Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(425,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.425");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 425.11 | ||
Character | \(\chi\) | \(=\) | 684.425 |
Dual form | 684.3.be.a.581.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.89926 | − | 2.32224i | −0.633088 | − | 0.774080i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.60071 | + | 0.924171i | 0.320142 | + | 0.184834i | 0.651456 | − | 0.758686i | \(-0.274159\pi\) |
−0.331314 | + | 0.943521i | \(0.607492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46982 | − | 4.27785i | 0.352831 | − | 0.611121i | −0.633913 | − | 0.773404i | \(-0.718552\pi\) |
0.986744 | + | 0.162283i | \(0.0518858\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.78559 | + | 8.82109i | −0.198399 | + | 0.980121i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.4350 | − | 6.02464i | −0.948635 | − | 0.547694i | −0.0559781 | − | 0.998432i | \(-0.517828\pi\) |
−0.892657 | + | 0.450738i | \(0.851161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.2235 | 0.786425 | 0.393212 | − | 0.919448i | \(-0.371364\pi\) | ||||
0.393212 | + | 0.919448i | \(0.371364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.894026 | − | 5.47248i | −0.0596017 | − | 0.364832i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.2730 | + | 9.39522i | −0.957235 | + | 0.552660i | −0.895321 | − | 0.445422i | \(-0.853054\pi\) |
−0.0619139 | + | 0.998081i | \(0.519720\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.26716 | − | 17.1071i | 0.435114 | − | 0.900375i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.6250 | + | 2.38925i | −0.696429 | + | 0.113774i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 18.8234i | − | 0.818410i | −0.912442 | − | 0.409205i | \(-0.865806\pi\) | ||
0.912442 | − | 0.409205i | \(-0.134194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.7918 | − | 18.6920i | −0.431673 | − | 0.747679i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 23.8760 | − | 12.6070i | 0.884296 | − | 0.466926i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.07286 | + | 2.35147i | −0.140443 | + | 0.0810850i | −0.568575 | − | 0.822631i | \(-0.692505\pi\) |
0.428132 | + | 0.903716i | \(0.359172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.2830 | + | 24.7388i | 0.460740 | + | 0.798026i | 0.998998 | − | 0.0447545i | \(-0.0142506\pi\) |
−0.538258 | + | 0.842780i | \(0.680917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.82812 | + | 35.6749i | 0.176610 | + | 1.08106i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.90692 | − | 4.56506i | 0.225912 | − | 0.130430i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −52.8630 | −1.42873 | −0.714365 | − | 0.699773i | \(-0.753285\pi\) | ||||
−0.714365 | + | 0.699773i | \(0.753285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.4172 | − | 23.7415i | −0.497876 | − | 0.608755i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.43514 | − | 3.71533i | −0.156955 | − | 0.0906178i | 0.419466 | − | 0.907771i | \(-0.362217\pi\) |
−0.576420 | + | 0.817153i | \(0.695551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.3991 | −0.962771 | −0.481385 | − | 0.876509i | \(-0.659866\pi\) | ||||
−0.481385 | + | 0.876509i | \(0.659866\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.0104 | + | 12.4698i | −0.244676 | + | 0.277107i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.74062 | − | 2.15965i | 0.0795878 | − | 0.0459500i | −0.459678 | − | 0.888086i | \(-0.652035\pi\) |
0.539266 | + | 0.842136i | \(0.318702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.3000 | + | 21.3043i | 0.251021 | + | 0.434781i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.7246 | + | 19.9458i | 1.03382 | + | 0.391094i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −41.4703 | − | 23.9429i | −0.782459 | − | 0.451753i | 0.0548421 | − | 0.998495i | \(-0.482534\pi\) |
−0.837301 | + | 0.546742i | \(0.815868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1356 | − | 19.2874i | −0.202465 | − | 0.350680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −55.4284 | + | 13.2926i | −0.972428 | + | 0.233204i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −44.0498 | − | 25.4322i | −0.746606 | − | 0.431053i | 0.0778600 | − | 0.996964i | \(-0.475191\pi\) |
−0.824466 | + | 0.565911i | \(0.808525\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.5107 | − | 19.9371i | −0.188699 | − | 0.326837i | 0.756117 | − | 0.654436i | \(-0.227094\pi\) |
−0.944817 | + | 0.327599i | \(0.893761\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 33.3252 | + | 29.4250i | 0.528971 | + | 0.467063i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.3649 | + | 9.44828i | 0.251768 | + | 0.145358i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38.7932 | 0.579004 | 0.289502 | − | 0.957177i | \(-0.406510\pi\) | ||||
0.289502 | + | 0.957177i | \(0.406510\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −43.7125 | + | 35.7507i | −0.633515 | + | 0.518126i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −95.0990 | + | 54.9054i | −1.33942 | + | 0.773316i | −0.986722 | − | 0.162420i | \(-0.948070\pi\) |
−0.352701 | + | 0.935736i | \(0.614737\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5505 | + | 20.0061i | 0.158226 | + | 0.274056i | 0.934229 | − | 0.356673i | \(-0.116089\pi\) |
−0.776003 | + | 0.630730i | \(0.782756\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −22.9107 | + | 60.5622i | −0.305477 | + | 0.807496i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −51.5450 | + | 29.7595i | −0.669415 | + | 0.386487i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −149.029 | −1.88644 | −0.943218 | − | 0.332173i | \(-0.892218\pi\) | ||||
−0.943218 | + | 0.332173i | \(0.892218\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −74.6233 | − | 31.5018i | −0.921275 | − | 0.388911i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −64.2549 | − | 37.0976i | −0.774156 | − | 0.446959i | 0.0601995 | − | 0.998186i | \(-0.480826\pi\) |
−0.834355 | + | 0.551227i | \(0.814160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −34.7311 | −0.408602 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.1961 | + | 4.99210i | 0.151679 | + | 0.0573805i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.22299 | + | 5.32490i | 0.103629 | + | 0.0598303i | 0.550919 | − | 0.834559i | \(-0.314277\pi\) |
−0.447290 | + | 0.894389i | \(0.647611\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.2502 | − | 43.7346i | 0.277475 | − | 0.480601i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 30.3223 | − | 80.1540i | 0.326047 | − | 0.861871i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 29.0433 | − | 19.7433i | 0.305718 | − | 0.207824i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 100.686 | 1.03800 | 0.519000 | − | 0.854774i | \(-0.326305\pi\) | ||||
0.519000 | + | 0.854774i | \(0.326305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 71.7765 | − | 81.2904i | 0.725016 | − | 0.821115i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −127.441 | + | 73.5780i | −1.26179 | + | 0.728495i | −0.973421 | − | 0.229025i | \(-0.926446\pi\) |
−0.288369 | + | 0.957519i | \(0.593113\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −28.4113 | − | 49.2098i | −0.275838 | − | 0.477765i | 0.694509 | − | 0.719484i | \(-0.255622\pi\) |
−0.970346 | + | 0.241720i | \(0.922289\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.6185 | − | 9.69151i | −0.243986 | − | 0.0923001i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 62.5758i | 0.584821i | 0.956293 | + | 0.292410i | \(0.0944573\pi\) | ||||
−0.956293 | + | 0.292410i | \(0.905543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −32.2512 | − | 55.8606i | −0.295882 | − | 0.512483i | 0.679308 | − | 0.733854i | \(-0.262280\pi\) |
−0.975190 | + | 0.221371i | \(0.928947\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 100.401 | + | 122.761i | 0.904512 | + | 1.10595i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −110.388 | + | 63.7326i | −0.976885 | + | 0.564005i | −0.901328 | − | 0.433137i | \(-0.857407\pi\) |
−0.0755570 | + | 0.997141i | \(0.524073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.3961 | − | 30.1309i | 0.151270 | − | 0.262008i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.2551 | + | 90.1826i | −0.156026 | + | 0.770791i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 92.8178i | 0.779982i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.0925 | + | 20.9449i | 0.0999384 | + | 0.173098i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.59414 | + | 22.0003i | 0.0292206 | + | 0.178864i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 86.1025i | − | 0.688820i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118.378 | − | 205.036i | 0.932109 | − | 1.61446i | 0.152399 | − | 0.988319i | \(-0.451300\pi\) |
0.779710 | − | 0.626141i | \(-0.215367\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 78.6279 | + | 96.1387i | 0.609518 | + | 0.745261i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 217.986 | + | 125.854i | 1.66402 | + | 0.960720i | 0.970768 | + | 0.240019i | \(0.0771538\pi\) |
0.693247 | + | 0.720700i | \(0.256180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −52.7633 | − | 77.6171i | −0.396717 | − | 0.583587i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 49.8696 | + | 1.88535i | 0.369404 | + | 0.0139655i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.56119 | − | 2.63340i | 0.0332934 | − | 0.0192219i | −0.483261 | − | 0.875476i | \(-0.660548\pi\) |
0.516554 | + | 0.856254i | \(0.327214\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 162.679 | 1.17035 | 0.585176 | − | 0.810906i | \(-0.301025\pi\) | ||||
0.585176 | + | 0.810906i | \(0.301025\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1197 | − | 4.58488i | −0.0859550 | − | 0.0325169i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −106.682 | − | 61.5930i | −0.746030 | − | 0.430720i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.69263 | −0.0599492 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 26.1126 | − | 69.0260i | 0.177637 | − | 0.469565i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 61.8394 | + | 35.7030i | 0.415029 | + | 0.239617i | 0.692948 | − | 0.720987i | \(-0.256311\pi\) |
−0.277919 | + | 0.960605i | \(0.589645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.78566 | − | 13.4852i | 0.0515607 | − | 0.0893057i | −0.839093 | − | 0.543988i | \(-0.816914\pi\) |
0.890654 | + | 0.454682i | \(0.150247\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −53.8191 | − | 160.322i | −0.351759 | − | 1.04785i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 52.7996i | 0.340642i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 74.6100 | − | 129.228i | 0.475223 | − | 0.823110i | −0.524375 | − | 0.851488i | \(-0.675701\pi\) |
0.999597 | + | 0.0283778i | \(0.00903416\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.1619 | + | 141.778i | 0.145672 | + | 0.891685i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −80.5238 | − | 46.4904i | −0.500148 | − | 0.288760i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 157.638 | 0.967101 | 0.483551 | − | 0.875316i | \(-0.339347\pi\) | ||||
0.483551 | + | 0.875316i | \(0.339347\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −23.6406 | + | 62.4914i | −0.143276 | + | 0.378736i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 246.867i | − | 1.47825i | −0.673571 | − | 0.739123i | \(-0.735240\pi\) | ||
0.673571 | − | 0.739123i | \(-0.264760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64.4797 | −0.381536 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 136.142 | + | 103.472i | 0.796151 | + | 0.605098i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 104.588i | 0.604553i | 0.953220 | + | 0.302276i | \(0.0977465\pi\) | ||||
−0.953220 | + | 0.302276i | \(0.902253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −106.615 | −0.609230 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.6026 | + | 150.597i | 0.138998 | + | 0.850828i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 238.780i | − | 1.33397i | −0.745072 | − | 0.666985i | \(-0.767585\pi\) | ||
0.745072 | − | 0.666985i | \(-0.232415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 108.062 | − | 187.169i | 0.597029 | − | 1.03408i | −0.396228 | − | 0.918152i | \(-0.629681\pi\) |
0.993257 | − | 0.115933i | \(-0.0369857\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.4368 | + | 64.5963i | −0.133535 | + | 0.352985i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −84.6185 | − | 48.8545i | −0.457397 | − | 0.264078i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 226.411 | 1.21075 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.03853 | − | 133.275i | 0.0266589 | − | 0.705158i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 150.835 | + | 87.0849i | 0.789714 | + | 0.455942i | 0.839862 | − | 0.542800i | \(-0.182636\pi\) |
−0.0501477 | + | 0.998742i | \(0.515969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.5500 | − | 37.3257i | 0.111658 | − | 0.193397i | −0.804781 | − | 0.593572i | \(-0.797717\pi\) |
0.916439 | + | 0.400175i | \(0.131051\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.14009 | − | 55.9480i | −0.0468723 | − | 0.286913i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 229.707i | − | 1.16603i | −0.812463 | − | 0.583013i | \(-0.801874\pi\) | ||
0.812463 | − | 0.583013i | \(-0.198126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −32.8318 | + | 56.8663i | −0.164984 | + | 0.285760i | −0.936650 | − | 0.350268i | \(-0.886090\pi\) |
0.771666 | + | 0.636028i | \(0.219424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −73.6786 | − | 90.0872i | −0.366560 | − | 0.448195i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.2308i | 0.114437i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.86720 | − | 11.8943i | −0.0334985 | − | 0.0580211i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 166.043 | + | 33.6110i | 0.802141 | + | 0.162372i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −189.332 | + | 128.706i | −0.905895 | + | 0.615818i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77.2746 | − | 133.844i | 0.366230 | − | 0.634329i | −0.622743 | − | 0.782427i | \(-0.713982\pi\) |
0.988973 | + | 0.148097i | \(0.0473149\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 308.122 | + | 116.563i | 1.44658 | + | 0.547243i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −66.2681 | − | 38.2599i | −0.308224 | − | 0.177953i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 141.105 | 0.650254 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.5215 | − | 64.8200i | 0.111970 | − | 0.295982i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −166.367 | + | 96.0522i | −0.752793 | + | 0.434625i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 130.874 | 0.586878 | 0.293439 | − | 0.955978i | \(-0.405200\pi\) | ||||
0.293439 | + | 0.955978i | \(0.405200\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 184.153 | − | 61.8193i | 0.818460 | − | 0.274752i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 140.131 | + | 80.9047i | 0.617318 | + | 0.356409i | 0.775824 | − | 0.630949i | \(-0.217334\pi\) |
−0.158506 | + | 0.987358i | \(0.550668\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 168.547 | + | 291.933i | 0.736015 | + | 1.27482i | 0.954277 | + | 0.298925i | \(0.0966280\pi\) |
−0.218262 | + | 0.975890i | \(0.570039\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 167.006 | + | 63.1786i | 0.722970 | + | 0.273501i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.44103 | − | 4.29608i | 0.0319357 | − | 0.0184381i | −0.483947 | − | 0.875097i | \(-0.660797\pi\) |
0.515883 | + | 0.856659i | \(0.327464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.98355 | 0.0339725 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 283.044 | + | 346.080i | 1.19428 | + | 1.46025i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −216.237 | + | 124.844i | −0.904756 | + | 0.522361i | −0.878740 | − | 0.477300i | \(-0.841615\pi\) |
−0.0260161 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −138.916 | − | 240.609i | −0.576414 | − | 0.998378i | −0.995886 | − | 0.0906101i | \(-0.971118\pi\) |
0.419473 | − | 0.907768i | \(-0.362215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 68.5746 | + | 233.123i | 0.282200 | + | 0.959356i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 45.4693i | 0.185589i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 84.5195 | − | 174.895i | 0.342184 | − | 0.708077i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.8875 | + | 219.673i | 0.144127 | + | 0.882223i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −413.219 | − | 238.572i | −1.64629 | − | 0.950486i | −0.978529 | − | 0.206110i | \(-0.933919\pi\) |
−0.667761 | − | 0.744376i | \(-0.732747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −113.404 | + | 196.422i | −0.448239 | + | 0.776372i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 65.9636 | + | 80.6540i | 0.258681 | + | 0.316290i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 176.278i | 0.685908i | 0.939352 | + | 0.342954i | \(0.111428\pi\) | ||||
−0.939352 | + | 0.342954i | \(0.888572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −130.562 | + | 226.140i | −0.504100 | + | 0.873127i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.4700 | − | 40.1258i | −0.0516093 | − | 0.153739i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 188.617i | 0.717177i | 0.933496 | + | 0.358588i | \(0.116742\pi\) | ||||
−0.933496 | + | 0.358588i | \(0.883258\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −44.2547 | − | 76.6513i | −0.166999 | − | 0.289250i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.15121 | − | 31.5314i | −0.0192929 | − | 0.118095i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 356.589 | − | 205.877i | 1.32561 | − | 0.765340i | 0.340991 | − | 0.940067i | \(-0.389237\pi\) |
0.984617 | + | 0.174726i | \(0.0559041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3004 | + | 42.0896i | 0.0896695 | + | 0.155312i | 0.907371 | − | 0.420330i | \(-0.138086\pi\) |
−0.817702 | + | 0.575642i | \(0.804752\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −149.519 | + | 24.4266i | −0.547689 | + | 0.0894747i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 260.067i | 0.945699i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −76.9499 | + | 133.281i | −0.277798 | + | 0.481159i | −0.970837 | − | 0.239740i | \(-0.922938\pi\) |
0.693040 | + | 0.720900i | \(0.256271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −243.727 | + | 81.8178i | −0.873573 | + | 0.293254i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 116.407 | − | 67.2076i | 0.414260 | − | 0.239173i | −0.278359 | − | 0.960477i | \(-0.589790\pi\) |
0.692618 | + | 0.721304i | \(0.256457\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.8317 | − | 55.1341i | 0.112480 | − | 0.194820i | −0.804290 | − | 0.594237i | \(-0.797454\pi\) |
0.916769 | + | 0.399417i | \(0.130787\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −101.009 | − | 29.9477i | −0.354419 | − | 0.105080i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.7872 | + | 18.3524i | −0.110757 | + | 0.0639455i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0401 | − | 55.4951i | 0.110866 | − | 0.192025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −191.229 | − | 233.817i | −0.657145 | − | 0.803495i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 186.208 | − | 107.507i | 0.635523 | − | 0.366919i | −0.147365 | − | 0.989082i | \(-0.547079\pi\) |
0.782888 | + | 0.622163i | \(0.213746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −47.0073 | − | 81.4191i | −0.159347 | − | 0.275997i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −325.098 | − | 12.2905i | −1.09461 | − | 0.0413822i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 192.442i | − | 0.643618i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −102.248 | + | 177.099i | −0.339695 | + | 0.588369i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 412.909 | + | 156.204i | 1.36274 | + | 0.515525i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 42.5513i | − | 0.139512i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −137.106 | − | 237.474i | −0.446599 | − | 0.773532i | 0.551563 | − | 0.834133i | \(-0.314032\pi\) |
−0.998162 | + | 0.0606011i | \(0.980698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −60.3164 | + | 159.440i | −0.195199 | + | 0.515987i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −395.495 | + | 228.339i | −1.27169 | + | 0.734209i | −0.975305 | − | 0.220861i | \(-0.929113\pi\) |
−0.296382 | + | 0.955070i | \(0.595780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −49.7646 | − | 86.1947i | −0.158992 | − | 0.275383i | 0.775513 | − | 0.631331i | \(-0.217491\pi\) |
−0.934506 | + | 0.355949i | \(0.884158\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.1503 | + | 77.8990i | 0.0830168 | + | 0.247299i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 107.225 | − | 61.9065i | 0.338250 | − | 0.195289i | −0.321248 | − | 0.946995i | \(-0.604102\pi\) |
0.659498 | + | 0.751706i | \(0.270769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 56.6669 | 0.177639 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 145.316 | − | 118.848i | 0.452698 | − | 0.370243i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.1937 | + | 356.056i | 0.0810951 | + | 1.10234i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −110.330 | − | 191.098i | −0.339478 | − | 0.587993i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −68.4683 | + | 180.989i | −0.209383 | + | 0.553483i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 21.3358i | − | 0.0648503i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 284.794 | − | 493.278i | 0.860406 | − | 1.49027i | −0.0111320 | − | 0.999938i | \(-0.503544\pi\) |
0.871538 | − | 0.490328i | \(-0.163123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 94.3920 | − | 466.310i | 0.283459 | − | 1.40033i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 62.0968 | + | 35.8516i | 0.185364 | + | 0.107020i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 88.6716 | − | 153.584i | 0.263120 | − | 0.455738i | −0.703949 | − | 0.710250i | \(-0.748582\pi\) |
0.967069 | + | 0.254513i | \(0.0819150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 357.658 | + | 135.303i | 1.05504 | + | 0.399123i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 344.199i | − | 1.00938i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 363.557 | 1.05993 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −103.011 | + | 16.8286i | −0.298582 | + | 0.0487787i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 336.292 | + | 194.158i | 0.969140 | + | 0.559533i | 0.898974 | − | 0.438002i | \(-0.144314\pi\) |
0.0701662 | + | 0.997535i | \(0.477647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −165.385 | + | 286.456i | −0.473884 | + | 0.820791i | −0.999553 | − | 0.0298982i | \(-0.990482\pi\) |
0.525669 | + | 0.850689i | \(0.323815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 244.097 | − | 128.888i | 0.695432 | − | 0.367202i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −152.631 | − | 88.1216i | −0.432383 | − | 0.249636i | 0.267979 | − | 0.963425i | \(-0.413644\pi\) |
−0.700361 | + | 0.713789i | \(0.746978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −202.968 | −0.571741 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 215.545 | − | 176.285i | 0.603768 | − | 0.493797i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 208.764 | − | 120.530i | 0.581515 | − | 0.335738i | −0.180220 | − | 0.983626i | \(-0.557681\pi\) |
0.761735 | + | 0.647888i | \(0.224348\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −224.308 | − | 282.855i | −0.621352 | − | 0.783532i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.6721 | − | 67.8617i | 0.0707222 | − | 0.186947i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 42.6987i | 0.116983i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −95.1953 | − | 164.883i | −0.259388 | − | 0.449273i | 0.706690 | − | 0.707523i | \(-0.250187\pi\) |
−0.966078 | + | 0.258250i | \(0.916854\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 44.2638 | − | 50.1309i | 0.119956 | − | 0.135856i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −204.848 | + | 118.269i | −0.552151 | + | 0.318785i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 143.800 | + | 249.069i | 0.385523 | + | 0.667745i | 0.991842 | − | 0.127477i | \(-0.0406878\pi\) |
−0.606319 | + | 0.795222i | \(0.707354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −199.951 | + | 163.531i | −0.533202 | + | 0.436084i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −41.6390 | + | 24.0403i | −0.110448 | + | 0.0637673i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 127.708 | 0.336961 | 0.168481 | − | 0.985705i | \(-0.446114\pi\) | ||||
0.168481 | + | 0.985705i | \(0.446114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −700.975 | + | 114.517i | −1.83983 | + | 0.300568i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −335.294 | − | 193.582i | −0.875441 | − | 0.505436i | −0.00628842 | − | 0.999980i | \(-0.502002\pi\) |
−0.869152 | + | 0.494544i | \(0.835335\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −110.011 | −0.285744 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 73.9221 | − | 365.186i | 0.191013 | − | 0.943632i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.4521 | + | 9.49861i | −0.0422933 | + | 0.0244180i | −0.520998 | − | 0.853558i | \(-0.674440\pi\) |
0.478704 | + | 0.877976i | \(0.341107\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 176.850 | + | 306.314i | 0.452302 | + | 0.783411i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −121.749 | − | 745.246i | −0.309794 | − | 1.89630i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −238.552 | − | 137.728i | −0.603928 | − | 0.348678i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 112.212 | + | 194.357i | 0.282650 | + | 0.489564i | 0.972037 | − | 0.234829i | \(-0.0754531\pi\) |
−0.689387 | + | 0.724394i | \(0.742120\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −80.0341 | + | 269.944i | −0.200587 | + | 0.676553i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 152.211 | + | 87.8792i | 0.379579 | + | 0.219150i | 0.677635 | − | 0.735398i | \(-0.263005\pi\) |
−0.298056 | + | 0.954548i | \(0.596338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 146.022 | + | 252.918i | 0.362338 | + | 0.627587i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −90.3373 | − | 119.390i | −0.223055 | − | 0.294790i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 551.625 | + | 318.481i | 1.35534 | + | 0.782508i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −634.354 | −1.55099 | −0.775494 | − | 0.631355i | \(-0.782499\pi\) | ||||
−0.775494 | + | 0.631355i | \(0.782499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.7783 | − | 5.59065i | −0.0359569 | − | 0.0136026i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −217.590 | + | 125.625i | −0.526852 | + | 0.304178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −68.5690 | − | 118.765i | −0.165227 | − | 0.286181i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −308.970 | − | 377.779i | −0.740936 | − | 0.905946i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −329.899 | + | 190.467i | −0.787348 | + | 0.454575i | −0.839028 | − | 0.544088i | \(-0.816876\pi\) |
0.0516803 | + | 0.998664i | \(0.483542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 269.508 | 0.640161 | 0.320080 | − | 0.947390i | \(-0.396290\pi\) | ||||
0.320080 | + | 0.947390i | \(0.396290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.3712 | + | 36.8527i | 0.0292464 | + | 0.0871221i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 351.230 | + | 202.783i | 0.826424 | + | 0.477136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −113.717 | −0.266316 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 59.5839 | + | 364.723i | 0.138890 | + | 0.850170i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −601.019 | − | 346.999i | −1.39448 | − | 0.805101i | −0.400669 | − | 0.916223i | \(-0.631222\pi\) |
−0.993807 | + | 0.111122i | \(0.964556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −324.494 | + | 562.041i | −0.749409 | + | 1.29802i | 0.198697 | + | 0.980061i | \(0.436329\pi\) |
−0.948106 | + | 0.317954i | \(0.897004\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.5096 | + | 20.1864i | 0.0379531 | + | 0.0464054i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −322.015 | − | 155.616i | −0.736877 | − | 0.356102i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 326.884 | 0.744611 | 0.372306 | − | 0.928110i | \(-0.378567\pi\) | ||||
0.372306 | + | 0.928110i | \(0.378567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −209.890 | + | 70.4588i | −0.475940 | + | 0.159771i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 697.089 | − | 402.464i | 1.57356 | − | 0.908497i | 0.577836 | − | 0.816153i | \(-0.303897\pi\) |
0.995727 | − | 0.0923447i | \(-0.0294362\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.84223 | + | 17.0472i | 0.0221174 | + | 0.0383084i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.5384 | − | 211.415i | −0.0772671 | − | 0.472965i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 201.130i | 0.447951i | 0.974595 | + | 0.223975i | \(0.0719035\pi\) | ||||
−0.974595 | + | 0.223975i | \(0.928096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.7670 | + | 77.5388i | 0.0992617 | + | 0.171926i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −46.1028 | + | 7.53171i | −0.101772 | + | 0.0166263i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 80.8366 | − | 46.6710i | 0.177663 | − | 0.102574i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −211.138 | + | 365.702i | −0.462010 | + | 0.800224i | −0.999061 | − | 0.0433255i | \(-0.986205\pi\) |
0.537051 | + | 0.843549i | \(0.319538\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −270.089 | + | 429.474i | −0.588428 | + | 0.935673i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 364.726i | − | 0.791163i | −0.918431 | − | 0.395582i | \(-0.870543\pi\) | ||
0.918431 | − | 0.395582i | \(-0.129457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 168.041 | + | 291.055i | 0.362939 | + | 0.628629i | 0.988443 | − | 0.151592i | \(-0.0484400\pi\) |
−0.625504 | + | 0.780221i | \(0.715107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 122.613 | − | 100.280i | 0.263684 | − | 0.215657i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.3762i | 0.0714693i | 0.999361 | + | 0.0357347i | \(0.0113771\pi\) | ||||
−0.999361 | + | 0.0357347i | \(0.988623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 95.8122 | − | 165.952i | 0.204290 | − | 0.353841i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −441.803 | + | 72.1763i | −0.938011 | + | 0.153241i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 431.999 | + | 249.415i | 0.913317 | + | 0.527304i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −408.984 | + | 30.0874i | −0.861019 | + | 0.0633420i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 285.252 | − | 323.061i | 0.598012 | − | 0.677277i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 417.401 | − | 240.987i | 0.871401 | − | 0.503104i | 0.00358759 | − | 0.999994i | \(-0.498858\pi\) |
0.867814 | + | 0.496890i | \(0.165525\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −540.446 | −1.12359 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 44.9740 | + | 275.293i | 0.0931138 | + | 0.569965i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 161.169 | + | 93.0510i | 0.332308 | + | 0.191858i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −887.516 | −1.82241 | −0.911207 | − | 0.411948i | \(-0.864849\pi\) | ||||
−0.911207 | + | 0.411948i | \(0.864849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −299.395 | − | 366.072i | −0.612260 | − | 0.748614i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −806.106 | − | 465.406i | −1.64176 | − | 0.947873i | −0.980206 | − | 0.197978i | \(-0.936563\pi\) |
−0.661557 | − | 0.749895i | \(-0.730104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.1851 | − | 76.5308i | 0.0896249 | − | 0.155235i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 190.020 | − | 63.7886i | 0.383878 | − | 0.128866i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 542.425i | 1.09140i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 326.171 | − | 564.945i | 0.653649 | − | 1.13215i | −0.328581 | − | 0.944476i | \(-0.606570\pi\) |
0.982231 | − | 0.187678i | \(-0.0600962\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −573.284 | + | 468.865i | −1.14428 | + | 0.935859i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 264.025 | + | 152.435i | 0.524901 | + | 0.303052i | 0.738937 | − | 0.673774i | \(-0.235328\pi\) |
−0.214037 | + | 0.976826i | \(0.568661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −271.994 | −0.538603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 122.464 | + | 149.737i | 0.241546 | + | 0.295340i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 51.6476i | 0.101469i | 0.998712 | + | 0.0507344i | \(0.0161562\pi\) | ||||
−0.998712 | + | 0.0507344i | \(0.983844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 114.111 | 0.223309 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.2828 | − | 512.674i | −0.0356390 | − | 0.999365i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 105.027i | − | 0.203937i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −52.0445 | −0.100666 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 242.877 | − | 198.639i | 0.467972 | − | 0.382735i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 733.507i | − | 1.40788i | −0.710258 | − | 0.703941i | \(-0.751422\pi\) | ||
0.710258 | − | 0.703941i | \(-0.248578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 376.499 | − | 652.115i | 0.719883 | − | 1.24687i | −0.241163 | − | 0.970485i | \(-0.577529\pi\) |
0.961046 | − | 0.276389i | \(-0.0891378\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 202.490 | + | 247.586i | 0.385696 | + | 0.471592i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −464.853 | − | 268.383i | −0.882074 | − | 0.509265i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 174.678 | 0.330204 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 302.994 | − | 343.156i | 0.570611 | − | 0.646244i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −65.7897 | − | 37.9837i | −0.123433 | − | 0.0712640i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −57.8307 | + | 100.166i | −0.108095 | + | 0.187226i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −554.505 | + | 453.507i | −1.03260 | + | 0.844520i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 296.413i | − | 0.549931i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −161.332 | + | 279.436i | −0.298211 | + | 0.516517i | −0.975727 | − | 0.218992i | \(-0.929723\pi\) |
0.677516 | + | 0.735508i | \(0.263057\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −639.891 | + | 104.537i | −1.17844 | + | 0.192518i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 119.222i | − | 0.218757i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −54.0558 | − | 93.6274i | −0.0988223 | − | 0.171165i | 0.812375 | − | 0.583135i | \(-0.198174\pi\) |
−0.911197 | + | 0.411970i | \(0.864841\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 196.420 | − | 65.9371i | 0.357778 | − | 0.120104i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.55586 | + | 89.1149i | 0.0118981 | + | 0.161733i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −368.073 | + | 637.521i | −0.665593 | + | 1.15284i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 47.2609 | + | 289.292i | 0.0851548 | + | 0.521247i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 605.693 | + | 349.697i | 1.08742 | + | 0.627822i | 0.932888 | − | 0.360165i | \(-0.117280\pi\) |
0.154532 | + | 0.987988i | \(0.450613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −423.245 | −0.757146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −430.014 | − | 525.781i | −0.766514 | − | 0.937221i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −973.582 | + | 562.098i | −1.72928 | + | 0.998398i | −0.836348 | + | 0.548199i | \(0.815314\pi\) |
−0.892928 | + | 0.450199i | \(0.851353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −235.599 | −0.416990 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −319.066 | + | 241.423i | −0.562726 | + | 0.425791i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 76.7723 | + | 44.3245i | 0.134925 | + | 0.0778989i | 0.565943 | − | 0.824444i | \(-0.308512\pi\) |
−0.431018 | + | 0.902343i | \(0.641846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −387.994 | − | 672.025i | −0.679499 | − | 1.17693i | −0.975132 | − | 0.221625i | \(-0.928864\pi\) |
0.295633 | − | 0.955302i | \(-0.404469\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −84.2443 | − | 515.673i | −0.147023 | − | 0.899953i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −351.847 | + | 203.139i | −0.611908 | + | 0.353285i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 749.821 | 1.29952 | 0.649758 | − | 0.760141i | \(-0.274870\pi\) | ||||
0.649758 | + | 0.760141i | \(0.274870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −127.608 | + | 20.8471i | −0.220394 | + | 0.0360053i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −317.396 | + | 183.248i | −0.546292 | + | 0.315402i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 288.495 | + | 499.687i | 0.494845 | + | 0.857097i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −112.565 | + | 127.485i | −0.192419 | + | 0.217924i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 104.373i | − | 0.177807i | −0.996040 | − | 0.0889036i | \(-0.971664\pi\) | ||
0.996040 | − | 0.0889036i | \(-0.0283363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 541.290 | − | 39.8207i | 0.918998 | − | 0.0676073i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −533.435 | + | 436.275i | −0.902598 | + | 0.738197i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 785.885 | + | 453.731i | 1.32527 | + | 0.765145i | 0.984564 | − | 0.175025i | \(-0.0560005\pi\) |
0.340706 | + | 0.940170i | \(0.389334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −85.7795 | + | 148.574i | −0.144167 | + | 0.249705i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 194.413 | − | 31.7608i | 0.325650 | − | 0.0532007i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 97.6804i | − | 0.163072i | −0.996670 | − | 0.0815362i | \(-0.974017\pi\) | ||
0.996670 | − | 0.0815362i | \(-0.0259826\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −456.977 | + | 791.508i | −0.760361 | + | 1.31698i | 0.182303 | + | 0.983242i | \(0.441645\pi\) |
−0.942664 | + | 0.333742i | \(0.891689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −69.2690 | + | 342.199i | −0.114874 | + | 0.567494i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 44.7023i | 0.0738881i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 107.749 | + | 186.627i | 0.177511 | + | 0.307457i | 0.941027 | − | 0.338331i | \(-0.109862\pi\) |
−0.763517 | + | 0.645788i | \(0.776529\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 53.9474 | − | 44.1213i | 0.0885836 | − | 0.0724488i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.2424 | − | 22.0792i | 0.0625898 | − | 0.0361362i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 401.592 | + | 695.578i | 0.655126 | + | 1.13471i | 0.981862 | + | 0.189596i | \(0.0607178\pi\) |
−0.326736 | + | 0.945116i | \(0.605949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.5789 | + | 38.5378i | −0.0237055 | + | 0.0626630i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 384.264i | 0.622794i | 0.950280 | + | 0.311397i | \(0.100797\pi\) | ||||
−0.950280 | + | 0.311397i | \(0.899203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −55.6379 | + | 96.3677i | −0.0898835 | + | 0.155683i | −0.907462 | − | 0.420135i | \(-0.861983\pi\) |
0.817578 | + | 0.575818i | \(0.195316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −237.307 | − | 449.429i | −0.382137 | − | 0.723717i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.5582 | − | 26.3030i | 0.0731271 | − | 0.0422200i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −190.222 | + | 329.474i | −0.304355 | + | 0.527159i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 658.477 | + | 195.228i | 1.05020 | + | 0.311368i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 860.240 | − | 496.660i | 1.36763 | − | 0.789602i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −396.481 | + | 686.725i | −0.628337 | + | 1.08831i | 0.359548 | + | 0.933127i | \(0.382931\pi\) |
−0.987885 | + | 0.155186i | \(0.950402\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −457.582 | + | 74.7540i | −0.722878 | + | 0.118095i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 378.977 | − | 218.803i | 0.596815 | − | 0.344571i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 125.749 | + | 217.804i | 0.197409 | + | 0.341922i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −314.517 | − | 936.916i | −0.492203 | − | 1.46622i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 536.996i | 0.837747i | 0.908045 | + | 0.418873i | \(0.137575\pi\) | ||||
−0.908045 | + | 0.418873i | \(0.862425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 251.413 | − | 435.461i | 0.391001 | − | 0.677233i | −0.601581 | − | 0.798812i | \(-0.705462\pi\) |
0.992582 | + | 0.121579i | \(0.0387957\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.0119 | + | 226.556i | 0.0573828 | + | 0.351249i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 42.7301i | − | 0.0660435i | −0.999455 | − | 0.0330217i | \(-0.989487\pi\) | ||
0.999455 | − | 0.0330217i | \(-0.0105131\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 306.439 | + | 530.768i | 0.472171 | + | 0.817824i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −267.996 | − | 327.680i | −0.411668 | − | 0.503348i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 539.034 | − | 311.211i | 0.825473 | − | 0.476587i | −0.0268270 | − | 0.999640i | \(-0.508540\pi\) |
0.852300 | + | 0.523053i | \(0.175207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 232.622 | + | 402.913i | 0.355148 | + | 0.615134i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −197.100 | + | 66.1655i | −0.300000 | + | 0.100708i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 797.682 | − | 460.542i | 1.21044 | − | 0.698850i | 0.247587 | − | 0.968866i | \(-0.420362\pi\) |
0.962856 | + | 0.270016i | \(0.0870290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −111.337 | −0.168437 | −0.0842183 | − | 0.996447i | \(-0.526839\pi\) | ||||
−0.0842183 | + | 0.996447i | \(0.526839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 539.031 | + | 203.916i | 0.813019 | + | 0.307566i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.7273 | − | 173.005i | −0.0191389 | − | 0.260158i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.2627 | + | 76.6652i | 0.0663608 | + | 0.114940i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −248.564 | − | 303.920i | −0.371545 | − | 0.454291i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 277.390i | 0.413399i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 223.538 | − | 387.179i | 0.332152 | − | 0.575304i | −0.650782 | − | 0.759265i | \(-0.725559\pi\) |
0.982934 | + | 0.183961i | \(0.0588921\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −493.315 | − | 310.237i | −0.730837 | − | 0.459611i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 202.443 | + | 116.881i | 0.299030 | + | 0.172645i | 0.642007 | − | 0.766699i | \(-0.278102\pi\) |
−0.342977 | + | 0.939344i | \(0.611435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 248.676 | − | 430.719i | 0.366238 | − | 0.634343i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −78.2657 | − | 479.077i | −0.114928 | − | 0.703491i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 496.474i | 0.726902i | 0.931613 | + | 0.363451i | \(0.118402\pi\) | ||||
−0.931613 | + | 0.363451i | \(0.881598\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.73487 | 0.0142115 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 357.822 | − | 945.865i | 0.520847 | − | 1.37680i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −423.973 | − | 244.781i | −0.615345 | − | 0.355270i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 237.938 | − | 412.120i | 0.344338 | − | 0.596411i | −0.640895 | − | 0.767628i | \(-0.721437\pi\) |
0.985233 | + | 0.171217i | \(0.0547701\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −170.473 | − | 507.821i | −0.245993 | − | 0.732787i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 260.402 | + | 150.343i | 0.374679 | + | 0.216321i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 139.625 | 0.200323 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.1090 | − | 9.12046i | −0.0344907 | − | 0.0130479i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 484.715 | − | 279.850i | 0.691462 | − | 0.399216i | −0.112697 | − | 0.993629i | \(-0.535949\pi\) |
0.804160 | + | 0.594413i | \(0.202616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −437.027 | + | 904.335i | −0.621661 | + | 1.28639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.1629 | − | 18.5397i | −0.0215076 | − | 0.0262975i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 726.896i | 1.02814i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −345.343 | − | 598.151i | −0.487084 | − | 0.843654i | 0.512806 | − | 0.858505i | \(-0.328606\pi\) |
−0.999890 | + | 0.0148505i | \(0.995273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 266.105 | − | 1314.59i | 0.374268 | − | 1.84894i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 465.669 | − | 268.854i | 0.653113 | − | 0.377075i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −113.845 | − | 197.185i | −0.159224 | − | 0.275784i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 700.609 | + | 265.041i | 0.977140 | + | 0.369653i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 673.685 | − | 388.952i | 0.936975 | − | 0.540963i | 0.0479641 | − | 0.998849i | \(-0.484727\pi\) |
0.889011 | + | 0.457886i | \(0.151393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −280.682 | −0.389296 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −294.914 | + | 779.576i | −0.407904 | + | 1.07825i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 87.9071 | + | 50.7532i | 0.121251 | + | 0.0700044i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −421.433 | −0.579688 | −0.289844 | − | 0.957074i | \(-0.593603\pi\) | ||||
−0.289844 | + | 0.957074i | \(0.593603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 411.127 | − | 602.010i | 0.563960 | − | 0.825802i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 673.688 | − | 388.954i | 0.921597 | − | 0.532085i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 216.673 | + | 375.289i | 0.295598 | + | 0.511990i | 0.975124 | − | 0.221661i | \(-0.0711479\pi\) |
−0.679526 | + | 0.733651i | \(0.737815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 105.591 | − | 86.3582i | 0.143661 | − | 0.117494i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −404.807 | − | 233.715i | −0.549263 | − | 0.317117i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 354.109 | + | 613.335i | 0.479174 | + | 0.829953i | 0.999715 | − | 0.0238836i | \(-0.00760311\pi\) |
−0.520541 | + | 0.853837i | \(0.674270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −566.673 | + | 135.897i | −0.764741 | + | 0.183397i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 706.541 | + | 407.921i | 0.950930 | + | 0.549019i | 0.893370 | − | 0.449323i | \(-0.148335\pi\) |
0.0575600 | + | 0.998342i | \(0.481668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 65.9913 | + | 114.300i | 0.0885790 | + | 0.153423i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 441.974 | − | 500.557i | 0.591666 | − | 0.670090i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 267.690 | + | 154.551i | 0.357396 | + | 0.206343i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1082.49 | −1.44140 | −0.720700 | − | 0.693247i | \(-0.756180\pi\) | ||||
−0.720700 | + | 0.693247i | \(0.756180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 230.790 | + | 1412.70i | 0.306494 | + | 1.87610i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.9252 | − | 14.3906i | 0.0330135 | − | 0.0190604i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 160.866 | + | 278.628i | 0.212505 | + | 0.368069i | 0.952498 | − | 0.304546i | \(-0.0985046\pi\) |
−0.739993 | + | 0.672614i | \(0.765171\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 671.524 | − | 109.705i | 0.884749 | − | 0.144539i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 958.373 | − | 553.317i | 1.25936 | − | 0.727092i | 0.286410 | − | 0.958107i | \(-0.407538\pi\) |
0.972950 | + | 0.231015i | \(0.0742048\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −318.618 | −0.417585 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 62.0157 | − | 306.367i | 0.0810663 | − | 0.400479i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −450.344 | − | 260.006i | −0.587150 | − | 0.338991i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −840.541 | −1.09303 | −0.546516 | − | 0.837449i | \(-0.684046\pi\) | ||||
−0.546516 | + | 0.837449i | \(0.684046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 409.361 | − | 334.799i | 0.530948 | − | 0.434240i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 676.445 | + | 390.545i | 0.875090 | + | 0.505233i | 0.869036 | − | 0.494748i | \(-0.164740\pi\) |
0.00605359 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 308.278 | − | 533.953i | 0.397778 | − | 0.688972i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 773.123 | − | 126.303i | 0.995010 | − | 0.162552i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −116.759 | + | 79.3715i | −0.149883 | + | 0.101889i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1323.14 | 1.69416 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −67.5987 | + | 107.490i | −0.0863329 | + | 0.137280i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 238.858 | − | 137.905i | 0.304278 | − | 0.175675i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −383.786 | − | 664.737i | −0.487657 | − | 0.844647i | 0.512242 | − | 0.858841i | \(-0.328815\pi\) |
−0.999899 | + | 0.0141942i | \(0.995482\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 438.015 | − | 358.234i | 0.555152 | − | 0.454036i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 629.631i | 0.795993i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −117.680 | − | 203.827i | −0.148398 | − | 0.257033i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −93.9515 | + | 248.351i | −0.118178 | + | 0.312391i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −796.725 | + | 459.990i | −0.999655 | + | 0.577151i | −0.908146 | − | 0.418653i | \(-0.862502\pi\) |
−0.0915091 | + | 0.995804i | \(0.529169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.5808 | + | 70.2880i | −0.0507894 | + | 0.0879699i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −63.4399 | + | 71.8488i | −0.0792009 | + | 0.0896988i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 278.351i | − | 0.346639i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −85.9302 | − | 148.835i | −0.106746 | − | 0.184889i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1155.35 | − | 437.070i | −1.43166 | − | 0.541599i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1141.94i | − | 1.41155i | −0.708438 | − | 0.705773i | \(-0.750600\pi\) | ||
0.708438 | − | 0.705773i | \(-0.249400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −618.024 | + | 1070.45i | −0.762052 | + | 1.31991i | 0.179739 | + | 0.983714i | \(0.442475\pi\) |
−0.941791 | + | 0.336198i | \(0.890859\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.5892 | − | 136.371i | 0.0634553 | − | 0.167738i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 252.332 | + | 145.684i | 0.309610 | + | 0.178753i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −342.253 | + | 708.221i | −0.418915 | + | 0.866855i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 340.701 | + | 300.827i | 0.415996 | + | 0.367310i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1061.61 | − | 612.923i | 1.29308 | − | 0.746557i | 0.313877 | − | 0.949464i | \(-0.398372\pi\) |
0.979198 | + | 0.202906i | \(0.0650387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 266.361 | 0.323646 | 0.161823 | − | 0.986820i | \(-0.448263\pi\) | ||||
0.161823 | + | 0.986820i | \(0.448263\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 603.938 | − | 493.936i | 0.732046 | − | 0.598710i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −725.041 | − | 418.603i | −0.876712 | − | 0.506170i | −0.00713916 | − | 0.999975i | \(-0.502272\pi\) |
−0.869573 | + | 0.493805i | \(0.835606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −425.019 | −0.512689 | −0.256344 | − | 0.966586i | \(-0.582518\pi\) | ||||
−0.256344 | + | 0.966586i | \(0.582518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 455.659 | − | 74.4399i | 0.548326 | − | 0.0895787i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −400.316 | − | 231.123i | −0.480572 | − | 0.277458i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 228.147 | − | 395.163i | 0.273230 | − | 0.473249i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 652.902 | + | 410.599i | 0.780050 | + | 0.490560i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 242.391i | − | 0.288904i | −0.989512 | − | 0.144452i | \(-0.953858\pi\) | ||
0.989512 | − | 0.144452i | \(-0.0461420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −409.441 | + | 709.173i | −0.486850 | + | 0.843250i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −377.160 | − | 142.680i | −0.447402 | − | 0.169253i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −103.213 | − | 59.5902i | −0.122146 | − | 0.0705210i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 119.465 | 0.141045 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −188.491 | + | 30.7934i | −0.222016 | + | 0.0362702i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 995.064i | 1.16929i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1433.19 | 1.68017 | 0.840087 | − | 0.542452i | \(-0.182504\pi\) | ||||
0.840087 | + | 0.542452i | \(0.182504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 122.298 | + | 291.447i | 0.143039 | + | 0.340873i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1339.15i | − | 1.56261i | −0.624152 | − | 0.781303i | \(-0.714555\pi\) | ||
0.624152 | − | 0.781303i | \(-0.285445\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 355.159 | 0.413457 | 0.206728 | − | 0.978398i | \(-0.433718\pi\) | ||||
0.206728 | + | 0.978398i | \(0.433718\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 102.991 | + | 38.9616i | 0.119618 | + | 0.0452515i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 71.3787i | − | 0.0827100i | −0.999145 | − | 0.0413550i | \(-0.986833\pi\) | ||
0.999145 | − | 0.0413550i | \(-0.0131675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −96.6568 | + | 167.415i | −0.111742 | + | 0.193543i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −189.726 | + | 30.9950i | −0.218830 | + | 0.0357498i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1555.11 | + | 897.843i | 1.78954 | + | 1.03319i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 396.604 | 0.455343 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −179.784 | + | 888.160i | −0.205939 | + | 1.01737i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −368.333 | − | 212.657i | −0.420952 | − | 0.243037i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −363.008 | + | 628.749i | −0.413920 | + | 0.716931i | −0.995314 | − | 0.0966909i | \(-0.969174\pi\) |
0.581394 | + | 0.813622i | \(0.302508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −603.316 | − | 228.235i | −0.686367 | − | 0.259653i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 738.131i | − | 0.837833i | −0.908025 | − | 0.418916i | \(-0.862410\pi\) | ||
0.908025 | − | 0.418916i | \(-0.137590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 172.011 | − | 297.931i | 0.194803 | − | 0.337408i | −0.752033 | − | 0.659125i | \(-0.770927\pi\) |
0.946836 | + | 0.321717i | \(0.104260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −99.7953 | + | 263.799i | −0.112763 | + | 0.298077i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 688.643i | − | 0.776373i | −0.921581 | − | 0.388186i | \(-0.873102\pi\) | ||
0.921581 | − | 0.388186i | \(-0.126898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −584.743 | − | 1012.80i | −0.657754 | − | 1.13926i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 588.906 | + | 778.299i | 0.660949 | + | 0.873512i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.02108 | − | 81.8456i | −0.00674253 | − | 0.0916524i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 220.674 | − | 382.219i | 0.246563 | − | 0.427060i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −446.896 | + | 365.498i | −0.498212 | + | 0.407467i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −116.345 | − | 67.1718i | −0.129416 | − | 0.0747183i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 899.795 | 0.998663 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 605.463 | − | 98.9131i | 0.670502 | − | 0.109538i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 345.953 | − | 199.736i | 0.382268 | − | 0.220703i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 559.726 | 0.617118 | 0.308559 | − | 0.951205i | \(-0.400153\pi\) | ||||
0.308559 | + | 0.951205i | \(0.400153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −421.480 | − | 1255.55i | −0.463675 | − | 1.38124i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.3919 | + | 14.0827i | 0.0267749 | + | 0.0154585i | 0.513328 | − | 0.858193i | \(-0.328413\pi\) |
−0.486553 | + | 0.873651i | \(0.661746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 446.999 | + | 774.225i | 0.489594 | + | 0.848001i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −98.8143 | + | 80.8161i | −0.107994 | + | 0.0883237i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1076.77 | − | 621.674i | 1.17423 | − | 0.677943i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 212.578 | 0.231314 | 0.115657 | − | 0.993289i | \(-0.463103\pi\) | ||||
0.115657 | + | 0.993289i | \(0.463103\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −291.072 | + | 769.419i | −0.316039 | + | 0.835417i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −972.246 | + | 561.327i | −1.05335 | + | 0.608155i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 570.488 | + | 988.115i | 0.616744 | + | 1.06823i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 484.815 | − | 162.750i | 0.522993 | − | 0.175566i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1315.09i | 1.41559i | 0.706416 | + | 0.707797i | \(0.250311\pi\) | ||||
−0.706416 | + | 0.707797i | \(0.749689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 466.141 | − | 34.2923i | 0.500689 | − | 0.0368338i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1281.41 | + | 484.758i | 1.37343 | + | 0.519569i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 362.419 | + | 209.243i | 0.387614 | + | 0.223789i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −201.216 | + | 348.516i | −0.214745 | + | 0.371948i | −0.953194 | − | 0.302361i | \(-0.902225\pi\) |
0.738449 | + | 0.674309i | \(0.235559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −105.649 | + | 279.272i | −0.112512 | + | 0.297414i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 905.907i | − | 0.962707i | −0.876527 | − | 0.481353i | \(-0.840145\pi\) | ||
0.876527 | − | 0.481353i | \(-0.159855\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −69.9353 | + | 121.131i | −0.0741625 | + | 0.128453i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 131.234 | − | 208.678i | 0.138872 | − | 0.220823i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1486.69i | 1.56989i | 0.619563 | + | 0.784947i | \(0.287310\pi\) | ||||
−0.619563 | + | 0.784947i | \(0.712690\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 118.087 | + | 204.533i | 0.124433 | + | 0.215525i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −347.411 | − | 131.426i | −0.365311 | − | 0.138198i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −910.211 | + | 525.511i | −0.955101 | + | 0.551428i | −0.894662 | − | 0.446744i | \(-0.852583\pi\) |
−0.0604392 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 160.963 | + | 278.795i | 0.168547 | + | 0.291932i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −107.625 | − | 131.594i | −0.112461 | − | 0.137507i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 26.0161i | − | 0.0271284i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.4944 | − | 125.564i | 0.0754364 | − | 0.130660i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −551.987 | − | 111.735i | −0.573195 | − | 0.116028i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 68.9906 | − | 39.8317i | 0.0714928 | − | 0.0412764i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 578.495 | − | 1001.98i | 0.598237 | − | 1.03618i | −0.394845 | − | 0.918748i | \(-0.629202\pi\) |
0.993081 | − | 0.117429i | \(-0.0374651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 777.099 | − | 737.072i | 0.801959 | − | 0.760653i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −453.947 | + | 262.086i | −0.467504 | + | 0.269914i | −0.715194 | − | 0.698926i | \(-0.753662\pi\) |
0.247690 | + | 0.968839i | \(0.420329\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 401.787 | − | 695.916i | 0.412936 | − | 0.715227i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −234.228 | + | 619.159i | −0.240234 | + | 0.635034i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −379.565 | + | 219.142i | −0.388501 | + | 0.224301i | −0.681510 | − | 0.731809i | \(-0.738677\pi\) |
0.293010 | + | 0.956109i | \(0.405343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.1612 | − | 111.130i | −0.0655375 | − | 0.113514i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 550.339 | − | 184.746i | 0.560998 | − | 0.188324i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 802.644i | 0.816525i | 0.912865 | + | 0.408262i | \(0.133865\pi\) | ||||
−0.912865 | + | 0.408262i | \(0.866135\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 212.289 | − | 367.695i | 0.215522 | − | 0.373294i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.5467 | + | 40.5222i | −0.0501993 | + | 0.0410560i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 779.274i | 0.787942i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −767.110 | − | 1328.67i | −0.774077 | − | 1.34074i | −0.935312 | − | 0.353824i | \(-0.884881\pi\) |
0.161236 | − | 0.986916i | \(-0.448452\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1686.41 | + | 275.505i | −1.69830 | + | 0.277447i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −105.108 | + | 60.6843i | −0.105637 | + | 0.0609893i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −464.248 | − | 804.100i | −0.465644 | − | 0.806520i | 0.533586 | − | 0.845746i | \(-0.320844\pi\) |
−0.999230 | + | 0.0392260i | \(0.987511\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1262.16 | + | 666.444i | −1.26342 | + | 0.667111i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.3.be.a.425.11 | yes | 80 | |
3.2 | odd | 2 | 2052.3.be.a.197.16 | 80 | |||
9.4 | even | 3 | 2052.3.m.a.881.16 | 80 | |||
9.5 | odd | 6 | 684.3.m.a.653.17 | yes | 80 | ||
19.11 | even | 3 | 684.3.m.a.353.17 | ✓ | 80 | ||
57.11 | odd | 6 | 2052.3.m.a.1493.25 | 80 | |||
171.49 | even | 3 | 2052.3.be.a.125.16 | 80 | |||
171.68 | odd | 6 | inner | 684.3.be.a.581.11 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.17 | ✓ | 80 | 19.11 | even | 3 | ||
684.3.m.a.653.17 | yes | 80 | 9.5 | odd | 6 | ||
684.3.be.a.425.11 | yes | 80 | 1.1 | even | 1 | trivial | |
684.3.be.a.581.11 | yes | 80 | 171.68 | odd | 6 | inner | |
2052.3.m.a.881.16 | 80 | 9.4 | even | 3 | |||
2052.3.m.a.1493.25 | 80 | 57.11 | odd | 6 | |||
2052.3.be.a.125.16 | 80 | 171.49 | even | 3 | |||
2052.3.be.a.197.16 | 80 | 3.2 | odd | 2 |