Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,4,Mod(1,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, 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("78.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.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: | \(4.60214898045\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 78.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −20.0000 | −1.78885 | −0.894427 | − | 0.447214i | \(-0.852416\pi\) | ||||
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −32.0000 | −1.72784 | −0.863919 | − | 0.503631i | \(-0.831997\pi\) | ||||
−0.863919 | + | 0.503631i | \(0.831997\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −40.0000 | −1.26491 | ||||||||
\(11\) | 50.0000 | 1.37051 | 0.685253 | − | 0.728305i | \(-0.259692\pi\) | ||||
0.685253 | + | 0.728305i | \(0.259692\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | −64.0000 | −1.22177 | ||||||||
\(15\) | 60.0000 | 1.03280 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −30.0000 | −0.428004 | −0.214002 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214002 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −120.000 | −1.44894 | −0.724471 | − | 0.689306i | \(-0.757916\pi\) | ||||
−0.724471 | + | 0.689306i | \(0.757916\pi\) | |||||||
\(20\) | −80.0000 | −0.894427 | ||||||||
\(21\) | 96.0000 | 0.997567 | ||||||||
\(22\) | 100.000 | 0.969094 | ||||||||
\(23\) | −20.0000 | −0.181317 | −0.0906584 | − | 0.995882i | \(-0.528897\pi\) | ||||
−0.0906584 | + | 0.995882i | \(0.528897\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 275.000 | 2.20000 | ||||||||
\(26\) | −26.0000 | −0.196116 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −128.000 | −0.863919 | ||||||||
\(29\) | 82.0000 | 0.525070 | 0.262535 | − | 0.964923i | \(-0.415442\pi\) | ||||
0.262535 | + | 0.964923i | \(0.415442\pi\) | |||||||
\(30\) | 120.000 | 0.730297 | ||||||||
\(31\) | −44.0000 | −0.254924 | −0.127462 | − | 0.991843i | \(-0.540683\pi\) | ||||
−0.127462 | + | 0.991843i | \(0.540683\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −150.000 | −0.791262 | ||||||||
\(34\) | −60.0000 | −0.302645 | ||||||||
\(35\) | 640.000 | 3.09085 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −306.000 | −1.35962 | −0.679812 | − | 0.733386i | \(-0.737939\pi\) | ||||
−0.679812 | + | 0.733386i | \(0.737939\pi\) | |||||||
\(38\) | −240.000 | −1.02456 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | −160.000 | −0.632456 | ||||||||
\(41\) | 108.000 | 0.411385 | 0.205692 | − | 0.978617i | \(-0.434055\pi\) | ||||
0.205692 | + | 0.978617i | \(0.434055\pi\) | |||||||
\(42\) | 192.000 | 0.705387 | ||||||||
\(43\) | −356.000 | −1.26255 | −0.631273 | − | 0.775561i | \(-0.717467\pi\) | ||||
−0.631273 | + | 0.775561i | \(0.717467\pi\) | |||||||
\(44\) | 200.000 | 0.685253 | ||||||||
\(45\) | −180.000 | −0.596285 | ||||||||
\(46\) | −40.0000 | −0.128210 | ||||||||
\(47\) | −178.000 | −0.552425 | −0.276212 | − | 0.961097i | \(-0.589079\pi\) | ||||
−0.276212 | + | 0.961097i | \(0.589079\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 550.000 | 1.55563 | ||||||||
\(51\) | 90.0000 | 0.247108 | ||||||||
\(52\) | −52.0000 | −0.138675 | ||||||||
\(53\) | 198.000 | 0.513158 | 0.256579 | − | 0.966523i | \(-0.417405\pi\) | ||||
0.256579 | + | 0.966523i | \(0.417405\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −1000.00 | −2.45164 | ||||||||
\(56\) | −256.000 | −0.610883 | ||||||||
\(57\) | 360.000 | 0.836547 | ||||||||
\(58\) | 164.000 | 0.371280 | ||||||||
\(59\) | 94.0000 | 0.207420 | 0.103710 | − | 0.994608i | \(-0.466929\pi\) | ||||
0.103710 | + | 0.994608i | \(0.466929\pi\) | |||||||
\(60\) | 240.000 | 0.516398 | ||||||||
\(61\) | −62.0000 | −0.130136 | −0.0650679 | − | 0.997881i | \(-0.520726\pi\) | ||||
−0.0650679 | + | 0.997881i | \(0.520726\pi\) | |||||||
\(62\) | −88.0000 | −0.180258 | ||||||||
\(63\) | −288.000 | −0.575946 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 260.000 | 0.496139 | ||||||||
\(66\) | −300.000 | −0.559507 | ||||||||
\(67\) | −140.000 | −0.255279 | −0.127640 | − | 0.991821i | \(-0.540740\pi\) | ||||
−0.127640 | + | 0.991821i | \(0.540740\pi\) | |||||||
\(68\) | −120.000 | −0.214002 | ||||||||
\(69\) | 60.0000 | 0.104683 | ||||||||
\(70\) | 1280.00 | 2.18556 | ||||||||
\(71\) | −778.000 | −1.30045 | −0.650223 | − | 0.759744i | \(-0.725324\pi\) | ||||
−0.650223 | + | 0.759744i | \(0.725324\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 62.0000 | 0.0994048 | 0.0497024 | − | 0.998764i | \(-0.484173\pi\) | ||||
0.0497024 | + | 0.998764i | \(0.484173\pi\) | |||||||
\(74\) | −612.000 | −0.961399 | ||||||||
\(75\) | −825.000 | −1.27017 | ||||||||
\(76\) | −480.000 | −0.724471 | ||||||||
\(77\) | −1600.00 | −2.36801 | ||||||||
\(78\) | 78.0000 | 0.113228 | ||||||||
\(79\) | −1096.00 | −1.56088 | −0.780441 | − | 0.625230i | \(-0.785005\pi\) | ||||
−0.780441 | + | 0.625230i | \(0.785005\pi\) | |||||||
\(80\) | −320.000 | −0.447214 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 216.000 | 0.290893 | ||||||||
\(83\) | −462.000 | −0.610977 | −0.305488 | − | 0.952196i | \(-0.598820\pi\) | ||||
−0.305488 | + | 0.952196i | \(0.598820\pi\) | |||||||
\(84\) | 384.000 | 0.498784 | ||||||||
\(85\) | 600.000 | 0.765637 | ||||||||
\(86\) | −712.000 | −0.892755 | ||||||||
\(87\) | −246.000 | −0.303149 | ||||||||
\(88\) | 400.000 | 0.484547 | ||||||||
\(89\) | 1224.00 | 1.45779 | 0.728897 | − | 0.684623i | \(-0.240033\pi\) | ||||
0.728897 | + | 0.684623i | \(0.240033\pi\) | |||||||
\(90\) | −360.000 | −0.421637 | ||||||||
\(91\) | 416.000 | 0.479216 | ||||||||
\(92\) | −80.0000 | −0.0906584 | ||||||||
\(93\) | 132.000 | 0.147180 | ||||||||
\(94\) | −356.000 | −0.390623 | ||||||||
\(95\) | 2400.00 | 2.59195 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 614.000 | 0.642704 | 0.321352 | − | 0.946960i | \(-0.395863\pi\) | ||||
0.321352 | + | 0.946960i | \(0.395863\pi\) | |||||||
\(98\) | 1362.00 | 1.40391 | ||||||||
\(99\) | 450.000 | 0.456835 | ||||||||
\(100\) | 1100.00 | 1.10000 | ||||||||
\(101\) | 1058.00 | 1.04233 | 0.521163 | − | 0.853457i | \(-0.325498\pi\) | ||||
0.521163 | + | 0.853457i | \(0.325498\pi\) | |||||||
\(102\) | 180.000 | 0.174732 | ||||||||
\(103\) | 1768.00 | 1.69132 | 0.845661 | − | 0.533720i | \(-0.179206\pi\) | ||||
0.845661 | + | 0.533720i | \(0.179206\pi\) | |||||||
\(104\) | −104.000 | −0.0980581 | ||||||||
\(105\) | −1920.00 | −1.78450 | ||||||||
\(106\) | 396.000 | 0.362858 | ||||||||
\(107\) | −1808.00 | −1.63351 | −0.816757 | − | 0.576982i | \(-0.804230\pi\) | ||||
−0.816757 | + | 0.576982i | \(0.804230\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −1886.00 | −1.65730 | −0.828652 | − | 0.559765i | \(-0.810891\pi\) | ||||
−0.828652 | + | 0.559765i | \(0.810891\pi\) | |||||||
\(110\) | −2000.00 | −1.73357 | ||||||||
\(111\) | 918.000 | 0.784979 | ||||||||
\(112\) | −512.000 | −0.431959 | ||||||||
\(113\) | 1246.00 | 1.03729 | 0.518645 | − | 0.854990i | \(-0.326437\pi\) | ||||
0.518645 | + | 0.854990i | \(0.326437\pi\) | |||||||
\(114\) | 720.000 | 0.591528 | ||||||||
\(115\) | 400.000 | 0.324349 | ||||||||
\(116\) | 328.000 | 0.262535 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 188.000 | 0.146668 | ||||||||
\(119\) | 960.000 | 0.739521 | ||||||||
\(120\) | 480.000 | 0.365148 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | −124.000 | −0.0920199 | ||||||||
\(123\) | −324.000 | −0.237513 | ||||||||
\(124\) | −176.000 | −0.127462 | ||||||||
\(125\) | −3000.00 | −2.14663 | ||||||||
\(126\) | −576.000 | −0.407255 | ||||||||
\(127\) | 1624.00 | 1.13470 | 0.567349 | − | 0.823477i | \(-0.307969\pi\) | ||||
0.567349 | + | 0.823477i | \(0.307969\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1068.00 | 0.728931 | ||||||||
\(130\) | 520.000 | 0.350823 | ||||||||
\(131\) | −2072.00 | −1.38192 | −0.690960 | − | 0.722893i | \(-0.742812\pi\) | ||||
−0.690960 | + | 0.722893i | \(0.742812\pi\) | |||||||
\(132\) | −600.000 | −0.395631 | ||||||||
\(133\) | 3840.00 | 2.50354 | ||||||||
\(134\) | −280.000 | −0.180510 | ||||||||
\(135\) | 540.000 | 0.344265 | ||||||||
\(136\) | −240.000 | −0.151322 | ||||||||
\(137\) | −756.000 | −0.471456 | −0.235728 | − | 0.971819i | \(-0.575747\pi\) | ||||
−0.235728 | + | 0.971819i | \(0.575747\pi\) | |||||||
\(138\) | 120.000 | 0.0740223 | ||||||||
\(139\) | 172.000 | 0.104956 | 0.0524779 | − | 0.998622i | \(-0.483288\pi\) | ||||
0.0524779 | + | 0.998622i | \(0.483288\pi\) | |||||||
\(140\) | 2560.00 | 1.54542 | ||||||||
\(141\) | 534.000 | 0.318943 | ||||||||
\(142\) | −1556.00 | −0.919554 | ||||||||
\(143\) | −650.000 | −0.380110 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −1640.00 | −0.939273 | ||||||||
\(146\) | 124.000 | 0.0702898 | ||||||||
\(147\) | −2043.00 | −1.14628 | ||||||||
\(148\) | −1224.00 | −0.679812 | ||||||||
\(149\) | 1272.00 | 0.699371 | 0.349686 | − | 0.936867i | \(-0.386288\pi\) | ||||
0.349686 | + | 0.936867i | \(0.386288\pi\) | |||||||
\(150\) | −1650.00 | −0.898146 | ||||||||
\(151\) | 1404.00 | 0.756662 | 0.378331 | − | 0.925670i | \(-0.376498\pi\) | ||||
0.378331 | + | 0.925670i | \(0.376498\pi\) | |||||||
\(152\) | −960.000 | −0.512278 | ||||||||
\(153\) | −270.000 | −0.142668 | ||||||||
\(154\) | −3200.00 | −1.67444 | ||||||||
\(155\) | 880.000 | 0.456021 | ||||||||
\(156\) | 156.000 | 0.0800641 | ||||||||
\(157\) | −2170.00 | −1.10309 | −0.551544 | − | 0.834146i | \(-0.685961\pi\) | ||||
−0.551544 | + | 0.834146i | \(0.685961\pi\) | |||||||
\(158\) | −2192.00 | −1.10371 | ||||||||
\(159\) | −594.000 | −0.296272 | ||||||||
\(160\) | −640.000 | −0.316228 | ||||||||
\(161\) | 640.000 | 0.313286 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 248.000 | 0.119171 | 0.0595855 | − | 0.998223i | \(-0.481022\pi\) | ||||
0.0595855 | + | 0.998223i | \(0.481022\pi\) | |||||||
\(164\) | 432.000 | 0.205692 | ||||||||
\(165\) | 3000.00 | 1.41545 | ||||||||
\(166\) | −924.000 | −0.432026 | ||||||||
\(167\) | 102.000 | 0.0472635 | 0.0236317 | − | 0.999721i | \(-0.492477\pi\) | ||||
0.0236317 | + | 0.999721i | \(0.492477\pi\) | |||||||
\(168\) | 768.000 | 0.352693 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 1200.00 | 0.541387 | ||||||||
\(171\) | −1080.00 | −0.482980 | ||||||||
\(172\) | −1424.00 | −0.631273 | ||||||||
\(173\) | 682.000 | 0.299720 | 0.149860 | − | 0.988707i | \(-0.452118\pi\) | ||||
0.149860 | + | 0.988707i | \(0.452118\pi\) | |||||||
\(174\) | −492.000 | −0.214359 | ||||||||
\(175\) | −8800.00 | −3.80124 | ||||||||
\(176\) | 800.000 | 0.342627 | ||||||||
\(177\) | −282.000 | −0.119754 | ||||||||
\(178\) | 2448.00 | 1.03082 | ||||||||
\(179\) | −612.000 | −0.255548 | −0.127774 | − | 0.991803i | \(-0.540783\pi\) | ||||
−0.127774 | + | 0.991803i | \(0.540783\pi\) | |||||||
\(180\) | −720.000 | −0.298142 | ||||||||
\(181\) | −66.0000 | −0.0271035 | −0.0135518 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135518 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(182\) | 832.000 | 0.338857 | ||||||||
\(183\) | 186.000 | 0.0751340 | ||||||||
\(184\) | −160.000 | −0.0641052 | ||||||||
\(185\) | 6120.00 | 2.43217 | ||||||||
\(186\) | 264.000 | 0.104072 | ||||||||
\(187\) | −1500.00 | −0.586582 | ||||||||
\(188\) | −712.000 | −0.276212 | ||||||||
\(189\) | 864.000 | 0.332522 | ||||||||
\(190\) | 4800.00 | 1.83278 | ||||||||
\(191\) | 608.000 | 0.230332 | 0.115166 | − | 0.993346i | \(-0.463260\pi\) | ||||
0.115166 | + | 0.993346i | \(0.463260\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 1370.00 | 0.510957 | 0.255479 | − | 0.966815i | \(-0.417767\pi\) | ||||
0.255479 | + | 0.966815i | \(0.417767\pi\) | |||||||
\(194\) | 1228.00 | 0.454460 | ||||||||
\(195\) | −780.000 | −0.286446 | ||||||||
\(196\) | 2724.00 | 0.992711 | ||||||||
\(197\) | −4908.00 | −1.77503 | −0.887514 | − | 0.460781i | \(-0.847569\pi\) | ||||
−0.887514 | + | 0.460781i | \(0.847569\pi\) | |||||||
\(198\) | 900.000 | 0.323031 | ||||||||
\(199\) | −328.000 | −0.116841 | −0.0584204 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584204 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(200\) | 2200.00 | 0.777817 | ||||||||
\(201\) | 420.000 | 0.147386 | ||||||||
\(202\) | 2116.00 | 0.737036 | ||||||||
\(203\) | −2624.00 | −0.907235 | ||||||||
\(204\) | 360.000 | 0.123554 | ||||||||
\(205\) | −2160.00 | −0.735907 | ||||||||
\(206\) | 3536.00 | 1.19595 | ||||||||
\(207\) | −180.000 | −0.0604390 | ||||||||
\(208\) | −208.000 | −0.0693375 | ||||||||
\(209\) | −6000.00 | −1.98578 | ||||||||
\(210\) | −3840.00 | −1.26183 | ||||||||
\(211\) | 1316.00 | 0.429371 | 0.214685 | − | 0.976683i | \(-0.431127\pi\) | ||||
0.214685 | + | 0.976683i | \(0.431127\pi\) | |||||||
\(212\) | 792.000 | 0.256579 | ||||||||
\(213\) | 2334.00 | 0.750812 | ||||||||
\(214\) | −3616.00 | −1.15507 | ||||||||
\(215\) | 7120.00 | 2.25851 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 1408.00 | 0.440467 | ||||||||
\(218\) | −3772.00 | −1.17189 | ||||||||
\(219\) | −186.000 | −0.0573914 | ||||||||
\(220\) | −4000.00 | −1.22582 | ||||||||
\(221\) | 390.000 | 0.118707 | ||||||||
\(222\) | 1836.00 | 0.555064 | ||||||||
\(223\) | −1932.00 | −0.580163 | −0.290081 | − | 0.957002i | \(-0.593682\pi\) | ||||
−0.290081 | + | 0.957002i | \(0.593682\pi\) | |||||||
\(224\) | −1024.00 | −0.305441 | ||||||||
\(225\) | 2475.00 | 0.733333 | ||||||||
\(226\) | 2492.00 | 0.733475 | ||||||||
\(227\) | 4998.00 | 1.46136 | 0.730680 | − | 0.682720i | \(-0.239203\pi\) | ||||
0.730680 | + | 0.682720i | \(0.239203\pi\) | |||||||
\(228\) | 1440.00 | 0.418273 | ||||||||
\(229\) | −78.0000 | −0.0225082 | −0.0112541 | − | 0.999937i | \(-0.503582\pi\) | ||||
−0.0112541 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(230\) | 800.000 | 0.229350 | ||||||||
\(231\) | 4800.00 | 1.36717 | ||||||||
\(232\) | 656.000 | 0.185640 | ||||||||
\(233\) | −1282.00 | −0.360458 | −0.180229 | − | 0.983625i | \(-0.557684\pi\) | ||||
−0.180229 | + | 0.983625i | \(0.557684\pi\) | |||||||
\(234\) | −234.000 | −0.0653720 | ||||||||
\(235\) | 3560.00 | 0.988208 | ||||||||
\(236\) | 376.000 | 0.103710 | ||||||||
\(237\) | 3288.00 | 0.901175 | ||||||||
\(238\) | 1920.00 | 0.522921 | ||||||||
\(239\) | 294.000 | 0.0795702 | 0.0397851 | − | 0.999208i | \(-0.487333\pi\) | ||||
0.0397851 | + | 0.999208i | \(0.487333\pi\) | |||||||
\(240\) | 960.000 | 0.258199 | ||||||||
\(241\) | −4962.00 | −1.32627 | −0.663134 | − | 0.748501i | \(-0.730774\pi\) | ||||
−0.663134 | + | 0.748501i | \(0.730774\pi\) | |||||||
\(242\) | 2338.00 | 0.621043 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −248.000 | −0.0650679 | ||||||||
\(245\) | −13620.0 | −3.55163 | ||||||||
\(246\) | −648.000 | −0.167947 | ||||||||
\(247\) | 1560.00 | 0.401864 | ||||||||
\(248\) | −352.000 | −0.0901291 | ||||||||
\(249\) | 1386.00 | 0.352748 | ||||||||
\(250\) | −6000.00 | −1.51789 | ||||||||
\(251\) | 744.000 | 0.187095 | 0.0935475 | − | 0.995615i | \(-0.470179\pi\) | ||||
0.0935475 | + | 0.995615i | \(0.470179\pi\) | |||||||
\(252\) | −1152.00 | −0.287973 | ||||||||
\(253\) | −1000.00 | −0.248496 | ||||||||
\(254\) | 3248.00 | 0.802353 | ||||||||
\(255\) | −1800.00 | −0.442041 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1026.00 | −0.249028 | −0.124514 | − | 0.992218i | \(-0.539737\pi\) | ||||
−0.124514 | + | 0.992218i | \(0.539737\pi\) | |||||||
\(258\) | 2136.00 | 0.515432 | ||||||||
\(259\) | 9792.00 | 2.34921 | ||||||||
\(260\) | 1040.00 | 0.248069 | ||||||||
\(261\) | 738.000 | 0.175023 | ||||||||
\(262\) | −4144.00 | −0.977165 | ||||||||
\(263\) | −5532.00 | −1.29703 | −0.648513 | − | 0.761204i | \(-0.724609\pi\) | ||||
−0.648513 | + | 0.761204i | \(0.724609\pi\) | |||||||
\(264\) | −1200.00 | −0.279753 | ||||||||
\(265\) | −3960.00 | −0.917966 | ||||||||
\(266\) | 7680.00 | 1.77027 | ||||||||
\(267\) | −3672.00 | −0.841658 | ||||||||
\(268\) | −560.000 | −0.127640 | ||||||||
\(269\) | −3534.00 | −0.801010 | −0.400505 | − | 0.916294i | \(-0.631165\pi\) | ||||
−0.400505 | + | 0.916294i | \(0.631165\pi\) | |||||||
\(270\) | 1080.00 | 0.243432 | ||||||||
\(271\) | 2392.00 | 0.536176 | 0.268088 | − | 0.963394i | \(-0.413608\pi\) | ||||
0.268088 | + | 0.963394i | \(0.413608\pi\) | |||||||
\(272\) | −480.000 | −0.107001 | ||||||||
\(273\) | −1248.00 | −0.276675 | ||||||||
\(274\) | −1512.00 | −0.333370 | ||||||||
\(275\) | 13750.0 | 3.01511 | ||||||||
\(276\) | 240.000 | 0.0523417 | ||||||||
\(277\) | 6102.00 | 1.32359 | 0.661794 | − | 0.749686i | \(-0.269796\pi\) | ||||
0.661794 | + | 0.749686i | \(0.269796\pi\) | |||||||
\(278\) | 344.000 | 0.0742149 | ||||||||
\(279\) | −396.000 | −0.0849746 | ||||||||
\(280\) | 5120.00 | 1.09278 | ||||||||
\(281\) | −7540.00 | −1.60071 | −0.800354 | − | 0.599528i | \(-0.795355\pi\) | ||||
−0.800354 | + | 0.599528i | \(0.795355\pi\) | |||||||
\(282\) | 1068.00 | 0.225527 | ||||||||
\(283\) | −2756.00 | −0.578895 | −0.289447 | − | 0.957194i | \(-0.593472\pi\) | ||||
−0.289447 | + | 0.957194i | \(0.593472\pi\) | |||||||
\(284\) | −3112.00 | −0.650223 | ||||||||
\(285\) | −7200.00 | −1.49646 | ||||||||
\(286\) | −1300.00 | −0.268778 | ||||||||
\(287\) | −3456.00 | −0.710806 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4013.00 | −0.816813 | ||||||||
\(290\) | −3280.00 | −0.664166 | ||||||||
\(291\) | −1842.00 | −0.371065 | ||||||||
\(292\) | 248.000 | 0.0497024 | ||||||||
\(293\) | 968.000 | 0.193007 | 0.0965037 | − | 0.995333i | \(-0.469234\pi\) | ||||
0.0965037 | + | 0.995333i | \(0.469234\pi\) | |||||||
\(294\) | −4086.00 | −0.810545 | ||||||||
\(295\) | −1880.00 | −0.371043 | ||||||||
\(296\) | −2448.00 | −0.480700 | ||||||||
\(297\) | −1350.00 | −0.263754 | ||||||||
\(298\) | 2544.00 | 0.494530 | ||||||||
\(299\) | 260.000 | 0.0502883 | ||||||||
\(300\) | −3300.00 | −0.635085 | ||||||||
\(301\) | 11392.0 | 2.18147 | ||||||||
\(302\) | 2808.00 | 0.535041 | ||||||||
\(303\) | −3174.00 | −0.601787 | ||||||||
\(304\) | −1920.00 | −0.362235 | ||||||||
\(305\) | 1240.00 | 0.232794 | ||||||||
\(306\) | −540.000 | −0.100882 | ||||||||
\(307\) | −6436.00 | −1.19649 | −0.598244 | − | 0.801314i | \(-0.704135\pi\) | ||||
−0.598244 | + | 0.801314i | \(0.704135\pi\) | |||||||
\(308\) | −6400.00 | −1.18401 | ||||||||
\(309\) | −5304.00 | −0.976485 | ||||||||
\(310\) | 1760.00 | 0.322456 | ||||||||
\(311\) | 7932.00 | 1.44625 | 0.723123 | − | 0.690719i | \(-0.242706\pi\) | ||||
0.723123 | + | 0.690719i | \(0.242706\pi\) | |||||||
\(312\) | 312.000 | 0.0566139 | ||||||||
\(313\) | 10358.0 | 1.87051 | 0.935254 | − | 0.353978i | \(-0.115171\pi\) | ||||
0.935254 | + | 0.353978i | \(0.115171\pi\) | |||||||
\(314\) | −4340.00 | −0.780001 | ||||||||
\(315\) | 5760.00 | 1.03028 | ||||||||
\(316\) | −4384.00 | −0.780441 | ||||||||
\(317\) | −2820.00 | −0.499643 | −0.249822 | − | 0.968292i | \(-0.580372\pi\) | ||||
−0.249822 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(318\) | −1188.00 | −0.209496 | ||||||||
\(319\) | 4100.00 | 0.719611 | ||||||||
\(320\) | −1280.00 | −0.223607 | ||||||||
\(321\) | 5424.00 | 0.943110 | ||||||||
\(322\) | 1280.00 | 0.221527 | ||||||||
\(323\) | 3600.00 | 0.620153 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −3575.00 | −0.610170 | ||||||||
\(326\) | 496.000 | 0.0842666 | ||||||||
\(327\) | 5658.00 | 0.956844 | ||||||||
\(328\) | 864.000 | 0.145446 | ||||||||
\(329\) | 5696.00 | 0.954500 | ||||||||
\(330\) | 6000.00 | 1.00088 | ||||||||
\(331\) | −4180.00 | −0.694120 | −0.347060 | − | 0.937843i | \(-0.612820\pi\) | ||||
−0.347060 | + | 0.937843i | \(0.612820\pi\) | |||||||
\(332\) | −1848.00 | −0.305488 | ||||||||
\(333\) | −2754.00 | −0.453208 | ||||||||
\(334\) | 204.000 | 0.0334203 | ||||||||
\(335\) | 2800.00 | 0.456658 | ||||||||
\(336\) | 1536.00 | 0.249392 | ||||||||
\(337\) | −5026.00 | −0.812414 | −0.406207 | − | 0.913781i | \(-0.633149\pi\) | ||||
−0.406207 | + | 0.913781i | \(0.633149\pi\) | |||||||
\(338\) | 338.000 | 0.0543928 | ||||||||
\(339\) | −3738.00 | −0.598880 | ||||||||
\(340\) | 2400.00 | 0.382818 | ||||||||
\(341\) | −2200.00 | −0.349374 | ||||||||
\(342\) | −2160.00 | −0.341519 | ||||||||
\(343\) | −10816.0 | −1.70265 | ||||||||
\(344\) | −2848.00 | −0.446378 | ||||||||
\(345\) | −1200.00 | −0.187263 | ||||||||
\(346\) | 1364.00 | 0.211934 | ||||||||
\(347\) | −7332.00 | −1.13430 | −0.567150 | − | 0.823614i | \(-0.691954\pi\) | ||||
−0.567150 | + | 0.823614i | \(0.691954\pi\) | |||||||
\(348\) | −984.000 | −0.151575 | ||||||||
\(349\) | −8162.00 | −1.25187 | −0.625934 | − | 0.779876i | \(-0.715282\pi\) | ||||
−0.625934 | + | 0.779876i | \(0.715282\pi\) | |||||||
\(350\) | −17600.0 | −2.68788 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 1600.00 | 0.242274 | ||||||||
\(353\) | 1244.00 | 0.187568 | 0.0937839 | − | 0.995593i | \(-0.470104\pi\) | ||||
0.0937839 | + | 0.995593i | \(0.470104\pi\) | |||||||
\(354\) | −564.000 | −0.0846787 | ||||||||
\(355\) | 15560.0 | 2.32631 | ||||||||
\(356\) | 4896.00 | 0.728897 | ||||||||
\(357\) | −2880.00 | −0.426963 | ||||||||
\(358\) | −1224.00 | −0.180699 | ||||||||
\(359\) | 9558.00 | 1.40516 | 0.702579 | − | 0.711605i | \(-0.252032\pi\) | ||||
0.702579 | + | 0.711605i | \(0.252032\pi\) | |||||||
\(360\) | −1440.00 | −0.210819 | ||||||||
\(361\) | 7541.00 | 1.09943 | ||||||||
\(362\) | −132.000 | −0.0191651 | ||||||||
\(363\) | −3507.00 | −0.507079 | ||||||||
\(364\) | 1664.00 | 0.239608 | ||||||||
\(365\) | −1240.00 | −0.177821 | ||||||||
\(366\) | 372.000 | 0.0531277 | ||||||||
\(367\) | −11032.0 | −1.56912 | −0.784558 | − | 0.620055i | \(-0.787110\pi\) | ||||
−0.784558 | + | 0.620055i | \(0.787110\pi\) | |||||||
\(368\) | −320.000 | −0.0453292 | ||||||||
\(369\) | 972.000 | 0.137128 | ||||||||
\(370\) | 12240.0 | 1.71980 | ||||||||
\(371\) | −6336.00 | −0.886654 | ||||||||
\(372\) | 528.000 | 0.0735901 | ||||||||
\(373\) | 5474.00 | 0.759874 | 0.379937 | − | 0.925012i | \(-0.375946\pi\) | ||||
0.379937 | + | 0.925012i | \(0.375946\pi\) | |||||||
\(374\) | −3000.00 | −0.414776 | ||||||||
\(375\) | 9000.00 | 1.23935 | ||||||||
\(376\) | −1424.00 | −0.195312 | ||||||||
\(377\) | −1066.00 | −0.145628 | ||||||||
\(378\) | 1728.00 | 0.235129 | ||||||||
\(379\) | −7040.00 | −0.954144 | −0.477072 | − | 0.878864i | \(-0.658302\pi\) | ||||
−0.477072 | + | 0.878864i | \(0.658302\pi\) | |||||||
\(380\) | 9600.00 | 1.29597 | ||||||||
\(381\) | −4872.00 | −0.655118 | ||||||||
\(382\) | 1216.00 | 0.162869 | ||||||||
\(383\) | −1830.00 | −0.244148 | −0.122074 | − | 0.992521i | \(-0.538955\pi\) | ||||
−0.122074 | + | 0.992521i | \(0.538955\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 32000.0 | 4.23603 | ||||||||
\(386\) | 2740.00 | 0.361301 | ||||||||
\(387\) | −3204.00 | −0.420849 | ||||||||
\(388\) | 2456.00 | 0.321352 | ||||||||
\(389\) | 10158.0 | 1.32399 | 0.661994 | − | 0.749509i | \(-0.269711\pi\) | ||||
0.661994 | + | 0.749509i | \(0.269711\pi\) | |||||||
\(390\) | −1560.00 | −0.202548 | ||||||||
\(391\) | 600.000 | 0.0776044 | ||||||||
\(392\) | 5448.00 | 0.701953 | ||||||||
\(393\) | 6216.00 | 0.797852 | ||||||||
\(394\) | −9816.00 | −1.25513 | ||||||||
\(395\) | 21920.0 | 2.79219 | ||||||||
\(396\) | 1800.00 | 0.228418 | ||||||||
\(397\) | −12658.0 | −1.60022 | −0.800109 | − | 0.599854i | \(-0.795225\pi\) | ||||
−0.800109 | + | 0.599854i | \(0.795225\pi\) | |||||||
\(398\) | −656.000 | −0.0826189 | ||||||||
\(399\) | −11520.0 | −1.44542 | ||||||||
\(400\) | 4400.00 | 0.550000 | ||||||||
\(401\) | 15720.0 | 1.95765 | 0.978827 | − | 0.204689i | \(-0.0656182\pi\) | ||||
0.978827 | + | 0.204689i | \(0.0656182\pi\) | |||||||
\(402\) | 840.000 | 0.104217 | ||||||||
\(403\) | 572.000 | 0.0707031 | ||||||||
\(404\) | 4232.00 | 0.521163 | ||||||||
\(405\) | −1620.00 | −0.198762 | ||||||||
\(406\) | −5248.00 | −0.641512 | ||||||||
\(407\) | −15300.0 | −1.86337 | ||||||||
\(408\) | 720.000 | 0.0873660 | ||||||||
\(409\) | 7654.00 | 0.925345 | 0.462672 | − | 0.886529i | \(-0.346891\pi\) | ||||
0.462672 | + | 0.886529i | \(0.346891\pi\) | |||||||
\(410\) | −4320.00 | −0.520365 | ||||||||
\(411\) | 2268.00 | 0.272195 | ||||||||
\(412\) | 7072.00 | 0.845661 | ||||||||
\(413\) | −3008.00 | −0.358387 | ||||||||
\(414\) | −360.000 | −0.0427368 | ||||||||
\(415\) | 9240.00 | 1.09295 | ||||||||
\(416\) | −416.000 | −0.0490290 | ||||||||
\(417\) | −516.000 | −0.0605962 | ||||||||
\(418\) | −12000.0 | −1.40416 | ||||||||
\(419\) | −1848.00 | −0.215467 | −0.107734 | − | 0.994180i | \(-0.534359\pi\) | ||||
−0.107734 | + | 0.994180i | \(0.534359\pi\) | |||||||
\(420\) | −7680.00 | −0.892251 | ||||||||
\(421\) | −12542.0 | −1.45192 | −0.725962 | − | 0.687735i | \(-0.758605\pi\) | ||||
−0.725962 | + | 0.687735i | \(0.758605\pi\) | |||||||
\(422\) | 2632.00 | 0.303611 | ||||||||
\(423\) | −1602.00 | −0.184142 | ||||||||
\(424\) | 1584.00 | 0.181429 | ||||||||
\(425\) | −8250.00 | −0.941609 | ||||||||
\(426\) | 4668.00 | 0.530905 | ||||||||
\(427\) | 1984.00 | 0.224854 | ||||||||
\(428\) | −7232.00 | −0.816757 | ||||||||
\(429\) | 1950.00 | 0.219457 | ||||||||
\(430\) | 14240.0 | 1.59701 | ||||||||
\(431\) | −5238.00 | −0.585396 | −0.292698 | − | 0.956205i | \(-0.594553\pi\) | ||||
−0.292698 | + | 0.956205i | \(0.594553\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −8258.00 | −0.916522 | −0.458261 | − | 0.888818i | \(-0.651528\pi\) | ||||
−0.458261 | + | 0.888818i | \(0.651528\pi\) | |||||||
\(434\) | 2816.00 | 0.311457 | ||||||||
\(435\) | 4920.00 | 0.542290 | ||||||||
\(436\) | −7544.00 | −0.828652 | ||||||||
\(437\) | 2400.00 | 0.262718 | ||||||||
\(438\) | −372.000 | −0.0405818 | ||||||||
\(439\) | −6304.00 | −0.685361 | −0.342681 | − | 0.939452i | \(-0.611335\pi\) | ||||
−0.342681 | + | 0.939452i | \(0.611335\pi\) | |||||||
\(440\) | −8000.00 | −0.866784 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 780.000 | 0.0839385 | ||||||||
\(443\) | 12744.0 | 1.36678 | 0.683392 | − | 0.730051i | \(-0.260504\pi\) | ||||
0.683392 | + | 0.730051i | \(0.260504\pi\) | |||||||
\(444\) | 3672.00 | 0.392490 | ||||||||
\(445\) | −24480.0 | −2.60778 | ||||||||
\(446\) | −3864.00 | −0.410237 | ||||||||
\(447\) | −3816.00 | −0.403782 | ||||||||
\(448\) | −2048.00 | −0.215980 | ||||||||
\(449\) | −11776.0 | −1.23774 | −0.618868 | − | 0.785495i | \(-0.712409\pi\) | ||||
−0.618868 | + | 0.785495i | \(0.712409\pi\) | |||||||
\(450\) | 4950.00 | 0.518545 | ||||||||
\(451\) | 5400.00 | 0.563805 | ||||||||
\(452\) | 4984.00 | 0.518645 | ||||||||
\(453\) | −4212.00 | −0.436859 | ||||||||
\(454\) | 9996.00 | 1.03334 | ||||||||
\(455\) | −8320.00 | −0.857248 | ||||||||
\(456\) | 2880.00 | 0.295764 | ||||||||
\(457\) | 2134.00 | 0.218434 | 0.109217 | − | 0.994018i | \(-0.465166\pi\) | ||||
0.109217 | + | 0.994018i | \(0.465166\pi\) | |||||||
\(458\) | −156.000 | −0.0159157 | ||||||||
\(459\) | 810.000 | 0.0823694 | ||||||||
\(460\) | 1600.00 | 0.162175 | ||||||||
\(461\) | 2724.00 | 0.275205 | 0.137602 | − | 0.990488i | \(-0.456060\pi\) | ||||
0.137602 | + | 0.990488i | \(0.456060\pi\) | |||||||
\(462\) | 9600.00 | 0.966737 | ||||||||
\(463\) | −5648.00 | −0.566922 | −0.283461 | − | 0.958984i | \(-0.591483\pi\) | ||||
−0.283461 | + | 0.958984i | \(0.591483\pi\) | |||||||
\(464\) | 1312.00 | 0.131267 | ||||||||
\(465\) | −2640.00 | −0.263284 | ||||||||
\(466\) | −2564.00 | −0.254882 | ||||||||
\(467\) | −18224.0 | −1.80579 | −0.902897 | − | 0.429856i | \(-0.858564\pi\) | ||||
−0.902897 | + | 0.429856i | \(0.858564\pi\) | |||||||
\(468\) | −468.000 | −0.0462250 | ||||||||
\(469\) | 4480.00 | 0.441081 | ||||||||
\(470\) | 7120.00 | 0.698768 | ||||||||
\(471\) | 6510.00 | 0.636868 | ||||||||
\(472\) | 752.000 | 0.0733339 | ||||||||
\(473\) | −17800.0 | −1.73033 | ||||||||
\(474\) | 6576.00 | 0.637227 | ||||||||
\(475\) | −33000.0 | −3.18767 | ||||||||
\(476\) | 3840.00 | 0.369761 | ||||||||
\(477\) | 1782.00 | 0.171053 | ||||||||
\(478\) | 588.000 | 0.0562646 | ||||||||
\(479\) | 9066.00 | 0.864794 | 0.432397 | − | 0.901683i | \(-0.357668\pi\) | ||||
0.432397 | + | 0.901683i | \(0.357668\pi\) | |||||||
\(480\) | 1920.00 | 0.182574 | ||||||||
\(481\) | 3978.00 | 0.377092 | ||||||||
\(482\) | −9924.00 | −0.937813 | ||||||||
\(483\) | −1920.00 | −0.180876 | ||||||||
\(484\) | 4676.00 | 0.439144 | ||||||||
\(485\) | −12280.0 | −1.14970 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 8948.00 | 0.832593 | 0.416296 | − | 0.909229i | \(-0.363328\pi\) | ||||
0.416296 | + | 0.909229i | \(0.363328\pi\) | |||||||
\(488\) | −496.000 | −0.0460100 | ||||||||
\(489\) | −744.000 | −0.0688034 | ||||||||
\(490\) | −27240.0 | −2.51138 | ||||||||
\(491\) | 8720.00 | 0.801483 | 0.400741 | − | 0.916191i | \(-0.368753\pi\) | ||||
0.400741 | + | 0.916191i | \(0.368753\pi\) | |||||||
\(492\) | −1296.00 | −0.118756 | ||||||||
\(493\) | −2460.00 | −0.224732 | ||||||||
\(494\) | 3120.00 | 0.284161 | ||||||||
\(495\) | −9000.00 | −0.817212 | ||||||||
\(496\) | −704.000 | −0.0637309 | ||||||||
\(497\) | 24896.0 | 2.24696 | ||||||||
\(498\) | 2772.00 | 0.249430 | ||||||||
\(499\) | 6604.00 | 0.592456 | 0.296228 | − | 0.955117i | \(-0.404271\pi\) | ||||
0.296228 | + | 0.955117i | \(0.404271\pi\) | |||||||
\(500\) | −12000.0 | −1.07331 | ||||||||
\(501\) | −306.000 | −0.0272876 | ||||||||
\(502\) | 1488.00 | 0.132296 | ||||||||
\(503\) | 3404.00 | 0.301743 | 0.150872 | − | 0.988553i | \(-0.451792\pi\) | ||||
0.150872 | + | 0.988553i | \(0.451792\pi\) | |||||||
\(504\) | −2304.00 | −0.203628 | ||||||||
\(505\) | −21160.0 | −1.86457 | ||||||||
\(506\) | −2000.00 | −0.175713 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 6496.00 | 0.567349 | ||||||||
\(509\) | −76.0000 | −0.00661815 | −0.00330908 | − | 0.999995i | \(-0.501053\pi\) | ||||
−0.00330908 | + | 0.999995i | \(0.501053\pi\) | |||||||
\(510\) | −3600.00 | −0.312570 | ||||||||
\(511\) | −1984.00 | −0.171755 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 3240.00 | 0.278849 | ||||||||
\(514\) | −2052.00 | −0.176089 | ||||||||
\(515\) | −35360.0 | −3.02553 | ||||||||
\(516\) | 4272.00 | 0.364466 | ||||||||
\(517\) | −8900.00 | −0.757102 | ||||||||
\(518\) | 19584.0 | 1.66114 | ||||||||
\(519\) | −2046.00 | −0.173043 | ||||||||
\(520\) | 2080.00 | 0.175412 | ||||||||
\(521\) | 12054.0 | 1.01362 | 0.506809 | − | 0.862058i | \(-0.330825\pi\) | ||||
0.506809 | + | 0.862058i | \(0.330825\pi\) | |||||||
\(522\) | 1476.00 | 0.123760 | ||||||||
\(523\) | 276.000 | 0.0230758 | 0.0115379 | − | 0.999933i | \(-0.496327\pi\) | ||||
0.0115379 | + | 0.999933i | \(0.496327\pi\) | |||||||
\(524\) | −8288.00 | −0.690960 | ||||||||
\(525\) | 26400.0 | 2.19465 | ||||||||
\(526\) | −11064.0 | −0.917136 | ||||||||
\(527\) | 1320.00 | 0.109108 | ||||||||
\(528\) | −2400.00 | −0.197816 | ||||||||
\(529\) | −11767.0 | −0.967124 | ||||||||
\(530\) | −7920.00 | −0.649100 | ||||||||
\(531\) | 846.000 | 0.0691399 | ||||||||
\(532\) | 15360.0 | 1.25177 | ||||||||
\(533\) | −1404.00 | −0.114098 | ||||||||
\(534\) | −7344.00 | −0.595142 | ||||||||
\(535\) | 36160.0 | 2.92212 | ||||||||
\(536\) | −1120.00 | −0.0902549 | ||||||||
\(537\) | 1836.00 | 0.147540 | ||||||||
\(538\) | −7068.00 | −0.566400 | ||||||||
\(539\) | 34050.0 | 2.72103 | ||||||||
\(540\) | 2160.00 | 0.172133 | ||||||||
\(541\) | 13778.0 | 1.09494 | 0.547470 | − | 0.836825i | \(-0.315591\pi\) | ||||
0.547470 | + | 0.836825i | \(0.315591\pi\) | |||||||
\(542\) | 4784.00 | 0.379134 | ||||||||
\(543\) | 198.000 | 0.0156482 | ||||||||
\(544\) | −960.000 | −0.0756611 | ||||||||
\(545\) | 37720.0 | 2.96467 | ||||||||
\(546\) | −2496.00 | −0.195639 | ||||||||
\(547\) | −10844.0 | −0.847634 | −0.423817 | − | 0.905748i | \(-0.639310\pi\) | ||||
−0.423817 | + | 0.905748i | \(0.639310\pi\) | |||||||
\(548\) | −3024.00 | −0.235728 | ||||||||
\(549\) | −558.000 | −0.0433786 | ||||||||
\(550\) | 27500.0 | 2.13201 | ||||||||
\(551\) | −9840.00 | −0.760795 | ||||||||
\(552\) | 480.000 | 0.0370112 | ||||||||
\(553\) | 35072.0 | 2.69695 | ||||||||
\(554\) | 12204.0 | 0.935917 | ||||||||
\(555\) | −18360.0 | −1.40421 | ||||||||
\(556\) | 688.000 | 0.0524779 | ||||||||
\(557\) | 20544.0 | 1.56280 | 0.781398 | − | 0.624033i | \(-0.214507\pi\) | ||||
0.781398 | + | 0.624033i | \(0.214507\pi\) | |||||||
\(558\) | −792.000 | −0.0600861 | ||||||||
\(559\) | 4628.00 | 0.350167 | ||||||||
\(560\) | 10240.0 | 0.772712 | ||||||||
\(561\) | 4500.00 | 0.338663 | ||||||||
\(562\) | −15080.0 | −1.13187 | ||||||||
\(563\) | 6988.00 | 0.523107 | 0.261553 | − | 0.965189i | \(-0.415765\pi\) | ||||
0.261553 | + | 0.965189i | \(0.415765\pi\) | |||||||
\(564\) | 2136.00 | 0.159471 | ||||||||
\(565\) | −24920.0 | −1.85556 | ||||||||
\(566\) | −5512.00 | −0.409340 | ||||||||
\(567\) | −2592.00 | −0.191982 | ||||||||
\(568\) | −6224.00 | −0.459777 | ||||||||
\(569\) | −706.000 | −0.0520159 | −0.0260080 | − | 0.999662i | \(-0.508280\pi\) | ||||
−0.0260080 | + | 0.999662i | \(0.508280\pi\) | |||||||
\(570\) | −14400.0 | −1.05816 | ||||||||
\(571\) | −17532.0 | −1.28492 | −0.642462 | − | 0.766318i | \(-0.722087\pi\) | ||||
−0.642462 | + | 0.766318i | \(0.722087\pi\) | |||||||
\(572\) | −2600.00 | −0.190055 | ||||||||
\(573\) | −1824.00 | −0.132982 | ||||||||
\(574\) | −6912.00 | −0.502616 | ||||||||
\(575\) | −5500.00 | −0.398897 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −14814.0 | −1.06883 | −0.534415 | − | 0.845222i | \(-0.679468\pi\) | ||||
−0.534415 | + | 0.845222i | \(0.679468\pi\) | |||||||
\(578\) | −8026.00 | −0.577574 | ||||||||
\(579\) | −4110.00 | −0.295001 | ||||||||
\(580\) | −6560.00 | −0.469637 | ||||||||
\(581\) | 14784.0 | 1.05567 | ||||||||
\(582\) | −3684.00 | −0.262383 | ||||||||
\(583\) | 9900.00 | 0.703287 | ||||||||
\(584\) | 496.000 | 0.0351449 | ||||||||
\(585\) | 2340.00 | 0.165380 | ||||||||
\(586\) | 1936.00 | 0.136477 | ||||||||
\(587\) | 14170.0 | 0.996352 | 0.498176 | − | 0.867076i | \(-0.334003\pi\) | ||||
0.498176 | + | 0.867076i | \(0.334003\pi\) | |||||||
\(588\) | −8172.00 | −0.573142 | ||||||||
\(589\) | 5280.00 | 0.369369 | ||||||||
\(590\) | −3760.00 | −0.262367 | ||||||||
\(591\) | 14724.0 | 1.02481 | ||||||||
\(592\) | −4896.00 | −0.339906 | ||||||||
\(593\) | −11744.0 | −0.813269 | −0.406634 | − | 0.913591i | \(-0.633298\pi\) | ||||
−0.406634 | + | 0.913591i | \(0.633298\pi\) | |||||||
\(594\) | −2700.00 | −0.186502 | ||||||||
\(595\) | −19200.0 | −1.32290 | ||||||||
\(596\) | 5088.00 | 0.349686 | ||||||||
\(597\) | 984.000 | 0.0674580 | ||||||||
\(598\) | 520.000 | 0.0355592 | ||||||||
\(599\) | −15076.0 | −1.02836 | −0.514181 | − | 0.857682i | \(-0.671904\pi\) | ||||
−0.514181 | + | 0.857682i | \(0.671904\pi\) | |||||||
\(600\) | −6600.00 | −0.449073 | ||||||||
\(601\) | 20230.0 | 1.37304 | 0.686522 | − | 0.727109i | \(-0.259137\pi\) | ||||
0.686522 | + | 0.727109i | \(0.259137\pi\) | |||||||
\(602\) | 22784.0 | 1.54254 | ||||||||
\(603\) | −1260.00 | −0.0850931 | ||||||||
\(604\) | 5616.00 | 0.378331 | ||||||||
\(605\) | −23380.0 | −1.57113 | ||||||||
\(606\) | −6348.00 | −0.425528 | ||||||||
\(607\) | −28056.0 | −1.87604 | −0.938021 | − | 0.346577i | \(-0.887344\pi\) | ||||
−0.938021 | + | 0.346577i | \(0.887344\pi\) | |||||||
\(608\) | −3840.00 | −0.256139 | ||||||||
\(609\) | 7872.00 | 0.523792 | ||||||||
\(610\) | 2480.00 | 0.164610 | ||||||||
\(611\) | 2314.00 | 0.153215 | ||||||||
\(612\) | −1080.00 | −0.0713340 | ||||||||
\(613\) | 27446.0 | 1.80837 | 0.904187 | − | 0.427136i | \(-0.140478\pi\) | ||||
0.904187 | + | 0.427136i | \(0.140478\pi\) | |||||||
\(614\) | −12872.0 | −0.846045 | ||||||||
\(615\) | 6480.00 | 0.424876 | ||||||||
\(616\) | −12800.0 | −0.837219 | ||||||||
\(617\) | 8804.00 | 0.574450 | 0.287225 | − | 0.957863i | \(-0.407267\pi\) | ||||
0.287225 | + | 0.957863i | \(0.407267\pi\) | |||||||
\(618\) | −10608.0 | −0.690480 | ||||||||
\(619\) | 3508.00 | 0.227784 | 0.113892 | − | 0.993493i | \(-0.463668\pi\) | ||||
0.113892 | + | 0.993493i | \(0.463668\pi\) | |||||||
\(620\) | 3520.00 | 0.228011 | ||||||||
\(621\) | 540.000 | 0.0348945 | ||||||||
\(622\) | 15864.0 | 1.02265 | ||||||||
\(623\) | −39168.0 | −2.51883 | ||||||||
\(624\) | 624.000 | 0.0400320 | ||||||||
\(625\) | 25625.0 | 1.64000 | ||||||||
\(626\) | 20716.0 | 1.32265 | ||||||||
\(627\) | 18000.0 | 1.14649 | ||||||||
\(628\) | −8680.00 | −0.551544 | ||||||||
\(629\) | 9180.00 | 0.581925 | ||||||||
\(630\) | 11520.0 | 0.728520 | ||||||||
\(631\) | 22084.0 | 1.39326 | 0.696632 | − | 0.717428i | \(-0.254681\pi\) | ||||
0.696632 | + | 0.717428i | \(0.254681\pi\) | |||||||
\(632\) | −8768.00 | −0.551855 | ||||||||
\(633\) | −3948.00 | −0.247897 | ||||||||
\(634\) | −5640.00 | −0.353301 | ||||||||
\(635\) | −32480.0 | −2.02981 | ||||||||
\(636\) | −2376.00 | −0.148136 | ||||||||
\(637\) | −8853.00 | −0.550657 | ||||||||
\(638\) | 8200.00 | 0.508842 | ||||||||
\(639\) | −7002.00 | −0.433482 | ||||||||
\(640\) | −2560.00 | −0.158114 | ||||||||
\(641\) | −7342.00 | −0.452405 | −0.226202 | − | 0.974080i | \(-0.572631\pi\) | ||||
−0.226202 | + | 0.974080i | \(0.572631\pi\) | |||||||
\(642\) | 10848.0 | 0.666879 | ||||||||
\(643\) | 2996.00 | 0.183749 | 0.0918746 | − | 0.995771i | \(-0.470714\pi\) | ||||
0.0918746 | + | 0.995771i | \(0.470714\pi\) | |||||||
\(644\) | 2560.00 | 0.156643 | ||||||||
\(645\) | −21360.0 | −1.30395 | ||||||||
\(646\) | 7200.00 | 0.438514 | ||||||||
\(647\) | 9344.00 | 0.567775 | 0.283888 | − | 0.958858i | \(-0.408376\pi\) | ||||
0.283888 | + | 0.958858i | \(0.408376\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 4700.00 | 0.284270 | ||||||||
\(650\) | −7150.00 | −0.431455 | ||||||||
\(651\) | −4224.00 | −0.254304 | ||||||||
\(652\) | 992.000 | 0.0595855 | ||||||||
\(653\) | −16686.0 | −0.999960 | −0.499980 | − | 0.866037i | \(-0.666659\pi\) | ||||
−0.499980 | + | 0.866037i | \(0.666659\pi\) | |||||||
\(654\) | 11316.0 | 0.676591 | ||||||||
\(655\) | 41440.0 | 2.47205 | ||||||||
\(656\) | 1728.00 | 0.102846 | ||||||||
\(657\) | 558.000 | 0.0331349 | ||||||||
\(658\) | 11392.0 | 0.674934 | ||||||||
\(659\) | 31356.0 | 1.85350 | 0.926750 | − | 0.375679i | \(-0.122590\pi\) | ||||
0.926750 | + | 0.375679i | \(0.122590\pi\) | |||||||
\(660\) | 12000.0 | 0.707726 | ||||||||
\(661\) | 590.000 | 0.0347176 | 0.0173588 | − | 0.999849i | \(-0.494474\pi\) | ||||
0.0173588 | + | 0.999849i | \(0.494474\pi\) | |||||||
\(662\) | −8360.00 | −0.490817 | ||||||||
\(663\) | −1170.00 | −0.0685355 | ||||||||
\(664\) | −3696.00 | −0.216013 | ||||||||
\(665\) | −76800.0 | −4.47846 | ||||||||
\(666\) | −5508.00 | −0.320466 | ||||||||
\(667\) | −1640.00 | −0.0952040 | ||||||||
\(668\) | 408.000 | 0.0236317 | ||||||||
\(669\) | 5796.00 | 0.334957 | ||||||||
\(670\) | 5600.00 | 0.322906 | ||||||||
\(671\) | −3100.00 | −0.178352 | ||||||||
\(672\) | 3072.00 | 0.176347 | ||||||||
\(673\) | 5938.00 | 0.340109 | 0.170054 | − | 0.985435i | \(-0.445606\pi\) | ||||
0.170054 | + | 0.985435i | \(0.445606\pi\) | |||||||
\(674\) | −10052.0 | −0.574464 | ||||||||
\(675\) | −7425.00 | −0.423390 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | 9486.00 | 0.538518 | 0.269259 | − | 0.963068i | \(-0.413221\pi\) | ||||
0.269259 | + | 0.963068i | \(0.413221\pi\) | |||||||
\(678\) | −7476.00 | −0.423472 | ||||||||
\(679\) | −19648.0 | −1.11049 | ||||||||
\(680\) | 4800.00 | 0.270694 | ||||||||
\(681\) | −14994.0 | −0.843717 | ||||||||
\(682\) | −4400.00 | −0.247045 | ||||||||
\(683\) | 26162.0 | 1.46568 | 0.732841 | − | 0.680400i | \(-0.238194\pi\) | ||||
0.732841 | + | 0.680400i | \(0.238194\pi\) | |||||||
\(684\) | −4320.00 | −0.241490 | ||||||||
\(685\) | 15120.0 | 0.843366 | ||||||||
\(686\) | −21632.0 | −1.20396 | ||||||||
\(687\) | 234.000 | 0.0129951 | ||||||||
\(688\) | −5696.00 | −0.315637 | ||||||||
\(689\) | −2574.00 | −0.142325 | ||||||||
\(690\) | −2400.00 | −0.132415 | ||||||||
\(691\) | −17348.0 | −0.955064 | −0.477532 | − | 0.878614i | \(-0.658468\pi\) | ||||
−0.477532 | + | 0.878614i | \(0.658468\pi\) | |||||||
\(692\) | 2728.00 | 0.149860 | ||||||||
\(693\) | −14400.0 | −0.789337 | ||||||||
\(694\) | −14664.0 | −0.802072 | ||||||||
\(695\) | −3440.00 | −0.187751 | ||||||||
\(696\) | −1968.00 | −0.107179 | ||||||||
\(697\) | −3240.00 | −0.176074 | ||||||||
\(698\) | −16324.0 | −0.885204 | ||||||||
\(699\) | 3846.00 | 0.208110 | ||||||||
\(700\) | −35200.0 | −1.90062 | ||||||||
\(701\) | 30.0000 | 0.00161638 | 0.000808191 | − | 1.00000i | \(-0.499743\pi\) | ||||
0.000808191 | 1.00000i | \(0.499743\pi\) | ||||||||
\(702\) | 702.000 | 0.0377426 | ||||||||
\(703\) | 36720.0 | 1.97002 | ||||||||
\(704\) | 3200.00 | 0.171313 | ||||||||
\(705\) | −10680.0 | −0.570542 | ||||||||
\(706\) | 2488.00 | 0.132630 | ||||||||
\(707\) | −33856.0 | −1.80097 | ||||||||
\(708\) | −1128.00 | −0.0598769 | ||||||||
\(709\) | 31466.0 | 1.66676 | 0.833378 | − | 0.552703i | \(-0.186404\pi\) | ||||
0.833378 | + | 0.552703i | \(0.186404\pi\) | |||||||
\(710\) | 31120.0 | 1.64495 | ||||||||
\(711\) | −9864.00 | −0.520294 | ||||||||
\(712\) | 9792.00 | 0.515408 | ||||||||
\(713\) | 880.000 | 0.0462220 | ||||||||
\(714\) | −5760.00 | −0.301908 | ||||||||
\(715\) | 13000.0 | 0.679961 | ||||||||
\(716\) | −2448.00 | −0.127774 | ||||||||
\(717\) | −882.000 | −0.0459399 | ||||||||
\(718\) | 19116.0 | 0.993597 | ||||||||
\(719\) | −28892.0 | −1.49859 | −0.749297 | − | 0.662234i | \(-0.769609\pi\) | ||||
−0.749297 | + | 0.662234i | \(0.769609\pi\) | |||||||
\(720\) | −2880.00 | −0.149071 | ||||||||
\(721\) | −56576.0 | −2.92233 | ||||||||
\(722\) | 15082.0 | 0.777415 | ||||||||
\(723\) | 14886.0 | 0.765721 | ||||||||
\(724\) | −264.000 | −0.0135518 | ||||||||
\(725\) | 22550.0 | 1.15515 | ||||||||
\(726\) | −7014.00 | −0.358559 | ||||||||
\(727\) | 13384.0 | 0.682786 | 0.341393 | − | 0.939921i | \(-0.389101\pi\) | ||||
0.341393 | + | 0.939921i | \(0.389101\pi\) | |||||||
\(728\) | 3328.00 | 0.169428 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −2480.00 | −0.125738 | ||||||||
\(731\) | 10680.0 | 0.540375 | ||||||||
\(732\) | 744.000 | 0.0375670 | ||||||||
\(733\) | 7130.00 | 0.359280 | 0.179640 | − | 0.983732i | \(-0.442507\pi\) | ||||
0.179640 | + | 0.983732i | \(0.442507\pi\) | |||||||
\(734\) | −22064.0 | −1.10953 | ||||||||
\(735\) | 40860.0 | 2.05054 | ||||||||
\(736\) | −640.000 | −0.0320526 | ||||||||
\(737\) | −7000.00 | −0.349862 | ||||||||
\(738\) | 1944.00 | 0.0969643 | ||||||||
\(739\) | −29268.0 | −1.45689 | −0.728444 | − | 0.685105i | \(-0.759756\pi\) | ||||
−0.728444 | + | 0.685105i | \(0.759756\pi\) | |||||||
\(740\) | 24480.0 | 1.21608 | ||||||||
\(741\) | −4680.00 | −0.232016 | ||||||||
\(742\) | −12672.0 | −0.626959 | ||||||||
\(743\) | −9898.00 | −0.488725 | −0.244362 | − | 0.969684i | \(-0.578579\pi\) | ||||
−0.244362 | + | 0.969684i | \(0.578579\pi\) | |||||||
\(744\) | 1056.00 | 0.0520361 | ||||||||
\(745\) | −25440.0 | −1.25107 | ||||||||
\(746\) | 10948.0 | 0.537312 | ||||||||
\(747\) | −4158.00 | −0.203659 | ||||||||
\(748\) | −6000.00 | −0.293291 | ||||||||
\(749\) | 57856.0 | 2.82245 | ||||||||
\(750\) | 18000.0 | 0.876356 | ||||||||
\(751\) | −15120.0 | −0.734669 | −0.367335 | − | 0.930089i | \(-0.619730\pi\) | ||||
−0.367335 | + | 0.930089i | \(0.619730\pi\) | |||||||
\(752\) | −2848.00 | −0.138106 | ||||||||
\(753\) | −2232.00 | −0.108019 | ||||||||
\(754\) | −2132.00 | −0.102975 | ||||||||
\(755\) | −28080.0 | −1.35356 | ||||||||
\(756\) | 3456.00 | 0.166261 | ||||||||
\(757\) | −5454.00 | −0.261861 | −0.130931 | − | 0.991392i | \(-0.541797\pi\) | ||||
−0.130931 | + | 0.991392i | \(0.541797\pi\) | |||||||
\(758\) | −14080.0 | −0.674682 | ||||||||
\(759\) | 3000.00 | 0.143469 | ||||||||
\(760\) | 19200.0 | 0.916391 | ||||||||
\(761\) | −11988.0 | −0.571044 | −0.285522 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285522 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(762\) | −9744.00 | −0.463239 | ||||||||
\(763\) | 60352.0 | 2.86355 | ||||||||
\(764\) | 2432.00 | 0.115166 | ||||||||
\(765\) | 5400.00 | 0.255212 | ||||||||
\(766\) | −3660.00 | −0.172639 | ||||||||
\(767\) | −1222.00 | −0.0575279 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 1338.00 | 0.0627432 | 0.0313716 | − | 0.999508i | \(-0.490012\pi\) | ||||
0.0313716 | + | 0.999508i | \(0.490012\pi\) | |||||||
\(770\) | 64000.0 | 2.99532 | ||||||||
\(771\) | 3078.00 | 0.143776 | ||||||||
\(772\) | 5480.00 | 0.255479 | ||||||||
\(773\) | −14408.0 | −0.670401 | −0.335200 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335200 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(774\) | −6408.00 | −0.297585 | ||||||||
\(775\) | −12100.0 | −0.560832 | ||||||||
\(776\) | 4912.00 | 0.227230 | ||||||||
\(777\) | −29376.0 | −1.35632 | ||||||||
\(778\) | 20316.0 | 0.936200 | ||||||||
\(779\) | −12960.0 | −0.596072 | ||||||||
\(780\) | −3120.00 | −0.143223 | ||||||||
\(781\) | −38900.0 | −1.78227 | ||||||||
\(782\) | 1200.00 | 0.0548746 | ||||||||
\(783\) | −2214.00 | −0.101050 | ||||||||
\(784\) | 10896.0 | 0.496356 | ||||||||
\(785\) | 43400.0 | 1.97326 | ||||||||
\(786\) | 12432.0 | 0.564166 | ||||||||
\(787\) | −10660.0 | −0.482831 | −0.241415 | − | 0.970422i | \(-0.577612\pi\) | ||||
−0.241415 | + | 0.970422i | \(0.577612\pi\) | |||||||
\(788\) | −19632.0 | −0.887514 | ||||||||
\(789\) | 16596.0 | 0.748838 | ||||||||
\(790\) | 43840.0 | 1.97438 | ||||||||
\(791\) | −39872.0 | −1.79227 | ||||||||
\(792\) | 3600.00 | 0.161516 | ||||||||
\(793\) | 806.000 | 0.0360932 | ||||||||
\(794\) | −25316.0 | −1.13153 | ||||||||
\(795\) | 11880.0 | 0.529988 | ||||||||
\(796\) | −1312.00 | −0.0584204 | ||||||||
\(797\) | 1974.00 | 0.0877323 | 0.0438662 | − | 0.999037i | \(-0.486032\pi\) | ||||
0.0438662 | + | 0.999037i | \(0.486032\pi\) | |||||||
\(798\) | −23040.0 | −1.02206 | ||||||||
\(799\) | 5340.00 | 0.236440 | ||||||||
\(800\) | 8800.00 | 0.388909 | ||||||||
\(801\) | 11016.0 | 0.485932 | ||||||||
\(802\) | 31440.0 | 1.38427 | ||||||||
\(803\) | 3100.00 | 0.136235 | ||||||||
\(804\) | 1680.00 | 0.0736928 | ||||||||
\(805\) | −12800.0 | −0.560423 | ||||||||
\(806\) | 1144.00 | 0.0499946 | ||||||||
\(807\) | 10602.0 | 0.462464 | ||||||||
\(808\) | 8464.00 | 0.368518 | ||||||||
\(809\) | 31734.0 | 1.37912 | 0.689560 | − | 0.724229i | \(-0.257804\pi\) | ||||
0.689560 | + | 0.724229i | \(0.257804\pi\) | |||||||
\(810\) | −3240.00 | −0.140546 | ||||||||
\(811\) | −38824.0 | −1.68100 | −0.840502 | − | 0.541808i | \(-0.817740\pi\) | ||||
−0.840502 | + | 0.541808i | \(0.817740\pi\) | |||||||
\(812\) | −10496.0 | −0.453617 | ||||||||
\(813\) | −7176.00 | −0.309561 | ||||||||
\(814\) | −30600.0 | −1.31760 | ||||||||
\(815\) | −4960.00 | −0.213179 | ||||||||
\(816\) | 1440.00 | 0.0617771 | ||||||||
\(817\) | 42720.0 | 1.82936 | ||||||||
\(818\) | 15308.0 | 0.654317 | ||||||||
\(819\) | 3744.00 | 0.159739 | ||||||||
\(820\) | −8640.00 | −0.367954 | ||||||||
\(821\) | −16736.0 | −0.711438 | −0.355719 | − | 0.934593i | \(-0.615764\pi\) | ||||
−0.355719 | + | 0.934593i | \(0.615764\pi\) | |||||||
\(822\) | 4536.00 | 0.192471 | ||||||||
\(823\) | 42096.0 | 1.78296 | 0.891479 | − | 0.453062i | \(-0.149668\pi\) | ||||
0.891479 | + | 0.453062i | \(0.149668\pi\) | |||||||
\(824\) | 14144.0 | 0.597973 | ||||||||
\(825\) | −41250.0 | −1.74078 | ||||||||
\(826\) | −6016.00 | −0.253418 | ||||||||
\(827\) | 24858.0 | 1.04522 | 0.522610 | − | 0.852572i | \(-0.324958\pi\) | ||||
0.522610 | + | 0.852572i | \(0.324958\pi\) | |||||||
\(828\) | −720.000 | −0.0302195 | ||||||||
\(829\) | 922.000 | 0.0386277 | 0.0193139 | − | 0.999813i | \(-0.493852\pi\) | ||||
0.0193139 | + | 0.999813i | \(0.493852\pi\) | |||||||
\(830\) | 18480.0 | 0.772832 | ||||||||
\(831\) | −18306.0 | −0.764173 | ||||||||
\(832\) | −832.000 | −0.0346688 | ||||||||
\(833\) | −20430.0 | −0.849769 | ||||||||
\(834\) | −1032.00 | −0.0428480 | ||||||||
\(835\) | −2040.00 | −0.0845474 | ||||||||
\(836\) | −24000.0 | −0.992892 | ||||||||
\(837\) | 1188.00 | 0.0490601 | ||||||||
\(838\) | −3696.00 | −0.152358 | ||||||||
\(839\) | −14294.0 | −0.588181 | −0.294090 | − | 0.955778i | \(-0.595017\pi\) | ||||
−0.294090 | + | 0.955778i | \(0.595017\pi\) | |||||||
\(840\) | −15360.0 | −0.630917 | ||||||||
\(841\) | −17665.0 | −0.724302 | ||||||||
\(842\) | −25084.0 | −1.02666 | ||||||||
\(843\) | 22620.0 | 0.924169 | ||||||||
\(844\) | 5264.00 | 0.214685 | ||||||||
\(845\) | −3380.00 | −0.137604 | ||||||||
\(846\) | −3204.00 | −0.130208 | ||||||||
\(847\) | −37408.0 | −1.51754 | ||||||||
\(848\) | 3168.00 | 0.128290 | ||||||||
\(849\) | 8268.00 | 0.334225 | ||||||||
\(850\) | −16500.0 | −0.665818 | ||||||||
\(851\) | 6120.00 | 0.246523 | ||||||||
\(852\) | 9336.00 | 0.375406 | ||||||||
\(853\) | 37966.0 | 1.52395 | 0.761976 | − | 0.647605i | \(-0.224229\pi\) | ||||
0.761976 | + | 0.647605i | \(0.224229\pi\) | |||||||
\(854\) | 3968.00 | 0.158996 | ||||||||
\(855\) | 21600.0 | 0.863982 | ||||||||
\(856\) | −14464.0 | −0.577534 | ||||||||
\(857\) | 39038.0 | 1.55602 | 0.778012 | − | 0.628249i | \(-0.216228\pi\) | ||||
0.778012 | + | 0.628249i | \(0.216228\pi\) | |||||||
\(858\) | 3900.00 | 0.155179 | ||||||||
\(859\) | 20564.0 | 0.816804 | 0.408402 | − | 0.912802i | \(-0.366086\pi\) | ||||
0.408402 | + | 0.912802i | \(0.366086\pi\) | |||||||
\(860\) | 28480.0 | 1.12926 | ||||||||
\(861\) | 10368.0 | 0.410384 | ||||||||
\(862\) | −10476.0 | −0.413937 | ||||||||
\(863\) | 39866.0 | 1.57248 | 0.786242 | − | 0.617918i | \(-0.212024\pi\) | ||||
0.786242 | + | 0.617918i | \(0.212024\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −13640.0 | −0.536155 | ||||||||
\(866\) | −16516.0 | −0.648079 | ||||||||
\(867\) | 12039.0 | 0.471587 | ||||||||
\(868\) | 5632.00 | 0.220233 | ||||||||
\(869\) | −54800.0 | −2.13920 | ||||||||
\(870\) | 9840.00 | 0.383457 | ||||||||
\(871\) | 1820.00 | 0.0708018 | ||||||||
\(872\) | −15088.0 | −0.585945 | ||||||||
\(873\) | 5526.00 | 0.214235 | ||||||||
\(874\) | 4800.00 | 0.185769 | ||||||||
\(875\) | 96000.0 | 3.70902 | ||||||||
\(876\) | −744.000 | −0.0286957 | ||||||||
\(877\) | 30990.0 | 1.19322 | 0.596612 | − | 0.802530i | \(-0.296513\pi\) | ||||
0.596612 | + | 0.802530i | \(0.296513\pi\) | |||||||
\(878\) | −12608.0 | −0.484623 | ||||||||
\(879\) | −2904.00 | −0.111433 | ||||||||
\(880\) | −16000.0 | −0.612909 | ||||||||
\(881\) | −4458.00 | −0.170481 | −0.0852405 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852405 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(882\) | 12258.0 | 0.467969 | ||||||||
\(883\) | −3164.00 | −0.120586 | −0.0602928 | − | 0.998181i | \(-0.519203\pi\) | ||||
−0.0602928 | + | 0.998181i | \(0.519203\pi\) | |||||||
\(884\) | 1560.00 | 0.0593535 | ||||||||
\(885\) | 5640.00 | 0.214222 | ||||||||
\(886\) | 25488.0 | 0.966463 | ||||||||
\(887\) | −32512.0 | −1.23072 | −0.615359 | − | 0.788247i | \(-0.710989\pi\) | ||||
−0.615359 | + | 0.788247i | \(0.710989\pi\) | |||||||
\(888\) | 7344.00 | 0.277532 | ||||||||
\(889\) | −51968.0 | −1.96057 | ||||||||
\(890\) | −48960.0 | −1.84398 | ||||||||
\(891\) | 4050.00 | 0.152278 | ||||||||
\(892\) | −7728.00 | −0.290081 | ||||||||
\(893\) | 21360.0 | 0.800431 | ||||||||
\(894\) | −7632.00 | −0.285517 | ||||||||
\(895\) | 12240.0 | 0.457138 | ||||||||
\(896\) | −4096.00 | −0.152721 | ||||||||
\(897\) | −780.000 | −0.0290339 | ||||||||
\(898\) | −23552.0 | −0.875212 | ||||||||
\(899\) | −3608.00 | −0.133853 | ||||||||
\(900\) | 9900.00 | 0.366667 | ||||||||
\(901\) | −5940.00 | −0.219634 | ||||||||
\(902\) | 10800.0 | 0.398670 | ||||||||
\(903\) | −34176.0 | −1.25948 | ||||||||
\(904\) | 9968.00 | 0.366738 | ||||||||
\(905\) | 1320.00 | 0.0484843 | ||||||||
\(906\) | −8424.00 | −0.308906 | ||||||||
\(907\) | 10500.0 | 0.384396 | 0.192198 | − | 0.981356i | \(-0.438438\pi\) | ||||
0.192198 | + | 0.981356i | \(0.438438\pi\) | |||||||
\(908\) | 19992.0 | 0.730680 | ||||||||
\(909\) | 9522.00 | 0.347442 | ||||||||
\(910\) | −16640.0 | −0.606166 | ||||||||
\(911\) | 9840.00 | 0.357864 | 0.178932 | − | 0.983861i | \(-0.442736\pi\) | ||||
0.178932 | + | 0.983861i | \(0.442736\pi\) | |||||||
\(912\) | 5760.00 | 0.209137 | ||||||||
\(913\) | −23100.0 | −0.837348 | ||||||||
\(914\) | 4268.00 | 0.154456 | ||||||||
\(915\) | −3720.00 | −0.134404 | ||||||||
\(916\) | −312.000 | −0.0112541 | ||||||||
\(917\) | 66304.0 | 2.38773 | ||||||||
\(918\) | 1620.00 | 0.0582440 | ||||||||
\(919\) | −35040.0 | −1.25774 | −0.628870 | − | 0.777511i | \(-0.716482\pi\) | ||||
−0.628870 | + | 0.777511i | \(0.716482\pi\) | |||||||
\(920\) | 3200.00 | 0.114675 | ||||||||
\(921\) | 19308.0 | 0.690793 | ||||||||
\(922\) | 5448.00 | 0.194599 | ||||||||
\(923\) | 10114.0 | 0.360679 | ||||||||
\(924\) | 19200.0 | 0.683586 | ||||||||
\(925\) | −84150.0 | −2.99117 | ||||||||
\(926\) | −11296.0 | −0.400874 | ||||||||
\(927\) | 15912.0 | 0.563774 | ||||||||
\(928\) | 2624.00 | 0.0928201 | ||||||||
\(929\) | 44172.0 | 1.56000 | 0.779998 | − | 0.625782i | \(-0.215220\pi\) | ||||
0.779998 | + | 0.625782i | \(0.215220\pi\) | |||||||
\(930\) | −5280.00 | −0.186170 | ||||||||
\(931\) | −81720.0 | −2.87676 | ||||||||
\(932\) | −5128.00 | −0.180229 | ||||||||
\(933\) | −23796.0 | −0.834990 | ||||||||
\(934\) | −36448.0 | −1.27689 | ||||||||
\(935\) | 30000.0 | 1.04931 | ||||||||
\(936\) | −936.000 | −0.0326860 | ||||||||
\(937\) | −54018.0 | −1.88334 | −0.941671 | − | 0.336535i | \(-0.890745\pi\) | ||||
−0.941671 | + | 0.336535i | \(0.890745\pi\) | |||||||
\(938\) | 8960.00 | 0.311892 | ||||||||
\(939\) | −31074.0 | −1.07994 | ||||||||
\(940\) | 14240.0 | 0.494104 | ||||||||
\(941\) | −1672.00 | −0.0579231 | −0.0289616 | − | 0.999581i | \(-0.509220\pi\) | ||||
−0.0289616 | + | 0.999581i | \(0.509220\pi\) | |||||||
\(942\) | 13020.0 | 0.450334 | ||||||||
\(943\) | −2160.00 | −0.0745910 | ||||||||
\(944\) | 1504.00 | 0.0518549 | ||||||||
\(945\) | −17280.0 | −0.594834 | ||||||||
\(946\) | −35600.0 | −1.22353 | ||||||||
\(947\) | 5238.00 | 0.179738 | 0.0898691 | − | 0.995954i | \(-0.471355\pi\) | ||||
0.0898691 | + | 0.995954i | \(0.471355\pi\) | |||||||
\(948\) | 13152.0 | 0.450588 | ||||||||
\(949\) | −806.000 | −0.0275699 | ||||||||
\(950\) | −66000.0 | −2.25402 | ||||||||
\(951\) | 8460.00 | 0.288469 | ||||||||
\(952\) | 7680.00 | 0.261460 | ||||||||
\(953\) | −50042.0 | −1.70096 | −0.850482 | − | 0.526004i | \(-0.823690\pi\) | ||||
−0.850482 | + | 0.526004i | \(0.823690\pi\) | |||||||
\(954\) | 3564.00 | 0.120953 | ||||||||
\(955\) | −12160.0 | −0.412030 | ||||||||
\(956\) | 1176.00 | 0.0397851 | ||||||||
\(957\) | −12300.0 | −0.415468 | ||||||||
\(958\) | 18132.0 | 0.611501 | ||||||||
\(959\) | 24192.0 | 0.814599 | ||||||||
\(960\) | 3840.00 | 0.129099 | ||||||||
\(961\) | −27855.0 | −0.935014 | ||||||||
\(962\) | 7956.00 | 0.266644 | ||||||||
\(963\) | −16272.0 | −0.544505 | ||||||||
\(964\) | −19848.0 | −0.663134 | ||||||||
\(965\) | −27400.0 | −0.914028 | ||||||||
\(966\) | −3840.00 | −0.127899 | ||||||||
\(967\) | 37676.0 | 1.25293 | 0.626463 | − | 0.779452i | \(-0.284502\pi\) | ||||
0.626463 | + | 0.779452i | \(0.284502\pi\) | |||||||
\(968\) | 9352.00 | 0.310521 | ||||||||
\(969\) | −10800.0 | −0.358045 | ||||||||
\(970\) | −24560.0 | −0.812963 | ||||||||
\(971\) | −17364.0 | −0.573880 | −0.286940 | − | 0.957949i | \(-0.592638\pi\) | ||||
−0.286940 | + | 0.957949i | \(0.592638\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −5504.00 | −0.181346 | ||||||||
\(974\) | 17896.0 | 0.588732 | ||||||||
\(975\) | 10725.0 | 0.352282 | ||||||||
\(976\) | −992.000 | −0.0325340 | ||||||||
\(977\) | −14904.0 | −0.488046 | −0.244023 | − | 0.969769i | \(-0.578467\pi\) | ||||
−0.244023 | + | 0.969769i | \(0.578467\pi\) | |||||||
\(978\) | −1488.00 | −0.0486513 | ||||||||
\(979\) | 61200.0 | 1.99792 | ||||||||
\(980\) | −54480.0 | −1.77582 | ||||||||
\(981\) | −16974.0 | −0.552434 | ||||||||
\(982\) | 17440.0 | 0.566734 | ||||||||
\(983\) | −18038.0 | −0.585272 | −0.292636 | − | 0.956224i | \(-0.594533\pi\) | ||||
−0.292636 | + | 0.956224i | \(0.594533\pi\) | |||||||
\(984\) | −2592.00 | −0.0839735 | ||||||||
\(985\) | 98160.0 | 3.17527 | ||||||||
\(986\) | −4920.00 | −0.158909 | ||||||||
\(987\) | −17088.0 | −0.551081 | ||||||||
\(988\) | 6240.00 | 0.200932 | ||||||||
\(989\) | 7120.00 | 0.228921 | ||||||||
\(990\) | −18000.0 | −0.577856 | ||||||||
\(991\) | 46176.0 | 1.48015 | 0.740075 | − | 0.672524i | \(-0.234790\pi\) | ||||
0.740075 | + | 0.672524i | \(0.234790\pi\) | |||||||
\(992\) | −1408.00 | −0.0450646 | ||||||||
\(993\) | 12540.0 | 0.400750 | ||||||||
\(994\) | 49792.0 | 1.58884 | ||||||||
\(995\) | 6560.00 | 0.209011 | ||||||||
\(996\) | 5544.00 | 0.176374 | ||||||||
\(997\) | 55838.0 | 1.77373 | 0.886864 | − | 0.462030i | \(-0.152879\pi\) | ||||
0.886864 | + | 0.462030i | \(0.152879\pi\) | |||||||
\(998\) | 13208.0 | 0.418930 | ||||||||
\(999\) | 8262.00 | 0.261660 |
(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 | 78.4.a.d.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 234.4.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 624.4.a.e.1.1 | 1 | |||
5.4 | even | 2 | 1950.4.a.h.1.1 | 1 | |||
8.3 | odd | 2 | 2496.4.a.i.1.1 | 1 | |||
8.5 | even | 2 | 2496.4.a.r.1.1 | 1 | |||
12.11 | even | 2 | 1872.4.a.r.1.1 | 1 | |||
13.5 | odd | 4 | 1014.4.b.e.337.1 | 2 | |||
13.8 | odd | 4 | 1014.4.b.e.337.2 | 2 | |||
13.12 | even | 2 | 1014.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.4.a.d.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
234.4.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
624.4.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
1014.4.a.d.1.1 | 1 | 13.12 | even | 2 | |||
1014.4.b.e.337.1 | 2 | 13.5 | odd | 4 | |||
1014.4.b.e.337.2 | 2 | 13.8 | odd | 4 | |||
1872.4.a.r.1.1 | 1 | 12.11 | even | 2 | |||
1950.4.a.h.1.1 | 1 | 5.4 | even | 2 | |||
2496.4.a.i.1.1 | 1 | 8.3 | odd | 2 | |||
2496.4.a.r.1.1 | 1 | 8.5 | even | 2 |