Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 56x^{6} - 154x^{5} + 917x^{4} - 1582x^{3} + 4294x^{2} - 3528x + 4971 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.3 | ||
Root | \(0.500000 - 1.77696i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.69 |
Dual form | 76.3.h.a.65.3 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 2.28889 | − | 1.32149i | 0.762963 | − | 0.440497i | −0.0673955 | − | 0.997726i | \(-0.521469\pi\) |
0.830359 | + | 0.557229i | \(0.188136\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.81674 | − | 8.34284i | −0.963348 | − | 1.66857i | −0.713989 | − | 0.700157i | \(-0.753113\pi\) |
−0.249360 | − | 0.968411i | \(-0.580220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.59243 | 1.08463 | 0.542316 | − | 0.840174i | \(-0.317547\pi\) | ||||
0.542316 | + | 0.840174i | \(0.317547\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00732 | + | 1.74474i | −0.111925 | + | 0.193860i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.61883 | −0.419894 | −0.209947 | − | 0.977713i | \(-0.567329\pi\) | ||||
−0.209947 | + | 0.977713i | \(0.567329\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.8169 | + | 11.4413i | 1.52438 | + | 0.880099i | 0.999583 | + | 0.0288692i | \(0.00919064\pi\) |
0.524793 | + | 0.851230i | \(0.324143\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −22.0500 | − | 12.7306i | −1.47000 | − | 0.848704i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.02053 | + | 5.23171i | 0.177678 | + | 0.307748i | 0.941085 | − | 0.338171i | \(-0.109808\pi\) |
−0.763407 | + | 0.645918i | \(0.776475\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.21998 | − | 18.8699i | −0.116841 | − | 0.993151i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.3782 | − | 10.0333i | 0.827534 | − | 0.477777i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11.8651 | + | 20.5510i | −0.515875 | + | 0.893521i | 0.483955 | + | 0.875093i | \(0.339200\pi\) |
−0.999830 | + | 0.0184287i | \(0.994134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −33.9020 | + | 58.7200i | −1.35608 | + | 2.34880i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.1115i | 1.07820i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.1836 | + | 5.87948i | 0.351157 | + | 0.202741i | 0.665195 | − | 0.746670i | \(-0.268348\pi\) |
−0.314038 | + | 0.949411i | \(0.601682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.22078i | − | 0.136154i | −0.997680 | − | 0.0680771i | \(-0.978314\pi\) | ||
0.997680 | − | 0.0680771i | \(-0.0216864\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.5720 | + | 6.10375i | −0.320364 | + | 0.184962i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −36.5708 | − | 63.3424i | −1.04488 | − | 1.80978i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.8554i | − | 0.320417i | −0.987083 | − | 0.160209i | \(-0.948783\pi\) | ||
0.987083 | − | 0.160209i | \(-0.0512167\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 60.4782 | 1.55072 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.64514 | + | 4.41392i | −0.186467 | + | 0.107657i | −0.590327 | − | 0.807164i | \(-0.701001\pi\) |
0.403861 | + | 0.914821i | \(0.367668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.5058 | − | 19.9286i | −0.267576 | − | 0.463456i | 0.700659 | − | 0.713496i | \(-0.252889\pi\) |
−0.968235 | + | 0.250041i | \(0.919556\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19.4081 | 0.431291 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.0941 | − | 57.3207i | 0.704130 | − | 1.21959i | −0.262874 | − | 0.964830i | \(-0.584670\pi\) |
0.967004 | − | 0.254759i | \(-0.0819962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.64494 | 0.176427 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.8273 | + | 7.98320i | 0.271124 | + | 0.156533i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40.7377 | + | 23.5199i | 0.768635 | + | 0.443772i | 0.832388 | − | 0.554194i | \(-0.186973\pi\) |
−0.0637523 | + | 0.997966i | \(0.520307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.2477 | + | 38.5342i | 0.404504 | + | 0.700622i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −30.0176 | − | 40.2573i | −0.526625 | − | 0.706269i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.52242 | + | 4.34307i | −0.127499 | + | 0.0736114i | −0.562393 | − | 0.826870i | \(-0.690119\pi\) |
0.434894 | + | 0.900482i | \(0.356786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.57907 | + | 6.19914i | −0.0586733 | + | 0.101625i | −0.893870 | − | 0.448326i | \(-0.852020\pi\) |
0.835197 | + | 0.549951i | \(0.185354\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.64803 | + | 13.2468i | −0.121397 | + | 0.210266i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 220.439i | − | 3.39137i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −77.3224 | − | 44.6421i | −1.15407 | − | 0.666300i | −0.204191 | − | 0.978931i | \(-0.565456\pi\) |
−0.949875 | + | 0.312631i | \(0.898790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 62.7186i | 0.908965i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −67.9840 | + | 39.2506i | −0.957521 | + | 0.552825i | −0.895409 | − | 0.445244i | \(-0.853117\pi\) |
−0.0621119 | + | 0.998069i | \(0.519784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43.1234 | + | 74.6919i | 0.590731 | + | 1.02318i | 0.994134 | + | 0.108154i | \(0.0344939\pi\) |
−0.403403 | + | 0.915022i | \(0.632173\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 179.205i | 2.38940i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −35.0682 | −0.455431 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 57.9637 | − | 33.4653i | 0.733717 | − | 0.423612i | −0.0860632 | − | 0.996290i | \(-0.527429\pi\) |
0.819781 | + | 0.572678i | \(0.194095\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.4047 | + | 50.9304i | 0.363021 | + | 0.628770i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.30752 | 0.0639460 | 0.0319730 | − | 0.999489i | \(-0.489821\pi\) | ||||
0.0319730 | + | 0.999489i | \(0.489821\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.0982 | − | 50.3996i | 0.342332 | − | 0.592936i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 31.0787 | 0.357227 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −99.6601 | − | 57.5388i | −1.11978 | − | 0.646503i | −0.178432 | − | 0.983952i | \(-0.557103\pi\) |
−0.941344 | + | 0.337449i | \(0.890436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 150.458 | + | 86.8671i | 1.65339 | + | 0.954584i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.57772 | − | 9.66090i | −0.0599755 | − | 0.103881i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −146.735 | + | 109.412i | −1.54458 | + | 1.15171i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −49.2806 | + | 28.4521i | −0.508047 | + | 0.293321i | −0.732031 | − | 0.681272i | \(-0.761427\pi\) |
0.223983 | + | 0.974593i | \(0.428094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.65266 | − | 8.05865i | 0.0469966 | − | 0.0814005i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.2533 | + | 29.8836i | −0.170825 | + | 0.295877i | −0.938708 | − | 0.344712i | \(-0.887977\pi\) |
0.767884 | + | 0.640589i | \(0.221310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 50.3577i | 0.488910i | 0.969661 | + | 0.244455i | \(0.0786090\pi\) | ||||
−0.969661 | + | 0.244455i | \(0.921391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −167.413 | − | 96.6558i | −1.59441 | − | 0.920532i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 184.188i | − | 1.72138i | −0.509126 | − | 0.860692i | \(-0.670031\pi\) | ||
0.509126 | − | 0.860692i | \(-0.329969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.7493 | + | 10.2476i | −0.162838 | + | 0.0940145i | −0.579204 | − | 0.815182i | \(-0.696637\pi\) |
0.416366 | + | 0.909197i | \(0.363303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.6669 | − | 27.1358i | −0.141143 | − | 0.244467i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 138.686i | 1.22731i | 0.789576 | + | 0.613653i | \(0.210301\pi\) | ||||
−0.789576 | + | 0.613653i | \(0.789699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 228.605 | 1.98787 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −39.9241 | + | 23.0502i | −0.341231 | + | 0.197010i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.9331 | + | 39.7214i | 0.192715 | + | 0.333793i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −99.6664 | −0.823689 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.6659 | + | 20.2060i | −0.0948449 | + | 0.164276i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 412.351 | 3.29881 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −151.220 | − | 87.3070i | −1.19071 | − | 0.687457i | −0.232242 | − | 0.972658i | \(-0.574606\pi\) |
−0.958468 | + | 0.285201i | \(0.907940\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −52.6709 | − | 30.4096i | −0.408302 | − | 0.235733i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2446 | + | 19.4763i | 0.0858370 | + | 0.148674i | 0.905748 | − | 0.423818i | \(-0.139310\pi\) |
−0.819911 | + | 0.572492i | \(0.805977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.8550 | − | 143.268i | −0.126730 | − | 1.07720i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 242.873 | − | 140.223i | 1.79906 | − | 1.03869i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 38.3769 | − | 66.4708i | 0.280124 | − | 0.485188i | −0.691291 | − | 0.722576i | \(-0.742958\pi\) |
0.971415 | + | 0.237388i | \(0.0762912\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −84.7624 | + | 146.813i | −0.609801 | + | 1.05621i | 0.381472 | + | 0.924381i | \(0.375417\pi\) |
−0.991273 | + | 0.131826i | \(0.957916\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 174.934i | − | 1.24067i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −91.5309 | − | 52.8454i | −0.640077 | − | 0.369548i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 113.280i | − | 0.781240i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.7873 | − | 11.4242i | 0.134608 | − | 0.0777157i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 97.6855 | + | 169.196i | 0.655607 | + | 1.13555i | 0.981741 | + | 0.190222i | \(0.0609207\pi\) |
−0.326134 | + | 0.945324i | \(0.605746\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 162.149i | − | 1.07383i | −0.843635 | − | 0.536917i | \(-0.819589\pi\) | ||
0.843635 | − | 0.536917i | \(-0.180411\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.1706 | −0.0795464 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −35.2133 | + | 20.3304i | −0.227183 | + | 0.131164i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −65.6679 | − | 113.740i | −0.418267 | − | 0.724460i | 0.577498 | − | 0.816392i | \(-0.304029\pi\) |
−0.995765 | + | 0.0919322i | \(0.970696\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 124.325 | 0.781920 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −90.0851 | + | 156.032i | −0.559535 | + | 0.969142i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −99.1996 | −0.608586 | −0.304293 | − | 0.952578i | \(-0.598420\pi\) | ||||
−0.304293 | + | 0.952578i | \(0.598420\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 101.845 | + | 58.8003i | 0.617244 | + | 0.356366i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −183.454 | − | 105.917i | −1.09853 | − | 0.634235i | −0.162693 | − | 0.986677i | \(-0.552018\pi\) |
−0.935834 | + | 0.352442i | \(0.885351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 177.306 | + | 307.103i | 1.04915 | + | 1.81718i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 35.1592 | + | 15.1348i | 0.205609 | + | 0.0885075i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 147.823 | − | 85.3459i | 0.854471 | − | 0.493329i | −0.00768594 | − | 0.999970i | \(-0.502447\pi\) |
0.862157 | + | 0.506641i | \(0.169113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −257.398 | + | 445.827i | −1.47085 | + | 2.54758i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.4787 | + | 19.8816i | −0.0648512 | + | 0.112326i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 192.935i | 1.07785i | 0.842354 | + | 0.538925i | \(0.181170\pi\) | ||||
−0.842354 | + | 0.538925i | \(0.818830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −263.715 | − | 152.256i | −1.45699 | − | 0.841194i | −0.458129 | − | 0.888886i | \(-0.651480\pi\) |
−0.998862 | + | 0.0476914i | \(0.984814\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.9188i | 0.103382i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −98.9081 | + | 57.1046i | −0.534638 | + | 0.308674i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.9513 | − | 24.1644i | −0.0746060 | − | 0.129221i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 221.027i | 1.16946i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 201.179 | 1.05329 | 0.526647 | − | 0.850084i | \(-0.323449\pi\) | ||||
0.526647 | + | 0.850084i | \(0.323449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 33.0963 | − | 19.1081i | 0.171483 | − | 0.0990059i | −0.411802 | − | 0.911273i | \(-0.635100\pi\) |
0.583285 | + | 0.812268i | \(0.301767\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −291.308 | − | 504.560i | −1.49389 | − | 2.58749i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 100.500 | 0.510151 | 0.255076 | − | 0.966921i | \(-0.417900\pi\) | ||||
0.255076 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 49.2159 | − | 85.2444i | 0.247316 | − | 0.428364i | −0.715464 | − | 0.698649i | \(-0.753785\pi\) |
0.962780 | + | 0.270285i | \(0.0871181\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −235.977 | −1.17401 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 77.3179 | + | 44.6395i | 0.380876 | + | 0.219899i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 73.6493 | + | 42.5215i | 0.359265 | + | 0.207422i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −23.9040 | − | 41.4030i | −0.115478 | − | 0.200015i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.2537 | + | 87.1568i | 0.0490609 | + | 0.417018i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 279.837 | − | 161.564i | 1.32624 | − | 0.765707i | 0.341527 | − | 0.939872i | \(-0.389056\pi\) |
0.984716 | + | 0.174165i | \(0.0557226\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −103.739 | + | 179.680i | −0.487036 | + | 0.843570i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −110.841 | + | 191.982i | −0.515538 | + | 0.892938i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 32.0460i | − | 0.147677i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 197.409 | + | 113.974i | 0.901412 | + | 0.520430i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 138.235i | 0.625497i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 256.629 | − | 148.165i | 1.15080 | − | 0.664415i | 0.201718 | − | 0.979444i | \(-0.435347\pi\) |
0.949082 | + | 0.315028i | \(0.102014\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −68.3006 | − | 118.300i | −0.303558 | − | 0.525778i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 214.461i | 0.944762i | 0.881394 | + | 0.472381i | \(0.156605\pi\) | ||||
−0.881394 | + | 0.472381i | \(0.843395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 118.681 | 0.518256 | 0.259128 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259128 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −80.2671 | + | 46.3423i | −0.347477 | + | 0.200616i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 91.9447 | + | 159.253i | 0.394612 | + | 0.683489i | 0.993052 | − | 0.117679i | \(-0.0375455\pi\) |
−0.598439 | + | 0.801168i | \(0.704212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −637.623 | −2.71329 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 88.4483 | − | 153.197i | 0.373200 | − | 0.646401i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.2428 | −0.0888822 | −0.0444411 | − | 0.999012i | \(-0.514151\pi\) | ||||
−0.0444411 | + | 0.999012i | \(0.514151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 68.4562 | + | 39.5232i | 0.284051 | + | 0.163997i | 0.635256 | − | 0.772302i | \(-0.280895\pi\) |
−0.351205 | + | 0.936299i | \(0.614228\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −92.2937 | − | 53.2858i | −0.379809 | − | 0.219283i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −41.6404 | − | 72.1234i | −0.169961 | − | 0.294381i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 171.902 | − | 399.341i | 0.695961 | − | 1.61677i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.1483 | − | 7.01383i | 0.0487884 | − | 0.0281680i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 180.962 | − | 313.436i | 0.720965 | − | 1.24875i | −0.239649 | − | 0.970860i | \(-0.577032\pi\) |
0.960614 | − | 0.277888i | \(-0.0896344\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 54.8030 | − | 94.9216i | 0.216613 | − | 0.375184i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 153.812i | − | 0.603184i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 111.378 | + | 64.3044i | 0.433379 | + | 0.250212i | 0.700785 | − | 0.713372i | \(-0.252833\pi\) |
−0.267406 | + | 0.963584i | \(0.586166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 90.0116i | − | 0.347535i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.5163 | + | 11.8451i | −0.0786065 | + | 0.0453835i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −115.623 | − | 200.266i | −0.439633 | − | 0.761466i | 0.558028 | − | 0.829822i | \(-0.311558\pi\) |
−0.997661 | + | 0.0683558i | \(0.978225\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 453.157i | − | 1.71003i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −304.148 | −1.13913 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −211.625 | + | 122.182i | −0.786710 | + | 0.454207i | −0.838803 | − | 0.544435i | \(-0.816744\pi\) |
0.0520931 | + | 0.998642i | \(0.483411\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 221.354 | + | 383.397i | 0.816805 | + | 1.41475i | 0.908025 | + | 0.418917i | \(0.137590\pi\) |
−0.0912198 | + | 0.995831i | \(0.529077\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 459.176 | 1.68197 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 156.588 | − | 271.218i | 0.569410 | − | 0.986247i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 89.7022 | 0.323835 | 0.161917 | − | 0.986804i | \(-0.448232\pi\) | ||||
0.161917 | + | 0.986804i | \(0.448232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.36415 | + | 4.25170i | 0.0263948 | + | 0.0152391i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 368.458 | + | 212.729i | 1.31124 | + | 0.757044i | 0.982301 | − | 0.187308i | \(-0.0599762\pi\) |
0.328937 | + | 0.944352i | \(0.393310\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 74.4153 | + | 128.891i | 0.262952 | + | 0.455446i | 0.967025 | − | 0.254682i | \(-0.0819707\pi\) |
−0.704073 | + | 0.710127i | \(0.748637\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −191.273 | + | 444.342i | −0.671135 | + | 1.55909i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −58.0452 | + | 33.5124i | −0.202248 | + | 0.116768i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 126.253 | − | 218.676i | 0.436861 | − | 0.756665i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −75.1985 | + | 130.248i | −0.258414 | + | 0.447586i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 42.5442i | − | 0.145202i | −0.997361 | − | 0.0726011i | \(-0.976870\pi\) | ||
0.997361 | − | 0.0726011i | \(-0.0231300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 72.4671 | + | 41.8389i | 0.245651 | + | 0.141827i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 134.461i | − | 0.452732i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −470.260 | + | 271.505i | −1.57277 | + | 0.908042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −87.3568 | − | 151.306i | −0.290222 | − | 0.502679i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 91.2004i | 0.300991i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 68.9579 | 0.226091 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 249.511 | − | 144.055i | 0.812740 | − | 0.469235i | −0.0351668 | − | 0.999381i | \(-0.511196\pi\) |
0.847906 | + | 0.530146i | \(0.177863\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 66.5473 | + | 115.263i | 0.215363 | + | 0.373020i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 269.870 | 0.867750 | 0.433875 | − | 0.900973i | \(-0.357146\pi\) | ||||
0.433875 | + | 0.900973i | \(0.357146\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −88.8271 | + | 153.853i | −0.283793 | + | 0.491543i | −0.972316 | − | 0.233671i | \(-0.924926\pi\) |
0.688523 | + | 0.725214i | \(0.258259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 147.354 | 0.467792 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −505.362 | − | 291.771i | −1.59420 | − | 0.920413i | −0.992575 | − | 0.121635i | \(-0.961186\pi\) |
−0.601627 | − | 0.798777i | \(-0.705480\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −47.0362 | − | 27.1563i | −0.147449 | − | 0.0851296i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −243.403 | − | 421.586i | −0.758264 | − | 1.31335i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 92.0161 | − | 68.6112i | 0.284880 | − | 0.212419i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1343.66 | + | 775.765i | −4.13435 | + | 2.38697i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.0842 | + | 46.9112i | −0.0828262 | + | 0.143459i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 251.265 | − | 435.203i | 0.763722 | − | 1.32281i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.6891i | 0.0987586i | 0.998780 | + | 0.0493793i | \(0.0157243\pi\) | ||||
−0.998780 | + | 0.0493793i | \(0.984276\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.6846 | + | 11.9423i | 0.0621160 | + | 0.0358627i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 860.118i | 2.56752i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −255.755 | + | 147.660i | −0.758918 | + | 0.438161i | −0.828907 | − | 0.559386i | \(-0.811037\pi\) |
0.0699892 | + | 0.997548i | \(0.477704\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 183.272 | + | 317.436i | 0.540624 | + | 0.936389i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.4951i | 0.0571704i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −306.393 | −0.893274 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 523.251 | − | 302.099i | 1.51667 | − | 0.875650i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 85.7263 | + | 148.482i | 0.247050 | + | 0.427903i | 0.962706 | − | 0.270550i | \(-0.0872055\pi\) |
−0.715656 | + | 0.698453i | \(0.753872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 127.644 | 0.365743 | 0.182872 | − | 0.983137i | \(-0.441461\pi\) | ||||
0.182872 | + | 0.983137i | \(0.441461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −333.073 | + | 576.900i | −0.948926 | + | 1.64359i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −184.494 | −0.522647 | −0.261323 | − | 0.965251i | \(-0.584159\pi\) | ||||
−0.261323 | + | 0.965251i | \(0.584159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 654.923 | + | 378.120i | 1.84485 | + | 1.06513i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 104.983 | + | 60.6119i | 0.294070 | + | 0.169781i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −131.720 | − | 228.145i | −0.366907 | − | 0.635502i | 0.622173 | − | 0.782880i | \(-0.286250\pi\) |
−0.989080 | + | 0.147378i | \(0.952917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −351.143 | + | 83.7815i | −0.972696 | + | 0.232082i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −228.125 | + | 131.708i | −0.628444 | + | 0.362832i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 415.428 | − | 719.543i | 1.13816 | − | 1.97135i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 60.5658 | − | 104.903i | 0.165029 | − | 0.285839i | −0.771636 | − | 0.636064i | \(-0.780561\pi\) |
0.936666 | + | 0.350225i | \(0.113895\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 17.7850i | − | 0.0481979i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 309.298 | + | 178.573i | 0.833687 | + | 0.481329i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 335.187i | − | 0.898625i | −0.893375 | − | 0.449312i | \(-0.851669\pi\) | ||
0.893375 | − | 0.449312i | \(-0.148331\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 943.827 | − | 544.919i | 2.51687 | − | 1.45312i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 134.538 | + | 233.026i | 0.356864 | + | 0.618106i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 315.980i | − | 0.833721i | −0.908970 | − | 0.416861i | \(-0.863130\pi\) | ||
0.908970 | − | 0.416861i | \(-0.136870\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −461.502 | −1.21129 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −408.291 | + | 235.727i | −1.06603 | + | 0.615475i | −0.927095 | − | 0.374825i | \(-0.877703\pi\) |
−0.138939 | + | 0.990301i | \(0.544369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 168.914 | + | 292.568i | 0.438738 | + | 0.759917i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 46.3602 | 0.119794 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 235.508 | − | 407.912i | 0.605420 | − | 1.04862i | −0.386566 | − | 0.922262i | \(-0.626339\pi\) |
0.991985 | − | 0.126355i | \(-0.0403280\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −143.356 | −0.366639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 51.4755 | + | 29.7194i | 0.130981 | + | 0.0756219i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −558.392 | − | 322.388i | −1.41365 | − | 0.816172i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −110.236 | − | 190.934i | −0.277672 | − | 0.480942i | 0.693134 | − | 0.720809i | \(-0.256230\pi\) |
−0.970806 | + | 0.239867i | \(0.922896\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −227.907 | − | 305.651i | −0.571195 | − | 0.766042i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 79.1787 | − | 45.7138i | 0.197453 | − | 0.114000i | −0.398014 | − | 0.917379i | \(-0.630300\pi\) |
0.595467 | + | 0.803380i | \(0.296967\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48.2912 | − | 83.6428i | 0.119829 | − | 0.207550i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 283.269 | − | 490.637i | 0.699431 | − | 1.21145i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 54.7583i | 0.134541i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 291.494 | + | 168.294i | 0.712699 | + | 0.411477i | 0.812060 | − | 0.583575i | \(-0.198346\pi\) |
−0.0993606 | + | 0.995051i | \(0.531680\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 202.859i | − | 0.493574i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −57.1134 | + | 32.9745i | −0.138289 | + | 0.0798413i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.5649 | − | 44.2798i | −0.0616023 | − | 0.106698i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 448.051i | 1.07446i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −213.808 | −0.510281 | −0.255141 | − | 0.966904i | \(-0.582122\pi\) | ||||
−0.255141 | + | 0.966904i | \(0.582122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 524.575 | − | 302.863i | 1.24602 | − | 0.719391i | 0.275708 | − | 0.961242i | \(-0.411088\pi\) |
0.970313 | + | 0.241851i | \(0.0777545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 66.6730 | + | 115.481i | 0.157619 | + | 0.273005i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −409.608 | −0.963783 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.1738 | + | 47.0665i | −0.0636390 | + | 0.110226i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −279.339 | −0.651140 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 138.813 | + | 80.1437i | 0.322072 | + | 0.185948i | 0.652316 | − | 0.757947i | \(-0.273798\pi\) |
−0.330244 | + | 0.943896i | \(0.607131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 377.175 | + | 217.762i | 0.871073 | + | 0.502914i | 0.867705 | − | 0.497080i | \(-0.165594\pi\) |
0.00336832 | + | 0.999994i | \(0.498928\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −149.698 | − | 259.285i | −0.344134 | − | 0.596057i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 414.135 | + | 178.270i | 0.947677 | + | 0.407941i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 320.878 | − | 185.259i | 0.730930 | − | 0.422003i | −0.0878324 | − | 0.996135i | \(-0.527994\pi\) |
0.818762 | + | 0.574133i | \(0.194661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.70826 | + | 15.0831i | −0.0197466 | + | 0.0342021i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −144.384 | + | 250.081i | −0.325924 | + | 0.564517i | −0.981699 | − | 0.190439i | \(-0.939009\pi\) |
0.655775 | + | 0.754957i | \(0.272342\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1108.60i | 2.49123i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 447.183 | + | 258.181i | 1.00041 | + | 0.577586i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 76.8398i | − | 0.171135i | −0.996332 | − | 0.0855677i | \(-0.972730\pi\) | ||
0.996332 | − | 0.0855677i | \(-0.0272704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.3116 | − | 20.3872i | 0.0782963 | − | 0.0452044i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −214.278 | − | 371.141i | −0.473021 | − | 0.819296i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1673.67i | − | 3.67839i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 97.5752 | 0.213513 | 0.106756 | − | 0.994285i | \(-0.465954\pi\) | ||||
0.106756 | + | 0.994285i | \(0.465954\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −152.303 | + | 87.9321i | −0.331815 | + | 0.191573i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −156.003 | − | 270.204i | −0.338401 | − | 0.586127i | 0.645732 | − | 0.763565i | \(-0.276553\pi\) |
−0.984132 | + | 0.177438i | \(0.943219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 114.000 | 0.246220 | 0.123110 | − | 0.992393i | \(-0.460713\pi\) | ||||
0.123110 | + | 0.992393i | \(0.460713\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −53.7329 | + | 93.0681i | −0.115555 | + | 0.200147i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −651.304 | −1.39466 | −0.697328 | − | 0.716752i | \(-0.745628\pi\) | ||||
−0.697328 | + | 0.716752i | \(0.745628\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −587.065 | − | 338.942i | −1.25174 | − | 0.722691i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −300.613 | − | 173.559i | −0.638245 | − | 0.368491i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 53.1433 | + | 92.0469i | 0.112354 | + | 0.194602i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1183.30 | + | 509.369i | 2.49116 | + | 1.07236i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −82.0721 | + | 47.3843i | −0.172059 | + | 0.0993382i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −216.179 | + | 374.433i | −0.451313 | + | 0.781697i | −0.998468 | − | 0.0553341i | \(-0.982378\pi\) |
0.547155 | + | 0.837031i | \(0.315711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 135.642 | − | 234.938i | 0.281999 | − | 0.488437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 476.186i | 0.985893i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 474.743 | + | 274.093i | 0.978853 | + | 0.565141i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 100.949i | 0.207287i | 0.994615 | + | 0.103643i | \(0.0330501\pi\) | ||||
−0.994615 | + | 0.103643i | \(0.966950\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −227.057 | + | 131.091i | −0.464329 | + | 0.268080i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −112.182 | − | 194.304i | −0.228476 | − | 0.395732i | 0.728881 | − | 0.684641i | \(-0.240041\pi\) |
−0.957357 | + | 0.288909i | \(0.906708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 71.0365i | 0.144090i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −89.6427 | −0.181096 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −516.164 | + | 298.007i | −1.03856 | + | 0.599612i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −332.278 | − | 575.523i | −0.665888 | − | 1.15335i | −0.979044 | − | 0.203651i | \(-0.934719\pi\) |
0.313155 | − | 0.949702i | \(-0.398614\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −559.874 | −1.11751 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −180.202 | + | 312.119i | −0.358255 | + | 0.620515i | −0.987669 | − | 0.156554i | \(-0.949961\pi\) |
0.629415 | + | 0.777070i | \(0.283295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 332.419 | 0.658255 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 811.668 | + | 468.617i | 1.60092 | + | 0.924294i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −670.407 | − | 387.060i | −1.31711 | − | 0.760432i | −0.333845 | − | 0.942628i | \(-0.608346\pi\) |
−0.983262 | + | 0.182196i | \(0.941679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 327.411 | + | 567.092i | 0.640726 | + | 1.10977i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 549.330 | − | 64.6270i | 1.07082 | − | 0.125979i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 420.126 | − | 242.560i | 0.815780 | − | 0.470991i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −152.856 | + | 264.755i | −0.295660 | + | 0.512098i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 225.568 | − | 390.695i | 0.434620 | − | 0.752784i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 196.045i | 0.376285i | 0.982142 | + | 0.188143i | \(0.0602468\pi\) | ||||
−0.982142 | + | 0.188143i | \(0.939753\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −285.968 | − | 165.104i | −0.546784 | − | 0.315686i | 0.201040 | − | 0.979583i | \(-0.435568\pi\) |
−0.747824 | + | 0.663897i | \(0.768901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1360.60i | 2.59162i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.0819 | − | 12.7490i | 0.0419011 | − | 0.0241916i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0622 | − | 29.5526i | −0.0322537 | − | 0.0558651i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 17.4995i | − | 0.0329558i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −202.004 | −0.378994 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1536.65 | + | 887.186i | −2.87225 | + | 1.65829i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 254.962 | + | 441.607i | 0.474790 | + | 0.822360i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −39.9296 | −0.0740808 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −328.577 | + | 569.111i | −0.607350 | + | 1.05196i | 0.384325 | + | 0.923198i | \(0.374434\pi\) |
−0.991675 | + | 0.128764i | \(0.958899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −804.820 | −1.48217 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 170.988 | + | 98.7199i | 0.313739 | + | 0.181137i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 51.3126 | + | 29.6253i | 0.0938072 | + | 0.0541596i | 0.546170 | − | 0.837675i | \(-0.316085\pi\) |
−0.452363 | + | 0.891834i | \(0.649419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.21057 | − | 12.4891i | −0.0131340 | − | 0.0227488i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 88.3377 | − | 205.215i | 0.160322 | − | 0.372440i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 440.085 | − | 254.083i | 0.795814 | − | 0.459463i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −150.926 | + | 261.412i | −0.271940 | + | 0.471013i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 120.377 | − | 208.499i | 0.216117 | − | 0.374325i | −0.737501 | − | 0.675346i | \(-0.763994\pi\) |
0.953617 | + | 0.301021i | \(0.0973275\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 526.564i | − | 0.941974i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −63.8660 | − | 36.8731i | −0.113843 | − | 0.0657274i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 919.141i | − | 1.63258i | −0.577645 | − | 0.816288i | \(-0.696028\pi\) | ||
0.577645 | − | 0.816288i | \(-0.303972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1157.03 | − | 668.012i | 2.04784 | − | 1.18232i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 223.253 | + | 386.685i | 0.393744 | + | 0.681985i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 726.404i | − | 1.27663i | −0.769774 | − | 0.638316i | \(-0.779631\pi\) | ||
0.769774 | − | 0.638316i | \(-0.220369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −924.876 | −1.61975 | −0.809874 | − | 0.586604i | \(-0.800464\pi\) | ||||
−0.809874 | + | 0.586604i | \(0.800464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 460.477 | − | 265.857i | 0.803625 | − | 0.463973i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −804.503 | − | 1393.44i | −1.39913 | − | 2.42337i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 161.154 | 0.279296 | 0.139648 | − | 0.990201i | \(-0.455403\pi\) | ||||
0.139648 | + | 0.990201i | \(0.455403\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 50.5024 | − | 87.4728i | 0.0872236 | − | 0.151076i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.2969 | 0.0693579 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −188.161 | − | 108.635i | −0.322745 | − | 0.186337i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 384.608 | + | 222.053i | 0.657449 | + | 0.379578i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 294.997 | + | 510.950i | 0.502550 | + | 0.870442i | 0.999996 | + | 0.00294722i | \(0.000938130\pi\) |
−0.497445 | + | 0.867495i | \(0.665729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −79.6456 | + | 9.37006i | −0.135222 | + | 0.0159084i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 230.033 | − | 132.810i | 0.389226 | − | 0.224720i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.99383 | + | 17.3098i | −0.0168530 | + | 0.0291903i | −0.874329 | − | 0.485334i | \(-0.838698\pi\) |
0.857476 | + | 0.514524i | \(0.172031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 220.926 | − | 382.655i | 0.371304 | − | 0.643118i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 260.153i | − | 0.435768i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 931.550 | + | 537.831i | 1.55518 | + | 0.897881i | 0.997707 | + | 0.0676825i | \(0.0215605\pi\) |
0.557468 | + | 0.830198i | \(0.311773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5736i | 0.0242489i | 0.999926 | + | 0.0121244i | \(0.00385942\pi\) | ||||
−0.999926 | + | 0.0121244i | \(0.996141\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 155.777 | − | 89.9382i | 0.258337 | − | 0.149151i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 480.067 | + | 831.501i | 0.793499 | + | 1.37438i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 437.145i | 0.720173i | 0.932919 | + | 0.360086i | \(0.117253\pi\) | ||||
−0.932919 | + | 0.360086i | \(0.882747\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 235.963 | 0.387460 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1311.65 | − | 757.279i | 2.14672 | − | 1.23941i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 534.944 | + | 926.551i | 0.872666 | + | 1.51150i | 0.859228 | + | 0.511592i | \(0.170944\pi\) |
0.0134375 | + | 0.999910i | \(0.495723\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 224.767 | 0.365475 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −99.8317 | + | 172.914i | −0.161802 | + | 0.280249i | −0.935515 | − | 0.353287i | \(-0.885064\pi\) |
0.773713 | + | 0.633536i | \(0.218397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −432.305 | −0.698393 | −0.349196 | − | 0.937050i | \(-0.613545\pi\) | ||||
−0.349196 | + | 0.937050i | \(0.613545\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −598.270 | − | 345.412i | −0.963399 | − | 0.556218i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −756.662 | − | 436.859i | −1.21455 | − | 0.701218i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1138.64 | − | 1972.18i | −1.82182 | − | 3.15549i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 138.647 | + | 185.942i | 0.221127 | + | 0.296558i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 62.0242 | − | 35.8097i | 0.0986077 | − | 0.0569312i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 102.220 | − | 177.051i | 0.161997 | − | 0.280587i | −0.773588 | − | 0.633689i | \(-0.781540\pi\) |
0.935585 | + | 0.353102i | \(0.114873\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 427.011 | − | 739.605i | 0.674583 | − | 1.16841i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1682.14i | 2.64904i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 171.316 | + | 98.9093i | 0.268942 | + | 0.155274i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 158.152i | − | 0.247500i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.0248 | + | 19.6442i | −0.0530808 | + | 0.0306462i | −0.526306 | − | 0.850296i | \(-0.676423\pi\) |
0.473225 | + | 0.880942i | \(0.343090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −383.822 | − | 664.799i | −0.596923 | − | 1.03390i | −0.993272 | − | 0.115801i | \(-0.963056\pi\) |
0.396349 | − | 0.918100i | \(-0.370277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 585.900i | 0.908372i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 963.932 | 1.48985 | 0.744924 | − | 0.667149i | \(-0.232486\pi\) | ||||
0.744924 | + | 0.667149i | \(0.232486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.7448 | − | 20.0599i | 0.0535359 | − | 0.0309090i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.3485 | − | 73.3497i | −0.0650514 | − | 0.112672i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −824.035 | −1.26192 | −0.630961 | − | 0.775815i | \(-0.717339\pi\) | ||||
−0.630961 | + | 0.775815i | \(0.717339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 108.325 | − | 187.625i | 0.165382 | − | 0.286450i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −173.757 | −0.264470 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −144.310 | − | 83.3177i | −0.218984 | − | 0.126430i | 0.386496 | − | 0.922291i | \(-0.373685\pi\) |
−0.605480 | + | 0.795861i | \(0.707019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 273.938 | + | 158.158i | 0.414430 | + | 0.239271i | 0.692692 | − | 0.721234i | \(-0.256425\pi\) |
−0.278261 | + | 0.960505i | \(0.589758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 182.676 | + | 316.404i | 0.275530 | + | 0.477231i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1114.08 | + | 830.704i | −1.67530 | + | 1.24918i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −241.658 | + | 139.522i | −0.362306 | + | 0.209178i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 391.596 | − | 678.265i | 0.585346 | − | 1.01385i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.5311 | − | 28.6328i | 0.0246366 | − | 0.0426718i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 582.475i | − | 0.865491i | −0.901516 | − | 0.432745i | \(-0.857545\pi\) | ||
0.901516 | − | 0.432745i | \(-0.142455\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1709.43 | − | 986.938i | −2.53248 | − | 1.46213i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 956.276i | − | 1.41252i | −0.707953 | − | 0.706260i | \(-0.750381\pi\) | ||
0.707953 | − | 0.706260i | \(-0.249619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −374.159 | + | 216.021i | −0.551044 | + | 0.318146i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 283.408 | + | 490.878i | 0.416165 | + | 0.720819i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 240.373i | − | 0.351937i | −0.984396 | − | 0.175969i | \(-0.943694\pi\) | ||
0.984396 | − | 0.175969i | \(-0.0563057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −739.407 | −1.07943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 271.647 | − | 156.835i | 0.395410 | − | 0.228290i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 538.196 | + | 932.183i | 0.781126 | + | 1.35295i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 868.890 | 1.25744 | 0.628719 | − | 0.777632i | \(-0.283579\pi\) | ||||
0.628719 | + | 0.777632i | \(0.283579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35.3250 | − | 61.1847i | 0.0509740 | − | 0.0882896i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1633.11 | 2.34980 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.1847 | − | 26.6648i | −0.0662622 | − | 0.0382565i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 420.902 | + | 243.008i | 0.602149 | + | 0.347651i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 467.106 | + | 809.052i | 0.666343 | + | 1.15414i | 0.978919 | + | 0.204247i | \(0.0654746\pi\) |
−0.312576 | + | 0.949893i | \(0.601192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −223.711 | + | 26.3189i | −0.318223 | + | 0.0374379i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1459.45 | + | 842.613i | −2.07014 | + | 1.19520i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −130.994 | + | 226.889i | −0.185282 | + | 0.320918i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −514.968 | + | 891.950i | −0.726330 | + | 1.25804i | 0.232095 | + | 0.972693i | \(0.425442\pi\) |
−0.958424 | + | 0.285347i | \(0.907891\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 134.842i | 0.189651i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 86.7413 | + | 50.0801i | 0.121657 | + | 0.0702386i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1018.17i | 1.42402i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.6225 | + | 28.0722i | −0.0678138 | + | 0.0391523i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 352.663 | + | 610.831i | 0.490491 | + | 0.849556i | 0.999940 | − | 0.0109450i | \(-0.00348397\pi\) |
−0.509449 | + | 0.860501i | \(0.670151\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 382.337i | 0.530288i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 208.918 | 0.288960 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −690.486 | + | 398.652i | −0.952394 | + | 0.549865i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 426.231 | + | 738.253i | 0.586287 | + | 1.01548i | 0.994714 | + | 0.102688i | \(0.0327442\pi\) |
−0.408427 | + | 0.912791i | \(0.633922\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −810.951 | −1.11242 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 69.5070 | − | 120.390i | 0.0950849 | − | 0.164692i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1327.83 | 1.81150 | 0.905751 | − | 0.423809i | \(-0.139307\pi\) | ||||
0.905751 | + | 0.423809i | \(0.139307\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −190.621 | − | 110.055i | −0.259348 | − | 0.149735i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 357.139 | + | 206.195i | 0.484585 | + | 0.279776i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −197.639 | − | 342.320i | −0.267441 | − | 0.463221i | 0.700760 | − | 0.713398i | \(-0.252845\pi\) |
−0.968200 | + | 0.250177i | \(0.919511\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −134.261 | − | 1141.22i | −0.181188 | − | 1.54010i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −916.709 | + | 529.262i | −1.23379 | + | 0.712332i | −0.967819 | − | 0.251648i | \(-0.919027\pi\) |
−0.265976 | + | 0.963980i | \(0.585694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 941.052 | − | 1629.95i | 1.26316 | − | 2.18785i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.34639 | + | 9.26022i | −0.00715715 | + | 0.0123965i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1398.43i | − | 1.86707i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 207.032 | + | 119.530i | 0.275674 | + | 0.159161i | 0.631464 | − | 0.775406i | \(-0.282455\pi\) |
−0.355789 | + | 0.934566i | \(0.615788\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 956.559i | − | 1.27033i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1352.78 | + | 781.030i | −1.79177 | + | 1.03448i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 92.7004 | + | 160.562i | 0.122458 | + | 0.212103i | 0.920736 | − | 0.390185i | \(-0.127589\pi\) |
−0.798279 | + | 0.602288i | \(0.794256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 289.687i | − | 0.381669i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −712.211 | −0.935888 | −0.467944 | − | 0.883758i | \(-0.655005\pi\) | ||||
−0.467944 | + | 0.883758i | \(0.655005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −134.760 | + | 77.8040i | −0.176619 | + | 0.101971i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 58.6226 | + | 101.537i | 0.0766309 | + | 0.132729i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −198.761 | −0.259141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −395.236 | + | 684.568i | −0.513961 | + | 0.890206i | 0.485908 | + | 0.874010i | \(0.338489\pi\) |
−0.999869 | + | 0.0161960i | \(0.994844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 339.911 | 0.440870 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 334.502 | + | 193.125i | 0.432732 | + | 0.249838i | 0.700510 | − | 0.713643i | \(-0.252956\pi\) |
−0.267778 | + | 0.963481i | \(0.586289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 247.844 | + | 143.093i | 0.319799 | + | 0.184636i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −118.949 | − | 206.027i | −0.153088 | − | 0.265156i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 100.262 | + | 134.464i | 0.128706 | + | 0.172611i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 314.007 | − | 181.292i | 0.402057 | − | 0.232128i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −171.161 | + | 296.459i | −0.218596 | + | 0.378619i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −632.611 | + | 1095.71i | −0.805874 | + | 1.39581i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 606.206i | − | 0.770274i | −0.922859 | − | 0.385137i | \(-0.874154\pi\) | ||
0.922859 | − | 0.385137i | \(-0.125846\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −529.298 | − | 305.590i | −0.670847 | − | 0.387314i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1052.96i | 1.33118i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −141.852 | + | 81.8984i | −0.178880 | + | 0.103277i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −598.843 | − | 1037.23i | −0.753262 | − | 1.30469i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 332.769i | − | 0.417526i | −0.977966 | − | 0.208763i | \(-0.933056\pi\) | ||
0.977966 | − | 0.208763i | \(-0.0669438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 399.847 | 0.500434 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 200.780 | − | 115.920i | 0.250662 | − | 0.144720i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −199.180 | − | 344.989i | −0.248044 | − | 0.429626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1735.67 | 2.15611 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −322.924 | + | 559.321i | −0.400154 | + | 0.693087i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −603.251 | −0.745675 | −0.372838 | − | 0.927897i | \(-0.621615\pi\) | ||||
−0.372838 | + | 0.927897i | \(0.621615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −905.988 | − | 523.073i | −1.11713 | − | 0.644972i | −0.176460 | − | 0.984308i | \(-0.556465\pi\) |
−0.940665 | + | 0.339335i | \(0.889798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1013.31 | + | 585.035i | 1.24638 | + | 0.719600i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 477.819 | + | 827.606i | 0.586281 | + | 1.01547i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −350.507 | + | 261.354i | −0.429017 | + | 0.319894i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −303.121 | + | 175.007i | −0.370111 | + | 0.213683i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −166.613 | + | 288.583i | −0.202940 | + | 0.351502i | −0.949474 | − | 0.313845i | \(-0.898383\pi\) |
0.746535 | + | 0.665346i | \(0.231716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 208.418 | − | 360.990i | 0.253241 | − | 0.438627i | −0.711175 | − | 0.703015i | \(-0.751837\pi\) |
0.964416 | + | 0.264388i | \(0.0851700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 827.717i | − | 1.00329i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 734.915 | + | 424.303i | 0.888651 | + | 0.513063i | 0.873501 | − | 0.486822i | \(-0.161844\pi\) |
0.0151501 | + | 0.999885i | \(0.495177\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 958.797i | − | 1.15657i | −0.815835 | − | 0.578285i | \(-0.803722\pi\) | ||
0.815835 | − | 0.578285i | \(-0.196278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 205.318 | − | 118.541i | 0.247074 | − | 0.142648i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.1123 | + | 45.2278i | 0.0313473 | + | 0.0542951i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2040.70i | 2.44396i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 122.873 | 0.146802 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 931.117 | − | 537.581i | 1.10979 | − | 0.640740i | 0.171018 | − | 0.985268i | \(-0.445294\pi\) |
0.938776 | + | 0.344528i | \(0.111961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −351.363 | − | 608.579i | −0.417792 | − | 0.723638i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1124.48 | 1.33390 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1708.08 | − | 2958.47i | 2.02139 | − | 3.50115i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −756.710 | −0.893400 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 340.657 | + | 196.678i | 0.401245 | + | 0.231659i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 243.641 | + | 140.666i | 0.286300 | + | 0.165295i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −83.4052 | − | 144.462i | −0.0977787 | − | 0.169358i | 0.812986 | − | 0.582283i | \(-0.197840\pi\) |
−0.910765 | + | 0.412925i | \(0.864507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43.0856 | − | 366.228i | −0.0503925 | − | 0.428337i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 581.227 | − | 335.571i | 0.678211 | − | 0.391565i | −0.120970 | − | 0.992656i | \(-0.538600\pi\) |
0.799181 | + | 0.601091i | \(0.205267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −396.070 | + | 686.014i | −0.461083 | + | 0.798619i | −0.999015 | − | 0.0443690i | \(-0.985872\pi\) |
0.537932 | + | 0.842988i | \(0.319206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −88.5726 | + | 153.412i | −0.102872 | + | 0.178179i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 570.060i | − | 0.660556i | −0.943884 | − | 0.330278i | \(-0.892857\pi\) | ||
0.943884 | − | 0.330278i | \(-0.107143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1424.05 | − | 822.178i | −1.64631 | − | 0.950495i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 667.368i | − | 0.769744i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −267.725 | + | 154.571i | −0.308084 | + | 0.177872i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1021.53 | − | 1769.34i | −1.17282 | − | 2.03138i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 114.642i | − | 0.131320i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3130.75 | 3.57800 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 255.489 | − | 147.506i | 0.291321 | − | 0.168194i | −0.347216 | − | 0.937785i | \(-0.612873\pi\) |
0.638537 | + | 0.769591i | \(0.279540\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −56.2218 | − | 97.3790i | −0.0639611 | − | 0.110784i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −976.298 | −1.10817 | −0.554085 | − | 0.832460i | \(-0.686932\pi\) | ||||
−0.554085 | + | 0.832460i | \(0.686932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 147.883 | − | 256.141i | 0.167478 | − | 0.290081i | −0.770054 | − | 0.637978i | \(-0.779771\pi\) |
0.937533 | + | 0.347897i | \(0.113104\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 221.159 | 0.249897 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 793.272 | + | 457.996i | 0.894331 | + | 0.516342i | 0.875357 | − | 0.483477i | \(-0.160626\pi\) |
0.0189746 | + | 0.999820i | \(0.493960\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1148.13 | − | 662.872i | −1.29148 | − | 0.745638i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −135.815 | − | 235.239i | −0.152430 | − | 0.264017i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1155.10 | − | 497.231i | −1.29351 | − | 0.556809i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1609.63 | − | 929.319i | 1.79847 | − | 1.03835i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −717.582 | + | 1242.89i | −0.799979 | + | 1.38560i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.8160 | − | 42.9826i | 0.0276040 | − | 0.0478116i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 284.170i | 0.315394i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −399.900 | − | 230.882i | −0.442857 | − | 0.255684i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2933.51i | 3.24145i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −407.014 | + | 234.989i | −0.448747 | + | 0.259084i | −0.707301 | − | 0.706913i | \(-0.750087\pi\) |
0.258554 | + | 0.965997i | \(0.416754\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.7593 | − | 60.2050i | −0.0382391 | − | 0.0662321i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 440.064i | 0.483056i | 0.970394 | + | 0.241528i | \(0.0776486\pi\) | ||||
−0.970394 | + | 0.241528i | \(0.922351\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.5145 | −0.0268505 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 157.837 | − | 91.1272i | 0.172499 | − | 0.0995925i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 85.3741 | + | 147.872i | 0.0931016 | + | 0.161257i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −609.475 | −0.663194 | −0.331597 | − | 0.943421i | \(-0.607587\pi\) | ||||
−0.331597 | + | 0.943421i | \(0.607587\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 380.735 | − | 659.453i | 0.413394 | − | 0.716019i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1796.31 | −1.94616 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 696.151 | + | 401.923i | 0.752596 | + | 0.434512i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −87.8610 | − | 50.7265i | −0.0947799 | − | 0.0547212i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 663.351 | + | 1148.96i | 0.714048 | + | 1.23677i | 0.963326 | + | 0.268335i | \(0.0864736\pi\) |
−0.249277 | + | 0.968432i | \(0.580193\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.1916 | − | 163.129i | −0.0206140 | − | 0.175219i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 617.703 | − | 356.631i | 0.662061 | − | 0.382241i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −134.400 | + | 232.787i | −0.143743 | + | 0.248970i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −911.033 | + | 1577.96i | −0.972288 | + | 1.68405i | −0.283678 | + | 0.958920i | \(0.591555\pi\) |
−0.688610 | + | 0.725132i | \(0.741779\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 469.537i | 0.500039i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 961.497 | + | 555.121i | 1.02178 | + | 0.589926i | 0.914620 | − | 0.404315i | \(-0.132490\pi\) |
0.107163 | + | 0.994242i | \(0.465823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 209.487i | − | 0.222149i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1843.99 | − | 1064.63i | 1.95132 | − | 1.12659i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 431.526 | + | 747.425i | 0.455677 | + | 0.789255i | 0.998727 | − | 0.0504450i | \(-0.0160639\pi\) |
−0.543050 | + | 0.839700i | \(0.682731\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1973.55i | 2.07961i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1542.29 | −1.62176 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1494.57 | + | 862.890i | −1.56828 | + | 0.905446i | −0.571909 | + | 0.820317i | \(0.693797\pi\) |
−0.996370 | + | 0.0851297i | \(0.972870\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −969.029 | − | 1678.41i | −1.01469 | − | 1.75749i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −143.547 | −0.149997 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 291.374 | − | 504.675i | 0.303831 | − | 0.526251i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 943.185 | 0.981462 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 321.360 | + | 185.537i | 0.333707 | + | 0.192666i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −318.832 | − | 184.078i | −0.330396 | − | 0.190754i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −767.279 | − | 1328.97i | −0.793463 | − | 1.37432i | −0.923811 | − | 0.382850i | \(-0.874943\pi\) |
0.130348 | − | 0.991468i | \(-0.458391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 119.946 | − | 278.642i | 0.123783 | − | 0.287556i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1048.94 | − | 605.609i | 1.08027 | − | 0.623696i | 0.149303 | − | 0.988792i | \(-0.452297\pi\) |
0.930970 | + | 0.365096i | \(0.118964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −643.552 | + | 1114.67i | −0.661410 | + | 1.14560i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2050.33 | + | 3551.28i | −2.10291 | + | 3.64234i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 918.806i | − | 0.940436i | −0.882550 | − | 0.470218i | \(-0.844175\pi\) | ||
0.882550 | − | 0.470218i | \(-0.155825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 460.313 | + | 265.762i | 0.470187 | + | 0.271463i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 41.2905i | − | 0.0420903i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −542.556 | + | 313.245i | −0.551939 | + | 0.318662i | −0.749904 | − | 0.661547i | \(-0.769900\pi\) |
0.197965 | + | 0.980209i | \(0.436567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −484.081 | − | 838.453i | −0.491453 | − | 0.851222i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1328.18i | − | 1.34567i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 546.070 | 0.552143 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −216.951 | + | 125.257i | −0.218921 | + | 0.126394i | −0.605451 | − | 0.795883i | \(-0.707007\pi\) |
0.386530 | + | 0.922277i | \(0.373674\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.1983 | + | 74.8217i | 0.0435028 | + | 0.0753491i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −948.241 | −0.953006 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −643.120 | + | 1113.92i | −0.645055 | + | 1.11727i | 0.339234 | + | 0.940702i | \(0.389832\pi\) |
−0.984289 | + | 0.176566i | \(0.943501\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 345.130 | 0.345475 |
(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 | 76.3.h.a.69.3 | yes | 8 | |
3.2 | odd | 2 | 684.3.y.h.145.4 | 8 | |||
4.3 | odd | 2 | 304.3.r.c.145.2 | 8 | |||
19.7 | even | 3 | 1444.3.c.b.721.6 | 8 | |||
19.8 | odd | 6 | inner | 76.3.h.a.65.3 | ✓ | 8 | |
19.12 | odd | 6 | 1444.3.c.b.721.3 | 8 | |||
57.8 | even | 6 | 684.3.y.h.217.4 | 8 | |||
76.27 | even | 6 | 304.3.r.c.65.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.h.a.65.3 | ✓ | 8 | 19.8 | odd | 6 | inner | |
76.3.h.a.69.3 | yes | 8 | 1.1 | even | 1 | trivial | |
304.3.r.c.65.2 | 8 | 76.27 | even | 6 | |||
304.3.r.c.145.2 | 8 | 4.3 | odd | 2 | |||
684.3.y.h.145.4 | 8 | 3.2 | odd | 2 | |||
684.3.y.h.217.4 | 8 | 57.8 | even | 6 | |||
1444.3.c.b.721.3 | 8 | 19.12 | odd | 6 | |||
1444.3.c.b.721.6 | 8 | 19.7 | even | 3 |