Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 48x^{7} + 29x^{6} + 772x^{5} - 150x^{4} - 4745x^{3} - 966x^{2} + 9428x + 5144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.614643\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61464 | 0.570863 | 0.285431 | − | 0.958399i | \(-0.407863\pi\) | ||||
0.285431 | + | 0.958399i | \(0.407863\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.39293 | −0.674116 | ||||||||
\(5\) | 1.20859 | 0.108100 | 0.0540499 | − | 0.998538i | \(-0.482787\pi\) | ||||
0.0540499 | + | 0.998538i | \(0.482787\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28.2769 | −1.52681 | −0.763406 | − | 0.645919i | \(-0.776474\pi\) | ||||
−0.763406 | + | 0.645919i | \(0.776474\pi\) | |||||||
\(8\) | −21.6248 | −0.955690 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.95145 | 0.0617101 | ||||||||
\(11\) | −31.7768 | −0.871005 | −0.435502 | − | 0.900188i | \(-0.643429\pi\) | ||||
−0.435502 | + | 0.900188i | \(0.643429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −45.6572 | −0.871600 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.22709 | 0.128548 | ||||||||
\(17\) | 16.0963 | 0.229643 | 0.114822 | − | 0.993386i | \(-0.463370\pi\) | ||||
0.114822 | + | 0.993386i | \(0.463370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.5273 | 0.706688 | 0.353344 | − | 0.935493i | \(-0.385044\pi\) | ||||
0.353344 | + | 0.935493i | \(0.385044\pi\) | |||||||
\(20\) | −6.51785 | −0.0728718 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −51.3081 | −0.497224 | ||||||||
\(23\) | −152.860 | −1.38580 | −0.692902 | − | 0.721031i | \(-0.743668\pi\) | ||||
−0.692902 | + | 0.721031i | \(0.743668\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −123.539 | −0.988314 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 152.496 | 1.02925 | ||||||||
\(29\) | −265.310 | −1.69886 | −0.849429 | − | 0.527703i | \(-0.823053\pi\) | ||||
−0.849429 | + | 0.527703i | \(0.823053\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 56.9241 | 0.329802 | 0.164901 | − | 0.986310i | \(-0.447269\pi\) | ||||
0.164901 | + | 0.986310i | \(0.447269\pi\) | |||||||
\(32\) | 186.282 | 1.02907 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 25.9899 | 0.131095 | ||||||||
\(35\) | −34.1753 | −0.165048 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −444.864 | −1.97663 | −0.988314 | − | 0.152434i | \(-0.951289\pi\) | ||||
−0.988314 | + | 0.152434i | \(0.951289\pi\) | |||||||
\(38\) | 94.5007 | 0.403422 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −26.1356 | −0.103310 | ||||||||
\(41\) | −189.276 | −0.720976 | −0.360488 | − | 0.932764i | \(-0.617390\pi\) | ||||
−0.360488 | + | 0.932764i | \(0.617390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −132.752 | −0.470802 | −0.235401 | − | 0.971898i | \(-0.575640\pi\) | ||||
−0.235401 | + | 0.971898i | \(0.575640\pi\) | |||||||
\(44\) | 171.370 | 0.587158 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −246.814 | −0.791104 | ||||||||
\(47\) | 113.693 | 0.352847 | 0.176424 | − | 0.984314i | \(-0.443547\pi\) | ||||
0.176424 | + | 0.984314i | \(0.443547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 456.586 | 1.33115 | ||||||||
\(50\) | −199.472 | −0.564192 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −300.506 | −0.778824 | −0.389412 | − | 0.921064i | \(-0.627322\pi\) | ||||
−0.389412 | + | 0.921064i | \(0.627322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −38.4051 | −0.0941554 | ||||||||
\(56\) | 611.483 | 1.45916 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −428.381 | −0.969814 | ||||||||
\(59\) | 513.561 | 1.13322 | 0.566610 | − | 0.823986i | \(-0.308255\pi\) | ||||
0.566610 | + | 0.823986i | \(0.308255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 619.902 | 1.30115 | 0.650577 | − | 0.759441i | \(-0.274527\pi\) | ||||
0.650577 | + | 0.759441i | \(0.274527\pi\) | |||||||
\(62\) | 91.9121 | 0.188272 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 234.963 | 0.458911 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −597.308 | −1.08915 | −0.544573 | − | 0.838713i | \(-0.683308\pi\) | ||||
−0.544573 | + | 0.838713i | \(0.683308\pi\) | |||||||
\(68\) | −86.8064 | −0.154806 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −55.1809 | −0.0942197 | ||||||||
\(71\) | 826.673 | 1.38180 | 0.690902 | − | 0.722949i | \(-0.257214\pi\) | ||||
0.690902 | + | 0.722949i | \(0.257214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 332.560 | 0.533194 | 0.266597 | − | 0.963808i | \(-0.414101\pi\) | ||||
0.266597 | + | 0.963808i | \(0.414101\pi\) | |||||||
\(74\) | −718.297 | −1.12838 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −315.633 | −0.476390 | ||||||||
\(77\) | 898.549 | 1.32986 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 679.621 | 0.967891 | 0.483945 | − | 0.875098i | \(-0.339203\pi\) | ||||
0.483945 | + | 0.875098i | \(0.339203\pi\) | |||||||
\(80\) | 9.94319 | 0.0138960 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −305.614 | −0.411578 | ||||||||
\(83\) | 88.2682 | 0.116731 | 0.0583656 | − | 0.998295i | \(-0.481411\pi\) | ||||
0.0583656 | + | 0.998295i | \(0.481411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.4539 | 0.0248244 | ||||||||
\(86\) | −214.347 | −0.268763 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 687.166 | 0.832411 | ||||||||
\(89\) | 1484.39 | 1.76792 | 0.883959 | − | 0.467564i | \(-0.154868\pi\) | ||||
0.883959 | + | 0.467564i | \(0.154868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 824.363 | 0.934193 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 183.574 | 0.201427 | ||||||||
\(95\) | 70.7356 | 0.0763929 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −154.995 | −0.162241 | −0.0811206 | − | 0.996704i | \(-0.525850\pi\) | ||||
−0.0811206 | + | 0.996704i | \(0.525850\pi\) | |||||||
\(98\) | 737.223 | 0.759906 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 666.238 | 0.666238 | ||||||||
\(101\) | 1963.48 | 1.93440 | 0.967198 | − | 0.254025i | \(-0.0817544\pi\) | ||||
0.967198 | + | 0.254025i | \(0.0817544\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1620.75 | −1.55046 | −0.775228 | − | 0.631682i | \(-0.782365\pi\) | ||||
−0.775228 | + | 0.631682i | \(0.782365\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −485.210 | −0.444601 | ||||||||
\(107\) | −321.126 | −0.290135 | −0.145068 | − | 0.989422i | \(-0.546340\pi\) | ||||
−0.145068 | + | 0.989422i | \(0.546340\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1305.27 | 1.14699 | 0.573495 | − | 0.819209i | \(-0.305587\pi\) | ||||
0.573495 | + | 0.819209i | \(0.305587\pi\) | |||||||
\(110\) | −62.0106 | −0.0537498 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −232.637 | −0.196269 | ||||||||
\(113\) | 1086.88 | 0.904820 | 0.452410 | − | 0.891810i | \(-0.350564\pi\) | ||||
0.452410 | + | 0.891810i | \(0.350564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −184.745 | −0.149805 | ||||||||
\(116\) | 1430.80 | 1.14523 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 829.217 | 0.646912 | ||||||||
\(119\) | −455.155 | −0.350622 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −321.238 | −0.241351 | ||||||||
\(122\) | 1000.92 | 0.742780 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −306.988 | −0.222325 | ||||||||
\(125\) | −300.383 | −0.214936 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1326.41 | 0.926774 | 0.463387 | − | 0.886156i | \(-0.346634\pi\) | ||||
0.463387 | + | 0.886156i | \(0.346634\pi\) | |||||||
\(128\) | −1110.88 | −0.767098 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2379.32 | −1.58689 | −0.793443 | − | 0.608644i | \(-0.791714\pi\) | ||||
−0.793443 | + | 0.608644i | \(0.791714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1654.97 | −1.07898 | ||||||||
\(134\) | −964.440 | −0.621753 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −348.080 | −0.219468 | ||||||||
\(137\) | 1633.55 | 1.01871 | 0.509355 | − | 0.860556i | \(-0.329884\pi\) | ||||
0.509355 | + | 0.860556i | \(0.329884\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1254.97 | −0.765791 | −0.382895 | − | 0.923792i | \(-0.625073\pi\) | ||||
−0.382895 | + | 0.923792i | \(0.625073\pi\) | |||||||
\(140\) | 184.305 | 0.111261 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1334.78 | 0.788820 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −320.652 | −0.183646 | ||||||||
\(146\) | 536.965 | 0.304380 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2399.12 | 1.33248 | ||||||||
\(149\) | 461.974 | 0.254002 | 0.127001 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127001 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 766.065 | 0.412857 | 0.206429 | − | 0.978462i | \(-0.433816\pi\) | ||||
0.206429 | + | 0.978462i | \(0.433816\pi\) | |||||||
\(152\) | −1265.64 | −0.675375 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1450.84 | 0.759167 | ||||||||
\(155\) | 68.7980 | 0.0356516 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3424.00 | −1.74054 | −0.870270 | − | 0.492576i | \(-0.836055\pi\) | ||||
−0.870270 | + | 0.492576i | \(0.836055\pi\) | |||||||
\(158\) | 1097.35 | 0.552533 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 225.139 | 0.111243 | ||||||||
\(161\) | 4322.41 | 2.11586 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1722.36 | 0.827640 | 0.413820 | − | 0.910359i | \(-0.364194\pi\) | ||||
0.413820 | + | 0.910359i | \(0.364194\pi\) | |||||||
\(164\) | 1020.75 | 0.486021 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 142.522 | 0.0666375 | ||||||||
\(167\) | −2360.22 | −1.09365 | −0.546824 | − | 0.837247i | \(-0.684163\pi\) | ||||
−0.546824 | + | 0.837247i | \(0.684163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 31.4111 | 0.0141713 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 715.921 | 0.317375 | ||||||||
\(173\) | −4240.41 | −1.86354 | −0.931769 | − | 0.363052i | \(-0.881735\pi\) | ||||
−0.931769 | + | 0.363052i | \(0.881735\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3493.31 | 1.50897 | ||||||||
\(176\) | −261.430 | −0.111966 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2396.76 | 1.00924 | ||||||||
\(179\) | 145.366 | 0.0606991 | 0.0303496 | − | 0.999539i | \(-0.490338\pi\) | ||||
0.0303496 | + | 0.999539i | \(0.490338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1447.40 | 0.594388 | 0.297194 | − | 0.954817i | \(-0.403949\pi\) | ||||
0.297194 | + | 0.954817i | \(0.403949\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3305.57 | 1.32440 | ||||||||
\(185\) | −537.659 | −0.213673 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −511.490 | −0.200020 | ||||||||
\(188\) | −613.138 | −0.237860 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 114.213 | 0.0436098 | ||||||||
\(191\) | 3772.56 | 1.42918 | 0.714589 | − | 0.699544i | \(-0.246614\pi\) | ||||
0.714589 | + | 0.699544i | \(0.246614\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4396.27 | −1.63964 | −0.819819 | − | 0.572622i | \(-0.805926\pi\) | ||||
−0.819819 | + | 0.572622i | \(0.805926\pi\) | |||||||
\(194\) | −250.262 | −0.0926175 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2462.33 | −0.897352 | ||||||||
\(197\) | 1220.50 | 0.441405 | 0.220703 | − | 0.975341i | \(-0.429165\pi\) | ||||
0.220703 | + | 0.975341i | \(0.429165\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1851.42 | 0.659516 | 0.329758 | − | 0.944066i | \(-0.393033\pi\) | ||||
0.329758 | + | 0.944066i | \(0.393033\pi\) | |||||||
\(200\) | 2671.51 | 0.944522 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3170.33 | 1.10427 | ||||||||
\(203\) | 7502.16 | 2.59384 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −228.758 | −0.0779373 | ||||||||
\(206\) | −2616.93 | −0.885097 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1859.81 | −0.615529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 565.901 | 0.184636 | 0.0923180 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923180 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(212\) | 1620.61 | 0.525017 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −518.505 | −0.165627 | ||||||||
\(215\) | −160.443 | −0.0508936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1609.64 | −0.503546 | ||||||||
\(218\) | 2107.54 | 0.654774 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 207.116 | 0.0634717 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1073.79 | −0.322448 | −0.161224 | − | 0.986918i | \(-0.551544\pi\) | ||||
−0.161224 | + | 0.986918i | \(0.551544\pi\) | |||||||
\(224\) | −5267.49 | −1.57120 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1754.92 | 0.516528 | ||||||||
\(227\) | −5756.24 | −1.68306 | −0.841531 | − | 0.540208i | \(-0.818345\pi\) | ||||
−0.841531 | + | 0.540208i | \(0.818345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2577.30 | −0.743725 | −0.371862 | − | 0.928288i | \(-0.621281\pi\) | ||||
−0.371862 | + | 0.928288i | \(0.621281\pi\) | |||||||
\(230\) | −298.298 | −0.0855182 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5737.28 | 1.62358 | ||||||||
\(233\) | 347.566 | 0.0977246 | 0.0488623 | − | 0.998806i | \(-0.484440\pi\) | ||||
0.0488623 | + | 0.998806i | \(0.484440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 137.408 | 0.0381427 | ||||||||
\(236\) | −2769.60 | −0.763921 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −734.914 | −0.200157 | ||||||||
\(239\) | 2201.35 | 0.595788 | 0.297894 | − | 0.954599i | \(-0.403716\pi\) | ||||
0.297894 | + | 0.954599i | \(0.403716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −699.561 | −0.186982 | −0.0934910 | − | 0.995620i | \(-0.529803\pi\) | ||||
−0.0934910 | + | 0.995620i | \(0.529803\pi\) | |||||||
\(242\) | −518.685 | −0.137778 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3343.09 | −0.877128 | ||||||||
\(245\) | 551.826 | 0.143897 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1230.97 | −0.315189 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −485.011 | −0.122699 | ||||||||
\(251\) | −6033.42 | −1.51724 | −0.758618 | − | 0.651536i | \(-0.774125\pi\) | ||||
−0.758618 | + | 0.651536i | \(0.774125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4857.39 | 1.20704 | ||||||||
\(254\) | 2141.69 | 0.529061 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3673.37 | −0.896819 | ||||||||
\(257\) | 3501.49 | 0.849872 | 0.424936 | − | 0.905223i | \(-0.360297\pi\) | ||||
0.424936 | + | 0.905223i | \(0.360297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12579.4 | 3.01794 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3841.75 | −0.905894 | ||||||||
\(263\) | 66.3098 | 0.0155469 | 0.00777346 | − | 0.999970i | \(-0.497526\pi\) | ||||
0.00777346 | + | 0.999970i | \(0.497526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −363.189 | −0.0841907 | ||||||||
\(266\) | −2672.19 | −0.615949 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3221.24 | 0.734211 | ||||||||
\(269\) | −3128.48 | −0.709096 | −0.354548 | − | 0.935038i | \(-0.615365\pi\) | ||||
−0.354548 | + | 0.935038i | \(0.615365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1260.57 | 0.282561 | 0.141280 | − | 0.989970i | \(-0.454878\pi\) | ||||
0.141280 | + | 0.989970i | \(0.454878\pi\) | |||||||
\(272\) | 132.426 | 0.0295202 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2637.60 | 0.581544 | ||||||||
\(275\) | 3925.68 | 0.860826 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1534.66 | −0.332884 | −0.166442 | − | 0.986051i | \(-0.553228\pi\) | ||||
−0.166442 | + | 0.986051i | \(0.553228\pi\) | |||||||
\(278\) | −2026.32 | −0.437161 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 739.034 | 0.157735 | ||||||||
\(281\) | 652.474 | 0.138517 | 0.0692586 | − | 0.997599i | \(-0.477937\pi\) | ||||
0.0692586 | + | 0.997599i | \(0.477937\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 922.235 | 0.193714 | 0.0968572 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968572 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(284\) | −4458.19 | −0.931496 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5352.16 | 1.10079 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4653.91 | −0.947264 | ||||||||
\(290\) | −517.739 | −0.104837 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1793.47 | −0.359434 | ||||||||
\(293\) | 5570.98 | 1.11078 | 0.555392 | − | 0.831588i | \(-0.312568\pi\) | ||||
0.555392 | + | 0.831588i | \(0.312568\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 620.686 | 0.122501 | ||||||||
\(296\) | 9620.10 | 1.88904 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 745.923 | 0.145000 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3753.82 | 0.718825 | ||||||||
\(302\) | 1236.92 | 0.235685 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 481.509 | 0.0908435 | ||||||||
\(305\) | 749.209 | 0.140654 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7069.91 | 1.31434 | 0.657168 | − | 0.753744i | \(-0.271754\pi\) | ||||
0.657168 | + | 0.753744i | \(0.271754\pi\) | |||||||
\(308\) | −4845.81 | −0.896480 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 111.084 | 0.0203521 | ||||||||
\(311\) | 6857.82 | 1.25039 | 0.625195 | − | 0.780468i | \(-0.285019\pi\) | ||||
0.625195 | + | 0.780468i | \(0.285019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3820.23 | 0.689879 | 0.344940 | − | 0.938625i | \(-0.387899\pi\) | ||||
0.344940 | + | 0.938625i | \(0.387899\pi\) | |||||||
\(314\) | −5528.53 | −0.993609 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3665.15 | −0.652471 | ||||||||
\(317\) | 6324.21 | 1.12051 | 0.560257 | − | 0.828319i | \(-0.310702\pi\) | ||||
0.560257 | + | 0.828319i | \(0.310702\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8430.70 | 1.47971 | ||||||||
\(320\) | 283.974 | 0.0496082 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6979.16 | 1.20787 | ||||||||
\(323\) | 942.075 | 0.162286 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2780.99 | 0.472469 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4093.06 | 0.689030 | ||||||||
\(329\) | −3214.89 | −0.538731 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7928.22 | −1.31654 | −0.658269 | − | 0.752783i | \(-0.728711\pi\) | ||||
−0.658269 | + | 0.752783i | \(0.728711\pi\) | |||||||
\(332\) | −476.024 | −0.0786904 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3810.91 | −0.624323 | ||||||||
\(335\) | −721.902 | −0.117737 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9305.11 | −1.50410 | −0.752050 | − | 0.659106i | \(-0.770935\pi\) | ||||
−0.752050 | + | 0.659106i | \(0.770935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −104.914 | −0.0167345 | ||||||||
\(341\) | −1808.86 | −0.287259 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3211.86 | −0.505609 | ||||||||
\(344\) | 2870.73 | 0.449940 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6846.74 | −1.06382 | ||||||||
\(347\) | 2063.17 | 0.319184 | 0.159592 | − | 0.987183i | \(-0.448982\pi\) | ||||
0.159592 | + | 0.987183i | \(0.448982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3148.44 | −0.482900 | −0.241450 | − | 0.970413i | \(-0.577623\pi\) | ||||
−0.241450 | + | 0.970413i | \(0.577623\pi\) | |||||||
\(350\) | 5640.46 | 0.861414 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5919.44 | −0.896328 | ||||||||
\(353\) | 4543.87 | 0.685116 | 0.342558 | − | 0.939497i | \(-0.388707\pi\) | ||||
0.342558 | + | 0.939497i | \(0.388707\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 999.111 | 0.149373 | ||||||||
\(356\) | −8005.19 | −1.19178 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 234.714 | 0.0346509 | ||||||||
\(359\) | 21.5084 | 0.00316204 | 0.00158102 | − | 0.999999i | \(-0.499497\pi\) | ||||
0.00158102 | + | 0.999999i | \(0.499497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3433.56 | −0.500591 | ||||||||
\(362\) | 2337.03 | 0.339314 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 401.929 | 0.0576381 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13050.8 | −1.85626 | −0.928129 | − | 0.372258i | \(-0.878584\pi\) | ||||
−0.928129 | + | 0.372258i | \(0.878584\pi\) | |||||||
\(368\) | −1257.59 | −0.178143 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −868.128 | −0.121978 | ||||||||
\(371\) | 8497.39 | 1.18912 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10150.6 | −1.40905 | −0.704527 | − | 0.709677i | \(-0.748841\pi\) | ||||
−0.704527 | + | 0.709677i | \(0.748841\pi\) | |||||||
\(374\) | −825.873 | −0.114184 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2458.59 | −0.337213 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3443.65 | 0.466724 | 0.233362 | − | 0.972390i | \(-0.425027\pi\) | ||||
0.233362 | + | 0.972390i | \(0.425027\pi\) | |||||||
\(380\) | −381.472 | −0.0514977 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6091.34 | 0.815865 | ||||||||
\(383\) | 5784.45 | 0.771728 | 0.385864 | − | 0.922556i | \(-0.373903\pi\) | ||||
0.385864 | + | 0.922556i | \(0.373903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1085.98 | 0.143758 | ||||||||
\(386\) | −7098.40 | −0.936008 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 835.879 | 0.109369 | ||||||||
\(389\) | 2235.07 | 0.291318 | 0.145659 | − | 0.989335i | \(-0.453470\pi\) | ||||
0.145659 | + | 0.989335i | \(0.453470\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2460.49 | −0.318241 | ||||||||
\(392\) | −9873.57 | −1.27217 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1970.67 | 0.251982 | ||||||||
\(395\) | 821.385 | 0.104629 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3585.93 | −0.453332 | −0.226666 | − | 0.973973i | \(-0.572783\pi\) | ||||
−0.226666 | + | 0.973973i | \(0.572783\pi\) | |||||||
\(398\) | 2989.38 | 0.376493 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1016.37 | −0.127046 | ||||||||
\(401\) | −4130.00 | −0.514321 | −0.257160 | − | 0.966369i | \(-0.582787\pi\) | ||||
−0.257160 | + | 0.966369i | \(0.582787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10588.9 | −1.30401 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12113.3 | 1.48072 | ||||||||
\(407\) | 14136.3 | 1.72165 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10133.6 | −1.22512 | −0.612558 | − | 0.790425i | \(-0.709860\pi\) | ||||
−0.612558 | + | 0.790425i | \(0.709860\pi\) | |||||||
\(410\) | −369.363 | −0.0444915 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8740.57 | 1.04519 | ||||||||
\(413\) | −14521.9 | −1.73021 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 106.680 | 0.0126186 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3002.92 | −0.351382 | ||||||||
\(419\) | 7801.05 | 0.909561 | 0.454781 | − | 0.890604i | \(-0.349718\pi\) | ||||
0.454781 | + | 0.890604i | \(0.349718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12154.2 | −1.40704 | −0.703518 | − | 0.710678i | \(-0.748388\pi\) | ||||
−0.703518 | + | 0.710678i | \(0.748388\pi\) | |||||||
\(422\) | 913.728 | 0.105402 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6498.38 | 0.744314 | ||||||||
\(425\) | −1988.53 | −0.226960 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17528.9 | −1.98662 | ||||||||
\(428\) | 1731.81 | 0.195585 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −259.058 | −0.0290532 | ||||||||
\(431\) | 13124.4 | 1.46678 | 0.733390 | − | 0.679808i | \(-0.237937\pi\) | ||||
0.733390 | + | 0.679808i | \(0.237937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4457.79 | −0.494752 | −0.247376 | − | 0.968920i | \(-0.579568\pi\) | ||||
−0.247376 | + | 0.968920i | \(0.579568\pi\) | |||||||
\(434\) | −2598.99 | −0.287456 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7039.21 | −0.773204 | ||||||||
\(437\) | −8946.48 | −0.979332 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4830.11 | −0.525122 | −0.262561 | − | 0.964915i | \(-0.584567\pi\) | ||||
−0.262561 | + | 0.964915i | \(0.584567\pi\) | |||||||
\(440\) | 830.503 | 0.0899834 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9154.26 | −0.981788 | −0.490894 | − | 0.871219i | \(-0.663330\pi\) | ||||
−0.490894 | + | 0.871219i | \(0.663330\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1794.02 | 0.191112 | ||||||||
\(446\) | −1733.78 | −0.184074 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6644.02 | −0.700671 | ||||||||
\(449\) | −2576.20 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6014.59 | 0.627973 | ||||||||
\(452\) | −5861.44 | −0.609954 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9294.28 | −0.960797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1489.35 | 0.152448 | 0.0762240 | − | 0.997091i | \(-0.475714\pi\) | ||||
0.0762240 | + | 0.997091i | \(0.475714\pi\) | |||||||
\(458\) | −4161.42 | −0.424565 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 996.319 | 0.100986 | ||||||||
\(461\) | 13869.1 | 1.40118 | 0.700592 | − | 0.713562i | \(-0.252919\pi\) | ||||
0.700592 | + | 0.713562i | \(0.252919\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10538.6 | 1.05782 | 0.528908 | − | 0.848679i | \(-0.322602\pi\) | ||||
0.528908 | + | 0.848679i | \(0.322602\pi\) | |||||||
\(464\) | −2182.73 | −0.218385 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 561.196 | 0.0557873 | ||||||||
\(467\) | −12356.9 | −1.22443 | −0.612214 | − | 0.790692i | \(-0.709721\pi\) | ||||
−0.612214 | + | 0.790692i | \(0.709721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16890.1 | 1.66292 | ||||||||
\(470\) | 221.866 | 0.0217742 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11105.6 | −1.08301 | ||||||||
\(473\) | 4218.42 | 0.410070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7230.42 | −0.698430 | ||||||||
\(476\) | 2454.62 | 0.236360 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3554.39 | 0.340113 | ||||||||
\(479\) | 4204.24 | 0.401037 | 0.200518 | − | 0.979690i | \(-0.435737\pi\) | ||||
0.200518 | + | 0.979690i | \(0.435737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1129.54 | −0.106741 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1732.41 | 0.162699 | ||||||||
\(485\) | −187.326 | −0.0175382 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12581.8 | 1.17071 | 0.585355 | − | 0.810777i | \(-0.300955\pi\) | ||||
0.585355 | + | 0.810777i | \(0.300955\pi\) | |||||||
\(488\) | −13405.3 | −1.24350 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 891.002 | 0.0821457 | ||||||||
\(491\) | −3085.05 | −0.283557 | −0.141778 | − | 0.989898i | \(-0.545282\pi\) | ||||
−0.141778 | + | 0.989898i | \(0.545282\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4270.53 | −0.390131 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 468.319 | 0.0423955 | ||||||||
\(497\) | −23375.8 | −2.10975 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6275.13 | 0.562953 | 0.281477 | − | 0.959568i | \(-0.409176\pi\) | ||||
0.281477 | + | 0.959568i | \(0.409176\pi\) | |||||||
\(500\) | 1619.94 | 0.144892 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9741.83 | −0.866133 | ||||||||
\(503\) | 17843.6 | 1.58173 | 0.790863 | − | 0.611994i | \(-0.209632\pi\) | ||||
0.790863 | + | 0.611994i | \(0.209632\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2373.05 | 0.209108 | ||||||||
\(506\) | 7842.96 | 0.689055 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7153.26 | −0.624753 | ||||||||
\(509\) | 10033.0 | 0.873684 | 0.436842 | − | 0.899538i | \(-0.356097\pi\) | ||||
0.436842 | + | 0.899538i | \(0.356097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9403.77 | −0.814086 | ||||||||
\(512\) | 2955.83 | 0.255138 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5653.66 | 0.485160 | ||||||||
\(515\) | −1958.82 | −0.167604 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3612.79 | −0.307332 | ||||||||
\(518\) | 20311.2 | 1.72283 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2406.44 | 0.202357 | 0.101179 | − | 0.994868i | \(-0.467739\pi\) | ||||
0.101179 | + | 0.994868i | \(0.467739\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1987.60 | 0.166179 | 0.0830895 | − | 0.996542i | \(-0.473521\pi\) | ||||
0.0830895 | + | 0.996542i | \(0.473521\pi\) | |||||||
\(524\) | 12831.5 | 1.06975 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 107.067 | 0.00887515 | ||||||||
\(527\) | 916.270 | 0.0757369 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11199.2 | 0.920455 | ||||||||
\(530\) | −586.421 | −0.0480613 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8925.15 | 0.727358 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −388.111 | −0.0313635 | ||||||||
\(536\) | 12916.7 | 1.04089 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5051.38 | −0.404797 | ||||||||
\(539\) | −14508.8 | −1.15944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9255.22 | −0.735514 | −0.367757 | − | 0.929922i | \(-0.619874\pi\) | ||||
−0.367757 | + | 0.929922i | \(0.619874\pi\) | |||||||
\(542\) | 2035.37 | 0.161303 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2998.46 | 0.236320 | ||||||||
\(545\) | 1577.54 | 0.123989 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7539.31 | −0.589319 | −0.294660 | − | 0.955602i | \(-0.595206\pi\) | ||||
−0.294660 | + | 0.955602i | \(0.595206\pi\) | |||||||
\(548\) | −8809.60 | −0.686729 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6338.57 | 0.491414 | ||||||||
\(551\) | −15527.9 | −1.20056 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19217.6 | −1.47779 | ||||||||
\(554\) | −2477.93 | −0.190031 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6767.94 | 0.516232 | ||||||||
\(557\) | 13615.2 | 1.03572 | 0.517860 | − | 0.855465i | \(-0.326729\pi\) | ||||
0.517860 | + | 0.855465i | \(0.326729\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −281.163 | −0.0212166 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1053.51 | 0.0790743 | ||||||||
\(563\) | 4751.68 | 0.355700 | 0.177850 | − | 0.984058i | \(-0.443086\pi\) | ||||
0.177850 | + | 0.984058i | \(0.443086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1313.59 | 0.0978109 | ||||||||
\(566\) | 1489.08 | 0.110584 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17876.6 | −1.32058 | ||||||||
\(569\) | −17296.9 | −1.27438 | −0.637191 | − | 0.770706i | \(-0.719904\pi\) | ||||
−0.637191 | + | 0.770706i | \(0.719904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3685.46 | 0.270108 | 0.135054 | − | 0.990838i | \(-0.456879\pi\) | ||||
0.135054 | + | 0.990838i | \(0.456879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8641.83 | 0.628402 | ||||||||
\(575\) | 18884.2 | 1.36961 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10066.3 | 0.726287 | 0.363143 | − | 0.931733i | \(-0.381704\pi\) | ||||
0.363143 | + | 0.931733i | \(0.381704\pi\) | |||||||
\(578\) | −7514.40 | −0.540758 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1729.25 | 0.123799 | ||||||||
\(581\) | −2495.95 | −0.178227 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9549.10 | 0.678359 | ||||||||
\(584\) | −7191.53 | −0.509568 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8995.14 | 0.634106 | ||||||||
\(587\) | −19809.2 | −1.39286 | −0.696432 | − | 0.717622i | \(-0.745230\pi\) | ||||
−0.696432 | + | 0.717622i | \(0.745230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3331.61 | 0.233067 | ||||||||
\(590\) | 1002.19 | 0.0699311 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3659.94 | −0.254092 | ||||||||
\(593\) | −5085.44 | −0.352165 | −0.176082 | − | 0.984375i | \(-0.556343\pi\) | ||||
−0.176082 | + | 0.984375i | \(0.556343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −550.097 | −0.0379022 | ||||||||
\(596\) | −2491.39 | −0.171227 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20473.7 | 1.39655 | 0.698273 | − | 0.715832i | \(-0.253952\pi\) | ||||
0.698273 | + | 0.715832i | \(0.253952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6131.90 | 0.416182 | 0.208091 | − | 0.978109i | \(-0.433275\pi\) | ||||
0.208091 | + | 0.978109i | \(0.433275\pi\) | |||||||
\(602\) | 6061.07 | 0.410350 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4131.33 | −0.278314 | ||||||||
\(605\) | −388.246 | −0.0260900 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27464.1 | 1.83647 | 0.918233 | − | 0.396041i | \(-0.129616\pi\) | ||||
0.918233 | + | 0.396041i | \(0.129616\pi\) | |||||||
\(608\) | 10902.6 | 0.727234 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1209.71 | 0.0802943 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13563.4 | −0.893669 | −0.446835 | − | 0.894617i | \(-0.647449\pi\) | ||||
−0.446835 | + | 0.894617i | \(0.647449\pi\) | |||||||
\(614\) | 11415.4 | 0.750305 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19431.0 | −1.27093 | ||||||||
\(617\) | 4983.73 | 0.325182 | 0.162591 | − | 0.986694i | \(-0.448015\pi\) | ||||
0.162591 | + | 0.986694i | \(0.448015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10088.7 | −0.655085 | −0.327543 | − | 0.944836i | \(-0.606221\pi\) | ||||
−0.327543 | + | 0.944836i | \(0.606221\pi\) | |||||||
\(620\) | −371.023 | −0.0240333 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11072.9 | 0.713801 | ||||||||
\(623\) | −41973.9 | −2.69928 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15079.4 | 0.965080 | ||||||||
\(626\) | 6168.31 | 0.393826 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18465.4 | 1.17333 | ||||||||
\(629\) | −7160.69 | −0.453919 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6909.71 | 0.435929 | 0.217964 | − | 0.975957i | \(-0.430058\pi\) | ||||
0.217964 | + | 0.975957i | \(0.430058\pi\) | |||||||
\(632\) | −14696.7 | −0.925004 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10211.3 | 0.639660 | ||||||||
\(635\) | 1603.10 | 0.100184 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13612.6 | 0.844713 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1342.60 | −0.0829232 | ||||||||
\(641\) | −24827.6 | −1.52984 | −0.764922 | − | 0.644123i | \(-0.777222\pi\) | ||||
−0.764922 | + | 0.644123i | \(0.777222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9712.36 | 0.595674 | 0.297837 | − | 0.954617i | \(-0.403735\pi\) | ||||
0.297837 | + | 0.954617i | \(0.403735\pi\) | |||||||
\(644\) | −23310.5 | −1.42634 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1521.12 | 0.0926432 | ||||||||
\(647\) | −422.401 | −0.0256666 | −0.0128333 | − | 0.999918i | \(-0.504085\pi\) | ||||
−0.0128333 | + | 0.999918i | \(0.504085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16319.3 | −0.987039 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9288.54 | −0.557925 | ||||||||
\(653\) | 5691.05 | 0.341053 | 0.170527 | − | 0.985353i | \(-0.445453\pi\) | ||||
0.170527 | + | 0.985353i | \(0.445453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2875.63 | −0.171542 | ||||||||
\(656\) | −1557.19 | −0.0926802 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5190.90 | −0.307542 | ||||||||
\(659\) | 11497.8 | 0.679655 | 0.339827 | − | 0.940488i | \(-0.389631\pi\) | ||||
0.339827 | + | 0.940488i | \(0.389631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22058.8 | 1.29802 | 0.649008 | − | 0.760781i | \(-0.275184\pi\) | ||||
0.649008 | + | 0.760781i | \(0.275184\pi\) | |||||||
\(662\) | −12801.2 | −0.751562 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1908.78 | −0.111559 | ||||||||
\(665\) | −2000.19 | −0.116638 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40555.3 | 2.35429 | ||||||||
\(668\) | 12728.5 | 0.737246 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1165.61 | −0.0672114 | ||||||||
\(671\) | −19698.5 | −1.13331 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4767.64 | −0.273074 | −0.136537 | − | 0.990635i | \(-0.543597\pi\) | ||||
−0.136537 | + | 0.990635i | \(0.543597\pi\) | |||||||
\(674\) | −15024.4 | −0.858634 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14024.5 | 0.796165 | 0.398082 | − | 0.917350i | \(-0.369676\pi\) | ||||
0.398082 | + | 0.917350i | \(0.369676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4382.80 | 0.247712 | ||||||||
\(680\) | −420.687 | −0.0237244 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2920.67 | −0.163986 | ||||||||
\(683\) | −4652.81 | −0.260666 | −0.130333 | − | 0.991470i | \(-0.541605\pi\) | ||||
−0.130333 | + | 0.991470i | \(0.541605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1974.29 | 0.110122 | ||||||||
\(686\) | −5186.00 | −0.288633 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1092.16 | −0.0605207 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10978.9 | 0.604426 | 0.302213 | − | 0.953240i | \(-0.402275\pi\) | ||||
0.302213 | + | 0.953240i | \(0.402275\pi\) | |||||||
\(692\) | 22868.2 | 1.25624 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3331.28 | 0.182210 | ||||||||
\(695\) | −1516.74 | −0.0827818 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3046.66 | −0.165567 | ||||||||
\(698\) | −5083.60 | −0.275669 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18839.2 | −1.01722 | ||||||||
\(701\) | 4451.47 | 0.239843 | 0.119921 | − | 0.992783i | \(-0.461736\pi\) | ||||
0.119921 | + | 0.992783i | \(0.461736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26036.7 | −1.39686 | ||||||||
\(704\) | −7466.35 | −0.399714 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7336.74 | 0.391107 | ||||||||
\(707\) | −55521.3 | −2.95346 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18370.9 | 0.973107 | 0.486554 | − | 0.873651i | \(-0.338254\pi\) | ||||
0.486554 | + | 0.873651i | \(0.338254\pi\) | |||||||
\(710\) | 1613.21 | 0.0852713 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −32099.6 | −1.68958 | ||||||||
\(713\) | −8701.42 | −0.457042 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −783.947 | −0.0409183 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.7284 | 0.00180509 | ||||||||
\(719\) | 31594.0 | 1.63874 | 0.819372 | − | 0.573263i | \(-0.194323\pi\) | ||||
0.819372 | + | 0.573263i | \(0.194323\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45829.8 | 2.36725 | ||||||||
\(722\) | −5543.97 | −0.285769 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7805.71 | −0.400687 | ||||||||
\(725\) | 32776.2 | 1.67901 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21370.5 | −1.09022 | −0.545109 | − | 0.838365i | \(-0.683512\pi\) | ||||
−0.545109 | + | 0.838365i | \(0.683512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 648.972 | 0.0329035 | ||||||||
\(731\) | −2136.82 | −0.108116 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13371.4 | −0.673785 | −0.336893 | − | 0.941543i | \(-0.609376\pi\) | ||||
−0.336893 | + | 0.941543i | \(0.609376\pi\) | |||||||
\(734\) | −21072.4 | −1.05967 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28475.1 | −1.42610 | ||||||||
\(737\) | 18980.5 | 0.948652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6426.29 | 0.319885 | 0.159942 | − | 0.987126i | \(-0.448869\pi\) | ||||
0.159942 | + | 0.987126i | \(0.448869\pi\) | |||||||
\(740\) | 2899.56 | 0.144040 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13720.2 | 0.678822 | ||||||||
\(743\) | 25071.8 | 1.23795 | 0.618975 | − | 0.785411i | \(-0.287548\pi\) | ||||
0.618975 | + | 0.785411i | \(0.287548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 558.338 | 0.0274576 | ||||||||
\(746\) | −16389.6 | −0.804376 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2758.43 | 0.134837 | ||||||||
\(749\) | 9080.47 | 0.442982 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5426.94 | 0.263691 | 0.131846 | − | 0.991270i | \(-0.457910\pi\) | ||||
0.131846 | + | 0.991270i | \(0.457910\pi\) | |||||||
\(752\) | 935.362 | 0.0453579 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 925.860 | 0.0446298 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2227.69 | −0.106957 | −0.0534786 | − | 0.998569i | \(-0.517031\pi\) | ||||
−0.0534786 | + | 0.998569i | \(0.517031\pi\) | |||||||
\(758\) | 5560.26 | 0.266435 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1529.64 | −0.0730079 | ||||||||
\(761\) | −30769.6 | −1.46570 | −0.732851 | − | 0.680390i | \(-0.761811\pi\) | ||||
−0.732851 | + | 0.680390i | \(0.761811\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36909.0 | −1.75124 | ||||||||
\(764\) | −20345.2 | −0.963432 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9339.83 | 0.440551 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1346.49 | 0.0631415 | 0.0315707 | − | 0.999502i | \(-0.489949\pi\) | ||||
0.0315707 | + | 0.999502i | \(0.489949\pi\) | |||||||
\(770\) | 1753.47 | 0.0820658 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23708.8 | 1.10531 | ||||||||
\(773\) | 18487.6 | 0.860226 | 0.430113 | − | 0.902775i | \(-0.358474\pi\) | ||||
0.430113 | + | 0.902775i | \(0.358474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7032.36 | −0.325948 | ||||||||
\(776\) | 3351.75 | 0.155052 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3608.84 | 0.166302 | ||||||||
\(779\) | −11077.8 | −0.509505 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26269.0 | −1.20356 | ||||||||
\(782\) | −3972.81 | −0.181672 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3756.37 | 0.171117 | ||||||||
\(785\) | −4138.22 | −0.188152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1388.74 | −0.0629010 | −0.0314505 | − | 0.999505i | \(-0.510013\pi\) | ||||
−0.0314505 | + | 0.999505i | \(0.510013\pi\) | |||||||
\(788\) | −6582.05 | −0.297558 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1326.24 | 0.0597287 | ||||||||
\(791\) | −30733.5 | −1.38149 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5790.00 | −0.258790 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9984.57 | −0.444590 | ||||||||
\(797\) | −27516.6 | −1.22295 | −0.611473 | − | 0.791265i | \(-0.709423\pi\) | ||||
−0.611473 | + | 0.791265i | \(0.709423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1830.04 | 0.0810290 | ||||||||
\(800\) | −23013.2 | −1.01705 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6668.48 | −0.293606 | ||||||||
\(803\) | −10567.7 | −0.464414 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5224.04 | 0.228724 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −42459.9 | −1.84868 | ||||||||
\(809\) | −31550.8 | −1.37116 | −0.685580 | − | 0.727998i | \(-0.740451\pi\) | ||||
−0.685580 | + | 0.727998i | \(0.740451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16536.1 | 0.715980 | 0.357990 | − | 0.933725i | \(-0.383462\pi\) | ||||
0.357990 | + | 0.933725i | \(0.383462\pi\) | |||||||
\(812\) | −40458.6 | −1.74855 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22825.1 | 0.982826 | ||||||||
\(815\) | 2081.63 | 0.0894677 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7769.61 | −0.332710 | ||||||||
\(818\) | −16362.1 | −0.699373 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1233.68 | 0.0525388 | ||||||||
\(821\) | −3643.64 | −0.154889 | −0.0774445 | − | 0.996997i | \(-0.524676\pi\) | ||||
−0.0774445 | + | 0.996997i | \(0.524676\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26439.9 | −1.11985 | −0.559925 | − | 0.828543i | \(-0.689170\pi\) | ||||
−0.559925 | + | 0.828543i | \(0.689170\pi\) | |||||||
\(824\) | 35048.3 | 1.48175 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23447.7 | −0.987713 | ||||||||
\(827\) | 13793.7 | 0.579995 | 0.289997 | − | 0.957027i | \(-0.406346\pi\) | ||||
0.289997 | + | 0.957027i | \(0.406346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34019.6 | −1.42527 | −0.712636 | − | 0.701534i | \(-0.752499\pi\) | ||||
−0.712636 | + | 0.701534i | \(0.752499\pi\) | |||||||
\(830\) | 172.251 | 0.00720350 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7349.36 | 0.305691 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2852.54 | −0.118223 | ||||||||
\(836\) | 10029.8 | 0.414938 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12595.9 | 0.519234 | ||||||||
\(839\) | −26565.2 | −1.09312 | −0.546562 | − | 0.837418i | \(-0.684064\pi\) | ||||
−0.546562 | + | 0.837418i | \(0.684064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46000.5 | 1.88612 | ||||||||
\(842\) | −19624.8 | −0.803224 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3051.86 | −0.124466 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9083.63 | 0.368497 | ||||||||
\(848\) | −2472.29 | −0.100116 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3210.77 | −0.129563 | ||||||||
\(851\) | 68001.9 | 2.73922 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15220.2 | −0.610939 | −0.305470 | − | 0.952202i | \(-0.598813\pi\) | ||||
−0.305470 | + | 0.952202i | \(0.598813\pi\) | |||||||
\(854\) | −28303.0 | −1.13408 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6944.29 | 0.277279 | ||||||||
\(857\) | −39559.1 | −1.57680 | −0.788398 | − | 0.615165i | \(-0.789089\pi\) | ||||
−0.788398 | + | 0.615165i | \(0.789089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41510.0 | 1.64878 | 0.824390 | − | 0.566022i | \(-0.191518\pi\) | ||||
0.824390 | + | 0.566022i | \(0.191518\pi\) | |||||||
\(860\) | 865.257 | 0.0343082 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21191.3 | 0.837330 | ||||||||
\(863\) | −34778.6 | −1.37182 | −0.685908 | − | 0.727688i | \(-0.740595\pi\) | ||||
−0.685908 | + | 0.727688i | \(0.740595\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5124.92 | −0.201448 | ||||||||
\(866\) | −7197.74 | −0.282435 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8680.67 | 0.339448 | ||||||||
\(869\) | −21596.2 | −0.843037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −28226.1 | −1.09617 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14445.4 | −0.559064 | ||||||||
\(875\) | 8493.91 | 0.328167 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28204.1 | −1.08596 | −0.542979 | − | 0.839746i | \(-0.682704\pi\) | ||||
−0.542979 | + | 0.839746i | \(0.682704\pi\) | |||||||
\(878\) | −7798.90 | −0.299772 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −315.962 | −0.0121035 | ||||||||
\(881\) | 1006.27 | 0.0384813 | 0.0192406 | − | 0.999815i | \(-0.493875\pi\) | ||||
0.0192406 | + | 0.999815i | \(0.493875\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20823.5 | 0.793620 | 0.396810 | − | 0.917901i | \(-0.370117\pi\) | ||||
0.396810 | + | 0.917901i | \(0.370117\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14780.9 | −0.560466 | ||||||||
\(887\) | −17301.0 | −0.654917 | −0.327458 | − | 0.944866i | \(-0.606192\pi\) | ||||
−0.327458 | + | 0.944866i | \(0.606192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37507.0 | −1.41501 | ||||||||
\(890\) | 2896.70 | 0.109098 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5790.85 | 0.217368 | ||||||||
\(893\) | 6654.14 | 0.249353 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 175.688 | 0.00656156 | ||||||||
\(896\) | 31412.2 | 1.17121 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4159.64 | −0.154576 | ||||||||
\(899\) | −15102.6 | −0.560287 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4837.04 | −0.178852 | ||||||||
\(902\) | 9711.42 | 0.358486 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23503.5 | −0.864728 | ||||||||
\(905\) | 1749.31 | 0.0642532 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1878.58 | 0.0687732 | 0.0343866 | − | 0.999409i | \(-0.489052\pi\) | ||||
0.0343866 | + | 0.999409i | \(0.489052\pi\) | |||||||
\(908\) | 31043.0 | 1.13458 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29940.8 | 1.08890 | 0.544448 | − | 0.838795i | \(-0.316739\pi\) | ||||
0.544448 | + | 0.838795i | \(0.316739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2804.88 | −0.101673 | ||||||||
\(914\) | 2404.77 | 0.0870269 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13899.2 | 0.501357 | ||||||||
\(917\) | 67279.9 | 2.42288 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10648.8 | 0.382233 | 0.191116 | − | 0.981567i | \(-0.438789\pi\) | ||||
0.191116 | + | 0.981567i | \(0.438789\pi\) | |||||||
\(920\) | 3995.08 | 0.143167 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22393.6 | 0.799884 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54958.2 | 1.95353 | ||||||||
\(926\) | 17016.0 | 0.603867 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49422.6 | −1.74825 | ||||||||
\(929\) | −22670.9 | −0.800654 | −0.400327 | − | 0.916372i | \(-0.631103\pi\) | ||||
−0.400327 | + | 0.916372i | \(0.631103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26722.7 | 0.940711 | ||||||||
\(932\) | −1874.40 | −0.0658777 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19952.0 | −0.698980 | ||||||||
\(935\) | −618.182 | −0.0216222 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18160.3 | −0.633161 | −0.316580 | − | 0.948566i | \(-0.602535\pi\) | ||||
−0.316580 | + | 0.948566i | \(0.602535\pi\) | |||||||
\(938\) | 27271.4 | 0.949300 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −741.034 | −0.0257126 | ||||||||
\(941\) | −17564.9 | −0.608503 | −0.304251 | − | 0.952592i | \(-0.598406\pi\) | ||||
−0.304251 | + | 0.952592i | \(0.598406\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28932.8 | 0.999132 | ||||||||
\(944\) | 4225.11 | 0.145673 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6811.25 | 0.234094 | ||||||||
\(947\) | 40490.9 | 1.38942 | 0.694708 | − | 0.719292i | \(-0.255533\pi\) | ||||
0.694708 | + | 0.719292i | \(0.255533\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −11674.5 | −0.398708 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9842.65 | 0.335086 | ||||||||
\(953\) | 11971.4 | 0.406917 | 0.203458 | − | 0.979084i | \(-0.434782\pi\) | ||||
0.203458 | + | 0.979084i | \(0.434782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4559.49 | 0.154494 | ||||||||
\(956\) | −11871.7 | −0.401630 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6788.35 | 0.228937 | ||||||||
\(959\) | −46191.7 | −1.55538 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26550.6 | −0.891230 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3772.68 | 0.126048 | ||||||||
\(965\) | −5313.30 | −0.177245 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 341.617 | 0.0113605 | 0.00568027 | − | 0.999984i | \(-0.498192\pi\) | ||||
0.00568027 | + | 0.999984i | \(0.498192\pi\) | |||||||
\(968\) | 6946.71 | 0.230657 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −302.465 | −0.0100119 | ||||||||
\(971\) | 2743.85 | 0.0906843 | 0.0453422 | − | 0.998972i | \(-0.485562\pi\) | ||||
0.0453422 | + | 0.998972i | \(0.485562\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35486.6 | 1.16922 | ||||||||
\(974\) | 20315.1 | 0.668314 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5099.99 | 0.167261 | ||||||||
\(977\) | −19743.5 | −0.646520 | −0.323260 | − | 0.946310i | \(-0.604779\pi\) | ||||
−0.323260 | + | 0.946310i | \(0.604779\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47169.0 | −1.53986 | ||||||||
\(980\) | −2975.96 | −0.0970035 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4981.26 | −0.161872 | ||||||||
\(983\) | 17848.8 | 0.579135 | 0.289567 | − | 0.957158i | \(-0.406489\pi\) | ||||
0.289567 | + | 0.957158i | \(0.406489\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1475.08 | 0.0477158 | ||||||||
\(986\) | −6895.37 | −0.222711 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20292.4 | 0.652439 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38391.0 | 1.23061 | 0.615303 | − | 0.788291i | \(-0.289034\pi\) | ||||
0.615303 | + | 0.788291i | \(0.289034\pi\) | |||||||
\(992\) | 10603.9 | 0.339391 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −37743.6 | −1.20438 | ||||||||
\(995\) | 2237.61 | 0.0712935 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7060.87 | −0.224293 | −0.112146 | − | 0.993692i | \(-0.535773\pi\) | ||||
−0.112146 | + | 0.993692i | \(0.535773\pi\) | |||||||
\(998\) | 10132.1 | 0.321369 | ||||||||
\(999\) | 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.bj.1.5 | 9 | ||
3.2 | odd | 2 | 507.4.a.n.1.5 | ✓ | 9 | ||
13.12 | even | 2 | 1521.4.a.be.1.5 | 9 | |||
39.5 | even | 4 | 507.4.b.j.337.11 | 18 | |||
39.8 | even | 4 | 507.4.b.j.337.8 | 18 | |||
39.38 | odd | 2 | 507.4.a.q.1.5 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.n.1.5 | ✓ | 9 | 3.2 | odd | 2 | ||
507.4.a.q.1.5 | yes | 9 | 39.38 | odd | 2 | ||
507.4.b.j.337.8 | 18 | 39.8 | even | 4 | |||
507.4.b.j.337.11 | 18 | 39.5 | even | 4 | |||
1521.4.a.be.1.5 | 9 | 13.12 | even | 2 | |||
1521.4.a.bj.1.5 | 9 | 1.1 | even | 1 | trivial |