Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
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: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.14324\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.69820 | −1.66106 | −0.830532 | − | 0.556970i | \(-0.811964\pi\) | ||||
−0.830532 | + | 0.556970i | \(0.811964\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.0731 | 1.75914 | ||||||||
\(5\) | −4.47249 | −0.400032 | −0.200016 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200016 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.2096 | 1.46918 | 0.734589 | − | 0.678512i | \(-0.237375\pi\) | ||||
0.734589 | + | 0.678512i | \(0.237375\pi\) | |||||||
\(8\) | −28.5326 | −1.26098 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 21.0127 | 0.664479 | ||||||||
\(11\) | 5.99207 | 0.164243 | 0.0821216 | − | 0.996622i | \(-0.473830\pi\) | ||||
0.0821216 | + | 0.996622i | \(0.473830\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −127.836 | −2.44040 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 21.4672 | 0.335425 | ||||||||
\(17\) | −105.037 | −1.49854 | −0.749268 | − | 0.662267i | \(-0.769594\pi\) | ||||
−0.749268 | + | 0.662267i | \(0.769594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −156.462 | −1.88920 | −0.944599 | − | 0.328227i | \(-0.893549\pi\) | ||||
−0.944599 | + | 0.328227i | \(0.893549\pi\) | |||||||
\(20\) | −62.9418 | −0.703711 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −28.1519 | −0.272819 | ||||||||
\(23\) | 175.423 | 1.59036 | 0.795181 | − | 0.606372i | \(-0.207376\pi\) | ||||
0.795181 | + | 0.606372i | \(0.207376\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −104.997 | −0.839975 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 382.923 | 2.58449 | ||||||||
\(29\) | −204.886 | −1.31195 | −0.655973 | − | 0.754785i | \(-0.727741\pi\) | ||||
−0.655973 | + | 0.754785i | \(0.727741\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.9570 | 0.185150 | 0.0925748 | − | 0.995706i | \(-0.470490\pi\) | ||||
0.0925748 | + | 0.995706i | \(0.470490\pi\) | |||||||
\(32\) | 127.404 | 0.703813 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 493.483 | 2.48916 | ||||||||
\(35\) | −121.695 | −0.587718 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 344.140 | 1.52909 | 0.764545 | − | 0.644571i | \(-0.222964\pi\) | ||||
0.764545 | + | 0.644571i | \(0.222964\pi\) | |||||||
\(38\) | 735.088 | 3.13808 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 127.612 | 0.504430 | ||||||||
\(41\) | −46.5921 | −0.177475 | −0.0887373 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887373 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −173.286 | −0.614554 | −0.307277 | − | 0.951620i | \(-0.599418\pi\) | ||||
−0.307277 | + | 0.951620i | \(0.599418\pi\) | |||||||
\(44\) | 84.3269 | 0.288926 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −824.175 | −2.64169 | ||||||||
\(47\) | 265.613 | 0.824334 | 0.412167 | − | 0.911108i | \(-0.364772\pi\) | ||||
0.412167 | + | 0.911108i | \(0.364772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 397.361 | 1.15849 | ||||||||
\(50\) | 493.296 | 1.39525 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −172.912 | −0.448137 | −0.224068 | − | 0.974573i | \(-0.571934\pi\) | ||||
−0.224068 | + | 0.974573i | \(0.571934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −26.7995 | −0.0657025 | ||||||||
\(56\) | −776.360 | −1.85260 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 962.596 | 2.17923 | ||||||||
\(59\) | 137.566 | 0.303551 | 0.151775 | − | 0.988415i | \(-0.451501\pi\) | ||||
0.151775 | + | 0.988415i | \(0.451501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.9384 | −0.123710 | −0.0618548 | − | 0.998085i | \(-0.519702\pi\) | ||||
−0.0618548 | + | 0.998085i | \(0.519702\pi\) | |||||||
\(62\) | −150.140 | −0.307546 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −770.306 | −1.50450 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 211.668 | 0.385961 | 0.192980 | − | 0.981203i | \(-0.438185\pi\) | ||||
0.192980 | + | 0.981203i | \(0.438185\pi\) | |||||||
\(68\) | −1478.19 | −2.63613 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 571.746 | 0.976238 | ||||||||
\(71\) | 436.317 | 0.729314 | 0.364657 | − | 0.931142i | \(-0.381186\pi\) | ||||
0.364657 | + | 0.931142i | \(0.381186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1159.11 | 1.85840 | 0.929199 | − | 0.369579i | \(-0.120498\pi\) | ||||
0.929199 | + | 0.369579i | \(0.120498\pi\) | |||||||
\(74\) | −1616.84 | −2.53992 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2201.90 | −3.32336 | ||||||||
\(77\) | 163.042 | 0.241303 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1017.51 | −1.44910 | −0.724548 | − | 0.689224i | \(-0.757952\pi\) | ||||
−0.724548 | + | 0.689224i | \(0.757952\pi\) | |||||||
\(80\) | −96.0118 | −0.134181 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 218.899 | 0.294797 | ||||||||
\(83\) | 150.251 | 0.198701 | 0.0993504 | − | 0.995053i | \(-0.468324\pi\) | ||||
0.0993504 | + | 0.995053i | \(0.468324\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 469.775 | 0.599462 | ||||||||
\(86\) | 814.131 | 1.02081 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −170.969 | −0.207107 | ||||||||
\(89\) | −565.984 | −0.674092 | −0.337046 | − | 0.941488i | \(-0.609428\pi\) | ||||
−0.337046 | + | 0.941488i | \(0.609428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2468.75 | 2.79766 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1247.90 | −1.36927 | ||||||||
\(95\) | 699.773 | 0.755739 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −286.741 | −0.300145 | −0.150073 | − | 0.988675i | \(-0.547951\pi\) | ||||
−0.150073 | + | 0.988675i | \(0.547951\pi\) | |||||||
\(98\) | −1866.88 | −1.92432 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1477.63 | −1.47763 | ||||||||
\(101\) | 1218.57 | 1.20052 | 0.600258 | − | 0.799807i | \(-0.295065\pi\) | ||||
0.600258 | + | 0.799807i | \(0.295065\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74.2485 | 0.0710283 | 0.0355142 | − | 0.999369i | \(-0.488693\pi\) | ||||
0.0355142 | + | 0.999369i | \(0.488693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 812.374 | 0.744384 | ||||||||
\(107\) | 1253.46 | 1.13249 | 0.566246 | − | 0.824237i | \(-0.308395\pi\) | ||||
0.566246 | + | 0.824237i | \(0.308395\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 722.643 | 0.635015 | 0.317507 | − | 0.948256i | \(-0.397154\pi\) | ||||
0.317507 | + | 0.948256i | \(0.397154\pi\) | |||||||
\(110\) | 125.909 | 0.109136 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 584.113 | 0.492799 | ||||||||
\(113\) | 855.913 | 0.712544 | 0.356272 | − | 0.934382i | \(-0.384048\pi\) | ||||
0.356272 | + | 0.934382i | \(0.384048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −784.580 | −0.636195 | ||||||||
\(116\) | −2883.38 | −2.30789 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −646.310 | −0.504218 | ||||||||
\(119\) | −2858.00 | −2.20162 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1295.10 | −0.973024 | ||||||||
\(122\) | 276.905 | 0.205490 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 449.733 | 0.325703 | ||||||||
\(125\) | 1028.66 | 0.736048 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 726.104 | 0.507333 | 0.253667 | − | 0.967292i | \(-0.418363\pi\) | ||||
0.253667 | + | 0.967292i | \(0.418363\pi\) | |||||||
\(128\) | 2599.82 | 1.79526 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1456.91 | 0.971685 | 0.485843 | − | 0.874046i | \(-0.338513\pi\) | ||||
0.485843 | + | 0.874046i | \(0.338513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4257.25 | −2.77557 | ||||||||
\(134\) | −994.460 | −0.641106 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2996.97 | 1.88962 | ||||||||
\(137\) | −1806.80 | −1.12675 | −0.563377 | − | 0.826200i | \(-0.690498\pi\) | ||||
−0.563377 | + | 0.826200i | \(0.690498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1229.28 | 0.750117 | 0.375059 | − | 0.927001i | \(-0.377623\pi\) | ||||
0.375059 | + | 0.927001i | \(0.377623\pi\) | |||||||
\(140\) | −1712.62 | −1.03388 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2049.90 | −1.21144 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 916.352 | 0.524820 | ||||||||
\(146\) | −5445.71 | −3.08692 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4843.12 | 2.68988 | ||||||||
\(149\) | −446.127 | −0.245290 | −0.122645 | − | 0.992451i | \(-0.539138\pi\) | ||||
−0.122645 | + | 0.992451i | \(0.539138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 207.208 | 0.111671 | 0.0558355 | − | 0.998440i | \(-0.482218\pi\) | ||||
0.0558355 | + | 0.998440i | \(0.482218\pi\) | |||||||
\(152\) | 4464.26 | 2.38223 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −766.002 | −0.400819 | ||||||||
\(155\) | −142.927 | −0.0740658 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1096.60 | 0.557442 | 0.278721 | − | 0.960372i | \(-0.410089\pi\) | ||||
0.278721 | + | 0.960372i | \(0.410089\pi\) | |||||||
\(158\) | 4780.46 | 2.40704 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −569.812 | −0.281547 | ||||||||
\(161\) | 4773.20 | 2.33653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3154.25 | −1.51571 | −0.757853 | − | 0.652425i | \(-0.773752\pi\) | ||||
−0.757853 | + | 0.652425i | \(0.773752\pi\) | |||||||
\(164\) | −655.694 | −0.312202 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −705.908 | −0.330055 | ||||||||
\(167\) | −3679.65 | −1.70503 | −0.852514 | − | 0.522705i | \(-0.824923\pi\) | ||||
−0.852514 | + | 0.522705i | \(0.824923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2207.10 | −0.995745 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2438.66 | −1.08108 | ||||||||
\(173\) | 3666.99 | 1.61154 | 0.805768 | − | 0.592231i | \(-0.201753\pi\) | ||||
0.805768 | + | 0.592231i | \(0.201753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2856.92 | −1.23407 | ||||||||
\(176\) | 128.633 | 0.0550913 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2659.11 | 1.11971 | ||||||||
\(179\) | −4173.50 | −1.74269 | −0.871347 | − | 0.490666i | \(-0.836753\pi\) | ||||
−0.871347 | + | 0.490666i | \(0.836753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −499.197 | −0.205000 | −0.102500 | − | 0.994733i | \(-0.532684\pi\) | ||||
−0.102500 | + | 0.994733i | \(0.532684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5005.29 | −2.00541 | ||||||||
\(185\) | −1539.16 | −0.611685 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −629.386 | −0.246124 | ||||||||
\(188\) | 3738.00 | 1.45012 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3287.68 | −1.25533 | ||||||||
\(191\) | 3086.68 | 1.16934 | 0.584671 | − | 0.811271i | \(-0.301224\pi\) | ||||
0.584671 | + | 0.811271i | \(0.301224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1644.14 | 0.613201 | 0.306601 | − | 0.951838i | \(-0.400808\pi\) | ||||
0.306601 | + | 0.951838i | \(0.400808\pi\) | |||||||
\(194\) | 1347.17 | 0.498561 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5592.10 | 2.03794 | ||||||||
\(197\) | 1371.21 | 0.495911 | 0.247956 | − | 0.968771i | \(-0.420241\pi\) | ||||
0.247956 | + | 0.968771i | \(0.420241\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4627.33 | −1.64836 | −0.824178 | − | 0.566332i | \(-0.808362\pi\) | ||||
−0.824178 | + | 0.566332i | \(0.808362\pi\) | |||||||
\(200\) | 2995.83 | 1.05919 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5725.08 | −1.99413 | ||||||||
\(203\) | −5574.87 | −1.92748 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 208.383 | 0.0709955 | ||||||||
\(206\) | −348.834 | −0.117983 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −937.528 | −0.310288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5088.31 | 1.66016 | 0.830080 | − | 0.557644i | \(-0.188294\pi\) | ||||
0.830080 | + | 0.557644i | \(0.188294\pi\) | |||||||
\(212\) | −2433.40 | −0.788334 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5889.01 | −1.88114 | ||||||||
\(215\) | 775.019 | 0.245841 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 869.535 | 0.272018 | ||||||||
\(218\) | −3395.12 | −1.05480 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −377.151 | −0.115580 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4744.82 | 1.42483 | 0.712415 | − | 0.701759i | \(-0.247602\pi\) | ||||
0.712415 | + | 0.701759i | \(0.247602\pi\) | |||||||
\(224\) | 3466.60 | 1.03403 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4021.25 | −1.18358 | ||||||||
\(227\) | −1145.52 | −0.334937 | −0.167469 | − | 0.985877i | \(-0.553559\pi\) | ||||
−0.167469 | + | 0.985877i | \(0.553559\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1348.47 | 0.389123 | 0.194561 | − | 0.980890i | \(-0.437672\pi\) | ||||
0.194561 | + | 0.980890i | \(0.437672\pi\) | |||||||
\(230\) | 3686.12 | 1.05676 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5845.94 | 1.65433 | ||||||||
\(233\) | 952.002 | 0.267673 | 0.133836 | − | 0.991003i | \(-0.457270\pi\) | ||||
0.133836 | + | 0.991003i | \(0.457270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1187.95 | −0.329760 | ||||||||
\(236\) | 1935.97 | 0.533987 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13427.5 | 3.65703 | ||||||||
\(239\) | 3069.12 | 0.830647 | 0.415323 | − | 0.909674i | \(-0.363668\pi\) | ||||
0.415323 | + | 0.909674i | \(0.363668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2508.17 | 0.670396 | 0.335198 | − | 0.942148i | \(-0.391197\pi\) | ||||
0.335198 | + | 0.942148i | \(0.391197\pi\) | |||||||
\(242\) | 6084.62 | 1.61626 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −829.446 | −0.217622 | ||||||||
\(245\) | −1777.19 | −0.463432 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −911.815 | −0.233469 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4832.85 | −1.22262 | ||||||||
\(251\) | −3405.91 | −0.856490 | −0.428245 | − | 0.903663i | \(-0.640868\pi\) | ||||
−0.428245 | + | 0.903663i | \(0.640868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1051.15 | 0.261206 | ||||||||
\(254\) | −3411.38 | −0.842714 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6052.04 | −1.47755 | ||||||||
\(257\) | 4733.95 | 1.14901 | 0.574506 | − | 0.818501i | \(-0.305194\pi\) | ||||
0.574506 | + | 0.818501i | \(0.305194\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9363.91 | 2.24651 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6844.85 | −1.61403 | ||||||||
\(263\) | 1866.11 | 0.437526 | 0.218763 | − | 0.975778i | \(-0.429798\pi\) | ||||
0.218763 | + | 0.975778i | \(0.429798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 773.346 | 0.179269 | ||||||||
\(266\) | 20001.4 | 4.61040 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2978.83 | 0.678958 | ||||||||
\(269\) | −1580.19 | −0.358164 | −0.179082 | − | 0.983834i | \(-0.557313\pi\) | ||||
−0.179082 | + | 0.983834i | \(0.557313\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4922.09 | 1.10330 | 0.551652 | − | 0.834074i | \(-0.313998\pi\) | ||||
0.551652 | + | 0.834074i | \(0.313998\pi\) | |||||||
\(272\) | −2254.84 | −0.502646 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8488.71 | 1.87161 | ||||||||
\(275\) | −629.148 | −0.137960 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2687.08 | 0.582856 | 0.291428 | − | 0.956593i | \(-0.405870\pi\) | ||||
0.291428 | + | 0.956593i | \(0.405870\pi\) | |||||||
\(278\) | −5775.41 | −1.24599 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3472.26 | 0.741098 | ||||||||
\(281\) | −883.753 | −0.187617 | −0.0938083 | − | 0.995590i | \(-0.529904\pi\) | ||||
−0.0938083 | + | 0.995590i | \(0.529904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −469.776 | −0.0986759 | −0.0493379 | − | 0.998782i | \(-0.515711\pi\) | ||||
−0.0493379 | + | 0.998782i | \(0.515711\pi\) | |||||||
\(284\) | 6140.33 | 1.28296 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1267.75 | −0.260742 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6119.68 | 1.24561 | ||||||||
\(290\) | −4305.20 | −0.871760 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16312.2 | 3.26918 | ||||||||
\(293\) | 3403.76 | 0.678668 | 0.339334 | − | 0.940666i | \(-0.389798\pi\) | ||||
0.339334 | + | 0.940666i | \(0.389798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −615.261 | −0.121430 | ||||||||
\(296\) | −9819.22 | −1.92814 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2095.99 | 0.407442 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4715.03 | −0.902889 | ||||||||
\(302\) | −973.504 | −0.185493 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3358.79 | −0.633684 | ||||||||
\(305\) | 263.602 | 0.0494878 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −888.862 | −0.165244 | −0.0826222 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826222 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(308\) | 2294.50 | 0.424484 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 671.501 | 0.123028 | ||||||||
\(311\) | 1218.36 | 0.222145 | 0.111072 | − | 0.993812i | \(-0.464571\pi\) | ||||
0.111072 | + | 0.993812i | \(0.464571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4870.41 | −0.879526 | −0.439763 | − | 0.898114i | \(-0.644938\pi\) | ||||
−0.439763 | + | 0.898114i | \(0.644938\pi\) | |||||||
\(314\) | −5152.06 | −0.925948 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14319.5 | −2.54916 | ||||||||
\(317\) | −4340.93 | −0.769120 | −0.384560 | − | 0.923100i | \(-0.625647\pi\) | ||||
−0.384560 | + | 0.923100i | \(0.625647\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1227.69 | −0.215478 | ||||||||
\(320\) | 3445.19 | 0.601849 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22425.4 | −3.88112 | ||||||||
\(323\) | 16434.2 | 2.83103 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14819.3 | 2.51769 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1329.39 | 0.223791 | ||||||||
\(329\) | 7227.23 | 1.21109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 907.289 | 0.150662 | 0.0753310 | − | 0.997159i | \(-0.475999\pi\) | ||||
0.0753310 | + | 0.997159i | \(0.475999\pi\) | |||||||
\(332\) | 2114.49 | 0.349542 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17287.7 | 2.83216 | ||||||||
\(335\) | −946.684 | −0.154397 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8660.88 | 1.39997 | 0.699983 | − | 0.714160i | \(-0.253191\pi\) | ||||
0.699983 | + | 0.714160i | \(0.253191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6611.19 | 1.05454 | ||||||||
\(341\) | 191.488 | 0.0304096 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1479.14 | 0.232846 | ||||||||
\(344\) | 4944.29 | 0.774937 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17228.2 | −2.67687 | ||||||||
\(347\) | 347.605 | 0.0537763 | 0.0268882 | − | 0.999638i | \(-0.491440\pi\) | ||||
0.0268882 | + | 0.999638i | \(0.491440\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10970.2 | 1.68258 | 0.841292 | − | 0.540581i | \(-0.181795\pi\) | ||||
0.841292 | + | 0.540581i | \(0.181795\pi\) | |||||||
\(350\) | 13422.4 | 2.04988 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 763.411 | 0.115596 | ||||||||
\(353\) | 10384.8 | 1.56580 | 0.782901 | − | 0.622146i | \(-0.213739\pi\) | ||||
0.782901 | + | 0.622146i | \(0.213739\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1951.42 | −0.291749 | ||||||||
\(356\) | −7965.15 | −1.18582 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19608.0 | 2.89473 | ||||||||
\(359\) | 8665.80 | 1.27399 | 0.636996 | − | 0.770867i | \(-0.280177\pi\) | ||||
0.636996 | + | 0.770867i | \(0.280177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17621.2 | 2.56907 | ||||||||
\(362\) | 2345.33 | 0.340518 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5184.09 | −0.743419 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1234.22 | 0.175547 | 0.0877734 | − | 0.996140i | \(-0.472025\pi\) | ||||
0.0877734 | + | 0.996140i | \(0.472025\pi\) | |||||||
\(368\) | 3765.85 | 0.533447 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7231.31 | 1.01605 | ||||||||
\(371\) | −4704.85 | −0.658393 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −427.483 | −0.0593410 | −0.0296705 | − | 0.999560i | \(-0.509446\pi\) | ||||
−0.0296705 | + | 0.999560i | \(0.509446\pi\) | |||||||
\(374\) | 2956.98 | 0.408829 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7578.64 | −1.03946 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 124.241 | 0.0168386 | 0.00841929 | − | 0.999965i | \(-0.497320\pi\) | ||||
0.00841929 | + | 0.999965i | \(0.497320\pi\) | |||||||
\(380\) | 9847.98 | 1.32945 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14501.8 | −1.94235 | ||||||||
\(383\) | −9341.21 | −1.24625 | −0.623125 | − | 0.782122i | \(-0.714137\pi\) | ||||
−0.623125 | + | 0.782122i | \(0.714137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −729.202 | −0.0965288 | ||||||||
\(386\) | −7724.51 | −1.01857 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4035.33 | −0.527997 | ||||||||
\(389\) | −11368.9 | −1.48182 | −0.740908 | − | 0.671607i | \(-0.765604\pi\) | ||||
−0.740908 | + | 0.671607i | \(0.765604\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18425.9 | −2.38321 | ||||||||
\(392\) | −11337.7 | −1.46082 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6442.21 | −0.823741 | ||||||||
\(395\) | 4550.80 | 0.579685 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12077.8 | −1.52687 | −0.763436 | − | 0.645883i | \(-0.776489\pi\) | ||||
−0.763436 | + | 0.645883i | \(0.776489\pi\) | |||||||
\(398\) | 21740.1 | 2.73802 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2253.99 | −0.281748 | ||||||||
\(401\) | 4856.74 | 0.604823 | 0.302411 | − | 0.953178i | \(-0.402208\pi\) | ||||
0.302411 | + | 0.953178i | \(0.402208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 17149.0 | 2.11187 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26191.8 | 3.20167 | ||||||||
\(407\) | 2062.11 | 0.251143 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2981.80 | 0.360490 | 0.180245 | − | 0.983622i | \(-0.442311\pi\) | ||||
0.180245 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(410\) | −979.023 | −0.117928 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1044.91 | 0.124949 | ||||||||
\(413\) | 3743.10 | 0.445971 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −671.995 | −0.0794866 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4404.70 | 0.515409 | ||||||||
\(419\) | −7774.01 | −0.906408 | −0.453204 | − | 0.891407i | \(-0.649719\pi\) | ||||
−0.453204 | + | 0.891407i | \(0.649719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3959.71 | 0.458396 | 0.229198 | − | 0.973380i | \(-0.426390\pi\) | ||||
0.229198 | + | 0.973380i | \(0.426390\pi\) | |||||||
\(422\) | −23905.9 | −2.75763 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4933.62 | 0.565089 | ||||||||
\(425\) | 11028.5 | 1.25873 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1603.69 | −0.181752 | ||||||||
\(428\) | 17640.1 | 1.99221 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3641.19 | −0.408358 | ||||||||
\(431\) | −4375.12 | −0.488961 | −0.244480 | − | 0.969654i | \(-0.578617\pi\) | ||||
−0.244480 | + | 0.969654i | \(0.578617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8992.74 | 0.998068 | 0.499034 | − | 0.866582i | \(-0.333688\pi\) | ||||
0.499034 | + | 0.866582i | \(0.333688\pi\) | |||||||
\(434\) | −4085.25 | −0.451839 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10169.8 | 1.11708 | ||||||||
\(437\) | −27447.0 | −3.00451 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −195.465 | −0.0212506 | −0.0106253 | − | 0.999944i | \(-0.503382\pi\) | ||||
−0.0106253 | + | 0.999944i | \(0.503382\pi\) | |||||||
\(440\) | 764.659 | 0.0828493 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7369.97 | −0.790424 | −0.395212 | − | 0.918590i | \(-0.629329\pi\) | ||||
−0.395212 | + | 0.918590i | \(0.629329\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2531.36 | 0.269658 | ||||||||
\(446\) | −22292.1 | −2.36673 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20959.7 | −2.21038 | ||||||||
\(449\) | 164.281 | 0.0172670 | 0.00863351 | − | 0.999963i | \(-0.497252\pi\) | ||||
0.00863351 | + | 0.999963i | \(0.497252\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −279.183 | −0.0291490 | ||||||||
\(452\) | 12045.3 | 1.25346 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5381.88 | 0.556352 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11687.0 | 1.19627 | 0.598133 | − | 0.801397i | \(-0.295909\pi\) | ||||
0.598133 | + | 0.801397i | \(0.295909\pi\) | |||||||
\(458\) | −6335.36 | −0.646358 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11041.5 | −1.11915 | ||||||||
\(461\) | −1057.53 | −0.106842 | −0.0534211 | − | 0.998572i | \(-0.517013\pi\) | ||||
−0.0534211 | + | 0.998572i | \(0.517013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8554.74 | 0.858688 | 0.429344 | − | 0.903141i | \(-0.358745\pi\) | ||||
0.429344 | + | 0.903141i | \(0.358745\pi\) | |||||||
\(464\) | −4398.33 | −0.440059 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4472.70 | −0.444622 | ||||||||
\(467\) | 7705.26 | 0.763506 | 0.381753 | − | 0.924264i | \(-0.375321\pi\) | ||||
0.381753 | + | 0.924264i | \(0.375321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5759.40 | 0.567046 | ||||||||
\(470\) | 5581.24 | 0.547752 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3925.10 | −0.382770 | ||||||||
\(473\) | −1038.34 | −0.100936 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16428.0 | 1.58688 | ||||||||
\(476\) | −40220.9 | −3.87295 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14419.3 | −1.37976 | ||||||||
\(479\) | 4508.59 | 0.430069 | 0.215034 | − | 0.976606i | \(-0.431014\pi\) | ||||
0.215034 | + | 0.976606i | \(0.431014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11783.9 | −1.11357 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18226.0 | −1.71168 | ||||||||
\(485\) | 1282.45 | 0.120068 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6725.73 | 0.625815 | 0.312908 | − | 0.949784i | \(-0.398697\pi\) | ||||
0.312908 | + | 0.949784i | \(0.398697\pi\) | |||||||
\(488\) | 1681.67 | 0.155995 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8349.61 | 0.769790 | ||||||||
\(491\) | −11517.5 | −1.05861 | −0.529303 | − | 0.848433i | \(-0.677546\pi\) | ||||
−0.529303 | + | 0.848433i | \(0.677546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21520.5 | 1.96600 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 686.026 | 0.0621038 | ||||||||
\(497\) | 11872.0 | 1.07149 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19907.9 | 1.78598 | 0.892988 | − | 0.450080i | \(-0.148605\pi\) | ||||
0.892988 | + | 0.450080i | \(0.148605\pi\) | |||||||
\(500\) | 14476.4 | 1.29481 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16001.6 | 1.42269 | ||||||||
\(503\) | 5735.48 | 0.508415 | 0.254207 | − | 0.967150i | \(-0.418185\pi\) | ||||
0.254207 | + | 0.967150i | \(0.418185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5450.04 | −0.480244 | ||||||||
\(506\) | −4938.51 | −0.433881 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10218.5 | 0.892469 | ||||||||
\(509\) | −9253.84 | −0.805834 | −0.402917 | − | 0.915237i | \(-0.632004\pi\) | ||||
−0.402917 | + | 0.915237i | \(0.632004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31538.8 | 2.73032 | ||||||||
\(512\) | 7635.12 | 0.659039 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22241.1 | −1.90858 | ||||||||
\(515\) | −332.076 | −0.0284136 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1591.57 | 0.135391 | ||||||||
\(518\) | −43993.5 | −3.73159 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3887.42 | −0.326892 | −0.163446 | − | 0.986552i | \(-0.552261\pi\) | ||||
−0.163446 | + | 0.986552i | \(0.552261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4782.27 | 0.399836 | 0.199918 | − | 0.979813i | \(-0.435932\pi\) | ||||
0.199918 | + | 0.979813i | \(0.435932\pi\) | |||||||
\(524\) | 20503.2 | 1.70933 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8767.37 | −0.726759 | ||||||||
\(527\) | −3356.65 | −0.277453 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18606.4 | 1.52925 | ||||||||
\(530\) | −3633.34 | −0.297777 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −59912.7 | −4.88261 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5606.09 | −0.453033 | ||||||||
\(536\) | −6039.44 | −0.486687 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7424.06 | 0.594933 | ||||||||
\(539\) | 2381.01 | 0.190274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14872.6 | −1.18192 | −0.590962 | − | 0.806699i | \(-0.701252\pi\) | ||||
−0.590962 | + | 0.806699i | \(0.701252\pi\) | |||||||
\(542\) | −23125.0 | −1.83266 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13382.0 | −1.05469 | ||||||||
\(545\) | −3232.01 | −0.254026 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16965.3 | 1.32611 | 0.663055 | − | 0.748570i | \(-0.269259\pi\) | ||||
0.663055 | + | 0.748570i | \(0.269259\pi\) | |||||||
\(548\) | −25427.3 | −1.98212 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2955.86 | 0.229161 | ||||||||
\(551\) | 32056.8 | 2.47852 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27686.0 | −2.12898 | ||||||||
\(554\) | −12624.5 | −0.968162 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17299.8 | 1.31956 | ||||||||
\(557\) | −1934.05 | −0.147125 | −0.0735623 | − | 0.997291i | \(-0.523437\pi\) | ||||
−0.0735623 | + | 0.997291i | \(0.523437\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2612.44 | −0.197135 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4152.05 | 0.311643 | ||||||||
\(563\) | −6592.13 | −0.493473 | −0.246736 | − | 0.969083i | \(-0.579358\pi\) | ||||
−0.246736 | + | 0.969083i | \(0.579358\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3828.06 | −0.285040 | ||||||||
\(566\) | 2207.10 | 0.163907 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12449.3 | −0.919646 | ||||||||
\(569\) | 14477.7 | 1.06667 | 0.533336 | − | 0.845903i | \(-0.320938\pi\) | ||||
0.533336 | + | 0.845903i | \(0.320938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4998.21 | −0.366320 | −0.183160 | − | 0.983083i | \(-0.558633\pi\) | ||||
−0.183160 | + | 0.983083i | \(0.558633\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5956.15 | 0.433109 | ||||||||
\(575\) | −18418.9 | −1.33586 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9291.73 | 0.670398 | 0.335199 | − | 0.942147i | \(-0.391196\pi\) | ||||
0.335199 | + | 0.942147i | \(0.391196\pi\) | |||||||
\(578\) | −28751.5 | −2.06904 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12895.9 | 0.923230 | ||||||||
\(581\) | 4088.26 | 0.291927 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1036.10 | −0.0736034 | ||||||||
\(584\) | −33072.3 | −2.34339 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15991.5 | −1.12731 | ||||||||
\(587\) | 5602.64 | 0.393945 | 0.196972 | − | 0.980409i | \(-0.436889\pi\) | ||||
0.196972 | + | 0.980409i | \(0.436889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5000.04 | −0.349784 | ||||||||
\(590\) | 2890.62 | 0.201703 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7387.73 | 0.512895 | ||||||||
\(593\) | 10885.8 | 0.753839 | 0.376919 | − | 0.926246i | \(-0.376983\pi\) | ||||
0.376919 | + | 0.926246i | \(0.376983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12782.4 | 0.880717 | ||||||||
\(596\) | −6278.38 | −0.431498 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20403.2 | −1.39174 | −0.695872 | − | 0.718166i | \(-0.744982\pi\) | ||||
−0.695872 | + | 0.718166i | \(0.744982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6312.19 | −0.428419 | −0.214209 | − | 0.976788i | \(-0.568717\pi\) | ||||
−0.214209 | + | 0.976788i | \(0.568717\pi\) | |||||||
\(602\) | 22152.2 | 1.49976 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2916.05 | 0.196445 | ||||||||
\(605\) | 5792.30 | 0.389241 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21848.6 | −1.46097 | −0.730484 | − | 0.682930i | \(-0.760705\pi\) | ||||
−0.730484 | + | 0.682930i | \(0.760705\pi\) | |||||||
\(608\) | −19933.8 | −1.32964 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1238.45 | −0.0822025 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1335.14 | −0.0879704 | −0.0439852 | − | 0.999032i | \(-0.514005\pi\) | ||||
−0.0439852 | + | 0.999032i | \(0.514005\pi\) | |||||||
\(614\) | 4176.05 | 0.274482 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4652.00 | −0.304277 | ||||||||
\(617\) | −18908.3 | −1.23374 | −0.616871 | − | 0.787064i | \(-0.711600\pi\) | ||||
−0.616871 | + | 0.787064i | \(0.711600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6722.49 | 0.436510 | 0.218255 | − | 0.975892i | \(-0.429964\pi\) | ||||
0.218255 | + | 0.975892i | \(0.429964\pi\) | |||||||
\(620\) | −2011.43 | −0.130292 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5724.11 | −0.368997 | ||||||||
\(623\) | −15400.2 | −0.990362 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8523.93 | 0.545532 | ||||||||
\(626\) | 22882.2 | 1.46095 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15432.6 | 0.980617 | ||||||||
\(629\) | −36147.3 | −2.29140 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8098.44 | −0.510925 | −0.255463 | − | 0.966819i | \(-0.582228\pi\) | ||||
−0.255463 | + | 0.966819i | \(0.582228\pi\) | |||||||
\(632\) | 29032.2 | 1.82727 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20394.6 | 1.27756 | ||||||||
\(635\) | −3247.50 | −0.202950 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5767.94 | 0.357923 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11627.7 | −0.718163 | ||||||||
\(641\) | 10955.9 | 0.675090 | 0.337545 | − | 0.941309i | \(-0.390403\pi\) | ||||
0.337545 | + | 0.941309i | \(0.390403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28125.0 | −1.72495 | −0.862473 | − | 0.506104i | \(-0.831085\pi\) | ||||
−0.862473 | + | 0.506104i | \(0.831085\pi\) | |||||||
\(644\) | 67173.7 | 4.11027 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −77211.1 | −4.70253 | ||||||||
\(647\) | 29001.4 | 1.76223 | 0.881115 | − | 0.472901i | \(-0.156793\pi\) | ||||
0.881115 | + | 0.472901i | \(0.156793\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 824.302 | 0.0498562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44390.1 | −2.66634 | ||||||||
\(653\) | −19506.3 | −1.16898 | −0.584488 | − | 0.811402i | \(-0.698705\pi\) | ||||
−0.584488 | + | 0.811402i | \(0.698705\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6516.01 | −0.388705 | ||||||||
\(656\) | −1000.20 | −0.0595294 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −33955.0 | −2.01171 | ||||||||
\(659\) | −5985.86 | −0.353833 | −0.176917 | − | 0.984226i | \(-0.556612\pi\) | ||||
−0.176917 | + | 0.984226i | \(0.556612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −280.836 | −0.0165254 | −0.00826268 | − | 0.999966i | \(-0.502630\pi\) | ||||
−0.00826268 | + | 0.999966i | \(0.502630\pi\) | |||||||
\(662\) | −4262.63 | −0.250259 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4287.04 | −0.250557 | ||||||||
\(665\) | 19040.5 | 1.11032 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35941.8 | −2.08647 | ||||||||
\(668\) | −51784.0 | −2.99938 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4447.71 | 0.256463 | ||||||||
\(671\) | −353.163 | −0.0203185 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14868.9 | −0.851640 | −0.425820 | − | 0.904808i | \(-0.640014\pi\) | ||||
−0.425820 | + | 0.904808i | \(0.640014\pi\) | |||||||
\(674\) | −40690.6 | −2.32543 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20769.5 | 1.17908 | 0.589540 | − | 0.807739i | \(-0.299309\pi\) | ||||
0.589540 | + | 0.807739i | \(0.299309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7802.09 | −0.440967 | ||||||||
\(680\) | −13403.9 | −0.755907 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −899.650 | −0.0505123 | ||||||||
\(683\) | −14980.8 | −0.839275 | −0.419638 | − | 0.907692i | \(-0.637843\pi\) | ||||
−0.419638 | + | 0.907692i | \(0.637843\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8080.90 | 0.450738 | ||||||||
\(686\) | −6949.30 | −0.386772 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3719.96 | −0.206137 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9472.45 | 0.521489 | 0.260745 | − | 0.965408i | \(-0.416032\pi\) | ||||
0.260745 | + | 0.965408i | \(0.416032\pi\) | |||||||
\(692\) | 51605.8 | 2.83491 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1633.12 | −0.0893260 | ||||||||
\(695\) | −5497.95 | −0.300071 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4893.87 | 0.265952 | ||||||||
\(698\) | −51540.3 | −2.79488 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −40205.7 | −2.17090 | ||||||||
\(701\) | −1035.34 | −0.0557834 | −0.0278917 | − | 0.999611i | \(-0.508879\pi\) | ||||
−0.0278917 | + | 0.999611i | \(0.508879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53844.8 | −2.88875 | ||||||||
\(704\) | −4615.72 | −0.247105 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −48790.0 | −2.60090 | ||||||||
\(707\) | 33156.7 | 1.76377 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16800.4 | 0.889917 | 0.444958 | − | 0.895551i | \(-0.353219\pi\) | ||||
0.444958 | + | 0.895551i | \(0.353219\pi\) | |||||||
\(710\) | 9168.18 | 0.484614 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16149.0 | 0.850013 | ||||||||
\(713\) | 5606.00 | 0.294455 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −58734.1 | −3.06564 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −40713.7 | −2.11618 | ||||||||
\(719\) | −14873.1 | −0.771449 | −0.385724 | − | 0.922614i | \(-0.626048\pi\) | ||||
−0.385724 | + | 0.922614i | \(0.626048\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2020.27 | 0.104353 | ||||||||
\(722\) | −82788.1 | −4.26739 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7025.24 | −0.360623 | ||||||||
\(725\) | 21512.4 | 1.10200 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2318.92 | −0.118300 | −0.0591500 | − | 0.998249i | \(-0.518839\pi\) | ||||
−0.0591500 | + | 0.998249i | \(0.518839\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24355.9 | 1.23487 | ||||||||
\(731\) | 18201.3 | 0.920931 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3350.95 | −0.168854 | −0.0844270 | − | 0.996430i | \(-0.526906\pi\) | ||||
−0.0844270 | + | 0.996430i | \(0.526906\pi\) | |||||||
\(734\) | −5798.61 | −0.291595 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22349.6 | 1.11932 | ||||||||
\(737\) | 1268.33 | 0.0633915 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29348.1 | −1.46088 | −0.730438 | − | 0.682979i | \(-0.760684\pi\) | ||||
−0.730438 | + | 0.682979i | \(0.760684\pi\) | |||||||
\(740\) | −21660.8 | −1.07604 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22104.3 | 1.09363 | ||||||||
\(743\) | −23622.2 | −1.16637 | −0.583187 | − | 0.812338i | \(-0.698195\pi\) | ||||
−0.583187 | + | 0.812338i | \(0.698195\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1995.30 | 0.0981236 | ||||||||
\(746\) | 2008.40 | 0.0985693 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8857.41 | −0.432966 | ||||||||
\(749\) | 34106.1 | 1.66383 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29751.4 | 1.44560 | 0.722798 | − | 0.691059i | \(-0.242856\pi\) | ||||
0.722798 | + | 0.691059i | \(0.242856\pi\) | |||||||
\(752\) | 5701.97 | 0.276502 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −926.735 | −0.0446720 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36907.2 | −1.77201 | −0.886006 | − | 0.463673i | \(-0.846531\pi\) | ||||
−0.886006 | + | 0.463673i | \(0.846531\pi\) | |||||||
\(758\) | −583.709 | −0.0279700 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19966.4 | −0.952968 | ||||||||
\(761\) | 20208.2 | 0.962613 | 0.481306 | − | 0.876552i | \(-0.340162\pi\) | ||||
0.481306 | + | 0.876552i | \(0.340162\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19662.8 | 0.932950 | ||||||||
\(764\) | 43439.1 | 2.05703 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43886.9 | 2.07010 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24751.0 | 1.16066 | 0.580329 | − | 0.814382i | \(-0.302924\pi\) | ||||
0.580329 | + | 0.814382i | \(0.302924\pi\) | |||||||
\(770\) | 3425.94 | 0.160341 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23138.2 | 1.07871 | ||||||||
\(773\) | 30673.4 | 1.42722 | 0.713612 | − | 0.700541i | \(-0.247058\pi\) | ||||
0.713612 | + | 0.700541i | \(0.247058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3355.38 | −0.155521 | ||||||||
\(776\) | 8181.46 | 0.378476 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 53413.4 | 2.46139 | ||||||||
\(779\) | 7289.87 | 0.335285 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2614.44 | 0.119785 | ||||||||
\(782\) | 86568.5 | 3.95867 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8530.23 | 0.388585 | ||||||||
\(785\) | −4904.55 | −0.222995 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29009.9 | 1.31397 | 0.656983 | − | 0.753905i | \(-0.271832\pi\) | ||||
0.656983 | + | 0.753905i | \(0.271832\pi\) | |||||||
\(788\) | 19297.1 | 0.872375 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21380.6 | −0.962894 | ||||||||
\(791\) | 23289.0 | 1.04685 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 56744.0 | 2.53623 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −65120.8 | −2.89968 | ||||||||
\(797\) | −6778.24 | −0.301252 | −0.150626 | − | 0.988591i | \(-0.548129\pi\) | ||||
−0.150626 | + | 0.988591i | \(0.548129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27899.1 | −1.23529 | ||||||||
\(800\) | −13377.0 | −0.591185 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22817.9 | −1.00465 | ||||||||
\(803\) | 6945.44 | 0.305229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21348.1 | −0.934685 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −34768.9 | −1.51382 | ||||||||
\(809\) | 34862.9 | 1.51510 | 0.757549 | − | 0.652778i | \(-0.226397\pi\) | ||||
0.757549 | + | 0.652778i | \(0.226397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22665.4 | 0.981370 | 0.490685 | − | 0.871337i | \(-0.336747\pi\) | ||||
0.490685 | + | 0.871337i | \(0.336747\pi\) | |||||||
\(812\) | −78455.6 | −3.39070 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9688.21 | −0.417164 | ||||||||
\(815\) | 14107.4 | 0.606331 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27112.6 | 1.16101 | ||||||||
\(818\) | −14009.1 | −0.598797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2932.59 | 0.124891 | ||||||||
\(821\) | −20748.7 | −0.882016 | −0.441008 | − | 0.897503i | \(-0.645379\pi\) | ||||
−0.441008 | + | 0.897503i | \(0.645379\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6141.41 | 0.260117 | 0.130058 | − | 0.991506i | \(-0.458484\pi\) | ||||
0.130058 | + | 0.991506i | \(0.458484\pi\) | |||||||
\(824\) | −2118.50 | −0.0895650 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17585.8 | −0.740786 | ||||||||
\(827\) | 28383.5 | 1.19346 | 0.596730 | − | 0.802442i | \(-0.296467\pi\) | ||||
0.596730 | + | 0.802442i | \(0.296467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −908.734 | −0.0380720 | −0.0190360 | − | 0.999819i | \(-0.506060\pi\) | ||||
−0.0190360 | + | 0.999819i | \(0.506060\pi\) | |||||||
\(830\) | 3157.17 | 0.132032 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41737.4 | −1.73603 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16457.2 | 0.682065 | ||||||||
\(836\) | −13193.9 | −0.545839 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36523.8 | 1.50560 | ||||||||
\(839\) | 27820.3 | 1.14477 | 0.572385 | − | 0.819985i | \(-0.306018\pi\) | ||||
0.572385 | + | 0.819985i | \(0.306018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17589.3 | 0.721200 | ||||||||
\(842\) | −18603.5 | −0.761425 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 71608.3 | 2.92045 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35239.0 | −1.42955 | ||||||||
\(848\) | −3711.93 | −0.150316 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −51814.1 | −2.09084 | ||||||||
\(851\) | 60370.3 | 2.43181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5802.11 | 0.232896 | 0.116448 | − | 0.993197i | \(-0.462849\pi\) | ||||
0.116448 | + | 0.993197i | \(0.462849\pi\) | |||||||
\(854\) | 7534.45 | 0.301901 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35764.5 | −1.42804 | ||||||||
\(857\) | 43311.1 | 1.72635 | 0.863173 | − | 0.504909i | \(-0.168474\pi\) | ||||
0.863173 | + | 0.504909i | \(0.168474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16698.2 | −0.663254 | −0.331627 | − | 0.943411i | \(-0.607598\pi\) | ||||
−0.331627 | + | 0.943411i | \(0.607598\pi\) | |||||||
\(860\) | 10906.9 | 0.432468 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20555.2 | 0.812196 | ||||||||
\(863\) | −19429.2 | −0.766369 | −0.383185 | − | 0.923672i | \(-0.625173\pi\) | ||||
−0.383185 | + | 0.923672i | \(0.625173\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16400.6 | −0.644666 | ||||||||
\(866\) | −42249.7 | −1.65786 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12237.0 | 0.478517 | ||||||||
\(869\) | −6096.98 | −0.238004 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20618.9 | −0.800738 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 128952. | 4.99068 | ||||||||
\(875\) | 27989.4 | 1.08139 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11619.7 | 0.447400 | 0.223700 | − | 0.974658i | \(-0.428186\pi\) | ||||
0.223700 | + | 0.974658i | \(0.428186\pi\) | |||||||
\(878\) | 918.332 | 0.0352986 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −575.309 | −0.0220383 | ||||||||
\(881\) | 51102.0 | 1.95422 | 0.977112 | − | 0.212726i | \(-0.0682341\pi\) | ||||
0.977112 | + | 0.212726i | \(0.0682341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37838.5 | −1.44209 | −0.721046 | − | 0.692888i | \(-0.756338\pi\) | ||||
−0.721046 | + | 0.692888i | \(0.756338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34625.6 | 1.31295 | ||||||||
\(887\) | 9626.92 | 0.364420 | 0.182210 | − | 0.983260i | \(-0.441675\pi\) | ||||
0.182210 | + | 0.983260i | \(0.441675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19757.0 | 0.745364 | ||||||||
\(890\) | −11892.8 | −0.447920 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 66774.3 | 2.50647 | ||||||||
\(893\) | −41558.3 | −1.55733 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18666.0 | 0.697133 | ||||||||
\(896\) | 70740.0 | 2.63757 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −771.825 | −0.0286816 | ||||||||
\(899\) | −6547.54 | −0.242906 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18162.0 | 0.671549 | ||||||||
\(902\) | 1311.66 | 0.0484184 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24421.4 | −0.898500 | ||||||||
\(905\) | 2232.65 | 0.0820065 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17066.0 | 0.624772 | 0.312386 | − | 0.949955i | \(-0.398872\pi\) | ||||
0.312386 | + | 0.949955i | \(0.398872\pi\) | |||||||
\(908\) | −16121.0 | −0.589200 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37423.9 | 1.36104 | 0.680521 | − | 0.732729i | \(-0.261754\pi\) | ||||
0.680521 | + | 0.732729i | \(0.261754\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 900.312 | 0.0326353 | ||||||||
\(914\) | −54907.7 | −1.98708 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18977.1 | 0.684520 | ||||||||
\(917\) | 39641.9 | 1.42758 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2783.88 | −0.0999256 | −0.0499628 | − | 0.998751i | \(-0.515910\pi\) | ||||
−0.0499628 | + | 0.998751i | \(0.515910\pi\) | |||||||
\(920\) | 22386.1 | 0.802227 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4968.50 | 0.177472 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36133.6 | −1.28440 | ||||||||
\(926\) | −40191.9 | −1.42634 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26103.3 | −0.923363 | ||||||||
\(929\) | −26585.2 | −0.938894 | −0.469447 | − | 0.882961i | \(-0.655547\pi\) | ||||
−0.469447 | + | 0.882961i | \(0.655547\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −62171.8 | −2.18861 | ||||||||
\(932\) | 13397.6 | 0.470873 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36200.9 | −1.26823 | ||||||||
\(935\) | 2814.92 | 0.0984576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34474.0 | 1.20194 | 0.600970 | − | 0.799272i | \(-0.294781\pi\) | ||||
0.600970 | + | 0.799272i | \(0.294781\pi\) | |||||||
\(938\) | −27058.8 | −0.941900 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16718.2 | −0.580092 | ||||||||
\(941\) | 41994.3 | 1.45481 | 0.727404 | − | 0.686209i | \(-0.240726\pi\) | ||||
0.727404 | + | 0.686209i | \(0.240726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8173.34 | −0.282249 | ||||||||
\(944\) | 2953.15 | 0.101819 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4878.32 | 0.167662 | ||||||||
\(947\) | 49352.0 | 1.69348 | 0.846739 | − | 0.532008i | \(-0.178562\pi\) | ||||
0.846739 | + | 0.532008i | \(0.178562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −77181.9 | −2.63591 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 81546.2 | 2.77618 | ||||||||
\(953\) | 51144.5 | 1.73844 | 0.869220 | − | 0.494425i | \(-0.164621\pi\) | ||||
0.869220 | + | 0.494425i | \(0.164621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13805.2 | −0.467774 | ||||||||
\(956\) | 43192.0 | 1.46122 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21182.3 | −0.714372 | ||||||||
\(959\) | −49162.3 | −1.65540 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28769.8 | −0.965720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35297.7 | 1.17932 | ||||||||
\(965\) | −7353.41 | −0.245300 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24895.1 | −0.827892 | −0.413946 | − | 0.910301i | \(-0.635850\pi\) | ||||
−0.413946 | + | 0.910301i | \(0.635850\pi\) | |||||||
\(968\) | 36952.4 | 1.22696 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6025.19 | −0.199440 | ||||||||
\(971\) | −42942.9 | −1.41926 | −0.709630 | − | 0.704574i | \(-0.751138\pi\) | ||||
−0.709630 | + | 0.704574i | \(0.751138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33448.2 | 1.10206 | ||||||||
\(974\) | −31598.8 | −1.03952 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1265.24 | −0.0414953 | ||||||||
\(977\) | −42555.7 | −1.39353 | −0.696764 | − | 0.717301i | \(-0.745377\pi\) | ||||
−0.696764 | + | 0.717301i | \(0.745377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3391.41 | −0.110715 | ||||||||
\(980\) | −25010.6 | −0.815240 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 54111.3 | 1.75841 | ||||||||
\(983\) | 4345.38 | 0.140993 | 0.0704965 | − | 0.997512i | \(-0.477542\pi\) | ||||
0.0704965 | + | 0.997512i | \(0.477542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6132.71 | −0.198380 | ||||||||
\(986\) | −101108. | −3.26565 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30398.4 | −0.977363 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7934.89 | 0.254349 | 0.127175 | − | 0.991880i | \(-0.459409\pi\) | ||||
0.127175 | + | 0.991880i | \(0.459409\pi\) | |||||||
\(992\) | 4071.43 | 0.130311 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −55777.0 | −1.77982 | ||||||||
\(995\) | 20695.7 | 0.659395 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2725.62 | 0.0865810 | 0.0432905 | − | 0.999063i | \(-0.486216\pi\) | ||||
0.0432905 | + | 0.999063i | \(0.486216\pi\) | |||||||
\(998\) | −93531.5 | −2.96662 | ||||||||
\(999\) | 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 | 1521.4.a.bf.1.2 | 9 | ||
3.2 | odd | 2 | 507.4.a.p.1.8 | yes | 9 | ||
13.12 | even | 2 | 1521.4.a.bi.1.8 | 9 | |||
39.5 | even | 4 | 507.4.b.k.337.3 | 18 | |||
39.8 | even | 4 | 507.4.b.k.337.16 | 18 | |||
39.38 | odd | 2 | 507.4.a.o.1.2 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.2 | ✓ | 9 | 39.38 | odd | 2 | ||
507.4.a.p.1.8 | yes | 9 | 3.2 | odd | 2 | ||
507.4.b.k.337.3 | 18 | 39.5 | even | 4 | |||
507.4.b.k.337.16 | 18 | 39.8 | even | 4 | |||
1521.4.a.bf.1.2 | 9 | 1.1 | even | 1 | trivial | ||
1521.4.a.bi.1.8 | 9 | 13.12 | even | 2 |