Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,4,Mod(125,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.125");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.x (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: | \(44.6054439643\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 125.16 | ||
Character | \(\chi\) | \(=\) | 756.125 |
Dual form | 756.4.x.a.629.16 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.99997 | − | 5.19610i | 0.268325 | − | 0.464753i | −0.700104 | − | 0.714041i | \(-0.746863\pi\) |
0.968430 | + | 0.249288i | \(0.0801964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.2235 | + | 8.93305i | 0.875984 | + | 0.482340i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 39.3810 | − | 22.7366i | 1.07944 | − | 0.623214i | 0.148694 | − | 0.988883i | \(-0.452493\pi\) |
0.930745 | + | 0.365669i | \(0.119160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.7627 | + | 13.1421i | 0.485634 | + | 0.280381i | 0.722761 | − | 0.691098i | \(-0.242873\pi\) |
−0.237127 | + | 0.971479i | \(0.576206\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −19.7249 | −0.281411 | −0.140706 | − | 0.990051i | \(-0.544937\pi\) | ||||
−0.140706 | + | 0.990051i | \(0.544937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 27.9162i | − | 0.337074i | −0.985695 | − | 0.168537i | \(-0.946096\pi\) | ||
0.985695 | − | 0.168537i | \(-0.0539043\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 60.3466 | + | 34.8411i | 0.547093 | + | 0.315864i | 0.747949 | − | 0.663757i | \(-0.231039\pi\) |
−0.200856 | + | 0.979621i | \(0.564372\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.5004 | + | 77.0769i | 0.356003 | + | 0.616615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 119.031 | − | 68.7227i | 0.762191 | − | 0.440051i | −0.0678907 | − | 0.997693i | \(-0.521627\pi\) |
0.830082 | + | 0.557641i | \(0.188294\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −138.202 | − | 79.7908i | −0.800702 | − | 0.462286i | 0.0430146 | − | 0.999074i | \(-0.486304\pi\) |
−0.843717 | + | 0.536789i | \(0.819637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 95.0869 | − | 57.4998i | 0.459218 | − | 0.277693i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −287.829 | −1.27889 | −0.639443 | − | 0.768839i | \(-0.720835\pi\) | ||||
−0.639443 | + | 0.768839i | \(0.720835\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −20.4288 | + | 35.3837i | −0.0778157 | + | 0.134781i | −0.902307 | − | 0.431093i | \(-0.858128\pi\) |
0.824492 | + | 0.565874i | \(0.191461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 55.4158 | + | 95.9830i | 0.196531 | + | 0.340402i | 0.947401 | − | 0.320048i | \(-0.103699\pi\) |
−0.750870 | + | 0.660450i | \(0.770366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 109.666 | + | 189.948i | 0.340351 | + | 0.589504i | 0.984498 | − | 0.175397i | \(-0.0561209\pi\) |
−0.644147 | + | 0.764902i | \(0.722788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 183.401 | + | 289.850i | 0.534697 | + | 0.845044i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 209.770i | 0.543664i | 0.962345 | + | 0.271832i | \(0.0876295\pi\) | ||||
−0.962345 | + | 0.271832i | \(0.912371\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 272.837i | − | 0.668897i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 413.880 | − | 716.860i | 0.913263 | − | 1.58182i | 0.103839 | − | 0.994594i | \(-0.466887\pi\) |
0.809425 | − | 0.587224i | \(-0.199779\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 594.209 | − | 343.066i | 1.24722 | − | 0.720085i | 0.276668 | − | 0.960965i | \(-0.410770\pi\) |
0.970555 | + | 0.240881i | \(0.0774363\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 136.575 | − | 78.8515i | 0.260616 | − | 0.150467i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −171.449 | + | 296.958i | −0.312624 | + | 0.541480i | −0.978930 | − | 0.204198i | \(-0.934541\pi\) |
0.666306 | + | 0.745679i | \(0.267875\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 387.476i | − | 0.647675i | −0.946113 | − | 0.323838i | \(-0.895027\pi\) | ||
0.946113 | − | 0.323838i | \(-0.104973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 220.721i | 0.353882i | 0.984221 | + | 0.176941i | \(0.0566202\pi\) | ||||
−0.984221 | + | 0.176941i | \(0.943380\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 842.004 | − | 17.0742i | 1.24617 | − | 0.0252699i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 242.301 | + | 419.677i | 0.345076 | + | 0.597688i | 0.985367 | − | 0.170443i | \(-0.0545200\pi\) |
−0.640292 | + | 0.768132i | \(0.721187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −354.323 | − | 613.706i | −0.468579 | − | 0.811602i | 0.530776 | − | 0.847512i | \(-0.321900\pi\) |
−0.999355 | + | 0.0359099i | \(0.988567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −59.1741 | + | 102.493i | −0.0755098 | + | 0.130787i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −140.929 | −0.167848 | −0.0839240 | − | 0.996472i | \(-0.526745\pi\) | ||||
−0.0839240 | + | 0.996472i | \(0.526745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 251.891 | + | 416.550i | 0.290169 | + | 0.479850i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −145.055 | − | 83.7476i | −0.156656 | − | 0.0904455i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1304.31 | − | 753.041i | 1.36528 | − | 0.788245i | 0.374960 | − | 0.927041i | \(-0.377657\pi\) |
0.990321 | + | 0.138796i | \(0.0443232\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −923.516 | − | 1599.58i | −0.909834 | − | 1.57588i | −0.814293 | − | 0.580454i | \(-0.802875\pi\) |
−0.0955414 | − | 0.995425i | \(-0.530458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 696.481 | + | 402.114i | 0.666275 | + | 0.384674i | 0.794664 | − | 0.607050i | \(-0.207647\pi\) |
−0.128389 | + | 0.991724i | \(0.540981\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 282.997i | 0.255685i | 0.991794 | + | 0.127843i | \(0.0408053\pi\) | ||||
−0.991794 | + | 0.127843i | \(0.959195\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1826.43 | 1.60496 | 0.802478 | − | 0.596681i | \(-0.203514\pi\) | ||||
0.802478 | + | 0.596681i | \(0.203514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 815.811 | + | 471.008i | 0.679159 | + | 0.392113i | 0.799538 | − | 0.600615i | \(-0.205078\pi\) |
−0.120379 | + | 0.992728i | \(0.538411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 362.076 | − | 209.044i | 0.293598 | − | 0.169509i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −320.006 | − | 176.204i | −0.246512 | − | 0.135736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 368.410 | − | 638.105i | 0.276792 | − | 0.479418i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1283.99 | 0.918749 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 320.551 | 0.223971 | 0.111985 | − | 0.993710i | \(-0.464279\pi\) | ||||
0.111985 | + | 0.993710i | \(0.464279\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 306.907 | − | 531.578i | 0.204691 | − | 0.354536i | −0.745343 | − | 0.666681i | \(-0.767714\pi\) |
0.950034 | + | 0.312145i | \(0.101048\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 249.377 | − | 452.897i | 0.162584 | − | 0.295272i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1515.86 | + | 875.182i | −0.945318 | + | 0.545780i | −0.891623 | − | 0.452778i | \(-0.850433\pi\) |
−0.0536948 | + | 0.998557i | \(0.517100\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1120.72 | + | 647.048i | 0.683872 | + | 0.394834i | 0.801312 | − | 0.598246i | \(-0.204135\pi\) |
−0.117440 | + | 0.993080i | \(0.537469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1195.23 | 0.698950 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 824.664i | − | 0.472308i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2499.23 | + | 1442.93i | 1.37413 | + | 0.793352i | 0.991445 | − | 0.130528i | \(-0.0416674\pi\) |
0.382681 | + | 0.923880i | \(0.375001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1540.63 | + | 2668.45i | 0.830297 | + | 1.43812i | 0.897803 | + | 0.440398i | \(0.145163\pi\) |
−0.0675056 | + | 0.997719i | \(0.521504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −829.202 | + | 478.740i | −0.429697 | + | 0.248086i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1090.13 | + | 629.388i | 0.554153 | + | 0.319941i | 0.750795 | − | 0.660535i | \(-0.229670\pi\) |
−0.196642 | + | 0.980475i | \(0.563004\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 667.793 | + | 1104.32i | 0.326891 | + | 0.540576i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2906.94 | −1.39687 | −0.698434 | − | 0.715675i | \(-0.746119\pi\) | ||||
−0.698434 | + | 0.715675i | \(0.746119\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −286.775 | + | 496.709i | −0.132882 | + | 0.230159i | −0.924786 | − | 0.380487i | \(-0.875756\pi\) |
0.791904 | + | 0.610645i | \(0.209090\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.072 | − | 1304.36i | −0.342773 | − | 0.593700i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1931.13 | − | 3344.82i | −0.848679 | − | 1.46995i | −0.882388 | − | 0.470523i | \(-0.844065\pi\) |
0.0337092 | − | 0.999432i | \(-0.489268\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 33.4177 | + | 1647.98i | 0.0144351 | + | 0.711860i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2248.26i | − | 0.938787i | −0.882989 | − | 0.469394i | \(-0.844473\pi\) | ||
0.882989 | − | 0.469394i | \(-0.155527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 166.407i | − | 0.0683368i | −0.999416 | − | 0.0341684i | \(-0.989122\pi\) | ||
0.999416 | − | 0.0341684i | \(-0.0108783\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −863.478 | + | 1495.59i | −0.343157 | + | 0.594366i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −776.787 | + | 448.478i | −0.303766 | + | 0.175379i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1758.88 | − | 1015.49i | 0.666324 | − | 0.384703i | −0.128358 | − | 0.991728i | \(-0.540971\pi\) |
0.794682 | + | 0.607025i | \(0.207637\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 251.118 | − | 434.949i | 0.0936573 | − | 0.162219i | −0.815390 | − | 0.578912i | \(-0.803478\pi\) |
0.909047 | + | 0.416693i | \(0.136811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3949.11i | − | 1.42823i | −0.700026 | − | 0.714117i | \(-0.746828\pi\) | ||
0.700026 | − | 0.714117i | \(-0.253172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 629.709i | − | 0.224316i | −0.993690 | − | 0.112158i | \(-0.964224\pi\) | ||
0.993690 | − | 0.112158i | \(-0.0357763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2545.00 | − | 51.6076i | 0.879922 | − | 0.0178431i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 122.572 | + | 212.300i | 0.0417599 | + | 0.0723302i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −634.720 | − | 1099.37i | −0.210069 | − | 0.363851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1494.95 | + | 2589.33i | −0.487757 | + | 0.844820i | −0.999901 | − | 0.0140797i | \(-0.995518\pi\) |
0.512144 | + | 0.858900i | \(0.328851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 664.983 | 0.210937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1529.33 | − | 2529.05i | −0.478424 | − | 0.791165i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −448.992 | − | 259.226i | −0.136663 | − | 0.0789023i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2829.72 | + | 1633.74i | −0.849740 | + | 0.490598i | −0.860563 | − | 0.509344i | \(-0.829888\pi\) |
0.0108230 | + | 0.999941i | \(0.496555\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2836.86 | + | 4913.59i | 0.829468 | + | 1.43668i | 0.898457 | + | 0.439063i | \(0.144689\pi\) |
−0.0689889 | + | 0.997617i | \(0.521977\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4528.48 | − | 2614.52i | −1.30677 | − | 0.754465i | −0.325215 | − | 0.945640i | \(-0.605437\pi\) |
−0.981556 | + | 0.191175i | \(0.938770\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3433.84i | − | 0.965487i | −0.875762 | − | 0.482743i | \(-0.839640\pi\) | ||
0.875762 | − | 0.482743i | \(-0.160360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1315.98 | 0.365299 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −469.677 | − | 271.168i | −0.127117 | − | 0.0733908i | 0.435093 | − | 0.900385i | \(-0.356715\pi\) |
−0.562210 | + | 0.826995i | \(0.690049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3110.33 | − | 1795.75i | 0.831343 | − | 0.479976i | −0.0229693 | − | 0.999736i | \(-0.507312\pi\) |
0.854312 | + | 0.519760i | \(0.173979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2056.29 | − | 83.4292i | 0.536210 | − | 0.0217555i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 366.876 | − | 635.448i | 0.0945092 | − | 0.163695i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4334.39 | 1.08998 | 0.544988 | − | 0.838444i | \(-0.316534\pi\) | ||||
0.544988 | + | 0.838444i | \(0.316534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3168.68 | 0.787404 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3282.88 | + | 5686.12i | −0.796812 | + | 1.38012i | 0.124870 | + | 0.992173i | \(0.460148\pi\) |
−0.921682 | + | 0.387946i | \(0.873185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4669.58 | − | 2571.19i | −1.12028 | − | 0.616857i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6274.79 | + | 3622.75i | −1.47118 | + | 0.849386i | −0.999476 | − | 0.0323711i | \(-0.989694\pi\) |
−0.471704 | + | 0.881757i | \(0.656361\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1089.99 | + | 629.305i | 0.252669 | + | 0.145879i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3455.87 | −0.783302 | −0.391651 | − | 0.920114i | \(-0.628096\pi\) | ||||
−0.391651 | + | 0.920114i | \(0.628096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2471.30i | − | 0.553951i | −0.960877 | − | 0.276975i | \(-0.910668\pi\) | ||
0.960877 | − | 0.276975i | \(-0.0893321\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3504.94 | + | 2023.58i | 0.768567 | + | 0.443732i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2256.85 | + | 3908.97i | 0.489533 | + | 0.847897i | 0.999927 | − | 0.0120440i | \(-0.00383381\pi\) |
−0.510394 | + | 0.859941i | \(0.670500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2090.48 | + | 1206.94i | −0.443799 | + | 0.256228i | −0.705208 | − | 0.709001i | \(-0.749146\pi\) |
0.261409 | + | 0.965228i | \(0.415813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3893.62 | − | 2247.98i | −0.817851 | − | 0.472187i | 0.0318238 | − | 0.999493i | \(-0.489868\pi\) |
−0.849675 | + | 0.527307i | \(0.823202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −647.511 | + | 391.555i | −0.133175 | + | 0.0805322i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4523.93 | −0.920808 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1569.64 | − | 2718.69i | 0.312966 | − | 0.542073i | −0.666037 | − | 0.745919i | \(-0.732011\pi\) |
0.979003 | + | 0.203845i | \(0.0653440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2483.25 | − | 4301.12i | −0.490103 | − | 0.848884i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 915.768 | + | 1586.16i | 0.177125 | + | 0.306789i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.6147 | + | 2052.21i | 0.00796888 | + | 0.392981i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4116.75i | − | 0.772868i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10294.0i | 1.91371i | 0.290560 | + | 0.956857i | \(0.406158\pi\) | ||||
−0.290560 | + | 0.956857i | \(0.593842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3940.59 | + | 6825.30i | −0.718489 | + | 1.24446i | 0.243109 | + | 0.969999i | \(0.421833\pi\) |
−0.961598 | + | 0.274461i | \(0.911501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7096.84 | + | 4097.36i | −1.28159 | + | 0.739925i | −0.977139 | − | 0.212604i | \(-0.931806\pi\) |
−0.304449 | + | 0.952529i | \(0.598472\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7590.80 | + | 4382.55i | −1.34493 | + | 0.776494i | −0.987526 | − | 0.157457i | \(-0.949670\pi\) |
−0.357401 | + | 0.933951i | \(0.616337\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3125.05 | − | 5412.74i | 0.548493 | − | 0.950017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 550.644i | 0.0948564i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2339.31i | 0.399266i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 82.3544 | + | 4061.26i | 0.0138004 | + | 0.680561i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3431.76 | − | 5943.98i | −0.569869 | − | 0.987041i | −0.996578 | − | 0.0826527i | \(-0.973661\pi\) |
0.426710 | − | 0.904389i | \(-0.359673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1028.68 | + | 1781.73i | 0.167770 | + | 0.290586i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2323.81 | − | 4024.96i | 0.375627 | − | 0.650605i | −0.614794 | − | 0.788688i | \(-0.710761\pi\) |
0.990421 | + | 0.138083i | \(0.0440941\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7256.70 | −1.15241 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 386.154 | + | 6340.70i | 0.0607882 | + | 0.998151i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8295.04 | − | 4789.14i | −1.28329 | − | 0.740907i | −0.305840 | − | 0.952083i | \(-0.598937\pi\) |
−0.977448 | + | 0.211176i | \(0.932271\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 755.168 | − | 435.997i | 0.115826 | − | 0.0668721i | −0.440968 | − | 0.897523i | \(-0.645365\pi\) |
0.556794 | + | 0.830651i | \(0.312031\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4148.63 | − | 7185.64i | −0.625523 | − | 1.08344i | −0.988440 | − | 0.151615i | \(-0.951552\pi\) |
0.362917 | − | 0.931821i | \(-0.381781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2013.36 | − | 1162.42i | −0.301009 | − | 0.173788i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 976.696i | 0.143588i | 0.997419 | + | 0.0717939i | \(0.0228724\pi\) | ||||
−0.997419 | + | 0.0717939i | \(0.977128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6079.69 | 0.886381 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1146.89 | + | 662.155i | 0.164468 | + | 0.0949556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6001.51 | + | 3464.97i | −0.853614 | + | 0.492834i | −0.861868 | − | 0.507132i | \(-0.830706\pi\) |
0.00825490 | + | 0.999966i | \(0.497372\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1873.89 | + | 3403.20i | −0.262231 | + | 0.476241i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2259.68 | − | 3913.89i | 0.313678 | − | 0.543307i | −0.665477 | − | 0.746418i | \(-0.731772\pi\) |
0.979156 | + | 0.203111i | \(0.0651053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3612.63 | 0.493528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2781.32 | 0.376958 | 0.188479 | − | 0.982077i | \(-0.439644\pi\) | ||||
0.188479 | + | 0.982077i | \(0.439644\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5449.44 | + | 9438.71i | −0.727033 | + | 1.25926i | 0.231099 | + | 0.972930i | \(0.425768\pi\) |
−0.958132 | + | 0.286327i | \(0.907566\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2437.27 | − | 4426.36i | 0.322635 | − | 0.585943i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1922.09 | + | 1109.72i | −0.250524 | + | 0.144640i | −0.620004 | − | 0.784598i | \(-0.712869\pi\) |
0.369480 | + | 0.929239i | \(0.379536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1190.33 | − | 687.237i | −0.153958 | − | 0.0888877i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2907.58 | 0.370370 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10873.7i | − | 1.37464i | −0.726354 | − | 0.687321i | \(-0.758786\pi\) | ||
0.726354 | − | 0.687321i | \(-0.241214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5301.00 | + | 3060.53i | 0.660147 | + | 0.381136i | 0.792333 | − | 0.610089i | \(-0.208866\pi\) |
−0.132186 | + | 0.991225i | \(0.542200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2097.23 | − | 3632.51i | −0.259232 | − | 0.449003i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11335.0 | + | 6544.26i | −1.38048 | + | 0.797020i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12155.0 | − | 7017.69i | −1.46950 | − | 0.848416i | −0.470085 | − | 0.882621i | \(-0.655777\pi\) |
−0.999415 | + | 0.0342045i | \(0.989110\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13118.3 | − | 7932.75i | 1.56298 | − | 0.945145i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4251.83 | −0.502926 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4144.18 | + | 7177.94i | −0.483190 | + | 0.836910i | −0.999814 | − | 0.0193028i | \(-0.993855\pi\) |
0.516624 | + | 0.856213i | \(0.327189\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7767.30 | + | 13453.4i | 0.899181 | + | 1.55743i | 0.828544 | + | 0.559924i | \(0.189170\pi\) |
0.0706368 | + | 0.997502i | \(0.477497\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −877.765 | − | 1520.33i | −0.100183 | − | 0.173522i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12704.7 | − | 257.627i | 1.43987 | − | 0.0291978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3167.89i | − | 0.354041i | −0.984207 | − | 0.177021i | \(-0.943354\pi\) | ||
0.984207 | − | 0.177021i | \(-0.0566459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2187.70i | − | 0.242804i | −0.992603 | − | 0.121402i | \(-0.961261\pi\) | ||
0.992603 | − | 0.121402i | \(-0.0387391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 972.630 | − | 1684.65i | 0.106470 | − | 0.184411i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1703.79 | + | 983.684i | −0.185234 | + | 0.106945i | −0.589749 | − | 0.807586i | \(-0.700773\pi\) |
0.404516 | + | 0.914531i | \(0.367440\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2229.21 | + | 1287.04i | −0.239081 | + | 0.138034i | −0.614754 | − | 0.788719i | \(-0.710745\pi\) |
0.375673 | + | 0.926752i | \(0.377412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −422.783 | + | 732.282i | −0.0450379 | + | 0.0780079i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9168.11i | − | 0.963630i | −0.876273 | − | 0.481815i | \(-0.839978\pi\) | ||
0.876273 | − | 0.481815i | \(-0.160022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1857.93i | 0.193983i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2920.10 | − | 59.2139i | 0.300871 | − | 0.00610108i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 449.418 | + | 778.415i | 0.0460019 | + | 0.0796777i | 0.888110 | − | 0.459632i | \(-0.152019\pi\) |
−0.842108 | + | 0.539310i | \(0.818685\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −750.955 | − | 1300.69i | −0.0758686 | − | 0.131408i | 0.825595 | − | 0.564263i | \(-0.190840\pi\) |
−0.901464 | + | 0.432855i | \(0.857506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 515.882 | − | 893.534i | 0.0517820 | − | 0.0896891i | −0.838973 | − | 0.544174i | \(-0.816843\pi\) |
0.890755 | + | 0.454485i | \(0.150177\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8619.68 | −0.854114 | −0.427057 | − | 0.904225i | \(-0.640450\pi\) | ||||
−0.427057 | + | 0.904225i | \(0.640450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5434.23 | + | 3286.12i | −0.535031 | + | 0.323537i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4364.66 | + | 2519.94i | 0.424286 | + | 0.244962i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2151.69 | − | 1242.28i | 0.207845 | − | 0.119999i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2037.51 | − | 3529.07i | −0.194355 | − | 0.336634i | 0.752334 | − | 0.658782i | \(-0.228928\pi\) |
−0.946689 | + | 0.322149i | \(0.895595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6551.77 | − | 3782.66i | −0.621070 | − | 0.358575i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9036.40i | − | 0.846025i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14817.8 | −1.37876 | −0.689381 | − | 0.724399i | \(-0.742117\pi\) | ||||
−0.689381 | + | 0.724399i | \(0.742117\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6217.36 | + | 3589.59i | 0.571457 | + | 0.329931i | 0.757731 | − | 0.652567i | \(-0.226308\pi\) |
−0.186274 | + | 0.982498i | \(0.559641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2347.88 | + | 1355.55i | −0.214489 | + | 0.123835i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3461.34 | − | 6286.20i | 0.312399 | − | 0.567353i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5380.59 | + | 9319.46i | −0.482702 | + | 0.836065i | −0.999803 | − | 0.0198598i | \(-0.993678\pi\) |
0.517100 | + | 0.855925i | \(0.327011\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11285.3 | 1.00037 | 0.500186 | − | 0.865918i | \(-0.333265\pi\) | ||||
0.500186 | + | 0.865918i | \(0.333265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11082.1 | −0.976527 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5404.52 | + | 9360.91i | −0.470631 | + | 0.815157i | −0.999436 | − | 0.0335864i | \(-0.989307\pi\) |
0.528805 | + | 0.848744i | \(0.322640\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1971.71 | + | 3580.85i | −0.170691 | + | 0.309995i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4178.84 | − | 2412.66i | 0.357557 | − | 0.206436i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8637.54 | + | 4986.89i | 0.734775 | + | 0.424223i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3085.93 | −0.259495 | −0.129747 | − | 0.991547i | \(-0.541417\pi\) | ||||
−0.129747 | + | 0.991547i | \(0.541417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2155.94i | − | 0.180254i | −0.995930 | − | 0.0901268i | \(-0.971273\pi\) | ||
0.995930 | − | 0.0901268i | \(-0.0287272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2726.01 | + | 1573.87i | 0.225327 | + | 0.130092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3655.69 | − | 6331.85i | −0.300460 | − | 0.520412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −930.030 | + | 536.953i | −0.0755799 | + | 0.0436361i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1470.48 | + | 848.982i | 0.118831 | + | 0.0686069i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13812.7 | + | 7244.67i | 1.10382 | + | 0.578942i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19410.4 | 1.54255 | 0.771273 | − | 0.636504i | \(-0.219620\pi\) | ||||
0.771273 | + | 0.636504i | \(0.219620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5479.23 | − | 9490.31i | 0.430651 | − | 0.745909i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2279.16 | − | 3947.62i | −0.178153 | − | 0.308570i | 0.763095 | − | 0.646286i | \(-0.223679\pi\) |
−0.941248 | + | 0.337716i | \(0.890346\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1918.48 | − | 3322.90i | −0.148330 | − | 0.256915i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 181.957 | + | 8973.10i | 0.0139920 | + | 0.690009i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4710.38i | − | 0.358322i | −0.983820 | − | 0.179161i | \(-0.942662\pi\) | ||
0.983820 | − | 0.179161i | \(-0.0573383\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2913.11i | 0.220414i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2316.26 | − | 4011.87i | 0.173390 | − | 0.300320i | −0.766213 | − | 0.642587i | \(-0.777861\pi\) |
0.939603 | + | 0.342267i | \(0.111195\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4894.81 | − | 2826.02i | 0.364471 | − | 0.210428i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6667.01 | − | 3849.20i | 0.491205 | − | 0.283597i | −0.233869 | − | 0.972268i | \(-0.575139\pi\) |
0.725074 | + | 0.688671i | \(0.241805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8556.34 | + | 14820.0i | −0.627096 | + | 1.08616i | 0.361036 | + | 0.932552i | \(0.382423\pi\) |
−0.988132 | + | 0.153610i | \(0.950910\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6201.77i | 0.449794i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2389.01i | − | 0.172367i | −0.996279 | − | 0.0861834i | \(-0.972533\pi\) | ||
0.996279 | − | 0.0861834i | \(-0.0274671\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −266.080 | − | 13121.6i | −0.0189998 | − | 0.936965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4769.48 | + | 8260.97i | 0.338819 | + | 0.586852i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7877.22 | + | 13643.7i | 0.553880 | + | 0.959348i | 0.997990 | + | 0.0633757i | \(0.0201866\pi\) |
−0.444110 | + | 0.895972i | \(0.646480\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2227.45 | + | 3858.06i | −0.155824 | + | 0.269896i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14439.8 | −0.999953 | −0.499976 | − | 0.866039i | \(-0.666658\pi\) | ||||
−0.499976 | + | 0.866039i | \(0.666658\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1875.58 | + | 1134.18i | −0.129229 | + | 0.0781458i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13069.6 | + | 7545.75i | 0.891504 | + | 0.514710i | 0.874434 | − | 0.485145i | \(-0.161233\pi\) |
0.0170695 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21885.4 | − | 12635.5i | 1.48540 | − | 0.857595i | 0.485536 | − | 0.874217i | \(-0.338624\pi\) |
0.999862 | + | 0.0166219i | \(0.00529115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2210.44 | − | 3828.59i | −0.148541 | − | 0.257280i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16922.0 | − | 9769.93i | −1.13154 | − | 0.653293i | −0.187216 | − | 0.982319i | \(-0.559947\pi\) |
−0.944321 | + | 0.329025i | \(0.893280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5764.97i | 0.381711i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22968.2 | 1.51334 | 0.756671 | − | 0.653796i | \(-0.226825\pi\) | ||||
0.756671 | + | 0.653796i | \(0.226825\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24539.5 | + | 14167.9i | 1.60117 | + | 0.924437i | 0.991253 | + | 0.131974i | \(0.0421316\pi\) |
0.609920 | + | 0.792463i | \(0.291202\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17347.3 | − | 10015.5i | 1.12641 | − | 0.650332i | 0.183379 | − | 0.983042i | \(-0.441297\pi\) |
0.943029 | + | 0.332710i | \(0.107963\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2286.36 | − | 1258.93i | −0.147032 | − | 0.0809597i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1710.61 | + | 2962.87i | −0.109479 | + | 0.189624i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5677.39 | 0.359893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7219.42 | 0.455469 | 0.227734 | − | 0.973723i | \(-0.426868\pi\) | ||||
0.227734 | + | 0.973723i | \(0.426868\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 961.643 | − | 1665.61i | 0.0600970 | − | 0.104091i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 365.481 | + | 9008.04i | 0.0227329 | + | 0.560301i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14946.4 | − | 8629.29i | 0.920976 | − | 0.531726i | 0.0370299 | − | 0.999314i | \(-0.488210\pi\) |
0.883946 | + | 0.467588i | \(0.154877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21951.3 | + | 12673.6i | 1.34631 | + | 0.777291i | 0.987724 | − | 0.156206i | \(-0.0499265\pi\) |
0.358584 | + | 0.933498i | \(0.383260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6799.46 | 0.413160 | 0.206580 | − | 0.978430i | \(-0.433767\pi\) | ||||
0.206580 | + | 0.978430i | \(0.433767\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 37640.9i | − | 2.27663i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19452.8 | − | 11231.1i | −1.16577 | − | 0.673058i | −0.213090 | − | 0.977033i | \(-0.568353\pi\) |
−0.952680 | + | 0.303975i | \(0.901686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1841.42 | − | 3189.43i | −0.109848 | − | 0.190262i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3236.46 | + | 1868.57i | −0.191312 | + | 0.110454i | −0.592597 | − | 0.805499i | \(-0.701897\pi\) |
0.401285 | + | 0.915953i | \(0.368564\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10205.8 | + | 5892.33i | 0.600545 | + | 0.346725i | 0.769256 | − | 0.638941i | \(-0.220627\pi\) |
−0.168711 | + | 0.985666i | \(0.553960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1605.17 | − | 2654.46i | −0.0936030 | − | 0.154790i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9577.50 | 0.555986 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15600.4 | − | 27020.6i | 0.897534 | − | 1.55457i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5712.35 | + | 9894.08i | 0.327184 | + | 0.566699i | 0.981952 | − | 0.189131i | \(-0.0605670\pi\) |
−0.654768 | + | 0.755830i | \(0.727234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15013.5 | − | 26004.1i | −0.852312 | − | 1.47625i | −0.879116 | − | 0.476607i | \(-0.841866\pi\) |
0.0268044 | − | 0.999641i | \(-0.491467\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27887.3 | − | 565.500i | 1.57617 | − | 0.0319615i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18482.4i | 1.03545i | 0.855548 | + | 0.517723i | \(0.173220\pi\) | ||||
−0.855548 | + | 0.517723i | \(0.826780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10502.1i | 0.585786i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2756.82 | + | 4774.94i | −0.152433 | + | 0.264022i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16408.4 | + | 9473.38i | −0.903334 | + | 0.521540i | −0.878280 | − | 0.478146i | \(-0.841309\pi\) |
−0.0250537 | + | 0.999686i | \(0.507976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6724.25 | − | 3882.25i | 0.367001 | − | 0.211888i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 402.956 | − | 697.941i | 0.0218982 | − | 0.0379288i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9045.09i | − | 0.487344i | −0.969858 | − | 0.243672i | \(-0.921648\pi\) | ||
0.969858 | − | 0.243672i | \(-0.0783521\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8035.08i | 0.431079i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −693.518 | − | 34200.5i | −0.0368917 | − | 1.81929i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1866.89 | − | 3233.55i | −0.0988893 | − | 0.171281i | 0.812336 | − | 0.583190i | \(-0.198196\pi\) |
−0.911225 | + | 0.411909i | \(0.864862\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5560.00 | − | 9630.20i | −0.292039 | − | 0.505826i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3585.64 | − | 6210.51i | 0.187546 | − | 0.324839i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35410.2 | −1.83669 | −0.918343 | − | 0.395785i | \(-0.870473\pi\) | ||||
−0.918343 | + | 0.395785i | \(0.870473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7707.23 | + | 12745.4i | 0.398103 | + | 0.658339i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10593.9 | + | 6116.37i | 0.542685 | + | 0.313319i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2328.92 | + | 1344.60i | −0.118810 | + | 0.0685951i | −0.558227 | − | 0.829688i | \(-0.688518\pi\) |
0.439417 | + | 0.898283i | \(0.355185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1093.07 | − | 1893.25i | −0.0553060 | − | 0.0957928i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10520.4 | − | 6073.96i | −0.530123 | − | 0.306066i | 0.210944 | − | 0.977498i | \(-0.432346\pi\) |
−0.741066 | + | 0.671432i | \(0.765680\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15592.7i | 0.779326i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33517.3 | −1.66841 | −0.834204 | − | 0.551456i | \(-0.814072\pi\) | ||||
−0.834204 | + | 0.551456i | \(0.814072\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21381.5 | − | 12344.6i | −1.05573 | − | 0.609529i | −0.131485 | − | 0.991318i | \(-0.541975\pi\) |
−0.924249 | + | 0.381790i | \(0.875308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14995.2 | − | 8657.49i | 0.737426 | − | 0.425753i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2528.03 | + | 4591.19i | −0.123327 | + | 0.223976i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4794.74 | + | 8304.74i | −0.232973 | + | 0.403521i | −0.958682 | − | 0.284481i | \(-0.908179\pi\) |
0.725709 | + | 0.688002i | \(0.241512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18487.4 | 0.891159 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13621.8 | −0.654022 | −0.327011 | − | 0.945021i | \(-0.606041\pi\) | ||||
−0.327011 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 839.906 | − | 1454.76i | 0.0400086 | − | 0.0692970i | −0.845328 | − | 0.534248i | \(-0.820595\pi\) |
0.885336 | + | 0.464951i | \(0.153928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29631.0 | + | 16315.6i | 1.40592 | + | 0.774134i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18842.0 | − | 10878.5i | 0.887023 | − | 0.512123i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30695.1 | + | 17721.8i | 1.43939 | + | 0.831034i | 0.997807 | − | 0.0661849i | \(-0.0210827\pi\) |
0.441586 | + | 0.897219i | \(0.354416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13901.4 | −0.646829 | −0.323415 | − | 0.946257i | \(-0.604831\pi\) | ||||
−0.323415 | + | 0.946257i | \(0.604831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 14202.9i | − | 0.658300i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 987.778 | + | 570.294i | 0.0454311 | + | 0.0262297i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8809.91 | − | 15259.2i | −0.403641 | − | 0.699126i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6540.73 | − | 3776.29i | 0.297387 | − | 0.171696i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3906.63 | − | 2255.49i | −0.176946 | − | 0.102160i | 0.408911 | − | 0.912574i | \(-0.365909\pi\) |
−0.585857 | + | 0.810415i | \(0.699242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9027.72 | + | 14929.1i | 0.405801 | + | 0.671070i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18034.4 | 0.807592 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15620.6 | − | 27055.6i | 0.694240 | − | 1.20246i | −0.276196 | − | 0.961101i | \(-0.589074\pi\) |
0.970436 | − | 0.241358i | \(-0.0775928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2163.16 | − | 3746.70i | −0.0957785 | − | 0.165893i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5018.45 | + | 8692.21i | 0.220544 | + | 0.381994i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7741.52 | − | 156.983i | 0.338948 | − | 0.00687319i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42276.5i | 1.83728i | 0.395091 | + | 0.918642i | \(0.370713\pi\) | ||||
−0.395091 | + | 0.918642i | \(0.629287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29402.1i | 1.27305i | 0.771254 | + | 0.636527i | \(0.219630\pi\) | ||||
−0.771254 | + | 0.636527i | \(0.780370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8720.74 | + | 15104.8i | −0.374815 | + | 0.649198i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2679.48 | − | 1547.00i | 0.114741 | − | 0.0662455i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36104.3 | + | 20844.8i | −1.53477 | + | 0.886103i | −0.535643 | + | 0.844445i | \(0.679931\pi\) |
−0.999132 | + | 0.0416579i | \(0.986736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4162.09 | − | 7208.95i | 0.176284 | − | 0.305332i | −0.764321 | − | 0.644836i | \(-0.776926\pi\) |
0.940605 | + | 0.339504i | \(0.110259\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7260.76i | 0.305298i | 0.988280 | + | 0.152649i | \(0.0487804\pi\) | ||||
−0.988280 | + | 0.152649i | \(0.951220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26509.9i | − | 1.11065i | −0.831634 | − | 0.555324i | \(-0.812594\pi\) | ||
0.831634 | − | 0.555324i | \(-0.187406\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3617.57 | − | 5717.26i | −0.150470 | − | 0.237805i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1720.63 | + | 2980.22i | 0.0713113 | + | 0.123515i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4438.40 | + | 7687.53i | 0.182635 | + | 0.316332i | 0.942777 | − | 0.333424i | \(-0.108204\pi\) |
−0.760142 | + | 0.649757i | \(0.774871\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2748.88 | + | 4761.19i | −0.112710 | + | 0.195219i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9036.78 | −0.367899 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11677.1 | − | 7061.25i | 0.473708 | − | 0.286455i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17369.5 | − | 10028.3i | −0.699669 | − | 0.403954i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13168.8 | + | 7603.02i | −0.528596 | + | 0.305185i | −0.740444 | − | 0.672118i | \(-0.765385\pi\) |
0.211849 | + | 0.977302i | \(0.432052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11826.9 | + | 20484.8i | 0.471410 | + | 0.816506i | 0.999465 | − | 0.0327038i | \(-0.0104118\pi\) |
−0.528055 | + | 0.849210i | \(0.677078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25545.4 | − | 14748.7i | −1.01467 | − | 0.585818i | −0.102112 | − | 0.994773i | \(-0.532560\pi\) |
−0.912555 | + | 0.408954i | \(0.865893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 36862.0i | − | 1.45399i | −0.686640 | − | 0.726997i | \(-0.740915\pi\) | ||
0.686640 | − | 0.726997i | \(-0.259085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23173.4 | −0.910888 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19084.1 | + | 11018.2i | 0.744976 | + | 0.430112i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7805.27 | + | 4506.38i | −0.303641 | + | 0.175307i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20830.8 | + | 11470.0i | 0.804810 | + | 0.443149i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4353.93 | − | 7541.22i | 0.167642 | − | 0.290364i | −0.769949 | − | 0.638106i | \(-0.779718\pi\) |
0.937590 | + | 0.347742i | \(0.113052\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18950.2 | 0.724685 | 0.362342 | − | 0.932045i | \(-0.381977\pi\) | ||||
0.362342 | + | 0.932045i | \(0.381977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5510.89 | 0.210030 | 0.105015 | − | 0.994471i | \(-0.466511\pi\) | ||||
0.105015 | + | 0.994471i | \(0.466511\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12652.8 | + | 21915.3i | −0.478962 | + | 0.829586i | −0.999709 | − | 0.0241247i | \(-0.992320\pi\) |
0.520747 | + | 0.853711i | \(0.325653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5200.44 | + | 2863.50i | 0.196195 | + | 0.108030i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5302.61 | − | 3061.46i | 0.198707 | − | 0.114723i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11682.2 | − | 6744.71i | −0.436304 | − | 0.251900i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21933.8 | −0.813717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 4137.70i | − | 0.152993i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −864.669 | − | 499.217i | −0.0317598 | − | 0.0183365i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9256.41 | + | 16032.6i | 0.338869 | + | 0.586938i | 0.984220 | − | 0.176948i | \(-0.0566224\pi\) |
−0.645351 | + | 0.763886i | \(0.723289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27338.9 | − | 15784.1i | 0.994266 | − | 0.574040i | 0.0877196 | − | 0.996145i | \(-0.472042\pi\) |
0.906547 | + | 0.422105i | \(0.138709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27907.2 | − | 16112.2i | −1.01160 | − | 0.584050i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9727.70 | − | 5882.42i | 0.350313 | − | 0.211837i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2352.27 | 0.0844332 | 0.0422166 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422166 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5092.23 | − | 8820.01i | 0.181596 | − | 0.314533i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12808.5 | − | 22185.0i | −0.455287 | − | 0.788580i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4728.40 | + | 8189.83i | 0.166990 | + | 0.289235i | 0.937360 | − | 0.348362i | \(-0.113262\pi\) |
−0.770370 | + | 0.637597i | \(0.779929\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8091.50 | − | 5119.86i | 0.284842 | − | 0.180233i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5381.68i | 0.188235i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34791.9i | 1.21302i | 0.795075 | + | 0.606511i | \(0.207431\pi\) | ||||
−0.795075 | + | 0.606511i | \(0.792569\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5515.38 | + | 9552.92i | −0.191069 | + | 0.330942i | −0.945605 | − | 0.325317i | \(-0.894529\pi\) |
0.754535 | + | 0.656259i | \(0.227862\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2465.62 | + | 1423.52i | −0.0851448 | + | 0.0491584i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26402.6 | − | 15243.5i | 0.905985 | − | 0.523071i | 0.0268478 | − | 0.999640i | \(-0.491453\pi\) |
0.879137 | + | 0.476569i | \(0.158120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2900.72 | + | 5024.20i | −0.0992218 | + | 0.171857i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21378.9i | − | 0.726685i | −0.931656 | − | 0.363343i | \(-0.881635\pi\) | ||
0.931656 | − | 0.363343i | \(-0.118365\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 12185.7i | − | 0.412902i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32410.5 | + | 657.221i | −1.09134 | + | 0.0221301i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2162.36 | − | 3745.31i | −0.0725842 | − | 0.125720i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1506.69 | − | 2609.67i | −0.0502613 | − | 0.0870550i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1999.31 | − | 3462.91i | 0.0664877 | − | 0.115160i | −0.830865 | − | 0.556474i | \(-0.812154\pi\) |
0.897353 | + | 0.441314i | \(0.145487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48223.6 | −1.59379 | −0.796895 | − | 0.604118i | \(-0.793525\pi\) | ||||
−0.796895 | + | 0.604118i | \(0.793525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12401.8 | + | 20508.8i | 0.408618 | + | 0.675727i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3157.95 | + | 1823.24i | 0.103410 | + | 0.0597038i | 0.550813 | − | 0.834629i | \(-0.314318\pi\) |
−0.447403 | + | 0.894332i | \(0.647651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5549.94 | + | 3204.26i | −0.181182 | + | 0.104605i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10473.4 | − | 18140.5i | −0.339828 | − | 0.588600i | 0.644572 | − | 0.764544i | \(-0.277036\pi\) |
−0.984400 | + | 0.175944i | \(0.943702\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20519.9 | − | 11847.2i | −0.663776 | − | 0.383232i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7722.99i | 0.248308i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6732.72 | 0.215814 | 0.107907 | − | 0.994161i | \(-0.465585\pi\) | ||||
0.107907 | + | 0.994161i | \(0.465585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3272.03 | − | 1889.11i | −0.104252 | − | 0.0601897i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35961.0 | + | 20762.1i | −1.14232 | + | 0.659520i | −0.947005 | − | 0.321220i | \(-0.895907\pi\) |
−0.195318 | + | 0.980740i | \(0.562574\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 756.4.x.a.125.16 | 48 | ||
3.2 | odd | 2 | 252.4.x.a.41.15 | yes | 48 | ||
7.6 | odd | 2 | inner | 756.4.x.a.125.9 | 48 | ||
9.2 | odd | 6 | inner | 756.4.x.a.629.9 | 48 | ||
9.4 | even | 3 | 2268.4.f.a.1133.18 | 48 | |||
9.5 | odd | 6 | 2268.4.f.a.1133.31 | 48 | |||
9.7 | even | 3 | 252.4.x.a.209.10 | yes | 48 | ||
21.20 | even | 2 | 252.4.x.a.41.10 | ✓ | 48 | ||
63.13 | odd | 6 | 2268.4.f.a.1133.32 | 48 | |||
63.20 | even | 6 | inner | 756.4.x.a.629.16 | 48 | ||
63.34 | odd | 6 | 252.4.x.a.209.15 | yes | 48 | ||
63.41 | even | 6 | 2268.4.f.a.1133.17 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.10 | ✓ | 48 | 21.20 | even | 2 | ||
252.4.x.a.41.15 | yes | 48 | 3.2 | odd | 2 | ||
252.4.x.a.209.10 | yes | 48 | 9.7 | even | 3 | ||
252.4.x.a.209.15 | yes | 48 | 63.34 | odd | 6 | ||
756.4.x.a.125.9 | 48 | 7.6 | odd | 2 | inner | ||
756.4.x.a.125.16 | 48 | 1.1 | even | 1 | trivial | ||
756.4.x.a.629.9 | 48 | 9.2 | odd | 6 | inner | ||
756.4.x.a.629.16 | 48 | 63.20 | even | 6 | inner | ||
2268.4.f.a.1133.17 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.18 | 48 | 9.4 | even | 3 | |||
2268.4.f.a.1133.31 | 48 | 9.5 | odd | 6 | |||
2268.4.f.a.1133.32 | 48 | 63.13 | odd | 6 |