Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 67x^{5} - 35x^{4} + 893x^{3} + 595x^{2} - 3064x - 2804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 544) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.97069\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.82555 | −1.89093 | −0.945464 | − | 0.325727i | \(-0.894391\pi\) | ||||
−0.945464 | + | 0.325727i | \(0.894391\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.78233 | 0.427745 | 0.213872 | − | 0.976862i | \(-0.431392\pi\) | ||||
0.213872 | + | 0.976862i | \(0.431392\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.4136 | −1.69618 | −0.848088 | − | 0.529855i | \(-0.822246\pi\) | ||||
−0.848088 | + | 0.529855i | \(0.822246\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 69.5414 | 2.57561 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.2655 | 0.692529 | 0.346265 | − | 0.938137i | \(-0.387450\pi\) | ||||
0.346265 | + | 0.938137i | \(0.387450\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.3323 | 1.54318 | 0.771591 | − | 0.636119i | \(-0.219461\pi\) | ||||
0.771591 | + | 0.636119i | \(0.219461\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −46.9890 | −0.808835 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.48512 | −0.102454 | −0.0512269 | − | 0.998687i | \(-0.516313\pi\) | ||||
−0.0512269 | + | 0.998687i | \(0.516313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 308.656 | 3.20735 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.5878 | 0.367963 | 0.183982 | − | 0.982930i | \(-0.441101\pi\) | ||||
0.183982 | + | 0.982930i | \(0.441101\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −102.129 | −0.817034 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −417.993 | −2.97936 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −222.207 | −1.42285 | −0.711426 | − | 0.702761i | \(-0.751951\pi\) | ||||
−0.711426 | + | 0.702761i | \(0.751951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −215.443 | −1.24822 | −0.624108 | − | 0.781338i | \(-0.714537\pi\) | ||||
−0.624108 | + | 0.781338i | \(0.714537\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −248.247 | −1.30952 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −150.230 | −0.725531 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 310.596 | 1.38005 | 0.690023 | − | 0.723787i | \(-0.257600\pi\) | ||||
0.690023 | + | 0.723787i | \(0.257600\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −710.704 | −2.91805 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −387.002 | −1.47414 | −0.737069 | − | 0.675818i | \(-0.763791\pi\) | ||||
−0.737069 | + | 0.675818i | \(0.763791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 463.310 | 1.64312 | 0.821560 | − | 0.570122i | \(-0.193104\pi\) | ||||
0.821560 | + | 0.570122i | \(0.193104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 332.570 | 1.10170 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 74.4547 | 0.231071 | 0.115535 | − | 0.993303i | \(-0.463142\pi\) | ||||
0.115535 | + | 0.993303i | \(0.463142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 643.817 | 1.87702 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 167.034 | 0.458617 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −270.732 | −0.701659 | −0.350829 | − | 0.936439i | \(-0.614100\pi\) | ||||
−0.350829 | + | 0.936439i | \(0.614100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 120.828 | 0.296226 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 83.3710 | 0.193733 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 385.027 | 0.849598 | 0.424799 | − | 0.905288i | \(-0.360345\pi\) | ||||
0.424799 | + | 0.905288i | \(0.360345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −724.989 | −1.52173 | −0.760863 | − | 0.648913i | \(-0.775224\pi\) | ||||
−0.760863 | + | 0.648913i | \(0.775224\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2184.55 | −4.36869 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 345.917 | 0.660088 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −532.662 | −0.971269 | −0.485634 | − | 0.874162i | \(-0.661411\pi\) | ||||
−0.485634 | + | 0.874162i | \(0.661411\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −398.798 | −0.695792 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 341.675 | 0.571118 | 0.285559 | − | 0.958361i | \(-0.407821\pi\) | ||||
0.285559 | + | 0.958361i | \(0.407821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −493.586 | −0.791368 | −0.395684 | − | 0.918387i | \(-0.629492\pi\) | ||||
−0.395684 | + | 0.918387i | \(0.629492\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1003.48 | 1.54495 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −793.680 | −1.17465 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −260.141 | −0.370482 | −0.185241 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185241 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2229.39 | 3.05815 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 137.179 | 0.181414 | 0.0907068 | − | 0.995878i | \(-0.471087\pi\) | ||||
0.0907068 | + | 0.995878i | \(0.471087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −81.2996 | −0.103743 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2183.30 | 2.69051 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 57.3408 | 0.0682934 | 0.0341467 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341467 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2272.22 | −2.61751 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2116.84 | 2.36029 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −40.5787 | −0.0438240 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 484.200 | 0.506836 | 0.253418 | − | 0.967357i | \(-0.418445\pi\) | ||||
0.253418 | + | 0.967357i | \(0.418445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1757.00 | 1.78368 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −576.967 | −0.568419 | −0.284210 | − | 0.958762i | \(-0.591731\pi\) | ||||
−0.284210 | + | 0.958762i | \(0.591731\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 343.211 | 0.328326 | 0.164163 | − | 0.986433i | \(-0.447508\pi\) | ||||
0.164163 | + | 0.986433i | \(0.447508\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1476.10 | 1.37193 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 188.330 | 0.170154 | 0.0850772 | − | 0.996374i | \(-0.472886\pi\) | ||||
0.0850772 | + | 0.996374i | \(0.472886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 373.234 | 0.327976 | 0.163988 | − | 0.986462i | \(-0.447564\pi\) | ||||
0.163988 | + | 0.986462i | \(0.447564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3051.78 | −2.60957 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1798.43 | 1.49719 | 0.748595 | − | 0.663028i | \(-0.230729\pi\) | ||||
0.748595 | + | 0.663028i | \(0.230729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 194.105 | 0.157394 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5030.09 | 3.97463 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 534.032 | 0.411383 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −692.657 | −0.520403 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3802.51 | 2.78749 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1086.21 | −0.777227 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1391.93 | −0.972546 | −0.486273 | − | 0.873807i | \(-0.661644\pi\) | ||||
−0.486273 | + | 0.873807i | \(0.661644\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4552.28 | −3.10702 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2323.79 | 1.54985 | 0.774927 | − | 0.632051i | \(-0.217787\pi\) | ||||
0.774927 | + | 0.632051i | \(0.217787\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 266.549 | 0.173780 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1998.98 | −1.27441 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2996.64 | 1.86876 | 0.934381 | − | 0.356276i | \(-0.115954\pi\) | ||||
0.934381 | + | 0.356276i | \(0.115954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −95.2438 | −0.0581185 | −0.0290592 | − | 0.999578i | \(-0.509251\pi\) | ||||
−0.0290592 | + | 0.999578i | \(0.509251\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −731.558 | −0.436939 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1827.51 | 1.06870 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1062.67 | −0.608618 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6325.85 | −3.54930 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 927.943 | 0.510202 | 0.255101 | − | 0.966914i | \(-0.417891\pi\) | ||||
0.255101 | + | 0.966914i | \(0.417891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −968.271 | −0.521833 | −0.260916 | − | 0.965361i | \(-0.584025\pi\) | ||||
−0.260916 | + | 0.965361i | \(0.584025\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1182.20 | −0.624677 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1030.32 | −0.533918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −586.667 | −0.298224 | −0.149112 | − | 0.988820i | \(-0.547641\pi\) | ||||
−0.149112 | + | 0.988820i | \(0.547641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2660.09 | 1.32679 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1275.01 | −0.624131 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1370.56 | 0.658594 | 0.329297 | − | 0.944226i | \(-0.393188\pi\) | ||||
0.329297 | + | 0.944226i | \(0.393188\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1187.20 | −0.560142 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 440.160 | 0.203956 | 0.101978 | − | 0.994787i | \(-0.467483\pi\) | ||||
0.101978 | + | 0.994787i | \(0.467483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3034.96 | 1.38141 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −590.068 | −0.263881 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −507.211 | −0.222905 | −0.111453 | − | 0.993770i | \(-0.535550\pi\) | ||||
−0.111453 | + | 0.993770i | \(0.535550\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3208.25 | 1.38583 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3783.10 | −1.60653 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4072.11 | 1.70036 | 0.850179 | − | 0.526494i | \(-0.176494\pi\) | ||||
0.850179 | + | 0.526494i | \(0.176494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2942.09 | 1.20820 | 0.604098 | − | 0.796910i | \(-0.293533\pi\) | ||||
0.604098 | + | 0.796910i | \(0.293533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7123.41 | 2.87747 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1485.37 | 0.590308 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −429.513 | −0.167963 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13130.7 | 5.05353 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3537.08 | −1.33997 | −0.669985 | − | 0.742375i | \(-0.733699\pi\) | ||||
−0.669985 | + | 0.742375i | \(0.733699\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3147.89 | 1.17404 | 0.587021 | − | 0.809572i | \(-0.300301\pi\) | ||||
0.587021 | + | 0.809572i | \(0.300301\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3398.82 | −1.24818 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3126.43 | −1.13070 | −0.565352 | − | 0.824850i | \(-0.691260\pi\) | ||||
−0.565352 | + | 0.824850i | \(0.691260\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4072.16 | 1.45059 | 0.725296 | − | 0.688437i | \(-0.241703\pi\) | ||||
0.725296 | + | 0.688437i | \(0.241703\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5233.69 | 1.83660 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6980.32 | 2.41341 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1850.77 | −0.630555 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2822.54 | 0.947729 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −214.380 | −0.0709522 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 666.790 | 0.217553 | 0.108777 | − | 0.994066i | \(-0.465307\pi\) | ||||
0.108777 | + | 0.994066i | \(0.465307\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3357.15 | −1.07994 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2215.70 | 0.702836 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6767.84 | 2.11719 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4849.76 | 1.49642 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1229.65 | −0.374277 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2608.78 | −0.783395 | −0.391697 | − | 0.920094i | \(-0.628112\pi\) | ||||
−0.391697 | + | 0.920094i | \(0.628112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7102.22 | −2.10436 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1978.70 | −0.578551 | −0.289276 | − | 0.957246i | \(-0.593414\pi\) | ||||
−0.289276 | + | 0.957246i | \(0.593414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1969.14 | 0.568229 | 0.284115 | − | 0.958790i | \(-0.408300\pi\) | ||||
0.284115 | + | 0.958790i | \(0.408300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7798.34 | 2.22118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1037.21 | −0.291631 | −0.145815 | − | 0.989312i | \(-0.546581\pi\) | ||||
−0.145815 | + | 0.989312i | \(0.546581\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 356.067 | 0.0988394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2556.02 | 0.700555 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6315.68 | −1.70932 | −0.854659 | − | 0.519189i | \(-0.826234\pi\) | ||||
−0.854659 | + | 0.519189i | \(0.826234\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2715.86 | −0.725910 | −0.362955 | − | 0.931807i | \(-0.618232\pi\) | ||||
−0.362955 | + | 0.931807i | \(0.618232\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10619.2 | −2.80338 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3078.94 | 0.802884 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −613.748 | −0.158105 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1347.86 | −0.343040 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1412.36 | 0.355168 | 0.177584 | − | 0.984106i | \(-0.443172\pi\) | ||||
0.177584 | + | 0.984106i | \(0.443172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1025.47 | 0.254825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 798.814 | 0.196171 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3979.51 | 0.965895 | 0.482947 | − | 0.875649i | \(-0.339566\pi\) | ||||
0.482947 | + | 0.875649i | \(0.339566\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9756.96 | −2.34080 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15452.6 | −3.66471 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2681.54 | 0.628710 | 0.314355 | − | 0.949305i | \(-0.398212\pi\) | ||||
0.314355 | + | 0.949305i | \(0.398212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1294.73 | −0.300131 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −563.405 | −0.129138 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3601.95 | 0.816412 | 0.408206 | − | 0.912890i | \(-0.366154\pi\) | ||||
0.408206 | + | 0.912890i | \(0.366154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1251.18 | −0.280458 | −0.140229 | − | 0.990119i | \(-0.544784\pi\) | ||||
−0.140229 | + | 0.990119i | \(0.544784\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22325.8 | 4.94952 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2580.34 | −0.565820 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2211.76 | 0.479754 | 0.239877 | − | 0.970803i | \(-0.422893\pi\) | ||||
0.239877 | + | 0.970803i | \(0.422893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14982.2 | −3.21491 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5455.27 | 1.15813 | 0.579064 | − | 0.815282i | \(-0.303418\pi\) | ||||
0.579064 | + | 0.815282i | \(0.303418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1640.92 | −0.344674 | −0.172337 | − | 0.985038i | \(-0.555132\pi\) | ||||
−0.172337 | + | 0.985038i | \(0.555132\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 398.708 | 0.0828681 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12157.2 | 2.50040 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4757.53 | −0.958390 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 949.282 | 0.189275 | 0.0946376 | − | 0.995512i | \(-0.469831\pi\) | ||||
0.0946376 | + | 0.995512i | \(0.469831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1841.33 | 0.363411 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10560.8 | −2.06330 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2935.81 | 0.567834 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14554.3 | −2.78702 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5669.02 | 1.07484 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3467.14 | −0.650910 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3433.54 | −0.638314 | −0.319157 | − | 0.947702i | \(-0.603400\pi\) | ||||
−0.319157 | + | 0.947702i | \(0.603400\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3372.23 | −0.620840 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4219.73 | −0.769386 | −0.384693 | − | 0.923044i | \(-0.625693\pi\) | ||||
−0.384693 | + | 0.923044i | \(0.625693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10302.4 | 1.86047 | 0.930233 | − | 0.366969i | \(-0.119605\pi\) | ||||
0.930233 | + | 0.366969i | \(0.119605\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10447.2 | −1.86868 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11088.2 | 1.96459 | 0.982295 | − | 0.187338i | \(-0.0599861\pi\) | ||||
0.982295 | + | 0.187338i | \(0.0599861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5614.15 | −0.985367 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1850.44 | −0.321750 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 144.247 | 0.0248487 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7387.24 | −1.26083 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3667.23 | −0.620178 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2338.89 | −0.391937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4136.16 | 0.686839 | 0.343419 | − | 0.939182i | \(-0.388415\pi\) | ||||
0.343419 | + | 0.939182i | \(0.388415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21599.3 | 3.55446 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2547.37 | −0.415455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10177.9 | −1.64518 | −0.822589 | − | 0.568636i | \(-0.807471\pi\) | ||||
−0.822589 | + | 0.568636i | \(0.807471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17670.6 | −2.83108 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5443.26 | −0.864426 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9449.74 | −1.48757 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1907.18 | −0.297621 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7857.54 | −1.21560 | −0.607802 | − | 0.794088i | \(-0.707949\pi\) | ||||
−0.607802 | + | 0.794088i | \(0.707949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9125.05 | −1.39958 | −0.699789 | − | 0.714349i | \(-0.746723\pi\) | ||||
−0.699789 | + | 0.714349i | \(0.746723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30234.4 | −4.59770 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6800.32 | 1.02534 | 0.512669 | − | 0.858586i | \(-0.328657\pi\) | ||||
0.512669 | + | 0.858586i | \(0.328657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1634.00 | 0.244293 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5247.16 | −0.777896 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5094.04 | −0.748894 | −0.374447 | − | 0.927248i | \(-0.622168\pi\) | ||||
−0.374447 | + | 0.927248i | \(0.622168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6787.00 | −0.989503 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6805.73 | 0.984045 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2360.49 | −0.338504 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12242.5 | 1.74129 | 0.870646 | − | 0.491909i | \(-0.163701\pi\) | ||||
0.870646 | + | 0.491909i | \(0.163701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26912.7 | −3.79680 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8504.68 | 1.19014 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2538.51 | 0.352384 | 0.176192 | − | 0.984356i | \(-0.443622\pi\) | ||||
0.176192 | + | 0.984356i | \(0.443622\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10672.6 | 1.46968 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16072.7 | −2.19572 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10337.5 | 1.40106 | 0.700528 | − | 0.713625i | \(-0.252948\pi\) | ||||
0.700528 | + | 0.713625i | \(0.252948\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13676.4 | 1.83902 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6184.48 | 0.825097 | 0.412549 | − | 0.910936i | \(-0.364639\pi\) | ||||
0.412549 | + | 0.910936i | \(0.364639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3795.64 | −0.502451 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32219.3 | 4.23203 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1150.38 | 0.149940 | 0.0749699 | − | 0.997186i | \(-0.476114\pi\) | ||||
0.0749699 | + | 0.997186i | \(0.476114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −689.993 | −0.0892442 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22832.6 | −2.93066 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1244.08 | −0.158472 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5511.93 | −0.696816 | −0.348408 | − | 0.937343i | \(-0.613278\pi\) | ||||
−0.348408 | + | 0.937343i | \(0.613278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2618.99 | −0.328605 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1138.27 | −0.141752 | −0.0708761 | − | 0.997485i | \(-0.522580\pi\) | ||||
−0.0708761 | + | 0.997485i | \(0.522580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15583.5 | −1.92622 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10661.7 | 1.30811 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7847.36 | 0.955722 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1848.76 | 0.223510 | 0.111755 | − | 0.993736i | \(-0.464353\pi\) | ||||
0.111755 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29443.6 | −3.53369 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12095.1 | −1.44107 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 656.035 | 0.0775987 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 935.822 | 0.109898 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2951.99 | −0.344187 | −0.172093 | − | 0.985081i | \(-0.555053\pi\) | ||||
−0.172093 | + | 0.985081i | \(0.555053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2836.80 | −0.328402 | −0.164201 | − | 0.986427i | \(-0.552504\pi\) | ||||
−0.164201 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5177.69 | 0.595148 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1736.20 | 0.198160 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22774.5 | 2.58112 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17956.3 | −2.02083 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2330.19 | −0.260420 | −0.130210 | − | 0.991486i | \(-0.541565\pi\) | ||||
−0.130210 | + | 0.991486i | \(0.541565\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6900.15 | −0.765820 | −0.382910 | − | 0.923786i | \(-0.625078\pi\) | ||||
−0.382910 | + | 0.923786i | \(0.625078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10441.3 | 1.15085 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −344.393 | −0.0376992 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11428.6 | 1.24250 | 0.621248 | − | 0.783614i | \(-0.286626\pi\) | ||||
0.621248 | + | 0.783614i | \(0.286626\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44771.9 | 4.83446 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13566.6 | 1.45501 | 0.727503 | − | 0.686105i | \(-0.240681\pi\) | ||||
0.727503 | + | 0.686105i | \(0.240681\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 274.223 | 0.0292121 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9117.55 | −0.964755 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7070.48 | −0.743154 | −0.371577 | − | 0.928402i | \(-0.621183\pi\) | ||||
−0.371577 | + | 0.928402i | \(0.621183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9777.79 | −1.02088 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9513.80 | 0.986749 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10866.5 | −1.11963 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11888.1 | 1.21686 | 0.608429 | − | 0.793608i | \(-0.291800\pi\) | ||||
0.608429 | + | 0.793608i | \(0.291800\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7105.88 | 0.722602 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15019.0 | 1.51737 | 0.758683 | − | 0.651460i | \(-0.225843\pi\) | ||||
0.758683 | + | 0.651460i | \(0.225843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8898.99 | 0.893242 | 0.446621 | − | 0.894723i | \(-0.352627\pi\) | ||||
0.446621 | + | 0.894723i | \(0.352627\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10123.5 | 1.00960 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16088.7 | 1.59421 | 0.797105 | − | 0.603841i | \(-0.206364\pi\) | ||||
0.797105 | + | 0.603841i | \(0.206364\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16732.8 | 1.64744 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5764.32 | 0.563919 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11705.7 | 1.13791 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 866.580 | 0.0837082 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18827.1 | −1.80720 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20715.7 | −1.97604 | −0.988020 | − | 0.154329i | \(-0.950679\pi\) | ||||
−0.988020 | + | 0.154329i | \(0.950679\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22466.1 | 2.12966 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12527.7 | 1.18019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2315.61 | 0.216796 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8182.89 | 0.761401 | 0.380700 | − | 0.924698i | \(-0.375683\pi\) | ||||
0.380700 | + | 0.924698i | \(0.375683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13466.5 | −1.24535 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2500.68 | −0.229845 | −0.114922 | − | 0.993374i | \(-0.536662\pi\) | ||||
−0.114922 | + | 0.993374i | \(0.536662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3777.51 | 0.345093 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8402.54 | 0.762962 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10733.3 | −0.968718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17638.8 | 1.58241 | 0.791203 | − | 0.611553i | \(-0.209455\pi\) | ||||
0.791203 | + | 0.611553i | \(0.209455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4324.82 | −0.385666 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5199.12 | −0.460870 | −0.230435 | − | 0.973088i | \(-0.574015\pi\) | ||||
−0.230435 | + | 0.973088i | \(0.574015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2759.25 | −0.243138 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29820.1 | −2.61215 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14573.8 | −1.26910 | −0.634549 | − | 0.772883i | \(-0.718814\pi\) | ||||
−0.634549 | + | 0.772883i | \(0.718814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15505.3 | 1.34230 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3546.72 | 0.305247 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1641.35 | 0.140440 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1881.13 | 0.160023 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4983.63 | 0.421497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6274.38 | 0.527612 | 0.263806 | − | 0.964576i | \(-0.415022\pi\) | ||||
0.263806 | + | 0.964576i | \(0.415022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12818.6 | 1.07174 | 0.535868 | − | 0.844302i | \(-0.319985\pi\) | ||||
0.535868 | + | 0.844302i | \(0.319985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −31522.8 | −2.62051 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3662.53 | 0.302737 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10519.6 | −0.864603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26775.3 | 2.18823 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27992.8 | −2.27486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 900.656 | 0.0727827 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40010.8 | −3.21525 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16266.3 | 1.29989 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6380.97 | 0.507097 | 0.253549 | − | 0.967323i | \(-0.418402\pi\) | ||||
0.253549 | + | 0.967323i | \(0.418402\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28907.6 | −2.28461 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1784.93 | 0.140290 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19317.0 | 1.50994 | 0.754968 | − | 0.655761i | \(-0.227652\pi\) | ||||
0.754968 | + | 0.655761i | \(0.227652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −50416.8 | −3.91937 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1885.45 | 0.145777 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8171.96 | 0.628403 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14594.6 | −1.11623 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15712.8 | 1.19528 | 0.597642 | − | 0.801763i | \(-0.296104\pi\) | ||||
0.597642 | + | 0.801763i | \(0.296104\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33512.3 | 2.53563 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4220.20 | 0.317606 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24974.0 | 1.86950 | 0.934751 | − | 0.355304i | \(-0.115623\pi\) | ||||
0.934751 | + | 0.355304i | \(0.115623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8600.71 | 0.640415 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −70033.3 | −5.18717 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5049.16 | −0.372007 | −0.186003 | − | 0.982549i | \(-0.559554\pi\) | ||||
−0.186003 | + | 0.982549i | \(0.559554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17697.6 | 1.29706 | 0.648530 | − | 0.761189i | \(-0.275384\pi\) | ||||
0.648530 | + | 0.761189i | \(0.275384\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34753.8 | 2.53379 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4145.21 | −0.300639 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19390.5 | −1.39903 | −0.699513 | − | 0.714620i | \(-0.746600\pi\) | ||||
−0.699513 | + | 0.714620i | \(0.746600\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30929.7 | −2.22003 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4309.29 | −0.307710 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6840.17 | −0.485919 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24055.6 | 1.70013 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15898.5 | 1.11789 | 0.558946 | − | 0.829204i | \(-0.311206\pi\) | ||||
0.558946 | + | 0.829204i | \(0.311206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1828.06 | 0.127884 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30718.9 | 2.13808 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5849.37 | 0.405067 | 0.202533 | − | 0.979275i | \(-0.435082\pi\) | ||||
0.202533 | + | 0.979275i | \(0.435082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2553.92 | 0.175967 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −40011.2 | −2.74297 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2126.73 | 0.145068 | 0.0725340 | − | 0.997366i | \(-0.476891\pi\) | ||||
0.0725340 | + | 0.997366i | \(0.476891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5400.05 | −0.366510 | −0.183255 | − | 0.983065i | \(-0.558663\pi\) | ||||
−0.183255 | + | 0.983065i | \(0.558663\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37042.1 | −2.50161 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3312.51 | −0.222600 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8805.60 | 0.588811 | 0.294406 | − | 0.955681i | \(-0.404878\pi\) | ||||
0.294406 | + | 0.955681i | \(0.404878\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −68585.5 | −4.56359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5385.48 | 0.356584 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6701.54 | 0.441554 | 0.220777 | − | 0.975324i | \(-0.429141\pi\) | ||||
0.220777 | + | 0.975324i | \(0.429141\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18184.9 | 1.19233 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 372.923 | 0.0243328 | 0.0121664 | − | 0.999926i | \(-0.496127\pi\) | ||||
0.0121664 | + | 0.999926i | \(0.496127\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24575.2 | −1.59573 | −0.797867 | − | 0.602834i | \(-0.794038\pi\) | ||||
−0.797867 | + | 0.602834i | \(0.794038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16965.4 | −1.09630 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1801.28 | −0.115838 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7571.56 | 0.484580 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2106.41 | 0.134165 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5280.14 | −0.334710 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1434.70 | 0.0905144 | 0.0452572 | − | 0.998975i | \(-0.485589\pi\) | ||||
0.0452572 | + | 0.998975i | \(0.485589\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6551.58 | −0.411377 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6656.65 | −0.416002 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46568.7 | 2.89658 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23760.6 | 1.47098 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15095.1 | 0.930138 | 0.465069 | − | 0.885274i | \(-0.346029\pi\) | ||||
0.465069 | + | 0.885274i | \(0.346029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24785.5 | −1.52013 | −0.760067 | − | 0.649845i | \(-0.774834\pi\) | ||||
−0.760067 | + | 0.649845i | \(0.774834\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21770.5 | −1.32901 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5515.74 | −0.335157 | −0.167578 | − | 0.985859i | \(-0.553595\pi\) | ||||
−0.167578 | + | 0.985859i | \(0.553595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9727.89 | 0.588371 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −66497.8 | −4.00346 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2126.79 | 0.127455 | 0.0637273 | − | 0.997967i | \(-0.479701\pi\) | ||||
0.0637273 | + | 0.997967i | \(0.479701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11113.2 | 0.662942 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34324.7 | −2.03826 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5366.36 | −0.317213 | −0.158607 | − | 0.987342i | \(-0.550700\pi\) | ||||
−0.158607 | + | 0.987342i | \(0.550700\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 295.485 | 0.0173873 | 0.00869367 | − | 0.999962i | \(-0.497233\pi\) | ||||
0.00869367 | + | 0.999962i | \(0.497233\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12082.0 | 0.707730 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1274.72 | 0.0743333 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9018.89 | −0.523557 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25632.7 | 1.48134 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18317.2 | −1.05384 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12772.8 | 0.731585 | 0.365792 | − | 0.930696i | \(-0.380798\pi\) | ||||
0.365792 | + | 0.930696i | \(0.380798\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 42689.3 | 2.43424 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −325.253 | −0.0184645 | −0.00923226 | − | 0.999957i | \(-0.502939\pi\) | ||||
−0.00923226 | + | 0.999957i | \(0.502939\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15210.5 | −0.859683 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19441.8 | 1.09400 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17438.3 | −0.976954 | −0.488477 | − | 0.872577i | \(-0.662447\pi\) | ||||
−0.488477 | + | 0.872577i | \(0.662447\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14330.9 | 0.799353 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19347.9 | −1.07448 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19582.7 | −1.08279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20220.1 | −1.11318 | −0.556592 | − | 0.830786i | \(-0.687891\pi\) | ||||
−0.556592 | + | 0.830786i | \(0.687891\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −55193.6 | −3.02544 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −455.487 | −0.0248599 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6579.04 | 0.357531 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10191.2 | 0.551453 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10335.5 | −0.556869 | −0.278435 | − | 0.960455i | \(-0.589816\pi\) | ||||
−0.278435 | + | 0.960455i | \(0.589816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2635.45 | −0.141391 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3498.56 | −0.186898 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18124.6 | 0.964140 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36807.0 | 1.94967 | 0.974835 | − | 0.222927i | \(-0.0715611\pi\) | ||||
0.974835 | + | 0.222927i | \(0.0715611\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18090.5 | −0.954217 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8744.36 | −0.459297 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8739.75 | 0.457130 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 62055.0 | 3.23220 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6204.20 | −0.321805 | −0.160902 | − | 0.986970i | \(-0.551440\pi\) | ||||
−0.160902 | + | 0.986970i | \(0.551440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10781.5 | −0.556899 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26684.9 | 1.37264 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22693.8 | 1.16252 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16362.3 | 0.834726 | 0.417363 | − | 0.908740i | \(-0.362954\pi\) | ||||
0.417363 | + | 0.908740i | \(0.362954\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 44145.9 | 2.24284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7876.27 | −0.398515 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15333.2 | 0.772640 | 0.386320 | − | 0.922365i | \(-0.373746\pi\) | ||||
0.386320 | + | 0.922365i | \(0.373746\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30252.3 | −1.51820 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13457.9 | −0.672632 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1454.83 | 0.0724178 | 0.0362089 | − | 0.999344i | \(-0.488472\pi\) | ||||
0.0362089 | + | 0.999344i | \(0.488472\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6030.41 | 0.298965 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21843.5 | 1.07855 | 0.539274 | − | 0.842130i | \(-0.318699\pi\) | ||||
0.539274 | + | 0.842130i | \(0.318699\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4437.73 | 0.218236 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9539.61 | 0.467251 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5916.12 | −0.288612 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −248.492 | −0.0120741 | −0.00603703 | − | 0.999982i | \(-0.501922\pi\) | ||||
−0.00603703 | + | 0.999982i | \(0.501922\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13877.2 | −0.671597 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4630.59 | −0.223211 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13766.8 | 0.660980 | 0.330490 | − | 0.943810i | \(-0.392786\pi\) | ||||
0.330490 | + | 0.943810i | \(0.392786\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10075.8 | −0.481856 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10363.2 | −0.493646 | −0.246823 | − | 0.969061i | \(-0.579387\pi\) | ||||
−0.246823 | + | 0.969061i | \(0.579387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11724.6 | −0.556305 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5653.69 | −0.267202 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27849.9 | 1.31108 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36605.3 | 1.71654 | 0.858271 | − | 0.513197i | \(-0.171539\pi\) | ||||
0.858271 | + | 0.513197i | \(0.171539\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39100.9 | −1.82644 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5876.31 | 0.273423 | 0.136712 | − | 0.990611i | \(-0.456347\pi\) | ||||
0.136712 | + | 0.990611i | \(0.456347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22003.0 | 1.01983 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 95867.5 | 4.42629 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3283.76 | 0.151031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8632.58 | 0.395516 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 92880.8 | 4.23920 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2805.63 | −0.127564 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8932.04 | 0.404565 | 0.202283 | − | 0.979327i | \(-0.435164\pi\) | ||||
0.202283 | + | 0.979327i | \(0.435164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26347.6 | −1.18885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56495.4 | −2.53950 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −52440.1 | −2.34830 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12721.4 | 0.567526 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3732.65 | 0.165894 | 0.0829468 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829468 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1265.73 | −0.0560429 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3987.56 | 0.175897 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12470.7 | −0.548046 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6097.53 | −0.266969 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35391.2 | −1.54378 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23045.5 | −1.00153 | −0.500764 | − | 0.865584i | \(-0.666948\pi\) | ||||
−0.500764 | + | 0.865584i | \(0.666948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36697.8 | 1.58894 | 0.794471 | − | 0.607301i | \(-0.207748\pi\) | ||||
0.794471 | + | 0.607301i | \(0.207748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12293.6 | 0.530325 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6554.49 | 0.281710 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3931.24 | −0.168344 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −158013. | −6.74168 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13102.3 | 0.556970 | 0.278485 | − | 0.960441i | \(-0.410168\pi\) | ||||
0.278485 | + | 0.960441i | \(0.410168\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3392.07 | 0.143670 | 0.0718348 | − | 0.997417i | \(-0.477115\pi\) | ||||
0.0718348 | + | 0.997417i | \(0.477115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25353.3 | 1.06993 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18548.1 | −0.779904 | −0.389952 | − | 0.920835i | \(-0.627508\pi\) | ||||
−0.389952 | + | 0.920835i | \(0.627508\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31374.4 | 1.31445 | 0.657224 | − | 0.753695i | \(-0.271730\pi\) | ||||
0.657224 | + | 0.753695i | \(0.271730\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21731.8 | −0.907181 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10944.9 | −0.455243 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2104.99 | 0.0872410 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 90053.6 | 3.71889 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30785.1 | 1.26677 | 0.633386 | − | 0.773836i | \(-0.281665\pi\) | ||||
0.633386 | + | 0.773836i | \(0.281665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24986.8 | 1.02451 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −53601.0 | −2.18994 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14514.2 | 0.590891 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21758.9 | 0.882696 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16123.0 | 0.651754 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12606.4 | 0.507806 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41137.6 | −1.65126 | −0.825630 | − | 0.564212i | \(-0.809180\pi\) | ||||
−0.825630 | + | 0.564212i | \(0.809180\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2821.90 | −0.112874 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19075.8 | −0.760345 | −0.380172 | − | 0.924916i | \(-0.624135\pi\) | ||||
−0.380172 | + | 0.924916i | \(0.624135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8716.76 | −0.346231 | −0.173115 | − | 0.984902i | \(-0.555383\pi\) | ||||
−0.173115 | + | 0.984902i | \(0.555383\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −119451. | −4.72807 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35845.2 | −1.41389 | −0.706943 | − | 0.707270i | \(-0.749926\pi\) | ||||
−0.706943 | + | 0.707270i | \(0.749926\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2425.65 | −0.0953465 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2839.58 | −0.111231 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6572.57 | −0.256570 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38528.6 | −1.49884 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33672.0 | 1.30541 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34121.7 | 1.31831 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20973.5 | −0.807556 | −0.403778 | − | 0.914857i | \(-0.632303\pi\) | ||||
−0.403778 | + | 0.914857i | \(0.632303\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9327.21 | −0.357906 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26246.8 | −1.00372 | −0.501861 | − | 0.864948i | \(-0.667351\pi\) | ||||
−0.501861 | + | 0.864948i | \(0.667351\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36750.5 | −1.40063 | −0.700313 | − | 0.713836i | \(-0.746956\pi\) | ||||
−0.700313 | + | 0.713836i | \(0.746956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18092.1 | −0.687184 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11807.1 | −0.446950 | −0.223475 | − | 0.974710i | \(-0.571740\pi\) | ||||
−0.223475 | + | 0.974710i | \(0.571740\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43725.4 | 1.64961 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 56326.6 | 2.11786 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −631.757 | −0.0236741 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19474.2 | 0.727319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28846.0 | −1.07373 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 47872.8 | 1.77603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4602.45 | 0.170177 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 143004. | 5.27006 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14070.0 | 0.516800 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21549.1 | 0.788894 | 0.394447 | − | 0.918919i | \(-0.370936\pi\) | ||||
0.394447 | + | 0.918919i | \(0.370936\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40123.1 | −1.46403 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8561.19 | 0.311356 | 0.155678 | − | 0.987808i | \(-0.450244\pi\) | ||||
0.155678 | + | 0.987808i | \(0.450244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3465.89 | 0.125634 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34066.5 | 1.23082 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −72998.8 | −2.62883 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18999.2 | −0.681965 | −0.340983 | − | 0.940070i | \(-0.610760\pi\) | ||||
−0.340983 | + | 0.940070i | \(0.610760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33736.4 | 1.20701 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24714.2 | 0.881339 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31721.0 | −1.12755 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23867.4 | 0.845639 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34845.6 | 1.23062 | 0.615311 | − | 0.788284i | \(-0.289030\pi\) | ||||
0.615311 | + | 0.788284i | \(0.289030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5462.86 | −0.192307 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41461.2 | 1.45485 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2054.07 | −0.0718453 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34508.0 | −1.20313 | −0.601563 | − | 0.798825i | \(-0.705455\pi\) | ||||
−0.601563 | + | 0.798825i | \(0.705455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −101227. | −3.51801 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 485.186 | 0.0168083 | 0.00840416 | − | 0.999965i | \(-0.497325\pi\) | ||||
0.00840416 | + | 0.999965i | \(0.497325\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15707.6 | −0.542428 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 62795.3 | 2.16162 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28153.8 | 0.966077 | 0.483038 | − | 0.875599i | \(-0.339533\pi\) | ||||
0.483038 | + | 0.875599i | \(0.339533\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35702.2 | −1.22123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −108948. | −3.71490 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47163.6 | −1.60313 | −0.801563 | − | 0.597910i | \(-0.795998\pi\) | ||||
−0.801563 | + | 0.597910i | \(0.795998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16915.5 | −0.573165 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 55162.1 | 1.86326 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −94135.4 | −3.16975 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16624.6 | 0.558041 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13096.7 | 0.438251 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15054.3 | 0.502190 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33489.3 | 1.11370 | 0.556848 | − | 0.830615i | \(-0.312011\pi\) | ||||
0.556848 | + | 0.830615i | \(0.312011\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1417.31 | −0.0469871 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18478.6 | −0.610717 | −0.305358 | − | 0.952238i | \(-0.598776\pi\) | ||||
−0.305358 | + | 0.952238i | \(0.598776\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2991.95 | 0.0985792 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 72583.7 | 2.38414 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38784.3 | 1.27003 | 0.635015 | − | 0.772500i | \(-0.280994\pi\) | ||||
0.635015 | + | 0.772500i | \(0.280994\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1448.74 | 0.0472952 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25955.2 | 0.844737 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11294.6 | −0.366473 | −0.183237 | − | 0.983069i | \(-0.558657\pi\) | ||||
−0.183237 | + | 0.983069i | \(0.558657\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14951.6 | −0.483653 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22980.9 | 0.741125 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18804.8 | 0.604607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25813.5 | −0.827439 | −0.413719 | − | 0.910404i | \(-0.635771\pi\) | ||||
−0.413719 | + | 0.910404i | \(0.635771\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40640.0 | −1.29876 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19474.4 | 0.620483 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8447.32 | 0.268334 | 0.134167 | − | 0.990959i | \(-0.457164\pi\) | ||||
0.134167 | + | 0.990959i | \(0.457164\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −129827. | −4.11166 |
(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 | 1088.4.a.bh.1.1 | 7 | ||
4.3 | odd | 2 | 1088.4.a.bg.1.7 | 7 | |||
8.3 | odd | 2 | 544.4.a.k.1.1 | ✓ | 7 | ||
8.5 | even | 2 | 544.4.a.l.1.7 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
544.4.a.k.1.1 | ✓ | 7 | 8.3 | odd | 2 | ||
544.4.a.l.1.7 | yes | 7 | 8.5 | even | 2 | ||
1088.4.a.bg.1.7 | 7 | 4.3 | odd | 2 | |||
1088.4.a.bh.1.1 | 7 | 1.1 | even | 1 | trivial |