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: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} + \cdots - 6889792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7\cdot 13^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.86163\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86163 | −0.658186 | −0.329093 | − | 0.944298i | \(-0.606743\pi\) | ||||
−0.329093 | + | 0.944298i | \(0.606743\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.53433 | −0.566791 | ||||||||
\(5\) | 3.46613 | 0.310020 | 0.155010 | − | 0.987913i | \(-0.450459\pi\) | ||||
0.155010 | + | 0.987913i | \(0.450459\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −21.2285 | −1.14623 | −0.573115 | − | 0.819475i | \(-0.694265\pi\) | ||||
−0.573115 | + | 0.819475i | \(0.694265\pi\) | |||||||
\(8\) | 23.3343 | 1.03124 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.45265 | −0.204051 | ||||||||
\(11\) | 54.1559 | 1.48442 | 0.742210 | − | 0.670168i | \(-0.233778\pi\) | ||||
0.742210 | + | 0.670168i | \(0.233778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 39.5196 | 0.754433 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.16523 | −0.111957 | ||||||||
\(17\) | 99.0529 | 1.41317 | 0.706584 | − | 0.707629i | \(-0.250235\pi\) | ||||
0.706584 | + | 0.707629i | \(0.250235\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −64.1160 | −0.774169 | −0.387085 | − | 0.922044i | \(-0.626518\pi\) | ||||
−0.387085 | + | 0.922044i | \(0.626518\pi\) | |||||||
\(20\) | −15.7166 | −0.175716 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −100.818 | −0.977024 | ||||||||
\(23\) | 153.983 | 1.39599 | 0.697994 | − | 0.716104i | \(-0.254076\pi\) | ||||
0.697994 | + | 0.716104i | \(0.254076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −112.986 | −0.903888 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 96.2569 | 0.649673 | ||||||||
\(29\) | −22.5438 | −0.144354 | −0.0721771 | − | 0.997392i | \(-0.522995\pi\) | ||||
−0.0721771 | + | 0.997392i | \(0.522995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 241.319 | 1.39814 | 0.699068 | − | 0.715055i | \(-0.253598\pi\) | ||||
0.699068 | + | 0.715055i | \(0.253598\pi\) | |||||||
\(32\) | −173.335 | −0.957552 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −184.400 | −0.930128 | ||||||||
\(35\) | −73.5806 | −0.355354 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.5346 | −0.153444 | −0.0767222 | − | 0.997053i | \(-0.524445\pi\) | ||||
−0.0767222 | + | 0.997053i | \(0.524445\pi\) | |||||||
\(38\) | 119.360 | 0.509547 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 80.8796 | 0.319705 | ||||||||
\(41\) | 117.778 | 0.448630 | 0.224315 | − | 0.974517i | \(-0.427986\pi\) | ||||
0.224315 | + | 0.974517i | \(0.427986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −101.468 | −0.359856 | −0.179928 | − | 0.983680i | \(-0.557586\pi\) | ||||
−0.179928 | + | 0.983680i | \(0.557586\pi\) | |||||||
\(44\) | −245.561 | −0.841356 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −286.660 | −0.918819 | ||||||||
\(47\) | −451.273 | −1.40053 | −0.700265 | − | 0.713883i | \(-0.746935\pi\) | ||||
−0.700265 | + | 0.713883i | \(0.746935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 107.649 | 0.313844 | ||||||||
\(50\) | 210.338 | 0.594926 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.41346 | 0.0166218 | 0.00831091 | − | 0.999965i | \(-0.497355\pi\) | ||||
0.00831091 | + | 0.999965i | \(0.497355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 187.711 | 0.460199 | ||||||||
\(56\) | −495.352 | −1.18204 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 41.9682 | 0.0950119 | ||||||||
\(59\) | 303.502 | 0.669704 | 0.334852 | − | 0.942271i | \(-0.391314\pi\) | ||||
0.334852 | + | 0.942271i | \(0.391314\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −622.411 | −1.30642 | −0.653210 | − | 0.757177i | \(-0.726578\pi\) | ||||
−0.653210 | + | 0.757177i | \(0.726578\pi\) | |||||||
\(62\) | −449.248 | −0.920234 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 380.008 | 0.742204 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −289.575 | −0.528018 | −0.264009 | − | 0.964520i | \(-0.585045\pi\) | ||||
−0.264009 | + | 0.964520i | \(0.585045\pi\) | |||||||
\(68\) | −449.138 | −0.800971 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 136.980 | 0.233889 | ||||||||
\(71\) | 949.340 | 1.58684 | 0.793422 | − | 0.608671i | \(-0.208297\pi\) | ||||
0.793422 | + | 0.608671i | \(0.208297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 56.4739 | 0.0905448 | 0.0452724 | − | 0.998975i | \(-0.485584\pi\) | ||||
0.0452724 | + | 0.998975i | \(0.485584\pi\) | |||||||
\(74\) | 64.2906 | 0.100995 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 290.723 | 0.438792 | ||||||||
\(77\) | −1149.65 | −1.70149 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −968.723 | −1.37962 | −0.689809 | − | 0.723991i | \(-0.742306\pi\) | ||||
−0.689809 | + | 0.723991i | \(0.742306\pi\) | |||||||
\(80\) | −24.8356 | −0.0347088 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −219.259 | −0.295282 | ||||||||
\(83\) | −480.985 | −0.636084 | −0.318042 | − | 0.948077i | \(-0.603025\pi\) | ||||
−0.318042 | + | 0.948077i | \(0.603025\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 343.330 | 0.438110 | ||||||||
\(86\) | 188.897 | 0.236852 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1263.69 | 1.53079 | ||||||||
\(89\) | 240.037 | 0.285887 | 0.142943 | − | 0.989731i | \(-0.454343\pi\) | ||||
0.142943 | + | 0.989731i | \(0.454343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −698.210 | −0.791233 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 840.104 | 0.921810 | ||||||||
\(95\) | −222.234 | −0.240008 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1871.81 | 1.95931 | 0.979657 | − | 0.200680i | \(-0.0643152\pi\) | ||||
0.979657 | + | 0.200680i | \(0.0643152\pi\) | |||||||
\(98\) | −200.402 | −0.206568 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 512.316 | 0.512316 | ||||||||
\(101\) | 1798.53 | 1.77189 | 0.885944 | − | 0.463792i | \(-0.153511\pi\) | ||||
0.885944 | + | 0.463792i | \(0.153511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 723.429 | 0.692054 | 0.346027 | − | 0.938225i | \(-0.387531\pi\) | ||||
0.346027 | + | 0.938225i | \(0.387531\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.9395 | −0.0109403 | ||||||||
\(107\) | −1767.01 | −1.59648 | −0.798241 | − | 0.602338i | \(-0.794236\pi\) | ||||
−0.798241 | + | 0.602338i | \(0.794236\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 401.486 | 0.352801 | 0.176401 | − | 0.984318i | \(-0.443555\pi\) | ||||
0.176401 | + | 0.984318i | \(0.443555\pi\) | |||||||
\(110\) | −349.449 | −0.302897 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 152.107 | 0.128328 | ||||||||
\(113\) | −1042.23 | −0.867649 | −0.433824 | − | 0.900997i | \(-0.642836\pi\) | ||||
−0.433824 | + | 0.900997i | \(0.642836\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 533.725 | 0.432784 | ||||||||
\(116\) | 102.221 | 0.0818187 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −565.008 | −0.440790 | ||||||||
\(119\) | −2102.74 | −1.61982 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1601.86 | 1.20350 | ||||||||
\(122\) | 1158.70 | 0.859867 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1094.22 | −0.792452 | ||||||||
\(125\) | −824.889 | −0.590243 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 818.340 | 0.571779 | 0.285889 | − | 0.958263i | \(-0.407711\pi\) | ||||
0.285889 | + | 0.958263i | \(0.407711\pi\) | |||||||
\(128\) | 679.248 | 0.469044 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1359.91 | 0.906993 | 0.453496 | − | 0.891258i | \(-0.350176\pi\) | ||||
0.453496 | + | 0.891258i | \(0.350176\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1361.09 | 0.887376 | ||||||||
\(134\) | 539.082 | 0.347534 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2311.33 | 1.45732 | ||||||||
\(137\) | 2233.38 | 1.39278 | 0.696390 | − | 0.717664i | \(-0.254789\pi\) | ||||
0.696390 | + | 0.717664i | \(0.254789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3119.54 | −1.90357 | −0.951784 | − | 0.306768i | \(-0.900752\pi\) | ||||
−0.951784 | + | 0.306768i | \(0.900752\pi\) | |||||||
\(140\) | 333.639 | 0.201412 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1767.32 | −1.04444 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −78.1395 | −0.0447527 | ||||||||
\(146\) | −105.134 | −0.0595953 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 156.591 | 0.0869710 | ||||||||
\(149\) | −2157.72 | −1.18636 | −0.593180 | − | 0.805070i | \(-0.702128\pi\) | ||||
−0.593180 | + | 0.805070i | \(0.702128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2588.04 | 1.39478 | 0.697391 | − | 0.716691i | \(-0.254344\pi\) | ||||
0.697391 | + | 0.716691i | \(0.254344\pi\) | |||||||
\(152\) | −1496.10 | −0.798354 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2140.22 | 1.11989 | ||||||||
\(155\) | 836.443 | 0.433450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1535.63 | −0.780614 | −0.390307 | − | 0.920685i | \(-0.627631\pi\) | ||||
−0.390307 | + | 0.920685i | \(0.627631\pi\) | |||||||
\(158\) | 1803.40 | 0.908046 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −600.802 | −0.296860 | ||||||||
\(161\) | −3268.83 | −1.60012 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2318.00 | −1.11386 | −0.556931 | − | 0.830559i | \(-0.688021\pi\) | ||||
−0.556931 | + | 0.830559i | \(0.688021\pi\) | |||||||
\(164\) | −534.044 | −0.254280 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 895.417 | 0.418662 | ||||||||
\(167\) | 1684.04 | 0.780327 | 0.390163 | − | 0.920746i | \(-0.372419\pi\) | ||||
0.390163 | + | 0.920746i | \(0.372419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −639.154 | −0.288358 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 460.091 | 0.203963 | ||||||||
\(173\) | 1269.76 | 0.558021 | 0.279011 | − | 0.960288i | \(-0.409993\pi\) | ||||
0.279011 | + | 0.960288i | \(0.409993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2398.52 | 1.03606 | ||||||||
\(176\) | −388.039 | −0.166191 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −446.861 | −0.188167 | ||||||||
\(179\) | −2236.72 | −0.933967 | −0.466984 | − | 0.884266i | \(-0.654659\pi\) | ||||
−0.466984 | + | 0.884266i | \(0.654659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3560.87 | −1.46230 | −0.731152 | − | 0.682214i | \(-0.761017\pi\) | ||||
−0.731152 | + | 0.682214i | \(0.761017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3593.09 | 1.43960 | ||||||||
\(185\) | −119.701 | −0.0475708 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5364.30 | 2.09773 | ||||||||
\(188\) | 2046.22 | 0.793808 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 413.718 | 0.157970 | ||||||||
\(191\) | 859.826 | 0.325732 | 0.162866 | − | 0.986648i | \(-0.447926\pi\) | ||||
0.162866 | + | 0.986648i | \(0.447926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4824.95 | 1.79952 | 0.899761 | − | 0.436383i | \(-0.143741\pi\) | ||||
0.899761 | + | 0.436383i | \(0.143741\pi\) | |||||||
\(194\) | −3484.62 | −1.28959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −488.114 | −0.177884 | ||||||||
\(197\) | 2722.78 | 0.984721 | 0.492360 | − | 0.870392i | \(-0.336134\pi\) | ||||
0.492360 | + | 0.870392i | \(0.336134\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1752.86 | 0.624405 | 0.312203 | − | 0.950016i | \(-0.398933\pi\) | ||||
0.312203 | + | 0.950016i | \(0.398933\pi\) | |||||||
\(200\) | −2636.45 | −0.932125 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3348.21 | −1.16623 | ||||||||
\(203\) | 478.570 | 0.165463 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 408.233 | 0.139084 | ||||||||
\(206\) | −1346.76 | −0.455500 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3472.26 | −1.14919 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3839.73 | 1.25279 | 0.626393 | − | 0.779508i | \(-0.284531\pi\) | ||||
0.626393 | + | 0.779508i | \(0.284531\pi\) | |||||||
\(212\) | −29.0807 | −0.00942110 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3289.53 | 1.05078 | ||||||||
\(215\) | −351.703 | −0.111562 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5122.84 | −1.60259 | ||||||||
\(218\) | −747.418 | −0.232209 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −851.144 | −0.260837 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1070.50 | −0.321461 | −0.160730 | − | 0.986998i | \(-0.551385\pi\) | ||||
−0.160730 | + | 0.986998i | \(0.551385\pi\) | |||||||
\(224\) | 3679.65 | 1.09757 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1940.24 | 0.571074 | ||||||||
\(227\) | 2762.09 | 0.807606 | 0.403803 | − | 0.914846i | \(-0.367688\pi\) | ||||
0.403803 | + | 0.914846i | \(0.367688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 443.465 | 0.127969 | 0.0639847 | − | 0.997951i | \(-0.479619\pi\) | ||||
0.0639847 | + | 0.997951i | \(0.479619\pi\) | |||||||
\(230\) | −993.599 | −0.284852 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −526.043 | −0.148864 | ||||||||
\(233\) | 4535.09 | 1.27512 | 0.637561 | − | 0.770399i | \(-0.279943\pi\) | ||||
0.637561 | + | 0.770399i | \(0.279943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1564.17 | −0.434192 | ||||||||
\(236\) | −1376.18 | −0.379582 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3914.53 | 1.06614 | ||||||||
\(239\) | 6158.94 | 1.66690 | 0.833449 | − | 0.552596i | \(-0.186363\pi\) | ||||
0.833449 | + | 0.552596i | \(0.186363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −794.221 | −0.212283 | −0.106142 | − | 0.994351i | \(-0.533850\pi\) | ||||
−0.106142 | + | 0.994351i | \(0.533850\pi\) | |||||||
\(242\) | −2982.07 | −0.792128 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2822.22 | 0.740467 | ||||||||
\(245\) | 373.123 | 0.0972978 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5631.02 | 1.44181 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1535.64 | 0.388490 | ||||||||
\(251\) | −5736.65 | −1.44261 | −0.721303 | − | 0.692620i | \(-0.756456\pi\) | ||||
−0.721303 | + | 0.692620i | \(0.756456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8339.09 | 2.07223 | ||||||||
\(254\) | −1523.45 | −0.376337 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4304.58 | −1.05092 | ||||||||
\(257\) | 3815.47 | 0.926080 | 0.463040 | − | 0.886337i | \(-0.346759\pi\) | ||||
0.463040 | + | 0.886337i | \(0.346759\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 733.116 | 0.175883 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2531.65 | −0.596970 | ||||||||
\(263\) | −1307.88 | −0.306644 | −0.153322 | − | 0.988176i | \(-0.548997\pi\) | ||||
−0.153322 | + | 0.988176i | \(0.548997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.2299 | 0.00515309 | ||||||||
\(266\) | −2533.84 | −0.584059 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1313.03 | 0.299276 | ||||||||
\(269\) | 4631.27 | 1.04972 | 0.524858 | − | 0.851190i | \(-0.324118\pi\) | ||||
0.524858 | + | 0.851190i | \(0.324118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3912.21 | 0.876937 | 0.438468 | − | 0.898747i | \(-0.355521\pi\) | ||||
0.438468 | + | 0.898747i | \(0.355521\pi\) | |||||||
\(272\) | −709.736 | −0.158214 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4157.73 | −0.916708 | ||||||||
\(275\) | −6118.86 | −1.34175 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7619.61 | −1.65277 | −0.826387 | − | 0.563103i | \(-0.809607\pi\) | ||||
−0.826387 | + | 0.563103i | \(0.809607\pi\) | |||||||
\(278\) | 5807.43 | 1.25290 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1716.95 | −0.366455 | ||||||||
\(281\) | 7136.58 | 1.51506 | 0.757531 | − | 0.652799i | \(-0.226405\pi\) | ||||
0.757531 | + | 0.652799i | \(0.226405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8223.69 | 1.72738 | 0.863689 | − | 0.504025i | \(-0.168148\pi\) | ||||
0.863689 | + | 0.504025i | \(0.168148\pi\) | |||||||
\(284\) | −4304.62 | −0.899410 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2500.25 | −0.514233 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4898.48 | 0.997044 | ||||||||
\(290\) | 145.467 | 0.0294556 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −256.071 | −0.0513200 | ||||||||
\(293\) | −6094.65 | −1.21520 | −0.607600 | − | 0.794243i | \(-0.707867\pi\) | ||||
−0.607600 | + | 0.794243i | \(0.707867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1051.97 | 0.207621 | ||||||||
\(296\) | −805.840 | −0.158238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4016.89 | 0.780846 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2154.02 | 0.412478 | ||||||||
\(302\) | −4817.99 | −0.918026 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 459.406 | 0.0866734 | ||||||||
\(305\) | −2157.36 | −0.405016 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −189.227 | −0.0351783 | −0.0175892 | − | 0.999845i | \(-0.505599\pi\) | ||||
−0.0175892 | + | 0.999845i | \(0.505599\pi\) | |||||||
\(308\) | 5212.88 | 0.964388 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1557.15 | −0.285291 | ||||||||
\(311\) | 2282.65 | 0.416196 | 0.208098 | − | 0.978108i | \(-0.433273\pi\) | ||||
0.208098 | + | 0.978108i | \(0.433273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5417.71 | −0.978361 | −0.489180 | − | 0.872183i | \(-0.662704\pi\) | ||||
−0.489180 | + | 0.872183i | \(0.662704\pi\) | |||||||
\(314\) | 2858.77 | 0.513789 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4392.51 | 0.781955 | ||||||||
\(317\) | −2033.88 | −0.360360 | −0.180180 | − | 0.983634i | \(-0.557668\pi\) | ||||
−0.180180 | + | 0.983634i | \(0.557668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1220.88 | −0.214282 | ||||||||
\(320\) | 1317.16 | 0.230098 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6085.35 | 1.05318 | ||||||||
\(323\) | −6350.88 | −1.09403 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4315.26 | 0.733128 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2748.27 | 0.462645 | ||||||||
\(329\) | 9579.84 | 1.60533 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6413.08 | 1.06494 | 0.532469 | − | 0.846449i | \(-0.321264\pi\) | ||||
0.532469 | + | 0.846449i | \(0.321264\pi\) | |||||||
\(332\) | 2180.95 | 0.360527 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3135.05 | −0.513600 | ||||||||
\(335\) | −1003.70 | −0.163696 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10577.9 | 1.70984 | 0.854922 | − | 0.518756i | \(-0.173605\pi\) | ||||
0.854922 | + | 0.518756i | \(0.173605\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1556.77 | −0.248317 | ||||||||
\(341\) | 13068.9 | 2.07542 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4996.16 | 0.786493 | ||||||||
\(344\) | −2367.70 | −0.371098 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2363.82 | −0.367282 | ||||||||
\(347\) | 5339.55 | 0.826058 | 0.413029 | − | 0.910718i | \(-0.364471\pi\) | ||||
0.413029 | + | 0.910718i | \(0.364471\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2188.63 | 0.335687 | 0.167843 | − | 0.985814i | \(-0.446320\pi\) | ||||
0.167843 | + | 0.985814i | \(0.446320\pi\) | |||||||
\(350\) | −4465.16 | −0.681923 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9387.13 | −1.42141 | ||||||||
\(353\) | 5534.31 | 0.834452 | 0.417226 | − | 0.908803i | \(-0.363002\pi\) | ||||
0.417226 | + | 0.908803i | \(0.363002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3290.53 | 0.491953 | ||||||||
\(356\) | −1088.41 | −0.162038 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4163.94 | 0.614724 | ||||||||
\(359\) | 4937.93 | 0.725945 | 0.362972 | − | 0.931800i | \(-0.381762\pi\) | ||||
0.362972 | + | 0.931800i | \(0.381762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2748.14 | −0.400662 | ||||||||
\(362\) | 6629.02 | 0.962468 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 195.746 | 0.0280707 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −451.014 | −0.0641492 | −0.0320746 | − | 0.999485i | \(-0.510211\pi\) | ||||
−0.0320746 | + | 0.999485i | \(0.510211\pi\) | |||||||
\(368\) | −1103.32 | −0.156290 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 222.839 | 0.0313104 | ||||||||
\(371\) | −136.148 | −0.0190524 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3759.18 | −0.521831 | −0.260915 | − | 0.965362i | \(-0.584024\pi\) | ||||
−0.260915 | + | 0.965362i | \(0.584024\pi\) | |||||||
\(374\) | −9986.35 | −1.38070 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10530.1 | −1.44428 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6247.82 | −0.846778 | −0.423389 | − | 0.905948i | \(-0.639160\pi\) | ||||
−0.423389 | + | 0.905948i | \(0.639160\pi\) | |||||||
\(380\) | 1007.68 | 0.136034 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1600.68 | −0.214392 | ||||||||
\(383\) | 7950.94 | 1.06077 | 0.530384 | − | 0.847757i | \(-0.322048\pi\) | ||||
0.530384 | + | 0.847757i | \(0.322048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3984.82 | −0.527495 | ||||||||
\(386\) | −8982.28 | −1.18442 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8487.40 | −1.11052 | ||||||||
\(389\) | 11176.0 | 1.45668 | 0.728338 | − | 0.685218i | \(-0.240293\pi\) | ||||
0.728338 | + | 0.685218i | \(0.240293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15252.5 | 1.97276 | ||||||||
\(392\) | 2511.90 | 0.323649 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5068.81 | −0.648129 | ||||||||
\(395\) | −3357.72 | −0.427709 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7407.12 | −0.936404 | −0.468202 | − | 0.883621i | \(-0.655098\pi\) | ||||
−0.468202 | + | 0.883621i | \(0.655098\pi\) | |||||||
\(398\) | −3263.17 | −0.410975 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 809.570 | 0.101196 | ||||||||
\(401\) | −4464.87 | −0.556022 | −0.278011 | − | 0.960578i | \(-0.589675\pi\) | ||||
−0.278011 | + | 0.960578i | \(0.589675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8155.14 | −1.00429 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −890.921 | −0.108906 | ||||||||
\(407\) | −1870.25 | −0.227776 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2362.97 | −0.285676 | −0.142838 | − | 0.989746i | \(-0.545623\pi\) | ||||
−0.142838 | + | 0.989746i | \(0.545623\pi\) | |||||||
\(410\) | −759.980 | −0.0915433 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3280.26 | −0.392250 | ||||||||
\(413\) | −6442.88 | −0.767635 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1667.16 | −0.197199 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6464.07 | 0.756382 | ||||||||
\(419\) | 15637.3 | 1.82323 | 0.911614 | − | 0.411048i | \(-0.134837\pi\) | ||||
0.911614 | + | 0.411048i | \(0.134837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4087.68 | 0.473210 | 0.236605 | − | 0.971606i | \(-0.423965\pi\) | ||||
0.236605 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(422\) | −7148.16 | −0.824566 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 149.654 | 0.0171411 | ||||||||
\(425\) | −11191.6 | −1.27735 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13212.8 | 1.49746 | ||||||||
\(428\) | 8012.22 | 0.904872 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 654.740 | 0.0734288 | ||||||||
\(431\) | 1822.93 | 0.203730 | 0.101865 | − | 0.994798i | \(-0.467519\pi\) | ||||
0.101865 | + | 0.994798i | \(0.467519\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6100.85 | −0.677109 | −0.338555 | − | 0.940947i | \(-0.609938\pi\) | ||||
−0.338555 | + | 0.940947i | \(0.609938\pi\) | |||||||
\(434\) | 9536.85 | 1.05480 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1820.47 | −0.199965 | ||||||||
\(437\) | −9872.78 | −1.08073 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2269.61 | −0.246749 | −0.123374 | − | 0.992360i | \(-0.539372\pi\) | ||||
−0.123374 | + | 0.992360i | \(0.539372\pi\) | |||||||
\(440\) | 4380.11 | 0.474576 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1508.03 | −0.161735 | −0.0808674 | − | 0.996725i | \(-0.525769\pi\) | ||||
−0.0808674 | + | 0.996725i | \(0.525769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 832.000 | 0.0886305 | ||||||||
\(446\) | 1992.87 | 0.211581 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8067.00 | −0.850737 | ||||||||
\(449\) | 4573.69 | 0.480725 | 0.240363 | − | 0.970683i | \(-0.422734\pi\) | ||||
0.240363 | + | 0.970683i | \(0.422734\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6378.37 | 0.665955 | ||||||||
\(452\) | 4725.79 | 0.491776 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5142.00 | −0.531555 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8999.57 | 0.921186 | 0.460593 | − | 0.887611i | \(-0.347637\pi\) | ||||
0.460593 | + | 0.887611i | \(0.347637\pi\) | |||||||
\(458\) | −825.569 | −0.0842277 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2420.08 | −0.245298 | ||||||||
\(461\) | −4945.51 | −0.499643 | −0.249821 | − | 0.968292i | \(-0.580372\pi\) | ||||
−0.249821 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3371.96 | 0.338463 | 0.169231 | − | 0.985576i | \(-0.445872\pi\) | ||||
0.169231 | + | 0.985576i | \(0.445872\pi\) | |||||||
\(464\) | 161.531 | 0.0161614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8442.67 | −0.839268 | ||||||||
\(467\) | −6411.64 | −0.635322 | −0.317661 | − | 0.948204i | \(-0.602897\pi\) | ||||
−0.317661 | + | 0.948204i | \(0.602897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6147.24 | 0.605230 | ||||||||
\(470\) | 2911.91 | 0.285779 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7082.00 | 0.690626 | ||||||||
\(473\) | −5495.12 | −0.534177 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7244.21 | 0.699762 | ||||||||
\(476\) | 9534.53 | 0.918098 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11465.7 | −1.09713 | ||||||||
\(479\) | −13472.4 | −1.28512 | −0.642559 | − | 0.766237i | \(-0.722127\pi\) | ||||
−0.642559 | + | 0.766237i | \(0.722127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1478.55 | 0.139722 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7263.37 | −0.682134 | ||||||||
\(485\) | 6487.93 | 0.607426 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14439.2 | −1.34354 | −0.671770 | − | 0.740760i | \(-0.734466\pi\) | ||||
−0.671770 | + | 0.740760i | \(0.734466\pi\) | |||||||
\(488\) | −14523.5 | −1.34723 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −694.618 | −0.0640401 | ||||||||
\(491\) | 12856.5 | 1.18168 | 0.590842 | − | 0.806787i | \(-0.298796\pi\) | ||||
0.590842 | + | 0.806787i | \(0.298796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2233.03 | −0.203997 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1729.11 | −0.156531 | ||||||||
\(497\) | −20153.1 | −1.81889 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2996.45 | 0.268817 | 0.134409 | − | 0.990926i | \(-0.457087\pi\) | ||||
0.134409 | + | 0.990926i | \(0.457087\pi\) | |||||||
\(500\) | 3740.32 | 0.334544 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10679.5 | 0.949503 | ||||||||
\(503\) | 20295.0 | 1.79902 | 0.899511 | − | 0.436899i | \(-0.143923\pi\) | ||||
0.899511 | + | 0.436899i | \(0.143923\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6233.94 | 0.549320 | ||||||||
\(506\) | −15524.3 | −1.36391 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3710.62 | −0.324079 | ||||||||
\(509\) | −16270.4 | −1.41684 | −0.708421 | − | 0.705790i | \(-0.750592\pi\) | ||||
−0.708421 | + | 0.705790i | \(0.750592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1198.86 | −0.103785 | ||||||||
\(512\) | 2579.55 | 0.222658 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7103.00 | −0.609533 | ||||||||
\(515\) | 2507.50 | 0.214550 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24439.1 | −2.07897 | ||||||||
\(518\) | −1364.79 | −0.115764 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10390.5 | 0.873734 | 0.436867 | − | 0.899526i | \(-0.356088\pi\) | ||||
0.436867 | + | 0.899526i | \(0.356088\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14355.4 | −1.20023 | −0.600113 | − | 0.799916i | \(-0.704878\pi\) | ||||
−0.600113 | + | 0.799916i | \(0.704878\pi\) | |||||||
\(524\) | −6166.29 | −0.514076 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2434.79 | 0.201829 | ||||||||
\(527\) | 23903.4 | 1.97580 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11543.8 | 0.948780 | ||||||||
\(530\) | −41.3838 | −0.00339169 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6171.61 | −0.502957 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6124.69 | −0.494941 | ||||||||
\(536\) | −6757.03 | −0.544513 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8621.72 | −0.690909 | ||||||||
\(539\) | 5829.80 | 0.465876 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14187.5 | −1.12748 | −0.563741 | − | 0.825951i | \(-0.690638\pi\) | ||||
−0.563741 | + | 0.825951i | \(0.690638\pi\) | |||||||
\(542\) | −7283.09 | −0.577188 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17169.4 | −1.35318 | ||||||||
\(545\) | 1391.60 | 0.109375 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8864.63 | 0.692915 | 0.346457 | − | 0.938066i | \(-0.387385\pi\) | ||||
0.346457 | + | 0.938066i | \(0.387385\pi\) | |||||||
\(548\) | −10126.9 | −0.789415 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11391.1 | 0.883120 | ||||||||
\(551\) | 1445.42 | 0.111755 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20564.5 | 1.58136 | ||||||||
\(554\) | 14184.9 | 1.08783 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14145.0 | 1.07893 | ||||||||
\(557\) | 16846.3 | 1.28151 | 0.640755 | − | 0.767746i | \(-0.278622\pi\) | ||||
0.640755 | + | 0.767746i | \(0.278622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 527.222 | 0.0397842 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13285.7 | −0.997193 | ||||||||
\(563\) | −4754.01 | −0.355875 | −0.177938 | − | 0.984042i | \(-0.556943\pi\) | ||||
−0.177938 | + | 0.984042i | \(0.556943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3612.49 | −0.268988 | ||||||||
\(566\) | −15309.5 | −1.13694 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22152.2 | 1.63642 | ||||||||
\(569\) | −8299.82 | −0.611506 | −0.305753 | − | 0.952111i | \(-0.598908\pi\) | ||||
−0.305753 | + | 0.952111i | \(0.598908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9383.57 | 0.687723 | 0.343862 | − | 0.939020i | \(-0.388265\pi\) | ||||
0.343862 | + | 0.939020i | \(0.388265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4654.54 | 0.338461 | ||||||||
\(575\) | −17397.9 | −1.26182 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24230.2 | −1.74821 | −0.874105 | − | 0.485736i | \(-0.838551\pi\) | ||||
−0.874105 | + | 0.485736i | \(0.838551\pi\) | |||||||
\(578\) | −9119.16 | −0.656241 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 354.310 | 0.0253654 | ||||||||
\(581\) | 10210.6 | 0.729099 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 347.327 | 0.0246738 | ||||||||
\(584\) | 1317.78 | 0.0933735 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11346.0 | 0.799827 | ||||||||
\(587\) | 446.729 | 0.0314113 | 0.0157057 | − | 0.999877i | \(-0.495001\pi\) | ||||
0.0157057 | + | 0.999877i | \(0.495001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15472.4 | −1.08239 | ||||||||
\(590\) | −1958.39 | −0.136654 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 247.448 | 0.0171791 | ||||||||
\(593\) | −9449.99 | −0.654409 | −0.327205 | − | 0.944954i | \(-0.606107\pi\) | ||||
−0.327205 | + | 0.944954i | \(0.606107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7288.37 | −0.502175 | ||||||||
\(596\) | 9783.83 | 0.672418 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3273.52 | −0.223293 | −0.111646 | − | 0.993748i | \(-0.535612\pi\) | ||||
−0.111646 | + | 0.993748i | \(0.535612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15211.4 | 1.03242 | 0.516211 | − | 0.856462i | \(-0.327342\pi\) | ||||
0.516211 | + | 0.856462i | \(0.327342\pi\) | |||||||
\(602\) | −4009.99 | −0.271487 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11735.0 | −0.790550 | ||||||||
\(605\) | 5552.25 | 0.373109 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14322.4 | 0.957705 | 0.478852 | − | 0.877895i | \(-0.341053\pi\) | ||||
0.478852 | + | 0.877895i | \(0.341053\pi\) | |||||||
\(608\) | 11113.6 | 0.741307 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4016.20 | 0.266576 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17695.5 | −1.16593 | −0.582966 | − | 0.812497i | \(-0.698108\pi\) | ||||
−0.582966 | + | 0.812497i | \(0.698108\pi\) | |||||||
\(614\) | 352.271 | 0.0231539 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26826.2 | −1.75464 | ||||||||
\(617\) | 24230.3 | 1.58100 | 0.790499 | − | 0.612463i | \(-0.209821\pi\) | ||||
0.790499 | + | 0.612463i | \(0.209821\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16761.3 | 1.08836 | 0.544178 | − | 0.838970i | \(-0.316842\pi\) | ||||
0.544178 | + | 0.838970i | \(0.316842\pi\) | |||||||
\(620\) | −3792.71 | −0.245676 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4249.45 | −0.273935 | ||||||||
\(623\) | −5095.63 | −0.327692 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11264.1 | 0.720901 | ||||||||
\(626\) | 10085.8 | 0.643943 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6963.04 | 0.442445 | ||||||||
\(629\) | −3420.75 | −0.216843 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26812.2 | 1.69156 | 0.845780 | − | 0.533531i | \(-0.179135\pi\) | ||||
0.845780 | + | 0.533531i | \(0.179135\pi\) | |||||||
\(632\) | −22604.5 | −1.42272 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3786.33 | 0.237184 | ||||||||
\(635\) | 2836.47 | 0.177263 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2272.82 | 0.141038 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2354.36 | 0.145413 | ||||||||
\(641\) | −23803.2 | −1.46673 | −0.733363 | − | 0.679838i | \(-0.762050\pi\) | ||||
−0.733363 | + | 0.679838i | \(0.762050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9688.90 | −0.594235 | −0.297117 | − | 0.954841i | \(-0.596025\pi\) | ||||
−0.297117 | + | 0.954841i | \(0.596025\pi\) | |||||||
\(644\) | 14821.9 | 0.906935 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11823.0 | 0.720076 | ||||||||
\(647\) | 14666.7 | 0.891204 | 0.445602 | − | 0.895231i | \(-0.352990\pi\) | ||||
0.445602 | + | 0.895231i | \(0.352990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16436.4 | 0.994122 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10510.6 | 0.631327 | ||||||||
\(653\) | 16774.9 | 1.00528 | 0.502642 | − | 0.864494i | \(-0.332361\pi\) | ||||
0.502642 | + | 0.864494i | \(0.332361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4713.63 | 0.281186 | ||||||||
\(656\) | −843.906 | −0.0502271 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17834.1 | −1.05661 | ||||||||
\(659\) | −33153.6 | −1.95976 | −0.979880 | − | 0.199587i | \(-0.936040\pi\) | ||||
−0.979880 | + | 0.199587i | \(0.936040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26998.6 | −1.58869 | −0.794343 | − | 0.607469i | \(-0.792185\pi\) | ||||
−0.794343 | + | 0.607469i | \(0.792185\pi\) | |||||||
\(662\) | −11938.8 | −0.700928 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11223.5 | −0.655956 | ||||||||
\(665\) | 4717.69 | 0.275104 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3471.36 | −0.201517 | ||||||||
\(668\) | −7635.97 | −0.442282 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1868.52 | 0.107742 | ||||||||
\(671\) | −33707.2 | −1.93928 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31725.4 | −1.81713 | −0.908563 | − | 0.417749i | \(-0.862819\pi\) | ||||
−0.908563 | + | 0.417749i | \(0.862819\pi\) | |||||||
\(674\) | −19692.2 | −1.12540 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28609.6 | −1.62416 | −0.812081 | − | 0.583544i | \(-0.801665\pi\) | ||||
−0.812081 | + | 0.583544i | \(0.801665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39735.7 | −2.24582 | ||||||||
\(680\) | 8011.36 | 0.451797 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24329.4 | −1.36601 | ||||||||
\(683\) | −16876.6 | −0.945482 | −0.472741 | − | 0.881201i | \(-0.656735\pi\) | ||||
−0.472741 | + | 0.881201i | \(0.656735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7741.18 | 0.431789 | ||||||||
\(686\) | −9301.00 | −0.517659 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 727.045 | 0.0402882 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14682.7 | −0.808329 | −0.404165 | − | 0.914686i | \(-0.632438\pi\) | ||||
−0.404165 | + | 0.914686i | \(0.632438\pi\) | |||||||
\(692\) | −5757.49 | −0.316282 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9940.27 | −0.543700 | ||||||||
\(695\) | −10812.7 | −0.590144 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11666.3 | 0.633990 | ||||||||
\(698\) | −4074.42 | −0.220944 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10875.7 | −0.587232 | ||||||||
\(701\) | 12377.6 | 0.666898 | 0.333449 | − | 0.942768i | \(-0.391787\pi\) | ||||
0.333449 | + | 0.942768i | \(0.391787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2214.22 | 0.118792 | ||||||||
\(704\) | 20579.7 | 1.10174 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10302.8 | −0.549224 | ||||||||
\(707\) | −38180.1 | −2.03099 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25093.4 | 1.32920 | 0.664599 | − | 0.747200i | \(-0.268602\pi\) | ||||
0.664599 | + | 0.747200i | \(0.268602\pi\) | |||||||
\(710\) | −6125.76 | −0.323797 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5601.10 | 0.294818 | ||||||||
\(713\) | 37159.1 | 1.95178 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10142.0 | 0.529364 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9192.61 | −0.477807 | ||||||||
\(719\) | 19834.1 | 1.02877 | 0.514385 | − | 0.857559i | \(-0.328020\pi\) | ||||
0.514385 | + | 0.857559i | \(0.328020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15357.3 | −0.793253 | ||||||||
\(722\) | 5116.02 | 0.263710 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16146.1 | 0.828821 | ||||||||
\(725\) | 2547.13 | 0.130480 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26992.7 | 1.37703 | 0.688517 | − | 0.725221i | \(-0.258262\pi\) | ||||
0.688517 | + | 0.725221i | \(0.258262\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −364.406 | −0.0184757 | ||||||||
\(731\) | −10050.7 | −0.508537 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12248.4 | 0.617195 | 0.308597 | − | 0.951193i | \(-0.400140\pi\) | ||||
0.308597 | + | 0.951193i | \(0.400140\pi\) | |||||||
\(734\) | 839.622 | 0.0422221 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26690.7 | −1.33673 | ||||||||
\(737\) | −15682.2 | −0.783800 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13980.0 | 0.695889 | 0.347945 | − | 0.937515i | \(-0.386880\pi\) | ||||
0.347945 | + | 0.937515i | \(0.386880\pi\) | |||||||
\(740\) | 542.764 | 0.0269627 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 253.458 | 0.0125401 | ||||||||
\(743\) | 13730.3 | 0.677949 | 0.338975 | − | 0.940795i | \(-0.389920\pi\) | ||||
0.338975 | + | 0.940795i | \(0.389920\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7478.94 | −0.367795 | ||||||||
\(746\) | 6998.20 | 0.343462 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −24323.5 | −1.18898 | ||||||||
\(749\) | 37511.0 | 1.82994 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16795.7 | −0.816092 | −0.408046 | − | 0.912961i | \(-0.633790\pi\) | ||||
−0.408046 | + | 0.912961i | \(0.633790\pi\) | |||||||
\(752\) | 3233.47 | 0.156799 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8970.49 | 0.432410 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3680.42 | −0.176707 | −0.0883533 | − | 0.996089i | \(-0.528160\pi\) | ||||
−0.0883533 | + | 0.996089i | \(0.528160\pi\) | |||||||
\(758\) | 11631.1 | 0.557338 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5185.68 | −0.247506 | ||||||||
\(761\) | 17732.8 | 0.844695 | 0.422347 | − | 0.906434i | \(-0.361206\pi\) | ||||
0.422347 | + | 0.906434i | \(0.361206\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8522.93 | −0.404392 | ||||||||
\(764\) | −3898.74 | −0.184622 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14801.7 | −0.698183 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5198.88 | −0.243792 | −0.121896 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121896 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(770\) | 7418.27 | 0.347190 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21877.9 | −1.01995 | ||||||||
\(773\) | −10049.6 | −0.467605 | −0.233802 | − | 0.972284i | \(-0.575117\pi\) | ||||
−0.233802 | + | 0.972284i | \(0.575117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27265.7 | −1.26376 | ||||||||
\(776\) | 43677.4 | 2.02052 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20805.6 | −0.958764 | ||||||||
\(779\) | −7551.45 | −0.347316 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51412.4 | 2.35554 | ||||||||
\(782\) | −28394.5 | −1.29845 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −771.326 | −0.0351369 | ||||||||
\(785\) | −5322.68 | −0.242006 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2283.57 | 0.103431 | 0.0517157 | − | 0.998662i | \(-0.483531\pi\) | ||||
0.0517157 | + | 0.998662i | \(0.483531\pi\) | |||||||
\(788\) | −12346.0 | −0.558131 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6250.83 | 0.281512 | ||||||||
\(791\) | 22124.9 | 0.994526 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13789.3 | 0.616328 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7948.02 | −0.353907 | ||||||||
\(797\) | −15767.9 | −0.700787 | −0.350394 | − | 0.936603i | \(-0.613952\pi\) | ||||
−0.350394 | + | 0.936603i | \(0.613952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44699.9 | −1.97918 | ||||||||
\(800\) | 19584.5 | 0.865519 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8311.94 | 0.365966 | ||||||||
\(803\) | 3058.40 | 0.134407 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11330.2 | −0.496070 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 41967.5 | 1.82724 | ||||||||
\(809\) | −35014.4 | −1.52168 | −0.760842 | − | 0.648937i | \(-0.775214\pi\) | ||||
−0.760842 | + | 0.648937i | \(0.775214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15741.1 | 0.681561 | 0.340780 | − | 0.940143i | \(-0.389309\pi\) | ||||
0.340780 | + | 0.940143i | \(0.389309\pi\) | |||||||
\(812\) | −2169.99 | −0.0937831 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3481.72 | 0.149919 | ||||||||
\(815\) | −8034.47 | −0.345319 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6505.75 | 0.278589 | ||||||||
\(818\) | 4398.98 | 0.188028 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1851.06 | −0.0788317 | ||||||||
\(821\) | −28093.1 | −1.19422 | −0.597111 | − | 0.802158i | \(-0.703685\pi\) | ||||
−0.597111 | + | 0.802158i | \(0.703685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17076.7 | −0.723276 | −0.361638 | − | 0.932319i | \(-0.617782\pi\) | ||||
−0.361638 | + | 0.932319i | \(0.617782\pi\) | |||||||
\(824\) | 16880.7 | 0.713674 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11994.3 | 0.505247 | ||||||||
\(827\) | 21398.3 | 0.899748 | 0.449874 | − | 0.893092i | \(-0.351469\pi\) | ||||
0.449874 | + | 0.893092i | \(0.351469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34951.3 | −1.46430 | −0.732152 | − | 0.681141i | \(-0.761484\pi\) | ||||
−0.732152 | + | 0.681141i | \(0.761484\pi\) | |||||||
\(830\) | 3103.63 | 0.129793 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10662.9 | 0.443514 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5837.08 | 0.241917 | ||||||||
\(836\) | 15744.4 | 0.651352 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29110.9 | −1.20002 | ||||||||
\(839\) | −14168.0 | −0.582996 | −0.291498 | − | 0.956571i | \(-0.594154\pi\) | ||||
−0.291498 | + | 0.956571i | \(0.594154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23880.8 | −0.979162 | ||||||||
\(842\) | −7609.76 | −0.311460 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17410.6 | −0.710068 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34005.1 | −1.37949 | ||||||||
\(848\) | −45.9539 | −0.00186092 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20834.6 | 0.840731 | ||||||||
\(851\) | −5317.74 | −0.214206 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2604.09 | −0.104528 | −0.0522639 | − | 0.998633i | \(-0.516644\pi\) | ||||
−0.0522639 | + | 0.998633i | \(0.516644\pi\) | |||||||
\(854\) | −24597.5 | −0.985606 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41232.0 | −1.64636 | ||||||||
\(857\) | −7726.51 | −0.307973 | −0.153986 | − | 0.988073i | \(-0.549211\pi\) | ||||
−0.153986 | + | 0.988073i | \(0.549211\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16487.4 | 0.654883 | 0.327441 | − | 0.944872i | \(-0.393814\pi\) | ||||
0.327441 | + | 0.944872i | \(0.393814\pi\) | |||||||
\(860\) | 1594.74 | 0.0632326 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3393.63 | −0.134092 | ||||||||
\(863\) | 19510.7 | 0.769585 | 0.384792 | − | 0.923003i | \(-0.374273\pi\) | ||||
0.384792 | + | 0.923003i | \(0.374273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4401.13 | 0.172998 | ||||||||
\(866\) | 11357.5 | 0.445664 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23228.7 | 0.908332 | ||||||||
\(869\) | −52462.1 | −2.04793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9368.39 | 0.363823 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18379.5 | 0.711322 | ||||||||
\(875\) | 17511.1 | 0.676554 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8989.31 | 0.346120 | 0.173060 | − | 0.984911i | \(-0.444635\pi\) | ||||
0.173060 | + | 0.984911i | \(0.444635\pi\) | |||||||
\(878\) | 4225.18 | 0.162407 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1344.99 | −0.0515224 | ||||||||
\(881\) | 36597.1 | 1.39953 | 0.699766 | − | 0.714372i | \(-0.253287\pi\) | ||||
0.699766 | + | 0.714372i | \(0.253287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5749.48 | −0.219123 | −0.109561 | − | 0.993980i | \(-0.534945\pi\) | ||||
−0.109561 | + | 0.993980i | \(0.534945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2807.39 | 0.106452 | ||||||||
\(887\) | 14331.4 | 0.542503 | 0.271252 | − | 0.962508i | \(-0.412562\pi\) | ||||
0.271252 | + | 0.962508i | \(0.412562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17372.1 | −0.655390 | ||||||||
\(890\) | −1548.88 | −0.0583353 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4853.98 | 0.182201 | ||||||||
\(893\) | 28933.8 | 1.08425 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7752.75 | −0.289548 | ||||||||
\(896\) | −14419.4 | −0.537632 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8514.52 | −0.316407 | ||||||||
\(899\) | −5440.25 | −0.201827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 635.272 | 0.0234894 | ||||||||
\(902\) | −11874.2 | −0.438323 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24319.6 | −0.894754 | ||||||||
\(905\) | −12342.4 | −0.453343 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25035.2 | −0.916516 | −0.458258 | − | 0.888819i | \(-0.651526\pi\) | ||||
−0.458258 | + | 0.888819i | \(0.651526\pi\) | |||||||
\(908\) | −12524.2 | −0.457744 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41464.5 | −1.50799 | −0.753996 | − | 0.656879i | \(-0.771876\pi\) | ||||
−0.753996 | + | 0.656879i | \(0.771876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26048.2 | −0.944216 | ||||||||
\(914\) | −16753.9 | −0.606312 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2010.82 | −0.0725319 | ||||||||
\(917\) | −28868.9 | −1.03962 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6761.65 | 0.242705 | 0.121353 | − | 0.992609i | \(-0.461277\pi\) | ||||
0.121353 | + | 0.992609i | \(0.461277\pi\) | |||||||
\(920\) | 12454.1 | 0.446304 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9206.71 | 0.328858 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3901.92 | 0.138697 | ||||||||
\(926\) | −6277.34 | −0.222771 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3907.63 | 0.138227 | ||||||||
\(929\) | 1309.62 | 0.0462512 | 0.0231256 | − | 0.999733i | \(-0.492638\pi\) | ||||
0.0231256 | + | 0.999733i | \(0.492638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6901.99 | −0.242968 | ||||||||
\(932\) | −20563.6 | −0.722728 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11936.1 | 0.418160 | ||||||||
\(935\) | 18593.3 | 0.650339 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31660.7 | −1.10385 | −0.551926 | − | 0.833893i | \(-0.686107\pi\) | ||||
−0.551926 | + | 0.833893i | \(0.686107\pi\) | |||||||
\(938\) | −11443.9 | −0.398354 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7092.46 | 0.246096 | ||||||||
\(941\) | 54545.0 | 1.88960 | 0.944802 | − | 0.327643i | \(-0.106254\pi\) | ||||
0.944802 | + | 0.327643i | \(0.106254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18135.8 | 0.626282 | ||||||||
\(944\) | −2174.66 | −0.0749778 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10229.9 | 0.351588 | ||||||||
\(947\) | −25624.5 | −0.879286 | −0.439643 | − | 0.898173i | \(-0.644895\pi\) | ||||
−0.439643 | + | 0.898173i | \(0.644895\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −13486.0 | −0.460574 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −49066.0 | −1.67042 | ||||||||
\(953\) | −44620.8 | −1.51670 | −0.758348 | − | 0.651850i | \(-0.773993\pi\) | ||||
−0.758348 | + | 0.651850i | \(0.773993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2980.27 | 0.100983 | ||||||||
\(956\) | −27926.7 | −0.944783 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25080.7 | 0.845846 | ||||||||
\(959\) | −47411.3 | −1.59645 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28444.0 | 0.954786 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3601.26 | 0.120320 | ||||||||
\(965\) | 16723.9 | 0.557887 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13882.9 | 0.461679 | 0.230839 | − | 0.972992i | \(-0.425853\pi\) | ||||
0.230839 | + | 0.972992i | \(0.425853\pi\) | |||||||
\(968\) | 37378.3 | 1.24110 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12078.1 | −0.399799 | ||||||||
\(971\) | 13687.2 | 0.452363 | 0.226181 | − | 0.974085i | \(-0.427376\pi\) | ||||
0.226181 | + | 0.974085i | \(0.427376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 66223.1 | 2.18193 | ||||||||
\(974\) | 26880.5 | 0.884299 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4459.72 | 0.146262 | ||||||||
\(977\) | 23474.5 | 0.768694 | 0.384347 | − | 0.923189i | \(-0.374427\pi\) | ||||
0.384347 | + | 0.923189i | \(0.374427\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12999.4 | 0.424376 | ||||||||
\(980\) | −1691.86 | −0.0551476 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23934.1 | −0.777768 | ||||||||
\(983\) | 528.996 | 0.0171641 | 0.00858207 | − | 0.999963i | \(-0.497268\pi\) | ||||
0.00858207 | + | 0.999963i | \(0.497268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9437.49 | 0.305283 | ||||||||
\(986\) | 4157.07 | 0.134268 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15624.4 | −0.502354 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52472.4 | 1.68198 | 0.840989 | − | 0.541052i | \(-0.181974\pi\) | ||||
0.840989 | + | 0.541052i | \(0.181974\pi\) | |||||||
\(992\) | −41829.2 | −1.33879 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 37517.6 | 1.19717 | ||||||||
\(995\) | 6075.62 | 0.193578 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5163.27 | −0.164015 | −0.0820073 | − | 0.996632i | \(-0.526133\pi\) | ||||
−0.0820073 | + | 0.996632i | \(0.526133\pi\) | |||||||
\(998\) | −5578.29 | −0.176932 | ||||||||
\(999\) | 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.bn.1.6 | yes | 18 | |
3.2 | odd | 2 | inner | 1521.4.a.bn.1.13 | yes | 18 | |
13.12 | even | 2 | 1521.4.a.bm.1.13 | yes | 18 | ||
39.38 | odd | 2 | 1521.4.a.bm.1.6 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.4.a.bm.1.6 | ✓ | 18 | 39.38 | odd | 2 | ||
1521.4.a.bm.1.13 | yes | 18 | 13.12 | even | 2 | ||
1521.4.a.bn.1.6 | yes | 18 | 1.1 | even | 1 | trivial | |
1521.4.a.bn.1.13 | yes | 18 | 3.2 | odd | 2 | inner |