Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,4,Mod(37,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.d (of order \(2\), degree \(1\), 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: | \(4.24813752041\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.8248384.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + x^{4} - 12x^{3} + 4x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(1.88322 - 0.673417i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.37 |
Dual form | 72.4.d.d.37.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55664 | − | 1.20980i | −0.903907 | − | 0.427729i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.07277 | + | 6.18604i | 0.634096 | + | 0.773255i | ||||
\(5\) | 0.612661i | 0.0547981i | 0.999625 | + | 0.0273990i | \(0.00872248\pi\) | ||||
−0.999625 | + | 0.0273990i | \(0.991278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.7441 | −1.22807 | −0.614034 | − | 0.789279i | \(-0.710454\pi\) | ||||
−0.614034 | + | 0.789279i | \(0.710454\pi\) | |||||||
\(8\) | −5.48534 | − | 21.9525i | −0.242420 | − | 0.970171i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.741198 | − | 1.56635i | 0.0234387 | − | 0.0495324i | ||||
\(11\) | 60.2630i | 1.65182i | 0.563805 | + | 0.825908i | \(0.309337\pi\) | ||||
−0.563805 | + | 0.825908i | \(0.690663\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.9062i | 1.12873i | 0.825524 | + | 0.564367i | \(0.190880\pi\) | ||||
−0.825524 | + | 0.564367i | \(0.809120\pi\) | |||||||
\(14\) | 58.1485 | + | 27.5159i | 1.11006 | + | 0.525281i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.5341 | + | 62.7606i | −0.195845 | + | 0.980635i | ||||
\(17\) | −47.1643 | −0.672883 | −0.336442 | − | 0.941704i | \(-0.609223\pi\) | ||||
−0.336442 | + | 0.941704i | \(0.609223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.1643i | 0.352144i | 0.984377 | + | 0.176072i | \(0.0563392\pi\) | ||||
−0.984377 | + | 0.176072i | \(0.943661\pi\) | |||||||
\(20\) | −3.78994 | + | 3.10789i | −0.0423729 | + | 0.0347472i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 72.9062 | − | 154.070i | 0.706529 | − | 1.49309i | ||||
\(23\) | −109.488 | −0.992604 | −0.496302 | − | 0.868150i | \(-0.665309\pi\) | ||||
−0.496302 | + | 0.868150i | \(0.665309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 124.625 | 0.996997 | ||||||||
\(26\) | 64.0059 | − | 135.262i | 0.482792 | − | 1.02027i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −115.376 | − | 140.696i | −0.778713 | − | 0.949609i | ||||
\(29\) | 10.4250i | 0.0667542i | 0.999443 | + | 0.0333771i | \(0.0106262\pi\) | ||||
−0.999443 | + | 0.0333771i | \(0.989374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −220.881 | −1.27972 | −0.639860 | − | 0.768492i | \(-0.721008\pi\) | ||||
−0.639860 | + | 0.768492i | \(0.721008\pi\) | |||||||
\(32\) | 107.973 | − | 145.292i | 0.596472 | − | 0.802634i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 120.582 | + | 57.0593i | 0.608224 | + | 0.287812i | ||||
\(35\) | − | 13.9345i | − | 0.0672958i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 408.348i | − | 1.81438i | −0.420725 | − | 0.907188i | \(-0.638224\pi\) | ||
0.420725 | − | 0.907188i | \(-0.361776\pi\) | |||||||
\(38\) | 35.2829 | − | 74.5624i | 0.150622 | − | 0.318306i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.4494 | − | 3.36066i | 0.0531635 | − | 0.0132842i | ||||
\(41\) | 360.742 | 1.37411 | 0.687054 | − | 0.726606i | \(-0.258903\pi\) | ||||
0.687054 | + | 0.726606i | \(0.258903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 236.414i | 0.838436i | 0.907886 | + | 0.419218i | \(0.137696\pi\) | ||||
−0.907886 | + | 0.419218i | \(0.862304\pi\) | |||||||
\(44\) | −372.789 | + | 305.700i | −1.27727 | + | 1.04741i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 279.922 | + | 132.459i | 0.897222 | + | 0.424565i | ||||
\(47\) | −129.113 | −0.400703 | −0.200352 | − | 0.979724i | \(-0.564208\pi\) | ||||
−0.200352 | + | 0.979724i | \(0.564208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 174.296 | 0.508152 | ||||||||
\(50\) | −318.620 | − | 150.771i | −0.901193 | − | 0.426445i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −327.279 | + | 268.381i | −0.872798 | + | 0.715725i | ||||
\(53\) | 117.819i | 0.305353i | 0.988276 | + | 0.152677i | \(0.0487893\pi\) | ||||
−0.988276 | + | 0.152677i | \(0.951211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −36.9208 | −0.0905163 | ||||||||
\(56\) | 124.759 | + | 499.290i | 0.297709 | + | 1.19144i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.6122 | − | 26.6529i | 0.0285527 | − | 0.0603396i | ||||
\(59\) | − | 262.854i | − | 0.580012i | −0.957025 | − | 0.290006i | \(-0.906343\pi\) | ||
0.957025 | − | 0.290006i | \(-0.0936574\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 273.465i | 0.573993i | 0.957932 | + | 0.286996i | \(0.0926568\pi\) | ||||
−0.957932 | + | 0.286996i | \(0.907343\pi\) | |||||||
\(62\) | 564.711 | + | 267.221i | 1.15675 | + | 0.547373i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −451.822 | + | 240.834i | −0.882465 | + | 0.470378i | ||||
\(65\) | −32.4135 | −0.0618524 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 89.4077i | 0.163028i | 0.996672 | + | 0.0815141i | \(0.0259756\pi\) | ||||
−0.996672 | + | 0.0815141i | \(0.974024\pi\) | |||||||
\(68\) | −239.253 | − | 291.760i | −0.426672 | − | 0.520310i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.8579 | + | 35.6253i | −0.0287844 | + | 0.0608291i | ||||
\(71\) | 350.521 | 0.585904 | 0.292952 | − | 0.956127i | \(-0.405362\pi\) | ||||
0.292952 | + | 0.956127i | \(0.405362\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 532.610 | 0.853936 | 0.426968 | − | 0.904267i | \(-0.359582\pi\) | ||||
0.426968 | + | 0.904267i | \(0.359582\pi\) | |||||||
\(74\) | −494.019 | + | 1044.00i | −0.776062 | + | 1.64003i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −180.411 | + | 147.943i | −0.272297 | + | 0.223293i | ||||
\(77\) | − | 1370.63i | − | 2.02854i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −166.561 | −0.237210 | −0.118605 | − | 0.992942i | \(-0.537842\pi\) | ||||
−0.118605 | + | 0.992942i | \(0.537842\pi\) | |||||||
\(80\) | −38.4510 | − | 7.67915i | −0.0537369 | − | 0.0107319i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −922.286 | − | 436.426i | −1.24207 | − | 0.587746i | ||||
\(83\) | 361.934i | 0.478644i | 0.970940 | + | 0.239322i | \(0.0769252\pi\) | ||||
−0.970940 | + | 0.239322i | \(0.923075\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 28.8957i | − | 0.0368727i | ||||||
\(86\) | 286.013 | − | 604.423i | 0.358623 | − | 0.757868i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1322.92 | − | 330.563i | 1.60254 | − | 0.400433i | ||||
\(89\) | −40.3285 | −0.0480316 | −0.0240158 | − | 0.999712i | \(-0.507645\pi\) | ||||
−0.0240158 | + | 0.999712i | \(0.507645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1203.31i | − | 1.38616i | ||||||
\(92\) | −555.408 | − | 677.299i | −0.629406 | − | 0.767535i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 330.095 | + | 156.201i | 0.362199 | + | 0.171392i | ||||
\(95\) | −17.8678 | −0.0192968 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −614.921 | −0.643667 | −0.321834 | − | 0.946796i | \(-0.604299\pi\) | ||||
−0.321834 | + | 0.946796i | \(0.604299\pi\) | |||||||
\(98\) | −445.612 | − | 210.864i | −0.459322 | − | 0.217351i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 632.192 | + | 770.933i | 0.632192 | + | 0.770933i | ||||
\(101\) | 1664.99i | 1.64033i | 0.572130 | + | 0.820163i | \(0.306117\pi\) | ||||
−0.572130 | + | 0.820163i | \(0.693883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 396.858 | 0.379647 | 0.189823 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189823 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(104\) | 1161.42 | − | 290.208i | 1.09506 | − | 0.273628i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 142.538 | − | 301.221i | 0.130608 | − | 0.276011i | ||||
\(107\) | 350.630i | 0.316791i | 0.987376 | + | 0.158396i | \(0.0506321\pi\) | ||||
−0.987376 | + | 0.158396i | \(0.949368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 597.009i | 0.524615i | 0.964984 | + | 0.262308i | \(0.0844835\pi\) | ||||
−0.964984 | + | 0.262308i | \(0.915516\pi\) | |||||||
\(110\) | 94.3930 | + | 44.6668i | 0.0818183 | + | 0.0387165i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 285.077 | − | 1427.44i | 0.240511 | − | 1.20429i | ||||
\(113\) | −496.422 | −0.413270 | −0.206635 | − | 0.978418i | \(-0.566251\pi\) | ||||
−0.206635 | + | 0.978418i | \(0.566251\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 67.0792i | − | 0.0543928i | ||||||
\(116\) | −64.4893 | + | 52.8835i | −0.0516180 | + | 0.0423285i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −318.001 | + | 672.023i | −0.248088 | + | 0.524277i | ||||
\(119\) | 1072.71 | 0.826346 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2300.63 | −1.72849 | ||||||||
\(122\) | 330.838 | − | 699.149i | 0.245513 | − | 0.518836i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1120.48 | − | 1366.37i | −0.811465 | − | 0.989549i | ||||
\(125\) | 152.935i | 0.109432i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1799.85 | 1.25756 | 0.628782 | − | 0.777581i | \(-0.283554\pi\) | ||||
0.628782 | + | 0.777581i | \(0.283554\pi\) | |||||||
\(128\) | 1446.50 | − | 69.1093i | 0.998861 | − | 0.0477223i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 82.8696 | + | 39.2139i | 0.0559088 | + | 0.0264561i | ||||
\(131\) | − | 1121.45i | − | 0.747949i | −0.927439 | − | 0.373974i | \(-0.877995\pi\) | ||
0.927439 | − | 0.373974i | \(-0.122005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 663.316i | − | 0.432457i | ||||||
\(134\) | 108.166 | − | 228.583i | 0.0697319 | − | 0.147362i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 258.712 | + | 1035.37i | 0.163120 | + | 0.652812i | ||||
\(137\) | −2449.55 | −1.52759 | −0.763793 | − | 0.645461i | \(-0.776665\pi\) | ||||
−0.763793 | + | 0.645461i | \(0.776665\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2457.56i | 1.49962i | 0.661652 | + | 0.749811i | \(0.269856\pi\) | ||||
−0.661652 | + | 0.749811i | \(0.730144\pi\) | |||||||
\(140\) | 86.1990 | − | 70.6862i | 0.0520368 | − | 0.0426720i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −896.153 | − | 424.060i | −0.529602 | − | 0.250608i | ||||
\(143\) | −3188.28 | −1.86446 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.38698 | −0.00365800 | ||||||||
\(146\) | −1361.69 | − | 644.352i | −0.771878 | − | 0.365253i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2526.05 | − | 2071.45i | 1.40297 | − | 1.15049i | ||||
\(149\) | 2084.96i | 1.14635i | 0.819432 | + | 0.573177i | \(0.194289\pi\) | ||||
−0.819432 | + | 0.573177i | \(0.805711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1057.80 | 0.570084 | 0.285042 | − | 0.958515i | \(-0.407992\pi\) | ||||
0.285042 | + | 0.958515i | \(0.407992\pi\) | |||||||
\(152\) | 640.228 | − | 159.976i | 0.341640 | − | 0.0853669i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1658.19 | + | 3504.20i | −0.867666 | + | 1.83361i | ||||
\(155\) | − | 135.325i | − | 0.0701262i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3193.01i | 1.62312i | 0.584270 | + | 0.811559i | \(0.301381\pi\) | ||||
−0.584270 | + | 0.811559i | \(0.698619\pi\) | |||||||
\(158\) | 425.836 | + | 201.506i | 0.214416 | + | 0.101461i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 89.0149 | + | 66.1508i | 0.0439828 | + | 0.0326855i | ||||
\(161\) | 2490.22 | 1.21899 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 846.854i | − | 0.406937i | −0.979081 | − | 0.203469i | \(-0.934779\pi\) | ||
0.979081 | − | 0.203469i | \(-0.0652215\pi\) | |||||||
\(164\) | 1829.96 | + | 2231.56i | 0.871316 | + | 1.06254i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 437.868 | − | 925.334i | 0.204730 | − | 0.432650i | ||||
\(167\) | 2630.15 | 1.21873 | 0.609363 | − | 0.792892i | \(-0.291425\pi\) | ||||
0.609363 | + | 0.792892i | \(0.291425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −602.062 | −0.274038 | ||||||||
\(170\) | −34.9580 | + | 73.8758i | −0.0157715 | + | 0.0333295i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1462.46 | + | 1199.27i | −0.648324 | + | 0.531648i | ||||
\(173\) | − | 429.843i | − | 0.188904i | −0.995529 | − | 0.0944519i | \(-0.969890\pi\) | ||
0.995529 | − | 0.0944519i | \(-0.0301099\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2834.48 | −1.22438 | ||||||||
\(176\) | −3782.14 | − | 755.341i | −1.61983 | − | 0.323500i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 103.105 | + | 48.7895i | 0.0434161 | + | 0.0205445i | ||||
\(179\) | 1516.30i | 0.633149i | 0.948568 | + | 0.316574i | \(0.102533\pi\) | ||||
−0.948568 | + | 0.316574i | \(0.897467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3380.20i | − | 1.38811i | −0.719921 | − | 0.694056i | \(-0.755822\pi\) | ||
0.719921 | − | 0.694056i | \(-0.244178\pi\) | |||||||
\(182\) | −1455.76 | + | 3076.41i | −0.592901 | + | 1.25296i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 600.581 | + | 2403.54i | 0.240627 | + | 0.962996i | ||||
\(185\) | 250.179 | 0.0994244 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2842.26i | − | 1.11148i | ||||||
\(188\) | −654.960 | − | 798.697i | −0.254084 | − | 0.309846i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 45.6815 | + | 21.6165i | 0.0174425 | + | 0.00825381i | ||||
\(191\) | 2799.71 | 1.06063 | 0.530314 | − | 0.847801i | \(-0.322074\pi\) | ||||
0.530314 | + | 0.847801i | \(0.322074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 624.106 | 0.232768 | 0.116384 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116384 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(194\) | 1572.13 | + | 743.931i | 0.581816 | + | 0.275315i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 884.164 | + | 1078.20i | 0.322217 | + | 0.392931i | ||||
\(197\) | − | 4779.25i | − | 1.72846i | −0.503094 | − | 0.864232i | \(-0.667805\pi\) | ||
0.503094 | − | 0.864232i | \(-0.332195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2615.92 | 0.931846 | 0.465923 | − | 0.884825i | \(-0.345722\pi\) | ||||
0.465923 | + | 0.884825i | \(0.345722\pi\) | |||||||
\(200\) | −683.609 | − | 2735.82i | −0.241692 | − | 0.967258i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2014.31 | − | 4256.78i | 0.701615 | − | 1.48270i | ||||
\(203\) | − | 237.107i | − | 0.0819787i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 221.013i | 0.0752985i | ||||||||
\(206\) | −1014.62 | − | 480.119i | −0.343165 | − | 0.162386i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3320.42 | − | 663.131i | −1.10687 | − | 0.221057i | ||||
\(209\) | −1757.52 | −0.581677 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1745.78i | − | 0.569595i | −0.958588 | − | 0.284798i | \(-0.908074\pi\) | ||
0.958588 | − | 0.284798i | \(-0.0919264\pi\) | |||||||
\(212\) | −728.834 | + | 597.670i | −0.236116 | + | 0.193623i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 424.192 | − | 896.432i | 0.135501 | − | 0.286350i | ||||
\(215\) | −144.841 | −0.0459447 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5023.74 | 1.57158 | ||||||||
\(218\) | 722.261 | − | 1526.33i | 0.224393 | − | 0.474203i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −187.290 | − | 228.393i | −0.0573960 | − | 0.0699921i | ||||
\(221\) | − | 2495.28i | − | 0.759505i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3385.60 | −1.01667 | −0.508333 | − | 0.861161i | \(-0.669738\pi\) | ||||
−0.508333 | + | 0.861161i | \(0.669738\pi\) | |||||||
\(224\) | −2455.75 | + | 3304.55i | −0.732508 | + | 0.985690i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1269.17 | + | 600.572i | 0.373557 | + | 0.176767i | ||||
\(227\) | − | 3847.72i | − | 1.12503i | −0.826787 | − | 0.562515i | \(-0.809834\pi\) | ||
0.826787 | − | 0.562515i | \(-0.190166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1335.15i | 0.385279i | 0.981270 | + | 0.192640i | \(0.0617049\pi\) | ||||
−0.981270 | + | 0.192640i | \(0.938295\pi\) | |||||||
\(230\) | −81.1525 | + | 171.497i | −0.0232654 | + | 0.0491660i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 228.854 | − | 57.1846i | 0.0647630 | − | 0.0161826i | ||||
\(233\) | 5146.38 | 1.44700 | 0.723499 | − | 0.690325i | \(-0.242532\pi\) | ||||
0.723499 | + | 0.690325i | \(0.242532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 79.1025i | − | 0.0219578i | ||||||
\(236\) | 1626.03 | − | 1333.40i | 0.448497 | − | 0.367783i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2742.53 | − | 1297.77i | −0.746940 | − | 0.353452i | ||||
\(239\) | −7085.07 | −1.91755 | −0.958777 | − | 0.284160i | \(-0.908285\pi\) | ||||
−0.958777 | + | 0.284160i | \(0.908285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2538.40 | 0.678476 | 0.339238 | − | 0.940701i | \(-0.389831\pi\) | ||||
0.339238 | + | 0.940701i | \(0.389831\pi\) | |||||||
\(242\) | 5881.86 | + | 2783.30i | 1.56240 | + | 0.739327i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1691.66 | + | 1387.22i | −0.443843 | + | 0.363966i | ||||
\(245\) | 106.784i | 0.0278458i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1542.97 | −0.397477 | ||||||||
\(248\) | 1211.61 | + | 4848.87i | 0.310230 | + | 1.24155i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 185.021 | − | 391.000i | 0.0468071 | − | 0.0989160i | ||||
\(251\) | 1696.99i | 0.426746i | 0.976971 | + | 0.213373i | \(0.0684449\pi\) | ||||
−0.976971 | + | 0.213373i | \(0.931555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6598.09i | − | 1.63960i | ||||||
\(254\) | −4601.56 | − | 2177.46i | −1.13672 | − | 0.537897i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3781.79 | − | 1573.29i | −0.923289 | − | 0.384105i | ||||
\(257\) | 382.902 | 0.0929369 | 0.0464685 | − | 0.998920i | \(-0.485203\pi\) | ||||
0.0464685 | + | 0.998920i | \(0.485203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9287.52i | 2.22818i | ||||||||
\(260\) | −164.426 | − | 200.511i | −0.0392203 | − | 0.0478276i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1356.73 | + | 2867.13i | −0.319919 | + | 0.676076i | ||||
\(263\) | 5002.02 | 1.17277 | 0.586383 | − | 0.810034i | \(-0.300551\pi\) | ||||
0.586383 | + | 0.810034i | \(0.300551\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −72.1833 | −0.0167328 | ||||||||
\(266\) | −802.480 | + | 1695.86i | −0.184974 | + | 0.390901i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −553.079 | + | 453.545i | −0.126062 | + | 0.103376i | ||||
\(269\) | 6117.47i | 1.38658i | 0.720661 | + | 0.693288i | \(0.243839\pi\) | ||||
−0.720661 | + | 0.693288i | \(0.756161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3956.12 | −0.886780 | −0.443390 | − | 0.896329i | \(-0.646224\pi\) | ||||
−0.443390 | + | 0.896329i | \(0.646224\pi\) | |||||||
\(272\) | 591.161 | − | 2960.06i | 0.131781 | − | 0.659853i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6262.61 | + | 2963.47i | 1.38080 | + | 0.653393i | ||||
\(275\) | 7510.25i | 1.64686i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4842.17i | 1.05032i | 0.851004 | + | 0.525158i | \(0.175994\pi\) | ||||
−0.851004 | + | 0.525158i | \(0.824006\pi\) | |||||||
\(278\) | 2973.16 | − | 6283.09i | 0.641432 | − | 1.35552i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −305.896 | + | 76.4353i | −0.0652884 | + | 0.0163139i | ||||
\(281\) | −1878.68 | −0.398835 | −0.199417 | − | 0.979915i | \(-0.563905\pi\) | ||||
−0.199417 | + | 0.979915i | \(0.563905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5724.87i | 1.20250i | 0.799060 | + | 0.601251i | \(0.205331\pi\) | ||||
−0.799060 | + | 0.601251i | \(0.794669\pi\) | |||||||
\(284\) | 1778.11 | + | 2168.33i | 0.371519 | + | 0.453053i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8151.27 | + | 3857.19i | 1.68530 | + | 0.797483i | ||||
\(287\) | −8204.77 | −1.68750 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2688.53 | −0.547228 | ||||||||
\(290\) | 16.3292 | + | 7.72697i | 0.00330649 | + | 0.00156463i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2701.81 | + | 3294.75i | 0.541477 | + | 0.660310i | ||||
\(293\) | 5088.75i | 1.01464i | 0.861759 | + | 0.507318i | \(0.169363\pi\) | ||||
−0.861759 | + | 0.507318i | \(0.830637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 161.041 | 0.0317836 | ||||||||
\(296\) | −8964.24 | + | 2239.93i | −1.76026 | + | 0.439842i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2522.39 | − | 5330.49i | 0.490329 | − | 1.03620i | ||||
\(299\) | − | 5792.61i | − | 1.12038i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 5377.02i | − | 1.02966i | ||||||
\(302\) | −2704.41 | − | 1279.73i | −0.515303 | − | 0.243841i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1830.37 | − | 365.547i | −0.345325 | − | 0.0689657i | ||||
\(305\) | −167.541 | −0.0314537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7219.21i | − | 1.34209i | −0.741416 | − | 0.671046i | \(-0.765845\pi\) | ||
0.741416 | − | 0.671046i | \(-0.234155\pi\) | |||||||
\(308\) | 8478.76 | − | 6952.88i | 1.56858 | − | 1.28629i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −163.716 | + | 345.976i | −0.0299950 | + | 0.0633875i | ||||
\(311\) | 1537.06 | 0.280252 | 0.140126 | − | 0.990134i | \(-0.455249\pi\) | ||||
0.140126 | + | 0.990134i | \(0.455249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2200.93 | −0.397456 | −0.198728 | − | 0.980055i | \(-0.563681\pi\) | ||||
−0.198728 | + | 0.980055i | \(0.563681\pi\) | |||||||
\(314\) | 3862.90 | − | 8163.35i | 0.694255 | − | 1.46715i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −844.925 | − | 1030.35i | −0.150414 | − | 0.183424i | ||||
\(317\) | 2840.41i | 0.503260i | 0.967824 | + | 0.251630i | \(0.0809665\pi\) | ||||
−0.967824 | + | 0.251630i | \(0.919033\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −628.240 | −0.110266 | ||||||||
\(320\) | −147.549 | − | 276.814i | −0.0257758 | − | 0.0483574i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6366.58 | − | 3012.67i | −1.10185 | − | 0.521395i | ||||
\(323\) | − | 1375.51i | − | 0.236952i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6593.41i | 1.12534i | ||||||||
\(326\) | −1024.52 | + | 2165.10i | −0.174059 | + | 0.367833i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1978.79 | − | 7919.18i | −0.333112 | − | 1.33312i | ||||
\(329\) | 2936.56 | 0.492091 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2118.52i | − | 0.351795i | −0.984408 | − | 0.175898i | \(-0.943717\pi\) | ||
0.984408 | − | 0.175898i | \(-0.0562828\pi\) | |||||||
\(332\) | −2238.94 | + | 1836.01i | −0.370114 | + | 0.303506i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6724.33 | − | 3181.96i | −1.10161 | − | 0.521284i | ||||
\(335\) | −54.7766 | −0.00893364 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −659.599 | −0.106619 | −0.0533096 | − | 0.998578i | \(-0.516977\pi\) | ||||
−0.0533096 | + | 0.998578i | \(0.516977\pi\) | |||||||
\(338\) | 1539.25 | + | 728.375i | 0.247705 | + | 0.117214i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 178.750 | − | 146.581i | 0.0285120 | − | 0.0233808i | ||||
\(341\) | − | 13310.9i | − | 2.11386i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3837.03 | 0.604023 | ||||||||
\(344\) | 5189.86 | − | 1296.81i | 0.813426 | − | 0.203254i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −520.024 | + | 1098.95i | −0.0807996 | + | 0.170751i | ||||
\(347\) | 8377.42i | 1.29603i | 0.761626 | + | 0.648017i | \(0.224401\pi\) | ||||
−0.761626 | + | 0.648017i | \(0.775599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3254.18i | − | 0.499119i | −0.968360 | − | 0.249559i | \(-0.919714\pi\) | ||
0.968360 | − | 0.249559i | \(-0.0802857\pi\) | |||||||
\(350\) | 7246.73 | + | 3429.16i | 1.10673 | + | 0.523703i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8755.74 | + | 6506.77i | 1.32580 | + | 0.985261i | ||||
\(353\) | −11117.5 | −1.67627 | −0.838137 | − | 0.545459i | \(-0.816355\pi\) | ||||
−0.838137 | + | 0.545459i | \(0.816355\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 214.750i | 0.0321064i | ||||||||
\(356\) | −204.577 | − | 249.474i | −0.0304566 | − | 0.0371407i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1834.42 | − | 3876.63i | 0.270816 | − | 0.572308i | ||||
\(359\) | 4756.56 | 0.699281 | 0.349640 | − | 0.936884i | \(-0.386304\pi\) | ||||
0.349640 | + | 0.936884i | \(0.386304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6008.45 | 0.875994 | ||||||||
\(362\) | −4089.37 | + | 8641.94i | −0.593736 | + | 1.25472i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7443.69 | − | 6104.09i | 1.07186 | − | 0.878959i | ||||
\(365\) | 326.310i | 0.0467940i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1837.40 | 0.261339 | 0.130670 | − | 0.991426i | \(-0.458287\pi\) | ||||
0.130670 | + | 0.991426i | \(0.458287\pi\) | |||||||
\(368\) | 1372.34 | − | 6871.55i | 0.194397 | − | 0.973382i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −639.616 | − | 302.666i | −0.0898704 | − | 0.0425267i | ||||
\(371\) | − | 2679.70i | − | 0.374995i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5598.07i | 0.777097i | 0.921428 | + | 0.388549i | \(0.127023\pi\) | ||||
−0.921428 | + | 0.388549i | \(0.872977\pi\) | |||||||
\(374\) | −3438.56 | + | 7266.62i | −0.475412 | + | 1.00467i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 708.229 | + | 2834.35i | 0.0971386 | + | 0.388751i | ||||
\(377\) | −551.546 | −0.0753476 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3460.18i | − | 0.468965i | −0.972120 | − | 0.234482i | \(-0.924661\pi\) | ||
0.972120 | − | 0.234482i | \(-0.0753395\pi\) | |||||||
\(380\) | −90.6392 | − | 110.531i | −0.0122360 | − | 0.0149214i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7157.84 | − | 3387.09i | −0.958709 | − | 0.453661i | ||||
\(383\) | −5059.63 | −0.675027 | −0.337513 | − | 0.941321i | \(-0.609586\pi\) | ||||
−0.337513 | + | 0.941321i | \(0.609586\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 839.732 | 0.111160 | ||||||||
\(386\) | −1595.61 | − | 755.044i | −0.210400 | − | 0.0995614i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3119.35 | − | 3803.92i | −0.408147 | − | 0.497719i | ||||
\(389\) | − | 2192.22i | − | 0.285732i | −0.989742 | − | 0.142866i | \(-0.954368\pi\) | ||
0.989742 | − | 0.142866i | \(-0.0456318\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5163.93 | 0.667906 | ||||||||
\(392\) | −956.074 | − | 3826.23i | −0.123186 | − | 0.492995i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5781.93 | + | 12218.8i | −0.739314 | + | 1.56237i | ||||
\(395\) | − | 102.045i | − | 0.0129986i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5519.94i | 0.697828i | 0.937155 | + | 0.348914i | \(0.113449\pi\) | ||||
−0.937155 | + | 0.348914i | \(0.886551\pi\) | |||||||
\(398\) | −6687.94 | − | 3164.73i | −0.842302 | − | 0.398577i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1562.06 | + | 7821.52i | −0.195257 | + | 0.977690i | ||||
\(401\) | 7352.64 | 0.915645 | 0.457822 | − | 0.889044i | \(-0.348630\pi\) | ||||
0.457822 | + | 0.889044i | \(0.348630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11685.9i | − | 1.44446i | ||||||
\(404\) | −10299.7 | + | 8446.12i | −1.26839 | + | 1.04012i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −286.853 | + | 606.197i | −0.0350647 | + | 0.0741011i | ||||
\(407\) | 24608.2 | 2.99702 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11311.2 | −1.36749 | −0.683745 | − | 0.729721i | \(-0.739650\pi\) | ||||
−0.683745 | + | 0.729721i | \(0.739650\pi\) | |||||||
\(410\) | 267.381 | − | 565.049i | 0.0322074 | − | 0.0680628i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2013.17 | + | 2454.98i | 0.240732 | + | 0.293564i | ||||
\(413\) | 5978.40i | 0.712295i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −221.743 | −0.0262288 | ||||||||
\(416\) | 7686.86 | + | 5712.43i | 0.905960 | + | 0.673257i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4493.35 | + | 2126.25i | 0.525782 | + | 0.248800i | ||||
\(419\) | − | 13042.2i | − | 1.52065i | −0.649543 | − | 0.760325i | \(-0.725040\pi\) | ||
0.649543 | − | 0.760325i | \(-0.274960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4544.38i | − | 0.526080i | −0.964785 | − | 0.263040i | \(-0.915275\pi\) | ||
0.964785 | − | 0.263040i | \(-0.0847251\pi\) | |||||||
\(422\) | −2112.05 | + | 4463.33i | −0.243632 | + | 0.514861i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2586.42 | − | 646.279i | 0.296245 | − | 0.0740238i | ||||
\(425\) | −5877.83 | −0.670863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6219.72i | − | 0.704903i | ||||||
\(428\) | −2169.01 | + | 1778.66i | −0.244960 | + | 0.200876i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 370.307 | + | 175.229i | 0.0415297 | + | 0.0196519i | ||||
\(431\) | −7713.83 | −0.862093 | −0.431047 | − | 0.902330i | \(-0.641856\pi\) | ||||
−0.431047 | + | 0.902330i | \(0.641856\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15068.3 | −1.67237 | −0.836183 | − | 0.548451i | \(-0.815218\pi\) | ||||
−0.836183 | + | 0.548451i | \(0.815218\pi\) | |||||||
\(434\) | −12843.9 | − | 6077.72i | −1.42057 | − | 0.672212i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3693.12 | + | 3028.49i | −0.405661 | + | 0.332656i | ||||
\(437\) | − | 3193.14i | − | 0.349540i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11004.7 | 1.19642 | 0.598208 | − | 0.801341i | \(-0.295880\pi\) | ||||
0.598208 | + | 0.801341i | \(0.295880\pi\) | |||||||
\(440\) | 202.523 | + | 810.502i | 0.0219430 | + | 0.0878163i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3018.79 | + | 6379.52i | −0.324862 | + | 0.686522i | ||||
\(443\) | − | 2513.04i | − | 0.269522i | −0.990878 | − | 0.134761i | \(-0.956973\pi\) | ||
0.990878 | − | 0.134761i | \(-0.0430266\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 24.7077i | − | 0.00263204i | ||||||
\(446\) | 8655.74 | + | 4095.90i | 0.918972 | + | 0.434858i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10276.3 | − | 5477.56i | 1.08373 | − | 0.577657i | ||||
\(449\) | 15752.7 | 1.65571 | 0.827855 | − | 0.560942i | \(-0.189561\pi\) | ||||
0.827855 | + | 0.560942i | \(0.189561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21739.4i | 2.26977i | ||||||||
\(452\) | −2518.23 | − | 3070.89i | −0.262053 | − | 0.319563i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4654.97 | + | 9837.20i | −0.481208 | + | 1.01692i | ||||
\(455\) | 737.218 | 0.0759590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5257.06 | −0.538107 | −0.269053 | − | 0.963125i | \(-0.586711\pi\) | ||||
−0.269053 | + | 0.963125i | \(0.586711\pi\) | |||||||
\(458\) | 1615.26 | − | 3413.48i | 0.164795 | − | 0.348257i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 414.954 | − | 340.277i | 0.0420595 | − | 0.0344902i | ||||
\(461\) | 8066.31i | 0.814936i | 0.913220 | + | 0.407468i | \(0.133588\pi\) | ||||
−0.913220 | + | 0.407468i | \(0.866412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5683.43 | 0.570478 | 0.285239 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285239 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(464\) | −654.279 | − | 130.668i | −0.0654615 | − | 0.0130735i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13157.4 | − | 6226.09i | −1.30795 | − | 0.618923i | ||||
\(467\) | 11139.3i | 1.10378i | 0.833916 | + | 0.551891i | \(0.186094\pi\) | ||||
−0.833916 | + | 0.551891i | \(0.813906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2033.50i | − | 0.200210i | ||||||
\(470\) | −95.6982 | + | 202.236i | −0.00939198 | + | 0.0198478i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5770.30 | + | 1441.85i | −0.562711 | + | 0.140607i | ||||
\(473\) | −14247.0 | −1.38494 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3634.59i | 0.351087i | ||||||||
\(476\) | 5441.61 | + | 6635.83i | 0.523983 | + | 0.638976i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18114.0 | + | 8571.53i | 1.73329 | + | 0.820193i | ||||
\(479\) | −3477.35 | −0.331699 | −0.165850 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165850 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21604.1 | 2.04795 | ||||||||
\(482\) | −6489.76 | − | 3070.96i | −0.613279 | − | 0.290204i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11670.5 | − | 14231.8i | −1.09603 | − | 1.33657i | ||||
\(485\) | − | 376.738i | − | 0.0352717i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −478.797 | −0.0445510 | −0.0222755 | − | 0.999752i | \(-0.507091\pi\) | ||||
−0.0222755 | + | 0.999752i | \(0.507091\pi\) | |||||||
\(488\) | 6003.23 | − | 1500.05i | 0.556871 | − | 0.139147i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 129.188 | − | 273.009i | 0.0119104 | − | 0.0251700i | ||||
\(491\) | − | 16601.8i | − | 1.52592i | −0.646444 | − | 0.762961i | \(-0.723745\pi\) | ||
0.646444 | − | 0.762961i | \(-0.276255\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 491.687i | − | 0.0449178i | ||||||
\(494\) | 3944.81 | + | 1866.68i | 0.359282 | + | 0.170012i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2768.54 | − | 13862.6i | 0.250627 | − | 1.25494i | ||||
\(497\) | −7972.29 | −0.719530 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9482.20i | − | 0.850664i | −0.905037 | − | 0.425332i | \(-0.860157\pi\) | ||
0.905037 | − | 0.425332i | \(-0.139843\pi\) | |||||||
\(500\) | −946.063 | + | 775.805i | −0.0846185 | + | 0.0693901i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2053.02 | − | 4338.59i | 0.182532 | − | 0.385738i | ||||
\(503\) | −16561.2 | −1.46805 | −0.734023 | − | 0.679124i | \(-0.762360\pi\) | ||||
−0.734023 | + | 0.679124i | \(0.762360\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1020.08 | −0.0898867 | ||||||||
\(506\) | −7982.37 | + | 16868.9i | −0.701304 | + | 1.48204i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9130.21 | + | 11133.9i | 0.797417 | + | 0.972418i | ||||
\(509\) | − | 4197.35i | − | 0.365509i | −0.983159 | − | 0.182755i | \(-0.941499\pi\) | ||
0.983159 | − | 0.182755i | \(-0.0585014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12113.8 | −1.04869 | ||||||||
\(512\) | 7765.29 | + | 8597.56i | 0.670275 | + | 0.742113i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −978.941 | − | 463.235i | −0.0840063 | − | 0.0397518i | ||||
\(515\) | 243.140i | 0.0208039i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7780.73i | − | 0.661888i | ||||||
\(518\) | 11236.0 | − | 23744.8i | 0.953057 | − | 2.01407i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 177.799 | + | 711.558i | 0.0149943 | + | 0.0600074i | ||||
\(521\) | 15755.5 | 1.32488 | 0.662440 | − | 0.749115i | \(-0.269521\pi\) | ||||
0.662440 | + | 0.749115i | \(0.269521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11555.1i | 0.966098i | 0.875593 | + | 0.483049i | \(0.160471\pi\) | ||||
−0.875593 | + | 0.483049i | \(0.839529\pi\) | |||||||
\(524\) | 6937.31 | − | 5688.84i | 0.578355 | − | 0.474271i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12788.3 | − | 6051.44i | −1.06007 | − | 0.501626i | ||||
\(527\) | 10417.7 | 0.861102 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −179.314 | −0.0147378 | ||||||||
\(530\) | 184.546 | + | 87.3274i | 0.0151249 | + | 0.00715709i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4103.30 | − | 3364.85i | 0.334399 | − | 0.274219i | ||||
\(533\) | 19085.5i | 1.55100i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −214.817 | −0.0173595 | ||||||||
\(536\) | 1962.72 | − | 490.432i | 0.158165 | − | 0.0395213i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7400.92 | − | 15640.1i | 0.593079 | − | 1.25334i | ||||
\(539\) | 10503.6i | 0.839373i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7475.65i | 0.594091i | 0.954863 | + | 0.297045i | \(0.0960013\pi\) | ||||
−0.954863 | + | 0.297045i | \(0.903999\pi\) | |||||||
\(542\) | 10114.4 | + | 4786.12i | 0.801566 | + | 0.379301i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5092.46 | + | 6852.60i | −0.401356 | + | 0.540079i | ||||
\(545\) | −365.764 | −0.0287479 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6028.08i | − | 0.471192i | −0.971851 | − | 0.235596i | \(-0.924296\pi\) | ||
0.971851 | − | 0.235596i | \(-0.0757043\pi\) | |||||||
\(548\) | −12426.0 | − | 15153.0i | −0.968636 | − | 1.18121i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9085.90 | − | 19201.0i | 0.704408 | − | 1.48860i | ||||
\(551\) | −304.037 | −0.0235071 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3788.29 | 0.291310 | ||||||||
\(554\) | 5858.06 | − | 12379.7i | 0.449251 | − | 0.949389i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15202.6 | + | 12466.6i | −1.15959 | + | 0.950904i | ||||
\(557\) | − | 19381.5i | − | 1.47436i | −0.675696 | − | 0.737181i | \(-0.736157\pi\) | ||
0.675696 | − | 0.737181i | \(-0.263843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12507.7 | −0.946370 | ||||||||
\(560\) | 874.535 | + | 174.656i | 0.0659926 | + | 0.0131796i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4803.10 | + | 2272.83i | 0.360510 | + | 0.170593i | ||||
\(563\) | 20565.0i | 1.53946i | 0.638372 | + | 0.769728i | \(0.279608\pi\) | ||||
−0.638372 | + | 0.769728i | \(0.720392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 304.139i | − | 0.0226464i | ||||||
\(566\) | 6925.95 | − | 14636.4i | 0.514345 | − | 1.08695i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1922.73 | − | 7694.80i | −0.142035 | − | 0.568427i | ||||
\(569\) | −15252.9 | −1.12379 | −0.561895 | − | 0.827209i | \(-0.689927\pi\) | ||||
−0.561895 | + | 0.827209i | \(0.689927\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16492.8i | − | 1.20876i | −0.796697 | − | 0.604379i | \(-0.793421\pi\) | ||
0.796697 | − | 0.604379i | \(-0.206579\pi\) | |||||||
\(572\) | −16173.4 | − | 19722.8i | −1.18225 | − | 1.44170i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20976.6 | + | 9926.13i | 1.52534 | + | 0.721792i | ||||
\(575\) | −13644.9 | −0.989623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10298.2 | −0.743016 | −0.371508 | − | 0.928430i | \(-0.621159\pi\) | ||||
−0.371508 | + | 0.928430i | \(0.621159\pi\) | |||||||
\(578\) | 6873.60 | + | 3252.59i | 0.494644 | + | 0.234065i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −32.3997 | − | 39.5101i | −0.00231952 | − | 0.00282857i | ||||
\(581\) | − | 8231.89i | − | 0.587808i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7100.14 | −0.504387 | ||||||||
\(584\) | −2921.55 | − | 11692.1i | −0.207011 | − | 0.828464i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6156.38 | − | 13010.1i | 0.433989 | − | 0.917136i | ||||
\(587\) | 13104.8i | 0.921453i | 0.887542 | + | 0.460727i | \(0.152411\pi\) | ||||
−0.887542 | + | 0.460727i | \(0.847589\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6441.82i | − | 0.450646i | ||||||
\(590\) | −411.722 | − | 194.827i | −0.0287294 | − | 0.0135948i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25628.2 | + | 5118.27i | 1.77924 | + | 0.355337i | ||||
\(593\) | −4163.34 | −0.288310 | −0.144155 | − | 0.989555i | \(-0.546046\pi\) | ||||
−0.144155 | + | 0.989555i | \(0.546046\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 657.208i | 0.0452822i | ||||||||
\(596\) | −12897.6 | + | 10576.5i | −0.886423 | + | 0.726898i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7007.90 | + | 14809.6i | −0.479221 | + | 1.01272i | ||||
\(599\) | 5718.60 | 0.390076 | 0.195038 | − | 0.980796i | \(-0.437517\pi\) | ||||
0.195038 | + | 0.980796i | \(0.437517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17473.0 | 1.18592 | 0.592959 | − | 0.805233i | \(-0.297960\pi\) | ||||
0.592959 | + | 0.805233i | \(0.297960\pi\) | |||||||
\(602\) | −6505.13 | + | 13747.1i | −0.440414 | + | 0.930713i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5365.98 | + | 6543.60i | 0.361488 | + | 0.440820i | ||||
\(605\) | − | 1409.50i | − | 0.0947181i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5647.60 | −0.377643 | −0.188821 | − | 0.982011i | \(-0.560467\pi\) | ||||
−0.188821 | + | 0.982011i | \(0.560467\pi\) | |||||||
\(608\) | 4237.34 | + | 3148.95i | 0.282643 | + | 0.210044i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 428.342 | + | 202.691i | 0.0284312 | + | 0.0134537i | ||||
\(611\) | − | 6830.87i | − | 0.452287i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16023.6i | 1.05577i | 0.849317 | + | 0.527884i | \(0.177014\pi\) | ||||
−0.849317 | + | 0.527884i | \(0.822986\pi\) | |||||||
\(614\) | −8733.81 | + | 18456.9i | −0.574052 | + | 1.21313i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30088.7 | + | 7518.37i | −1.96803 | + | 0.491760i | ||||
\(617\) | 21022.1 | 1.37167 | 0.685834 | − | 0.727758i | \(-0.259438\pi\) | ||||
0.685834 | + | 0.727758i | \(0.259438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17824.2i | 1.15737i | 0.815550 | + | 0.578686i | \(0.196434\pi\) | ||||
−0.815550 | + | 0.578686i | \(0.803566\pi\) | |||||||
\(620\) | 837.125 | − | 686.472i | 0.0542254 | − | 0.0444667i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3929.69 | − | 1859.53i | −0.253322 | − | 0.119872i | ||||
\(623\) | 917.238 | 0.0589861 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15484.4 | 0.991001 | ||||||||
\(626\) | 5626.97 | + | 2662.68i | 0.359263 | + | 0.170004i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19752.0 | + | 16197.4i | −1.25508 | + | 1.02921i | ||||
\(629\) | 19259.4i | 1.22086i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22339.0 | −1.40935 | −0.704677 | − | 0.709528i | \(-0.748908\pi\) | ||||
−0.704677 | + | 0.709528i | \(0.748908\pi\) | |||||||
\(632\) | 913.644 | + | 3656.42i | 0.0575044 | + | 0.230134i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3436.33 | − | 7261.89i | 0.215259 | − | 0.454900i | ||||
\(635\) | 1102.70i | 0.0689121i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9221.34i | 0.573568i | ||||||||
\(638\) | 1606.18 | + | 760.046i | 0.0996698 | + | 0.0471638i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 42.3406 | + | 886.217i | 0.00261509 | + | 0.0547356i | ||||
\(641\) | 5268.43 | 0.324634 | 0.162317 | − | 0.986739i | \(-0.448103\pi\) | ||||
0.162317 | + | 0.986739i | \(0.448103\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21965.8i | 1.34719i | 0.739099 | + | 0.673597i | \(0.235252\pi\) | ||||
−0.739099 | + | 0.673597i | \(0.764748\pi\) | |||||||
\(644\) | 12632.3 | + | 15404.6i | 0.772953 | + | 0.942586i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1664.09 | + | 3516.68i | −0.101351 | + | 0.214182i | ||||
\(647\) | −3165.40 | −0.192341 | −0.0961706 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961706 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15840.4 | 0.958073 | ||||||||
\(650\) | 7976.71 | − | 16856.9i | 0.481342 | − | 1.01721i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5238.67 | − | 4295.89i | 0.314666 | − | 0.258037i | ||||
\(653\) | − | 12094.7i | − | 0.724814i | −0.932020 | − | 0.362407i | \(-0.881955\pi\) | ||
0.932020 | − | 0.362407i | \(-0.118045\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 687.067 | 0.0409861 | ||||||||
\(656\) | −4521.57 | + | 22640.4i | −0.269112 | + | 1.34750i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7507.72 | − | 3552.66i | −0.444805 | − | 0.210482i | ||||
\(659\) | − | 7523.17i | − | 0.444706i | −0.974966 | − | 0.222353i | \(-0.928626\pi\) | ||
0.974966 | − | 0.222353i | \(-0.0713737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24141.1i | − | 1.42054i | −0.703928 | − | 0.710271i | \(-0.748572\pi\) | ||
0.703928 | − | 0.710271i | \(-0.251428\pi\) | |||||||
\(662\) | −2562.98 | + | 5416.28i | −0.150473 | + | 0.317990i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7945.36 | − | 1985.33i | 0.464367 | − | 0.116033i | ||||
\(665\) | 406.388 | 0.0236978 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1141.41i | − | 0.0662604i | ||||||
\(668\) | 13342.1 | + | 16270.2i | 0.772789 | + | 0.942385i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 140.044 | + | 66.2688i | 0.00807518 | + | 0.00382118i | ||||
\(671\) | −16479.8 | −0.948130 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 944.143 | 0.0540773 | 0.0270387 | − | 0.999634i | \(-0.491392\pi\) | ||||
0.0270387 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(674\) | 1686.35 | + | 797.983i | 0.0963738 | + | 0.0456041i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3054.12 | − | 3724.38i | −0.173766 | − | 0.211901i | ||||
\(677\) | 4450.51i | 0.252654i | 0.991989 | + | 0.126327i | \(0.0403189\pi\) | ||||
−0.991989 | + | 0.126327i | \(0.959681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13985.8 | 0.790468 | ||||||||
\(680\) | −634.332 | + | 158.503i | −0.0357728 | + | 0.00893869i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16103.5 | + | 34031.2i | −0.904160 | + | 1.91073i | ||||
\(683\) | − | 1726.40i | − | 0.0967189i | −0.998830 | − | 0.0483594i | \(-0.984601\pi\) | ||
0.998830 | − | 0.0483594i | \(-0.0153993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1500.75i | − | 0.0837088i | ||||||
\(686\) | −9809.87 | − | 4642.03i | −0.545981 | − | 0.258358i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14837.5 | − | 2963.23i | −0.822199 | − | 0.164204i | ||||
\(689\) | −6233.37 | −0.344662 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 683.143i | 0.0376092i | 0.999823 | + | 0.0188046i | \(0.00598605\pi\) | ||||
−0.999823 | + | 0.0188046i | \(0.994014\pi\) | |||||||
\(692\) | 2659.02 | − | 2180.49i | 0.146071 | − | 0.119783i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10135.0 | − | 21418.0i | 0.554351 | − | 1.17149i | ||||
\(695\) | −1505.65 | −0.0821764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17014.1 | −0.924614 | ||||||||
\(698\) | −3936.91 | + | 8319.76i | −0.213487 | + | 0.451157i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14378.7 | − | 17534.2i | −0.776375 | − | 0.946758i | ||||
\(701\) | − | 19533.2i | − | 1.05244i | −0.850349 | − | 0.526220i | \(-0.823609\pi\) | ||
0.850349 | − | 0.526220i | \(-0.176391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11909.2 | 0.638922 | ||||||||
\(704\) | −14513.4 | − | 27228.1i | −0.776978 | − | 1.45767i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28423.4 | + | 13450.0i | 1.51520 | + | 0.716991i | ||||
\(707\) | − | 37868.8i | − | 2.01443i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 26081.9i | − | 1.38156i | −0.723066 | − | 0.690779i | \(-0.757268\pi\) | ||
0.723066 | − | 0.690779i | \(-0.242732\pi\) | |||||||
\(710\) | 259.805 | − | 549.038i | 0.0137328 | − | 0.0290212i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 221.216 | + | 885.311i | 0.0116438 | + | 0.0465989i | ||||
\(713\) | 24183.8 | 1.27025 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1953.34i | − | 0.102169i | ||||||
\(716\) | −9379.89 | + | 7691.84i | −0.489585 | + | 0.401477i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12160.8 | − | 5754.49i | −0.632085 | − | 0.299103i | ||||
\(719\) | 30077.3 | 1.56007 | 0.780036 | − | 0.625734i | \(-0.215200\pi\) | ||||
0.780036 | + | 0.625734i | \(0.215200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9026.21 | −0.466232 | ||||||||
\(722\) | −15361.4 | − | 7269.02i | −0.791818 | − | 0.374688i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20910.0 | − | 17147.0i | 1.07336 | − | 0.880196i | ||||
\(725\) | 1299.21i | 0.0665537i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23049.9 | 1.17589 | 0.587946 | − | 0.808900i | \(-0.299937\pi\) | ||||
0.587946 | + | 0.808900i | \(0.299937\pi\) | |||||||
\(728\) | −26415.5 | + | 6600.54i | −1.34481 | + | 0.336033i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 394.769 | − | 834.254i | 0.0200152 | − | 0.0422975i | ||||
\(731\) | − | 11150.3i | − | 0.564169i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4444.57i | 0.223962i | 0.993710 | + | 0.111981i | \(0.0357195\pi\) | ||||
−0.993710 | + | 0.111981i | \(0.964280\pi\) | |||||||
\(734\) | −4697.56 | − | 2222.89i | −0.236226 | − | 0.111782i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11821.8 | + | 15907.8i | −0.592060 | + | 0.796698i | ||||
\(737\) | −5387.98 | −0.269293 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28465.1i | − | 1.41692i | −0.705749 | − | 0.708462i | \(-0.749390\pi\) | ||
0.705749 | − | 0.708462i | \(-0.250610\pi\) | |||||||
\(740\) | 1269.10 | + | 1547.61i | 0.0630446 | + | 0.0768803i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3241.90 | + | 6851.01i | −0.160396 | + | 0.338960i | ||||
\(743\) | −4389.76 | −0.216749 | −0.108374 | − | 0.994110i | \(-0.534565\pi\) | ||||
−0.108374 | + | 0.994110i | \(0.534565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1277.38 | −0.0628180 | ||||||||
\(746\) | 6772.55 | − | 14312.2i | 0.332387 | − | 0.702423i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17582.3 | − | 14418.1i | 0.859456 | − | 0.704784i | ||||
\(749\) | − | 7974.77i | − | 0.389041i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14121.9 | 0.686171 | 0.343085 | − | 0.939304i | \(-0.388528\pi\) | ||||
0.343085 | + | 0.939304i | \(0.388528\pi\) | |||||||
\(752\) | 1618.31 | − | 8103.21i | 0.0784758 | − | 0.392944i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1410.10 | + | 667.260i | 0.0681073 | + | 0.0322284i | ||||
\(755\) | 648.074i | 0.0312395i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 17006.3i | − | 0.816516i | −0.912866 | − | 0.408258i | \(-0.866136\pi\) | ||
0.912866 | − | 0.408258i | \(-0.133864\pi\) | |||||||
\(758\) | −4186.13 | + | 8846.42i | −0.200590 | + | 0.423900i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 98.0110 | + | 392.243i | 0.00467794 | + | 0.0187212i | ||||
\(761\) | 4603.38 | 0.219280 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 13578.5i | − | 0.644264i | ||||||
\(764\) | 14202.3 | + | 17319.1i | 0.672540 | + | 0.820136i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12935.6 | + | 6121.15i | 0.610161 | + | 0.288728i | ||||
\(767\) | 13906.6 | 0.654679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12459.1 | −0.584248 | −0.292124 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292124 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(770\) | −2146.89 | − | 1015.91i | −0.100478 | − | 0.0475465i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3165.94 | + | 3860.74i | 0.147597 | + | 0.179989i | ||||
\(773\) | 27068.1i | 1.25947i | 0.776808 | + | 0.629737i | \(0.216837\pi\) | ||||
−0.776808 | + | 0.629737i | \(0.783163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27527.2 | −1.27588 | ||||||||
\(776\) | 3373.05 | + | 13499.0i | 0.156038 | + | 0.624468i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2652.15 | + | 5604.70i | −0.122216 | + | 0.258275i | ||||
\(779\) | 10520.8i | 0.483884i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21123.4i | 0.967804i | ||||||||
\(782\) | −13202.3 | − | 6247.33i | −0.603725 | − | 0.285683i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2184.64 | + | 10938.9i | −0.0995191 | + | 0.498312i | ||||
\(785\) | −1956.23 | −0.0889438 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 6986.86i | − | 0.316461i | −0.987402 | − | 0.158230i | \(-0.949421\pi\) | ||
0.987402 | − | 0.158230i | \(-0.0505789\pi\) | |||||||
\(788\) | 29564.6 | − | 24244.0i | 1.33654 | − | 1.09601i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −123.455 | + | 260.893i | −0.00555990 | + | 0.0117496i | ||||
\(791\) | 11290.7 | 0.507523 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14468.0 | −0.647885 | ||||||||
\(794\) | 6678.02 | − | 14112.5i | 0.298481 | − | 0.630771i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13269.9 | + | 16182.1i | 0.590879 | + | 0.720554i | ||||
\(797\) | 27271.5i | 1.21205i | 0.795444 | + | 0.606027i | \(0.207238\pi\) | ||||
−0.795444 | + | 0.606027i | \(0.792762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6089.52 | 0.269627 | ||||||||
\(800\) | 13456.1 | − | 18107.0i | 0.594681 | − | 0.800224i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18798.0 | − | 8895.23i | −0.827658 | − | 0.391648i | ||||
\(803\) | 32096.7i | 1.41054i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1525.66i | 0.0667981i | ||||||||
\(806\) | −14137.7 | + | 29876.7i | −0.617838 | + | 1.30566i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 36550.7 | − | 9133.06i | 1.59140 | − | 0.397648i | ||||
\(809\) | −23785.9 | −1.03371 | −0.516853 | − | 0.856074i | \(-0.672897\pi\) | ||||
−0.516853 | + | 0.856074i | \(0.672897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21703.5i | 0.939718i | 0.882741 | + | 0.469859i | \(0.155695\pi\) | ||||
−0.882741 | + | 0.469859i | \(0.844305\pi\) | |||||||
\(812\) | 1466.75 | − | 1202.79i | 0.0633904 | − | 0.0519823i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −62914.3 | − | 29771.1i | −2.70902 | − | 1.28191i | ||||
\(815\) | 518.835 | 0.0222994 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6894.83 | −0.295250 | ||||||||
\(818\) | 28918.7 | + | 13684.3i | 1.23608 | + | 0.584915i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1367.19 | + | 1121.15i | −0.0582249 | + | 0.0477465i | ||||
\(821\) | − | 33240.4i | − | 1.41303i | −0.707698 | − | 0.706515i | \(-0.750266\pi\) | ||
0.707698 | − | 0.706515i | \(-0.249734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17227.5 | −0.729665 | −0.364832 | − | 0.931073i | \(-0.618874\pi\) | ||||
−0.364832 | + | 0.931073i | \(0.618874\pi\) | |||||||
\(824\) | −2176.90 | − | 8712.02i | −0.0920341 | − | 0.368322i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7232.67 | − | 15284.6i | 0.304669 | − | 0.643848i | ||||
\(827\) | − | 21678.4i | − | 0.911528i | −0.890101 | − | 0.455764i | \(-0.849366\pi\) | ||
0.890101 | − | 0.455764i | \(-0.150634\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34269.8i | 1.43575i | 0.696170 | + | 0.717877i | \(0.254886\pi\) | ||||
−0.696170 | + | 0.717877i | \(0.745114\pi\) | |||||||
\(830\) | 566.916 | + | 268.265i | 0.0237084 | + | 0.0112188i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12741.6 | − | 23904.2i | −0.530931 | − | 0.996067i | ||||
\(833\) | −8220.55 | −0.341927 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1611.39i | 0.0667838i | ||||||||
\(836\) | −8915.51 | − | 10872.1i | −0.368839 | − | 0.449784i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15778.4 | + | 33344.1i | −0.650426 | + | 1.37453i | ||||
\(839\) | −33444.1 | −1.37618 | −0.688092 | − | 0.725623i | \(-0.741552\pi\) | ||||
−0.688092 | + | 0.725623i | \(0.741552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24280.3 | 0.995544 | ||||||||
\(842\) | −5497.80 | + | 11618.3i | −0.225020 | + | 0.475527i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10799.5 | − | 8855.95i | 0.440442 | − | 0.361178i | ||||
\(845\) | − | 368.860i | − | 0.0150168i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52325.8 | 2.12271 | ||||||||
\(848\) | −7394.41 | − | 1476.76i | −0.299440 | − | 0.0598020i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15027.5 | + | 7111.00i | 0.606397 | + | 0.286947i | ||||
\(851\) | 44709.3i | 1.80096i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37037.3i | 1.48667i | 0.668917 | + | 0.743337i | \(0.266758\pi\) | ||||
−0.668917 | + | 0.743337i | \(0.733242\pi\) | |||||||
\(854\) | −7524.62 | + | 15901.6i | −0.301507 | + | 0.637166i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7697.19 | − | 1923.32i | 0.307342 | − | 0.0767966i | ||||
\(857\) | −35794.2 | −1.42673 | −0.713365 | − | 0.700793i | \(-0.752830\pi\) | ||||
−0.713365 | + | 0.700793i | \(0.752830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 20582.1i | − | 0.817522i | −0.912641 | − | 0.408761i | \(-0.865961\pi\) | ||
0.912641 | − | 0.408761i | \(-0.134039\pi\) | |||||||
\(860\) | −734.747 | − | 895.994i | −0.0291333 | − | 0.0355269i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19721.4 | + | 9332.19i | 0.779252 | + | 0.368742i | ||||
\(863\) | 25677.7 | 1.01284 | 0.506420 | − | 0.862287i | \(-0.330969\pi\) | ||||
0.506420 | + | 0.862287i | \(0.330969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 263.348 | 0.0103516 | ||||||||
\(866\) | 38524.0 | + | 18229.6i | 1.51166 | + | 0.715319i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 25484.2 | + | 31077.0i | 0.996534 | + | 1.21523i | ||||
\(869\) | − | 10037.5i | − | 0.391827i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4730.22 | −0.184015 | ||||||||
\(872\) | 13105.8 | − | 3274.80i | 0.508967 | − | 0.127177i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3863.07 | + | 8163.71i | −0.149508 | + | 0.315951i | ||||
\(875\) | − | 3478.38i | − | 0.134389i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32783.0i | 1.26226i | 0.775676 | + | 0.631131i | \(0.217409\pi\) | ||||
−0.775676 | + | 0.631131i | \(0.782591\pi\) | |||||||
\(878\) | −28135.0 | − | 13313.5i | −1.08145 | − | 0.511742i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 462.768 | − | 2317.17i | 0.0177272 | − | 0.0887634i | ||||
\(881\) | −26615.7 | −1.01783 | −0.508914 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508914 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19203.4i | 0.731875i | 0.930639 | + | 0.365937i | \(0.119252\pi\) | ||||
−0.930639 | + | 0.365937i | \(0.880748\pi\) | |||||||
\(884\) | 15435.9 | − | 12658.0i | 0.587291 | − | 0.481599i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3040.28 | + | 6424.93i | −0.115282 | + | 0.243623i | ||||
\(887\) | −23198.0 | −0.878144 | −0.439072 | − | 0.898452i | \(-0.644693\pi\) | ||||
−0.439072 | + | 0.898452i | \(0.644693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40936.0 | −1.54438 | ||||||||
\(890\) | −29.8914 | + | 63.1686i | −0.00112580 | + | 0.00237912i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17174.4 | − | 20943.4i | −0.644664 | − | 0.786142i | ||||
\(893\) | − | 3765.48i | − | 0.141105i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −928.979 | −0.0346953 | ||||||||
\(896\) | −32899.5 | + | 1571.83i | −1.22667 | + | 0.0586063i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40273.8 | − | 19057.6i | −1.49661 | − | 0.708195i | ||||
\(899\) | − | 2302.68i | − | 0.0854266i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5556.86i | − | 0.205467i | ||||||
\(902\) | 26300.3 | − | 55579.7i | 0.970848 | − | 2.05166i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2723.05 | + | 10897.7i | 0.100185 | + | 0.400942i | ||||
\(905\) | 2070.92 | 0.0760659 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16151.3i | − | 0.591285i | −0.955299 | − | 0.295643i | \(-0.904466\pi\) | ||
0.955299 | − | 0.295643i | \(-0.0955337\pi\) | |||||||
\(908\) | 23802.1 | − | 19518.6i | 0.869935 | − | 0.713377i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1884.80 | − | 891.887i | −0.0686599 | − | 0.0324899i | ||||
\(911\) | 3487.34 | 0.126829 | 0.0634143 | − | 0.997987i | \(-0.479801\pi\) | ||||
0.0634143 | + | 0.997987i | \(0.479801\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21811.2 | −0.790632 | ||||||||
\(914\) | 13440.4 | + | 6359.99i | 0.486398 | + | 0.230164i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8259.27 | + | 6772.89i | −0.297919 | + | 0.244304i | ||||
\(917\) | 25506.3i | 0.918532i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17055.5 | 0.612198 | 0.306099 | − | 0.952000i | \(-0.400976\pi\) | ||||
0.306099 | + | 0.952000i | \(0.400976\pi\) | |||||||
\(920\) | −1472.55 | + | 367.953i | −0.0527703 | + | 0.0131859i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9758.62 | − | 20622.6i | 0.348572 | − | 0.736626i | ||||
\(923\) | 18544.7i | 0.661329i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 50890.2i | − | 1.80893i | ||||||
\(926\) | −14530.4 | − | 6875.81i | −0.515659 | − | 0.244010i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1514.67 | + | 1125.62i | 0.0535792 | + | 0.0398170i | ||||
\(929\) | 55339.3 | 1.95438 | 0.977192 | − | 0.212359i | \(-0.0681146\pi\) | ||||
0.977192 | + | 0.212359i | \(0.0681146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5083.22i | 0.178943i | ||||||||
\(932\) | 26106.4 | + | 31835.7i | 0.917536 | + | 1.11890i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13476.4 | − | 28479.2i | 0.472120 | − | 0.997717i | ||||
\(935\) | 1741.34 | 0.0609069 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20457.6 | −0.713255 | −0.356627 | − | 0.934247i | \(-0.616073\pi\) | ||||
−0.356627 | + | 0.934247i | \(0.616073\pi\) | |||||||
\(938\) | −2460.13 | + | 5198.92i | −0.0856356 | + | 0.180971i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 489.331 | − | 401.268i | 0.0169789 | − | 0.0139233i | ||||
\(941\) | 55891.0i | 1.93623i | 0.250502 | + | 0.968116i | \(0.419404\pi\) | ||||
−0.250502 | + | 0.968116i | \(0.580596\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39497.0 | −1.36395 | ||||||||
\(944\) | 16496.9 | + | 3294.64i | 0.568780 | + | 0.113593i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36424.3 | + | 17236.0i | 1.25186 | + | 0.592379i | ||||
\(947\) | − | 54727.0i | − | 1.87792i | −0.344027 | − | 0.938960i | \(-0.611791\pi\) | ||
0.344027 | − | 0.938960i | \(-0.388209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28178.4i | 0.963865i | ||||||||
\(950\) | 4397.12 | − | 9292.31i | 0.150170 | − | 0.317350i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5884.19 | − | 23548.7i | −0.200323 | − | 0.801698i | ||||
\(953\) | −29958.8 | −1.01832 | −0.509160 | − | 0.860672i | \(-0.670044\pi\) | ||||
−0.509160 | + | 0.860672i | \(0.670044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1715.27i | 0.0581204i | ||||||||
\(956\) | −35940.9 | − | 43828.5i | −1.21591 | − | 1.48276i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8890.31 | + | 4206.90i | 0.299825 | + | 0.141877i | ||||
\(959\) | 55713.0 | 1.87598 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18997.2 | 0.637682 | ||||||||
\(962\) | −55233.8 | − | 26136.7i | −1.85115 | − | 0.875966i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12876.7 | + | 15702.6i | 0.430219 | + | 0.524634i | ||||
\(965\) | 382.365i | 0.0127552i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13498.5 | 0.448896 | 0.224448 | − | 0.974486i | \(-0.427942\pi\) | ||||
0.224448 | + | 0.974486i | \(0.427942\pi\) | |||||||
\(968\) | 12619.7 | + | 50504.4i | 0.419022 | + | 1.67694i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −455.778 | + | 963.182i | −0.0150867 | + | 0.0318824i | ||||
\(971\) | 9652.36i | 0.319010i | 0.987197 | + | 0.159505i | \(0.0509899\pi\) | ||||
−0.987197 | + | 0.159505i | \(0.949010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 55895.1i | − | 1.84164i | ||||||
\(974\) | 1224.11 | + | 579.249i | 0.0402700 | + | 0.0190558i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17162.8 | − | 3427.63i | −0.562877 | − | 0.112414i | ||||
\(977\) | −12169.8 | −0.398511 | −0.199256 | − | 0.979948i | \(-0.563852\pi\) | ||||
−0.199256 | + | 0.979948i | \(0.563852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2430.32i | − | 0.0793394i | ||||||
\(980\) | −660.573 | + | 541.693i | −0.0215319 | + | 0.0176569i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20084.8 | + | 42444.7i | −0.652681 | + | 1.37929i | ||||
\(983\) | −47545.2 | −1.54268 | −0.771341 | − | 0.636423i | \(-0.780413\pi\) | ||||
−0.771341 | + | 0.636423i | \(0.780413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2928.06 | 0.0947165 | ||||||||
\(986\) | −594.843 | + | 1257.06i | −0.0192126 | + | 0.0406015i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7827.12 | − | 9544.86i | −0.252038 | − | 0.307351i | ||||
\(989\) | − | 25884.5i | − | 0.832234i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −892.350 | −0.0286039 | −0.0143019 | − | 0.999898i | \(-0.504553\pi\) | ||||
−0.0143019 | + | 0.999898i | \(0.504553\pi\) | |||||||
\(992\) | −23849.1 | + | 32092.2i | −0.763317 | + | 1.02715i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20382.2 | + | 9644.88i | 0.650388 | + | 0.307764i | ||||
\(995\) | 1602.67i | 0.0510634i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4458.57i | − | 0.141629i | −0.997489 | − | 0.0708146i | \(-0.977440\pi\) | ||
0.997489 | − | 0.0708146i | \(-0.0225599\pi\) | |||||||
\(998\) | −11471.6 | + | 24242.5i | −0.363854 | + | 0.768921i | ||||
\(999\) | 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 | 72.4.d.d.37.1 | 6 | ||
3.2 | odd | 2 | 24.4.d.a.13.6 | yes | 6 | ||
4.3 | odd | 2 | 288.4.d.d.145.4 | 6 | |||
8.3 | odd | 2 | 288.4.d.d.145.3 | 6 | |||
8.5 | even | 2 | inner | 72.4.d.d.37.2 | 6 | ||
12.11 | even | 2 | 96.4.d.a.49.5 | 6 | |||
16.3 | odd | 4 | 2304.4.a.bw.1.2 | 3 | |||
16.5 | even | 4 | 2304.4.a.bt.1.2 | 3 | |||
16.11 | odd | 4 | 2304.4.a.bu.1.2 | 3 | |||
16.13 | even | 4 | 2304.4.a.bv.1.2 | 3 | |||
24.5 | odd | 2 | 24.4.d.a.13.5 | ✓ | 6 | ||
24.11 | even | 2 | 96.4.d.a.49.2 | 6 | |||
48.5 | odd | 4 | 768.4.a.r.1.2 | 3 | |||
48.11 | even | 4 | 768.4.a.t.1.2 | 3 | |||
48.29 | odd | 4 | 768.4.a.s.1.2 | 3 | |||
48.35 | even | 4 | 768.4.a.q.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.d.a.13.5 | ✓ | 6 | 24.5 | odd | 2 | ||
24.4.d.a.13.6 | yes | 6 | 3.2 | odd | 2 | ||
72.4.d.d.37.1 | 6 | 1.1 | even | 1 | trivial | ||
72.4.d.d.37.2 | 6 | 8.5 | even | 2 | inner | ||
96.4.d.a.49.2 | 6 | 24.11 | even | 2 | |||
96.4.d.a.49.5 | 6 | 12.11 | even | 2 | |||
288.4.d.d.145.3 | 6 | 8.3 | odd | 2 | |||
288.4.d.d.145.4 | 6 | 4.3 | odd | 2 | |||
768.4.a.q.1.2 | 3 | 48.35 | even | 4 | |||
768.4.a.r.1.2 | 3 | 48.5 | odd | 4 | |||
768.4.a.s.1.2 | 3 | 48.29 | odd | 4 | |||
768.4.a.t.1.2 | 3 | 48.11 | even | 4 | |||
2304.4.a.bt.1.2 | 3 | 16.5 | even | 4 | |||
2304.4.a.bu.1.2 | 3 | 16.11 | odd | 4 | |||
2304.4.a.bv.1.2 | 3 | 16.13 | even | 4 | |||
2304.4.a.bw.1.2 | 3 | 16.3 | odd | 4 |