Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, 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("252.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.10 | ||
Character | \(\chi\) | \(=\) | 252.41 |
Dual form | 252.4.x.a.209.10 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −0.494604 | − | 5.17256i | −0.0951865 | − | 0.995459i | ||||
\(4\) | 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 | ||||||||
\(7\) | −0.375477 | + | 18.5165i | −0.0202739 | + | 0.999794i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.5107 | + | 5.11673i | −0.981879 | + | 0.189509i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.3810 | + | 22.7366i | −1.07944 | + | 0.623214i | −0.930745 | − | 0.365669i | \(-0.880840\pi\) |
−0.148694 | + | 0.988883i | \(0.547507\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.7627 | − | 13.1421i | −0.485634 | − | 0.280381i | 0.237127 | − | 0.971479i | \(-0.423794\pi\) |
−0.722761 | + | 0.691098i | \(0.757127\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −28.3609 | − | 12.9475i | −0.488184 | − | 0.222869i | ||||
\(16\) | 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 | \(0.0539043\pi\) | ||||
−0.985695 | + | 0.168537i | \(0.946096\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 95.9632 | − | 7.21613i | 0.997185 | − | 0.0749852i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −60.3466 | − | 34.8411i | −0.547093 | − | 0.315864i | 0.200856 | − | 0.979621i | \(-0.435628\pi\) |
−0.747949 | + | 0.663757i | \(0.768961\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.5004 | + | 77.0769i | 0.356003 | + | 0.616615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 39.5789 | + | 134.598i | 0.282110 | + | 0.959382i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −119.031 | + | 68.7227i | −0.762191 | + | 0.440051i | −0.830082 | − | 0.557641i | \(-0.811706\pi\) |
0.0678907 | + | 0.997693i | \(0.478373\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 138.202 | + | 79.7908i | 0.800702 | + | 0.462286i | 0.843717 | − | 0.536789i | \(-0.180363\pi\) |
−0.0430146 | + | 0.999074i | \(0.513696\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 137.085 | + | 192.455i | 0.723133 | + | 1.01522i | ||||
\(34\) | 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 | ||||||||
\(39\) | −56.7196 | + | 124.242i | −0.232882 | + | 0.510117i | ||||
\(40\) | 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 | ||||||||
\(45\) | −52.9443 | + | 153.102i | −0.175388 | + | 0.507181i | ||||
\(46\) | 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 | ||||||||
\(49\) | −342.718 | − | 13.9050i | −0.999178 | − | 0.0405394i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.75601 | + | 102.028i | 0.0267866 | + | 0.280133i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 209.770i | − | 0.543664i | −0.962345 | − | 0.271832i | \(-0.912371\pi\) | ||
0.962345 | − | 0.271832i | \(-0.0876295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 272.837i | 0.668897i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 144.398 | − | 13.8074i | 0.335544 | − | 0.0320849i | ||||
\(58\) | 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 | −0.970555 | − | 0.240881i | \(-0.922564\pi\) |
−0.276668 | + | 0.960965i | \(0.589230\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −84.7896 | − | 492.806i | −0.169563 | − | 0.985519i | ||||
\(64\) | 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 | ||||||||
\(69\) | −150.370 | + | 329.379i | −0.262354 | + | 0.574675i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 387.476i | 0.647675i | 0.946113 | + | 0.323838i | \(0.104973\pi\) | ||||
−0.946113 | + | 0.323838i | \(0.895027\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 220.721i | − | 0.353882i | −0.984221 | − | 0.176941i | \(-0.943380\pi\) | ||
0.984221 | − | 0.176941i | \(-0.0566202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 376.675 | − | 268.303i | 0.579929 | − | 0.413080i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −406.215 | − | 737.734i | −0.601202 | − | 1.09185i | ||||
\(78\) | 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 | ||||||||
\(81\) | 676.638 | − | 271.297i | 0.928173 | − | 0.372149i | ||||
\(82\) | 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 | ||||||||
\(87\) | 414.346 | + | 581.706i | 0.510604 | + | 0.716844i | ||||
\(88\) | 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 | ||||||||
\(93\) | 344.368 | − | 754.321i | 0.383970 | − | 0.841070i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 145.055 | + | 83.7476i | 0.156656 | + | 0.0904455i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1304.31 | + | 753.041i | −1.36528 | + | 0.788245i | −0.990321 | − | 0.138796i | \(-0.955677\pi\) |
−0.374960 | + | 0.927041i | \(0.622343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 927.683 | − | 804.267i | 0.941774 | − | 0.816484i | ||||
\(100\) | 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 | 0.128389 | − | 0.991724i | \(-0.459019\pi\) |
−0.794664 | + | 0.607050i | \(0.792353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 250.391 | − | 520.282i | 0.232720 | − | 0.483565i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 282.997i | − | 0.255685i | −0.991794 | − | 0.127843i | \(-0.959195\pi\) | ||
0.991794 | − | 0.127843i | \(-0.0408053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1826.43 | 1.60496 | 0.802478 | − | 0.596681i | \(-0.203514\pi\) | ||||
0.802478 | + | 0.596681i | \(0.203514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 142.361 | + | 1488.81i | 0.121733 | + | 1.27308i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −815.811 | − | 471.008i | −0.679159 | − | 0.392113i | 0.120379 | − | 0.992728i | \(-0.461589\pi\) |
−0.799538 | + | 0.600615i | \(0.794922\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −362.076 | + | 209.044i | −0.293598 | + | 0.169509i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 670.701 | + | 231.935i | 0.529968 | + | 0.183268i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.40625 | − | 365.235i | 0.00570529 | − | 0.281353i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 368.410 | − | 638.105i | 0.276792 | − | 0.479418i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 193.129 | + | 88.1683i | 0.141576 | + | 0.0646331i | ||||
\(124\) | 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 | ||||||||
\(129\) | 469.069 | − | 334.115i | 0.320149 | − | 0.228040i | ||||
\(130\) | 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 | ||||||||
\(133\) | −516.908 | − | 10.4819i | −0.337005 | − | 0.00683379i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 818.118 | + | 198.133i | 0.521573 | + | 0.126315i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1515.86 | − | 875.182i | 0.945318 | − | 0.545780i | 0.0536948 | − | 0.998557i | \(-0.482900\pi\) |
0.891623 | + | 0.452778i | \(0.149567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1120.72 | − | 647.048i | −0.683872 | − | 0.394834i | 0.117440 | − | 0.993080i | \(-0.462531\pi\) |
−0.801312 | + | 0.598246i | \(0.795865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 928.274 | − | 661.204i | 0.554431 | − | 0.394918i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1195.23 | 0.698950 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 824.664i | 0.472308i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 97.5851 | + | 1779.61i | 0.0547530 | + | 0.998500i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2499.23 | − | 1442.93i | −1.37413 | − | 0.793352i | −0.382681 | − | 0.923880i | \(-0.624999\pi\) |
−0.991445 | + | 0.130528i | \(0.958333\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 522.922 | − | 100.927i | 0.276312 | − | 0.0533298i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 829.202 | − | 478.740i | 0.429697 | − | 0.248086i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1090.13 | − | 629.388i | −0.554153 | − | 0.319941i | 0.196642 | − | 0.980475i | \(-0.436996\pi\) |
−0.750795 | + | 0.660535i | \(0.770330\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1085.05 | + | 103.753i | −0.541195 | + | 0.0517495i | ||||
\(160\) | 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 | ||||||||
\(165\) | 1411.27 | − | 134.946i | 0.665860 | − | 0.0636700i | ||||
\(166\) | 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 | ||||||||
\(171\) | −142.840 | − | 740.078i | −0.0638785 | − | 0.330966i | ||||
\(172\) | 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 | ||||||||
\(175\) | −1443.90 | + | 795.048i | −0.623706 | + | 0.343429i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3912.71 | − | 1786.25i | −1.66157 | − | 0.758549i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2248.26i | 0.938787i | 0.882989 | + | 0.469394i | \(0.155527\pi\) | ||||
−0.882989 | + | 0.469394i | \(0.844473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 166.407i | 0.0683368i | 0.999416 | + | 0.0341684i | \(0.0108783\pi\) | ||||
−0.999416 | + | 0.0341684i | \(0.989122\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2068.43 | + | 2903.90i | 0.835534 | + | 1.17302i | ||||
\(184\) | 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 | ||||||||
\(189\) | −2507.13 | + | 682.323i | −0.964904 | + | 0.262601i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1758.88 | + | 1015.49i | −0.666324 | + | 0.384703i | −0.794682 | − | 0.607025i | \(-0.792363\pi\) |
0.128358 | + | 0.991728i | \(0.459029\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 475.415 | + | 667.441i | 0.174591 | + | 0.245110i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3949.11i | 1.42823i | 0.700026 | + | 0.714117i | \(0.253172\pi\) | ||||
−0.700026 | + | 0.714117i | \(0.746828\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 629.709i | 0.224316i | 0.993690 | + | 0.112158i | \(0.0357763\pi\) | ||||
−0.993690 | + | 0.112158i | \(0.964224\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1620.83 | + | 739.952i | 0.568779 | + | 0.259663i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1227.81 | − | 2229.84i | −0.424508 | − | 0.770956i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 122.572 | + | 212.300i | 0.0417599 | + | 0.0723302i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1778.10 | + | 614.886i | 0.597038 | + | 0.206462i | ||||
\(208\) | 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 | ||||||||
\(213\) | 2004.24 | − | 191.647i | 0.644735 | − | 0.0616500i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 664.983 | 0.210937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1529.33 | + | 2529.05i | −0.478424 | + | 0.791165i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1141.69 | + | 109.169i | −0.352275 | + | 0.0336848i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 448.992 | + | 259.226i | 0.136663 | + | 0.0789023i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2829.72 | − | 1633.74i | 0.849740 | − | 0.490598i | −0.0108230 | − | 0.999941i | \(-0.503445\pi\) |
0.860563 | + | 0.509344i | \(0.170112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1574.12 | − | 1815.67i | −0.466406 | − | 0.537976i | ||||
\(226\) | 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 | 0.981556 | − | 0.191175i | \(-0.0612298\pi\) |
0.325215 | + | 0.945640i | \(0.394563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3615.06 | + | 2466.06i | −1.02967 | + | 0.702402i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3433.84i | 0.965487i | 0.875762 | + | 0.482743i | \(0.160360\pi\) | ||||
−0.875762 | + | 0.482743i | \(0.839640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1315.98 | 0.365299 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2050.96 | − | 1460.89i | 0.562128 | − | 0.400401i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 469.677 | + | 271.168i | 0.127117 | + | 0.0733908i | 0.562210 | − | 0.826995i | \(-0.309951\pi\) |
−0.435093 | + | 0.900385i | \(0.643285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3110.33 | + | 1795.75i | −0.831343 | + | 0.479976i | −0.854312 | − | 0.519760i | \(-0.826021\pi\) |
0.0229693 | + | 0.999736i | \(0.492688\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1737.97 | − | 3365.77i | −0.458809 | − | 0.888535i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1100.40 | + | 1739.08i | −0.286946 | + | 0.453493i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 366.876 | − | 635.448i | 0.0945092 | − | 0.163695i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2999.18 | + | 2136.30i | −0.763315 | + | 0.543705i | ||||
\(250\) | 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 | ||||||||
\(255\) | 559.416 | + | 255.388i | 0.137380 | + | 0.0627178i | ||||
\(256\) | 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 | ||||||||
\(259\) | 108.073 | − | 5329.57i | 0.0259279 | − | 1.27862i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2803.97 | − | 2430.94i | 0.664986 | − | 0.576519i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6274.79 | − | 3622.75i | 1.47118 | − | 0.849386i | 0.471704 | − | 0.881757i | \(-0.343639\pi\) |
0.999476 | + | 0.0323711i | \(0.0103058\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1089.99 | − | 629.305i | −0.252669 | − | 0.145879i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 69.7041 | + | 728.965i | 0.0159769 | + | 0.167086i | ||||
\(268\) | 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 | \(0.0893321\pi\) | ||||
−0.960877 | + | 0.276975i | \(0.910668\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2279.22 | − | 1096.89i | −0.505291 | − | 0.243176i | ||||
\(274\) | 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 | ||||||||
\(279\) | −4072.10 | − | 1408.17i | −0.873800 | − | 0.302169i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2090.48 | − | 1206.94i | 0.443799 | − | 0.256228i | −0.261409 | − | 0.965228i | \(-0.584187\pi\) |
0.705208 | + | 0.709001i | \(0.250854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3893.62 | + | 2247.98i | 0.817851 | + | 0.472187i | 0.849675 | − | 0.527307i | \(-0.176798\pi\) |
−0.0318238 | + | 0.999493i | \(0.510132\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 361.445 | − | 791.728i | 0.0751233 | − | 0.164554i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −647.511 | − | 391.555i | −0.133175 | − | 0.0805322i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4523.93 | −0.920808 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4540.27 | + | 6374.14i | 0.914622 | + | 1.28405i | ||||
\(292\) | 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 | ||||||||
\(297\) | −4618.96 | − | 4400.70i | −0.902421 | − | 0.859779i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 915.768 | + | 1586.16i | 0.177125 | + | 0.306789i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1798.07 | + | 990.065i | −0.344316 | + | 0.189589i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7817.13 | + | 5568.10i | −1.48212 | + | 1.05571i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4116.75i | 0.772868i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10294.0i | − | 1.91371i | −0.290560 | − | 0.956857i | \(-0.593842\pi\) | ||
0.290560 | − | 0.956857i | \(-0.406158\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1735.47 | + | 3801.48i | −0.319507 | + | 0.699865i | ||||
\(310\) | 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 | 0.304449 | − | 0.952529i | \(-0.401528\pi\) |
0.977139 | + | 0.212604i | \(0.0681943\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2815.03 | − | 1037.83i | −0.503521 | − | 0.185635i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7590.80 | − | 4382.55i | 1.34493 | − | 0.776494i | 0.357401 | − | 0.933951i | \(-0.383663\pi\) |
0.987526 | + | 0.157457i | \(0.0503295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3125.05 | − | 5412.74i | 0.548493 | − | 0.950017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1463.82 | + | 139.971i | −0.254524 | + | 0.0243378i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 550.644i | − | 0.0948564i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2339.31i | − | 0.399266i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −903.359 | − | 9447.32i | −0.152770 | − | 1.59767i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3558.33 | + | 1959.31i | −0.596283 | + | 0.328329i | ||||
\(330\) | 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 | ||||||||
\(333\) | 7630.55 | − | 1472.74i | 1.25571 | − | 0.242360i | ||||
\(334\) | 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 | ||||||||
\(339\) | −2032.82 | + | 4452.79i | −0.325686 | + | 0.713399i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7256.70 | −1.15241 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 386.154 | − | 6340.70i | 0.0607882 | − | 0.998151i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1260.38 | + | 1769.46i | 0.196686 | + | 0.276130i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8295.04 | + | 4789.14i | 1.28329 | + | 0.740907i | 0.977448 | − | 0.211176i | \(-0.0677294\pi\) |
0.305840 | + | 0.952083i | \(0.401063\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −755.168 | + | 435.997i | −0.115826 | + | 0.0668721i | −0.556794 | − | 0.830651i | \(-0.687969\pi\) |
0.440968 | + | 0.897523i | \(0.354635\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 867.966 | − | 3583.96i | 0.131990 | − | 0.545007i | ||||
\(352\) | 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 | ||||||||
\(357\) | −1892.86 | + | 142.337i | −0.280619 | + | 0.0211017i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 976.696i | − | 0.143588i | −0.997419 | − | 0.0717939i | \(-0.977128\pi\) | ||
0.997419 | − | 0.0717939i | \(-0.0228724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6079.69 | 0.886381 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3482.85 | − | 1590.01i | −0.503588 | − | 0.229901i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1146.89 | − | 662.155i | −0.164468 | − | 0.0949556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6001.51 | − | 3464.97i | 0.853614 | − | 0.492834i | −0.00825490 | − | 0.999966i | \(-0.502628\pi\) |
0.861868 | + | 0.507132i | \(0.169294\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 360.534 | − | 1042.58i | 0.0508635 | − | 0.147085i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3884.20 | + | 78.7640i | 0.543552 | + | 0.0110222i | ||||
\(372\) | 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 | ||||||||
\(375\) | −635.067 | − | 6641.52i | −0.0874525 | − | 0.914578i | ||||
\(376\) | 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 | ||||||||
\(381\) | −158.546 | − | 1658.07i | −0.0213190 | − | 0.222954i | ||||
\(382\) | 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 | ||||||||
\(385\) | −5051.97 | − | 102.444i | −0.668759 | − | 0.0135611i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1960.23 | − | 2261.03i | −0.257479 | − | 0.296989i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1922.09 | − | 1109.72i | 0.250524 | − | 0.144640i | −0.369480 | − | 0.929239i | \(-0.620464\pi\) |
0.620004 | + | 0.784598i | \(0.287131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1190.33 | + | 687.237i | 0.153958 | + | 0.0888877i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2901.41 | − | 1324.57i | −0.372410 | − | 0.170015i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2907.58 | 0.370370 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10873.7i | 1.37464i | 0.726354 | + | 0.687321i | \(0.241214\pi\) | ||||
−0.726354 | + | 0.687321i | \(0.758786\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 201.447 | + | 2678.92i | 0.0252756 | + | 0.336125i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5301.00 | − | 3060.53i | −0.660147 | − | 0.381136i | 0.132186 | − | 0.991225i | \(-0.457800\pi\) |
−0.792333 | + | 0.610089i | \(0.791134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2097.23 | − | 3632.51i | −0.259232 | − | 0.449003i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 620.209 | − | 4329.76i | 0.0760949 | − | 0.531228i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11335.0 | − | 6544.26i | 1.38048 | − | 0.797020i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12155.0 | + | 7017.69i | 1.46950 | + | 0.848416i | 0.999415 | − | 0.0342045i | \(-0.0108898\pi\) |
0.470085 | + | 0.882621i | \(0.344223\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5276.68 | − | 7408.00i | −0.633283 | − | 0.889075i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13118.3 | + | 7932.75i | 1.56298 | + | 0.945145i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4251.83 | −0.502926 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2792.58 | + | 6117.03i | −0.327946 | + | 0.718350i | ||||
\(418\) | 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 | ||||||||
\(423\) | −3879.25 | − | 4474.52i | −0.445899 | − | 0.514323i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −877.765 | − | 1520.33i | −0.100183 | − | 0.173522i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6129.26 | − | 11131.4i | −0.694651 | − | 1.26157i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −591.163 | − | 6182.37i | −0.0665306 | − | 0.695776i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3167.89i | 0.354041i | 0.984207 | + | 0.177021i | \(0.0566459\pi\) | ||||
−0.984207 | + | 0.177021i | \(0.943354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2187.70i | 0.242804i | 0.992603 | + | 0.121402i | \(0.0387391\pi\) | ||||
−0.992603 | + | 0.121402i | \(0.961261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4265.62 | − | 407.882i | 0.470163 | − | 0.0449573i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 972.630 | − | 1684.65i | 0.106470 | − | 0.184411i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1703.79 | − | 983.684i | 0.185234 | − | 0.106945i | −0.404516 | − | 0.914531i | \(-0.632560\pi\) |
0.589749 | + | 0.807586i | \(0.299227\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9156.86 | − | 1384.96i | 0.988754 | − | 0.149548i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2229.21 | − | 1287.04i | 0.239081 | − | 0.138034i | −0.375673 | − | 0.926752i | \(-0.622588\pi\) |
0.614754 | + | 0.788719i | \(0.289255\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −422.783 | + | 732.282i | −0.0450379 | + | 0.0780079i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6227.51 | + | 13641.1i | −0.658952 | + | 1.44340i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9168.11i | 0.963630i | 0.876273 | + | 0.481815i | \(0.160022\pi\) | ||||
−0.876273 | + | 0.481815i | \(0.839978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1857.93i | − | 0.193983i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13040.7 | − | 9288.84i | 1.35255 | − | 0.963416i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1408.77 | − | 2558.49i | −0.145152 | − | 0.263613i | ||||
\(456\) | 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 | ||||||||
\(459\) | −780.690 | − | 2654.92i | −0.0793889 | − | 0.269981i | ||||
\(460\) | 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 | ||||||||
\(465\) | −2886.44 | − | 4052.31i | −0.287861 | − | 0.404132i | ||||
\(466\) | 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 | ||||||||
\(471\) | −2716.37 | + | 5950.07i | −0.265740 | + | 0.582091i | ||||
\(472\) | 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 | ||||||||
\(477\) | 1073.34 | + | 5561.17i | 0.103029 | + | 0.533812i | ||||
\(478\) | 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 | ||||||||
\(483\) | −6042.47 | − | 2907.99i | −0.569237 | − | 0.273951i | ||||
\(484\) | 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 | ||||||||
\(489\) | 1437.78 | + | 15036.3i | 0.132963 | + | 1.39052i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6217.36 | − | 3589.59i | −0.571457 | − | 0.329931i | 0.186274 | − | 0.982498i | \(-0.440359\pi\) |
−0.757731 | + | 0.652567i | \(0.773692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2347.88 | − | 1355.55i | 0.214489 | − | 0.123835i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1396.03 | − | 7233.11i | −0.126762 | − | 0.656776i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7174.68 | − | 145.488i | −0.647542 | − | 0.0131309i | ||||
\(498\) | 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 | ||||||||
\(501\) | 2711.09 | + | 1237.69i | 0.241762 | + | 0.110371i | ||||
\(502\) | 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 | ||||||||
\(507\) | −6374.41 | + | 4540.45i | −0.558377 | + | 0.397729i | ||||
\(508\) | 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 | ||||||||
\(511\) | 4086.96 | + | 82.8755i | 0.353809 | + | 0.00717456i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3757.45 | + | 1104.89i | −0.323383 | + | 0.0950919i | ||||
\(514\) | 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 | ||||||||
\(519\) | −16346.1 | + | 11643.3i | −1.38250 | + | 0.984745i | ||||
\(520\) | 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 | \(0.0287272\pi\) | ||||
−0.995930 | + | 0.0901268i | \(0.971273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4826.59 | + | 7075.42i | 0.401238 | + | 0.588184i | ||||
\(526\) | 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 | ||||||||
\(531\) | −7304.27 | + | 21122.2i | −0.596946 | + | 1.72623i | ||||
\(532\) | 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 | ||||||||
\(537\) | 11629.3 | − | 1112.00i | 0.934525 | − | 0.0893599i | ||||
\(538\) | 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 | ||||||||
\(543\) | 860.752 | − | 82.3057i | 0.0680265 | − | 0.00650475i | ||||
\(544\) | 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 | ||||||||
\(549\) | 13997.5 | − | 12135.4i | 1.08816 | − | 0.943396i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1918.48 | − | 3322.90i | −0.148330 | − | 0.256915i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7861.91 | + | 4328.97i | −0.604561 | + | 0.332887i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8163.09 | + | 3726.67i | 0.624331 | + | 0.285024i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4710.38i | 0.358322i | 0.983820 | + | 0.179161i | \(0.0573383\pi\) | ||||
−0.983820 | + | 0.179161i | \(0.942662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2913.11i | − | 0.220414i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2703.98 | − | 3796.16i | −0.203498 | − | 0.285693i | ||||
\(562\) | 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 | ||||||||
\(567\) | 4769.39 | + | 12630.8i | 0.353255 | + | 0.935527i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6667.01 | + | 3849.20i | −0.491205 | + | 0.283597i | −0.725074 | − | 0.688671i | \(-0.758195\pi\) |
0.233869 | + | 0.972268i | \(0.424861\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 6122.62 | + | 8595.64i | 0.446381 | + | 0.626680i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6201.77i | − | 0.449794i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2389.01i | 0.172367i | 0.996279 | + | 0.0861834i | \(0.0274671\pi\) | ||||
−0.996279 | + | 0.0861834i | \(0.972533\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2374.00 | − | 1083.79i | −0.170398 | − | 0.0777910i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11496.7 | − | 6330.38i | 0.820935 | − | 0.452028i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4769.48 | + | 8260.97i | 0.338819 | + | 0.586852i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3217.24 | − | 2789.23i | 0.227379 | − | 0.197129i | ||||
\(586\) | 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 | ||||||||
\(591\) | 20427.0 | − | 1953.24i | 1.42175 | − | 0.135949i | ||||
\(592\) | 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 | ||||||||
\(597\) | 3257.21 | − | 311.457i | 0.223298 | − | 0.0213519i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13069.6 | − | 7545.75i | −0.891504 | − | 0.514710i | −0.0170695 | − | 0.999854i | \(-0.505434\pi\) |
−0.874434 | + | 0.485145i | \(0.838767\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21885.4 | + | 12635.5i | −1.48540 | + | 0.857595i | −0.999862 | − | 0.0166219i | \(-0.994709\pi\) |
−0.485536 | + | 0.874217i | \(0.661376\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3025.78 | − | 8749.83i | 0.204343 | − | 0.590913i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2210.44 | − | 3828.59i | −0.148541 | − | 0.257280i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16922.0 | + | 9769.93i | 1.13154 | + | 0.653293i | 0.944321 | − | 0.329025i | \(-0.106720\pi\) |
0.187216 | + | 0.982319i | \(0.440053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10926.7 | + | 7453.79i | −0.727048 | + | 0.495965i | ||||
\(610\) | 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 | ||||||||
\(615\) | 1037.51 | − | 739.013i | 0.0680268 | − | 0.0484551i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24539.5 | − | 14167.9i | −1.60117 | − | 0.924437i | −0.991253 | − | 0.131974i | \(-0.957868\pi\) |
−0.609920 | − | 0.792463i | \(-0.708798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17347.3 | + | 10015.5i | −1.12641 | + | 0.650332i | −0.943029 | − | 0.332710i | \(-0.892037\pi\) |
−0.183379 | + | 0.983042i | \(0.558703\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2301.08 | − | 9501.48i | 0.148694 | − | 0.613979i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 52.9157 | − | 2609.51i | 0.00340292 | − | 0.167813i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1710.61 | + | 2962.87i | −0.109479 | + | 0.189624i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5372.61 | + | 3826.88i | −0.342203 | + | 0.243749i | ||||
\(628\) | 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 | ||||||||
\(633\) | 14132.9 | + | 6452.03i | 0.887412 | + | 0.405127i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 961.643 | − | 1665.61i | 0.0600970 | − | 0.104091i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7618.45 | + | 4820.54i | 0.473868 | + | 0.299838i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1982.61 | − | 10272.3i | −0.122740 | − | 0.635939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14946.4 | + | 8629.29i | −0.920976 | + | 0.531726i | −0.883946 | − | 0.467588i | \(-0.845123\pi\) |
−0.0370299 | + | 0.999314i | \(0.511790\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21951.3 | − | 12673.6i | −1.34631 | − | 0.777291i | −0.358584 | − | 0.933498i | \(-0.616740\pi\) |
−0.987724 | + | 0.156206i | \(0.950074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −328.903 | − | 3439.66i | −0.0200784 | − | 0.209979i | ||||
\(646\) | 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 | ||||||||
\(651\) | 13838.1 | + | 6659.70i | 0.833112 | + | 0.400943i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19452.8 | + | 11231.1i | 1.16577 | + | 0.673058i | 0.952680 | − | 0.303975i | \(-0.0983139\pi\) |
0.213090 | + | 0.977033i | \(0.431647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1841.42 | − | 3189.43i | −0.109848 | − | 0.190262i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1129.37 | + | 5851.47i | 0.0670637 | + | 0.347470i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3236.46 | − | 1868.57i | 0.191312 | − | 0.110454i | −0.401285 | − | 0.915953i | \(-0.631436\pi\) |
0.592597 | + | 0.805499i | \(0.298103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10205.8 | − | 5892.33i | −0.600545 | − | 0.346725i | 0.168711 | − | 0.985666i | \(-0.446040\pi\) |
−0.769256 | + | 0.638941i | \(0.779373\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1118.79 | − | 2450.65i | 0.0655356 | − | 0.143553i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1605.17 | + | 2654.46i | −0.0936030 | + | 0.154790i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9577.50 | 0.555986 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9850.20 | − | 13828.8i | −0.569254 | − | 0.799184i | ||||
\(670\) | 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 | ||||||||
\(675\) | −8613.09 | + | 9040.26i | −0.491138 | + | 0.515496i | ||||
\(676\) | 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 | ||||||||
\(679\) | −13453.9 | − | 24433.9i | −0.760404 | − | 1.38098i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24012.7 | − | 17104.1i | 1.35120 | − | 0.962454i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18482.4i | − | 1.03545i | −0.855548 | − | 0.517723i | \(-0.826780\pi\) | ||
0.855548 | − | 0.517723i | \(-0.173220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10502.1i | − | 0.585786i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11284.0 | − | 24717.0i | 0.626652 | − | 1.37265i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2756.82 | + | 4774.94i | −0.152433 | + | 0.264022i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16408.4 | − | 9473.38i | 0.903334 | − | 0.521540i | 0.0250537 | − | 0.999686i | \(-0.492024\pi\) |
0.878280 | + | 0.478146i | \(0.158691\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14543.9 | + | 17479.4i | 0.797223 | + | 0.958134i | ||||
\(694\) | 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 | ||||||||
\(699\) | 17761.7 | − | 1698.39i | 0.961103 | − | 0.0919013i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9045.09i | 0.487344i | 0.969858 | + | 0.243672i | \(0.0783521\pi\) | ||||
−0.969858 | + | 0.243672i | \(0.921648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8035.08i | − | 0.431079i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −650.890 | − | 6807.00i | −0.0347715 | − | 0.363640i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29965.2 | − | 16499.6i | 1.59400 | − | 0.877698i | ||||
\(708\) | 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 | ||||||||
\(711\) | −8570.95 | − | 9886.16i | −0.452089 | − | 0.521463i | ||||
\(712\) | 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 | ||||||||
\(717\) | 1170.33 | − | 2563.55i | 0.0609578 | − | 0.133525i | ||||
\(718\) | 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 | ||||||||
\(723\) | 10827.0 | + | 15200.2i | 0.556929 | + | 0.781881i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10593.9 | − | 6116.37i | −0.542685 | − | 0.313319i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2328.92 | − | 1344.60i | 0.118810 | − | 0.0685951i | −0.439417 | − | 0.898283i | \(-0.644815\pi\) |
0.558227 | + | 0.829688i | \(0.311482\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16550.0 | + | 10654.5i | −0.840828 | + | 0.541302i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1093.07 | − | 1893.25i | −0.0553060 | − | 0.0957928i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10520.4 | + | 6073.96i | 0.530123 | + | 0.306066i | 0.741066 | − | 0.671432i | \(-0.234320\pi\) |
−0.210944 | + | 0.977498i | \(0.567654\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9539.76 | + | 4831.70i | 0.478748 | + | 0.242476i | ||||
\(736\) | 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 | ||||||||
\(741\) | −3468.35 | − | 1583.39i | −0.171947 | − | 0.0784985i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21381.5 | + | 12344.6i | 1.05573 | + | 0.609529i | 0.924249 | − | 0.381790i | \(-0.124692\pi\) |
0.131485 | + | 0.991318i | \(0.458025\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14995.2 | + | 8657.49i | −0.737426 | + | 0.425753i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12533.5 | + | 14456.8i | 0.613893 | + | 0.708095i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5240.10 | + | 106.259i | 0.255633 | + | 0.00518373i | ||||
\(750\) | 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 | ||||||||
\(753\) | −2143.80 | − | 22419.9i | −0.103751 | − | 1.08503i | ||||
\(754\) | 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 | ||||||||
\(759\) | −1567.24 | − | 16390.2i | −0.0749502 | − | 0.783829i | ||||
\(760\) | 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 | ||||||||
\(763\) | −685.783 | + | 33819.0i | −0.0325387 | + | 1.60463i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1044.32 | − | 3019.93i | 0.0493562 | − | 0.142727i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18842.0 | + | 10878.5i | −0.887023 | + | 0.512123i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30695.1 | − | 17721.8i | −1.43939 | − | 0.831034i | −0.441586 | − | 0.897219i | \(-0.645584\pi\) |
−0.997807 | + | 0.0661849i | \(0.978917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31035.5 | + | 14168.5i | 1.44970 | + | 0.661825i | ||||
\(772\) | 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 | ||||||||
\(777\) | −27621.0 | + | 2077.01i | −1.27529 | + | 0.0958974i | ||||
\(778\) | 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 | ||||||||
\(783\) | −13961.0 | − | 13301.3i | −0.637199 | − | 0.607090i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6540.73 | + | 3776.29i | −0.297387 | + | 0.171696i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3906.63 | + | 2255.49i | 0.176946 | + | 0.102160i | 0.585857 | − | 0.810415i | \(-0.300758\pi\) |
−0.408911 | + | 0.912574i | \(0.634091\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21842.4 | − | 30664.9i | −0.985566 | − | 1.38365i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9027.72 | − | 14929.1i | 0.405801 | − | 0.671070i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18034.4 | 0.807592 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2716.00 | + | 5949.28i | −0.121166 | + | 0.265408i | ||||
\(796\) | 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 | ||||||||
\(801\) | 3736.14 | − | 721.097i | 0.164806 | − | 0.0318086i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5018.45 | + | 8692.21i | 0.220544 | + | 0.381994i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3734.81 | − | 6782.85i | −0.163521 | − | 0.296974i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1709.29 | + | 17875.7i | 0.0745598 | + | 0.779745i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 42276.5i | − | 1.83728i | −0.395091 | − | 0.918642i | \(-0.629287\pi\) | ||
0.395091 | − | 0.918642i | \(-0.370713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29402.1i | − | 1.27305i | −0.771254 | − | 0.636527i | \(-0.780370\pi\) | ||
0.771254 | − | 0.636527i | \(-0.219630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12782.9 | − | 1222.31i | 0.551436 | − | 0.0527286i | ||||
\(814\) | 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 | ||||||||
\(819\) | −4546.44 | + | 12331.9i | −0.193975 | + | 0.526144i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36104.3 | − | 20844.8i | 1.53477 | − | 0.886103i | 0.535643 | − | 0.844445i | \(-0.320069\pi\) |
0.999132 | − | 0.0416579i | \(-0.0132640\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | −8733.52 | + | 19130.4i | −0.368560 | + | 0.807315i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7260.76i | − | 0.305298i | −0.988280 | − | 0.152649i | \(-0.951220\pi\) | ||
0.988280 | − | 0.152649i | \(-0.0487804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26509.9i | 1.11065i | 0.831634 | + | 0.555324i | \(0.187406\pi\) | ||||
−0.831634 | + | 0.555324i | \(0.812594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19103.1 | − | 13607.1i | 0.797450 | − | 0.568019i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6760.08 | + | 274.275i | 0.281180 | + | 0.0114082i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1720.63 | + | 2980.22i | 0.0713113 | + | 0.123515i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5269.78 | + | 21759.7i | −0.217623 | + | 0.898594i | ||||
\(838\) | 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 | ||||||||
\(843\) | −7276.92 | − | 10216.2i | −0.297308 | − | 0.417395i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9036.78 | −0.367899 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11677.1 | + | 7061.25i | 0.473708 | + | 0.286455i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9702.03 | − | 21251.9i | 0.392194 | − | 0.859083i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17369.5 | + | 10028.3i | 0.699669 | + | 0.403954i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13168.8 | − | 7603.02i | 0.528596 | − | 0.305185i | −0.211849 | − | 0.977302i | \(-0.567948\pi\) |
0.740444 | + | 0.672118i | \(0.234615\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4274.03 | − | 1478.00i | −0.170958 | − | 0.0591189i | ||||
\(856\) | 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 | 0.912555 | − | 0.408954i | \(-0.134107\pi\) |
0.102112 | + | 0.994773i | \(0.467440\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1705.08 | + | 3542.95i | −0.0674901 | + | 0.140236i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36862.0i | 1.45399i | 0.686640 | + | 0.726997i | \(0.259085\pi\) | ||||
−0.686640 | + | 0.726997i | \(0.740915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23173.4 | −0.910888 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2237.55 | + | 23400.3i | 0.0876485 | + | 0.916627i | ||||
\(868\) | 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 | ||||||||
\(873\) | 30725.0 | − | 26637.5i | 1.19116 | − | 1.03269i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −482.109 | + | 23775.0i | −0.0186266 | + | 0.918560i | ||||
\(876\) | 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 | ||||||||
\(879\) | −14838.9 | − | 6774.36i | −0.569402 | − | 0.259947i | ||||
\(880\) | 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 | ||||||||
\(885\) | −21019.6 | + | 14972.1i | −0.798378 | + | 0.568680i | ||||
\(886\) | 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 | ||||||||
\(889\) | −120.359 | + | 5935.47i | −0.00454075 | + | 0.223925i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20478.3 | + | 26068.4i | −0.769977 | + | 0.980163i | ||||
\(892\) | 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 | ||||||||
\(897\) | 7751.55 | − | 5521.38i | 0.288536 | − | 0.205522i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21933.8 | −0.813717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4137.70i | 0.152993i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6010.50 | + | 8810.94i | 0.221503 | + | 0.324706i | ||||
\(904\) | 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 | ||||||||
\(909\) | 32667.7 | + | 37680.6i | 1.19199 | + | 1.37490i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27338.9 | + | 15784.1i | −0.994266 | + | 0.574040i | −0.906547 | − | 0.422105i | \(-0.861291\pi\) |
−0.0877196 | + | 0.996145i | \(0.527958\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27907.2 | + | 16112.2i | 1.01160 | + | 0.584050i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21294.2 | − | 2036.16i | 0.769359 | − | 0.0735666i | ||||
\(916\) | 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 | ||||||||
\(921\) | −53246.4 | + | 5091.45i | −1.90502 | + | 0.182160i | ||||
\(922\) | 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 | ||||||||
\(927\) | 20521.7 | + | 7096.62i | 0.727100 | + | 0.251439i | ||||
\(928\) | 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 | ||||||||
\(931\) | 388.174 | − | 9567.38i | 0.0136648 | − | 0.336797i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37253.3 | + | 17007.1i | 1.30720 | + | 0.596771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5381.68i | − | 0.188235i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 34791.9i | − | 1.21302i | −0.795075 | − | 0.606511i | \(-0.792569\pi\) | ||
0.795075 | − | 0.606511i | \(-0.207431\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24704.0 | − | 34682.2i | −0.858555 | − | 1.20534i | ||||
\(940\) | 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 | ||||||||
\(945\) | −3975.90 | + | 15074.2i | −0.136863 | + | 0.518905i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26402.6 | + | 15243.5i | −0.905985 | + | 0.523071i | −0.879137 | − | 0.476569i | \(-0.841880\pi\) |
−0.0268478 | + | 0.999640i | \(0.508547\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2900.72 | + | 5024.20i | −0.0992218 | + | 0.171857i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26423.4 | − | 37096.2i | −0.900987 | − | 1.26491i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21378.9i | 0.726685i | 0.931656 | + | 0.363343i | \(0.118365\pi\) | ||||
−0.931656 | + | 0.363343i | \(0.881635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12185.7i | 0.412902i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29543.4 | − | 13487.3i | −0.997912 | − | 0.455573i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15636.1 | + | 28396.9i | 0.526502 | + | 0.956189i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2162.36 | − | 3745.31i | −0.0725842 | − | 0.125720i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1448.02 | + | 7502.45i | 0.0484546 | + | 0.251052i | ||||
\(964\) | 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 | ||||||||
\(969\) | −2848.24 | + | 272.350i | −0.0944257 | + | 0.00902905i | ||||
\(970\) | 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 | ||||||||
\(975\) | −12100.2 | + | 1157.03i | −0.397453 | + | 0.0380047i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3157.95 | − | 1823.24i | −0.103410 | − | 0.0597038i | 0.447403 | − | 0.894332i | \(-0.352349\pi\) |
−0.550813 | + | 0.834629i | \(0.685682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5549.94 | − | 3204.26i | 0.181182 | − | 0.104605i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48420.0 | + | 9345.36i | −1.57587 | + | 0.304153i | ||||
\(982\) | 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 | ||||||||
\(987\) | 11894.6 | + | 17436.6i | 0.383596 | + | 0.562324i | ||||
\(988\) | 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 | ||||||||
\(993\) | −29048.2 | + | 20690.9i | −0.928316 | + | 0.661234i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3272.03 | + | 1889.11i | 0.104252 | + | 0.0601897i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35961.0 | − | 20762.1i | 1.14232 | − | 0.659520i | 0.195318 | − | 0.980740i | \(-0.437426\pi\) |
0.947005 | + | 0.321220i | \(0.104093\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11392.0 | − | 38741.1i | −0.360786 | − | 1.22694i |
(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 | 252.4.x.a.41.10 | ✓ | 48 | |
3.2 | odd | 2 | 756.4.x.a.125.9 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.41.15 | yes | 48 | |
9.2 | odd | 6 | inner | 252.4.x.a.209.15 | yes | 48 | |
9.4 | even | 3 | 2268.4.f.a.1133.17 | 48 | |||
9.5 | odd | 6 | 2268.4.f.a.1133.32 | 48 | |||
9.7 | even | 3 | 756.4.x.a.629.16 | 48 | |||
21.20 | even | 2 | 756.4.x.a.125.16 | 48 | |||
63.13 | odd | 6 | 2268.4.f.a.1133.31 | 48 | |||
63.20 | even | 6 | inner | 252.4.x.a.209.10 | yes | 48 | |
63.34 | odd | 6 | 756.4.x.a.629.9 | 48 | |||
63.41 | even | 6 | 2268.4.f.a.1133.18 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.10 | ✓ | 48 | 1.1 | even | 1 | trivial | |
252.4.x.a.41.15 | yes | 48 | 7.6 | odd | 2 | inner | |
252.4.x.a.209.10 | yes | 48 | 63.20 | even | 6 | inner | |
252.4.x.a.209.15 | yes | 48 | 9.2 | odd | 6 | inner | |
756.4.x.a.125.9 | 48 | 3.2 | odd | 2 | |||
756.4.x.a.125.16 | 48 | 21.20 | even | 2 | |||
756.4.x.a.629.9 | 48 | 63.34 | odd | 6 | |||
756.4.x.a.629.16 | 48 | 9.7 | even | 3 | |||
2268.4.f.a.1133.17 | 48 | 9.4 | even | 3 | |||
2268.4.f.a.1133.18 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.31 | 48 | 63.13 | odd | 6 | |||
2268.4.f.a.1133.32 | 48 | 9.5 | odd | 6 |