Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(129,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("448.129");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(0.707107 - 2.60548i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.257 |
Dual form | 448.3.s.g.129.2 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −3.19104 | + | 1.84235i | −1.06368 | + | 0.614116i | −0.926448 | − | 0.376422i | \(-0.877154\pi\) |
−0.137233 | + | 0.990539i | \(0.543821\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.63938 | + | 1.52385i | 0.527877 | + | 0.304770i | 0.740151 | − | 0.672440i | \(-0.234754\pi\) |
−0.212275 | + | 0.977210i | \(0.568087\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.812549 | − | 6.95268i | −0.116078 | − | 0.993240i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.28850 | − | 3.96380i | 0.254278 | − | 0.440422i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.17516 | − | 2.03544i | −0.106833 | − | 0.185040i | 0.807653 | − | 0.589659i | \(-0.200738\pi\) |
−0.914486 | + | 0.404618i | \(0.867404\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.3073i | 1.94672i | 0.229292 | + | 0.973358i | \(0.426359\pi\) | ||||
−0.229292 | + | 0.973358i | \(0.573641\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.2298 | −0.748656 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.08674 | − | 1.78213i | 0.181573 | − | 0.104831i | −0.406459 | − | 0.913669i | \(-0.633236\pi\) |
0.588031 | + | 0.808838i | \(0.299903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.1772 | − | 8.18522i | −0.746169 | − | 0.430801i | 0.0781390 | − | 0.996942i | \(-0.475102\pi\) |
−0.824308 | + | 0.566142i | \(0.808436\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.4021 | + | 20.6893i | 0.733435 | + | 0.985205i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.83413 | + | 15.3012i | −0.384093 | + | 0.665268i | −0.991643 | − | 0.129013i | \(-0.958819\pi\) |
0.607550 | + | 0.794281i | \(0.292152\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.85577 | − | 13.6066i | −0.314231 | − | 0.544264i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 16.2974i | − | 0.603608i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −36.1220 | −1.24559 | −0.622793 | − | 0.782387i | \(-0.714002\pi\) | ||||
−0.622793 | + | 0.782387i | \(0.714002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.25629 | + | 3.61207i | −0.201816 | + | 0.116518i | −0.597502 | − | 0.801867i | \(-0.703840\pi\) |
0.395686 | + | 0.918386i | \(0.370507\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 0.227273 | + | 0.131216i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.45020 | − | 19.5890i | 0.241434 | − | 0.559685i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.4021 | − | 31.8734i | 0.497355 | − | 0.861445i | −0.502640 | − | 0.864496i | \(-0.667638\pi\) |
0.999995 | + | 0.00305120i | \(0.000971230\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −46.6249 | − | 80.7567i | −1.19551 | − | 2.07068i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 53.7118i | − | 1.31004i | −0.755610 | − | 0.655022i | \(-0.772659\pi\) | ||
0.755610 | − | 0.655022i | \(-0.227341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −51.2382 | −1.19159 | −0.595793 | − | 0.803138i | \(-0.703162\pi\) | ||||
−0.595793 | + | 0.803138i | \(0.703162\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.0805 | − | 6.97466i | 0.268455 | − | 0.154992i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 27.1609 | + | 15.6814i | 0.577892 | + | 0.333646i | 0.760295 | − | 0.649578i | \(-0.225054\pi\) |
−0.182403 | + | 0.983224i | \(0.558388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −47.6795 | + | 11.2988i | −0.973052 | + | 0.230588i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.56661 | + | 11.3737i | −0.128757 | + | 0.223014i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −35.1137 | − | 60.8187i | −0.662522 | − | 1.14752i | −0.979951 | − | 0.199240i | \(-0.936153\pi\) |
0.317428 | − | 0.948282i | \(-0.397181\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.16309i | − | 0.130238i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60.3201 | 1.05825 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −81.4102 | + | 47.0022i | −1.37983 | + | 0.796647i | −0.992139 | − | 0.125141i | \(-0.960062\pi\) |
−0.387695 | + | 0.921788i | \(0.626728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.89609 | + | 1.09471i | 0.0310835 | + | 0.0179461i | 0.515461 | − | 0.856913i | \(-0.327621\pi\) |
−0.484378 | + | 0.874859i | \(0.660954\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −29.4186 | − | 12.6904i | −0.466961 | − | 0.201435i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −38.5645 | + | 66.7957i | −0.593300 | + | 1.02763i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.4810 | − | 21.6177i | −0.186283 | − | 0.322652i | 0.757725 | − | 0.652574i | \(-0.226311\pi\) |
−0.944008 | + | 0.329922i | \(0.892977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 65.1022i | − | 0.943510i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −50.8890 | −0.716746 | −0.358373 | − | 0.933579i | \(-0.616668\pi\) | ||||
−0.358373 | + | 0.933579i | \(0.616668\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −68.9008 | + | 39.7799i | −0.943847 | + | 0.544930i | −0.891164 | − | 0.453681i | \(-0.850111\pi\) |
−0.0526830 | + | 0.998611i | \(0.516777\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 50.1362 | + | 28.9461i | 0.668483 | + | 0.385949i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.1969 | + | 9.82444i | −0.171389 | + | 0.127590i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −57.5117 | + | 99.6132i | −0.727996 | + | 1.26093i | 0.229733 | + | 0.973254i | \(0.426215\pi\) |
−0.957729 | + | 0.287672i | \(0.907119\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 50.6220 | + | 87.6799i | 0.624963 | + | 1.08247i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 154.132i | − | 1.85701i | −0.371318 | − | 0.928506i | \(-0.621094\pi\) | ||
0.371318 | − | 0.928506i | \(-0.378906\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8628 | 0.127797 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 115.267 | − | 66.5493i | 1.32491 | − | 0.764935i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 98.7274 | + | 57.0003i | 1.10930 | + | 0.640453i | 0.938647 | − | 0.344879i | \(-0.112080\pi\) |
0.170649 | + | 0.985332i | \(0.445414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 175.954 | − | 20.5634i | 1.93356 | − | 0.225972i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.3094 | − | 23.0525i | 0.143112 | − | 0.247877i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.9461 | − | 43.2079i | −0.262590 | − | 0.454820i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 53.9940i | − | 0.556640i | −0.960488 | − | 0.278320i | \(-0.910222\pi\) | ||
0.960488 | − | 0.278320i | \(-0.0897775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.7575 | −0.108661 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.0305 | + | 10.4099i | −0.178519 | + | 0.103068i | −0.586597 | − | 0.809879i | \(-0.699533\pi\) |
0.408077 | + | 0.912947i | \(0.366199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 105.870 | + | 61.1238i | 1.02786 | + | 0.593435i | 0.916371 | − | 0.400330i | \(-0.131105\pi\) |
0.111489 | + | 0.993766i | \(0.464438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.12480 | + | 78.0775i | 0.0869029 | + | 0.743596i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −57.2681 | + | 99.1912i | −0.535216 | + | 0.927021i | 0.463937 | + | 0.885868i | \(0.346436\pi\) |
−0.999153 | + | 0.0411525i | \(0.986897\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 82.9057 | + | 143.597i | 0.760603 | + | 1.31740i | 0.942540 | + | 0.334092i | \(0.108430\pi\) |
−0.181938 | + | 0.983310i | \(0.558237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 135.613i | 1.22174i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −123.071 | −1.08912 | −0.544560 | − | 0.838722i | \(-0.683303\pi\) | ||||
−0.544560 | + | 0.838722i | \(0.683303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −46.6333 | + | 26.9238i | −0.405507 | + | 0.234120i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 100.313 | + | 57.9158i | 0.857377 | + | 0.495007i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.8987 | − | 20.0130i | −0.125199 | − | 0.168177i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 57.7380 | − | 100.005i | 0.477173 | − | 0.826489i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 98.9559 | + | 171.397i | 0.804520 | + | 1.39347i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 124.076i | − | 0.992612i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 160.105 | 1.26067 | 0.630334 | − | 0.776324i | \(-0.282918\pi\) | ||||
0.630334 | + | 0.776324i | \(0.282918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 163.503 | − | 94.3987i | 1.26747 | − | 0.731773i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 53.3272 | + | 30.7885i | 0.407078 | + | 0.235027i | 0.689534 | − | 0.724254i | \(-0.257816\pi\) |
−0.282455 | + | 0.959280i | \(0.591149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −45.3895 | + | 105.221i | −0.341275 | + | 0.791132i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 24.8348 | − | 43.0151i | 0.183961 | − | 0.318630i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −47.5511 | − | 82.3609i | −0.347088 | − | 0.601174i | 0.638643 | − | 0.769503i | \(-0.279496\pi\) |
−0.985731 | + | 0.168329i | \(0.946163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 92.0558i | 0.662272i | 0.943583 | + | 0.331136i | \(0.107432\pi\) | ||||
−0.943583 | + | 0.331136i | \(0.892568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −115.562 | −0.819590 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 51.5116 | − | 29.7402i | 0.360221 | − | 0.207974i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −95.3398 | − | 55.0445i | −0.657516 | − | 0.379617i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 131.331 | − | 123.897i | 0.893409 | − | 0.842838i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −88.7225 | + | 153.672i | −0.595453 | + | 1.03136i | 0.398030 | + | 0.917373i | \(0.369694\pi\) |
−0.993483 | + | 0.113983i | \(0.963639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −114.894 | − | 199.002i | −0.760888 | − | 1.31790i | −0.942394 | − | 0.334506i | \(-0.891430\pi\) |
0.181506 | − | 0.983390i | \(-0.441903\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 16.3136i | − | 0.106625i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.0170 | −0.142045 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 42.9871 | − | 24.8186i | 0.273803 | − | 0.158080i | −0.356812 | − | 0.934176i | \(-0.616136\pi\) |
0.630615 | + | 0.776096i | \(0.282803\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 224.099 | + | 129.383i | 1.40942 | + | 0.813732i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 113.562 | + | 48.9879i | 0.705356 | + | 0.304273i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 33.2613 | − | 57.6103i | 0.204057 | − | 0.353438i | −0.745775 | − | 0.666198i | \(-0.767920\pi\) |
0.949832 | + | 0.312761i | \(0.101254\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.1969 | + | 22.8577i | 0.0799813 | + | 0.138532i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 164.292i | 0.983786i | 0.870656 | + | 0.491893i | \(0.163695\pi\) | ||||
−0.870656 | + | 0.491893i | \(0.836305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −471.460 | −2.78970 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −64.8891 | + | 37.4638i | −0.379469 | + | 0.219086i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 33.4995 | + | 19.3409i | 0.193639 | + | 0.111797i | 0.593685 | − | 0.804698i | \(-0.297673\pi\) |
−0.400046 | + | 0.916495i | \(0.631006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −88.2191 | + | 65.6747i | −0.504109 | + | 0.375284i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 173.189 | − | 299.972i | 0.978468 | − | 1.69476i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 51.2076 | + | 88.6942i | 0.286076 | + | 0.495498i | 0.972870 | − | 0.231354i | \(-0.0743157\pi\) |
−0.686794 | + | 0.726853i | \(0.740982\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 44.5843i | − | 0.246322i | −0.992387 | − | 0.123161i | \(-0.960697\pi\) | ||
0.992387 | − | 0.123161i | \(-0.0393032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.06735 | −0.0440839 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 97.1406 | − | 56.0842i | 0.525084 | − | 0.303158i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.25485 | − | 4.18859i | −0.0387960 | − | 0.0223989i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −113.311 | + | 13.2424i | −0.599527 | + | 0.0700659i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −165.031 | + | 285.842i | −0.864038 | + | 1.49656i | 0.00396184 | + | 0.999992i | \(0.498739\pi\) |
−0.868000 | + | 0.496565i | \(0.834594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −69.6777 | − | 120.685i | −0.361024 | − | 0.625312i | 0.627105 | − | 0.778934i | \(-0.284240\pi\) |
−0.988130 | + | 0.153622i | \(0.950906\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 284.197i | − | 1.45742i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −174.724 | −0.886925 | −0.443462 | − | 0.896293i | \(-0.646250\pi\) | ||||
−0.443462 | + | 0.896293i | \(0.646250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 197.009 | − | 113.743i | 0.989996 | − | 0.571574i | 0.0847227 | − | 0.996405i | \(-0.473000\pi\) |
0.905273 | + | 0.424830i | \(0.139666\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 79.6546 | + | 45.9886i | 0.396291 | + | 0.228799i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.3509 | + | 251.145i | 0.144586 | + | 1.23717i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 81.8487 | − | 141.766i | 0.399262 | − | 0.691542i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 40.4338 | + | 70.0335i | 0.195333 | + | 0.338326i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.4759i | 0.184095i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 251.350 | 1.19123 | 0.595617 | − | 0.803269i | \(-0.296908\pi\) | ||||
0.595617 | + | 0.803269i | \(0.296908\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 162.389 | − | 93.7552i | 0.762389 | − | 0.440165i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −135.237 | − | 78.0793i | −0.629011 | − | 0.363160i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.1971 | + | 40.5630i | 0.139157 | + | 0.186926i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 146.577 | − | 253.879i | 0.669301 | − | 1.15926i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 45.1009 | + | 78.1170i | 0.204076 | + | 0.353471i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 108.297i | − | 0.485636i | −0.970072 | − | 0.242818i | \(-0.921928\pi\) | ||
0.970072 | − | 0.242818i | \(-0.0780718\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −71.9118 | −0.319608 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −245.045 | + | 141.477i | −1.07949 | + | 0.623245i | −0.930759 | − | 0.365632i | \(-0.880853\pi\) |
−0.148733 | + | 0.988877i | \(0.547519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 153.011 | + | 88.3412i | 0.668172 | + | 0.385769i | 0.795384 | − | 0.606106i | \(-0.207269\pi\) |
−0.127212 | + | 0.991876i | \(0.540603\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.0119 | − | 55.6635i | 0.103947 | − | 0.240968i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −177.693 | + | 307.773i | −0.762630 | + | 1.32091i | 0.178861 | + | 0.983874i | \(0.442759\pi\) |
−0.941491 | + | 0.337039i | \(0.890575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 47.7921 | + | 82.7783i | 0.203370 | + | 0.352248i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 423.826i | − | 1.78830i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.5451 | −0.0734104 | −0.0367052 | − | 0.999326i | \(-0.511686\pi\) | ||||
−0.0367052 | + | 0.999326i | \(0.511686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 104.909 | − | 60.5693i | 0.435308 | − | 0.251325i | −0.266298 | − | 0.963891i | \(-0.585800\pi\) |
0.701605 | + | 0.712566i | \(0.252467\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −196.048 | − | 113.189i | −0.806783 | − | 0.465797i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −143.062 | − | 42.8346i | −0.583927 | − | 0.174835i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 207.146 | − | 358.787i | 0.838647 | − | 1.45258i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 283.965 | + | 491.842i | 1.14042 | + | 1.97527i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 219.342i | 0.873874i | 0.899492 | + | 0.436937i | \(0.143937\pi\) | ||||
−0.899492 | + | 0.436937i | \(0.856063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.5262 | 0.164135 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −34.6636 | + | 20.0130i | −0.135936 | + | 0.0784825i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 417.447 | + | 241.013i | 1.62431 | + | 0.937794i | 0.985749 | + | 0.168220i | \(0.0538019\pi\) |
0.638558 | + | 0.769574i | \(0.279531\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −236.559 | − | 102.045i | −0.913353 | − | 0.393998i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −82.6652 | + | 143.180i | −0.316725 | + | 0.548584i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −44.8439 | − | 77.6720i | −0.170509 | − | 0.295331i | 0.768089 | − | 0.640343i | \(-0.221208\pi\) |
−0.938598 | + | 0.345013i | \(0.887875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 214.032i | − | 0.807667i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −420.058 | −1.57325 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.9768 | − | 19.0392i | 0.122590 | − | 0.0707776i | −0.437451 | − | 0.899242i | \(-0.644119\pi\) |
0.560041 | + | 0.828465i | \(0.310785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −73.5803 | − | 42.4816i | −0.271514 | − | 0.156759i | 0.358062 | − | 0.933698i | \(-0.383438\pi\) |
−0.629575 | + | 0.776939i | \(0.716771\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −523.590 | + | 389.787i | −1.91791 | + | 1.42779i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.4636 | + | 31.9800i | −0.0671405 | + | 0.116291i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.2523 | + | 54.1306i | 0.112824 | + | 0.195417i | 0.916908 | − | 0.399099i | \(-0.130677\pi\) |
−0.804084 | + | 0.594516i | \(0.797344\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.0649i | 0.118512i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 58.6599 | 0.208754 | 0.104377 | − | 0.994538i | \(-0.466715\pi\) | ||||
0.104377 | + | 0.994538i | \(0.466715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 207.461 | − | 119.778i | 0.733078 | − | 0.423243i | −0.0864689 | − | 0.996255i | \(-0.527558\pi\) |
0.819547 | + | 0.573012i | \(0.194225\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 159.208 | + | 91.9187i | 0.558624 | + | 0.322522i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −373.441 | + | 43.6435i | −1.30119 | + | 0.152068i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −138.148 | + | 239.279i | −0.478021 | + | 0.827956i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 99.4759 | + | 172.297i | 0.341842 | + | 0.592087i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 196.503i | − | 0.670658i | −0.942101 | − | 0.335329i | \(-0.891152\pi\) | ||
0.942101 | − | 0.335329i | \(-0.108848\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −286.497 | −0.971176 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −33.1725 | + | 19.1521i | −0.111692 | + | 0.0644853i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −387.231 | − | 223.568i | −1.29509 | − | 0.747719i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.6336 | + | 356.243i | 0.138318 | + | 1.18353i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.3573 | − | 66.4368i | 0.126592 | − | 0.219263i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.33634 | + | 5.77871i | 0.0109388 | + | 0.0189466i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 246.955i | − | 0.804415i | −0.915549 | − | 0.402208i | \(-0.868243\pi\) | ||
0.915549 | − | 0.402208i | \(-0.131757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −450.446 | −1.45775 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −294.487 | + | 170.022i | −0.946905 | + | 0.546696i | −0.892118 | − | 0.451802i | \(-0.850781\pi\) |
−0.0547867 | + | 0.998498i | \(0.517448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 98.2049 | + | 56.6987i | 0.313754 | + | 0.181146i | 0.648605 | − | 0.761125i | \(-0.275353\pi\) |
−0.334851 | + | 0.942271i | \(0.608686\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −58.3086 | − | 78.3244i | −0.185107 | − | 0.248649i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 121.155 | − | 209.847i | 0.382192 | − | 0.661976i | −0.609183 | − | 0.793030i | \(-0.708503\pi\) |
0.991375 | + | 0.131053i | \(0.0418359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.4493 | + | 73.5243i | 0.133070 | + | 0.230484i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 422.031i | − | 1.31474i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −58.3484 | −0.180645 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 344.346 | − | 198.808i | 1.05953 | − | 0.611718i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −529.111 | − | 305.482i | −1.61808 | − | 0.934197i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 86.9579 | − | 201.583i | 0.264310 | − | 0.612715i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.8544 | − | 60.3697i | 0.105300 | − | 0.182386i | −0.808560 | − | 0.588413i | \(-0.799753\pi\) |
0.913861 | + | 0.406027i | \(0.133086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −84.2267 | − | 145.885i | −0.252933 | − | 0.438093i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 76.0764i | − | 0.227094i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 165.816 | 0.492037 | 0.246019 | − | 0.969265i | \(-0.420878\pi\) | ||||
0.246019 | + | 0.969265i | \(0.420878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 392.723 | − | 226.739i | 1.15848 | − | 0.668846i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7043 | + | 8.48956i | 0.0431212 | + | 0.0248961i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117.299 | + | 322.320i | 0.341979 | + | 0.939708i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 99.2059 | − | 171.830i | 0.287553 | − | 0.498057i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −283.452 | − | 490.953i | −0.816864 | − | 1.41485i | −0.907982 | − | 0.419010i | \(-0.862377\pi\) |
0.0911175 | − | 0.995840i | \(-0.470956\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 245.773i | 0.704219i | 0.935959 | + | 0.352110i | \(0.114536\pi\) | ||||
−0.935959 | + | 0.352110i | \(0.885464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 412.443 | 1.17505 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −137.837 | + | 79.5801i | −0.390472 | + | 0.225439i | −0.682365 | − | 0.731012i | \(-0.739048\pi\) |
0.291892 | + | 0.956451i | \(0.405715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −134.315 | − | 77.5471i | −0.378353 | − | 0.218442i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 84.4134 | + | 36.4138i | 0.236452 | + | 0.102000i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 102.513 | − | 177.557i | 0.285550 | − | 0.494588i | −0.687192 | − | 0.726476i | \(-0.741157\pi\) |
0.972743 | + | 0.231888i | \(0.0744902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −46.5044 | − | 80.5480i | −0.128821 | − | 0.223125i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 425.494i | 1.17216i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −242.474 | −0.664313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.46112 | + | 0.843577i | −0.00398125 | + | 0.00229858i | −0.501989 | − | 0.864874i | \(-0.667398\pi\) |
0.498008 | + | 0.867172i | \(0.334065\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −212.903 | − | 122.920i | −0.576973 | − | 0.333115i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −394.321 | + | 293.552i | −1.06286 | + | 0.791246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 231.702 | − | 401.320i | 0.621186 | − | 1.07593i | −0.368079 | − | 0.929795i | \(-0.619984\pi\) |
0.989265 | − | 0.146131i | \(-0.0466823\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 228.592 | + | 395.933i | 0.609579 | + | 1.05582i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 914.150i | − | 2.42480i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 493.215 | 1.30136 | 0.650680 | − | 0.759352i | \(-0.274484\pi\) | ||||
0.650680 | + | 0.759352i | \(0.274484\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −510.902 | + | 294.969i | −1.34095 | + | 0.774197i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −496.266 | − | 286.519i | −1.29573 | − | 0.748092i | −0.316069 | − | 0.948736i | \(-0.602363\pi\) |
−0.979664 | + | 0.200645i | \(0.935696\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −49.8027 | + | 5.82036i | −0.129358 | + | 0.0151178i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −117.259 | + | 203.098i | −0.302994 | + | 0.524801i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.2756 | − | 40.3146i | −0.0598346 | − | 0.103637i | 0.834556 | − | 0.550922i | \(-0.185724\pi\) |
−0.894391 | + | 0.447286i | \(0.852391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 62.9742i | 0.161059i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −226.893 | −0.577335 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −303.591 | + | 175.278i | −0.768584 | + | 0.443742i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −180.743 | − | 104.352i | −0.455273 | − | 0.262852i | 0.254782 | − | 0.966999i | \(-0.417996\pi\) |
−0.710055 | + | 0.704147i | \(0.751330\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −49.0131 | − | 419.386i | −0.122840 | − | 1.05109i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 110.595 | − | 191.556i | 0.275798 | − | 0.477696i | −0.694538 | − | 0.719456i | \(-0.744391\pi\) |
0.970336 | + | 0.241760i | \(0.0777246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −91.4118 | − | 158.330i | −0.226828 | − | 0.392878i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 308.561i | 0.761880i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −86.5022 | −0.212536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 83.5098 | − | 48.2144i | 0.204181 | − | 0.117884i | −0.394423 | − | 0.918929i | \(-0.629056\pi\) |
0.598604 | + | 0.801045i | \(0.295722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 303.475 | + | 175.211i | 0.738382 | + | 0.426305i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 392.941 | + | 527.827i | 0.951431 | + | 1.27803i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 234.874 | − | 406.813i | 0.565961 | − | 0.980273i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −169.599 | − | 293.754i | −0.406712 | − | 0.704446i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 239.093i | 0.570627i | 0.958434 | + | 0.285313i | \(0.0920977\pi\) | ||||
−0.958434 | + | 0.285313i | \(0.907902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −508.228 | −1.20719 | −0.603596 | − | 0.797290i | \(-0.706266\pi\) | ||||
−0.603596 | + | 0.797290i | \(0.706266\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 124.316 | − | 71.7737i | 0.293890 | − | 0.169678i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −48.4974 | − | 28.0000i | −0.114112 | − | 0.0658823i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.07049 | − | 14.0724i | 0.0142166 | − | 0.0329565i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −109.584 | + | 189.805i | −0.255440 | + | 0.442435i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 299.174 | + | 518.185i | 0.694140 | + | 1.20229i | 0.970470 | + | 0.241223i | \(0.0775486\pi\) |
−0.276329 | + | 0.961063i | \(0.589118\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 283.405i | 0.654516i | 0.944935 | + | 0.327258i | \(0.106125\pi\) | ||||
−0.944935 | + | 0.327258i | \(0.893875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 405.644 | 0.932516 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 250.487 | − | 144.619i | 0.573196 | − | 0.330935i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 296.596 | + | 171.240i | 0.675618 | + | 0.390068i | 0.798202 | − | 0.602390i | \(-0.205785\pi\) |
−0.122584 | + | 0.992458i | \(0.539118\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −64.3285 | + | 214.849i | −0.145870 | + | 0.487187i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 293.909 | − | 509.065i | 0.663451 | − | 1.14913i | −0.316252 | − | 0.948675i | \(-0.602425\pi\) |
0.979703 | − | 0.200455i | \(-0.0642421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 173.720 | + | 300.891i | 0.390381 | + | 0.676160i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 653.831i | − | 1.46271i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −265.522 | −0.591364 | −0.295682 | − | 0.955286i | \(-0.595547\pi\) | ||||
−0.295682 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −109.327 | + | 63.1202i | −0.242411 | + | 0.139956i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 733.264 | + | 423.350i | 1.61868 | + | 0.934547i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 495.745 | + | 213.852i | 1.08955 | + | 0.470004i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 198.296 | − | 343.458i | 0.433907 | − | 0.751550i | −0.563298 | − | 0.826254i | \(-0.690468\pi\) |
0.997206 | + | 0.0747039i | \(0.0238012\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.0441 | − | 50.3058i | −0.0632769 | − | 0.109599i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 143.388i | − | 0.311037i | −0.987833 | − | 0.155519i | \(-0.950295\pi\) | ||
0.987833 | − | 0.155519i | \(-0.0497049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 72.3400 | 0.156242 | 0.0781210 | − | 0.996944i | \(-0.475108\pi\) | ||||
0.0781210 | + | 0.996944i | \(0.475108\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 70.2572 | − | 40.5630i | 0.151091 | − | 0.0872323i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 453.684 | + | 261.935i | 0.971487 | + | 0.560888i | 0.899689 | − | 0.436531i | \(-0.143793\pi\) |
0.0717975 | + | 0.997419i | \(0.477126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −140.159 | + | 104.342i | −0.298847 | + | 0.222477i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −91.4491 | + | 158.394i | −0.194159 | + | 0.336294i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 60.2134 | + | 104.293i | 0.127301 | + | 0.220492i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 257.205i | 0.541484i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −321.431 | −0.673859 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −735.758 | + | 424.790i | −1.53603 | + | 0.886826i | −0.536963 | + | 0.843606i | \(0.680428\pi\) |
−0.999066 | + | 0.0432203i | \(0.986238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 806.631 | + | 465.709i | 1.67699 | + | 0.968209i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −452.635 | + | 52.8987i | −0.937132 | + | 0.109521i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 82.2788 | − | 142.511i | 0.169647 | − | 0.293837i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 202.982 | + | 351.574i | 0.416800 | + | 0.721919i | 0.995616 | − | 0.0935398i | \(-0.0298182\pi\) |
−0.578816 | + | 0.815458i | \(0.696485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 245.116i | 0.501260i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −661.455 | −1.34716 | −0.673580 | − | 0.739115i | \(-0.735244\pi\) | ||||
−0.673580 | + | 0.739115i | \(0.735244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −111.499 | + | 64.3740i | −0.226165 | + | 0.130576i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.3931 | − | 16.3927i | −0.0573597 | − | 0.0331167i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.3498 | + | 353.815i | 0.0831987 | + | 0.711901i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −119.784 | + | 207.472i | −0.240048 | + | 0.415775i | −0.960728 | − | 0.277493i | \(-0.910496\pi\) |
0.720680 | + | 0.693268i | \(0.243830\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −302.684 | − | 524.263i | −0.604159 | − | 1.04643i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 578.149i | 1.14940i | 0.818364 | + | 0.574701i | \(0.194882\pi\) | ||||
−0.818364 | + | 0.574701i | \(0.805118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −63.4524 | −0.125648 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1504.45 | − | 868.593i | 2.96735 | − | 1.71320i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −260.924 | − | 150.644i | −0.512621 | − | 0.295962i | 0.221290 | − | 0.975208i | \(-0.428973\pi\) |
−0.733910 | + | 0.679247i | \(0.762307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 332.562 | + | 446.722i | 0.650807 | + | 0.874212i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −133.398 | + | 231.052i | −0.260035 | + | 0.450393i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 186.287 | + | 322.659i | 0.361722 | + | 0.626521i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 73.7127i | − | 0.142578i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −142.531 | −0.274626 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −114.812 | + | 66.2868i | −0.220369 | + | 0.127230i | −0.606121 | − | 0.795372i | \(-0.707275\pi\) |
0.385752 | + | 0.922602i | \(0.373942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −96.1291 | − | 55.5001i | −0.183803 | − | 0.106119i | 0.405275 | − | 0.914195i | \(-0.367176\pi\) |
−0.589078 | + | 0.808076i | \(0.700509\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 160.515 | − | 372.101i | 0.305743 | − | 0.708764i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.8744 | + | 22.2990i | −0.0244295 | + | 0.0423132i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 108.416 | + | 187.783i | 0.204946 | + | 0.354976i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 430.258i | 0.810279i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1359.30 | 2.55028 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −302.305 | + | 174.536i | −0.565056 | + | 0.326235i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −326.811 | − | 188.685i | −0.608587 | − | 0.351368i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 79.0294 | + | 83.7711i | 0.146622 | + | 0.155419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.8522 | − | 74.2221i | 0.0792092 | − | 0.137194i | −0.823700 | − | 0.567026i | \(-0.808094\pi\) |
0.902909 | + | 0.429832i | \(0.141427\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 82.1399 | + | 142.271i | 0.151271 | + | 0.262008i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 505.343i | 0.927235i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 674.162 | 1.23247 | 0.616236 | − | 0.787562i | \(-0.288657\pi\) | ||||
0.616236 | + | 0.787562i | \(0.288657\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.67842 | − | 5.01049i | 0.0158077 | − | 0.00912657i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 512.109 | + | 295.666i | 0.929418 | + | 0.536600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 739.310 | + | 318.920i | 1.33691 | + | 0.576708i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −206.653 | + | 357.934i | −0.372348 | + | 0.644926i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 381.745 | + | 661.202i | 0.685359 | + | 1.18708i | 0.973324 | + | 0.229436i | \(0.0736882\pi\) |
−0.287964 | + | 0.957641i | \(0.592978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1296.70i | − | 2.31968i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.8674 | 0.0550221 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 307.458 | − | 177.511i | 0.546107 | − | 0.315295i | −0.201444 | − | 0.979500i | \(-0.564563\pi\) |
0.747550 | + | 0.664205i | \(0.231230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −324.830 | − | 187.541i | −0.574921 | − | 0.331931i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 568.478 | − | 423.203i | 1.00261 | − | 0.746390i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −263.535 | + | 456.455i | −0.463154 | + | 0.802206i | −0.999116 | − | 0.0420357i | \(-0.986616\pi\) |
0.535962 | + | 0.844242i | \(0.319949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −257.886 | − | 446.671i | −0.451639 | − | 0.782262i | 0.546849 | − | 0.837231i | \(-0.315827\pi\) |
−0.998488 | + | 0.0549695i | \(0.982494\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1216.18i | − | 2.12248i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 277.596 | 0.482775 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 182.029 | − | 105.095i | 0.315476 | − | 0.182140i | −0.333898 | − | 0.942609i | \(-0.608364\pi\) |
0.649374 | + | 0.760469i | \(0.275031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 444.689 | + | 256.741i | 0.768029 | + | 0.443422i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1071.63 | + | 125.240i | −1.84446 | + | 0.215559i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −82.5287 | + | 142.944i | −0.141559 | + | 0.245187i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 176.510 | + | 305.724i | 0.301726 | + | 0.522605i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 91.8797i | − | 0.156524i | −0.996933 | − | 0.0782621i | \(-0.975063\pi\) | ||
0.996933 | − | 0.0782621i | \(-0.0249371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 118.262 | 0.200785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 557.552 | − | 321.903i | 0.943405 | − | 0.544675i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −388.734 | − | 224.436i | −0.655538 | − | 0.378475i | 0.135037 | − | 0.990841i | \(-0.456885\pi\) |
−0.790575 | + | 0.612366i | \(0.790218\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.82654 | − | 75.5254i | −0.0148345 | − | 0.126933i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −419.110 | + | 725.919i | −0.702026 | + | 1.21595i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −98.8525 | − | 171.218i | −0.165029 | − | 0.285839i | 0.771636 | − | 0.636064i | \(-0.219439\pi\) |
−0.936666 | + | 0.350225i | \(0.886105\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 232.075i | 0.386148i | 0.981184 | + | 0.193074i | \(0.0618458\pi\) | ||||
−0.981184 | + | 0.193074i | \(0.938154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −114.251 | −0.189471 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 304.785 | − | 175.968i | 0.503777 | − | 0.290856i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 709.823 | + | 409.816i | 1.16940 | + | 0.675151i | 0.953538 | − | 0.301274i | \(-0.0974119\pi\) |
0.215858 | + | 0.976425i | \(0.430745\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −556.356 | − | 747.339i | −0.913557 | − | 1.22716i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −396.853 | + | 687.370i | −0.649514 | + | 1.12499i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −405.695 | − | 702.684i | −0.661819 | − | 1.14630i | −0.980137 | − | 0.198320i | \(-0.936451\pi\) |
0.318319 | − | 0.947984i | \(-0.396882\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 603.175i | 0.980773i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 248.808 | 0.403255 | 0.201627 | − | 0.979462i | \(-0.435377\pi\) | ||||
0.201627 | + | 0.979462i | \(0.435377\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −471.762 | + | 272.372i | −0.762136 | + | 0.440020i | −0.830062 | − | 0.557671i | \(-0.811695\pi\) |
0.0679258 | + | 0.997690i | \(0.478362\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 249.369 | + | 143.973i | 0.401561 | + | 0.231841i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 316.084 | − | 732.735i | 0.507358 | − | 1.17614i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.32049 | + | 12.6795i | −0.0117128 | + | 0.0202871i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −70.8861 | − | 122.778i | −0.113056 | − | 0.195819i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 131.180i | − | 0.208553i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −407.805 | −0.646284 | −0.323142 | − | 0.946350i | \(-0.604739\pi\) | ||||
−0.323142 | + | 0.946350i | \(0.604739\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −802.069 | + | 463.075i | −1.26709 | + | 0.731556i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 422.578 | + | 243.976i | 0.665478 | + | 0.384214i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −285.942 | − | 1206.64i | −0.448888 | − | 1.89425i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −116.459 | + | 201.714i | −0.182253 | + | 0.315671i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −322.840 | − | 559.175i | −0.503650 | − | 0.872347i | −0.999991 | − | 0.00421968i | \(-0.998657\pi\) |
0.496341 | − | 0.868128i | \(-0.334677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 932.869i | 1.45081i | 0.688324 | + | 0.725403i | \(0.258347\pi\) | ||||
−0.688324 | + | 0.725403i | \(0.741653\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 575.397 | 0.892089 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −420.287 | + | 242.653i | −0.649594 | + | 0.375043i | −0.788301 | − | 0.615290i | \(-0.789039\pi\) |
0.138707 | + | 0.990333i | \(0.455705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 191.341 | + | 110.471i | 0.294824 | + | 0.170217i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −171.092 | − | 73.8046i | −0.262813 | − | 0.113371i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −180.587 | + | 312.786i | −0.276550 | + | 0.478998i | −0.970525 | − | 0.241001i | \(-0.922524\pi\) |
0.693975 | + | 0.719999i | \(0.255858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 93.8340 | + | 162.525i | 0.143258 | + | 0.248130i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 364.146i | 0.554255i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 180.761 | 0.274296 | 0.137148 | − | 0.990551i | \(-0.456206\pi\) | ||||
0.137148 | + | 0.990551i | \(0.456206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −510.800 | + | 294.910i | −0.772768 | + | 0.446158i | −0.833861 | − | 0.551974i | \(-0.813875\pi\) |
0.0610929 | + | 0.998132i | \(0.480541\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −287.838 | − | 166.183i | −0.434144 | − | 0.250653i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −280.141 | + | 208.551i | −0.421264 | + | 0.313610i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 319.106 | − | 552.708i | 0.478420 | − | 0.828648i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 199.521 | + | 345.580i | 0.298237 | + | 0.516562i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.14585i | − | 0.00766893i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −416.772 | −0.619276 | −0.309638 | − | 0.950855i | \(-0.600208\pi\) | ||||
−0.309638 | + | 0.950855i | \(0.600208\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −221.752 | + | 128.029i | −0.328522 | + | 0.189672i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −398.113 | − | 229.851i | −0.588055 | − | 0.339514i | 0.176273 | − | 0.984341i | \(-0.443596\pi\) |
−0.764328 | + | 0.644827i | \(0.776929\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −375.403 | + | 43.8728i | −0.552877 | + | 0.0646139i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 521.299 | − | 902.916i | 0.765490 | − | 1.32587i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −560.093 | − | 970.109i | −0.820048 | − | 1.42036i | −0.905646 | − | 0.424034i | \(-0.860614\pi\) |
0.0855985 | − | 0.996330i | \(-0.472720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 289.843i | − | 0.423128i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −651.021 | −0.947629 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1539.16 | − | 888.633i | 2.23390 | − | 1.28974i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 370.080 | + | 213.666i | 0.535572 | + | 0.309213i | 0.743283 | − | 0.668978i | \(-0.233268\pi\) |
−0.207710 | + | 0.978190i | \(0.566601\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.74097 | + | 74.7932i | 0.0126132 | + | 0.107927i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −140.279 | + | 242.971i | −0.201840 | + | 0.349598i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −95.7214 | − | 165.794i | −0.137333 | − | 0.237868i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1309.49i | − | 1.87337i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 99.9460 | 0.142576 | 0.0712882 | − | 0.997456i | \(-0.477289\pi\) | ||||
0.0712882 | + | 0.997456i | \(0.477289\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −521.782 | + | 301.251i | −0.742222 | + | 0.428522i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −305.013 | − | 176.099i | −0.432643 | − | 0.249786i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 87.0272 | + | 116.901i | 0.123094 | + | 0.165349i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.5862 | − | 33.9244i | 0.0276252 | − | 0.0478482i | −0.851882 | − | 0.523733i | \(-0.824539\pi\) |
0.879507 | + | 0.475885i | \(0.157872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 263.231 | + | 455.930i | 0.370227 | + | 0.641251i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 127.638i | − | 0.179015i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 181.279 | 0.253536 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 55.9871 | − | 32.3242i | 0.0780853 | − | 0.0450825i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −668.482 | − | 385.948i | −0.929739 | − | 0.536785i | −0.0430100 | − | 0.999075i | \(-0.513695\pi\) |
−0.886729 | + | 0.462290i | \(0.847028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 338.950 | − | 785.744i | 0.470111 | − | 1.08980i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −223.180 | + | 386.559i | −0.308686 | + | 0.534659i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 283.766 | + | 491.497i | 0.391401 | + | 0.677927i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 963.864i | − | 1.32581i | −0.748703 | − | 0.662905i | \(-0.769323\pi\) | ||
0.748703 | − | 0.662905i | \(-0.230677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −77.0650 | −0.105713 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −158.159 | + | 91.3131i | −0.216360 | + | 0.124915i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 82.3471 | + | 47.5431i | 0.112343 | + | 0.0648610i | 0.555118 | − | 0.831771i | \(-0.312673\pi\) |
−0.442776 | + | 0.896632i | \(0.646006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 535.434 | − | 126.884i | 0.728481 | − | 0.172631i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.3344 | + | 50.8086i | −0.0398024 | + | 0.0689398i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −574.401 | − | 994.892i | −0.777268 | − | 1.34627i | −0.933511 | − | 0.358549i | \(-0.883271\pi\) |
0.156243 | − | 0.987719i | \(-0.450062\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1526.54i | 2.06011i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 232.652 | 0.313126 | 0.156563 | − | 0.987668i | \(-0.449959\pi\) | ||||
0.156563 | + | 0.987668i | \(0.449959\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −468.346 | + | 270.399i | −0.628652 | + | 0.362952i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −610.949 | − | 352.731i | −0.817869 | − | 0.472197i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 736.178 | + | 317.569i | 0.982881 | + | 0.423990i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −343.079 | + | 594.230i | −0.456829 | + | 0.791252i | −0.998791 | − | 0.0491513i | \(-0.984348\pi\) |
0.541962 | + | 0.840403i | \(0.317682\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −404.105 | − | 699.931i | −0.536660 | − | 0.929523i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 700.325i | − | 0.927582i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −657.058 | −0.867976 | −0.433988 | − | 0.900919i | \(-0.642894\pi\) | ||||
−0.433988 | + | 0.900919i | \(0.642894\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −132.512 | + | 76.5058i | −0.174588 | + | 0.100798i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1063.63 | − | 614.086i | −1.39767 | − | 0.806946i | −0.403523 | − | 0.914970i | \(-0.632214\pi\) |
−0.994148 | + | 0.108024i | \(0.965548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 931.018 | − | 693.096i | 1.22021 | − | 0.908383i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24.8595 | − | 43.0579i | 0.0324961 | − | 0.0562848i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1189.50 | − | 2060.27i | −1.55085 | − | 2.68614i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 499.279i | 0.649257i | 0.945842 | + | 0.324629i | \(0.105239\pi\) | ||||
−0.945842 | + | 0.324629i | \(0.894761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1776.12 | −2.30366 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 277.318 | − | 160.110i | 0.358756 | − | 0.207128i | −0.309779 | − | 0.950809i | \(-0.600255\pi\) |
0.668535 | + | 0.743681i | \(0.266922\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 98.2960 | + | 56.7512i | 0.126834 | + | 0.0732274i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 942.872 | − | 110.192i | 1.21348 | − | 0.141817i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −439.643 | + | 761.484i | −0.564368 | + | 0.977514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.8029 | + | 103.582i | 0.0765722 | + | 0.132627i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 588.695i | 0.751845i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 151.279 | 0.192712 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −490.946 | + | 283.448i | −0.623820 | + | 0.360162i | −0.778355 | − | 0.627825i | \(-0.783945\pi\) |
0.154535 | + | 0.987987i | \(0.450612\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 286.198 | + | 165.236i | 0.362735 | + | 0.209425i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 100.001 | + | 855.670i | 0.126423 | + | 1.08176i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.7041 | + | 47.9850i | −0.0349359 | + | 0.0605107i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 394.321 | + | 682.984i | 0.496002 | + | 0.859100i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1416.99i | 1.77791i | 0.457996 | + | 0.888954i | \(0.348567\pi\) | ||||
−0.457996 | + | 0.888954i | \(0.651433\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 111.785 | 0.139906 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 451.875 | − | 260.890i | 0.564139 | − | 0.325706i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 161.940 | + | 93.4959i | 0.201668 | + | 0.116433i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 225.084 | + | 302.350i | 0.279608 | + | 0.375590i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −70.1536 | + | 121.510i | −0.0869314 | + | 0.150570i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 498.631 | + | 863.654i | 0.616354 | + | 1.06756i | 0.990145 | + | 0.140044i | \(0.0447244\pi\) |
−0.373791 | + | 0.927513i | \(0.621942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1201.56i | 1.48158i | 0.671735 | + | 0.740792i | \(0.265550\pi\) | ||||
−0.671735 | + | 0.740792i | \(0.734450\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 313.064 | 0.385072 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 175.579 | − | 101.371i | 0.215434 | − | 0.124381i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 726.415 | + | 419.396i | 0.889125 | + | 0.513337i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 321.161 | − | 744.504i | 0.392138 | − | 0.909041i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −92.8952 | + | 160.899i | −0.113149 | + | 0.195980i | −0.917038 | − | 0.398799i | \(-0.869427\pi\) |
0.803889 | + | 0.594779i | \(0.202760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −429.451 | − | 743.831i | −0.521812 | − | 0.903805i | −0.999678 | − | 0.0253721i | \(-0.991923\pi\) |
0.477866 | − | 0.878433i | \(-0.341410\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 136.066i | − | 0.164928i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −217.847 | −0.263418 | −0.131709 | − | 0.991288i | \(-0.542046\pi\) | ||||
−0.131709 | + | 0.991288i | \(0.542046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −858.304 | + | 495.542i | −1.03535 | + | 0.597759i | −0.918512 | − | 0.395392i | \(-0.870609\pi\) |
−0.116836 | + | 0.993151i | \(0.537275\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −199.455 | − | 115.155i | −0.240018 | − | 0.138574i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −127.038 | + | 119.847i | −0.152507 | + | 0.143874i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −250.356 | + | 433.630i | −0.299828 | + | 0.519317i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 58.8674 | + | 101.961i | 0.0703314 | + | 0.121818i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 415.268i | − | 0.494956i | −0.968894 | − | 0.247478i | \(-0.920398\pi\) | ||
0.968894 | − | 0.247478i | \(-0.0796017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 463.798 | 0.551484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −187.186 | + | 108.072i | −0.222048 | + | 0.128199i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1244.36 | − | 718.433i | −1.47262 | − | 0.850217i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −742.218 | − | 320.175i | −0.876291 | − | 0.378010i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −441.345 | + | 764.432i | −0.519841 | + | 0.900391i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 325.134 | + | 563.148i | 0.382061 | + | 0.661749i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1335.36i | 1.56549i | 0.622343 | + | 0.782745i | \(0.286181\pi\) | ||||
−0.622343 | + | 0.782745i | \(0.713819\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −228.356 | −0.267084 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1392.35 | + | 803.874i | −1.62468 | + | 0.938009i | −0.639034 | + | 0.769178i | \(0.720666\pi\) |
−0.985645 | + | 0.168831i | \(0.946001\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −131.880 | − | 76.1410i | −0.153527 | − | 0.0886391i | 0.421268 | − | 0.906936i | \(-0.361585\pi\) |
−0.574796 | + | 0.818297i | \(0.694918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1111.26 | − | 827.277i | 1.29066 | − | 0.960833i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 480.137 | − | 831.622i | 0.556358 | − | 0.963641i | −0.441438 | − | 0.897292i | \(-0.645531\pi\) |
0.997796 | − | 0.0663494i | \(-0.0211352\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.9453 | + | 102.096i | 0.0681449 | + | 0.118030i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1018.07i | − | 1.17424i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 270.343 | 0.311096 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 547.085 | − | 315.860i | 0.628111 | − | 0.362640i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −214.022 | − | 123.565i | −0.245157 | − | 0.141541i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −862.664 | + | 100.818i | −0.985902 | + | 0.115221i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.97052 | − | 10.3413i | 0.00680790 | − | 0.0117916i | −0.862601 | − | 0.505884i | \(-0.831166\pi\) |
0.869409 | + | 0.494093i | \(0.164500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 362.027 | + | 627.049i | 0.411862 | + | 0.713366i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 625.457i | 0.709940i | 0.934878 | + | 0.354970i | \(0.115509\pi\) | ||||
−0.934878 | + | 0.354970i | \(0.884491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −78.6167 | −0.0890337 | −0.0445168 | − | 0.999009i | \(-0.514175\pi\) | ||||
−0.0445168 | + | 0.999009i | \(0.514175\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 914.224 | − | 527.827i | 1.03302 | − | 0.596415i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 633.661 | + | 365.844i | 0.714387 | + | 0.412451i | 0.812683 | − | 0.582706i | \(-0.198006\pi\) |
−0.0982963 | + | 0.995157i | \(0.531339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −130.093 | − | 1113.16i | −0.146336 | − | 1.25215i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 118.978 | − | 206.077i | 0.133534 | − | 0.231287i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −256.711 | − | 444.636i | −0.287470 | − | 0.497913i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 312.131i | 0.348749i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1647.56 | 1.83675 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 225.990 | − | 130.475i | 0.251379 | − | 0.145134i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −216.773 | − | 125.154i | −0.240592 | − | 0.138906i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −789.179 | − | 1060.08i | −0.873952 | − | 1.17396i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 67.9398 | − | 117.675i | 0.0750716 | − | 0.130028i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −143.851 | − | 249.157i | −0.158601 | − | 0.274704i | 0.775764 | − | 0.631024i | \(-0.217365\pi\) |
−0.934364 | + | 0.356319i | \(0.884032\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 95.2922i | 0.104832i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −249.315 | −0.273672 | −0.136836 | − | 0.990594i | \(-0.543693\pi\) | ||||
−0.136836 | + | 0.990594i | \(0.543693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −313.727 | + | 181.130i | −0.343622 | + | 0.198390i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.2928 | − | 12.2934i | −0.0232708 | − | 0.0134354i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 170.732 | − | 395.784i | 0.186185 | − | 0.431608i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0575 | − | 17.4201i | 0.0109440 | − | 0.0189555i | −0.860502 | − | 0.509448i | \(-0.829850\pi\) |
0.871446 | + | 0.490492i | \(0.163183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 454.978 | + | 788.045i | 0.494005 | + | 0.855641i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1287.86i | − | 1.39530i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −578.252 | −0.625137 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 484.566 | − | 279.764i | 0.522724 | − | 0.301795i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1067.50 | − | 616.321i | −1.14908 | − | 0.663424i | −0.200420 | − | 0.979710i | \(-0.564231\pi\) |
−0.948664 | + | 0.316286i | \(0.897564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 768.446 | + | 230.082i | 0.825398 | + | 0.247134i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 626.481 | − | 1085.10i | 0.671470 | − | 1.16302i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.7656 | − | 22.1106i | −0.0136530 | − | 0.0236477i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 283.840i | 0.302924i | 0.988463 | + | 0.151462i | \(0.0483981\pi\) | ||||
−0.988463 | + | 0.151462i | \(0.951602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −417.835 | −0.444979 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −561.263 | + | 324.045i | −0.596453 | + | 0.344362i | −0.767645 | − | 0.640875i | \(-0.778572\pi\) |
0.171192 | + | 0.985238i | \(0.445238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 821.853 | + | 474.497i | 0.871530 | + | 0.503178i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −319.250 | − | 137.716i | −0.337831 | − | 0.145732i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 859.101 | − | 1488.01i | 0.907181 | − | 1.57128i | 0.0892196 | − | 0.996012i | \(-0.471563\pi\) |
0.817962 | − | 0.575272i | \(-0.195104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1006.72 | − | 1743.69i | −1.06082 | − | 1.83740i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 892.839i | 0.938842i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1085.95 | 1.13950 | 0.569752 | − | 0.821817i | \(-0.307039\pi\) | ||||
0.569752 | + | 0.821817i | \(0.307039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −871.161 | + | 502.965i | −0.912211 | + | 0.526665i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −270.915 | − | 156.413i | −0.283088 | − | 0.163441i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −533.991 | + | 397.530i | −0.556821 | + | 0.414525i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −454.406 | + | 787.054i | −0.472847 | + | 0.818995i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 262.116 | + | 453.998i | 0.272187 | + | 0.471442i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 424.713i | − | 0.440117i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −969.512 | −1.00260 | −0.501299 | − | 0.865274i | \(-0.667144\pi\) | ||||
−0.501299 | + | 0.865274i | \(0.667144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 186.192 | − | 107.498i | 0.192149 | − | 0.110937i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 724.959 | + | 418.555i | 0.746611 | + | 0.431056i | 0.824468 | − | 0.565908i | \(-0.191474\pi\) |
−0.0778571 | + | 0.996965i | \(0.524808\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 640.035 | − | 74.7999i | 0.657795 | − | 0.0768755i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −732.549 | + | 1268.81i | −0.751332 | + | 1.30135i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −680.114 | − | 1177.99i | −0.696125 | − | 1.20572i | −0.969800 | − | 0.243901i | \(-0.921573\pi\) |
0.273675 | − | 0.961822i | \(-0.411761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 267.939i | − | 0.273686i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 758.919 | 0.773618 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 344.050 | − | 198.637i | 0.350000 | − | 0.202073i | −0.314685 | − | 0.949196i | \(-0.601899\pi\) |
0.664685 | + | 0.747123i | \(0.268566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −461.164 | − | 266.253i | −0.468187 | − | 0.270308i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 93.9000 | + | 803.467i | 0.0951368 | + | 0.814050i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 452.645 | − | 784.004i | 0.457680 | − | 0.792724i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −139.250 | − | 241.188i | −0.140514 | − | 0.243378i | 0.787176 | − | 0.616728i | \(-0.211542\pi\) |
−0.927690 | + | 0.373350i | \(0.878209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 256.856i | 0.258667i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 693.310 | 0.696794 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 716.547 | − | 413.699i | 0.718703 | − | 0.414943i | −0.0955720 | − | 0.995423i | \(-0.530468\pi\) |
0.814275 | + | 0.580479i | \(0.197135\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −519.455 | − | 299.907i | −0.519975 | − | 0.300208i |
(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 | 448.3.s.g.257.2 | 16 | ||
4.3 | odd | 2 | inner | 448.3.s.g.257.7 | 16 | ||
7.3 | odd | 6 | inner | 448.3.s.g.129.2 | 16 | ||
8.3 | odd | 2 | 224.3.s.a.33.2 | ✓ | 16 | ||
8.5 | even | 2 | 224.3.s.a.33.7 | yes | 16 | ||
28.3 | even | 6 | inner | 448.3.s.g.129.7 | 16 | ||
56.3 | even | 6 | 224.3.s.a.129.2 | yes | 16 | ||
56.5 | odd | 6 | 1568.3.c.h.97.3 | 16 | |||
56.19 | even | 6 | 1568.3.c.h.97.13 | 16 | |||
56.37 | even | 6 | 1568.3.c.h.97.14 | 16 | |||
56.45 | odd | 6 | 224.3.s.a.129.7 | yes | 16 | ||
56.51 | odd | 6 | 1568.3.c.h.97.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.a.33.2 | ✓ | 16 | 8.3 | odd | 2 | ||
224.3.s.a.33.7 | yes | 16 | 8.5 | even | 2 | ||
224.3.s.a.129.2 | yes | 16 | 56.3 | even | 6 | ||
224.3.s.a.129.7 | yes | 16 | 56.45 | odd | 6 | ||
448.3.s.g.129.2 | 16 | 7.3 | odd | 6 | inner | ||
448.3.s.g.129.7 | 16 | 28.3 | even | 6 | inner | ||
448.3.s.g.257.2 | 16 | 1.1 | even | 1 | trivial | ||
448.3.s.g.257.7 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.h.97.3 | 16 | 56.5 | odd | 6 | |||
1568.3.c.h.97.4 | 16 | 56.51 | odd | 6 | |||
1568.3.c.h.97.13 | 16 | 56.19 | even | 6 | |||
1568.3.c.h.97.14 | 16 | 56.37 | even | 6 |