Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [338,4,Mod(1,338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(338, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("338.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 338 = 2 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 338.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: | \(19.9426455819\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 338.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.66487 | −0.705305 | −0.352653 | − | 0.935754i | \(-0.614720\pi\) | ||||
−0.352653 | + | 0.935754i | \(0.614720\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 8.53079 | 0.763017 | 0.381509 | − | 0.924365i | \(-0.375405\pi\) | ||||
0.381509 | + | 0.924365i | \(0.375405\pi\) | |||||||
\(6\) | −7.32975 | −0.498726 | ||||||||
\(7\) | −4.20105 | −0.226835 | −0.113418 | − | 0.993547i | \(-0.536180\pi\) | ||||
−0.113418 | + | 0.993547i | \(0.536180\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −13.5687 | −0.502544 | ||||||||
\(10\) | 17.0616 | 0.539535 | ||||||||
\(11\) | −65.3726 | −1.79187 | −0.895935 | − | 0.444186i | \(-0.853493\pi\) | ||||
−0.895935 | + | 0.444186i | \(0.853493\pi\) | |||||||
\(12\) | −14.6595 | −0.352653 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −8.40209 | −0.160397 | ||||||||
\(15\) | −31.2643 | −0.538160 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −26.9019 | −0.383804 | −0.191902 | − | 0.981414i | \(-0.561466\pi\) | ||||
−0.191902 | + | 0.981414i | \(0.561466\pi\) | |||||||
\(18\) | −27.1374 | −0.355352 | ||||||||
\(19\) | −13.3730 | −0.161472 | −0.0807360 | − | 0.996736i | \(-0.525727\pi\) | ||||
−0.0807360 | + | 0.996736i | \(0.525727\pi\) | |||||||
\(20\) | 34.1232 | 0.381509 | ||||||||
\(21\) | 15.3963 | 0.159988 | ||||||||
\(22\) | −130.745 | −1.26704 | ||||||||
\(23\) | 159.929 | 1.44989 | 0.724946 | − | 0.688806i | \(-0.241865\pi\) | ||||
0.724946 | + | 0.688806i | \(0.241865\pi\) | |||||||
\(24\) | −29.3190 | −0.249363 | ||||||||
\(25\) | −52.2255 | −0.417804 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 148.679 | 1.05975 | ||||||||
\(28\) | −16.8042 | −0.113418 | ||||||||
\(29\) | −301.288 | −1.92923 | −0.964616 | − | 0.263658i | \(-0.915071\pi\) | ||||
−0.964616 | + | 0.263658i | \(0.915071\pi\) | |||||||
\(30\) | −62.5286 | −0.380537 | ||||||||
\(31\) | −73.0232 | −0.423076 | −0.211538 | − | 0.977370i | \(-0.567847\pi\) | ||||
−0.211538 | + | 0.977370i | \(0.567847\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 239.582 | 1.26382 | ||||||||
\(34\) | −53.8038 | −0.271390 | ||||||||
\(35\) | −35.8383 | −0.173079 | ||||||||
\(36\) | −54.2748 | −0.251272 | ||||||||
\(37\) | −118.781 | −0.527769 | −0.263885 | − | 0.964554i | \(-0.585004\pi\) | ||||
−0.263885 | + | 0.964554i | \(0.585004\pi\) | |||||||
\(38\) | −26.7459 | −0.114178 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 68.2464 | 0.269767 | ||||||||
\(41\) | −432.901 | −1.64897 | −0.824486 | − | 0.565883i | \(-0.808535\pi\) | ||||
−0.824486 | + | 0.565883i | \(0.808535\pi\) | |||||||
\(42\) | 30.7926 | 0.113129 | ||||||||
\(43\) | −356.508 | −1.26435 | −0.632174 | − | 0.774827i | \(-0.717837\pi\) | ||||
−0.632174 | + | 0.774827i | \(0.717837\pi\) | |||||||
\(44\) | −261.490 | −0.895935 | ||||||||
\(45\) | −115.752 | −0.383450 | ||||||||
\(46\) | 319.858 | 1.02523 | ||||||||
\(47\) | 588.614 | 1.82677 | 0.913385 | − | 0.407096i | \(-0.133459\pi\) | ||||
0.913385 | + | 0.407096i | \(0.133459\pi\) | |||||||
\(48\) | −58.6380 | −0.176326 | ||||||||
\(49\) | −325.351 | −0.948546 | ||||||||
\(50\) | −104.451 | −0.295432 | ||||||||
\(51\) | 98.5921 | 0.270699 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −269.462 | −0.698366 | −0.349183 | − | 0.937054i | \(-0.613541\pi\) | ||||
−0.349183 | + | 0.937054i | \(0.613541\pi\) | |||||||
\(54\) | 297.358 | 0.749358 | ||||||||
\(55\) | −557.680 | −1.36723 | ||||||||
\(56\) | −33.6084 | −0.0801983 | ||||||||
\(57\) | 49.0102 | 0.113887 | ||||||||
\(58\) | −602.576 | −1.36417 | ||||||||
\(59\) | 230.340 | 0.508265 | 0.254133 | − | 0.967169i | \(-0.418210\pi\) | ||||
0.254133 | + | 0.967169i | \(0.418210\pi\) | |||||||
\(60\) | −125.057 | −0.269080 | ||||||||
\(61\) | −380.816 | −0.799319 | −0.399659 | − | 0.916664i | \(-0.630872\pi\) | ||||
−0.399659 | + | 0.916664i | \(0.630872\pi\) | |||||||
\(62\) | −146.046 | −0.299160 | ||||||||
\(63\) | 57.0027 | 0.113995 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 479.164 | 0.893652 | ||||||||
\(67\) | 435.848 | 0.794736 | 0.397368 | − | 0.917659i | \(-0.369924\pi\) | ||||
0.397368 | + | 0.917659i | \(0.369924\pi\) | |||||||
\(68\) | −107.608 | −0.191902 | ||||||||
\(69\) | −586.120 | −1.02262 | ||||||||
\(70\) | −71.6765 | −0.122385 | ||||||||
\(71\) | 65.9622 | 0.110257 | 0.0551287 | − | 0.998479i | \(-0.482443\pi\) | ||||
0.0551287 | + | 0.998479i | \(0.482443\pi\) | |||||||
\(72\) | −108.550 | −0.177676 | ||||||||
\(73\) | 885.517 | 1.41975 | 0.709876 | − | 0.704326i | \(-0.248751\pi\) | ||||
0.709876 | + | 0.704326i | \(0.248751\pi\) | |||||||
\(74\) | −237.562 | −0.373189 | ||||||||
\(75\) | 191.400 | 0.294680 | ||||||||
\(76\) | −53.4918 | −0.0807360 | ||||||||
\(77\) | 274.633 | 0.406459 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −385.463 | −0.548962 | −0.274481 | − | 0.961592i | \(-0.588506\pi\) | ||||
−0.274481 | + | 0.961592i | \(0.588506\pi\) | |||||||
\(80\) | 136.493 | 0.190754 | ||||||||
\(81\) | −178.536 | −0.244905 | ||||||||
\(82\) | −865.803 | −1.16600 | ||||||||
\(83\) | −254.207 | −0.336179 | −0.168089 | − | 0.985772i | \(-0.553760\pi\) | ||||
−0.168089 | + | 0.985772i | \(0.553760\pi\) | |||||||
\(84\) | 61.5852 | 0.0799940 | ||||||||
\(85\) | −229.495 | −0.292849 | ||||||||
\(86\) | −713.016 | −0.894029 | ||||||||
\(87\) | 1104.18 | 1.36070 | ||||||||
\(88\) | −522.980 | −0.633522 | ||||||||
\(89\) | −372.612 | −0.443785 | −0.221892 | − | 0.975071i | \(-0.571223\pi\) | ||||
−0.221892 | + | 0.975071i | \(0.571223\pi\) | |||||||
\(90\) | −231.504 | −0.271140 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 639.716 | 0.724946 | ||||||||
\(93\) | 267.621 | 0.298398 | ||||||||
\(94\) | 1177.23 | 1.29172 | ||||||||
\(95\) | −114.082 | −0.123206 | ||||||||
\(96\) | −117.276 | −0.124682 | ||||||||
\(97\) | 1313.88 | 1.37531 | 0.687653 | − | 0.726039i | \(-0.258641\pi\) | ||||
0.687653 | + | 0.726039i | \(0.258641\pi\) | |||||||
\(98\) | −650.702 | −0.670723 | ||||||||
\(99\) | 887.020 | 0.900494 | ||||||||
\(100\) | −208.902 | −0.208902 | ||||||||
\(101\) | 1463.72 | 1.44204 | 0.721019 | − | 0.692915i | \(-0.243674\pi\) | ||||
0.721019 | + | 0.692915i | \(0.243674\pi\) | |||||||
\(102\) | 197.184 | 0.191413 | ||||||||
\(103\) | 210.886 | 0.201740 | 0.100870 | − | 0.994900i | \(-0.467837\pi\) | ||||
0.100870 | + | 0.994900i | \(0.467837\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 131.343 | 0.122074 | ||||||||
\(106\) | −538.924 | −0.493820 | ||||||||
\(107\) | 391.061 | 0.353321 | 0.176660 | − | 0.984272i | \(-0.443471\pi\) | ||||
0.176660 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(108\) | 594.717 | 0.529876 | ||||||||
\(109\) | 1331.40 | 1.16996 | 0.584978 | − | 0.811049i | \(-0.301103\pi\) | ||||
0.584978 | + | 0.811049i | \(0.301103\pi\) | |||||||
\(110\) | −1115.36 | −0.966776 | ||||||||
\(111\) | 435.317 | 0.372238 | ||||||||
\(112\) | −67.2167 | −0.0567088 | ||||||||
\(113\) | −711.912 | −0.592665 | −0.296332 | − | 0.955085i | \(-0.595764\pi\) | ||||
−0.296332 | + | 0.955085i | \(0.595764\pi\) | |||||||
\(114\) | 98.0204 | 0.0805303 | ||||||||
\(115\) | 1364.32 | 1.10629 | ||||||||
\(116\) | −1205.15 | −0.964616 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 460.679 | 0.359398 | ||||||||
\(119\) | 113.016 | 0.0870603 | ||||||||
\(120\) | −250.114 | −0.190268 | ||||||||
\(121\) | 2942.57 | 2.21080 | ||||||||
\(122\) | −761.631 | −0.565204 | ||||||||
\(123\) | 1586.53 | 1.16303 | ||||||||
\(124\) | −292.093 | −0.211538 | ||||||||
\(125\) | −1511.87 | −1.08181 | ||||||||
\(126\) | 114.005 | 0.0806064 | ||||||||
\(127\) | −1171.70 | −0.818677 | −0.409338 | − | 0.912383i | \(-0.634240\pi\) | ||||
−0.409338 | + | 0.912383i | \(0.634240\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1306.56 | 0.891751 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1128.61 | −0.752726 | −0.376363 | − | 0.926472i | \(-0.622825\pi\) | ||||
−0.376363 | + | 0.926472i | \(0.622825\pi\) | |||||||
\(132\) | 958.329 | 0.631908 | ||||||||
\(133\) | 56.1804 | 0.0366275 | ||||||||
\(134\) | 871.696 | 0.561963 | ||||||||
\(135\) | 1268.35 | 0.808610 | ||||||||
\(136\) | −215.215 | −0.135695 | ||||||||
\(137\) | −1747.93 | −1.09004 | −0.545022 | − | 0.838422i | \(-0.683479\pi\) | ||||
−0.545022 | + | 0.838422i | \(0.683479\pi\) | |||||||
\(138\) | −1172.24 | −0.723099 | ||||||||
\(139\) | 1676.54 | 1.02304 | 0.511518 | − | 0.859273i | \(-0.329083\pi\) | ||||
0.511518 | + | 0.859273i | \(0.329083\pi\) | |||||||
\(140\) | −143.353 | −0.0865396 | ||||||||
\(141\) | −2157.20 | −1.28843 | ||||||||
\(142\) | 131.924 | 0.0779637 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −217.099 | −0.125636 | ||||||||
\(145\) | −2570.22 | −1.47204 | ||||||||
\(146\) | 1771.03 | 1.00392 | ||||||||
\(147\) | 1192.37 | 0.669014 | ||||||||
\(148\) | −475.124 | −0.263885 | ||||||||
\(149\) | −896.961 | −0.493167 | −0.246584 | − | 0.969122i | \(-0.579308\pi\) | ||||
−0.246584 | + | 0.969122i | \(0.579308\pi\) | |||||||
\(150\) | 382.800 | 0.208370 | ||||||||
\(151\) | −2078.28 | −1.12005 | −0.560027 | − | 0.828475i | \(-0.689209\pi\) | ||||
−0.560027 | + | 0.828475i | \(0.689209\pi\) | |||||||
\(152\) | −106.984 | −0.0570890 | ||||||||
\(153\) | 365.024 | 0.192879 | ||||||||
\(154\) | 549.266 | 0.287410 | ||||||||
\(155\) | −622.946 | −0.322814 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3494.75 | −1.77650 | −0.888252 | − | 0.459357i | \(-0.848080\pi\) | ||||
−0.888252 | + | 0.459357i | \(0.848080\pi\) | |||||||
\(158\) | −770.927 | −0.388175 | ||||||||
\(159\) | 987.544 | 0.492562 | ||||||||
\(160\) | 272.985 | 0.134884 | ||||||||
\(161\) | −671.869 | −0.328887 | ||||||||
\(162\) | −357.071 | −0.173174 | ||||||||
\(163\) | −451.254 | −0.216840 | −0.108420 | − | 0.994105i | \(-0.534579\pi\) | ||||
−0.108420 | + | 0.994105i | \(0.534579\pi\) | |||||||
\(164\) | −1731.61 | −0.824486 | ||||||||
\(165\) | 2043.83 | 0.964313 | ||||||||
\(166\) | −508.414 | −0.237714 | ||||||||
\(167\) | 3203.35 | 1.48433 | 0.742164 | − | 0.670218i | \(-0.233800\pi\) | ||||
0.742164 | + | 0.670218i | \(0.233800\pi\) | |||||||
\(168\) | 123.170 | 0.0565643 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −458.989 | −0.207076 | ||||||||
\(171\) | 181.454 | 0.0811468 | ||||||||
\(172\) | −1426.03 | −0.632174 | ||||||||
\(173\) | 1899.38 | 0.834725 | 0.417362 | − | 0.908740i | \(-0.362955\pi\) | ||||
0.417362 | + | 0.908740i | \(0.362955\pi\) | |||||||
\(174\) | 2208.36 | 0.962159 | ||||||||
\(175\) | 219.402 | 0.0947727 | ||||||||
\(176\) | −1045.96 | −0.447967 | ||||||||
\(177\) | −844.165 | −0.358482 | ||||||||
\(178\) | −745.225 | −0.313803 | ||||||||
\(179\) | 2650.89 | 1.10691 | 0.553455 | − | 0.832879i | \(-0.313309\pi\) | ||||
0.553455 | + | 0.832879i | \(0.313309\pi\) | |||||||
\(180\) | −463.007 | −0.191725 | ||||||||
\(181\) | −2289.94 | −0.940387 | −0.470194 | − | 0.882563i | \(-0.655816\pi\) | ||||
−0.470194 | + | 0.882563i | \(0.655816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1395.64 | 0.563764 | ||||||||
\(184\) | 1279.43 | 0.512614 | ||||||||
\(185\) | −1013.30 | −0.402697 | ||||||||
\(186\) | 535.242 | 0.210999 | ||||||||
\(187\) | 1758.65 | 0.687727 | ||||||||
\(188\) | 2354.46 | 0.913385 | ||||||||
\(189\) | −624.608 | −0.240389 | ||||||||
\(190\) | −228.164 | −0.0871198 | ||||||||
\(191\) | −338.313 | −0.128165 | −0.0640825 | − | 0.997945i | \(-0.520412\pi\) | ||||
−0.0640825 | + | 0.997945i | \(0.520412\pi\) | |||||||
\(192\) | −234.552 | −0.0881632 | ||||||||
\(193\) | 2684.05 | 1.00105 | 0.500524 | − | 0.865723i | \(-0.333141\pi\) | ||||
0.500524 | + | 0.865723i | \(0.333141\pi\) | |||||||
\(194\) | 2627.77 | 0.972489 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1301.40 | −0.474273 | ||||||||
\(197\) | 1897.24 | 0.686156 | 0.343078 | − | 0.939307i | \(-0.388530\pi\) | ||||
0.343078 | + | 0.939307i | \(0.388530\pi\) | |||||||
\(198\) | 1774.04 | 0.636745 | ||||||||
\(199\) | −2415.60 | −0.860491 | −0.430245 | − | 0.902712i | \(-0.641573\pi\) | ||||
−0.430245 | + | 0.902712i | \(0.641573\pi\) | |||||||
\(200\) | −417.804 | −0.147716 | ||||||||
\(201\) | −1597.33 | −0.560532 | ||||||||
\(202\) | 2927.44 | 1.01967 | ||||||||
\(203\) | 1265.72 | 0.437618 | ||||||||
\(204\) | 394.368 | 0.135350 | ||||||||
\(205\) | −3692.99 | −1.25819 | ||||||||
\(206\) | 421.772 | 0.142652 | ||||||||
\(207\) | −2170.03 | −0.728635 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 874.225 | 0.289337 | ||||||||
\(210\) | 262.685 | 0.0863191 | ||||||||
\(211\) | 2668.42 | 0.870623 | 0.435312 | − | 0.900280i | \(-0.356638\pi\) | ||||
0.435312 | + | 0.900280i | \(0.356638\pi\) | |||||||
\(212\) | −1077.85 | −0.349183 | ||||||||
\(213\) | −241.743 | −0.0777651 | ||||||||
\(214\) | 782.122 | 0.249835 | ||||||||
\(215\) | −3041.30 | −0.964719 | ||||||||
\(216\) | 1189.43 | 0.374679 | ||||||||
\(217\) | 306.774 | 0.0959685 | ||||||||
\(218\) | 2662.81 | 0.827284 | ||||||||
\(219\) | −3245.31 | −1.00136 | ||||||||
\(220\) | −2230.72 | −0.683614 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 870.634 | 0.263212 | ||||||||
\(223\) | −286.358 | −0.0859907 | −0.0429953 | − | 0.999075i | \(-0.513690\pi\) | ||||
−0.0429953 | + | 0.999075i | \(0.513690\pi\) | |||||||
\(224\) | −134.433 | −0.0400992 | ||||||||
\(225\) | 708.632 | 0.209965 | ||||||||
\(226\) | −1423.82 | −0.419077 | ||||||||
\(227\) | 5201.24 | 1.52079 | 0.760393 | − | 0.649463i | \(-0.225006\pi\) | ||||
0.760393 | + | 0.649463i | \(0.225006\pi\) | |||||||
\(228\) | 196.041 | 0.0569435 | ||||||||
\(229\) | 890.458 | 0.256957 | 0.128478 | − | 0.991712i | \(-0.458991\pi\) | ||||
0.128478 | + | 0.991712i | \(0.458991\pi\) | |||||||
\(230\) | 2728.64 | 0.782267 | ||||||||
\(231\) | −1006.50 | −0.286678 | ||||||||
\(232\) | −2410.30 | −0.682087 | ||||||||
\(233\) | 4753.11 | 1.33642 | 0.668212 | − | 0.743971i | \(-0.267060\pi\) | ||||
0.668212 | + | 0.743971i | \(0.267060\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5021.35 | 1.39386 | ||||||||
\(236\) | 921.358 | 0.254133 | ||||||||
\(237\) | 1412.67 | 0.387186 | ||||||||
\(238\) | 226.032 | 0.0615609 | ||||||||
\(239\) | −2292.62 | −0.620491 | −0.310245 | − | 0.950656i | \(-0.600411\pi\) | ||||
−0.310245 | + | 0.950656i | \(0.600411\pi\) | |||||||
\(240\) | −500.229 | −0.134540 | ||||||||
\(241\) | 1975.21 | 0.527943 | 0.263972 | − | 0.964530i | \(-0.414967\pi\) | ||||
0.263972 | + | 0.964530i | \(0.414967\pi\) | |||||||
\(242\) | 5885.14 | 1.56327 | ||||||||
\(243\) | −3360.03 | −0.887020 | ||||||||
\(244\) | −1523.26 | −0.399659 | ||||||||
\(245\) | −2775.50 | −0.723757 | ||||||||
\(246\) | 3173.06 | 0.822385 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −584.186 | −0.149580 | ||||||||
\(249\) | 931.637 | 0.237109 | ||||||||
\(250\) | −3023.75 | −0.764955 | ||||||||
\(251\) | −7465.74 | −1.87742 | −0.938711 | − | 0.344705i | \(-0.887979\pi\) | ||||
−0.938711 | + | 0.344705i | \(0.887979\pi\) | |||||||
\(252\) | 228.011 | 0.0569974 | ||||||||
\(253\) | −10455.0 | −2.59802 | ||||||||
\(254\) | −2343.41 | −0.578892 | ||||||||
\(255\) | 841.069 | 0.206548 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −554.966 | −0.134700 | −0.0673499 | − | 0.997729i | \(-0.521454\pi\) | ||||
−0.0673499 | + | 0.997729i | \(0.521454\pi\) | |||||||
\(258\) | 2613.11 | 0.630563 | ||||||||
\(259\) | 499.004 | 0.119717 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4088.08 | 0.969525 | ||||||||
\(262\) | −2257.22 | −0.532258 | ||||||||
\(263\) | −1993.07 | −0.467292 | −0.233646 | − | 0.972322i | \(-0.575066\pi\) | ||||
−0.233646 | + | 0.972322i | \(0.575066\pi\) | |||||||
\(264\) | 1916.66 | 0.446826 | ||||||||
\(265\) | −2298.72 | −0.532866 | ||||||||
\(266\) | 112.361 | 0.0258996 | ||||||||
\(267\) | 1365.58 | 0.313004 | ||||||||
\(268\) | 1743.39 | 0.397368 | ||||||||
\(269\) | −5207.76 | −1.18038 | −0.590191 | − | 0.807263i | \(-0.700948\pi\) | ||||
−0.590191 | + | 0.807263i | \(0.700948\pi\) | |||||||
\(270\) | 2536.70 | 0.571773 | ||||||||
\(271\) | 4084.90 | 0.915646 | 0.457823 | − | 0.889043i | \(-0.348629\pi\) | ||||
0.457823 | + | 0.889043i | \(0.348629\pi\) | |||||||
\(272\) | −430.430 | −0.0959510 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3495.87 | −0.770778 | ||||||||
\(275\) | 3414.12 | 0.748651 | ||||||||
\(276\) | −2344.48 | −0.511308 | ||||||||
\(277\) | 437.993 | 0.0950051 | 0.0475026 | − | 0.998871i | \(-0.484874\pi\) | ||||
0.0475026 | + | 0.998871i | \(0.484874\pi\) | |||||||
\(278\) | 3353.07 | 0.723395 | ||||||||
\(279\) | 990.829 | 0.212614 | ||||||||
\(280\) | −286.706 | −0.0611927 | ||||||||
\(281\) | 5462.34 | 1.15963 | 0.579815 | − | 0.814748i | \(-0.303125\pi\) | ||||
0.579815 | + | 0.814748i | \(0.303125\pi\) | |||||||
\(282\) | −4314.40 | −0.911058 | ||||||||
\(283\) | −796.676 | −0.167341 | −0.0836704 | − | 0.996493i | \(-0.526664\pi\) | ||||
−0.0836704 | + | 0.996493i | \(0.526664\pi\) | |||||||
\(284\) | 263.849 | 0.0551287 | ||||||||
\(285\) | 418.096 | 0.0868978 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1818.64 | 0.374045 | ||||||||
\(288\) | −434.198 | −0.0888381 | ||||||||
\(289\) | −4189.29 | −0.852694 | ||||||||
\(290\) | −5140.45 | −1.04089 | ||||||||
\(291\) | −4815.22 | −0.970011 | ||||||||
\(292\) | 3542.07 | 0.709876 | ||||||||
\(293\) | 1697.32 | 0.338426 | 0.169213 | − | 0.985580i | \(-0.445877\pi\) | ||||
0.169213 | + | 0.985580i | \(0.445877\pi\) | |||||||
\(294\) | 2384.74 | 0.473065 | ||||||||
\(295\) | 1964.98 | 0.387815 | ||||||||
\(296\) | −950.247 | −0.186595 | ||||||||
\(297\) | −9719.54 | −1.89894 | ||||||||
\(298\) | −1793.92 | −0.348722 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 765.600 | 0.147340 | ||||||||
\(301\) | 1497.71 | 0.286798 | ||||||||
\(302\) | −4156.56 | −0.791997 | ||||||||
\(303\) | −5364.36 | −1.01708 | ||||||||
\(304\) | −213.967 | −0.0403680 | ||||||||
\(305\) | −3248.66 | −0.609894 | ||||||||
\(306\) | 730.047 | 0.136386 | ||||||||
\(307\) | −9385.86 | −1.74488 | −0.872442 | − | 0.488718i | \(-0.837465\pi\) | ||||
−0.872442 | + | 0.488718i | \(0.837465\pi\) | |||||||
\(308\) | 1098.53 | 0.203230 | ||||||||
\(309\) | −772.870 | −0.142288 | ||||||||
\(310\) | −1245.89 | −0.228264 | ||||||||
\(311\) | −3282.65 | −0.598527 | −0.299264 | − | 0.954170i | \(-0.596741\pi\) | ||||
−0.299264 | + | 0.954170i | \(0.596741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5924.67 | −1.06991 | −0.534955 | − | 0.844880i | \(-0.679672\pi\) | ||||
−0.534955 | + | 0.844880i | \(0.679672\pi\) | |||||||
\(314\) | −6989.49 | −1.25618 | ||||||||
\(315\) | 486.278 | 0.0869800 | ||||||||
\(316\) | −1541.85 | −0.274481 | ||||||||
\(317\) | −6467.88 | −1.14597 | −0.572985 | − | 0.819566i | \(-0.694215\pi\) | ||||
−0.572985 | + | 0.819566i | \(0.694215\pi\) | |||||||
\(318\) | 1975.09 | 0.348294 | ||||||||
\(319\) | 19696.0 | 3.45693 | ||||||||
\(320\) | 545.971 | 0.0953772 | ||||||||
\(321\) | −1433.19 | −0.249199 | ||||||||
\(322\) | −1343.74 | −0.232558 | ||||||||
\(323\) | 359.758 | 0.0619736 | ||||||||
\(324\) | −714.143 | −0.122452 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −902.508 | −0.153329 | ||||||||
\(327\) | −4879.42 | −0.825177 | ||||||||
\(328\) | −3463.21 | −0.582999 | ||||||||
\(329\) | −2472.80 | −0.414376 | ||||||||
\(330\) | 4087.65 | 0.681872 | ||||||||
\(331\) | −3509.24 | −0.582735 | −0.291368 | − | 0.956611i | \(-0.594110\pi\) | ||||
−0.291368 | + | 0.956611i | \(0.594110\pi\) | |||||||
\(332\) | −1016.83 | −0.168089 | ||||||||
\(333\) | 1611.70 | 0.265227 | ||||||||
\(334\) | 6406.70 | 1.04958 | ||||||||
\(335\) | 3718.13 | 0.606398 | ||||||||
\(336\) | 246.341 | 0.0399970 | ||||||||
\(337\) | −1834.82 | −0.296584 | −0.148292 | − | 0.988944i | \(-0.547378\pi\) | ||||
−0.148292 | + | 0.988944i | \(0.547378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2609.07 | 0.418010 | ||||||||
\(340\) | −917.978 | −0.146425 | ||||||||
\(341\) | 4773.71 | 0.758097 | ||||||||
\(342\) | 362.907 | 0.0573795 | ||||||||
\(343\) | 2807.77 | 0.441999 | ||||||||
\(344\) | −2852.06 | −0.447014 | ||||||||
\(345\) | −5000.07 | −0.780274 | ||||||||
\(346\) | 3798.76 | 0.590239 | ||||||||
\(347\) | −7259.30 | −1.12305 | −0.561527 | − | 0.827459i | \(-0.689786\pi\) | ||||
−0.561527 | + | 0.827459i | \(0.689786\pi\) | |||||||
\(348\) | 4416.73 | 0.680349 | ||||||||
\(349\) | 1795.24 | 0.275349 | 0.137674 | − | 0.990478i | \(-0.456037\pi\) | ||||
0.137674 | + | 0.990478i | \(0.456037\pi\) | |||||||
\(350\) | 438.804 | 0.0670144 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2091.92 | −0.316761 | ||||||||
\(353\) | 4552.38 | 0.686398 | 0.343199 | − | 0.939263i | \(-0.388489\pi\) | ||||
0.343199 | + | 0.939263i | \(0.388489\pi\) | |||||||
\(354\) | −1688.33 | −0.253485 | ||||||||
\(355\) | 562.710 | 0.0841283 | ||||||||
\(356\) | −1490.45 | −0.221892 | ||||||||
\(357\) | −414.190 | −0.0614041 | ||||||||
\(358\) | 5301.78 | 0.782703 | ||||||||
\(359\) | −10165.4 | −1.49445 | −0.747227 | − | 0.664569i | \(-0.768615\pi\) | ||||
−0.747227 | + | 0.664569i | \(0.768615\pi\) | |||||||
\(360\) | −926.014 | −0.135570 | ||||||||
\(361\) | −6680.16 | −0.973927 | ||||||||
\(362\) | −4579.88 | −0.664954 | ||||||||
\(363\) | −10784.2 | −1.55929 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7554.16 | 1.08330 | ||||||||
\(366\) | 2791.28 | 0.398641 | ||||||||
\(367\) | −10401.6 | −1.47945 | −0.739723 | − | 0.672911i | \(-0.765044\pi\) | ||||
−0.739723 | + | 0.672911i | \(0.765044\pi\) | |||||||
\(368\) | 2558.87 | 0.362473 | ||||||||
\(369\) | 5873.91 | 0.828681 | ||||||||
\(370\) | −2026.59 | −0.284750 | ||||||||
\(371\) | 1132.02 | 0.158414 | ||||||||
\(372\) | 1070.48 | 0.149199 | ||||||||
\(373\) | −7953.41 | −1.10405 | −0.552027 | − | 0.833826i | \(-0.686145\pi\) | ||||
−0.552027 | + | 0.833826i | \(0.686145\pi\) | |||||||
\(374\) | 3517.29 | 0.486296 | ||||||||
\(375\) | 5540.83 | 0.763006 | ||||||||
\(376\) | 4708.91 | 0.645861 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1249.22 | −0.169981 | ||||||||
\(379\) | −9014.81 | −1.22179 | −0.610897 | − | 0.791710i | \(-0.709191\pi\) | ||||
−0.610897 | + | 0.791710i | \(0.709191\pi\) | |||||||
\(380\) | −456.328 | −0.0616030 | ||||||||
\(381\) | 4294.15 | 0.577417 | ||||||||
\(382\) | −676.627 | −0.0906263 | ||||||||
\(383\) | 2496.24 | 0.333034 | 0.166517 | − | 0.986039i | \(-0.446748\pi\) | ||||
0.166517 | + | 0.986039i | \(0.446748\pi\) | |||||||
\(384\) | −469.104 | −0.0623408 | ||||||||
\(385\) | 2342.84 | 0.310135 | ||||||||
\(386\) | 5368.10 | 0.707848 | ||||||||
\(387\) | 4837.35 | 0.635391 | ||||||||
\(388\) | 5255.54 | 0.687653 | ||||||||
\(389\) | 10896.9 | 1.42029 | 0.710145 | − | 0.704056i | \(-0.248629\pi\) | ||||
0.710145 | + | 0.704056i | \(0.248629\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4302.40 | −0.556475 | ||||||||
\(392\) | −2602.81 | −0.335362 | ||||||||
\(393\) | 4136.21 | 0.530902 | ||||||||
\(394\) | 3794.48 | 0.485186 | ||||||||
\(395\) | −3288.31 | −0.418868 | ||||||||
\(396\) | 3548.08 | 0.450247 | ||||||||
\(397\) | −10887.1 | −1.37635 | −0.688174 | − | 0.725546i | \(-0.741587\pi\) | ||||
−0.688174 | + | 0.725546i | \(0.741587\pi\) | |||||||
\(398\) | −4831.21 | −0.608459 | ||||||||
\(399\) | −205.894 | −0.0258336 | ||||||||
\(400\) | −835.609 | −0.104451 | ||||||||
\(401\) | −9968.76 | −1.24144 | −0.620718 | − | 0.784034i | \(-0.713159\pi\) | ||||
−0.620718 | + | 0.784034i | \(0.713159\pi\) | |||||||
\(402\) | −3194.66 | −0.396356 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5854.89 | 0.721019 | ||||||||
\(405\) | −1523.05 | −0.186867 | ||||||||
\(406\) | 2531.45 | 0.309442 | ||||||||
\(407\) | 7765.01 | 0.945693 | ||||||||
\(408\) | 788.737 | 0.0957066 | ||||||||
\(409\) | −4036.32 | −0.487979 | −0.243989 | − | 0.969778i | \(-0.578456\pi\) | ||||
−0.243989 | + | 0.969778i | \(0.578456\pi\) | |||||||
\(410\) | −7385.98 | −0.889677 | ||||||||
\(411\) | 6405.96 | 0.768814 | ||||||||
\(412\) | 843.543 | 0.100870 | ||||||||
\(413\) | −967.667 | −0.115292 | ||||||||
\(414\) | −4340.06 | −0.515223 | ||||||||
\(415\) | −2168.59 | −0.256510 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6144.29 | −0.721552 | ||||||||
\(418\) | 1748.45 | 0.204592 | ||||||||
\(419\) | 15194.9 | 1.77164 | 0.885821 | − | 0.464028i | \(-0.153596\pi\) | ||||
0.885821 | + | 0.464028i | \(0.153596\pi\) | |||||||
\(420\) | 525.371 | 0.0610368 | ||||||||
\(421\) | −10154.8 | −1.17556 | −0.587782 | − | 0.809019i | \(-0.699999\pi\) | ||||
−0.587782 | + | 0.809019i | \(0.699999\pi\) | |||||||
\(422\) | 5336.84 | 0.615624 | ||||||||
\(423\) | −7986.73 | −0.918033 | ||||||||
\(424\) | −2155.69 | −0.246910 | ||||||||
\(425\) | 1404.97 | 0.160355 | ||||||||
\(426\) | −483.486 | −0.0549882 | ||||||||
\(427\) | 1599.82 | 0.181314 | ||||||||
\(428\) | 1564.24 | 0.176660 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6082.59 | −0.682159 | ||||||||
\(431\) | 6616.84 | 0.739494 | 0.369747 | − | 0.929133i | \(-0.379444\pi\) | ||||
0.369747 | + | 0.929133i | \(0.379444\pi\) | |||||||
\(432\) | 2378.87 | 0.264938 | ||||||||
\(433\) | 5697.60 | 0.632354 | 0.316177 | − | 0.948700i | \(-0.397601\pi\) | ||||
0.316177 | + | 0.948700i | \(0.397601\pi\) | |||||||
\(434\) | 613.548 | 0.0678600 | ||||||||
\(435\) | 9419.55 | 1.03824 | ||||||||
\(436\) | 5325.61 | 0.584978 | ||||||||
\(437\) | −2138.73 | −0.234117 | ||||||||
\(438\) | −6490.62 | −0.708068 | ||||||||
\(439\) | 436.007 | 0.0474020 | 0.0237010 | − | 0.999719i | \(-0.492455\pi\) | ||||
0.0237010 | + | 0.999719i | \(0.492455\pi\) | |||||||
\(440\) | −4461.44 | −0.483388 | ||||||||
\(441\) | 4414.59 | 0.476686 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6609.58 | 0.708873 | 0.354436 | − | 0.935080i | \(-0.384673\pi\) | ||||
0.354436 | + | 0.935080i | \(0.384673\pi\) | |||||||
\(444\) | 1741.27 | 0.186119 | ||||||||
\(445\) | −3178.68 | −0.338616 | ||||||||
\(446\) | −572.715 | −0.0608046 | ||||||||
\(447\) | 3287.25 | 0.347833 | ||||||||
\(448\) | −268.867 | −0.0283544 | ||||||||
\(449\) | −8015.31 | −0.842463 | −0.421231 | − | 0.906953i | \(-0.638402\pi\) | ||||
−0.421231 | + | 0.906953i | \(0.638402\pi\) | |||||||
\(450\) | 1417.26 | 0.148468 | ||||||||
\(451\) | 28299.9 | 2.95474 | ||||||||
\(452\) | −2847.65 | −0.296332 | ||||||||
\(453\) | 7616.64 | 0.789980 | ||||||||
\(454\) | 10402.5 | 1.07536 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 392.082 | 0.0402652 | ||||||||
\(457\) | 4507.03 | 0.461335 | 0.230668 | − | 0.973033i | \(-0.425909\pi\) | ||||
0.230668 | + | 0.973033i | \(0.425909\pi\) | |||||||
\(458\) | 1780.92 | 0.181696 | ||||||||
\(459\) | −3999.75 | −0.406737 | ||||||||
\(460\) | 5457.29 | 0.553146 | ||||||||
\(461\) | −2103.55 | −0.212521 | −0.106260 | − | 0.994338i | \(-0.533888\pi\) | ||||
−0.106260 | + | 0.994338i | \(0.533888\pi\) | |||||||
\(462\) | −2012.99 | −0.202712 | ||||||||
\(463\) | −5468.28 | −0.548883 | −0.274441 | − | 0.961604i | \(-0.588493\pi\) | ||||
−0.274441 | + | 0.961604i | \(0.588493\pi\) | |||||||
\(464\) | −4820.60 | −0.482308 | ||||||||
\(465\) | 2283.02 | 0.227683 | ||||||||
\(466\) | 9506.22 | 0.944994 | ||||||||
\(467\) | −6043.79 | −0.598872 | −0.299436 | − | 0.954116i | \(-0.596799\pi\) | ||||
−0.299436 | + | 0.954116i | \(0.596799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1831.02 | −0.180274 | ||||||||
\(470\) | 10042.7 | 0.985606 | ||||||||
\(471\) | 12807.8 | 1.25298 | ||||||||
\(472\) | 1842.72 | 0.179699 | ||||||||
\(473\) | 23305.8 | 2.26555 | ||||||||
\(474\) | 2825.35 | 0.273782 | ||||||||
\(475\) | 698.410 | 0.0674637 | ||||||||
\(476\) | 452.065 | 0.0435301 | ||||||||
\(477\) | 3656.25 | 0.350960 | ||||||||
\(478\) | −4585.24 | −0.438753 | ||||||||
\(479\) | 8481.30 | 0.809020 | 0.404510 | − | 0.914534i | \(-0.367442\pi\) | ||||
0.404510 | + | 0.914534i | \(0.367442\pi\) | |||||||
\(480\) | −1000.46 | −0.0951342 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3950.42 | 0.373312 | ||||||||
\(483\) | 2462.32 | 0.231965 | ||||||||
\(484\) | 11770.3 | 1.10540 | ||||||||
\(485\) | 11208.5 | 1.04938 | ||||||||
\(486\) | −6720.05 | −0.627218 | ||||||||
\(487\) | 6623.36 | 0.616289 | 0.308145 | − | 0.951340i | \(-0.400292\pi\) | ||||
0.308145 | + | 0.951340i | \(0.400292\pi\) | |||||||
\(488\) | −3046.53 | −0.282602 | ||||||||
\(489\) | 1653.79 | 0.152939 | ||||||||
\(490\) | −5551.01 | −0.511774 | ||||||||
\(491\) | 16379.4 | 1.50548 | 0.752739 | − | 0.658319i | \(-0.228732\pi\) | ||||
0.752739 | + | 0.658319i | \(0.228732\pi\) | |||||||
\(492\) | 6346.12 | 0.581514 | ||||||||
\(493\) | 8105.21 | 0.740447 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7566.99 | 0.687093 | ||||||||
\(496\) | −1168.37 | −0.105769 | ||||||||
\(497\) | −277.110 | −0.0250102 | ||||||||
\(498\) | 1863.27 | 0.167661 | ||||||||
\(499\) | 7915.70 | 0.710131 | 0.355065 | − | 0.934841i | \(-0.384459\pi\) | ||||
0.355065 | + | 0.934841i | \(0.384459\pi\) | |||||||
\(500\) | −6047.50 | −0.540905 | ||||||||
\(501\) | −11739.9 | −1.04690 | ||||||||
\(502\) | −14931.5 | −1.32754 | ||||||||
\(503\) | −479.511 | −0.0425056 | −0.0212528 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212528 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(504\) | 456.022 | 0.0403032 | ||||||||
\(505\) | 12486.7 | 1.10030 | ||||||||
\(506\) | −20909.9 | −1.83708 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4686.82 | −0.409338 | ||||||||
\(509\) | −1192.33 | −0.103829 | −0.0519145 | − | 0.998652i | \(-0.516532\pi\) | ||||
−0.0519145 | + | 0.998652i | \(0.516532\pi\) | |||||||
\(510\) | 1682.14 | 0.146052 | ||||||||
\(511\) | −3720.10 | −0.322050 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −1988.28 | −0.171120 | ||||||||
\(514\) | −1109.93 | −0.0952471 | ||||||||
\(515\) | 1799.02 | 0.153931 | ||||||||
\(516\) | 5226.23 | 0.445876 | ||||||||
\(517\) | −38479.2 | −3.27333 | ||||||||
\(518\) | 998.008 | 0.0846524 | ||||||||
\(519\) | −6961.00 | −0.588736 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23238.5 | −1.95412 | −0.977062 | − | 0.212955i | \(-0.931691\pi\) | ||||
−0.977062 | + | 0.212955i | \(0.931691\pi\) | |||||||
\(522\) | 8176.16 | 0.685557 | ||||||||
\(523\) | −11026.3 | −0.921884 | −0.460942 | − | 0.887430i | \(-0.652488\pi\) | ||||
−0.460942 | + | 0.887430i | \(0.652488\pi\) | |||||||
\(524\) | −4514.44 | −0.376363 | ||||||||
\(525\) | −804.080 | −0.0668437 | ||||||||
\(526\) | −3986.14 | −0.330425 | ||||||||
\(527\) | 1964.46 | 0.162378 | ||||||||
\(528\) | 3833.32 | 0.315954 | ||||||||
\(529\) | 13410.3 | 1.10219 | ||||||||
\(530\) | −4597.45 | −0.376793 | ||||||||
\(531\) | −3125.41 | −0.255426 | ||||||||
\(532\) | 224.722 | 0.0183138 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2731.16 | 0.221327 | ||||||||
\(535\) | 3336.06 | 0.269590 | ||||||||
\(536\) | 3486.79 | 0.280982 | ||||||||
\(537\) | −9715.18 | −0.780709 | ||||||||
\(538\) | −10415.5 | −0.834657 | ||||||||
\(539\) | 21269.0 | 1.69967 | ||||||||
\(540\) | 5073.41 | 0.404305 | ||||||||
\(541\) | −8987.70 | −0.714254 | −0.357127 | − | 0.934056i | \(-0.616244\pi\) | ||||
−0.357127 | + | 0.934056i | \(0.616244\pi\) | |||||||
\(542\) | 8169.80 | 0.647459 | ||||||||
\(543\) | 8392.35 | 0.663260 | ||||||||
\(544\) | −860.861 | −0.0678476 | ||||||||
\(545\) | 11357.9 | 0.892697 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10734.8 | −0.839101 | −0.419550 | − | 0.907732i | \(-0.637812\pi\) | ||||
−0.419550 | + | 0.907732i | \(0.637812\pi\) | |||||||
\(548\) | −6991.74 | −0.545022 | ||||||||
\(549\) | 5167.17 | 0.401693 | ||||||||
\(550\) | 6828.23 | 0.529376 | ||||||||
\(551\) | 4029.11 | 0.311517 | ||||||||
\(552\) | −4688.96 | −0.361550 | ||||||||
\(553\) | 1619.35 | 0.124524 | ||||||||
\(554\) | 875.985 | 0.0671788 | ||||||||
\(555\) | 3713.60 | 0.284024 | ||||||||
\(556\) | 6706.14 | 0.511518 | ||||||||
\(557\) | −13228.3 | −1.00628 | −0.503141 | − | 0.864204i | \(-0.667822\pi\) | ||||
−0.503141 | + | 0.864204i | \(0.667822\pi\) | |||||||
\(558\) | 1981.66 | 0.150341 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −573.412 | −0.0432698 | ||||||||
\(561\) | −6445.22 | −0.485058 | ||||||||
\(562\) | 10924.7 | 0.819983 | ||||||||
\(563\) | 10734.0 | 0.803522 | 0.401761 | − | 0.915745i | \(-0.368398\pi\) | ||||
0.401761 | + | 0.915745i | \(0.368398\pi\) | |||||||
\(564\) | −8628.79 | −0.644216 | ||||||||
\(565\) | −6073.18 | −0.452213 | ||||||||
\(566\) | −1593.35 | −0.118328 | ||||||||
\(567\) | 750.037 | 0.0555531 | ||||||||
\(568\) | 527.698 | 0.0389819 | ||||||||
\(569\) | 5313.45 | 0.391479 | 0.195739 | − | 0.980656i | \(-0.437289\pi\) | ||||
0.195739 | + | 0.980656i | \(0.437289\pi\) | |||||||
\(570\) | 836.192 | 0.0614460 | ||||||||
\(571\) | 4629.37 | 0.339287 | 0.169644 | − | 0.985505i | \(-0.445738\pi\) | ||||
0.169644 | + | 0.985505i | \(0.445738\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1239.88 | 0.0903954 | ||||||||
\(574\) | 3637.28 | 0.264490 | ||||||||
\(575\) | −8352.38 | −0.605771 | ||||||||
\(576\) | −868.397 | −0.0628180 | ||||||||
\(577\) | 504.750 | 0.0364177 | 0.0182088 | − | 0.999834i | \(-0.494204\pi\) | ||||
0.0182088 | + | 0.999834i | \(0.494204\pi\) | |||||||
\(578\) | −8378.58 | −0.602946 | ||||||||
\(579\) | −9836.71 | −0.706045 | ||||||||
\(580\) | −10280.9 | −0.736019 | ||||||||
\(581\) | 1067.94 | 0.0762572 | ||||||||
\(582\) | −9630.44 | −0.685901 | ||||||||
\(583\) | 17615.4 | 1.25138 | ||||||||
\(584\) | 7084.14 | 0.501958 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3394.65 | 0.239303 | ||||||||
\(587\) | −5532.93 | −0.389044 | −0.194522 | − | 0.980898i | \(-0.562316\pi\) | ||||
−0.194522 | + | 0.980898i | \(0.562316\pi\) | |||||||
\(588\) | 4769.49 | 0.334507 | ||||||||
\(589\) | 976.536 | 0.0683149 | ||||||||
\(590\) | 3929.96 | 0.274227 | ||||||||
\(591\) | −6953.15 | −0.483950 | ||||||||
\(592\) | −1900.49 | −0.131942 | ||||||||
\(593\) | 18079.8 | 1.25202 | 0.626009 | − | 0.779816i | \(-0.284687\pi\) | ||||
0.626009 | + | 0.779816i | \(0.284687\pi\) | |||||||
\(594\) | −19439.1 | −1.34275 | ||||||||
\(595\) | 964.117 | 0.0664285 | ||||||||
\(596\) | −3587.84 | −0.246584 | ||||||||
\(597\) | 8852.88 | 0.606909 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1837.55 | −0.125342 | −0.0626712 | − | 0.998034i | \(-0.519962\pi\) | ||||
−0.0626712 | + | 0.998034i | \(0.519962\pi\) | |||||||
\(600\) | 1531.20 | 0.104185 | ||||||||
\(601\) | −23487.3 | −1.59412 | −0.797060 | − | 0.603901i | \(-0.793612\pi\) | ||||
−0.797060 | + | 0.603901i | \(0.793612\pi\) | |||||||
\(602\) | 2995.41 | 0.202797 | ||||||||
\(603\) | −5913.89 | −0.399390 | ||||||||
\(604\) | −8313.12 | −0.560027 | ||||||||
\(605\) | 25102.5 | 1.68688 | ||||||||
\(606\) | −10728.7 | −0.719182 | ||||||||
\(607\) | −16310.8 | −1.09067 | −0.545335 | − | 0.838218i | \(-0.683598\pi\) | ||||
−0.545335 | + | 0.838218i | \(0.683598\pi\) | |||||||
\(608\) | −427.935 | −0.0285445 | ||||||||
\(609\) | −4638.72 | −0.308654 | ||||||||
\(610\) | −6497.32 | −0.431260 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1460.09 | 0.0964393 | ||||||||
\(613\) | −8453.11 | −0.556962 | −0.278481 | − | 0.960442i | \(-0.589831\pi\) | ||||
−0.278481 | + | 0.960442i | \(0.589831\pi\) | |||||||
\(614\) | −18771.7 | −1.23382 | ||||||||
\(615\) | 13534.4 | 0.887411 | ||||||||
\(616\) | 2197.06 | 0.143705 | ||||||||
\(617\) | 13410.3 | 0.875008 | 0.437504 | − | 0.899216i | \(-0.355863\pi\) | ||||
0.437504 | + | 0.899216i | \(0.355863\pi\) | |||||||
\(618\) | −1545.74 | −0.100613 | ||||||||
\(619\) | 890.135 | 0.0577990 | 0.0288995 | − | 0.999582i | \(-0.490800\pi\) | ||||
0.0288995 | + | 0.999582i | \(0.490800\pi\) | |||||||
\(620\) | −2491.78 | −0.161407 | ||||||||
\(621\) | 23778.1 | 1.53653 | ||||||||
\(622\) | −6565.30 | −0.423223 | ||||||||
\(623\) | 1565.36 | 0.100666 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6369.30 | −0.407635 | ||||||||
\(626\) | −11849.3 | −0.756541 | ||||||||
\(627\) | −3203.92 | −0.204071 | ||||||||
\(628\) | −13979.0 | −0.888252 | ||||||||
\(629\) | 3195.43 | 0.202560 | ||||||||
\(630\) | 972.557 | 0.0615041 | ||||||||
\(631\) | 10582.4 | 0.667639 | 0.333819 | − | 0.942637i | \(-0.391662\pi\) | ||||
0.333819 | + | 0.942637i | \(0.391662\pi\) | |||||||
\(632\) | −3083.71 | −0.194087 | ||||||||
\(633\) | −9779.42 | −0.614055 | ||||||||
\(634\) | −12935.8 | −0.810323 | ||||||||
\(635\) | −9995.57 | −0.624665 | ||||||||
\(636\) | 3950.17 | 0.246281 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 39391.9 | 2.44442 | ||||||||
\(639\) | −895.021 | −0.0554092 | ||||||||
\(640\) | 1091.94 | 0.0674419 | ||||||||
\(641\) | 26884.2 | 1.65657 | 0.828286 | − | 0.560305i | \(-0.189316\pi\) | ||||
0.828286 | + | 0.560305i | \(0.189316\pi\) | |||||||
\(642\) | −2866.38 | −0.176210 | ||||||||
\(643\) | −5691.12 | −0.349045 | −0.174523 | − | 0.984653i | \(-0.555838\pi\) | ||||
−0.174523 | + | 0.984653i | \(0.555838\pi\) | |||||||
\(644\) | −2687.48 | −0.164443 | ||||||||
\(645\) | 11146.0 | 0.680422 | ||||||||
\(646\) | 719.516 | 0.0438220 | ||||||||
\(647\) | 1809.79 | 0.109969 | 0.0549847 | − | 0.998487i | \(-0.482489\pi\) | ||||
0.0549847 | + | 0.998487i | \(0.482489\pi\) | |||||||
\(648\) | −1428.29 | −0.0865870 | ||||||||
\(649\) | −15057.9 | −0.910745 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1124.29 | −0.0676871 | ||||||||
\(652\) | −1805.02 | −0.108420 | ||||||||
\(653\) | 9459.16 | 0.566869 | 0.283435 | − | 0.958992i | \(-0.408526\pi\) | ||||
0.283435 | + | 0.958992i | \(0.408526\pi\) | |||||||
\(654\) | −9758.85 | −0.583488 | ||||||||
\(655\) | −9627.94 | −0.574343 | ||||||||
\(656\) | −6926.42 | −0.412243 | ||||||||
\(657\) | −12015.3 | −0.713488 | ||||||||
\(658\) | −4945.59 | −0.293008 | ||||||||
\(659\) | 1015.32 | 0.0600171 | 0.0300085 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300085 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(660\) | 8175.31 | 0.482157 | ||||||||
\(661\) | −23648.4 | −1.39156 | −0.695778 | − | 0.718257i | \(-0.744940\pi\) | ||||
−0.695778 | + | 0.718257i | \(0.744940\pi\) | |||||||
\(662\) | −7018.49 | −0.412056 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2033.66 | −0.118857 | ||||||||
\(665\) | 479.264 | 0.0279474 | ||||||||
\(666\) | 3223.40 | 0.187544 | ||||||||
\(667\) | −48184.7 | −2.79718 | ||||||||
\(668\) | 12813.4 | 0.742164 | ||||||||
\(669\) | 1049.46 | 0.0606497 | ||||||||
\(670\) | 7436.26 | 0.428788 | ||||||||
\(671\) | 24894.9 | 1.43228 | ||||||||
\(672\) | 492.682 | 0.0282822 | ||||||||
\(673\) | 17747.0 | 1.01649 | 0.508243 | − | 0.861214i | \(-0.330295\pi\) | ||||
0.508243 | + | 0.861214i | \(0.330295\pi\) | |||||||
\(674\) | −3669.63 | −0.209717 | ||||||||
\(675\) | −7764.85 | −0.442769 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10754.2 | 0.610511 | 0.305256 | − | 0.952270i | \(-0.401258\pi\) | ||||
0.305256 | + | 0.952270i | \(0.401258\pi\) | |||||||
\(678\) | 5218.14 | 0.295577 | ||||||||
\(679\) | −5519.69 | −0.311968 | ||||||||
\(680\) | −1835.96 | −0.103538 | ||||||||
\(681\) | −19061.9 | −1.07262 | ||||||||
\(682\) | 9547.42 | 0.536055 | ||||||||
\(683\) | 23981.7 | 1.34354 | 0.671768 | − | 0.740762i | \(-0.265535\pi\) | ||||
0.671768 | + | 0.740762i | \(0.265535\pi\) | |||||||
\(684\) | 725.815 | 0.0405734 | ||||||||
\(685\) | −14911.3 | −0.831723 | ||||||||
\(686\) | 5615.55 | 0.312540 | ||||||||
\(687\) | −3263.42 | −0.181233 | ||||||||
\(688\) | −5704.13 | −0.316087 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −10000.1 | −0.551737 | ||||||||
\(691\) | −29001.4 | −1.59662 | −0.798312 | − | 0.602244i | \(-0.794273\pi\) | ||||
−0.798312 | + | 0.602244i | \(0.794273\pi\) | |||||||
\(692\) | 7597.53 | 0.417362 | ||||||||
\(693\) | −3726.41 | −0.204264 | ||||||||
\(694\) | −14518.6 | −0.794119 | ||||||||
\(695\) | 14302.2 | 0.780594 | ||||||||
\(696\) | 8833.46 | 0.481079 | ||||||||
\(697\) | 11645.9 | 0.632882 | ||||||||
\(698\) | 3590.47 | 0.194701 | ||||||||
\(699\) | −17419.6 | −0.942587 | ||||||||
\(700\) | 877.608 | 0.0473864 | ||||||||
\(701\) | −31031.5 | −1.67196 | −0.835979 | − | 0.548761i | \(-0.815100\pi\) | ||||
−0.835979 | + | 0.548761i | \(0.815100\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1588.45 | 0.0852199 | ||||||||
\(704\) | −4183.84 | −0.223984 | ||||||||
\(705\) | −18402.6 | −0.983096 | ||||||||
\(706\) | 9104.75 | 0.485357 | ||||||||
\(707\) | −6149.16 | −0.327105 | ||||||||
\(708\) | −3376.66 | −0.179241 | ||||||||
\(709\) | 4382.59 | 0.232146 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(710\) | 1125.42 | 0.0594877 | ||||||||
\(711\) | 5230.23 | 0.275878 | ||||||||
\(712\) | −2980.90 | −0.156902 | ||||||||
\(713\) | −11678.5 | −0.613414 | ||||||||
\(714\) | −828.380 | −0.0434192 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10603.6 | 0.553455 | ||||||||
\(717\) | 8402.17 | 0.437636 | ||||||||
\(718\) | −20330.8 | −1.05674 | ||||||||
\(719\) | −28764.6 | −1.49199 | −0.745994 | − | 0.665953i | \(-0.768025\pi\) | ||||
−0.745994 | + | 0.665953i | \(0.768025\pi\) | |||||||
\(720\) | −1852.03 | −0.0958625 | ||||||||
\(721\) | −885.941 | −0.0457617 | ||||||||
\(722\) | −13360.3 | −0.688670 | ||||||||
\(723\) | −7238.89 | −0.372361 | ||||||||
\(724\) | −9159.77 | −0.470194 | ||||||||
\(725\) | 15734.9 | 0.806042 | ||||||||
\(726\) | −21568.3 | −1.10258 | ||||||||
\(727\) | 25408.5 | 1.29621 | 0.648107 | − | 0.761549i | \(-0.275561\pi\) | ||||
0.648107 | + | 0.761549i | \(0.275561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17134.5 | 0.870525 | ||||||||
\(730\) | 15108.3 | 0.766006 | ||||||||
\(731\) | 9590.74 | 0.485262 | ||||||||
\(732\) | 5582.57 | 0.281882 | ||||||||
\(733\) | 22341.8 | 1.12580 | 0.562902 | − | 0.826524i | \(-0.309685\pi\) | ||||
0.562902 | + | 0.826524i | \(0.309685\pi\) | |||||||
\(734\) | −20803.1 | −1.04613 | ||||||||
\(735\) | 10171.9 | 0.510470 | ||||||||
\(736\) | 5117.73 | 0.256307 | ||||||||
\(737\) | −28492.5 | −1.42406 | ||||||||
\(738\) | 11747.8 | 0.585966 | ||||||||
\(739\) | 8210.90 | 0.408718 | 0.204359 | − | 0.978896i | \(-0.434489\pi\) | ||||
0.204359 | + | 0.978896i | \(0.434489\pi\) | |||||||
\(740\) | −4053.18 | −0.201349 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2264.04 | 0.112016 | ||||||||
\(743\) | 32752.3 | 1.61718 | 0.808590 | − | 0.588373i | \(-0.200231\pi\) | ||||
0.808590 | + | 0.588373i | \(0.200231\pi\) | |||||||
\(744\) | 2140.97 | 0.105500 | ||||||||
\(745\) | −7651.79 | −0.376295 | ||||||||
\(746\) | −15906.8 | −0.780684 | ||||||||
\(747\) | 3449.26 | 0.168945 | ||||||||
\(748\) | 7034.58 | 0.343863 | ||||||||
\(749\) | −1642.87 | −0.0801455 | ||||||||
\(750\) | 11081.7 | 0.539527 | ||||||||
\(751\) | 8907.41 | 0.432804 | 0.216402 | − | 0.976304i | \(-0.430568\pi\) | ||||
0.216402 | + | 0.976304i | \(0.430568\pi\) | |||||||
\(752\) | 9417.83 | 0.456693 | ||||||||
\(753\) | 27361.0 | 1.32416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17729.4 | −0.854620 | ||||||||
\(756\) | −2498.43 | −0.120195 | ||||||||
\(757\) | −10744.6 | −0.515879 | −0.257940 | − | 0.966161i | \(-0.583044\pi\) | ||||
−0.257940 | + | 0.966161i | \(0.583044\pi\) | |||||||
\(758\) | −18029.6 | −0.863938 | ||||||||
\(759\) | 38316.2 | 1.83240 | ||||||||
\(760\) | −912.656 | −0.0435599 | ||||||||
\(761\) | 16997.8 | 0.809683 | 0.404841 | − | 0.914387i | \(-0.367327\pi\) | ||||
0.404841 | + | 0.914387i | \(0.367327\pi\) | |||||||
\(762\) | 8588.30 | 0.408296 | ||||||||
\(763\) | −5593.28 | −0.265387 | ||||||||
\(764\) | −1353.25 | −0.0640825 | ||||||||
\(765\) | 3113.94 | 0.147170 | ||||||||
\(766\) | 4992.48 | 0.235490 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −938.208 | −0.0440816 | ||||||||
\(769\) | −19032.4 | −0.892492 | −0.446246 | − | 0.894910i | \(-0.647239\pi\) | ||||
−0.446246 | + | 0.894910i | \(0.647239\pi\) | |||||||
\(770\) | 4685.68 | 0.219299 | ||||||||
\(771\) | 2033.88 | 0.0950045 | ||||||||
\(772\) | 10736.2 | 0.500524 | ||||||||
\(773\) | −23750.6 | −1.10511 | −0.552555 | − | 0.833477i | \(-0.686347\pi\) | ||||
−0.552555 | + | 0.833477i | \(0.686347\pi\) | |||||||
\(774\) | 9674.69 | 0.449289 | ||||||||
\(775\) | 3813.68 | 0.176763 | ||||||||
\(776\) | 10511.1 | 0.486244 | ||||||||
\(777\) | −1828.79 | −0.0844368 | ||||||||
\(778\) | 21793.7 | 1.00430 | ||||||||
\(779\) | 5789.17 | 0.266263 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4312.12 | −0.197567 | ||||||||
\(782\) | −8604.79 | −0.393487 | ||||||||
\(783\) | −44795.2 | −2.04451 | ||||||||
\(784\) | −5205.62 | −0.237136 | ||||||||
\(785\) | −29813.0 | −1.35550 | ||||||||
\(786\) | 8272.42 | 0.375404 | ||||||||
\(787\) | −17825.9 | −0.807403 | −0.403702 | − | 0.914891i | \(-0.632277\pi\) | ||||
−0.403702 | + | 0.914891i | \(0.632277\pi\) | |||||||
\(788\) | 7588.96 | 0.343078 | ||||||||
\(789\) | 7304.34 | 0.329584 | ||||||||
\(790\) | −6576.62 | −0.296184 | ||||||||
\(791\) | 2990.78 | 0.134437 | ||||||||
\(792\) | 7096.16 | 0.318373 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21774.3 | −0.973225 | ||||||||
\(795\) | 8424.53 | 0.375833 | ||||||||
\(796\) | −9662.42 | −0.430245 | ||||||||
\(797\) | −26461.2 | −1.17604 | −0.588020 | − | 0.808846i | \(-0.700092\pi\) | ||||
−0.588020 | + | 0.808846i | \(0.700092\pi\) | |||||||
\(798\) | −411.788 | −0.0182671 | ||||||||
\(799\) | −15834.8 | −0.701122 | ||||||||
\(800\) | −1671.22 | −0.0738581 | ||||||||
\(801\) | 5055.87 | 0.223021 | ||||||||
\(802\) | −19937.5 | −0.877828 | ||||||||
\(803\) | −57888.5 | −2.54401 | ||||||||
\(804\) | −6389.32 | −0.280266 | ||||||||
\(805\) | −5731.58 | −0.250946 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19085.8 | 0.832530 | ||||||||
\(808\) | 11709.8 | 0.509837 | ||||||||
\(809\) | 21873.3 | 0.950588 | 0.475294 | − | 0.879827i | \(-0.342342\pi\) | ||||
0.475294 | + | 0.879827i | \(0.342342\pi\) | |||||||
\(810\) | −3046.10 | −0.132135 | ||||||||
\(811\) | −39113.8 | −1.69355 | −0.846776 | − | 0.531949i | \(-0.821460\pi\) | ||||
−0.846776 | + | 0.531949i | \(0.821460\pi\) | |||||||
\(812\) | 5062.90 | 0.218809 | ||||||||
\(813\) | −14970.6 | −0.645810 | ||||||||
\(814\) | 15530.0 | 0.668706 | ||||||||
\(815\) | −3849.56 | −0.165453 | ||||||||
\(816\) | 1577.47 | 0.0676748 | ||||||||
\(817\) | 4767.57 | 0.204157 | ||||||||
\(818\) | −8072.65 | −0.345053 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14772.0 | −0.629097 | ||||||||
\(821\) | 26296.8 | 1.11786 | 0.558931 | − | 0.829214i | \(-0.311212\pi\) | ||||
0.558931 | + | 0.829214i | \(0.311212\pi\) | |||||||
\(822\) | 12811.9 | 0.543634 | ||||||||
\(823\) | 24681.1 | 1.04536 | 0.522678 | − | 0.852530i | \(-0.324933\pi\) | ||||
0.522678 | + | 0.852530i | \(0.324933\pi\) | |||||||
\(824\) | 1687.09 | 0.0713258 | ||||||||
\(825\) | −12512.3 | −0.528027 | ||||||||
\(826\) | −1935.33 | −0.0815241 | ||||||||
\(827\) | 3081.68 | 0.129578 | 0.0647888 | − | 0.997899i | \(-0.479363\pi\) | ||||
0.0647888 | + | 0.997899i | \(0.479363\pi\) | |||||||
\(828\) | −8680.12 | −0.364317 | ||||||||
\(829\) | −8498.53 | −0.356051 | −0.178026 | − | 0.984026i | \(-0.556971\pi\) | ||||
−0.178026 | + | 0.984026i | \(0.556971\pi\) | |||||||
\(830\) | −4337.18 | −0.181380 | ||||||||
\(831\) | −1605.19 | −0.0670076 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8752.57 | 0.364056 | ||||||||
\(834\) | −12288.6 | −0.510215 | ||||||||
\(835\) | 27327.1 | 1.13257 | ||||||||
\(836\) | 3496.90 | 0.144668 | ||||||||
\(837\) | −10857.0 | −0.448356 | ||||||||
\(838\) | 30389.7 | 1.25274 | ||||||||
\(839\) | −18680.1 | −0.768664 | −0.384332 | − | 0.923195i | \(-0.625568\pi\) | ||||
−0.384332 | + | 0.923195i | \(0.625568\pi\) | |||||||
\(840\) | 1050.74 | 0.0431596 | ||||||||
\(841\) | 66385.3 | 2.72194 | ||||||||
\(842\) | −20309.5 | −0.831249 | ||||||||
\(843\) | −20018.8 | −0.817894 | ||||||||
\(844\) | 10673.7 | 0.435312 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15973.5 | −0.649147 | ||||||||
\(847\) | −12361.9 | −0.501486 | ||||||||
\(848\) | −4311.39 | −0.174592 | ||||||||
\(849\) | 2919.72 | 0.118026 | ||||||||
\(850\) | 2809.93 | 0.113388 | ||||||||
\(851\) | −18996.5 | −0.765208 | ||||||||
\(852\) | −966.973 | −0.0388826 | ||||||||
\(853\) | −24129.9 | −0.968574 | −0.484287 | − | 0.874909i | \(-0.660921\pi\) | ||||
−0.484287 | + | 0.874909i | \(0.660921\pi\) | |||||||
\(854\) | 3199.65 | 0.128208 | ||||||||
\(855\) | 1547.94 | 0.0619164 | ||||||||
\(856\) | 3128.49 | 0.124918 | ||||||||
\(857\) | −7739.30 | −0.308482 | −0.154241 | − | 0.988033i | \(-0.549293\pi\) | ||||
−0.154241 | + | 0.988033i | \(0.549293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4302.59 | 0.170899 | 0.0854496 | − | 0.996342i | \(-0.472767\pi\) | ||||
0.0854496 | + | 0.996342i | \(0.472767\pi\) | |||||||
\(860\) | −12165.2 | −0.482360 | ||||||||
\(861\) | −6665.08 | −0.263816 | ||||||||
\(862\) | 13233.7 | 0.522901 | ||||||||
\(863\) | 16253.2 | 0.641096 | 0.320548 | − | 0.947232i | \(-0.396133\pi\) | ||||
0.320548 | + | 0.947232i | \(0.396133\pi\) | |||||||
\(864\) | 4757.73 | 0.187340 | ||||||||
\(865\) | 16203.2 | 0.636910 | ||||||||
\(866\) | 11395.2 | 0.447142 | ||||||||
\(867\) | 15353.2 | 0.601410 | ||||||||
\(868\) | 1227.10 | 0.0479842 | ||||||||
\(869\) | 25198.7 | 0.983669 | ||||||||
\(870\) | 18839.1 | 0.734144 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10651.2 | 0.413642 | ||||||||
\(873\) | −17827.7 | −0.691152 | ||||||||
\(874\) | −4277.45 | −0.165546 | ||||||||
\(875\) | 6351.46 | 0.245392 | ||||||||
\(876\) | −12981.2 | −0.500680 | ||||||||
\(877\) | 9441.33 | 0.363525 | 0.181762 | − | 0.983342i | \(-0.441820\pi\) | ||||
0.181762 | + | 0.983342i | \(0.441820\pi\) | |||||||
\(878\) | 872.014 | 0.0335183 | ||||||||
\(879\) | −6220.48 | −0.238693 | ||||||||
\(880\) | −8922.88 | −0.341807 | ||||||||
\(881\) | −11872.4 | −0.454021 | −0.227011 | − | 0.973892i | \(-0.572895\pi\) | ||||
−0.227011 | + | 0.973892i | \(0.572895\pi\) | |||||||
\(882\) | 8829.18 | 0.337068 | ||||||||
\(883\) | −493.891 | −0.0188231 | −0.00941153 | − | 0.999956i | \(-0.502996\pi\) | ||||
−0.00941153 | + | 0.999956i | \(0.502996\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7201.40 | −0.273528 | ||||||||
\(886\) | 13219.2 | 0.501249 | ||||||||
\(887\) | 20543.6 | 0.777664 | 0.388832 | − | 0.921309i | \(-0.372879\pi\) | ||||
0.388832 | + | 0.921309i | \(0.372879\pi\) | |||||||
\(888\) | 3482.54 | 0.131606 | ||||||||
\(889\) | 4922.38 | 0.185705 | ||||||||
\(890\) | −6357.36 | −0.239437 | ||||||||
\(891\) | 11671.3 | 0.438838 | ||||||||
\(892\) | −1145.43 | −0.0429953 | ||||||||
\(893\) | −7871.52 | −0.294972 | ||||||||
\(894\) | 6574.50 | 0.245955 | ||||||||
\(895\) | 22614.2 | 0.844592 | ||||||||
\(896\) | −537.734 | −0.0200496 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16030.6 | −0.595711 | ||||||||
\(899\) | 22001.0 | 0.816212 | ||||||||
\(900\) | 2834.53 | 0.104983 | ||||||||
\(901\) | 7249.03 | 0.268036 | ||||||||
\(902\) | 56599.7 | 2.08932 | ||||||||
\(903\) | −5488.90 | −0.202280 | ||||||||
\(904\) | −5695.30 | −0.209539 | ||||||||
\(905\) | −19535.0 | −0.717532 | ||||||||
\(906\) | 15233.3 | 0.558600 | ||||||||
\(907\) | −5386.61 | −0.197199 | −0.0985994 | − | 0.995127i | \(-0.531436\pi\) | ||||
−0.0985994 | + | 0.995127i | \(0.531436\pi\) | |||||||
\(908\) | 20805.0 | 0.760393 | ||||||||
\(909\) | −19860.8 | −0.724688 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31793.5 | 1.15627 | 0.578137 | − | 0.815940i | \(-0.303780\pi\) | ||||
0.578137 | + | 0.815940i | \(0.303780\pi\) | |||||||
\(912\) | 784.164 | 0.0284718 | ||||||||
\(913\) | 16618.2 | 0.602389 | ||||||||
\(914\) | 9014.07 | 0.326213 | ||||||||
\(915\) | 11905.9 | 0.430162 | ||||||||
\(916\) | 3561.83 | 0.128478 | ||||||||
\(917\) | 4741.34 | 0.170745 | ||||||||
\(918\) | −7999.51 | −0.287607 | ||||||||
\(919\) | −42991.4 | −1.54315 | −0.771575 | − | 0.636139i | \(-0.780531\pi\) | ||||
−0.771575 | + | 0.636139i | \(0.780531\pi\) | |||||||
\(920\) | 10914.6 | 0.391134 | ||||||||
\(921\) | 34398.0 | 1.23068 | ||||||||
\(922\) | −4207.10 | −0.150275 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4025.98 | −0.143339 | ||||||||
\(925\) | 6203.40 | 0.220504 | ||||||||
\(926\) | −10936.6 | −0.388119 | ||||||||
\(927\) | −2861.45 | −0.101383 | ||||||||
\(928\) | −9641.21 | −0.341043 | ||||||||
\(929\) | 40676.7 | 1.43655 | 0.718277 | − | 0.695757i | \(-0.244931\pi\) | ||||
0.718277 | + | 0.695757i | \(0.244931\pi\) | |||||||
\(930\) | 4566.04 | 0.160996 | ||||||||
\(931\) | 4350.91 | 0.153164 | ||||||||
\(932\) | 19012.4 | 0.668212 | ||||||||
\(933\) | 12030.5 | 0.422145 | ||||||||
\(934\) | −12087.6 | −0.423467 | ||||||||
\(935\) | 15002.6 | 0.524748 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21008.3 | 0.732456 | 0.366228 | − | 0.930525i | \(-0.380649\pi\) | ||||
0.366228 | + | 0.930525i | \(0.380649\pi\) | |||||||
\(938\) | −3662.04 | −0.127473 | ||||||||
\(939\) | 21713.2 | 0.754614 | ||||||||
\(940\) | 20085.4 | 0.696929 | ||||||||
\(941\) | −4525.50 | −0.156777 | −0.0783885 | − | 0.996923i | \(-0.524977\pi\) | ||||
−0.0783885 | + | 0.996923i | \(0.524977\pi\) | |||||||
\(942\) | 25615.6 | 0.885989 | ||||||||
\(943\) | −69233.5 | −2.39083 | ||||||||
\(944\) | 3685.43 | 0.127066 | ||||||||
\(945\) | −5328.40 | −0.183421 | ||||||||
\(946\) | 46611.7 | 1.60198 | ||||||||
\(947\) | −27401.6 | −0.940267 | −0.470134 | − | 0.882595i | \(-0.655794\pi\) | ||||
−0.470134 | + | 0.882595i | \(0.655794\pi\) | |||||||
\(948\) | 5650.70 | 0.193593 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1396.82 | 0.0477040 | ||||||||
\(951\) | 23704.0 | 0.808259 | ||||||||
\(952\) | 904.129 | 0.0307805 | ||||||||
\(953\) | 26226.2 | 0.891449 | 0.445725 | − | 0.895170i | \(-0.352946\pi\) | ||||
0.445725 | + | 0.895170i | \(0.352946\pi\) | |||||||
\(954\) | 7312.49 | 0.248166 | ||||||||
\(955\) | −2886.08 | −0.0977921 | ||||||||
\(956\) | −9170.48 | −0.310245 | ||||||||
\(957\) | −72183.2 | −2.43819 | ||||||||
\(958\) | 16962.6 | 0.572063 | ||||||||
\(959\) | 7343.15 | 0.247260 | ||||||||
\(960\) | −2000.91 | −0.0672700 | ||||||||
\(961\) | −24458.6 | −0.821007 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5306.19 | −0.177559 | ||||||||
\(964\) | 7900.83 | 0.263972 | ||||||||
\(965\) | 22897.1 | 0.763817 | ||||||||
\(966\) | 4924.63 | 0.164024 | ||||||||
\(967\) | 20843.6 | 0.693158 | 0.346579 | − | 0.938021i | \(-0.387343\pi\) | ||||
0.346579 | + | 0.938021i | \(0.387343\pi\) | |||||||
\(968\) | 23540.6 | 0.781635 | ||||||||
\(969\) | −1318.47 | −0.0437103 | ||||||||
\(970\) | 22417.0 | 0.742026 | ||||||||
\(971\) | 32577.3 | 1.07668 | 0.538339 | − | 0.842729i | \(-0.319052\pi\) | ||||
0.538339 | + | 0.842729i | \(0.319052\pi\) | |||||||
\(972\) | −13440.1 | −0.443510 | ||||||||
\(973\) | −7043.20 | −0.232060 | ||||||||
\(974\) | 13246.7 | 0.435782 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6093.05 | −0.199830 | ||||||||
\(977\) | −43864.1 | −1.43637 | −0.718186 | − | 0.695851i | \(-0.755027\pi\) | ||||
−0.718186 | + | 0.695851i | \(0.755027\pi\) | |||||||
\(978\) | 3307.58 | 0.108144 | ||||||||
\(979\) | 24358.6 | 0.795204 | ||||||||
\(980\) | −11102.0 | −0.361879 | ||||||||
\(981\) | −18065.4 | −0.587955 | ||||||||
\(982\) | 32758.7 | 1.06453 | ||||||||
\(983\) | −14758.8 | −0.478875 | −0.239437 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239437 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(984\) | 12692.2 | 0.411193 | ||||||||
\(985\) | 16185.0 | 0.523549 | ||||||||
\(986\) | 16210.4 | 0.523575 | ||||||||
\(987\) | 9062.49 | 0.292262 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −57016.0 | −1.83317 | ||||||||
\(990\) | 15134.0 | 0.485848 | ||||||||
\(991\) | 48622.4 | 1.55857 | 0.779284 | − | 0.626671i | \(-0.215583\pi\) | ||||
0.779284 | + | 0.626671i | \(0.215583\pi\) | |||||||
\(992\) | −2336.74 | −0.0747900 | ||||||||
\(993\) | 12860.9 | 0.411006 | ||||||||
\(994\) | −554.220 | −0.0176849 | ||||||||
\(995\) | −20607.0 | −0.656569 | ||||||||
\(996\) | 3726.55 | 0.118554 | ||||||||
\(997\) | −18812.3 | −0.597586 | −0.298793 | − | 0.954318i | \(-0.596584\pi\) | ||||
−0.298793 | + | 0.954318i | \(0.596584\pi\) | |||||||
\(998\) | 15831.4 | 0.502138 | ||||||||
\(999\) | −17660.2 | −0.559305 |
(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 | 338.4.a.k.1.2 | yes | 3 | |
13.2 | odd | 12 | 338.4.e.h.147.5 | 12 | |||
13.3 | even | 3 | 338.4.c.k.191.2 | 6 | |||
13.4 | even | 6 | 338.4.c.l.315.2 | 6 | |||
13.5 | odd | 4 | 338.4.b.f.337.2 | 6 | |||
13.6 | odd | 12 | 338.4.e.h.23.2 | 12 | |||
13.7 | odd | 12 | 338.4.e.h.23.5 | 12 | |||
13.8 | odd | 4 | 338.4.b.f.337.5 | 6 | |||
13.9 | even | 3 | 338.4.c.k.315.2 | 6 | |||
13.10 | even | 6 | 338.4.c.l.191.2 | 6 | |||
13.11 | odd | 12 | 338.4.e.h.147.2 | 12 | |||
13.12 | even | 2 | 338.4.a.j.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
338.4.a.j.1.2 | ✓ | 3 | 13.12 | even | 2 | ||
338.4.a.k.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
338.4.b.f.337.2 | 6 | 13.5 | odd | 4 | |||
338.4.b.f.337.5 | 6 | 13.8 | odd | 4 | |||
338.4.c.k.191.2 | 6 | 13.3 | even | 3 | |||
338.4.c.k.315.2 | 6 | 13.9 | even | 3 | |||
338.4.c.l.191.2 | 6 | 13.10 | even | 6 | |||
338.4.c.l.315.2 | 6 | 13.4 | even | 6 | |||
338.4.e.h.23.2 | 12 | 13.6 | odd | 12 | |||
338.4.e.h.23.5 | 12 | 13.7 | odd | 12 | |||
338.4.e.h.147.2 | 12 | 13.11 | odd | 12 | |||
338.4.e.h.147.5 | 12 | 13.2 | odd | 12 |