Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(445,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.445");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 445.20 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.20 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.224370 | − | 2.99160i | −0.0747901 | − | 0.997199i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.33945 | + | 2.31999i | 0.267889 | + | 0.463998i | 0.968317 | − | 0.249726i | \(-0.0803405\pi\) |
−0.700427 | + | 0.713724i | \(0.747007\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.94899 | + | 6.83985i | 0.564142 | + | 0.977122i | 0.997129 | + | 0.0757220i | \(0.0241262\pi\) |
−0.432987 | + | 0.901400i | \(0.642541\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.89932 | + | 1.34245i | −0.988813 | + | 0.149161i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.28360 | − | 7.41940i | −0.389418 | − | 0.674491i | 0.602954 | − | 0.797776i | \(-0.293990\pi\) |
−0.992371 | + | 0.123285i | \(0.960657\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 9.02994i | − | 0.694611i | −0.937752 | − | 0.347305i | \(-0.887097\pi\) | ||
0.937752 | − | 0.347305i | \(-0.112903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.63995 | − | 4.52762i | 0.442663 | − | 0.301842i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.47035 | + | 9.47493i | −0.321785 | + | 0.557349i | −0.980856 | − | 0.194732i | \(-0.937616\pi\) |
0.659071 | + | 0.752081i | \(0.270950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.2593 | − | 14.5158i | 0.645226 | − | 0.763992i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19.5761 | − | 13.3485i | 0.932193 | − | 0.635641i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 30.7444 | 1.33671 | 0.668356 | − | 0.743842i | \(-0.266998\pi\) | ||||
0.668356 | + | 0.743842i | \(0.266998\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.91176 | − | 15.4356i | 0.356471 | − | 0.617425i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.01282 | + | 26.3220i | 0.222697 | + | 0.974888i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.2739 | + | 19.2107i | 1.14738 | + | 0.662437i | 0.948246 | − | 0.317536i | \(-0.102855\pi\) |
0.199129 | + | 0.979973i | \(0.436189\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68676 | + | 2.70590i | 0.151186 | + | 0.0872872i | 0.573685 | − | 0.819076i | \(-0.305514\pi\) |
−0.422499 | + | 0.906364i | \(0.638847\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −21.2348 | + | 14.4795i | −0.643478 | + | 0.438772i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.5789 | + | 18.3232i | −0.302255 | + | 0.523521i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.16539i | − | 0.139605i | −0.997561 | − | 0.0698026i | \(-0.977763\pi\) | ||
0.997561 | − | 0.0698026i | \(-0.0222369\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −27.0139 | + | 2.02605i | −0.692665 | + | 0.0519500i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.170536 | − | 0.0984589i | 0.00415941 | − | 0.00240144i | −0.497919 | − | 0.867224i | \(-0.665902\pi\) |
0.502078 | + | 0.864822i | \(0.332569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57.5695 | 1.33882 | 0.669412 | − | 0.742891i | \(-0.266546\pi\) | ||||
0.669412 | + | 0.742891i | \(0.266546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15.0346 | − | 18.8482i | −0.334103 | − | 0.418848i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 26.2085 | − | 45.3945i | 0.557628 | − | 0.965840i | −0.440066 | − | 0.897965i | \(-0.645045\pi\) |
0.997694 | − | 0.0678744i | \(-0.0216217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68907 | + | 11.5858i | −0.136512 | + | 0.236445i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 29.5726 | + | 14.2392i | 0.579854 | + | 0.279200i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 47.6183 | − | 27.4924i | 0.898458 | − | 0.518725i | 0.0217584 | − | 0.999763i | \(-0.493074\pi\) |
0.876700 | + | 0.481038i | \(0.159740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4753 | − | 19.8758i | 0.208642 | − | 0.361378i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −46.1762 | − | 33.4180i | −0.810108 | − | 0.586280i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34.5173 | + | 19.9286i | −0.585039 | + | 0.337773i | −0.763133 | − | 0.646241i | \(-0.776340\pi\) |
0.178094 | + | 0.984013i | \(0.443007\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21.4222 | − | 37.1043i | 0.351184 | − | 0.608268i | −0.635273 | − | 0.772287i | \(-0.719113\pi\) |
0.986457 | + | 0.164019i | \(0.0524460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −44.3255 | − | 55.5687i | −0.703579 | − | 0.882043i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.9494 | − | 12.0951i | 0.322298 | − | 0.186079i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 93.6359i | 1.39755i | 0.715341 | + | 0.698775i | \(0.246271\pi\) | ||||
−0.715341 | + | 0.698775i | \(0.753729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.89812 | − | 91.9747i | −0.0999727 | − | 1.33297i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −96.9215 | − | 55.9577i | −1.36509 | − | 0.788136i | −0.374795 | − | 0.927108i | \(-0.622287\pi\) |
−0.990296 | + | 0.138972i | \(0.955620\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 59.8200 | − | 103.611i | 0.819451 | − | 1.41933i | −0.0866355 | − | 0.996240i | \(-0.527612\pi\) |
0.906087 | − | 0.423092i | \(-0.139055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −48.1767 | − | 23.1971i | −0.642356 | − | 0.309295i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33.8318 | − | 58.5983i | 0.439374 | − | 0.761017i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 22.7408i | − | 0.287858i | −0.989588 | − | 0.143929i | \(-0.954026\pi\) | ||
0.989588 | − | 0.143929i | \(-0.0459737\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 77.3956 | − | 23.8938i | 0.955502 | − | 0.294985i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.68953 | + | 8.12250i | 0.0565003 | + | 0.0978615i | 0.892892 | − | 0.450271i | \(-0.148672\pi\) |
−0.836392 | + | 0.548132i | \(0.815339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −29.3090 | −0.344812 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 50.0050 | − | 103.852i | 0.574770 | − | 1.19371i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −127.411 | + | 73.5609i | −1.43159 | + | 0.826527i | −0.997242 | − | 0.0742203i | \(-0.976353\pi\) |
−0.434344 | + | 0.900747i | \(0.643020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 61.7635 | − | 35.6592i | 0.678719 | − | 0.391859i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.04340 | − | 14.6280i | 0.0757355 | − | 0.157291i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 50.0973 | + | 8.99825i | 0.527340 | + | 0.0947185i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 122.729i | − | 1.26525i | −0.774460 | − | 0.632623i | \(-0.781978\pi\) | ||
0.774460 | − | 0.632623i | \(-0.218022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 48.0813 | + | 60.2771i | 0.485669 | + | 0.608860i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8938 | + | 24.0647i | −0.137562 | + | 0.238265i | −0.926573 | − | 0.376114i | \(-0.877260\pi\) |
0.789011 | + | 0.614379i | \(0.210593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 149.064 | + | 86.0622i | 1.44722 | + | 0.835555i | 0.998315 | − | 0.0580219i | \(-0.0184793\pi\) |
0.448909 | + | 0.893577i | \(0.351813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 57.1894 | + | 27.5367i | 0.544661 | + | 0.262254i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 114.895i | 1.07378i | 0.843651 | + | 0.536892i | \(0.180402\pi\) | ||||
−0.843651 | + | 0.536892i | \(0.819598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −42.3676 | − | 24.4610i | −0.388694 | − | 0.224412i | 0.292900 | − | 0.956143i | \(-0.405380\pi\) |
−0.681594 | + | 0.731731i | \(0.738713\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.4528 | + | 1.15896i | −0.139214 | + | 0.0104411i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −72.4213 | − | 41.8125i | −0.640897 | − | 0.370022i | 0.144063 | − | 0.989569i | \(-0.453983\pi\) |
−0.784960 | + | 0.619547i | \(0.787317\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41.1804 | + | 71.3266i | 0.358091 | + | 0.620231i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.1223 | + | 80.3603i | 0.103609 | + | 0.686840i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −86.4095 | −0.726130 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.8016 | − | 41.2256i | 0.196708 | − | 0.340708i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.332813 | − | 0.488084i | −0.00270579 | − | 0.00396816i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 114.720 | 0.917757 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −162.862 | + | 94.0285i | −1.28238 | + | 0.740382i | −0.977283 | − | 0.211940i | \(-0.932022\pi\) |
−0.305096 | + | 0.952322i | \(0.598689\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.9169 | − | 172.225i | −0.100131 | − | 1.33508i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 90.5467 | + | 156.832i | 0.691197 | + | 1.19719i | 0.971446 | + | 0.237260i | \(0.0762494\pi\) |
−0.280250 | + | 0.959927i | \(0.590417\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 147.698 | + | 26.5289i | 1.11051 | + | 0.199465i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −53.0129 | + | 49.2066i | −0.392688 | + | 0.364493i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −55.1530 | + | 95.5279i | −0.402577 | + | 0.697284i | −0.994036 | − | 0.109051i | \(-0.965219\pi\) |
0.591459 | + | 0.806335i | \(0.298552\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −165.460 | −1.19036 | −0.595181 | − | 0.803592i | \(-0.702920\pi\) | ||||
−0.595181 | + | 0.803592i | \(0.702920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −141.682 | − | 68.2202i | −1.00484 | − | 0.483831i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −66.9968 | + | 38.6806i | −0.468509 | + | 0.270494i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 102.927i | 0.709840i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 36.1609 | + | 17.4115i | 0.245993 | + | 0.118446i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 66.1128 | + | 114.511i | 0.443710 | + | 0.768528i | 0.997961 | − | 0.0638211i | \(-0.0203287\pi\) |
−0.554251 | + | 0.832349i | \(0.686995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1937 | − | 8.19471i | 0.0939977 | − | 0.0542696i | −0.452264 | − | 0.891884i | \(-0.649384\pi\) |
0.546262 | + | 0.837614i | \(0.316050\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 35.9628 | − | 91.6640i | 0.235051 | − | 0.599111i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4977i | 0.0935332i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −114.072 | − | 197.578i | −0.726573 | − | 1.25846i | −0.958323 | − | 0.285685i | \(-0.907779\pi\) |
0.231751 | − | 0.972775i | \(-0.425555\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −92.9304 | − | 136.286i | −0.584468 | − | 0.857146i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 121.409 | + | 210.287i | 0.754094 | + | 1.30613i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 158.988 | 0.975387 | 0.487693 | − | 0.873015i | \(-0.337838\pi\) | ||||
0.487693 | + | 0.873015i | \(0.337838\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −62.0351 | − | 29.8699i | −0.375970 | − | 0.181030i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 278.878i | 1.66993i | 0.550303 | + | 0.834965i | \(0.314512\pi\) | ||||
−0.550303 | + | 0.834965i | \(0.685488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 87.4602 | 0.517516 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −89.6126 | + | 145.639i | −0.524050 | + | 0.851687i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 41.5799i | − | 0.240346i | −0.992753 | − | 0.120173i | \(-0.961655\pi\) | ||
0.992753 | − | 0.120173i | \(-0.0383450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 140.770 | 0.804400 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 67.3630 | + | 98.7905i | 0.380582 | + | 0.558139i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 28.2132i | 0.157616i | 0.996890 | + | 0.0788079i | \(0.0251114\pi\) | ||||
−0.996890 | + | 0.0788079i | \(0.974889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 231.069 | − | 133.408i | 1.27663 | − | 0.737061i | 0.300400 | − | 0.953813i | \(-0.402880\pi\) |
0.976227 | + | 0.216753i | \(0.0695465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −115.808 | − | 55.7615i | −0.632829 | − | 0.304708i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.9837 | − | 6.91877i | 0.0647766 | − | 0.0373988i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 93.7311 | 0.501236 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −156.294 | + | 145.072i | −0.826952 | + | 0.767577i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −115.225 | − | 199.576i | −0.603274 | − | 1.04490i | −0.992322 | − | 0.123684i | \(-0.960529\pi\) |
0.389048 | − | 0.921218i | \(-0.372804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −72.4866 | + | 41.8502i | −0.375578 | + | 0.216840i | −0.675893 | − | 0.737000i | \(-0.736242\pi\) |
0.300314 | + | 0.953840i | \(0.402908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −40.8842 | − | 59.9583i | −0.209662 | − | 0.307478i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.8579 | −0.0601923 | −0.0300961 | − | 0.999547i | \(-0.509581\pi\) | ||||
−0.0300961 | + | 0.999547i | \(0.509581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −71.2816 | − | 123.463i | −0.358199 | − | 0.620419i | 0.629461 | − | 0.777032i | \(-0.283276\pi\) |
−0.987660 | + | 0.156613i | \(0.949942\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 280.121 | − | 21.0091i | 1.39364 | − | 0.104523i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 303.451i | 1.49483i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.456847 | + | 0.263761i | 0.00222852 | + | 0.00128664i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −273.604 | + | 41.2728i | −1.32176 | + | 0.199386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −160.213 | − | 28.7767i | −0.766568 | − | 0.137688i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 73.9286 | − | 42.6827i | 0.350372 | − | 0.202288i | −0.314477 | − | 0.949265i | \(-0.601829\pi\) |
0.664849 | + | 0.746978i | \(0.268496\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −145.657 | + | 302.505i | −0.683833 | + | 1.42021i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 77.1112 | + | 133.561i | 0.358657 | + | 0.621212i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42.7424i | 0.196969i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −323.385 | − | 155.710i | −1.47664 | − | 0.711004i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 85.5580 | + | 49.3969i | 0.387140 | + | 0.223516i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2042i | 0.0592117i | 0.999562 | + | 0.0296059i | \(0.00942522\pi\) | ||||
−0.999562 | + | 0.0296059i | \(0.990575\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −58.5870 | + | 149.330i | −0.260387 | + | 0.663690i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −302.960 | + | 174.914i | −1.33462 | + | 0.770545i | −0.986004 | − | 0.166719i | \(-0.946683\pi\) |
−0.348619 | + | 0.937264i | \(0.613349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −86.8786 | + | 150.478i | −0.379383 | + | 0.657110i | −0.990973 | − | 0.134065i | \(-0.957197\pi\) |
0.611590 | + | 0.791175i | \(0.290530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −182.893 | − | 88.0633i | −0.791747 | − | 0.381226i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 85.4215 | − | 147.954i | 0.366616 | − | 0.634997i | −0.622418 | − | 0.782685i | \(-0.713850\pi\) |
0.989034 | + | 0.147687i | \(0.0471830\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 140.420 | 0.597530 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −68.0313 | + | 5.10236i | −0.287052 | + | 0.0215289i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 60.5709 | − | 104.912i | 0.253435 | − | 0.438962i | −0.711034 | − | 0.703157i | \(-0.751773\pi\) |
0.964469 | + | 0.264195i | \(0.0851064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 127.958 | + | 73.8769i | 0.530948 | + | 0.306543i | 0.741402 | − | 0.671061i | \(-0.234161\pi\) |
−0.210454 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −88.8459 | − | 226.176i | −0.365621 | − | 0.930764i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −35.8386 | −0.146280 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −131.077 | − | 110.701i | −0.530677 | − | 0.448181i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.2471 | − | 15.8516i | 0.0933617 | − | 0.0636612i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 42.2197 | + | 73.1266i | 0.168206 | + | 0.291341i | 0.937789 | − | 0.347205i | \(-0.112869\pi\) |
−0.769583 | + | 0.638547i | \(0.779536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −131.696 | − | 228.105i | −0.520539 | − | 0.901600i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.57606 | + | 87.6807i | 0.0257885 | + | 0.343846i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 140.105i | 0.545156i | 0.962134 | + | 0.272578i | \(0.0878762\pi\) | ||||
−0.962134 | + | 0.272578i | \(0.912124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.3305 | − | 20.3981i | 0.136411 | − | 0.0787571i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −321.904 | − | 126.293i | −1.23335 | − | 0.483883i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −124.076 | −0.471770 | −0.235885 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235885 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 127.564 | + | 73.6493i | 0.481375 | + | 0.277922i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 248.652 | + | 364.658i | 0.931280 | + | 1.36576i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −49.9138 | − | 28.8177i | −0.185553 | − | 0.107129i | 0.404346 | − | 0.914606i | \(-0.367499\pi\) |
−0.589899 | + | 0.807477i | \(0.700833\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.3322 | + | 56.0009i | −0.119307 | + | 0.206646i | −0.919493 | − | 0.393106i | \(-0.871401\pi\) |
0.800186 | + | 0.599751i | \(0.204734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −120.536 | − | 176.771i | −0.441523 | − | 0.647511i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −152.698 | −0.555264 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 94.5582 | + | 163.780i | 0.341365 | + | 0.591262i | 0.984687 | − | 0.174334i | \(-0.0557773\pi\) |
−0.643321 | + | 0.765596i | \(0.722444\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −45.3415 | − | 17.7889i | −0.162514 | − | 0.0637596i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −50.6167 | − | 29.2236i | −0.180131 | − | 0.103998i | 0.407223 | − | 0.913329i | \(-0.366497\pi\) |
−0.587354 | + | 0.809330i | \(0.699830\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9633 | − | 22.4530i | −0.0458066 | − | 0.0793393i | 0.842213 | − | 0.539145i | \(-0.181252\pi\) |
−0.888020 | + | 0.459806i | \(0.847919\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.6788 | − | 151.890i | 0.0550134 | − | 0.532947i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.34689 | + | 0.777627i | 0.00469299 | + | 0.00270950i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 84.6505 | + | 146.619i | 0.292908 | + | 0.507332i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −367.155 | + | 27.5367i | −1.26170 | + | 0.0946278i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −43.1821 | − | 24.9312i | −0.147379 | − | 0.0850894i | 0.424497 | − | 0.905429i | \(-0.360451\pi\) |
−0.571876 | + | 0.820340i | \(0.693784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −92.4682 | − | 53.3865i | −0.313452 | − | 0.180971i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 169.537 | − | 157.364i | 0.570831 | − | 0.529846i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 277.620i | − | 0.928494i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 227.341 | + | 393.767i | 0.755287 | + | 1.30820i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 75.1094 | + | 36.1652i | 0.247886 | + | 0.119357i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 114.776 | 0.376313 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −264.700 | − | 152.825i | −0.862215 | − | 0.497800i | 0.00253851 | − | 0.999997i | \(-0.499192\pi\) |
−0.864753 | + | 0.502197i | \(0.832525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 224.018 | − | 465.250i | 0.724977 | − | 1.50566i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −169.216 | + | 293.091i | −0.544104 | + | 0.942415i | 0.454559 | + | 0.890717i | \(0.349797\pi\) |
−0.998663 | + | 0.0516988i | \(0.983536\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −265.989 | + | 460.707i | −0.849805 | + | 1.47191i | 0.0315766 | + | 0.999501i | \(0.489947\pi\) |
−0.881382 | + | 0.472404i | \(0.843386\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 69.5472 | − | 177.266i | 0.220785 | − | 0.562749i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −348.666 | − | 201.302i | −1.09989 | − | 0.635023i | −0.163699 | − | 0.986510i | \(-0.552343\pi\) |
−0.936193 | + | 0.351488i | \(0.885676\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 329.163i | − | 1.03186i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 343.719 | − | 25.7790i | 1.07078 | − | 0.0803084i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 70.4738 | + | 195.563i | 0.218185 | + | 0.605457i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −139.383 | − | 80.4727i | −0.428870 | − | 0.247608i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −63.6713 | + | 132.235i | −0.194713 | + | 0.404389i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 413.989 | 1.25832 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 139.693 | − | 80.6518i | 0.422033 | − | 0.243661i | −0.273914 | − | 0.961754i | \(-0.588318\pi\) |
0.695947 | + | 0.718093i | \(0.254985\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.93429 | + | 45.9685i | 0.0208237 | + | 0.138043i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −217.234 | + | 125.420i | −0.648461 | + | 0.374389i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −144.327 | + | 83.3271i | −0.428269 | + | 0.247261i | −0.698609 | − | 0.715504i | \(-0.746197\pi\) |
0.270340 | + | 0.962765i | \(0.412864\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −108.837 | + | 226.037i | −0.321053 | + | 0.666776i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 46.3640i | − | 0.135965i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 281.341 | 0.820236 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 204.141 | − | 139.199i | 0.591713 | − | 0.403475i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.67760 | + | 13.2980i | 0.0221257 | + | 0.0383228i | 0.876876 | − | 0.480716i | \(-0.159623\pi\) |
−0.854751 | + | 0.519039i | \(0.826290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −89.3968 | − | 154.840i | −0.256151 | − | 0.443667i | 0.709056 | − | 0.705152i | \(-0.249121\pi\) |
−0.965208 | + | 0.261485i | \(0.915788\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 237.686 | − | 54.2954i | 0.677167 | − | 0.154688i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −183.358 | − | 317.585i | −0.519428 | − | 0.899675i | −0.999745 | − | 0.0225805i | \(-0.992812\pi\) |
0.480317 | − | 0.877095i | \(-0.340522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 299.809i | − | 0.844533i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.3877 | + | 258.502i | 0.0543073 | + | 0.724096i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 170.933 | − | 296.065i | 0.476138 | − | 0.824695i | −0.523489 | − | 0.852033i | \(-0.675370\pi\) |
0.999626 | + | 0.0273381i | \(0.00870306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −60.4192 | − | 355.908i | −0.167366 | − | 0.985895i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −128.671 | − | 61.9551i | −0.354465 | − | 0.170675i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 320.503 | 0.878089 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.6813 | − | 18.5005i | 0.0291043 | − | 0.0504101i | −0.851106 | − | 0.524993i | \(-0.824068\pi\) |
0.880211 | + | 0.474583i | \(0.157401\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.38548 | + | 1.10515i | −0.00375468 | + | 0.00299500i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 376.088 | + | 217.135i | 1.01372 | + | 0.585269i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 565.547 | + | 326.519i | 1.51621 | + | 0.875386i | 0.999819 | + | 0.0190347i | \(0.00605930\pi\) |
0.516394 | + | 0.856351i | \(0.327274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.7397 | − | 343.195i | −0.0686392 | − | 0.915187i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 173.471 | − | 300.461i | 0.460136 | − | 0.796979i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 580.854i | 1.53260i | 0.642486 | + | 0.766298i | \(0.277903\pi\) | ||||
−0.642486 | + | 0.766298i | \(0.722097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 317.837 | + | 466.121i | 0.834218 | + | 1.22341i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −493.235 | + | 284.769i | −1.28782 | + | 0.743523i | −0.978265 | − | 0.207359i | \(-0.933513\pi\) |
−0.309555 | + | 0.950882i | \(0.600180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 181.263 | 0.470814 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −512.329 | + | 77.2842i | −1.32385 | + | 0.199701i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −244.004 | + | 422.627i | −0.627259 | + | 1.08644i | 0.360841 | + | 0.932627i | \(0.382490\pi\) |
−0.988099 | + | 0.153816i | \(0.950844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −168.182 | + | 291.300i | −0.430134 | + | 0.745014i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 448.861 | − | 306.068i | 1.14214 | − | 0.778798i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 52.7584 | − | 30.4601i | 0.133566 | − | 0.0771141i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 113.279 | − | 196.205i | 0.285337 | − | 0.494218i | −0.687354 | − | 0.726323i | \(-0.741228\pi\) |
0.972691 | + | 0.232104i | \(0.0745611\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 46.2247 | − | 447.806i | 0.115851 | − | 1.12232i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 243.178 | − | 140.399i | 0.606428 | − | 0.350121i | −0.165138 | − | 0.986270i | \(-0.552807\pi\) |
0.771566 | + | 0.636149i | \(0.219474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.4341 | − | 42.3212i | 0.0606306 | − | 0.105015i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 159.101 | + | 147.553i | 0.392841 | + | 0.364328i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −38.3242 | + | 22.1265i | −0.0941625 | + | 0.0543648i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.9875i | 0.0659841i | 0.999456 | + | 0.0329920i | \(0.0105036\pi\) | ||||
−0.999456 | + | 0.0329920i | \(0.989496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 298.156 | + | 143.562i | 0.725439 | + | 0.349299i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −272.617 | − | 157.396i | −0.660090 | − | 0.381103i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5627 | + | 21.7593i | −0.0302717 | + | 0.0524321i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.1244 | + | 494.991i | 0.0890273 | + | 1.18703i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −313.564 | + | 543.108i | −0.748362 | + | 1.29620i | 0.200246 | + | 0.979746i | \(0.435826\pi\) |
−0.948608 | + | 0.316455i | \(0.897507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 310.341i | − | 0.737152i | −0.929598 | − | 0.368576i | \(-0.879845\pi\) | ||
0.929598 | − | 0.368576i | \(-0.120155\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −172.298 | + | 439.163i | −0.407324 | + | 1.03821i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 97.5010 | + | 168.877i | 0.229414 | + | 0.397357i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 338.384 | 0.792469 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 130.749 | + | 191.749i | 0.304776 | + | 0.446966i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 99.2968 | − | 57.3290i | 0.230387 | − | 0.133014i | −0.380364 | − | 0.924837i | \(-0.624201\pi\) |
0.610751 | + | 0.791823i | \(0.290868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 198.843 | − | 114.802i | 0.459222 | − | 0.265132i | −0.252495 | − | 0.967598i | \(-0.581251\pi\) |
0.711717 | + | 0.702466i | \(0.247918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 307.916 | − | 23.0937i | 0.707852 | − | 0.0530890i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 376.904 | − | 446.280i | 0.862481 | − | 1.02124i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 528.851i | 1.20467i | 0.798243 | + | 0.602336i | \(0.205763\pi\) | ||||
−0.798243 | + | 0.602336i | \(0.794237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.9748 | − | 112.086i | 0.0997160 | − | 0.254162i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 366.673 | − | 635.095i | 0.827703 | − | 1.43362i | −0.0721324 | − | 0.997395i | \(-0.522980\pi\) |
0.899836 | − | 0.436229i | \(-0.143686\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −341.321 | − | 197.062i | −0.767013 | − | 0.442835i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 327.736 | − | 223.476i | 0.733191 | − | 0.499946i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 379.685i | − | 0.845623i | −0.906218 | − | 0.422811i | \(-0.861043\pi\) | ||
0.906218 | − | 0.422811i | \(-0.138957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.46101 | − | 0.843516i | −0.00323950 | − | 0.00187032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.6999 | − | 40.6231i | −0.0611477 | − | 0.0896756i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 165.458 | + | 95.5271i | 0.363643 | + | 0.209950i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −429.940 | − | 744.678i | −0.940788 | − | 1.62949i | −0.763973 | − | 0.645248i | \(-0.776754\pi\) |
−0.176815 | − | 0.984244i | \(-0.556579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −282.291 | − | 87.0194i | −0.615013 | − | 0.189585i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −62.3136 | −0.135171 | −0.0675853 | − | 0.997713i | \(-0.521529\pi\) | ||||
−0.0675853 | + | 0.997713i | \(0.521529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 253.463 | − | 439.011i | 0.547436 | − | 0.948188i | −0.451013 | − | 0.892517i | \(-0.648937\pi\) |
0.998449 | − | 0.0556702i | \(-0.0177295\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 43.3711 | − | 3.25284i | 0.0932713 | − | 0.00699536i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 721.660 | 1.54531 | 0.772655 | − | 0.634826i | \(-0.218928\pi\) | ||||
0.772655 | + | 0.634826i | \(0.218928\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −640.456 | + | 369.767i | −1.36558 | + | 0.788417i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −565.480 | + | 385.588i | −1.20060 | + | 0.818658i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −246.604 | − | 427.131i | −0.521362 | − | 0.903026i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −114.809 | − | 318.592i | −0.241703 | − | 0.670719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −386.863 | + | 308.589i | −0.811033 | + | 0.646937i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.1617 | + | 45.3133i | −0.0546172 | + | 0.0945998i | −0.892041 | − | 0.451954i | \(-0.850727\pi\) |
0.837424 | + | 0.546554i | \(0.184061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.6432 | −0.0969713 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 601.853 | − | 410.390i | 1.24607 | − | 0.849668i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 284.730 | − | 164.389i | 0.587071 | − | 0.338946i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 409.665i | 0.841201i | 0.907246 | + | 0.420601i | \(0.138181\pi\) | ||||
−0.907246 | + | 0.420601i | \(0.861819\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.6722 | − | 475.628i | −0.0729493 | − | 0.972655i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 318.398 | + | 551.481i | 0.648468 | + | 1.12318i | 0.983489 | + | 0.180969i | \(0.0579232\pi\) |
−0.335021 | + | 0.942211i | \(0.608743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −364.040 | + | 210.178i | −0.738417 | + | 0.426325i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −75.4400 | + | 192.286i | −0.152404 | + | 0.388457i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 883.905i | − | 1.77848i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −107.604 | − | 186.376i | −0.215639 | − | 0.373498i | 0.737831 | − | 0.674986i | \(-0.235850\pi\) |
−0.953470 | + | 0.301487i | \(0.902517\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 834.292 | − | 62.5720i | 1.66525 | − | 0.124894i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −59.6655 | − | 103.344i | −0.118619 | − | 0.205455i | 0.800601 | − | 0.599197i | \(-0.204513\pi\) |
−0.919221 | + | 0.393743i | \(0.871180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −74.4399 | −0.147406 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.6235 | − | 261.646i | −0.0387051 | − | 0.516067i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 702.755i | 1.38066i | 0.723496 | + | 0.690329i | \(0.242534\pi\) | ||||
−0.723496 | + | 0.690329i | \(0.757466\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 944.914 | 1.84915 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 455.798 | + | 235.408i | 0.888496 | + | 0.458885i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 461.103i | 0.895346i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −449.067 | −0.868601 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −124.390 | + | 9.32929i | −0.239673 | + | 0.0179755i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 881.609i | − | 1.69215i | −0.533066 | − | 0.846074i | \(-0.678960\pi\) | ||
0.533066 | − | 0.846074i | \(-0.321040\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 670.142 | − | 386.907i | 1.28134 | − | 0.739783i | 0.304248 | − | 0.952593i | \(-0.401595\pi\) |
0.977094 | + | 0.212810i | \(0.0682615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −31.5846 | − | 421.127i | −0.0601611 | − | 0.802147i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.2765 | + | 29.6045i | −0.0972988 | + | 0.0561755i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 416.215 | 0.786796 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 280.427 | − | 223.689i | 0.528112 | − | 0.421259i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.889078 | − | 1.53993i | −0.00166806 | − | 0.00288917i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −266.555 | + | 153.896i | −0.498233 | + | 0.287655i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 84.4026 | − | 6.33021i | 0.157174 | − | 0.0117881i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 114.613 | 0.212640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −246.112 | − | 426.278i | −0.454920 | − | 0.787944i | 0.543764 | − | 0.839238i | \(-0.316999\pi\) |
−0.998684 | + | 0.0512943i | \(0.983665\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −450.948 | − | 661.334i | −0.830475 | − | 1.21793i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 131.057i | − | 0.240471i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −460.560 | − | 265.904i | −0.841974 | − | 0.486114i | 0.0159610 | − | 0.999873i | \(-0.494919\pi\) |
−0.857935 | + | 0.513759i | \(0.828253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −140.832 | + | 358.962i | −0.256525 | + | 0.653846i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 686.774 | − | 247.489i | 1.24641 | − | 0.449163i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 155.544 | − | 89.8032i | 0.281273 | − | 0.162393i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.3870 | − | 34.2979i | −0.0421387 | − | 0.0617981i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −172.254 | − | 298.352i | −0.309253 | − | 0.535642i | 0.668946 | − | 0.743311i | \(-0.266746\pi\) |
−0.978199 | + | 0.207669i | \(0.933412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 519.849i | − | 0.929962i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.0305 | − | 280.406i | −0.0374875 | − | 0.499832i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −751.453 | − | 433.851i | −1.33473 | − | 0.770606i | −0.348709 | − | 0.937231i | \(-0.613380\pi\) |
−0.986020 | + | 0.166625i | \(0.946713\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 224.022i | − | 0.396500i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 469.065 | + | 435.019i | 0.827275 | + | 0.767228i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.8460 | + | 17.2316i | −0.0524534 | + | 0.0302840i | −0.525997 | − | 0.850486i | \(-0.676308\pi\) |
0.473544 | + | 0.880770i | \(0.342975\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −250.214 | + | 433.383i | −0.438203 | + | 0.758990i | −0.997551 | − | 0.0699428i | \(-0.977718\pi\) |
0.559348 | + | 0.828933i | \(0.311052\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −571.199 | + | 389.487i | −0.996856 | + | 0.679733i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 273.986 | − | 474.558i | 0.476498 | − | 0.825319i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −780.995 | −1.35354 | −0.676772 | − | 0.736193i | \(-0.736622\pi\) | ||||
−0.676772 | + | 0.736193i | \(0.736622\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 141.463 | + | 207.461i | 0.244322 | + | 0.358309i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.0378 | + | 64.1514i | −0.0637484 | + | 0.110415i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −407.955 | − | 235.533i | −0.699751 | − | 0.404001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −170.198 | + | 135.762i | −0.290937 | + | 0.232071i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 319.392 | 0.544109 | 0.272055 | − | 0.962282i | \(-0.412297\pi\) | ||||
0.272055 | + | 0.962282i | \(0.412297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 96.7349 | − | 34.8598i | 0.164236 | − | 0.0591847i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.66056 | + | 35.4740i | 0.00450179 | + | 0.0600237i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 154.888 | + | 268.273i | 0.261193 | + | 0.452400i | 0.966559 | − | 0.256443i | \(-0.0825507\pi\) |
−0.705366 | + | 0.708843i | \(0.749217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −115.741 | − | 200.469i | −0.194523 | − | 0.336923i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −353.359 | + | 240.947i | −0.591892 | + | 0.403597i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 657.969i | 1.09845i | 0.835676 | + | 0.549223i | \(0.185076\pi\) | ||||
−0.835676 | + | 0.549223i | \(0.814924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −757.787 | + | 437.508i | −1.26088 | + | 0.727967i | −0.973244 | − | 0.229774i | \(-0.926201\pi\) |
−0.287632 | + | 0.957741i | \(0.592868\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −125.702 | − | 833.295i | −0.208460 | − | 1.38192i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 127.524 | 0.210784 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 340.767 | + | 196.742i | 0.561396 | + | 0.324122i | 0.753706 | − | 0.657212i | \(-0.228264\pi\) |
−0.192310 | + | 0.981334i | \(0.561598\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 907.804 | − | 68.0855i | 1.49065 | − | 0.111799i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −409.909 | − | 236.661i | −0.670883 | − | 0.387334i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −581.450 | + | 1007.10i | −0.948533 | + | 1.64291i | −0.200014 | + | 0.979793i | \(0.564099\pi\) |
−0.748519 | + | 0.663114i | \(0.769235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.686564 | − | 1.42588i | 0.00111636 | − | 0.00231851i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −350.510 | −0.568087 | −0.284043 | − | 0.958811i | \(-0.591676\pi\) | ||||
−0.284043 | + | 0.958811i | \(0.591676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 367.778 | + | 637.010i | 0.594148 | + | 1.02909i | 0.993666 | + | 0.112370i | \(0.0358440\pi\) |
−0.399518 | + | 0.916725i | \(0.630823\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 184.860 | + | 809.252i | 0.297681 | + | 1.30314i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1006.29 | − | 580.983i | −1.61523 | − | 0.932556i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −69.1332 | − | 119.742i | −0.110613 | − | 0.191588i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −50.1414 | + | 485.749i | −0.0799703 | + | 0.774719i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.9417 | + | 28.2565i | 0.0778088 | + | 0.0449229i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −108.316 | − | 187.610i | −0.171658 | − | 0.297321i | 0.767341 | − | 0.641239i | \(-0.221579\pi\) |
−0.939000 | + | 0.343918i | \(0.888246\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −144.277 | − | 211.588i | −0.227925 | − | 0.334262i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −436.290 | − | 251.892i | −0.687071 | − | 0.396681i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 104.619 | + | 60.4019i | 0.164237 | + | 0.0948224i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 937.656 | + | 367.872i | 1.46738 | + | 0.575700i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 73.7982i | − | 0.115130i | −0.998342 | − | 0.0575649i | \(-0.981666\pi\) | ||
0.998342 | − | 0.0575649i | \(-0.0183336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −578.067 | − | 1001.24i | −0.899016 | − | 1.55714i | −0.828754 | − | 0.559613i | \(-0.810950\pi\) |
−0.0702619 | − | 0.997529i | \(-0.522384\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 382.258 | − | 260.653i | 0.592648 | − | 0.404113i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 616.353 | 0.952632 | 0.476316 | − | 0.879274i | \(-0.341972\pi\) | ||||
0.476316 | + | 0.879274i | \(0.341972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 295.716 | + | 170.732i | 0.455649 | + | 0.263069i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 127.868 | − | 9.59011i | 0.196418 | − | 0.0147314i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.0169 | − | 74.5074i | 0.0658758 | − | 0.114100i | −0.831206 | − | 0.555964i | \(-0.812349\pi\) |
0.897082 | + | 0.441864i | \(0.145683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −242.565 | + | 420.135i | −0.370328 | + | 0.641428i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −393.264 | + | 1002.37i | −0.598575 | + | 1.52568i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −105.736 | − | 61.0468i | −0.160449 | − | 0.0926356i | 0.417625 | − | 0.908619i | \(-0.362862\pi\) |
−0.578075 | + | 0.815984i | \(0.696196\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 57.5656i | 0.0870886i | 0.999051 | + | 0.0435443i | \(0.0138650\pi\) | ||||
−0.999051 | + | 0.0435443i | \(0.986135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 128.579 | − | 267.038i | 0.193935 | − | 0.402773i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 136.287 | + | 378.192i | 0.204943 | + | 0.568710i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1022.98 | + | 590.620i | 1.53371 | + | 0.885487i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.5017 | − | 2.96263i | 0.0590459 | − | 0.00442845i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −367.056 | −0.547029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −702.761 | + | 405.739i | −1.04422 | + | 0.602882i | −0.921026 | − | 0.389501i | \(-0.872648\pi\) |
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 459.881 | + | 141.764i | 0.681305 | + | 0.210020i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −72.6816 | + | 41.9627i | −0.107358 | + | 0.0619834i | −0.552718 | − | 0.833369i | \(-0.686409\pi\) |
0.445359 | + | 0.895352i | \(0.353076\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 839.447 | − | 484.655i | 1.23630 | − | 0.713778i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 591.247 | + | 867.088i | 0.868204 | + | 1.27326i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1065.59i | 1.56017i | 0.625675 | + | 0.780084i | \(0.284824\pi\) | ||||
−0.625675 | + | 0.780084i | \(0.715176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −295.498 | −0.431384 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 469.663 | + | 226.143i | 0.683644 | + | 0.329175i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −248.255 | − | 429.990i | −0.360312 | − | 0.624078i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −290.460 | − | 503.092i | −0.420348 | − | 0.728064i | 0.575626 | − | 0.817713i | \(-0.304759\pi\) |
−0.995973 | + | 0.0896497i | \(0.971425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −222.414 | + | 566.903i | −0.320944 | + | 0.818041i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −221.625 | − | 383.866i | −0.318885 | − | 0.552326i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.15442i | 0.00309099i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −461.786 | − | 222.350i | −0.660638 | − | 0.318098i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 341.550 | − | 591.583i | 0.487233 | − | 0.843913i | −0.512659 | − | 0.858592i | \(-0.671339\pi\) |
0.999892 | + | 0.0146796i | \(0.00467282\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −74.9800 | − | 63.3241i | −0.106657 | − | 0.0900770i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.5060 | − | 420.079i | −0.0446894 | − | 0.595857i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −219.466 | −0.310418 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −177.679 | + | 307.749i | −0.250605 | + | 0.434060i | −0.963693 | − | 0.267015i | \(-0.913963\pi\) |
0.713088 | + | 0.701075i | \(0.247296\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.5284 | + | 202.377i | 0.0429373 | + | 0.284638i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 144.091 | + | 83.1912i | 0.202092 | + | 0.116678i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −179.477 | − | 103.621i | −0.251017 | − | 0.144925i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −327.444 | − | 157.665i | −0.456687 | − | 0.219895i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 610.091 | − | 1056.71i | 0.848528 | − | 1.46969i | −0.0339943 | − | 0.999422i | \(-0.510823\pi\) |
0.882522 | − | 0.470271i | \(-0.155844\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1359.44i | 1.88549i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 192.300 | − | 399.376i | 0.265975 | − | 0.552387i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 593.058 | − | 342.402i | 0.818011 | − | 0.472279i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1445.67 | −1.98854 | −0.994269 | − | 0.106912i | \(-0.965904\pi\) | ||||
−0.994269 | + | 0.106912i | \(0.965904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −656.692 | + | 316.538i | −0.900812 | + | 0.434209i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −314.925 | + | 545.466i | −0.430814 | + | 0.746192i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 228.185 | − | 395.227i | 0.311302 | − | 0.539192i | −0.667342 | − | 0.744751i | \(-0.732568\pi\) |
0.978645 | + | 0.205560i | \(0.0659015\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.04112 | + | 107.215i | 0.0109403 | + | 0.145870i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 694.723 | − | 401.098i | 0.942636 | − | 0.544231i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −525.271 | + | 909.796i | −0.710786 | + | 1.23112i | 0.253777 | + | 0.967263i | \(0.418327\pi\) |
−0.964563 | + | 0.263854i | \(0.915006\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −301.762 | + | 416.968i | −0.407236 | + | 0.562710i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 785.956 | − | 453.772i | 1.05781 | − | 0.610729i | 0.132987 | − | 0.991118i | \(-0.457543\pi\) |
0.924827 | + | 0.380388i | \(0.124210\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −177.109 | + | 306.762i | −0.237730 | + | 0.411761i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52.6377 | − | 65.9892i | −0.0704654 | − | 0.0883390i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −785.864 | + | 453.719i | −1.04922 | + | 0.605766i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 540.881i | 0.720214i | 0.932911 | + | 0.360107i | \(0.117260\pi\) | ||||
−0.932911 | + | 0.360107i | \(0.882740\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 209.293 | − | 142.712i | 0.277945 | − | 0.189524i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.0233 | + | 21.9528i | 0.0503620 | + | 0.0290765i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −337.788 | + | 585.066i | −0.446219 | + | 0.772874i | −0.998136 | − | 0.0610249i | \(-0.980563\pi\) |
0.551917 | + | 0.833899i | \(0.313896\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −652.849 | + | 445.163i | −0.860144 | + | 0.586512i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 644.819 | − | 1116.86i | 0.847331 | − | 1.46762i | −0.0362499 | − | 0.999343i | \(-0.511541\pi\) |
0.883581 | − | 0.468278i | \(-0.155125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 386.384i | − | 0.506402i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 260.830 | − | 39.3459i | 0.340954 | − | 0.0514325i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 179.954 | + | 311.689i | 0.234620 | + | 0.406374i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 281.959 | 0.366656 | 0.183328 | − | 0.983052i | \(-0.441313\pi\) | ||||
0.183328 | + | 0.983052i | \(0.441313\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 419.138 | − | 31.4354i | 0.543629 | − | 0.0407722i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 70.8563 | − | 40.9089i | 0.0916640 | − | 0.0529222i | −0.453467 | − | 0.891273i | \(-0.649813\pi\) |
0.545131 | + | 0.838351i | \(0.316480\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 83.5346 | − | 48.2287i | 0.107787 | − | 0.0622306i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −68.9500 | − | 101.118i | −0.0887388 | − | 0.130139i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.661436 | − | 3.68251i | 0.000849084 | − | 0.00472723i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 958.800i | 1.22766i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −305.593 | + | 991.344i | −0.390285 | + | 1.26608i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 305.586 | − | 529.291i | 0.389282 | − | 0.674256i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 246.928 | + | 142.564i | 0.313758 | + | 0.181148i | 0.648607 | − | 0.761124i | \(-0.275352\pi\) |
−0.334849 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.8389 | + | 371.184i | 0.0352837 | + | 0.470449i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 660.469i | − | 0.834979i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −335.050 | − | 193.441i | −0.422509 | − | 0.243936i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 191.707 | − | 398.146i | 0.241141 | − | 0.500812i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1337.76 | − | 772.354i | −1.67849 | − | 0.969077i | −0.962625 | − | 0.270839i | \(-0.912699\pi\) |
−0.715866 | − | 0.698238i | \(-0.753968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 286.740 | + | 496.647i | 0.358873 | + | 0.621586i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1035.12 | − | 825.685i | 1.29229 | − | 1.03082i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1024.98 | −1.27644 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −325.242 | + | 563.336i | −0.404028 | + | 0.699797i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −75.0119 | + | 155.788i | −0.0929516 | + | 0.193046i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −814.325 | −1.00658 | −0.503291 | − | 0.864117i | \(-0.667878\pi\) | ||||
−0.503291 | + | 0.864117i | \(0.667878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 127.960 | − | 73.8776i | 0.157780 | − | 0.0910944i | −0.419031 | − | 0.907972i | \(-0.637630\pi\) |
0.576811 | + | 0.816877i | \(0.304297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 174.787 | + | 84.1599i | 0.214990 | + | 0.103518i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 212.956 | + | 368.851i | 0.261296 | + | 0.452577i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 705.761 | − | 835.669i | 0.863845 | − | 1.02285i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −501.782 | + | 400.256i | −0.612676 | + | 0.488714i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −678.314 | + | 1174.87i | −0.826204 | + | 1.43103i | 0.0747912 | + | 0.997199i | \(0.476171\pi\) |
−0.900995 | + | 0.433829i | \(0.857162\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1482.82 | −1.80172 | −0.900862 | − | 0.434106i | \(-0.857064\pi\) | ||||
−0.900862 | + | 0.434106i | \(0.857064\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.2608 | + | 456.810i | 0.0415282 | + | 0.553709i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 525.877 | − | 303.615i | 0.635885 | − | 0.367128i | −0.147143 | − | 0.989115i | \(-0.547008\pi\) |
0.783028 | + | 0.621987i | \(0.213674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 441.338i | − | 0.532374i | −0.963921 | − | 0.266187i | \(-0.914236\pi\) | ||
0.963921 | − | 0.266187i | \(-0.0857638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 468.747 | − | 319.627i | 0.564075 | − | 0.384630i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −73.1831 | − | 126.757i | −0.0878549 | − | 0.152169i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −646.995 | + | 373.543i | −0.774844 | + | 0.447356i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.0441 | + | 139.635i | −0.0514266 | + | 0.166828i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 897.554i | 1.06979i | 0.844918 | + | 0.534895i | \(0.179649\pi\) | ||||
−0.844918 | + | 0.534895i | \(0.820351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 317.601 | + | 550.101i | 0.377647 | + | 0.654103i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −76.0682 | + | 157.982i | −0.0902352 | + | 0.187404i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 117.148 | + | 202.907i | 0.138637 | + | 0.240126i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 375.970 | 0.443884 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −64.2618 | + | 43.8186i | −0.0756912 | + | 0.0516121i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 158.807i | − | 0.186612i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −197.907 | −0.232013 | −0.116006 | − | 0.993248i | \(-0.537009\pi\) | ||||
−0.116006 | + | 0.993248i | \(0.537009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −457.911 | − | 12.8251i | −0.535569 | − | 0.0150002i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 378.577i | − | 0.441747i | −0.975302 | − | 0.220874i | \(-0.929109\pi\) | ||
0.975302 | − | 0.220874i | \(-0.0708908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 291.780 | 0.339675 | 0.169837 | − | 0.985472i | \(-0.445676\pi\) | ||||
0.169837 | + | 0.985472i | \(0.445676\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.02415 | − | 4.20383i | 0.00235092 | − | 0.00488250i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 884.191i | − | 1.02456i | −0.858820 | − | 0.512278i | \(-0.828802\pi\) | ||
0.858820 | − | 0.512278i | \(-0.171198\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 96.4649 | − | 55.6941i | 0.111520 | − | 0.0643862i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 419.632 | − | 286.137i | 0.484005 | − | 0.330031i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −168.723 | + | 97.4123i | −0.194158 | + | 0.112097i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 845.526 | 0.970754 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 164.757 | + | 1092.20i | 0.188726 | + | 1.25109i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 453.027 | + | 784.666i | 0.517745 | + | 0.896761i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −787.508 | + | 454.668i | −0.897957 | + | 0.518436i | −0.876537 | − | 0.481335i | \(-0.840152\pi\) |
−0.0214201 | + | 0.999771i | \(0.506819\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −64.8953 | + | 134.777i | −0.0738286 | + | 0.153330i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −909.618 | −1.03248 | −0.516242 | − | 0.856443i | \(-0.672669\pi\) | ||||
−0.516242 | + | 0.856443i | \(0.672669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 659.262 | + | 1141.88i | 0.746616 | + | 1.29318i | 0.949436 | + | 0.313961i | \(0.101656\pi\) |
−0.202820 | + | 0.979216i | \(0.565011\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −138.964 | + | 288.606i | −0.157021 | + | 0.326109i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 673.904i | 0.759757i | 0.925036 | + | 0.379878i | \(0.124034\pi\) | ||||
−0.925036 | + | 0.379878i | \(0.875966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1286.28 | − | 742.636i | −1.44689 | − | 0.835361i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −508.809 | − | 471.878i | −0.571054 | − | 0.529605i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −337.641 | − | 936.943i | −0.378097 | − | 1.04921i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −65.4544 | + | 37.7901i | −0.0731334 | + | 0.0422236i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −830.526 | + | 62.2896i | −0.925893 | + | 0.0694421i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 103.965 | + | 180.072i | 0.115645 | + | 0.200302i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 601.573i | 0.667672i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1126.98 | − | 768.463i | 1.24804 | − | 0.851012i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 619.010 | + | 357.386i | 0.683989 | + | 0.394901i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1074.94i | − | 1.18516i | −0.805511 | − | 0.592581i | \(-0.798109\pi\) | ||
0.805511 | − | 0.592581i | \(-0.201891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 91.3394 | − | 232.811i | 0.100483 | − | 0.256118i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 420.259 | − | 242.637i | 0.461316 | − | 0.266341i | −0.251281 | − | 0.967914i | \(-0.580852\pi\) |
0.712598 | + | 0.701573i | \(0.247519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.1761 | − | 69.5870i | 0.0440045 | − | 0.0762180i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.7522 | − | 343.362i | −0.0281445 | − | 0.375260i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −715.137 | + | 1238.65i | −0.779866 | + | 1.35077i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1213.32 | 1.32026 | 0.660129 | − | 0.751153i | \(-0.270502\pi\) | ||||
0.660129 | + | 0.751153i | \(0.270502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −397.799 | + | 826.165i | −0.431921 | + | 0.897031i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −505.294 | + | 875.195i | −0.547448 | + | 0.948207i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −79.7311 | − | 46.0328i | −0.0861958 | − | 0.0497652i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1442.10 | − | 565.783i | −1.55567 | − | 0.610338i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −439.344 | −0.472921 | −0.236461 | − | 0.971641i | \(-0.575987\pi\) | ||||
−0.236461 | + | 0.971641i | \(0.575987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 86.1744 | + | 239.131i | 0.0925612 | + | 0.256854i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 914.778 | + | 440.466i | 0.980470 | + | 0.472097i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 125.548 | + | 217.455i | 0.134276 | + | 0.232572i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 602.042 | + | 1042.77i | 0.642521 | + | 1.11288i | 0.984868 | + | 0.173305i | \(0.0554447\pi\) |
−0.342347 | + | 0.939574i | \(0.611222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1437.93 | + | 692.363i | 1.53134 | + | 0.737341i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1603.25i | 1.70378i | 0.523723 | + | 0.851889i | \(0.324543\pi\) | ||||
−0.523723 | + | 0.851889i | \(0.675457\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.24302 | − | 3.02706i | 0.00555993 | − | 0.00321003i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −545.913 | − | 168.284i | −0.577686 | − | 0.178078i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −523.837 | −0.553154 | −0.276577 | − | 0.960992i | \(-0.589200\pi\) | ||||
−0.276577 | + | 0.960992i | \(0.589200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −935.603 | − | 540.171i | −0.985883 | − | 0.569200i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −523.985 | + | 1088.23i | −0.550983 | + | 1.14430i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 632.378 | + | 365.104i | 0.663566 | + | 0.383110i | 0.793634 | − | 0.608395i | \(-0.208186\pi\) |
−0.130068 | + | 0.991505i | \(0.541520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 308.676 | − | 534.643i | 0.323221 | − | 0.559836i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −984.724 | + | 73.8544i | −1.02897 | + | 0.0771729i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −871.195 | −0.908442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −465.856 | − | 806.887i | −0.484762 | − | 0.839632i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −154.241 | − | 1022.49i | −0.160167 | − | 1.06177i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −194.184 | − | 112.112i | −0.201227 | − | 0.116178i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −197.202 | − | 341.563i | −0.203931 | − | 0.353219i | 0.745860 | − | 0.666102i | \(-0.232039\pi\) |
−0.949792 | + | 0.312883i | \(0.898705\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 569.233 | − | 254.708i | 0.587443 | − | 0.262856i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −162.445 | − | 93.7875i | −0.167296 | − | 0.0965886i | 0.414014 | − | 0.910271i | \(-0.364126\pi\) |
−0.581310 | + | 0.813682i | \(0.697460\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −653.401 | − | 1131.72i | −0.671533 | − | 1.16313i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −209.469 | + | 435.033i | −0.214840 | + | 0.446188i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 577.746 | + | 333.562i | 0.591347 | + | 0.341415i | 0.765630 | − | 0.643281i | \(-0.222427\pi\) |
−0.174283 | + | 0.984696i | \(0.555761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1091.56 | + | 630.210i | 1.11497 | + | 0.643728i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 409.880 | + | 160.809i | 0.417819 | + | 0.163924i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1367.79i | − | 1.39145i | −0.718310 | − | 0.695723i | \(-0.755084\pi\) | ||
0.718310 | − | 0.695723i | \(-0.244916\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.8830 | − | 27.5102i | −0.0161249 | − | 0.0279291i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −92.8868 | − | 1238.49i | −0.0941102 | − | 1.25480i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1769.94 | 1.78962 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 377.503 | + | 217.952i | 0.380932 | + | 0.219931i | 0.678224 | − | 0.734856i | \(-0.262750\pi\) |
−0.297292 | + | 0.954787i | \(0.596083\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −272.621 | − | 399.809i | −0.274543 | − | 0.402628i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 190.956 | − | 330.745i | 0.191915 | − | 0.332407i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 224.276 | − | 388.457i | 0.224951 | − | 0.389626i | −0.731354 | − | 0.681998i | \(-0.761111\pi\) |
0.956305 | + | 0.292372i | \(0.0944446\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 135.963 | − | 31.0586i | 0.136099 | − | 0.0310897i |
(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 | 684.3.s.a.445.20 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.16 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.25 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.7 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.7 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.25 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.20 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.16 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.20 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.20 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.7 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.7 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.16 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.16 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.25 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.25 | 80 | 9.2 | odd | 6 |