Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1573,4,Mod(1,1573)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1573, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1573.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1573 = 11^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1573.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: | \(92.8100044390\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 6 x^{14} - 69 x^{13} + 418 x^{12} + 1806 x^{11} - 10742 x^{10} - 24098 x^{9} + 129758 x^{8} + \cdots + 47232 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-3.04830\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1573.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.04830 | 1.07774 | 0.538868 | − | 0.842390i | \(-0.318852\pi\) | ||||
0.538868 | + | 0.842390i | \(0.318852\pi\) | |||||||
\(3\) | 7.84090 | 1.50898 | 0.754490 | − | 0.656311i | \(-0.227884\pi\) | ||||
0.754490 | + | 0.656311i | \(0.227884\pi\) | |||||||
\(4\) | 1.29211 | 0.161513 | ||||||||
\(5\) | −10.4483 | −0.934523 | −0.467261 | − | 0.884119i | \(-0.654759\pi\) | ||||
−0.467261 | + | 0.884119i | \(0.654759\pi\) | |||||||
\(6\) | 23.9014 | 1.62628 | ||||||||
\(7\) | 17.4647 | 0.943007 | 0.471503 | − | 0.881864i | \(-0.343712\pi\) | ||||
0.471503 | + | 0.881864i | \(0.343712\pi\) | |||||||
\(8\) | −20.4476 | −0.903667 | ||||||||
\(9\) | 34.4796 | 1.27702 | ||||||||
\(10\) | −31.8495 | −1.00717 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 10.1313 | 0.243720 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 53.2377 | 1.01631 | ||||||||
\(15\) | −81.9239 | −1.41018 | ||||||||
\(16\) | −72.6673 | −1.13543 | ||||||||
\(17\) | −80.1657 | −1.14371 | −0.571854 | − | 0.820355i | \(-0.693776\pi\) | ||||
−0.571854 | + | 0.820355i | \(0.693776\pi\) | |||||||
\(18\) | 105.104 | 1.37629 | ||||||||
\(19\) | −53.2690 | −0.643197 | −0.321599 | − | 0.946876i | \(-0.604220\pi\) | ||||
−0.321599 | + | 0.946876i | \(0.604220\pi\) | |||||||
\(20\) | −13.5003 | −0.150938 | ||||||||
\(21\) | 136.939 | 1.42298 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −77.5267 | −0.702845 | −0.351422 | − | 0.936217i | \(-0.614302\pi\) | ||||
−0.351422 | + | 0.936217i | \(0.614302\pi\) | |||||||
\(24\) | −160.328 | −1.36362 | ||||||||
\(25\) | −15.8334 | −0.126667 | ||||||||
\(26\) | −39.6278 | −0.298910 | ||||||||
\(27\) | 58.6470 | 0.418023 | ||||||||
\(28\) | 22.5663 | 0.152308 | ||||||||
\(29\) | 67.3407 | 0.431202 | 0.215601 | − | 0.976482i | \(-0.430829\pi\) | ||||
0.215601 | + | 0.976482i | \(0.430829\pi\) | |||||||
\(30\) | −249.728 | −1.51980 | ||||||||
\(31\) | 15.3347 | 0.0888449 | 0.0444225 | − | 0.999013i | \(-0.485855\pi\) | ||||
0.0444225 | + | 0.999013i | \(0.485855\pi\) | |||||||
\(32\) | −57.9303 | −0.320023 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −244.369 | −1.23262 | ||||||||
\(35\) | −182.476 | −0.881261 | ||||||||
\(36\) | 44.5513 | 0.206256 | ||||||||
\(37\) | 251.763 | 1.11864 | 0.559318 | − | 0.828953i | \(-0.311063\pi\) | ||||
0.559318 | + | 0.828953i | \(0.311063\pi\) | |||||||
\(38\) | −162.380 | −0.693197 | ||||||||
\(39\) | −101.932 | −0.418516 | ||||||||
\(40\) | 213.643 | 0.844497 | ||||||||
\(41\) | −376.773 | −1.43517 | −0.717586 | − | 0.696470i | \(-0.754753\pi\) | ||||
−0.717586 | + | 0.696470i | \(0.754753\pi\) | |||||||
\(42\) | 417.431 | 1.53359 | ||||||||
\(43\) | 186.795 | 0.662463 | 0.331232 | − | 0.943549i | \(-0.392536\pi\) | ||||
0.331232 | + | 0.943549i | \(0.392536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −360.253 | −1.19341 | ||||||||
\(46\) | −236.324 | −0.757481 | ||||||||
\(47\) | −488.422 | −1.51582 | −0.757911 | − | 0.652358i | \(-0.773780\pi\) | ||||
−0.757911 | + | 0.652358i | \(0.773780\pi\) | |||||||
\(48\) | −569.777 | −1.71334 | ||||||||
\(49\) | −37.9833 | −0.110739 | ||||||||
\(50\) | −48.2649 | −0.136514 | ||||||||
\(51\) | −628.571 | −1.72583 | ||||||||
\(52\) | −16.7974 | −0.0447957 | ||||||||
\(53\) | −366.416 | −0.949643 | −0.474822 | − | 0.880082i | \(-0.657487\pi\) | ||||
−0.474822 | + | 0.880082i | \(0.657487\pi\) | |||||||
\(54\) | 178.773 | 0.450518 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −357.113 | −0.852164 | ||||||||
\(57\) | −417.677 | −0.970573 | ||||||||
\(58\) | 205.274 | 0.464721 | ||||||||
\(59\) | 27.8944 | 0.0615515 | 0.0307757 | − | 0.999526i | \(-0.490202\pi\) | ||||
0.0307757 | + | 0.999526i | \(0.490202\pi\) | |||||||
\(60\) | −105.854 | −0.227762 | ||||||||
\(61\) | 540.280 | 1.13403 | 0.567015 | − | 0.823708i | \(-0.308098\pi\) | ||||
0.567015 | + | 0.823708i | \(0.308098\pi\) | |||||||
\(62\) | 46.7447 | 0.0957513 | ||||||||
\(63\) | 602.177 | 1.20424 | ||||||||
\(64\) | 404.750 | 0.790527 | ||||||||
\(65\) | 135.828 | 0.259190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 608.159 | 1.10893 | 0.554466 | − | 0.832206i | \(-0.312923\pi\) | ||||
0.554466 | + | 0.832206i | \(0.312923\pi\) | |||||||
\(68\) | −103.583 | −0.184724 | ||||||||
\(69\) | −607.879 | −1.06058 | ||||||||
\(70\) | −556.242 | −0.949766 | ||||||||
\(71\) | −1180.76 | −1.97368 | −0.986838 | − | 0.161711i | \(-0.948299\pi\) | ||||
−0.986838 | + | 0.161711i | \(0.948299\pi\) | |||||||
\(72\) | −705.027 | −1.15400 | ||||||||
\(73\) | −82.2687 | −0.131902 | −0.0659508 | − | 0.997823i | \(-0.521008\pi\) | ||||
−0.0659508 | + | 0.997823i | \(0.521008\pi\) | |||||||
\(74\) | 767.447 | 1.20559 | ||||||||
\(75\) | −124.148 | −0.191138 | ||||||||
\(76\) | −68.8292 | −0.103885 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −310.718 | −0.451049 | ||||||||
\(79\) | −416.410 | −0.593035 | −0.296518 | − | 0.955027i | \(-0.595825\pi\) | ||||
−0.296518 | + | 0.955027i | \(0.595825\pi\) | |||||||
\(80\) | 759.249 | 1.06108 | ||||||||
\(81\) | −471.105 | −0.646234 | ||||||||
\(82\) | −1148.52 | −1.54674 | ||||||||
\(83\) | −1036.97 | −1.37135 | −0.685675 | − | 0.727908i | \(-0.740493\pi\) | ||||
−0.685675 | + | 0.727908i | \(0.740493\pi\) | |||||||
\(84\) | 176.940 | 0.229830 | ||||||||
\(85\) | 837.594 | 1.06882 | ||||||||
\(86\) | 569.405 | 0.713960 | ||||||||
\(87\) | 528.011 | 0.650675 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 830.391 | 0.989003 | 0.494502 | − | 0.869177i | \(-0.335351\pi\) | ||||
0.494502 | + | 0.869177i | \(0.335351\pi\) | |||||||
\(90\) | −1098.16 | −1.28618 | ||||||||
\(91\) | −227.041 | −0.261543 | ||||||||
\(92\) | −100.173 | −0.113519 | ||||||||
\(93\) | 120.238 | 0.134065 | ||||||||
\(94\) | −1488.85 | −1.63365 | ||||||||
\(95\) | 556.570 | 0.601083 | ||||||||
\(96\) | −454.225 | −0.482908 | ||||||||
\(97\) | 823.686 | 0.862192 | 0.431096 | − | 0.902306i | \(-0.358127\pi\) | ||||
0.431096 | + | 0.902306i | \(0.358127\pi\) | |||||||
\(98\) | −115.784 | −0.119347 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −20.4584 | −0.0204584 | ||||||||
\(101\) | −991.921 | −0.977226 | −0.488613 | − | 0.872501i | \(-0.662497\pi\) | ||||
−0.488613 | + | 0.872501i | \(0.662497\pi\) | |||||||
\(102\) | −1916.07 | −1.85999 | ||||||||
\(103\) | 408.601 | 0.390880 | 0.195440 | − | 0.980716i | \(-0.437387\pi\) | ||||
0.195440 | + | 0.980716i | \(0.437387\pi\) | |||||||
\(104\) | 265.819 | 0.250632 | ||||||||
\(105\) | −1430.78 | −1.32981 | ||||||||
\(106\) | −1116.94 | −1.02346 | ||||||||
\(107\) | 929.987 | 0.840236 | 0.420118 | − | 0.907470i | \(-0.361989\pi\) | ||||
0.420118 | + | 0.907470i | \(0.361989\pi\) | |||||||
\(108\) | 75.7782 | 0.0675163 | ||||||||
\(109\) | −160.203 | −0.140776 | −0.0703882 | − | 0.997520i | \(-0.522424\pi\) | ||||
−0.0703882 | + | 0.997520i | \(0.522424\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1974.04 | 1.68800 | ||||||||
\(112\) | −1269.11 | −1.07071 | ||||||||
\(113\) | 1096.27 | 0.912639 | 0.456319 | − | 0.889816i | \(-0.349167\pi\) | ||||
0.456319 | + | 0.889816i | \(0.349167\pi\) | |||||||
\(114\) | −1273.20 | −1.04602 | ||||||||
\(115\) | 810.021 | 0.656825 | ||||||||
\(116\) | 87.0113 | 0.0696448 | ||||||||
\(117\) | −448.235 | −0.354183 | ||||||||
\(118\) | 85.0302 | 0.0663362 | ||||||||
\(119\) | −1400.07 | −1.07852 | ||||||||
\(120\) | 1675.15 | 1.27433 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1646.93 | 1.22218 | ||||||||
\(123\) | −2954.24 | −2.16565 | ||||||||
\(124\) | 19.8141 | 0.0143496 | ||||||||
\(125\) | 1471.47 | 1.05290 | ||||||||
\(126\) | 1835.61 | 1.29785 | ||||||||
\(127\) | −755.663 | −0.527986 | −0.263993 | − | 0.964525i | \(-0.585040\pi\) | ||||
−0.263993 | + | 0.964525i | \(0.585040\pi\) | |||||||
\(128\) | 1697.24 | 1.17200 | ||||||||
\(129\) | 1464.64 | 0.999645 | ||||||||
\(130\) | 414.043 | 0.279338 | ||||||||
\(131\) | −2049.77 | −1.36709 | −0.683547 | − | 0.729906i | \(-0.739564\pi\) | ||||
−0.683547 | + | 0.729906i | \(0.739564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −930.329 | −0.606539 | ||||||||
\(134\) | 1853.85 | 1.19513 | ||||||||
\(135\) | −612.761 | −0.390652 | ||||||||
\(136\) | 1639.20 | 1.03353 | ||||||||
\(137\) | 1021.82 | 0.637226 | 0.318613 | − | 0.947885i | \(-0.396783\pi\) | ||||
0.318613 | + | 0.947885i | \(0.396783\pi\) | |||||||
\(138\) | −1852.99 | −1.14302 | ||||||||
\(139\) | −602.831 | −0.367852 | −0.183926 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183926 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(140\) | −235.779 | −0.142335 | ||||||||
\(141\) | −3829.66 | −2.28735 | ||||||||
\(142\) | −3599.32 | −2.12710 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2505.54 | −1.44997 | ||||||||
\(145\) | −703.594 | −0.402968 | ||||||||
\(146\) | −250.779 | −0.142155 | ||||||||
\(147\) | −297.823 | −0.167102 | ||||||||
\(148\) | 325.304 | 0.180674 | ||||||||
\(149\) | −976.886 | −0.537111 | −0.268556 | − | 0.963264i | \(-0.586546\pi\) | ||||
−0.268556 | + | 0.963264i | \(0.586546\pi\) | |||||||
\(150\) | −378.440 | −0.205997 | ||||||||
\(151\) | −2480.46 | −1.33680 | −0.668400 | − | 0.743802i | \(-0.733021\pi\) | ||||
−0.668400 | + | 0.743802i | \(0.733021\pi\) | |||||||
\(152\) | 1089.23 | 0.581236 | ||||||||
\(153\) | −2764.09 | −1.46054 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −160.221 | −0.0830276 | ||||||||
\(156\) | −131.706 | −0.0675959 | ||||||||
\(157\) | 2261.20 | 1.14945 | 0.574725 | − | 0.818347i | \(-0.305109\pi\) | ||||
0.574725 | + | 0.818347i | \(0.305109\pi\) | |||||||
\(158\) | −1269.34 | −0.639135 | ||||||||
\(159\) | −2873.03 | −1.43299 | ||||||||
\(160\) | 605.272 | 0.299068 | ||||||||
\(161\) | −1353.98 | −0.662787 | ||||||||
\(162\) | −1436.07 | −0.696470 | ||||||||
\(163\) | 1482.92 | 0.712584 | 0.356292 | − | 0.934375i | \(-0.384041\pi\) | ||||
0.356292 | + | 0.934375i | \(0.384041\pi\) | |||||||
\(164\) | −486.831 | −0.231799 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3160.99 | −1.47795 | ||||||||
\(167\) | −2460.07 | −1.13991 | −0.569957 | − | 0.821674i | \(-0.693040\pi\) | ||||
−0.569957 | + | 0.821674i | \(0.693040\pi\) | |||||||
\(168\) | −2800.08 | −1.28590 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 2553.23 | 1.15191 | ||||||||
\(171\) | −1836.70 | −0.821378 | ||||||||
\(172\) | 241.359 | 0.106997 | ||||||||
\(173\) | 4497.61 | 1.97657 | 0.988287 | − | 0.152608i | \(-0.0487672\pi\) | ||||
0.988287 | + | 0.152608i | \(0.0487672\pi\) | |||||||
\(174\) | 1609.53 | 0.701255 | ||||||||
\(175\) | −276.526 | −0.119448 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 218.717 | 0.0928800 | ||||||||
\(178\) | 2531.28 | 1.06588 | ||||||||
\(179\) | −1474.63 | −0.615750 | −0.307875 | − | 0.951427i | \(-0.599618\pi\) | ||||
−0.307875 | + | 0.951427i | \(0.599618\pi\) | |||||||
\(180\) | −465.485 | −0.192751 | ||||||||
\(181\) | 152.510 | 0.0626295 | 0.0313148 | − | 0.999510i | \(-0.490031\pi\) | ||||
0.0313148 | + | 0.999510i | \(0.490031\pi\) | |||||||
\(182\) | −692.089 | −0.281874 | ||||||||
\(183\) | 4236.28 | 1.71123 | ||||||||
\(184\) | 1585.24 | 0.635138 | ||||||||
\(185\) | −2630.49 | −1.04539 | ||||||||
\(186\) | 366.520 | 0.144487 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −631.092 | −0.244825 | ||||||||
\(189\) | 1024.25 | 0.394199 | ||||||||
\(190\) | 1696.59 | 0.647808 | ||||||||
\(191\) | 1281.24 | 0.485379 | 0.242690 | − | 0.970104i | \(-0.421970\pi\) | ||||
0.242690 | + | 0.970104i | \(0.421970\pi\) | |||||||
\(192\) | 3173.60 | 1.19289 | ||||||||
\(193\) | 2558.69 | 0.954292 | 0.477146 | − | 0.878824i | \(-0.341671\pi\) | ||||
0.477146 | + | 0.878824i | \(0.341671\pi\) | |||||||
\(194\) | 2510.84 | 0.929215 | ||||||||
\(195\) | 1065.01 | 0.391113 | ||||||||
\(196\) | −49.0785 | −0.0178857 | ||||||||
\(197\) | −4552.85 | −1.64659 | −0.823293 | − | 0.567617i | \(-0.807866\pi\) | ||||
−0.823293 | + | 0.567617i | \(0.807866\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4197.88 | −1.49538 | −0.747688 | − | 0.664050i | \(-0.768836\pi\) | ||||
−0.747688 | + | 0.664050i | \(0.768836\pi\) | |||||||
\(200\) | 323.756 | 0.114465 | ||||||||
\(201\) | 4768.51 | 1.67336 | ||||||||
\(202\) | −3023.67 | −1.05319 | ||||||||
\(203\) | 1176.09 | 0.406626 | ||||||||
\(204\) | −812.181 | −0.278745 | ||||||||
\(205\) | 3936.63 | 1.34120 | ||||||||
\(206\) | 1245.54 | 0.421265 | ||||||||
\(207\) | −2673.09 | −0.897549 | ||||||||
\(208\) | 944.675 | 0.314911 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4361.43 | −1.43318 | ||||||||
\(211\) | −5890.12 | −1.92176 | −0.960882 | − | 0.276957i | \(-0.910674\pi\) | ||||
−0.960882 | + | 0.276957i | \(0.910674\pi\) | |||||||
\(212\) | −473.448 | −0.153380 | ||||||||
\(213\) | −9258.25 | −2.97824 | ||||||||
\(214\) | 2834.87 | 0.905552 | ||||||||
\(215\) | −1951.68 | −0.619087 | ||||||||
\(216\) | −1199.19 | −0.377754 | ||||||||
\(217\) | 267.816 | 0.0837814 | ||||||||
\(218\) | −488.345 | −0.151720 | ||||||||
\(219\) | −645.060 | −0.199037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1042.15 | 0.317208 | ||||||||
\(222\) | 6017.47 | 1.81922 | ||||||||
\(223\) | 3816.32 | 1.14601 | 0.573004 | − | 0.819553i | \(-0.305778\pi\) | ||||
0.573004 | + | 0.819553i | \(0.305778\pi\) | |||||||
\(224\) | −1011.74 | −0.301784 | ||||||||
\(225\) | −545.930 | −0.161757 | ||||||||
\(226\) | 3341.75 | 0.983583 | ||||||||
\(227\) | 2512.37 | 0.734589 | 0.367295 | − | 0.930105i | \(-0.380284\pi\) | ||||
0.367295 | + | 0.930105i | \(0.380284\pi\) | |||||||
\(228\) | −539.683 | −0.156760 | ||||||||
\(229\) | −6568.50 | −1.89545 | −0.947726 | − | 0.319086i | \(-0.896624\pi\) | ||||
−0.947726 | + | 0.319086i | \(0.896624\pi\) | |||||||
\(230\) | 2469.18 | 0.707883 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1376.96 | −0.389663 | ||||||||
\(233\) | −2278.71 | −0.640701 | −0.320351 | − | 0.947299i | \(-0.603801\pi\) | ||||
−0.320351 | + | 0.947299i | \(0.603801\pi\) | |||||||
\(234\) | −1366.35 | −0.381715 | ||||||||
\(235\) | 5103.17 | 1.41657 | ||||||||
\(236\) | 36.0425 | 0.00994138 | ||||||||
\(237\) | −3265.03 | −0.894879 | ||||||||
\(238\) | −4267.84 | −1.16236 | ||||||||
\(239\) | −6162.16 | −1.66777 | −0.833885 | − | 0.551938i | \(-0.813889\pi\) | ||||
−0.833885 | + | 0.551938i | \(0.813889\pi\) | |||||||
\(240\) | 5953.19 | 1.60115 | ||||||||
\(241\) | 4554.46 | 1.21734 | 0.608670 | − | 0.793424i | \(-0.291703\pi\) | ||||
0.608670 | + | 0.793424i | \(0.291703\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5277.35 | −1.39318 | ||||||||
\(244\) | 698.099 | 0.183161 | ||||||||
\(245\) | 396.860 | 0.103488 | ||||||||
\(246\) | −9005.39 | −2.33399 | ||||||||
\(247\) | 692.497 | 0.178391 | ||||||||
\(248\) | −313.558 | −0.0802862 | ||||||||
\(249\) | −8130.76 | −2.06934 | ||||||||
\(250\) | 4485.47 | 1.13474 | ||||||||
\(251\) | 3136.97 | 0.788861 | 0.394430 | − | 0.918926i | \(-0.370942\pi\) | ||||
0.394430 | + | 0.918926i | \(0.370942\pi\) | |||||||
\(252\) | 778.077 | 0.194501 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2303.49 | −0.569030 | ||||||||
\(255\) | 6567.49 | 1.61283 | ||||||||
\(256\) | 1935.69 | 0.472580 | ||||||||
\(257\) | −587.868 | −0.142686 | −0.0713428 | − | 0.997452i | \(-0.522728\pi\) | ||||
−0.0713428 | + | 0.997452i | \(0.522728\pi\) | |||||||
\(258\) | 4464.65 | 1.07735 | ||||||||
\(259\) | 4396.97 | 1.05488 | ||||||||
\(260\) | 175.504 | 0.0418626 | ||||||||
\(261\) | 2321.88 | 0.550655 | ||||||||
\(262\) | −6248.31 | −1.47337 | ||||||||
\(263\) | 4976.91 | 1.16688 | 0.583440 | − | 0.812156i | \(-0.301706\pi\) | ||||
0.583440 | + | 0.812156i | \(0.301706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3828.42 | 0.887463 | ||||||||
\(266\) | −2835.92 | −0.653689 | ||||||||
\(267\) | 6511.01 | 1.49239 | ||||||||
\(268\) | 785.806 | 0.179107 | ||||||||
\(269\) | 4620.43 | 1.04726 | 0.523629 | − | 0.851946i | \(-0.324578\pi\) | ||||
0.523629 | + | 0.851946i | \(0.324578\pi\) | |||||||
\(270\) | −1867.88 | −0.421020 | ||||||||
\(271\) | −3469.18 | −0.777629 | −0.388815 | − | 0.921316i | \(-0.627115\pi\) | ||||
−0.388815 | + | 0.921316i | \(0.627115\pi\) | |||||||
\(272\) | 5825.43 | 1.29860 | ||||||||
\(273\) | −1780.21 | −0.394663 | ||||||||
\(274\) | 3114.81 | 0.686761 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −785.444 | −0.171298 | ||||||||
\(277\) | 7292.73 | 1.58187 | 0.790935 | − | 0.611900i | \(-0.209595\pi\) | ||||
0.790935 | + | 0.611900i | \(0.209595\pi\) | |||||||
\(278\) | −1837.61 | −0.396447 | ||||||||
\(279\) | 528.735 | 0.113457 | ||||||||
\(280\) | 3731.21 | 0.796366 | ||||||||
\(281\) | −1457.78 | −0.309479 | −0.154740 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154740 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(282\) | −11673.9 | −2.46515 | ||||||||
\(283\) | −150.436 | −0.0315988 | −0.0157994 | − | 0.999875i | \(-0.505029\pi\) | ||||
−0.0157994 | + | 0.999875i | \(0.505029\pi\) | |||||||
\(284\) | −1525.67 | −0.318775 | ||||||||
\(285\) | 4364.01 | 0.907022 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6580.24 | −1.35338 | ||||||||
\(288\) | −1997.42 | −0.408677 | ||||||||
\(289\) | 1513.54 | 0.308069 | ||||||||
\(290\) | −2144.76 | −0.434293 | ||||||||
\(291\) | 6458.44 | 1.30103 | ||||||||
\(292\) | −106.300 | −0.0213039 | ||||||||
\(293\) | 6900.87 | 1.37595 | 0.687975 | − | 0.725734i | \(-0.258500\pi\) | ||||
0.687975 | + | 0.725734i | \(0.258500\pi\) | |||||||
\(294\) | −907.853 | −0.180092 | ||||||||
\(295\) | −291.448 | −0.0575212 | ||||||||
\(296\) | −5147.95 | −1.01087 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2977.84 | −0.578864 | ||||||||
\(299\) | 1007.85 | 0.194934 | ||||||||
\(300\) | −160.413 | −0.0308714 | ||||||||
\(301\) | 3262.32 | 0.624707 | ||||||||
\(302\) | −7561.17 | −1.44072 | ||||||||
\(303\) | −7777.55 | −1.47462 | ||||||||
\(304\) | 3870.92 | 0.730304 | ||||||||
\(305\) | −5645.00 | −1.05978 | ||||||||
\(306\) | −8425.75 | −1.57408 | ||||||||
\(307\) | −50.8375 | −0.00945098 | −0.00472549 | − | 0.999989i | \(-0.501504\pi\) | ||||
−0.00472549 | + | 0.999989i | \(0.501504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3203.80 | 0.589830 | ||||||||
\(310\) | −488.402 | −0.0894818 | ||||||||
\(311\) | 7624.75 | 1.39023 | 0.695113 | − | 0.718901i | \(-0.255354\pi\) | ||||
0.695113 | + | 0.718901i | \(0.255354\pi\) | |||||||
\(312\) | 2084.26 | 0.378199 | ||||||||
\(313\) | 7560.97 | 1.36540 | 0.682702 | − | 0.730697i | \(-0.260805\pi\) | ||||
0.682702 | + | 0.730697i | \(0.260805\pi\) | |||||||
\(314\) | 6892.82 | 1.23880 | ||||||||
\(315\) | −6291.72 | −1.12539 | ||||||||
\(316\) | −538.046 | −0.0957831 | ||||||||
\(317\) | 8710.54 | 1.54332 | 0.771661 | − | 0.636035i | \(-0.219426\pi\) | ||||
0.771661 | + | 0.636035i | \(0.219426\pi\) | |||||||
\(318\) | −8757.84 | −1.54439 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4228.94 | −0.738765 | ||||||||
\(321\) | 7291.93 | 1.26790 | ||||||||
\(322\) | −4127.34 | −0.714309 | ||||||||
\(323\) | 4270.35 | 0.735630 | ||||||||
\(324\) | −608.718 | −0.104375 | ||||||||
\(325\) | 205.834 | 0.0351312 | ||||||||
\(326\) | 4520.38 | 0.767977 | ||||||||
\(327\) | −1256.13 | −0.212429 | ||||||||
\(328\) | 7704.12 | 1.29692 | ||||||||
\(329\) | −8530.15 | −1.42943 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6645.66 | 1.10356 | 0.551780 | − | 0.833990i | \(-0.313949\pi\) | ||||
0.551780 | + | 0.833990i | \(0.313949\pi\) | |||||||
\(332\) | −1339.87 | −0.221491 | ||||||||
\(333\) | 8680.68 | 1.42852 | ||||||||
\(334\) | −7499.01 | −1.22853 | ||||||||
\(335\) | −6354.22 | −1.03632 | ||||||||
\(336\) | −9951.00 | −1.61569 | ||||||||
\(337\) | 1308.28 | 0.211473 | 0.105737 | − | 0.994394i | \(-0.466280\pi\) | ||||
0.105737 | + | 0.994394i | \(0.466280\pi\) | |||||||
\(338\) | 515.162 | 0.0829027 | ||||||||
\(339\) | 8595.72 | 1.37715 | ||||||||
\(340\) | 1082.26 | 0.172629 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5598.79 | −0.885228 | ||||||||
\(343\) | −6653.77 | −1.04743 | ||||||||
\(344\) | −3819.51 | −0.598646 | ||||||||
\(345\) | 6351.29 | 0.991136 | ||||||||
\(346\) | 13710.1 | 2.13022 | ||||||||
\(347\) | −8499.42 | −1.31491 | −0.657453 | − | 0.753495i | \(-0.728366\pi\) | ||||
−0.657453 | + | 0.753495i | \(0.728366\pi\) | |||||||
\(348\) | 682.246 | 0.105093 | ||||||||
\(349\) | 1493.51 | 0.229071 | 0.114535 | − | 0.993419i | \(-0.463462\pi\) | ||||
0.114535 | + | 0.993419i | \(0.463462\pi\) | |||||||
\(350\) | −842.933 | −0.128733 | ||||||||
\(351\) | −762.411 | −0.115939 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10082.4 | 1.52020 | 0.760100 | − | 0.649806i | \(-0.225150\pi\) | ||||
0.760100 | + | 0.649806i | \(0.225150\pi\) | |||||||
\(354\) | 666.713 | 0.100100 | ||||||||
\(355\) | 12337.0 | 1.84445 | ||||||||
\(356\) | 1072.95 | 0.159737 | ||||||||
\(357\) | −10977.8 | −1.62747 | ||||||||
\(358\) | −4495.12 | −0.663615 | ||||||||
\(359\) | 7181.99 | 1.05585 | 0.527926 | − | 0.849290i | \(-0.322970\pi\) | ||||
0.527926 | + | 0.849290i | \(0.322970\pi\) | |||||||
\(360\) | 7366.32 | 1.07844 | ||||||||
\(361\) | −4021.41 | −0.586297 | ||||||||
\(362\) | 464.894 | 0.0674980 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −293.362 | −0.0422427 | ||||||||
\(365\) | 859.566 | 0.123265 | ||||||||
\(366\) | 12913.4 | 1.84425 | ||||||||
\(367\) | −455.980 | −0.0648554 | −0.0324277 | − | 0.999474i | \(-0.510324\pi\) | ||||
−0.0324277 | + | 0.999474i | \(0.510324\pi\) | |||||||
\(368\) | 5633.66 | 0.798029 | ||||||||
\(369\) | −12991.0 | −1.83275 | ||||||||
\(370\) | −8018.50 | −1.12665 | ||||||||
\(371\) | −6399.35 | −0.895520 | ||||||||
\(372\) | 155.360 | 0.0216533 | ||||||||
\(373\) | −8380.87 | −1.16339 | −0.581696 | − | 0.813407i | \(-0.697611\pi\) | ||||
−0.581696 | + | 0.813407i | \(0.697611\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11537.6 | 1.58880 | ||||||||
\(376\) | 9987.07 | 1.36980 | ||||||||
\(377\) | −875.429 | −0.119594 | ||||||||
\(378\) | 3122.23 | 0.424842 | ||||||||
\(379\) | −782.703 | −0.106081 | −0.0530405 | − | 0.998592i | \(-0.516891\pi\) | ||||
−0.0530405 | + | 0.998592i | \(0.516891\pi\) | |||||||
\(380\) | 719.147 | 0.0970828 | ||||||||
\(381\) | −5925.08 | −0.796721 | ||||||||
\(382\) | 3905.61 | 0.523111 | ||||||||
\(383\) | 9755.24 | 1.30149 | 0.650743 | − | 0.759298i | \(-0.274457\pi\) | ||||
0.650743 | + | 0.759298i | \(0.274457\pi\) | |||||||
\(384\) | 13307.9 | 1.76853 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7799.64 | 1.02847 | ||||||||
\(387\) | 6440.61 | 0.845981 | ||||||||
\(388\) | 1064.29 | 0.139256 | ||||||||
\(389\) | −5193.48 | −0.676914 | −0.338457 | − | 0.940982i | \(-0.609905\pi\) | ||||
−0.338457 | + | 0.940982i | \(0.609905\pi\) | |||||||
\(390\) | 3246.47 | 0.421516 | ||||||||
\(391\) | 6214.98 | 0.803850 | ||||||||
\(392\) | 776.669 | 0.100071 | ||||||||
\(393\) | −16072.0 | −2.06292 | ||||||||
\(394\) | −13878.4 | −1.77458 | ||||||||
\(395\) | 4350.77 | 0.554205 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6592.31 | 0.833396 | 0.416698 | − | 0.909045i | \(-0.363187\pi\) | ||||
0.416698 | + | 0.909045i | \(0.363187\pi\) | |||||||
\(398\) | −12796.4 | −1.61162 | ||||||||
\(399\) | −7294.61 | −0.915257 | ||||||||
\(400\) | 1150.57 | 0.143821 | ||||||||
\(401\) | −8166.00 | −1.01693 | −0.508467 | − | 0.861081i | \(-0.669788\pi\) | ||||
−0.508467 | + | 0.861081i | \(0.669788\pi\) | |||||||
\(402\) | 14535.8 | 1.80344 | ||||||||
\(403\) | −199.351 | −0.0246412 | ||||||||
\(404\) | −1281.67 | −0.157835 | ||||||||
\(405\) | 4922.24 | 0.603921 | ||||||||
\(406\) | 3585.06 | 0.438235 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 12852.8 | 1.55958 | ||||||||
\(409\) | −410.335 | −0.0496082 | −0.0248041 | − | 0.999692i | \(-0.507896\pi\) | ||||
−0.0248041 | + | 0.999692i | \(0.507896\pi\) | |||||||
\(410\) | 12000.0 | 1.44546 | ||||||||
\(411\) | 8011.98 | 0.961561 | ||||||||
\(412\) | 527.956 | 0.0631323 | ||||||||
\(413\) | 487.167 | 0.0580434 | ||||||||
\(414\) | −8148.37 | −0.967321 | ||||||||
\(415\) | 10834.5 | 1.28156 | ||||||||
\(416\) | 753.094 | 0.0887583 | ||||||||
\(417\) | −4726.73 | −0.555082 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13457.4 | 1.56906 | 0.784532 | − | 0.620088i | \(-0.212903\pi\) | ||||
0.784532 | + | 0.620088i | \(0.212903\pi\) | |||||||
\(420\) | −1848.72 | −0.214781 | ||||||||
\(421\) | 3027.78 | 0.350511 | 0.175255 | − | 0.984523i | \(-0.443925\pi\) | ||||
0.175255 | + | 0.984523i | \(0.443925\pi\) | |||||||
\(422\) | −17954.8 | −2.07115 | ||||||||
\(423\) | −16840.6 | −1.93574 | ||||||||
\(424\) | 7492.34 | 0.858161 | ||||||||
\(425\) | 1269.30 | 0.144870 | ||||||||
\(426\) | −28221.9 | −3.20975 | ||||||||
\(427\) | 9435.84 | 1.06940 | ||||||||
\(428\) | 1201.64 | 0.135709 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5949.31 | −0.667212 | ||||||||
\(431\) | −6192.47 | −0.692067 | −0.346033 | − | 0.938222i | \(-0.612472\pi\) | ||||
−0.346033 | + | 0.938222i | \(0.612472\pi\) | |||||||
\(432\) | −4261.72 | −0.474635 | ||||||||
\(433\) | −2121.11 | −0.235413 | −0.117707 | − | 0.993048i | \(-0.537554\pi\) | ||||
−0.117707 | + | 0.993048i | \(0.537554\pi\) | |||||||
\(434\) | 816.383 | 0.0902941 | ||||||||
\(435\) | −5516.81 | −0.608071 | ||||||||
\(436\) | −206.999 | −0.0227373 | ||||||||
\(437\) | 4129.77 | 0.452068 | ||||||||
\(438\) | −1966.33 | −0.214509 | ||||||||
\(439\) | −13914.2 | −1.51273 | −0.756367 | − | 0.654148i | \(-0.773027\pi\) | ||||
−0.756367 | + | 0.654148i | \(0.773027\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1309.65 | −0.141416 | ||||||||
\(442\) | 3176.79 | 0.341866 | ||||||||
\(443\) | −9407.56 | −1.00895 | −0.504477 | − | 0.863425i | \(-0.668315\pi\) | ||||
−0.504477 | + | 0.863425i | \(0.668315\pi\) | |||||||
\(444\) | 2550.67 | 0.272634 | ||||||||
\(445\) | −8676.16 | −0.924246 | ||||||||
\(446\) | 11633.3 | 1.23509 | ||||||||
\(447\) | −7659.66 | −0.810491 | ||||||||
\(448\) | 7068.85 | 0.745472 | ||||||||
\(449\) | −682.686 | −0.0717549 | −0.0358775 | − | 0.999356i | \(-0.511423\pi\) | ||||
−0.0358775 | + | 0.999356i | \(0.511423\pi\) | |||||||
\(450\) | −1664.16 | −0.174331 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1416.49 | 0.147403 | ||||||||
\(453\) | −19449.0 | −2.01721 | ||||||||
\(454\) | 7658.44 | 0.791692 | ||||||||
\(455\) | 2372.19 | 0.244418 | ||||||||
\(456\) | 8540.51 | 0.877074 | ||||||||
\(457\) | 8126.75 | 0.831846 | 0.415923 | − | 0.909400i | \(-0.363459\pi\) | ||||
0.415923 | + | 0.909400i | \(0.363459\pi\) | |||||||
\(458\) | −20022.7 | −2.04280 | ||||||||
\(459\) | −4701.48 | −0.478097 | ||||||||
\(460\) | 1046.63 | 0.106086 | ||||||||
\(461\) | −10093.9 | −1.01979 | −0.509894 | − | 0.860237i | \(-0.670315\pi\) | ||||
−0.509894 | + | 0.860237i | \(0.670315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −161.556 | −0.0162163 | −0.00810817 | − | 0.999967i | \(-0.502581\pi\) | ||||
−0.00810817 | + | 0.999967i | \(0.502581\pi\) | |||||||
\(464\) | −4893.47 | −0.489598 | ||||||||
\(465\) | −1256.28 | −0.125287 | ||||||||
\(466\) | −6946.19 | −0.690507 | ||||||||
\(467\) | −3326.27 | −0.329596 | −0.164798 | − | 0.986327i | \(-0.552697\pi\) | ||||
−0.164798 | + | 0.986327i | \(0.552697\pi\) | |||||||
\(468\) | −579.168 | −0.0572052 | ||||||||
\(469\) | 10621.3 | 1.04573 | ||||||||
\(470\) | 15556.0 | 1.52669 | ||||||||
\(471\) | 17729.9 | 1.73450 | ||||||||
\(472\) | −570.374 | −0.0556220 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −9952.77 | −0.964443 | ||||||||
\(475\) | 843.430 | 0.0814721 | ||||||||
\(476\) | −1809.04 | −0.174196 | ||||||||
\(477\) | −12633.9 | −1.21272 | ||||||||
\(478\) | −18784.1 | −1.79741 | ||||||||
\(479\) | 7542.27 | 0.719447 | 0.359723 | − | 0.933059i | \(-0.382871\pi\) | ||||
0.359723 | + | 0.933059i | \(0.382871\pi\) | |||||||
\(480\) | 4745.87 | 0.451289 | ||||||||
\(481\) | −3272.91 | −0.310254 | ||||||||
\(482\) | 13883.4 | 1.31197 | ||||||||
\(483\) | −10616.4 | −1.00013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8606.11 | −0.805738 | ||||||||
\(486\) | −16086.9 | −1.50148 | ||||||||
\(487\) | −12686.1 | −1.18041 | −0.590206 | − | 0.807252i | \(-0.700954\pi\) | ||||
−0.590206 | + | 0.807252i | \(0.700954\pi\) | |||||||
\(488\) | −11047.5 | −1.02478 | ||||||||
\(489\) | 11627.4 | 1.07528 | ||||||||
\(490\) | 1209.75 | 0.111532 | ||||||||
\(491\) | −13549.8 | −1.24541 | −0.622703 | − | 0.782458i | \(-0.713966\pi\) | ||||
−0.622703 | + | 0.782458i | \(0.713966\pi\) | |||||||
\(492\) | −3817.19 | −0.349781 | ||||||||
\(493\) | −5398.41 | −0.493169 | ||||||||
\(494\) | 2110.94 | 0.192258 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1114.33 | −0.100877 | ||||||||
\(497\) | −20621.7 | −1.86119 | ||||||||
\(498\) | −24785.0 | −2.23020 | ||||||||
\(499\) | −14538.2 | −1.30425 | −0.652123 | − | 0.758113i | \(-0.726121\pi\) | ||||
−0.652123 | + | 0.758113i | \(0.726121\pi\) | |||||||
\(500\) | 1901.29 | 0.170057 | ||||||||
\(501\) | −19289.1 | −1.72011 | ||||||||
\(502\) | 9562.42 | 0.850183 | ||||||||
\(503\) | −16031.1 | −1.42105 | −0.710526 | − | 0.703671i | \(-0.751543\pi\) | ||||
−0.710526 | + | 0.703671i | \(0.751543\pi\) | |||||||
\(504\) | −12313.1 | −1.08823 | ||||||||
\(505\) | 10363.9 | 0.913240 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1325.11 | 0.116075 | ||||||||
\(508\) | −976.397 | −0.0852768 | ||||||||
\(509\) | −8274.70 | −0.720569 | −0.360284 | − | 0.932843i | \(-0.617320\pi\) | ||||
−0.360284 | + | 0.932843i | \(0.617320\pi\) | |||||||
\(510\) | 20019.6 | 1.73821 | ||||||||
\(511\) | −1436.80 | −0.124384 | ||||||||
\(512\) | −7677.36 | −0.662685 | ||||||||
\(513\) | −3124.07 | −0.268871 | ||||||||
\(514\) | −1791.99 | −0.153777 | ||||||||
\(515\) | −4269.18 | −0.365286 | ||||||||
\(516\) | 1892.47 | 0.161456 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13403.2 | 1.13688 | ||||||||
\(519\) | 35265.3 | 2.98261 | ||||||||
\(520\) | −2777.36 | −0.234221 | ||||||||
\(521\) | −19947.8 | −1.67741 | −0.838703 | − | 0.544589i | \(-0.816686\pi\) | ||||
−0.838703 | + | 0.544589i | \(0.816686\pi\) | |||||||
\(522\) | 7077.78 | 0.593460 | ||||||||
\(523\) | 9418.37 | 0.787450 | 0.393725 | − | 0.919228i | \(-0.371186\pi\) | ||||
0.393725 | + | 0.919228i | \(0.371186\pi\) | |||||||
\(524\) | −2648.52 | −0.220804 | ||||||||
\(525\) | −2168.21 | −0.180245 | ||||||||
\(526\) | 15171.1 | 1.25759 | ||||||||
\(527\) | −1229.32 | −0.101613 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6156.61 | −0.506009 | ||||||||
\(530\) | 11670.1 | 0.956450 | ||||||||
\(531\) | 961.787 | 0.0786027 | ||||||||
\(532\) | −1202.08 | −0.0979642 | ||||||||
\(533\) | 4898.05 | 0.398045 | ||||||||
\(534\) | 19847.5 | 1.60840 | ||||||||
\(535\) | −9716.76 | −0.785219 | ||||||||
\(536\) | −12435.4 | −1.00210 | ||||||||
\(537\) | −11562.4 | −0.929155 | ||||||||
\(538\) | 14084.4 | 1.12867 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −791.752 | −0.0630955 | ||||||||
\(541\) | 20665.4 | 1.64228 | 0.821140 | − | 0.570728i | \(-0.193339\pi\) | ||||
0.821140 | + | 0.570728i | \(0.193339\pi\) | |||||||
\(542\) | −10575.1 | −0.838079 | ||||||||
\(543\) | 1195.81 | 0.0945068 | ||||||||
\(544\) | 4644.02 | 0.366013 | ||||||||
\(545\) | 1673.84 | 0.131559 | ||||||||
\(546\) | −5426.60 | −0.425343 | ||||||||
\(547\) | 13691.2 | 1.07019 | 0.535093 | − | 0.844793i | \(-0.320277\pi\) | ||||
0.535093 | + | 0.844793i | \(0.320277\pi\) | |||||||
\(548\) | 1320.30 | 0.102920 | ||||||||
\(549\) | 18628.7 | 1.44818 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3587.17 | −0.277348 | ||||||||
\(552\) | 12429.7 | 0.958410 | ||||||||
\(553\) | −7272.49 | −0.559236 | ||||||||
\(554\) | 22230.4 | 1.70484 | ||||||||
\(555\) | −20625.4 | −1.57747 | ||||||||
\(556\) | −778.922 | −0.0594130 | ||||||||
\(557\) | 18001.2 | 1.36936 | 0.684682 | − | 0.728842i | \(-0.259941\pi\) | ||||
0.684682 | + | 0.728842i | \(0.259941\pi\) | |||||||
\(558\) | 1611.74 | 0.122277 | ||||||||
\(559\) | −2428.33 | −0.183734 | ||||||||
\(560\) | 13260.1 | 1.00061 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4443.73 | −0.333537 | ||||||||
\(563\) | −6078.61 | −0.455032 | −0.227516 | − | 0.973774i | \(-0.573060\pi\) | ||||
−0.227516 | + | 0.973774i | \(0.573060\pi\) | |||||||
\(564\) | −4948.33 | −0.369437 | ||||||||
\(565\) | −11454.1 | −0.852882 | ||||||||
\(566\) | −458.572 | −0.0340552 | ||||||||
\(567\) | −8227.72 | −0.609403 | ||||||||
\(568\) | 24143.9 | 1.78355 | ||||||||
\(569\) | −5443.40 | −0.401053 | −0.200527 | − | 0.979688i | \(-0.564265\pi\) | ||||
−0.200527 | + | 0.979688i | \(0.564265\pi\) | |||||||
\(570\) | 13302.8 | 0.977530 | ||||||||
\(571\) | −4537.77 | −0.332574 | −0.166287 | − | 0.986077i | \(-0.553178\pi\) | ||||
−0.166287 | + | 0.986077i | \(0.553178\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10046.1 | 0.732428 | ||||||||
\(574\) | −20058.5 | −1.45858 | ||||||||
\(575\) | 1227.51 | 0.0890274 | ||||||||
\(576\) | 13955.6 | 1.00952 | ||||||||
\(577\) | −16056.4 | −1.15847 | −0.579235 | − | 0.815161i | \(-0.696649\pi\) | ||||
−0.579235 | + | 0.815161i | \(0.696649\pi\) | |||||||
\(578\) | 4613.73 | 0.332017 | ||||||||
\(579\) | 20062.4 | 1.44001 | ||||||||
\(580\) | −909.118 | −0.0650846 | ||||||||
\(581\) | −18110.4 | −1.29319 | ||||||||
\(582\) | 19687.2 | 1.40217 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1682.20 | 0.119195 | ||||||||
\(585\) | 4683.29 | 0.330992 | ||||||||
\(586\) | 21035.9 | 1.48291 | ||||||||
\(587\) | 18480.8 | 1.29946 | 0.649731 | − | 0.760165i | \(-0.274882\pi\) | ||||
0.649731 | + | 0.760165i | \(0.274882\pi\) | |||||||
\(588\) | −384.819 | −0.0269892 | ||||||||
\(589\) | −816.864 | −0.0571448 | ||||||||
\(590\) | −888.420 | −0.0619927 | ||||||||
\(591\) | −35698.5 | −2.48467 | ||||||||
\(592\) | −18294.9 | −1.27013 | ||||||||
\(593\) | −16507.6 | −1.14315 | −0.571573 | − | 0.820551i | \(-0.693667\pi\) | ||||
−0.571573 | + | 0.820551i | \(0.693667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14628.4 | 1.00791 | ||||||||
\(596\) | −1262.24 | −0.0867506 | ||||||||
\(597\) | −32915.1 | −2.25649 | ||||||||
\(598\) | 3072.22 | 0.210087 | ||||||||
\(599\) | 20635.1 | 1.40756 | 0.703781 | − | 0.710417i | \(-0.251494\pi\) | ||||
0.703781 | + | 0.710417i | \(0.251494\pi\) | |||||||
\(600\) | 2538.54 | 0.172725 | ||||||||
\(601\) | −10193.7 | −0.691865 | −0.345932 | − | 0.938259i | \(-0.612437\pi\) | ||||
−0.345932 | + | 0.938259i | \(0.612437\pi\) | |||||||
\(602\) | 9944.51 | 0.673269 | ||||||||
\(603\) | 20969.1 | 1.41613 | ||||||||
\(604\) | −3205.01 | −0.215911 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −23708.3 | −1.58925 | ||||||||
\(607\) | −14643.2 | −0.979158 | −0.489579 | − | 0.871959i | \(-0.662850\pi\) | ||||
−0.489579 | + | 0.871959i | \(0.662850\pi\) | |||||||
\(608\) | 3085.89 | 0.205838 | ||||||||
\(609\) | 9221.57 | 0.613591 | ||||||||
\(610\) | −17207.6 | −1.14216 | ||||||||
\(611\) | 6349.48 | 0.420413 | ||||||||
\(612\) | −3571.49 | −0.235897 | ||||||||
\(613\) | 24115.6 | 1.58894 | 0.794470 | − | 0.607304i | \(-0.207749\pi\) | ||||
0.794470 | + | 0.607304i | \(0.207749\pi\) | |||||||
\(614\) | −154.968 | −0.0101857 | ||||||||
\(615\) | 30866.7 | 2.02385 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5353.36 | 0.349300 | 0.174650 | − | 0.984631i | \(-0.444121\pi\) | ||||
0.174650 | + | 0.984631i | \(0.444121\pi\) | |||||||
\(618\) | 9766.12 | 0.635681 | ||||||||
\(619\) | 22942.2 | 1.48970 | 0.744852 | − | 0.667230i | \(-0.232520\pi\) | ||||
0.744852 | + | 0.667230i | \(0.232520\pi\) | |||||||
\(620\) | −207.023 | −0.0134101 | ||||||||
\(621\) | −4546.71 | −0.293805 | ||||||||
\(622\) | 23242.5 | 1.49830 | ||||||||
\(623\) | 14502.6 | 0.932637 | ||||||||
\(624\) | 7407.10 | 0.475194 | ||||||||
\(625\) | −13395.1 | −0.857288 | ||||||||
\(626\) | 23048.1 | 1.47154 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2921.71 | 0.185651 | ||||||||
\(629\) | −20182.7 | −1.27939 | ||||||||
\(630\) | −19179.0 | −1.21287 | ||||||||
\(631\) | 2562.47 | 0.161664 | 0.0808321 | − | 0.996728i | \(-0.474242\pi\) | ||||
0.0808321 | + | 0.996728i | \(0.474242\pi\) | |||||||
\(632\) | 8514.60 | 0.535906 | ||||||||
\(633\) | −46183.8 | −2.89991 | ||||||||
\(634\) | 26552.3 | 1.66329 | ||||||||
\(635\) | 7895.38 | 0.493415 | ||||||||
\(636\) | −3712.26 | −0.231447 | ||||||||
\(637\) | 493.783 | 0.0307133 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40712.3 | −2.52043 | ||||||||
\(640\) | −17733.2 | −1.09526 | ||||||||
\(641\) | −3746.10 | −0.230830 | −0.115415 | − | 0.993317i | \(-0.536820\pi\) | ||||
−0.115415 | + | 0.993317i | \(0.536820\pi\) | |||||||
\(642\) | 22228.0 | 1.36646 | ||||||||
\(643\) | −17190.8 | −1.05434 | −0.527168 | − | 0.849761i | \(-0.676746\pi\) | ||||
−0.527168 | + | 0.849761i | \(0.676746\pi\) | |||||||
\(644\) | −1749.49 | −0.107049 | ||||||||
\(645\) | −15302.9 | −0.934191 | ||||||||
\(646\) | 13017.3 | 0.792815 | ||||||||
\(647\) | −26594.3 | −1.61597 | −0.807984 | − | 0.589205i | \(-0.799441\pi\) | ||||
−0.807984 | + | 0.589205i | \(0.799441\pi\) | |||||||
\(648\) | 9632.99 | 0.583981 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 627.444 | 0.0378621 | ||||||||
\(651\) | 2099.92 | 0.126424 | ||||||||
\(652\) | 1916.09 | 0.115092 | ||||||||
\(653\) | 16019.5 | 0.960018 | 0.480009 | − | 0.877264i | \(-0.340633\pi\) | ||||
0.480009 | + | 0.877264i | \(0.340633\pi\) | |||||||
\(654\) | −3829.06 | −0.228942 | ||||||||
\(655\) | 21416.6 | 1.27758 | ||||||||
\(656\) | 27379.1 | 1.62953 | ||||||||
\(657\) | −2836.59 | −0.168442 | ||||||||
\(658\) | −26002.4 | −1.54055 | ||||||||
\(659\) | −2693.80 | −0.159234 | −0.0796172 | − | 0.996826i | \(-0.525370\pi\) | ||||
−0.0796172 | + | 0.996826i | \(0.525370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19207.5 | 1.13023 | 0.565117 | − | 0.825010i | \(-0.308831\pi\) | ||||
0.565117 | + | 0.825010i | \(0.308831\pi\) | |||||||
\(662\) | 20257.9 | 1.18935 | ||||||||
\(663\) | 8171.42 | 0.478660 | ||||||||
\(664\) | 21203.6 | 1.23924 | ||||||||
\(665\) | 9720.34 | 0.566825 | ||||||||
\(666\) | 26461.3 | 1.53957 | ||||||||
\(667\) | −5220.70 | −0.303068 | ||||||||
\(668\) | −3178.67 | −0.184111 | ||||||||
\(669\) | 29923.4 | 1.72930 | ||||||||
\(670\) | −19369.5 | −1.11688 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −7932.92 | −0.455386 | ||||||||
\(673\) | 1909.68 | 0.109380 | 0.0546899 | − | 0.998503i | \(-0.482583\pi\) | ||||
0.0546899 | + | 0.998503i | \(0.482583\pi\) | |||||||
\(674\) | 3988.02 | 0.227912 | ||||||||
\(675\) | −928.582 | −0.0529499 | ||||||||
\(676\) | 218.366 | 0.0124241 | ||||||||
\(677\) | 11495.3 | 0.652583 | 0.326291 | − | 0.945269i | \(-0.394201\pi\) | ||||
0.326291 | + | 0.945269i | \(0.394201\pi\) | |||||||
\(678\) | 26202.3 | 1.48421 | ||||||||
\(679\) | 14385.5 | 0.813053 | ||||||||
\(680\) | −17126.8 | −0.965859 | ||||||||
\(681\) | 19699.2 | 1.10848 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3936.68 | 0.220546 | 0.110273 | − | 0.993901i | \(-0.464828\pi\) | ||||
0.110273 | + | 0.993901i | \(0.464828\pi\) | |||||||
\(684\) | −2373.21 | −0.132663 | ||||||||
\(685\) | −10676.3 | −0.595502 | ||||||||
\(686\) | −20282.7 | −1.12886 | ||||||||
\(687\) | −51502.9 | −2.86020 | ||||||||
\(688\) | −13573.9 | −0.752179 | ||||||||
\(689\) | 4763.41 | 0.263384 | ||||||||
\(690\) | 19360.6 | 1.06818 | ||||||||
\(691\) | 13955.6 | 0.768299 | 0.384150 | − | 0.923271i | \(-0.374495\pi\) | ||||
0.384150 | + | 0.923271i | \(0.374495\pi\) | |||||||
\(692\) | 5811.39 | 0.319243 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25908.7 | −1.41712 | ||||||||
\(695\) | 6298.55 | 0.343766 | ||||||||
\(696\) | −10796.6 | −0.587993 | ||||||||
\(697\) | 30204.3 | 1.64142 | ||||||||
\(698\) | 4552.66 | 0.246878 | ||||||||
\(699\) | −17867.1 | −0.966806 | ||||||||
\(700\) | −357.301 | −0.0192924 | ||||||||
\(701\) | −21944.3 | −1.18235 | −0.591173 | − | 0.806544i | \(-0.701335\pi\) | ||||
−0.591173 | + | 0.806544i | \(0.701335\pi\) | |||||||
\(702\) | −2324.06 | −0.124951 | ||||||||
\(703\) | −13411.1 | −0.719504 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40013.4 | 2.13758 | ||||||||
\(706\) | 30734.1 | 1.63837 | ||||||||
\(707\) | −17323.6 | −0.921531 | ||||||||
\(708\) | 282.605 | 0.0150013 | ||||||||
\(709\) | 7288.13 | 0.386053 | 0.193026 | − | 0.981194i | \(-0.438170\pi\) | ||||
0.193026 | + | 0.981194i | \(0.438170\pi\) | |||||||
\(710\) | 37606.7 | 1.98782 | ||||||||
\(711\) | −14357.7 | −0.757320 | ||||||||
\(712\) | −16979.5 | −0.893729 | ||||||||
\(713\) | −1188.85 | −0.0624442 | ||||||||
\(714\) | −33463.6 | −1.75399 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1905.38 | −0.0994518 | ||||||||
\(717\) | −48316.9 | −2.51663 | ||||||||
\(718\) | 21892.8 | 1.13793 | ||||||||
\(719\) | 36744.7 | 1.90591 | 0.952954 | − | 0.303115i | \(-0.0980266\pi\) | ||||
0.952954 | + | 0.303115i | \(0.0980266\pi\) | |||||||
\(720\) | 26178.6 | 1.35503 | ||||||||
\(721\) | 7136.10 | 0.368602 | ||||||||
\(722\) | −12258.4 | −0.631873 | ||||||||
\(723\) | 35711.1 | 1.83694 | ||||||||
\(724\) | 197.058 | 0.0101155 | ||||||||
\(725\) | −1066.23 | −0.0546191 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8229.31 | 0.419819 | 0.209909 | − | 0.977721i | \(-0.432683\pi\) | ||||
0.209909 | + | 0.977721i | \(0.432683\pi\) | |||||||
\(728\) | 4642.46 | 0.236348 | ||||||||
\(729\) | −28659.3 | −1.45605 | ||||||||
\(730\) | 2620.21 | 0.132847 | ||||||||
\(731\) | −14974.5 | −0.757665 | ||||||||
\(732\) | 5473.72 | 0.276386 | ||||||||
\(733\) | −30208.8 | −1.52222 | −0.761110 | − | 0.648623i | \(-0.775345\pi\) | ||||
−0.761110 | + | 0.648623i | \(0.775345\pi\) | |||||||
\(734\) | −1389.96 | −0.0698970 | ||||||||
\(735\) | 3111.74 | 0.156161 | ||||||||
\(736\) | 4491.14 | 0.224926 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −39600.4 | −1.97522 | ||||||||
\(739\) | 21305.3 | 1.06053 | 0.530263 | − | 0.847833i | \(-0.322093\pi\) | ||||
0.530263 | + | 0.847833i | \(0.322093\pi\) | |||||||
\(740\) | −3398.87 | −0.168844 | ||||||||
\(741\) | 5429.80 | 0.269188 | ||||||||
\(742\) | −19507.1 | −0.965133 | ||||||||
\(743\) | −19246.6 | −0.950324 | −0.475162 | − | 0.879898i | \(-0.657611\pi\) | ||||
−0.475162 | + | 0.879898i | \(0.657611\pi\) | |||||||
\(744\) | −2458.58 | −0.121150 | ||||||||
\(745\) | 10206.8 | 0.501943 | ||||||||
\(746\) | −25547.4 | −1.25383 | ||||||||
\(747\) | −35754.3 | −1.75125 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16242.0 | 0.792348 | ||||||||
\(750\) | 35170.1 | 1.71231 | ||||||||
\(751\) | −20791.4 | −1.01024 | −0.505120 | − | 0.863049i | \(-0.668552\pi\) | ||||
−0.505120 | + | 0.863049i | \(0.668552\pi\) | |||||||
\(752\) | 35492.3 | 1.72110 | ||||||||
\(753\) | 24596.7 | 1.19038 | ||||||||
\(754\) | −2668.57 | −0.128890 | ||||||||
\(755\) | 25916.5 | 1.24927 | ||||||||
\(756\) | 1323.45 | 0.0636683 | ||||||||
\(757\) | −12952.7 | −0.621896 | −0.310948 | − | 0.950427i | \(-0.600647\pi\) | ||||
−0.310948 | + | 0.950427i | \(0.600647\pi\) | |||||||
\(758\) | −2385.91 | −0.114327 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11380.5 | −0.543178 | ||||||||
\(761\) | −4482.10 | −0.213504 | −0.106752 | − | 0.994286i | \(-0.534045\pi\) | ||||
−0.106752 | + | 0.994286i | \(0.534045\pi\) | |||||||
\(762\) | −18061.4 | −0.858655 | ||||||||
\(763\) | −2797.90 | −0.132753 | ||||||||
\(764\) | 1655.50 | 0.0783952 | ||||||||
\(765\) | 28879.9 | 1.36491 | ||||||||
\(766\) | 29736.8 | 1.40266 | ||||||||
\(767\) | −362.627 | −0.0170713 | ||||||||
\(768\) | 15177.5 | 0.713115 | ||||||||
\(769\) | −24493.9 | −1.14860 | −0.574300 | − | 0.818645i | \(-0.694726\pi\) | ||||
−0.574300 | + | 0.818645i | \(0.694726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4609.41 | −0.215310 | ||||||||
\(772\) | 3306.10 | 0.154131 | ||||||||
\(773\) | 17199.8 | 0.800301 | 0.400150 | − | 0.916449i | \(-0.368958\pi\) | ||||
0.400150 | + | 0.916449i | \(0.368958\pi\) | |||||||
\(774\) | 19632.9 | 0.911744 | ||||||||
\(775\) | −242.801 | −0.0112537 | ||||||||
\(776\) | −16842.4 | −0.779135 | ||||||||
\(777\) | 34476.1 | 1.59179 | ||||||||
\(778\) | −15831.3 | −0.729535 | ||||||||
\(779\) | 20070.3 | 0.923099 | ||||||||
\(780\) | 1376.11 | 0.0631699 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 18945.1 | 0.866337 | ||||||||
\(783\) | 3949.33 | 0.180252 | ||||||||
\(784\) | 2760.15 | 0.125735 | ||||||||
\(785\) | −23625.7 | −1.07419 | ||||||||
\(786\) | −48992.3 | −2.22328 | ||||||||
\(787\) | 4203.43 | 0.190389 | 0.0951945 | − | 0.995459i | \(-0.469653\pi\) | ||||
0.0951945 | + | 0.995459i | \(0.469653\pi\) | |||||||
\(788\) | −5882.77 | −0.265945 | ||||||||
\(789\) | 39023.4 | 1.76080 | ||||||||
\(790\) | 13262.4 | 0.597286 | ||||||||
\(791\) | 19146.0 | 0.860624 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7023.64 | −0.314523 | ||||||||
\(794\) | 20095.3 | 0.898181 | ||||||||
\(795\) | 30018.2 | 1.33917 | ||||||||
\(796\) | −5424.11 | −0.241523 | ||||||||
\(797\) | 29590.4 | 1.31512 | 0.657558 | − | 0.753404i | \(-0.271590\pi\) | ||||
0.657558 | + | 0.753404i | \(0.271590\pi\) | |||||||
\(798\) | −22236.1 | −0.986404 | ||||||||
\(799\) | 39154.7 | 1.73366 | ||||||||
\(800\) | 917.234 | 0.0405364 | ||||||||
\(801\) | 28631.6 | 1.26298 | ||||||||
\(802\) | −24892.4 | −1.09599 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6161.42 | 0.270269 | ||||||||
\(805\) | 14146.8 | 0.619390 | ||||||||
\(806\) | −607.681 | −0.0265566 | ||||||||
\(807\) | 36228.3 | 1.58029 | ||||||||
\(808\) | 20282.5 | 0.883087 | ||||||||
\(809\) | −22306.7 | −0.969423 | −0.484712 | − | 0.874674i | \(-0.661075\pi\) | ||||
−0.484712 | + | 0.874674i | \(0.661075\pi\) | |||||||
\(810\) | 15004.4 | 0.650867 | ||||||||
\(811\) | 29725.4 | 1.28705 | 0.643527 | − | 0.765424i | \(-0.277470\pi\) | ||||
0.643527 | + | 0.765424i | \(0.277470\pi\) | |||||||
\(812\) | 1519.63 | 0.0656755 | ||||||||
\(813\) | −27201.5 | −1.17343 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15494.0 | −0.665926 | ||||||||
\(816\) | 45676.6 | 1.95956 | ||||||||
\(817\) | −9950.37 | −0.426095 | ||||||||
\(818\) | −1250.82 | −0.0534645 | ||||||||
\(819\) | −7828.31 | −0.333997 | ||||||||
\(820\) | 5086.54 | 0.216622 | ||||||||
\(821\) | −30623.9 | −1.30180 | −0.650902 | − | 0.759162i | \(-0.725609\pi\) | ||||
−0.650902 | + | 0.759162i | \(0.725609\pi\) | |||||||
\(822\) | 24422.9 | 1.03631 | ||||||||
\(823\) | 31687.7 | 1.34212 | 0.671058 | − | 0.741405i | \(-0.265840\pi\) | ||||
0.671058 | + | 0.741405i | \(0.265840\pi\) | |||||||
\(824\) | −8354.92 | −0.353225 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1485.03 | 0.0625555 | ||||||||
\(827\) | 4744.08 | 0.199477 | 0.0997387 | − | 0.995014i | \(-0.468199\pi\) | ||||
0.0997387 | + | 0.995014i | \(0.468199\pi\) | |||||||
\(828\) | −3453.92 | −0.144966 | ||||||||
\(829\) | −23419.2 | −0.981159 | −0.490580 | − | 0.871396i | \(-0.663215\pi\) | ||||
−0.490580 | + | 0.871396i | \(0.663215\pi\) | |||||||
\(830\) | 33026.9 | 1.38118 | ||||||||
\(831\) | 57181.6 | 2.38701 | ||||||||
\(832\) | −5261.75 | −0.219253 | ||||||||
\(833\) | 3044.96 | 0.126653 | ||||||||
\(834\) | −14408.5 | −0.598231 | ||||||||
\(835\) | 25703.5 | 1.06528 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 899.335 | 0.0371393 | ||||||||
\(838\) | 41022.2 | 1.69104 | ||||||||
\(839\) | −22363.7 | −0.920239 | −0.460120 | − | 0.887857i | \(-0.652193\pi\) | ||||
−0.460120 | + | 0.887857i | \(0.652193\pi\) | |||||||
\(840\) | 29256.0 | 1.20170 | ||||||||
\(841\) | −19854.2 | −0.814065 | ||||||||
\(842\) | 9229.57 | 0.377758 | ||||||||
\(843\) | −11430.3 | −0.466998 | ||||||||
\(844\) | −7610.65 | −0.310390 | ||||||||
\(845\) | −1765.76 | −0.0718864 | ||||||||
\(846\) | −51335.1 | −2.08621 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 26626.5 | 1.07825 | ||||||||
\(849\) | −1179.55 | −0.0476820 | ||||||||
\(850\) | 3869.19 | 0.156132 | ||||||||
\(851\) | −19518.3 | −0.786227 | ||||||||
\(852\) | −11962.6 | −0.481025 | ||||||||
\(853\) | 8888.09 | 0.356767 | 0.178384 | − | 0.983961i | \(-0.442913\pi\) | ||||
0.178384 | + | 0.983961i | \(0.442913\pi\) | |||||||
\(854\) | 28763.2 | 1.15253 | ||||||||
\(855\) | 19190.3 | 0.767597 | ||||||||
\(856\) | −19016.0 | −0.759293 | ||||||||
\(857\) | 24013.3 | 0.957152 | 0.478576 | − | 0.878046i | \(-0.341153\pi\) | ||||
0.478576 | + | 0.878046i | \(0.341153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34041.5 | −1.35213 | −0.676067 | − | 0.736841i | \(-0.736317\pi\) | ||||
−0.676067 | + | 0.736841i | \(0.736317\pi\) | |||||||
\(860\) | −2521.78 | −0.0999908 | ||||||||
\(861\) | −51594.9 | −2.04222 | ||||||||
\(862\) | −18876.5 | −0.745865 | ||||||||
\(863\) | −13583.4 | −0.535789 | −0.267894 | − | 0.963448i | \(-0.586328\pi\) | ||||
−0.267894 | + | 0.963448i | \(0.586328\pi\) | |||||||
\(864\) | −3397.44 | −0.133777 | ||||||||
\(865\) | −46992.3 | −1.84715 | ||||||||
\(866\) | −6465.76 | −0.253713 | ||||||||
\(867\) | 11867.5 | 0.464871 | ||||||||
\(868\) | 346.047 | 0.0135318 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −16816.9 | −0.655339 | ||||||||
\(871\) | −7906.07 | −0.307562 | ||||||||
\(872\) | 3275.77 | 0.127215 | ||||||||
\(873\) | 28400.4 | 1.10104 | ||||||||
\(874\) | 12588.8 | 0.487210 | ||||||||
\(875\) | 25698.8 | 0.992888 | ||||||||
\(876\) | −833.486 | −0.0321471 | ||||||||
\(877\) | −4982.94 | −0.191861 | −0.0959304 | − | 0.995388i | \(-0.530583\pi\) | ||||
−0.0959304 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(878\) | −42414.7 | −1.63033 | ||||||||
\(879\) | 54109.0 | 2.07628 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6944.27 | 0.265560 | 0.132780 | − | 0.991146i | \(-0.457610\pi\) | ||||
0.132780 | + | 0.991146i | \(0.457610\pi\) | |||||||
\(882\) | −3992.20 | −0.152409 | ||||||||
\(883\) | −26384.2 | −1.00555 | −0.502774 | − | 0.864418i | \(-0.667687\pi\) | ||||
−0.502774 | + | 0.864418i | \(0.667687\pi\) | |||||||
\(884\) | 1346.57 | 0.0512332 | ||||||||
\(885\) | −2285.21 | −0.0867984 | ||||||||
\(886\) | −28677.0 | −1.08739 | ||||||||
\(887\) | 1306.21 | 0.0494454 | 0.0247227 | − | 0.999694i | \(-0.492130\pi\) | ||||
0.0247227 | + | 0.999694i | \(0.492130\pi\) | |||||||
\(888\) | −40364.6 | −1.52539 | ||||||||
\(889\) | −13197.5 | −0.497895 | ||||||||
\(890\) | −26447.5 | −0.996092 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4931.09 | 0.185095 | ||||||||
\(893\) | 26017.7 | 0.974973 | ||||||||
\(894\) | −23348.9 | −0.873494 | ||||||||
\(895\) | 15407.4 | 0.575432 | ||||||||
\(896\) | 29641.8 | 1.10521 | ||||||||
\(897\) | 7902.42 | 0.294152 | ||||||||
\(898\) | −2081.03 | −0.0773328 | ||||||||
\(899\) | 1032.65 | 0.0383101 | ||||||||
\(900\) | −705.400 | −0.0261259 | ||||||||
\(901\) | 29374.0 | 1.08612 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25579.5 | 0.942671 | ||||||||
\(904\) | −22416.1 | −0.824721 | ||||||||
\(905\) | −1593.46 | −0.0585287 | ||||||||
\(906\) | −59286.3 | −2.17401 | ||||||||
\(907\) | −48885.7 | −1.78966 | −0.894831 | − | 0.446404i | \(-0.852704\pi\) | ||||
−0.894831 | + | 0.446404i | \(0.852704\pi\) | |||||||
\(908\) | 3246.25 | 0.118646 | ||||||||
\(909\) | −34201.1 | −1.24794 | ||||||||
\(910\) | 7231.15 | 0.263418 | ||||||||
\(911\) | −29503.0 | −1.07297 | −0.536486 | − | 0.843909i | \(-0.680249\pi\) | ||||
−0.536486 | + | 0.843909i | \(0.680249\pi\) | |||||||
\(912\) | 30351.5 | 1.10201 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 24772.7 | 0.896509 | ||||||||
\(915\) | −44261.8 | −1.59918 | ||||||||
\(916\) | −8487.19 | −0.306141 | ||||||||
\(917\) | −35798.7 | −1.28918 | ||||||||
\(918\) | −14331.5 | −0.515262 | ||||||||
\(919\) | −25816.9 | −0.926684 | −0.463342 | − | 0.886180i | \(-0.653350\pi\) | ||||
−0.463342 | + | 0.886180i | \(0.653350\pi\) | |||||||
\(920\) | −16563.0 | −0.593550 | ||||||||
\(921\) | −398.612 | −0.0142613 | ||||||||
\(922\) | −30769.3 | −1.09906 | ||||||||
\(923\) | 15349.9 | 0.547399 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3986.26 | −0.141695 | ||||||||
\(926\) | −492.472 | −0.0174769 | ||||||||
\(927\) | 14088.4 | 0.499163 | ||||||||
\(928\) | −3901.06 | −0.137994 | ||||||||
\(929\) | −14202.9 | −0.501596 | −0.250798 | − | 0.968039i | \(-0.580693\pi\) | ||||
−0.250798 | + | 0.968039i | \(0.580693\pi\) | |||||||
\(930\) | −3829.51 | −0.135026 | ||||||||
\(931\) | 2023.33 | 0.0712267 | ||||||||
\(932\) | −2944.34 | −0.103482 | ||||||||
\(933\) | 59784.9 | 2.09782 | ||||||||
\(934\) | −10139.5 | −0.355218 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9165.35 | 0.320063 | ||||||||
\(937\) | −55535.3 | −1.93624 | −0.968122 | − | 0.250480i | \(-0.919412\pi\) | ||||
−0.968122 | + | 0.250480i | \(0.919412\pi\) | |||||||
\(938\) | 32377.0 | 1.12702 | ||||||||
\(939\) | 59284.8 | 2.06037 | ||||||||
\(940\) | 6593.83 | 0.228795 | ||||||||
\(941\) | 27893.4 | 0.966311 | 0.483156 | − | 0.875535i | \(-0.339491\pi\) | ||||
0.483156 | + | 0.875535i | \(0.339491\pi\) | |||||||
\(942\) | 54045.8 | 1.86933 | ||||||||
\(943\) | 29210.0 | 1.00870 | ||||||||
\(944\) | −2027.01 | −0.0698872 | ||||||||
\(945\) | −10701.7 | −0.368388 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33283.9 | −1.14211 | −0.571057 | − | 0.820910i | \(-0.693466\pi\) | ||||
−0.571057 | + | 0.820910i | \(0.693466\pi\) | |||||||
\(948\) | −4218.76 | −0.144535 | ||||||||
\(949\) | 1069.49 | 0.0365829 | ||||||||
\(950\) | 2571.02 | 0.0878053 | ||||||||
\(951\) | 68298.4 | 2.32884 | ||||||||
\(952\) | 28628.2 | 0.974627 | ||||||||
\(953\) | 26366.7 | 0.896224 | 0.448112 | − | 0.893977i | \(-0.352097\pi\) | ||||
0.448112 | + | 0.893977i | \(0.352097\pi\) | |||||||
\(954\) | −38511.8 | −1.30699 | ||||||||
\(955\) | −13386.8 | −0.453598 | ||||||||
\(956\) | −7962.17 | −0.269367 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22991.1 | 0.775373 | ||||||||
\(959\) | 17845.8 | 0.600908 | ||||||||
\(960\) | −33158.7 | −1.11478 | ||||||||
\(961\) | −29555.8 | −0.992107 | ||||||||
\(962\) | −9976.81 | −0.334371 | ||||||||
\(963\) | 32065.6 | 1.07300 | ||||||||
\(964\) | 5884.85 | 0.196616 | ||||||||
\(965\) | −26733.9 | −0.891808 | ||||||||
\(966\) | −32362.0 | −1.07788 | ||||||||
\(967\) | 40336.7 | 1.34141 | 0.670703 | − | 0.741726i | \(-0.265992\pi\) | ||||
0.670703 | + | 0.741726i | \(0.265992\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33483.4 | 1.11005 | ||||||||
\(970\) | −26234.0 | −0.868373 | ||||||||
\(971\) | 33695.9 | 1.11365 | 0.556824 | − | 0.830631i | \(-0.312020\pi\) | ||||
0.556824 | + | 0.830631i | \(0.312020\pi\) | |||||||
\(972\) | −6818.90 | −0.225017 | ||||||||
\(973\) | −10528.3 | −0.346887 | ||||||||
\(974\) | −38670.9 | −1.27217 | ||||||||
\(975\) | 1613.93 | 0.0530123 | ||||||||
\(976\) | −39260.7 | −1.28761 | ||||||||
\(977\) | −9413.52 | −0.308255 | −0.154127 | − | 0.988051i | \(-0.549257\pi\) | ||||
−0.154127 | + | 0.988051i | \(0.549257\pi\) | |||||||
\(978\) | 35443.8 | 1.15886 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 512.786 | 0.0167146 | ||||||||
\(981\) | −5523.73 | −0.179775 | ||||||||
\(982\) | −41303.9 | −1.34222 | ||||||||
\(983\) | −37657.2 | −1.22185 | −0.610925 | − | 0.791689i | \(-0.709202\pi\) | ||||
−0.610925 | + | 0.791689i | \(0.709202\pi\) | |||||||
\(984\) | 60407.2 | 1.95702 | ||||||||
\(985\) | 47569.5 | 1.53877 | ||||||||
\(986\) | −16456.0 | −0.531506 | ||||||||
\(987\) | −66884.0 | −2.15698 | ||||||||
\(988\) | 894.780 | 0.0288125 | ||||||||
\(989\) | −14481.6 | −0.465609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55077.2 | 1.76547 | 0.882737 | − | 0.469868i | \(-0.155698\pi\) | ||||
0.882737 | + | 0.469868i | \(0.155698\pi\) | |||||||
\(992\) | −888.344 | −0.0284324 | ||||||||
\(993\) | 52107.9 | 1.66525 | ||||||||
\(994\) | −62861.1 | −2.00587 | ||||||||
\(995\) | 43860.6 | 1.39746 | ||||||||
\(996\) | −10505.8 | −0.334226 | ||||||||
\(997\) | −27419.6 | −0.870999 | −0.435500 | − | 0.900189i | \(-0.643428\pi\) | ||||
−0.435500 | + | 0.900189i | \(0.643428\pi\) | |||||||
\(998\) | −44316.7 | −1.40563 | ||||||||
\(999\) | 14765.1 | 0.467616 |
(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 | 1573.4.a.h.1.12 | ✓ | 15 | |
11.10 | odd | 2 | 1573.4.a.k.1.4 | yes | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1573.4.a.h.1.12 | ✓ | 15 | 1.1 | even | 1 | trivial | |
1573.4.a.k.1.4 | yes | 15 | 11.10 | odd | 2 |