\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.63097 | − | 2.09634i | 0.279306 | − | 0.161257i | −0.353803 | − | 0.935320i | \(-0.615112\pi\) |
0.633109 | + | 0.774063i | \(0.281778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.85770 | 0.462218 | 0.231109 | − | 0.972928i | \(-0.425765\pi\) | ||||
0.231109 | + | 0.972928i | \(0.425765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.3580 | −0.703053 | −0.351527 | − | 0.936178i | \(-0.614337\pi\) | ||||
−0.351527 | + | 0.936178i | \(0.614337\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.340105 | − | 8.48818i | 0.0161955 | − | 0.404199i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.3679 | + | 21.4218i | 0.537734 | + | 0.931383i | 0.999026 | + | 0.0441340i | \(0.0140529\pi\) |
−0.461292 | + | 0.887249i | \(0.652614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.8054 | + | 3.23598i | 0.992792 | + | 0.119851i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.43628 | + | 1.40659i | 0.0840097 | + | 0.0485030i | 0.541416 | − | 0.840755i | \(-0.317888\pi\) |
−0.457407 | + | 0.889258i | \(0.651222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.0630 | + | 20.8937i | 0.389128 | + | 0.673990i | 0.992333 | − | 0.123597i | \(-0.0394429\pi\) |
−0.603204 | + | 0.797587i | \(0.706110\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.131636 | + | 3.28532i | −0.00398898 | + | 0.0995552i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 49.9138i | 1.34902i | 0.738264 | + | 0.674511i | \(0.235646\pi\) | ||||
−0.738264 | + | 0.674511i | \(0.764354\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.6324 | − | 6.72010i | −0.272626 | − | 0.172310i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.9104 | + | 10.9179i | −0.461229 | + | 0.266291i | −0.712561 | − | 0.701610i | \(-0.752465\pi\) |
0.251332 | + | 0.967901i | \(0.419131\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 42.4611 | + | 24.5149i | 0.987467 | + | 0.570114i | 0.904516 | − | 0.426439i | \(-0.140232\pi\) |
0.0829506 | + | 0.996554i | \(0.473566\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.8220 | − | 58.5815i | 0.719618 | − | 1.24641i | −0.241533 | − | 0.970393i | \(-0.577650\pi\) |
0.961151 | − | 0.276022i | \(-0.0890164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −20.4908 | − | 35.4912i | −0.418180 | − | 0.724310i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.9598 | − | 20.8704i | −0.214897 | − | 0.409224i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 49.8418 | 0.940412 | 0.470206 | − | 0.882557i | \(-0.344180\pi\) | ||||
0.470206 | + | 0.882557i | \(0.344180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.6315 | + | 35.4795i | 0.326869 | + | 0.622448i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 86.8838 | − | 50.1624i | 1.47261 | − | 0.850210i | 0.473081 | − | 0.881019i | \(-0.343142\pi\) |
0.999525 | + | 0.0308088i | \(0.00980829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41.5597 | + | 71.9835i | −0.681307 | + | 1.18006i | 0.293276 | + | 0.956028i | \(0.405255\pi\) |
−0.974582 | + | 0.224030i | \(0.928079\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −23.0194 | + | 10.9358i | −0.365387 | + | 0.173584i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49.8405 | − | 28.7754i | 0.743888 | − | 0.429484i | −0.0795931 | − | 0.996827i | \(-0.525362\pi\) |
0.823481 | + | 0.567343i | \(0.192029\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 39.6468 | − | 62.7284i | 0.574592 | − | 0.909107i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.2317i | 0.200446i | 0.994965 | + | 0.100223i | \(0.0319556\pi\) | ||||
−0.994965 | + | 0.100223i | \(0.968044\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 71.5532i | − | 0.980180i | −0.871672 | − | 0.490090i | \(-0.836964\pi\) | ||
0.871672 | − | 0.490090i | \(-0.163036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.55173 | − | 2.68768i | −0.0201524 | − | 0.0349049i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 54.4107 | − | 94.2421i | 0.688743 | − | 1.19294i | −0.283502 | − | 0.958972i | \(-0.591496\pi\) |
0.972245 | − | 0.233966i | \(-0.0751704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −28.7927 | − | 75.7098i | −0.355466 | − | 0.934689i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −40.2871 | + | 69.7793i | −0.485387 | + | 0.840715i | −0.999859 | − | 0.0167923i | \(-0.994655\pi\) |
0.514472 | + | 0.857507i | \(0.327988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.337884 | − | 8.43276i | 0.00388373 | − | 0.0969283i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 65.6139i | − | 0.737235i | −0.929581 | − | 0.368617i | \(-0.879831\pi\) | ||
0.929581 | − | 0.368617i | \(-0.120169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.8723 | 0.130465 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 38.6694 | − | 61.1820i | 0.415800 | − | 0.657871i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 134.102 | + | 77.4238i | 1.38249 | + | 0.798184i | 0.992454 | − | 0.122614i | \(-0.0391277\pi\) |
0.390040 | + | 0.920798i | \(0.372461\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.90957 | − | 4.23267i | 0.0899957 | − | 0.0427543i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 124.917 | + | 72.1209i | 1.23680 | + | 0.714068i | 0.968439 | − | 0.249250i | \(-0.0801841\pi\) |
0.268363 | + | 0.963318i | \(0.413517\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.5708 | + | 10.1445i | −0.170590 | + | 0.0984901i | −0.582864 | − | 0.812570i | \(-0.698068\pi\) |
0.412274 | + | 0.911060i | \(0.364735\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 156.290 | 1.46065 | 0.730325 | − | 0.683100i | \(-0.239369\pi\) | ||||
0.730325 | + | 0.683100i | \(0.239369\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −55.5439 | −0.509577 | −0.254788 | − | 0.966997i | \(-0.582006\pi\) | ||||
−0.254788 | + | 0.966997i | \(0.582006\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 132.574 | − | 69.6189i | 1.19436 | − | 0.627197i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −55.7238 | − | 96.5164i | −0.493131 | − | 0.854127i | 0.506838 | − | 0.862041i | \(-0.330814\pi\) |
−0.999969 | + | 0.00791409i | \(0.997481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.01902 | + | 37.6132i | −0.0258036 | + | 0.321481i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.2694 | + | 11.1252i | 0.161928 | + | 0.0934889i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.8994 | − | 103.749i | −0.495036 | − | 0.857428i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 55.3743 | + | 34.9988i | 0.450198 | + | 0.284543i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 144.448i | 1.13739i | 0.822549 | + | 0.568694i | \(0.192551\pi\) | ||||
−0.822549 | + | 0.568694i | \(0.807449\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.88886 | − | 146.972i | 0.0456501 | − | 1.13931i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 166.658 | − | 96.2201i | 1.27220 | − | 0.734504i | 0.296797 | − | 0.954940i | \(-0.404081\pi\) |
0.975401 | + | 0.220436i | \(0.0707480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32.7578 | − | 18.9127i | −0.246299 | − | 0.142201i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4505 | − | 28.4931i | 0.120077 | − | 0.207979i | −0.799721 | − | 0.600372i | \(-0.795019\pi\) |
0.919798 | + | 0.392393i | \(0.128353\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 80.1236 | + | 138.778i | 0.576429 | + | 0.998404i | 0.995885 | + | 0.0906285i | \(0.0288876\pi\) |
−0.419456 | + | 0.907776i | \(0.637779\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −202.770 | − | 8.12458i | −1.43808 | − | 0.0576211i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.59513 | −0.0321338 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −65.6860 | + | 103.927i | −0.446844 | + | 0.706987i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −39.1186 | + | 22.5851i | −0.262541 | + | 0.151578i | −0.625493 | − | 0.780230i | \(-0.715102\pi\) |
0.362952 | + | 0.931808i | \(0.381769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −134.134 | + | 232.328i | −0.888307 | + | 1.53859i | −0.0464318 | + | 0.998921i | \(0.514785\pi\) |
−0.841875 | + | 0.539672i | \(0.818548\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −40.1463 | + | 58.2193i | −0.262394 | + | 0.380519i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 180.403 | − | 104.156i | 1.14906 | − | 0.663412i | 0.200404 | − | 0.979713i | \(-0.435774\pi\) |
0.948659 | + | 0.316302i | \(0.102441\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −69.5184 | − | 132.382i | −0.437223 | − | 0.832593i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 70.0433i | 0.435052i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.6396i | 0.151163i | 0.997140 | + | 0.0755815i | \(0.0240813\pi\) | ||||
−0.997140 | + | 0.0755815i | \(0.975919\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −44.6359 | − | 77.3116i | −0.267281 | − | 0.462944i | 0.700878 | − | 0.713281i | \(-0.252792\pi\) |
−0.968159 | + | 0.250337i | \(0.919458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −75.7107 | + | 131.135i | −0.447992 | + | 0.775945i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 68.2484 | − | 98.9723i | 0.399113 | − | 0.578785i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 30.5959 | − | 52.9937i | 0.176855 | − | 0.306322i | −0.763947 | − | 0.645279i | \(-0.776741\pi\) |
0.940802 | + | 0.338958i | \(0.110074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −254.418 | − | 160.802i | −1.43739 | − | 0.908485i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 131.909i | 0.736924i | 0.929643 | + | 0.368462i | \(0.120115\pi\) | ||||
−0.929643 | + | 0.368462i | \(0.879885\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −311.741 | −1.72233 | −0.861163 | − | 0.508328i | \(-0.830264\pi\) | ||||
−0.861163 | + | 0.508328i | \(0.830264\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 249.158 | + | 9.98329i | 1.36152 | + | 0.0545535i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.45815 | − | 4.30596i | −0.0398832 | − | 0.0230265i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 61.1530 | + | 45.8875i | 0.323561 | + | 0.242791i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 303.129 | + | 175.012i | 1.58706 | + | 0.916291i | 0.993788 | + | 0.111290i | \(0.0354983\pi\) |
0.593274 | + | 0.805000i | \(0.297835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −171.510 | + | 99.0214i | −0.888653 | + | 0.513064i | −0.873502 | − | 0.486821i | \(-0.838156\pi\) |
−0.0151517 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −32.5493 | −0.165225 | −0.0826124 | − | 0.996582i | \(-0.526326\pi\) | ||||
−0.0826124 | + | 0.996582i | \(0.526326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −128.299 | −0.644717 | −0.322358 | − | 0.946618i | \(-0.604476\pi\) | ||||
−0.322358 | + | 0.946618i | \(0.604476\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −145.946 | − | 92.2433i | −0.726097 | − | 0.458922i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.98298 | + | 6.89873i | 0.0196206 | + | 0.0339839i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −221.908 | − | 17.8115i | −1.07202 | − | 0.0860457i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.6788 | + | 7.32010i | 0.0606640 | + | 0.0350244i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0757 | + | 31.3080i | 0.0856668 | + | 0.148379i | 0.905675 | − | 0.423972i | \(-0.139365\pi\) |
−0.820008 | + | 0.572352i | \(0.806031\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 37.8000 | − | 19.8500i | 0.177465 | − | 0.0931927i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 68.3166i | 0.314823i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −190.049 | + | 99.8010i | −0.867802 | + | 0.455712i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.5311 | − | 16.4724i | 0.129100 | − | 0.0745359i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 151.500 | + | 87.4685i | 0.679372 | + | 0.392236i | 0.799618 | − | 0.600508i | \(-0.205035\pi\) |
−0.120246 | + | 0.992744i | \(0.538368\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 68.1296 | − | 118.004i | 0.300130 | − | 0.519841i | −0.676035 | − | 0.736870i | \(-0.736303\pi\) |
0.976165 | + | 0.217028i | \(0.0696364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 97.1240 | + | 168.224i | 0.424122 | + | 0.734601i | 0.996338 | − | 0.0855017i | \(-0.0272493\pi\) |
−0.572216 | + | 0.820103i | \(0.693916\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.97427 | + | 7.87019i | −0.0215336 | + | 0.0340701i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 196.013 | 0.841258 | 0.420629 | − | 0.907233i | \(-0.361809\pi\) | ||||
0.420629 | + | 0.907233i | \(0.361809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −326.202 | − | 13.0703i | −1.37638 | − | 0.0551489i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −43.8109 | + | 25.2943i | −0.183309 | + | 0.105834i | −0.588847 | − | 0.808245i | \(-0.700418\pi\) |
0.405537 | + | 0.914079i | \(0.367084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −104.678 | + | 181.308i | −0.434351 | + | 0.752317i | −0.997242 | − | 0.0742134i | \(-0.976355\pi\) |
0.562892 | + | 0.826531i | \(0.309689\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −160.929 | + | 182.073i | −0.662261 | + | 0.749273i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −48.5026 | + | 28.0030i | −0.196367 | + | 0.113372i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 241.529 | + | 9.67759i | 0.969996 | + | 0.0388658i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 179.480i | − | 0.715061i | −0.933901 | − | 0.357531i | \(-0.883619\pi\) | ||
0.933901 | − | 0.357531i | \(-0.116381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 27.1100i | − | 0.107154i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −225.194 | − | 390.047i | −0.876241 | − | 1.51769i | −0.855435 | − | 0.517911i | \(-0.826710\pi\) |
−0.0208064 | − | 0.999784i | \(-0.506623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −70.6696 | + | 122.403i | −0.272856 | + | 0.472600i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.8691 | + | 10.8644i | −0.0876210 | + | 0.0416261i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −197.837 | + | 342.665i | −0.752234 | + | 1.30291i | 0.194504 | + | 0.980902i | \(0.437690\pi\) |
−0.946738 | + | 0.322005i | \(0.895643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −174.274 | + | 91.5170i | −0.652710 | + | 0.342760i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 374.710i | 1.39298i | 0.717569 | + | 0.696488i | \(0.245255\pi\) | ||||
−0.717569 | + | 0.696488i | \(0.754745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 41.1748 | 0.151936 | 0.0759682 | − | 0.997110i | \(-0.475795\pi\) | ||||
0.0759682 | + | 0.997110i | \(0.475795\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.5592 | − | 31.5333i | −0.0606565 | − | 0.115507i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.9981 | + | 9.81388i | 0.0613651 | + | 0.0354292i | 0.530369 | − | 0.847767i | \(-0.322054\pi\) |
−0.469004 | + | 0.883196i | \(0.655387\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −216.438 | − | 17.3724i | −0.775762 | − | 0.0622665i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 316.627 | + | 182.805i | 1.12679 | + | 0.650551i | 0.943125 | − | 0.332438i | \(-0.107871\pi\) |
0.183663 | + | 0.982989i | \(0.441205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.8524 | + | 12.0391i | −0.0736832 | + | 0.0425410i | −0.536389 | − | 0.843971i | \(-0.680212\pi\) |
0.462706 | + | 0.886512i | \(0.346879\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −61.8317 | −0.215441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −227.257 | −0.786355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.5984 | − | 464.171i | 0.0639121 | − | 1.59509i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −170.352 | − | 295.058i | −0.581406 | − | 1.00703i | −0.995313 | − | 0.0967059i | \(-0.969169\pi\) |
0.413907 | − | 0.910319i | \(-0.364164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.6691 | − | 17.7606i | −0.0796939 | − | 0.0598000i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 89.8149 | + | 51.8547i | 0.300384 | + | 0.173427i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 69.4180 | + | 120.235i | 0.230624 | + | 0.399453i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.3246 | − | 432.378i | 0.0571767 | − | 1.42699i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 401.187i | 1.30680i | 0.757014 | + | 0.653399i | \(0.226658\pi\) | ||||
−0.757014 | + | 0.653399i | \(0.773342\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51.4516 | + | 32.5194i | 0.166510 | + | 0.105241i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 78.7894 | − | 45.4891i | 0.253342 | − | 0.146267i | −0.367951 | − | 0.929845i | \(-0.619941\pi\) |
0.621294 | + | 0.783578i | \(0.286607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −402.942 | − | 232.638i | −1.28735 | − | 0.743254i | −0.309172 | − | 0.951006i | \(-0.600052\pi\) |
−0.978181 | + | 0.207752i | \(0.933385\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 96.7678 | − | 167.607i | 0.305261 | − | 0.528728i | −0.672058 | − | 0.740498i | \(-0.734590\pi\) |
0.977319 | + | 0.211770i | \(0.0679229\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.54160 | − | 2.67013i | −0.00483261 | − | 0.00837032i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −217.990 | − | 415.112i | −0.679096 | − | 1.29318i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −104.963 | −0.324964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 77.4715 | + | 147.527i | 0.236916 | + | 0.451153i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 165.883 | − | 95.7726i | 0.504204 | − | 0.291102i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −65.9739 | + | 114.270i | −0.199317 | + | 0.345227i | −0.948307 | − | 0.317354i | \(-0.897206\pi\) |
0.748990 | + | 0.662581i | \(0.230539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −369.822 | − | 255.018i | −1.11058 | − | 0.765821i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −303.562 | + | 175.261i | −0.900777 | + | 0.520064i | −0.877452 | − | 0.479664i | \(-0.840758\pi\) |
−0.0233245 | + | 0.999728i | \(0.507425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −178.630 | + | 282.624i | −0.526931 | + | 0.833699i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 26.4417i | − | 0.0775417i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 254.798i | − | 0.742851i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −114.673 | − | 198.620i | −0.330470 | − | 0.572392i | 0.652134 | − | 0.758104i | \(-0.273874\pi\) |
−0.982604 | + | 0.185712i | \(0.940541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −167.325 | + | 289.815i | −0.479440 | + | 0.830415i | −0.999722 | − | 0.0235800i | \(-0.992494\pi\) |
0.520282 | + | 0.853995i | \(0.325827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 104.113 | − | 44.4435i | 0.296619 | − | 0.126620i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5209 | − | 25.1509i | 0.0411356 | − | 0.0712489i | −0.844725 | − | 0.535201i | \(-0.820236\pi\) |
0.885860 | + | 0.463952i | \(0.153569\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.67244 | − | 66.6976i | 0.00748583 | − | 0.186828i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 293.412i | − | 0.817304i | −0.912690 | − | 0.408652i | \(-0.865999\pi\) | ||
0.912690 | − | 0.408652i | \(-0.134001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −182.563 | −0.505716 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −192.015 | + | 303.803i | −0.528967 | + | 0.836922i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 49.5815 | + | 28.6259i | 0.135099 | + | 0.0779997i | 0.566026 | − | 0.824387i | \(-0.308480\pi\) |
−0.430927 | + | 0.902387i | \(0.641813\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.7233 | − | 195.892i | 0.0426106 | − | 0.530874i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 122.227 | + | 70.5676i | 0.329452 | + | 0.190209i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 260.297 | − | 150.282i | 0.697847 | − | 0.402902i | −0.108698 | − | 0.994075i | \(-0.534668\pi\) |
0.806545 | + | 0.591173i | \(0.201335\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.7948 | 0.0312859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 198.314 | 0.523255 | 0.261627 | − | 0.965169i | \(-0.415741\pi\) | ||||
0.261627 | + | 0.965169i | \(0.415741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 383.662 | − | 201.474i | 1.00699 | − | 0.528803i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.1798 | + | 48.8088i | 0.0735765 | + | 0.127438i | 0.900466 | − | 0.434926i | \(-0.143225\pi\) |
−0.826890 | + | 0.562364i | \(0.809892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −398.577 | + | 189.352i | −1.02991 | + | 0.489282i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 620.660 | + | 358.338i | 1.59553 | + | 0.921179i | 0.992334 | + | 0.123584i | \(0.0394388\pi\) |
0.603194 | + | 0.797595i | \(0.293895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 97.1831 | + | 168.326i | 0.248550 | + | 0.430501i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −488.017 | − | 308.446i | −1.24177 | − | 0.784849i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 310.467i | − | 0.782032i | −0.920384 | − | 0.391016i | \(-0.872124\pi\) | ||
0.920384 | − | 0.391016i | \(-0.127876\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.54313 | + | 113.385i | −0.0113863 | + | 0.284173i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −426.833 | + | 246.432i | −1.06442 | + | 0.614544i | −0.926652 | − | 0.375920i | \(-0.877327\pi\) |
−0.137770 | + | 0.990464i | \(0.543993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 87.6008 | + | 50.5763i | 0.217372 | + | 0.125500i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.3524 | − | 47.3758i | 0.0672050 | − | 0.116402i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −341.160 | − | 590.906i | −0.834132 | − | 1.44476i | −0.894735 | − | 0.446597i | \(-0.852636\pi\) |
0.0606037 | − | 0.998162i | \(-0.480697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −98.6240 | − | 3.95167i | −0.239961 | − | 0.00961477i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 284.086 | 0.687859 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 256.847 | − | 406.377i | 0.615939 | − | 0.974526i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 192.209 | − | 110.972i | 0.458732 | − | 0.264849i | −0.252779 | − | 0.967524i | \(-0.581345\pi\) |
0.711511 | + | 0.702675i | \(0.248011\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −76.5614 | + | 132.608i | −0.181856 | + | 0.314984i | −0.942513 | − | 0.334171i | \(-0.891544\pi\) |
0.760657 | + | 0.649155i | \(0.224877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 261.240 | + | 549.898i | 0.617588 | + | 1.29999i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −203.833 | + | 117.683i | −0.477361 | + | 0.275604i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.40920 | + | 12.2049i | 0.0149399 | + | 0.0284496i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 328.398i | − | 0.761944i | −0.924587 | − | 0.380972i | \(-0.875589\pi\) | ||
0.924587 | − | 0.380972i | \(-0.124411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 171.691i | 0.396515i | 0.980150 | + | 0.198258i | \(0.0635283\pi\) | ||||
−0.980150 | + | 0.198258i | \(0.936472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −165.210 | − | 286.153i | −0.378056 | − | 0.654812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 49.2459 | − | 85.2965i | 0.112178 | − | 0.194297i | −0.804470 | − | 0.593993i | \(-0.797551\pi\) |
0.916648 | + | 0.399695i | \(0.130884\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 367.653 | + | 29.5096i | 0.833680 | + | 0.0669153i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −377.907 | + | 654.554i | −0.853063 | + | 1.47755i | 0.0253671 | + | 0.999678i | \(0.491925\pi\) |
−0.878430 | + | 0.477871i | \(0.841409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 114.549 | + | 72.3994i | 0.256262 | + | 0.161967i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 167.336i | − | 0.372686i | −0.982485 | − | 0.186343i | \(-0.940336\pi\) | ||
0.982485 | − | 0.186343i | \(-0.0596635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.9318 | 0.0530638 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 804.161 | + | 32.2212i | 1.77519 | + | 0.0711284i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 317.924 | + | 183.553i | 0.695676 | + | 0.401648i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.110059 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 210.629 | + | 25.4274i | 0.458886 | + | 0.0553973i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 467.957 | + | 270.175i | 1.01509 | + | 0.586063i | 0.912678 | − | 0.408679i | \(-0.134010\pi\) |
0.102413 | + | 0.994742i | \(0.467344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 155.651 | − | 89.8654i | 0.336180 | − | 0.194094i | −0.322401 | − | 0.946603i | \(-0.604490\pi\) |
0.658582 | + | 0.752509i | \(0.271157\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 56.0646 | 0.120053 | 0.0600264 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600264 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 162.965 | 0.347473 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −528.265 | − | 333.884i | −1.12158 | − | 0.708884i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.8680 | − | 46.5367i | −0.0568034 | − | 0.0983863i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −254.650 | + | 369.288i | −0.533858 | + | 0.774190i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −497.782 | − | 287.395i | −1.03921 | − | 0.599989i | −0.119601 | − | 0.992822i | \(-0.538162\pi\) |
−0.919610 | + | 0.392833i | \(0.871495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 104.637 | + | 181.236i | 0.217540 | + | 0.376790i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 186.038 | − | 97.6951i | 0.385173 | − | 0.202267i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 190.185i | − | 0.390524i | −0.980751 | − | 0.195262i | \(-0.937444\pi\) | ||
0.980751 | − | 0.195262i | \(-0.0625557\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 65.4438 | − | 34.3668i | 0.133832 | − | 0.0702797i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −340.176 | + | 196.401i | −0.692822 | + | 0.400001i | −0.804668 | − | 0.593724i | \(-0.797657\pi\) |
0.111846 | + | 0.993726i | \(0.464324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.1436 | + | 11.0525i | 0.0388308 | + | 0.0224190i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.1496 | + | 34.9002i | −0.0405425 | + | 0.0702217i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 150.303 | + | 260.332i | 0.301208 | + | 0.521707i | 0.976410 | − | 0.215926i | \(-0.0692769\pi\) |
−0.675202 | + | 0.737633i | \(0.735944\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −143.086 | + | 226.388i | −0.285601 | + | 0.451872i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 484.676 | 0.963572 | 0.481786 | − | 0.876289i | \(-0.339988\pi\) | ||||
0.481786 | + | 0.876289i | \(0.339988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 453.900 | + | 18.1869i | 0.895266 | + | 0.0358716i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −467.647 | + | 269.996i | −0.918755 | + | 0.530444i | −0.883238 | − | 0.468925i | \(-0.844641\pi\) |
−0.0355177 | + | 0.999369i | \(0.511308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 101.307 | − | 175.469i | 0.198253 | − | 0.343384i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −358.067 | − | 43.2263i | −0.697986 | − | 0.0842617i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −64.2045 | + | 37.0685i | −0.124187 | + | 0.0716992i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −183.428 | − | 7.34962i | −0.353426 | − | 0.0141611i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 103.769i | − | 0.199172i | −0.995029 | − | 0.0995862i | \(-0.968248\pi\) | ||
0.995029 | − | 0.0995862i | \(-0.0317519\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 142.380i | 0.272237i | 0.990693 | + | 0.136119i | \(0.0434629\pi\) | ||||
−0.990693 | + | 0.136119i | \(0.956537\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 94.7873 | + | 164.176i | 0.179862 | + | 0.311530i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.4290 | + | 71.7571i | −0.0783157 | + | 0.135647i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −72.2407 | + | 900.028i | −0.136047 | + | 1.69497i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.7754 | + | 79.2853i | −0.0858826 | + | 0.148753i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 350.357 | − | 183.985i | 0.652435 | − | 0.342616i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 44.9154i | 0.0833309i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −708.521 | −1.30965 | −0.654826 | − | 0.755780i | \(-0.727258\pi\) | ||||
−0.654826 | + | 0.755780i | \(0.727258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 434.811 | + | 827.999i | 0.800756 | + | 1.52486i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 419.382 | + | 242.130i | 0.766695 | + | 0.442652i | 0.831694 | − | 0.555234i | \(-0.187371\pi\) |
−0.0649994 | + | 0.997885i | \(0.520705\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −321.005 | − | 675.701i | −0.584709 | − | 1.23078i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.5439 | − | 18.7892i | −0.0590633 | − | 0.0341002i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 266.862 | − | 154.073i | 0.482571 | − | 0.278612i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 687.468 | 1.23423 | 0.617117 | − | 0.786871i | \(-0.288301\pi\) | ||||
0.617117 | + | 0.786871i | \(0.288301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 205.567 | 0.367740 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.03436 | + | 25.8151i | −0.00184378 | + | 0.0460162i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −415.869 | − | 720.306i | −0.738666 | − | 1.27941i | −0.953096 | − | 0.302667i | \(-0.902123\pi\) |
0.214431 | − | 0.976739i | \(-0.431210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.5842 | − | 226.428i | 0.0645224 | − | 0.399344i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −250.103 | − | 144.397i | −0.439548 | − | 0.253773i | 0.263858 | − | 0.964562i | \(-0.415005\pi\) |
−0.703406 | + | 0.710788i | \(0.748338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −164.400 | − | 284.750i | −0.287917 | − | 0.498686i | 0.685396 | − | 0.728171i | \(-0.259629\pi\) |
−0.973312 | + | 0.229485i | \(0.926296\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 42.0405 | − | 1049.23i | 0.0733691 | − | 1.83111i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 297.033i | − | 0.514788i | −0.966307 | − | 0.257394i | \(-0.917136\pi\) | ||
0.966307 | − | 0.257394i | \(-0.0828638\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 502.225 | + | 317.426i | 0.867400 | + | 0.548231i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −197.592 | + | 114.080i | −0.340089 | + | 0.196350i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.3074 | − | 27.3130i | −0.0811449 | − | 0.0468490i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −458.054 | + | 793.373i | −0.780331 | + | 1.35157i | 0.151419 | + | 0.988470i | \(0.451616\pi\) |
−0.931749 | + | 0.363103i | \(0.881717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −161.137 | − | 279.098i | −0.273578 | − | 0.473851i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 45.3991 | + | 86.4524i | 0.0768174 | + | 0.146282i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 620.630 | 1.04659 | 0.523297 | − | 0.852150i | \(-0.324702\pi\) | ||||
0.523297 | + | 0.852150i | \(0.324702\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 178.948 | + | 340.767i | 0.299746 | + | 0.570799i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 230.407 | − | 133.026i | 0.384653 | − | 0.222079i | −0.295188 | − | 0.955439i | \(-0.595382\pi\) |
0.679841 | + | 0.733360i | \(0.262049\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 504.140 | − | 873.197i | 0.838836 | − | 1.45291i | −0.0520330 | − | 0.998645i | \(-0.516570\pi\) |
0.890869 | − | 0.454261i | \(-0.150097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −41.4406 | + | 516.297i | −0.0687240 | + | 0.856215i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 998.861 | − | 576.693i | 1.64557 | − | 0.950071i | 0.666768 | − | 0.745265i | \(-0.267677\pi\) |
0.978803 | − | 0.204805i | \(-0.0656562\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.7680 | − | 20.2012i | 0.0209655 | − | 0.0331711i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 283.611i | − | 0.464174i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1168.56i | 1.90629i | 0.302515 | + | 0.953145i | \(0.402174\pi\) | ||||
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 458.134 | + | 793.512i | 0.742519 | + | 1.28608i | 0.951345 | + | 0.308128i | \(0.0997024\pi\) |
−0.208826 | + | 0.977953i | \(0.566964\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 83.6253 | − | 144.843i | 0.135097 | − | 0.233995i | −0.790537 | − | 0.612414i | \(-0.790199\pi\) |
0.925635 | + | 0.378418i | \(0.123532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 262.205 | + | 614.242i | 0.422231 | + | 0.989117i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 92.8982 | − | 160.904i | 0.149114 | − | 0.258274i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.75840 | − | 43.8854i | 0.00280447 | − | 0.0699926i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 392.208i | 0.623542i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 542.994 | 0.860530 | 0.430265 | − | 0.902703i | \(-0.358420\pi\) | ||||
0.430265 | + | 0.902703i | \(0.358420\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 57.9439 | − | 91.6777i | 0.0915386 | − | 0.144831i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −148.803 | − | 85.9117i | −0.233600 | − | 0.134869i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −105.445 | − | 72.7120i | −0.165016 | − | 0.113790i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −90.6386 | − | 52.3302i | −0.141402 | − | 0.0816384i | 0.427630 | − | 0.903954i | \(-0.359349\pi\) |
−0.569032 | + | 0.822315i | \(0.692682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −182.276 | + | 105.237i | −0.283478 | + | 0.163666i | −0.634997 | − | 0.772515i | \(-0.718999\pi\) |
0.351519 | + | 0.936181i | \(0.385665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 899.002 | 1.38949 | 0.694747 | − | 0.719254i | \(-0.255516\pi\) | ||||
0.694747 | + | 0.719254i | \(0.255516\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −109.955 | −0.169421 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 181.452 | − | 95.2867i | 0.278728 | − | 0.146370i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −220.178 | − | 381.359i | −0.337179 | − | 0.584011i | 0.646722 | − | 0.762726i | \(-0.276139\pi\) |
−0.983901 | + | 0.178715i | \(0.942806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 530.152 | + | 365.577i | 0.806929 | + | 0.556434i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −779.837 | − | 450.239i | −1.18336 | − | 0.683215i | −0.226573 | − | 0.973994i | \(-0.572752\pi\) |
−0.956790 | + | 0.290779i | \(0.906086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 268.406 | + | 464.893i | 0.406060 | + | 0.703317i | 0.994444 | − | 0.105264i | \(-0.0335689\pi\) |
−0.588384 | + | 0.808582i | \(0.700236\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −83.5462 | − | 52.8045i | −0.126012 | − | 0.0796448i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 69.5861i | 0.104327i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0113 | − | 524.390i | 0.0314070 | − | 0.783842i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 78.8929 | − | 45.5488i | 0.117575 | − | 0.0678820i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −127.704 | − | 73.7299i | −0.189753 | − | 0.109554i | 0.402114 | − | 0.915590i | \(-0.368276\pi\) |
−0.591867 | + | 0.806036i | \(0.701609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −439.279 | + | 760.854i | −0.648861 | + | 1.12386i | 0.334534 | + | 0.942384i | \(0.391421\pi\) |
−0.983395 | + | 0.181477i | \(0.941912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 219.238 | + | 379.732i | 0.322884 | + | 0.559251i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −408.450 | − | 16.3658i | −0.599780 | − | 0.0240320i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 395.518 | 0.579090 | 0.289545 | − | 0.957164i | \(-0.406496\pi\) | ||||
0.289545 | + | 0.957164i | \(0.406496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 311.343 | − | 492.601i | 0.453193 | − | 0.717032i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 180.974 | − | 104.486i | 0.262662 | − | 0.151648i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 370.319 | − | 641.412i | 0.535918 | − | 0.928237i | −0.463201 | − | 0.886253i | \(-0.653299\pi\) |
0.999118 | − | 0.0419833i | \(-0.0133676\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27.8416 | + | 2.23471i | 0.0401755 | + | 0.00322469i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −148.592 | + | 85.7897i | −0.213188 | + | 0.123084i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −273.395 | − | 520.620i | −0.391124 | − | 0.744807i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1221.15i | − | 1.74201i | −0.491275 | − | 0.871004i | \(-0.663469\pi\) | ||
0.491275 | − | 0.871004i | \(-0.336531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 666.750i | − | 0.948435i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 204.222 | + | 353.723i | 0.288857 | + | 0.500315i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 371.624 | − | 643.672i | 0.524153 | − | 0.907859i | −0.475452 | − | 0.879742i | \(-0.657715\pi\) |
0.999605 | − | 0.0281175i | \(-0.00895127\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 420.265 | + | 884.639i | 0.591091 | + | 1.24422i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −298.387 | + | 516.822i | −0.418495 | + | 0.724855i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 128.289 | + | 81.0840i | 0.178925 | + | 0.113088i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1187.47i | − | 1.65156i | −0.563993 | − | 0.825779i | \(-0.690736\pi\) | ||
0.563993 | − | 0.825779i | \(-0.309264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −57.4515 | −0.0796831 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 627.567 | + | 25.1454i | 0.868005 | + | 0.0347793i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −156.825 | − | 90.5432i | −0.215716 | − | 0.124544i | 0.388249 | − | 0.921554i | \(-0.373080\pi\) |
−0.603965 | + | 0.797011i | \(0.706413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 708.057 | + | 173.483i | 0.971271 | + | 0.237974i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 333.646 | + | 192.631i | 0.456425 | + | 0.263517i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −439.932 | + | 253.995i | −0.600180 | + | 0.346514i | −0.769112 | − | 0.639114i | \(-0.779301\pi\) |
0.168932 | + | 0.985628i | \(0.445968\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −63.0749 | −0.0855834 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1428.58 | 1.93313 | 0.966566 | − | 0.256418i | \(-0.0825423\pi\) | ||||
0.966566 | + | 0.256418i | \(0.0825423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 142.028 | + | 89.7672i | 0.191670 | + | 0.121143i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −358.142 | − | 620.319i | −0.482021 | − | 0.834885i | 0.517766 | − | 0.855522i | \(-0.326764\pi\) |
−0.999787 | + | 0.0206374i | \(0.993430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −311.176 | − | 655.010i | −0.416567 | − | 0.876854i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 383.268 | + | 221.280i | 0.511706 | + | 0.295433i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −265.708 | − | 460.219i | −0.353805 | − | 0.612809i | 0.633108 | − | 0.774064i | \(-0.281779\pi\) |
−0.986913 | + | 0.161255i | \(0.948446\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −476.708 | + | 250.336i | −0.633079 | + | 0.332451i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 952.388i | − | 1.25811i | −0.777362 | − | 0.629054i | \(-0.783442\pi\) | ||
0.777362 | − | 0.629054i | \(-0.216558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −72.0056 | + | 37.8126i | −0.0948690 | + | 0.0498189i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1203.10 | + | 694.609i | −1.58094 | + | 0.912758i | −0.586220 | + | 0.810152i | \(0.699385\pi\) |
−0.994722 | + | 0.102606i | \(0.967282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −136.210 | − | 78.6407i | −0.178519 | − | 0.103068i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 210.315 | − | 364.277i | 0.274205 | − | 0.474937i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −511.731 | − | 886.345i | −0.665450 | − | 1.15259i | −0.979163 | − | 0.203076i | \(-0.934906\pi\) |
0.313713 | − | 0.949518i | \(-0.398427\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −721.888 | + | 1142.16i | −0.936301 | + | 1.48140i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1030.13 | 1.33264 | 0.666320 | − | 0.745666i | \(-0.267868\pi\) | ||||
0.666320 | + | 0.745666i | \(0.267868\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 423.678 | + | 16.9759i | 0.545274 | + | 0.0218481i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 252.605 | − | 145.842i | 0.324268 | − | 0.187216i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.79885 | − | 13.5080i | 0.00998572 | − | 0.0172958i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 60.7538 | + | 45.5879i | 0.0775910 | + | 0.0582221i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −711.419 | + | 410.738i | −0.903963 | + | 0.521903i | −0.878484 | − | 0.477772i | \(-0.841444\pi\) |
−0.0254790 | + | 0.999675i | \(0.508111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1186.07 | + | 47.5236i | 1.50326 | + | 0.0602327i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 315.582i | − | 0.398966i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 348.494i | 0.439462i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −85.5591 | − | 148.193i | −0.107351 | − | 0.185938i | 0.807345 | − | 0.590080i | \(-0.200904\pi\) |
−0.914696 | + | 0.404142i | \(0.867570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 265.763 | − | 460.316i | 0.332620 | − | 0.576115i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 486.147 | + | 335.233i | 0.606925 | + | 0.418518i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39.2106 | + | 67.9148i | −0.0488302 | + | 0.0845763i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 995.248 | − | 522.639i | 1.23327 | − | 0.647632i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 605.283i | 0.748186i | 0.927391 | + | 0.374093i | \(0.122046\pi\) | ||||
−0.927391 | + | 0.374093i | \(0.877954\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1570.18 | 1.93610 | 0.968050 | − | 0.250756i | \(-0.0806791\pi\) | ||||
0.968050 | + | 0.250756i | \(0.0806791\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −57.4298 | − | 109.362i | −0.0706393 | − | 0.134517i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −567.196 | − | 327.471i | −0.694242 | − | 0.400821i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −60.6575 | + | 87.9642i | −0.0740629 | + | 0.107404i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1386.41 | − | 800.446i | −1.68869 | − | 0.974965i | −0.955523 | − | 0.294915i | \(-0.904709\pi\) |
−0.733166 | − | 0.680050i | \(-0.761958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 323.616 | − | 186.840i | 0.393215 | − | 0.227023i | −0.290337 | − | 0.956924i | \(-0.593768\pi\) |
0.683552 | + | 0.729902i | \(0.260434\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1490.30 | −1.80205 | −0.901027 | − | 0.433764i | \(-0.857185\pi\) | ||||
−0.901027 | + | 0.433764i | \(0.857185\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 85.8287 | 0.103533 | 0.0517664 | − | 0.998659i | \(-0.483515\pi\) | ||||
0.0517664 | + | 0.998659i | \(0.483515\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.35745 | − | 58.8360i | 0.00283688 | − | 0.0708015i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −161.011 | − | 278.879i | −0.193290 | − | 0.334789i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 255.741 | + | 599.099i | 0.305545 | + | 0.715769i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1114.95 | − | 643.717i | −1.32890 | − | 0.767243i | −0.343774 | − | 0.939053i | \(-0.611705\pi\) |
−0.985130 | + | 0.171810i | \(0.945039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −416.543 | − | 721.474i | −0.495295 | − | 0.857876i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.9126 | − | 1095.95i | 0.0520909 | − | 1.30006i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 339.230i | − | 0.400508i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 61.0609 | + | 38.5929i | 0.0719210 | + | 0.0454569i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1069.24 | + | 617.329i | −1.25646 | + | 0.725415i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 908.783 | + | 524.686i | 1.06540 | + | 0.615107i | 0.926920 | − | 0.375259i | \(-0.122446\pi\) |
0.138477 | + | 0.990366i | \(0.455779\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −351.333 | + | 608.526i | −0.409957 | + | 0.710066i | −0.994884 | − | 0.101020i | \(-0.967789\pi\) |
0.584928 | + | 0.811085i | \(0.301123\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 152.845 | + | 264.735i | 0.177934 | + | 0.308190i | 0.941173 | − | 0.337926i | \(-0.109725\pi\) |
−0.763239 | + | 0.646116i | \(0.776392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 86.2417 | + | 164.228i | 0.100165 | + | 0.190741i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −975.875 | −1.13079 | −0.565397 | − | 0.824819i | \(-0.691277\pi\) | ||||
−0.565397 | + | 0.824819i | \(0.691277\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 316.973 | + | 603.604i | 0.365598 | + | 0.696198i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −103.288 | + | 59.6333i | −0.118858 | + | 0.0686229i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 120.646 | − | 208.966i | 0.138515 | − | 0.239915i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1258.80 | + | 598.018i | −1.44192 | + | 0.685015i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −307.716 | + | 177.660i | −0.350874 | + | 0.202577i | −0.665070 | − | 0.746781i | \(-0.731598\pi\) |
0.314196 | + | 0.949358i | \(0.398265\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −546.085 | + | 864.005i | −0.621257 | + | 0.982941i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 645.657i | 0.732869i | 0.930444 | + | 0.366434i | \(0.119422\pi\) | ||||
−0.930444 | + | 0.366434i | \(0.880578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1069.33i | − | 1.21101i | −0.795840 | − | 0.605507i | \(-0.792970\pi\) | ||
0.795840 | − | 0.605507i | \(-0.207030\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 142.678 | + | 247.125i | 0.160854 | + | 0.278608i | 0.935175 | − | 0.354185i | \(-0.115242\pi\) |
−0.774321 | + | 0.632793i | \(0.781908\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −204.515 | + | 354.230i | −0.230050 | + | 0.398459i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.1598 | + | 87.6383i | −0.0158920 | + | 0.0983595i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −451.795 | + | 782.533i | −0.505930 | + | 0.876296i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.4563 | − | 310.879i | 0.0138866 | − | 0.346576i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 67.8706i | 0.0754957i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 391.642 | 0.434675 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 222.528 | − | 352.079i | 0.246432 | − | 0.389900i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1075.37 | − | 620.865i | −1.18563 | − | 0.684526i | −0.228323 | − | 0.973585i | \(-0.573324\pi\) |
−0.957311 | + | 0.289059i | \(0.906658\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1172.58 | + | 557.058i | −1.28997 | + | 0.612825i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −123.752 | − | 71.4483i | −0.135842 | − | 0.0784285i | 0.430539 | − | 0.902572i | \(-0.358324\pi\) |
−0.566381 | + | 0.824144i | \(0.691657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 76.4772 | − | 44.1541i | 0.0837647 | − | 0.0483616i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 544.926 | 0.594248 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −976.872 | −1.06297 | −0.531487 | − | 0.847067i | \(-0.678366\pi\) | ||||
−0.531487 | + | 0.847067i | \(0.678366\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1065.57 | − | 559.568i | 1.15697 | − | 0.607566i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.8345 | + | 51.6748i | 0.0323233 | + | 0.0559857i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6094 | − | 182.015i | 0.0157599 | − | 0.196349i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 784.088 | + | 452.693i | 0.844013 | + | 0.487291i | 0.858626 | − | 0.512602i | \(-0.171318\pi\) |
−0.0146135 | + | 0.999893i | \(0.504652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 273.717 | + | 474.092i | 0.294003 | + | 0.509229i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −230.715 | − | 145.821i | −0.247283 | − | 0.156293i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 601.348i | 0.641780i | 0.947116 | + | 0.320890i | \(0.103982\pi\) | ||||
−0.947116 | + | 0.320890i | \(0.896018\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −55.8834 | + | 1394.71i | −0.0595137 | + | 1.48532i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 430.443 | − | 248.517i | 0.457432 | − | 0.264098i | −0.253532 | − | 0.967327i | \(-0.581592\pi\) |
0.710964 | + | 0.703229i | \(0.248259\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −467.763 | − | 270.063i | −0.496037 | − | 0.286387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −636.420 | + | 1102.31i | −0.672038 | + | 1.16400i | 0.305287 | + | 0.952260i | \(0.401248\pi\) |
−0.977325 | + | 0.211744i | \(0.932086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −150.000 | − | 259.808i | −0.158061 | − | 0.273770i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −580.141 | − | 23.2451i | −0.610033 | − | 0.0244428i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1562.94 | 1.64002 | 0.820009 | − | 0.572351i | \(-0.193968\pi\) | ||||
0.820009 | + | 0.572351i | \(0.193968\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.94180 | + | 7.81881i | −0.00516384 | + | 0.00817013i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 80.6829 | − | 46.5823i | 0.0841324 | − | 0.0485738i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 189.469 | − | 328.170i | 0.197158 | − | 0.341488i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −798.510 | + | 1157.98i | −0.829190 | + | 1.20247i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 322.540 | − | 186.219i | 0.333547 | − | 0.192574i | −0.323868 | − | 0.946102i | \(-0.604983\pi\) |
0.657415 | + | 0.753529i | \(0.271650\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 146.401 | + | 278.787i | 0.151084 | + | 0.287706i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1250.51i | − | 1.28786i | −0.765086 | − | 0.643928i | \(-0.777304\pi\) | ||
0.765086 | − | 0.643928i | \(-0.222696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 453.766i | 0.466358i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −727.019 | − | 1259.23i | −0.744134 | − | 1.28888i | −0.950598 | − | 0.310424i | \(-0.899529\pi\) |
0.206464 | − | 0.978454i | \(-0.433804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.9560 | + | 62.2775i | −0.0367272 | + | 0.0636134i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 283.783 | − | 411.536i | 0.289279 | − | 0.419507i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −612.665 | + | 1061.17i | −0.623261 | + | 1.07952i | 0.365614 | + | 0.930767i | \(0.380859\pi\) |
−0.988874 | + | 0.148752i | \(0.952474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −485.747 | − | 307.011i | −0.492145 | − | 0.311055i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1212.79i | 1.22628i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 847.879 | 0.855579 | 0.427790 | − | 0.903878i | \(-0.359292\pi\) | ||||
0.427790 | + | 0.903878i | \(0.359292\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 395.526 | + | 15.8480i | 0.398314 | + | 0.0159597i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1021.68 | − | 589.869i | −1.02476 | − | 0.591644i | −0.109279 | − | 0.994011i | \(-0.534854\pi\) |
−0.915479 | + | 0.402367i | \(0.868188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −161.520 | + | 1337.96i | −0.161682 | + | 1.33930i |
(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 | 900.3.u.c.749.3 | 24 | ||
3.2 | odd | 2 | 2700.3.u.c.2249.9 | 24 | |||
5.2 | odd | 4 | 900.3.p.c.101.2 | 12 | |||
5.3 | odd | 4 | 180.3.o.b.101.5 | yes | 12 | ||
5.4 | even | 2 | inner | 900.3.u.c.749.10 | 24 | ||
9.4 | even | 3 | 2700.3.u.c.449.4 | 24 | |||
9.5 | odd | 6 | inner | 900.3.u.c.149.10 | 24 | ||
15.2 | even | 4 | 2700.3.p.c.1601.2 | 12 | |||
15.8 | even | 4 | 540.3.o.b.521.3 | 12 | |||
15.14 | odd | 2 | 2700.3.u.c.2249.4 | 24 | |||
20.3 | even | 4 | 720.3.bs.b.641.2 | 12 | |||
45.4 | even | 6 | 2700.3.u.c.449.9 | 24 | |||
45.13 | odd | 12 | 540.3.o.b.341.3 | 12 | |||
45.14 | odd | 6 | inner | 900.3.u.c.149.3 | 24 | ||
45.22 | odd | 12 | 2700.3.p.c.2501.2 | 12 | |||
45.23 | even | 12 | 180.3.o.b.41.5 | ✓ | 12 | ||
45.32 | even | 12 | 900.3.p.c.401.2 | 12 | |||
45.38 | even | 12 | 1620.3.g.b.161.2 | 12 | |||
45.43 | odd | 12 | 1620.3.g.b.161.8 | 12 | |||
60.23 | odd | 4 | 2160.3.bs.b.1601.1 | 12 | |||
180.23 | odd | 12 | 720.3.bs.b.401.2 | 12 | |||
180.103 | even | 12 | 2160.3.bs.b.881.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.o.b.41.5 | ✓ | 12 | 45.23 | even | 12 | ||
180.3.o.b.101.5 | yes | 12 | 5.3 | odd | 4 | ||
540.3.o.b.341.3 | 12 | 45.13 | odd | 12 | |||
540.3.o.b.521.3 | 12 | 15.8 | even | 4 | |||
720.3.bs.b.401.2 | 12 | 180.23 | odd | 12 | |||
720.3.bs.b.641.2 | 12 | 20.3 | even | 4 | |||
900.3.p.c.101.2 | 12 | 5.2 | odd | 4 | |||
900.3.p.c.401.2 | 12 | 45.32 | even | 12 | |||
900.3.u.c.149.3 | 24 | 45.14 | odd | 6 | inner | ||
900.3.u.c.149.10 | 24 | 9.5 | odd | 6 | inner | ||
900.3.u.c.749.3 | 24 | 1.1 | even | 1 | trivial | ||
900.3.u.c.749.10 | 24 | 5.4 | even | 2 | inner | ||
1620.3.g.b.161.2 | 12 | 45.38 | even | 12 | |||
1620.3.g.b.161.8 | 12 | 45.43 | odd | 12 | |||
2160.3.bs.b.881.1 | 12 | 180.103 | even | 12 | |||
2160.3.bs.b.1601.1 | 12 | 60.23 | odd | 4 | |||
2700.3.p.c.1601.2 | 12 | 15.2 | even | 4 | |||
2700.3.p.c.2501.2 | 12 | 45.22 | odd | 12 | |||
2700.3.u.c.449.4 | 24 | 9.4 | even | 3 | |||
2700.3.u.c.449.9 | 24 | 45.4 | even | 6 | |||
2700.3.u.c.2249.4 | 24 | 15.14 | odd | 2 | |||
2700.3.u.c.2249.9 | 24 | 3.2 | odd | 2 |