Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.65397 | 1.29187 | 0.645937 | − | 0.763391i | \(-0.276467\pi\) | ||||
0.645937 | + | 0.763391i | \(0.276467\pi\) | |||||||
\(3\) | 3.36009 | 0.646649 | 0.323325 | − | 0.946288i | \(-0.395199\pi\) | ||||
0.323325 | + | 0.946288i | \(0.395199\pi\) | |||||||
\(4\) | 5.35150 | 0.668938 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 12.2777 | 0.835389 | ||||||||
\(7\) | −1.36266 | −0.0735766 | −0.0367883 | − | 0.999323i | \(-0.511713\pi\) | ||||
−0.0367883 | + | 0.999323i | \(0.511713\pi\) | |||||||
\(8\) | −9.67753 | −0.427690 | ||||||||
\(9\) | −15.7098 | −0.581845 | ||||||||
\(10\) | 18.2699 | 0.577744 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 17.9815 | 0.432568 | ||||||||
\(13\) | −71.5168 | −1.52578 | −0.762892 | − | 0.646526i | \(-0.776221\pi\) | ||||
−0.762892 | + | 0.646526i | \(0.776221\pi\) | |||||||
\(14\) | −4.97911 | −0.0950517 | ||||||||
\(15\) | 16.8004 | 0.289190 | ||||||||
\(16\) | −78.1734 | −1.22146 | ||||||||
\(17\) | 55.9067 | 0.797610 | 0.398805 | − | 0.917036i | \(-0.369425\pi\) | ||||
0.398805 | + | 0.917036i | \(0.369425\pi\) | |||||||
\(18\) | −57.4032 | −0.751670 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 26.7575 | 0.299158 | ||||||||
\(21\) | −4.57865 | −0.0475783 | ||||||||
\(22\) | −40.1937 | −0.389515 | ||||||||
\(23\) | 125.854 | 1.14097 | 0.570486 | − | 0.821307i | \(-0.306755\pi\) | ||||
0.570486 | + | 0.821307i | \(0.306755\pi\) | |||||||
\(24\) | −32.5174 | −0.276566 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −261.320 | −1.97112 | ||||||||
\(27\) | −143.509 | −1.02290 | ||||||||
\(28\) | −7.29227 | −0.0492182 | ||||||||
\(29\) | −244.581 | −1.56612 | −0.783062 | − | 0.621944i | \(-0.786343\pi\) | ||||
−0.783062 | + | 0.621944i | \(0.786343\pi\) | |||||||
\(30\) | 61.3883 | 0.373597 | ||||||||
\(31\) | 59.2492 | 0.343273 | 0.171637 | − | 0.985160i | \(-0.445095\pi\) | ||||
0.171637 | + | 0.985160i | \(0.445095\pi\) | |||||||
\(32\) | −208.223 | −1.15028 | ||||||||
\(33\) | −36.9610 | −0.194972 | ||||||||
\(34\) | 204.282 | 1.03041 | ||||||||
\(35\) | −6.81329 | −0.0329045 | ||||||||
\(36\) | −84.0711 | −0.389218 | ||||||||
\(37\) | −106.327 | −0.472432 | −0.236216 | − | 0.971701i | \(-0.575907\pi\) | ||||
−0.236216 | + | 0.971701i | \(0.575907\pi\) | |||||||
\(38\) | −69.4254 | −0.296376 | ||||||||
\(39\) | −240.303 | −0.986648 | ||||||||
\(40\) | −48.3877 | −0.191269 | ||||||||
\(41\) | −523.023 | −1.99226 | −0.996128 | − | 0.0879158i | \(-0.971979\pi\) | ||||
−0.996128 | + | 0.0879158i | \(0.971979\pi\) | |||||||
\(42\) | −16.7303 | −0.0614651 | ||||||||
\(43\) | 286.782 | 1.01707 | 0.508533 | − | 0.861042i | \(-0.330188\pi\) | ||||
0.508533 | + | 0.861042i | \(0.330188\pi\) | |||||||
\(44\) | −58.8665 | −0.201692 | ||||||||
\(45\) | −78.5490 | −0.260209 | ||||||||
\(46\) | 459.867 | 1.47399 | ||||||||
\(47\) | −437.372 | −1.35739 | −0.678695 | − | 0.734420i | \(-0.737454\pi\) | ||||
−0.678695 | + | 0.734420i | \(0.737454\pi\) | |||||||
\(48\) | −262.670 | −0.789856 | ||||||||
\(49\) | −341.143 | −0.994586 | ||||||||
\(50\) | 91.3493 | 0.258375 | ||||||||
\(51\) | 187.852 | 0.515774 | ||||||||
\(52\) | −382.723 | −1.02066 | ||||||||
\(53\) | 235.160 | 0.609466 | 0.304733 | − | 0.952438i | \(-0.401433\pi\) | ||||
0.304733 | + | 0.952438i | \(0.401433\pi\) | |||||||
\(54\) | −524.377 | −1.32146 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 13.1872 | 0.0314680 | ||||||||
\(57\) | −63.8417 | −0.148352 | ||||||||
\(58\) | −893.692 | −2.02323 | ||||||||
\(59\) | −613.449 | −1.35363 | −0.676816 | − | 0.736152i | \(-0.736641\pi\) | ||||
−0.676816 | + | 0.736152i | \(0.736641\pi\) | |||||||
\(60\) | 89.9076 | 0.193450 | ||||||||
\(61\) | −126.914 | −0.266388 | −0.133194 | − | 0.991090i | \(-0.542523\pi\) | ||||
−0.133194 | + | 0.991090i | \(0.542523\pi\) | |||||||
\(62\) | 216.495 | 0.443465 | ||||||||
\(63\) | 21.4071 | 0.0428102 | ||||||||
\(64\) | −135.454 | −0.264559 | ||||||||
\(65\) | −357.584 | −0.682352 | ||||||||
\(66\) | −135.054 | −0.251879 | ||||||||
\(67\) | 585.333 | 1.06731 | 0.533655 | − | 0.845702i | \(-0.320818\pi\) | ||||
0.533655 | + | 0.845702i | \(0.320818\pi\) | |||||||
\(68\) | 299.185 | 0.533552 | ||||||||
\(69\) | 422.880 | 0.737809 | ||||||||
\(70\) | −24.8956 | −0.0425084 | ||||||||
\(71\) | 737.432 | 1.23264 | 0.616318 | − | 0.787498i | \(-0.288624\pi\) | ||||
0.616318 | + | 0.787498i | \(0.288624\pi\) | |||||||
\(72\) | 152.032 | 0.248849 | ||||||||
\(73\) | 152.003 | 0.243707 | 0.121854 | − | 0.992548i | \(-0.461116\pi\) | ||||
0.121854 | + | 0.992548i | \(0.461116\pi\) | |||||||
\(74\) | −388.515 | −0.610323 | ||||||||
\(75\) | 84.0022 | 0.129330 | ||||||||
\(76\) | −101.679 | −0.153465 | ||||||||
\(77\) | 14.9892 | 0.0221842 | ||||||||
\(78\) | −878.060 | −1.27462 | ||||||||
\(79\) | 457.791 | 0.651969 | 0.325984 | − | 0.945375i | \(-0.394304\pi\) | ||||
0.325984 | + | 0.945375i | \(0.394304\pi\) | |||||||
\(80\) | −390.867 | −0.546254 | ||||||||
\(81\) | −58.0374 | −0.0796123 | ||||||||
\(82\) | −1911.11 | −2.57374 | ||||||||
\(83\) | 1293.95 | 1.71119 | 0.855596 | − | 0.517644i | \(-0.173191\pi\) | ||||
0.855596 | + | 0.517644i | \(0.173191\pi\) | |||||||
\(84\) | −24.5027 | −0.0318269 | ||||||||
\(85\) | 279.534 | 0.356702 | ||||||||
\(86\) | 1047.89 | 1.31392 | ||||||||
\(87\) | −821.814 | −1.01273 | ||||||||
\(88\) | 106.453 | 0.128954 | ||||||||
\(89\) | −1090.77 | −1.29912 | −0.649558 | − | 0.760312i | \(-0.725046\pi\) | ||||
−0.649558 | + | 0.760312i | \(0.725046\pi\) | |||||||
\(90\) | −287.016 | −0.336157 | ||||||||
\(91\) | 97.4530 | 0.112262 | ||||||||
\(92\) | 673.508 | 0.763239 | ||||||||
\(93\) | 199.082 | 0.221977 | ||||||||
\(94\) | −1598.15 | −1.75358 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | −699.649 | −0.743829 | ||||||||
\(97\) | −1047.37 | −1.09633 | −0.548167 | − | 0.836369i | \(-0.684674\pi\) | ||||
−0.548167 | + | 0.836369i | \(0.684674\pi\) | |||||||
\(98\) | −1246.53 | −1.28488 | ||||||||
\(99\) | 172.808 | 0.175433 | ||||||||
\(100\) | 133.788 | 0.133788 | ||||||||
\(101\) | 1536.06 | 1.51330 | 0.756650 | − | 0.653820i | \(-0.226835\pi\) | ||||
0.756650 | + | 0.653820i | \(0.226835\pi\) | |||||||
\(102\) | 686.404 | 0.666315 | ||||||||
\(103\) | −948.160 | −0.907039 | −0.453520 | − | 0.891246i | \(-0.649832\pi\) | ||||
−0.453520 | + | 0.891246i | \(0.649832\pi\) | |||||||
\(104\) | 692.106 | 0.652563 | ||||||||
\(105\) | −22.8933 | −0.0212777 | ||||||||
\(106\) | 859.267 | 0.787353 | ||||||||
\(107\) | 1612.43 | 1.45682 | 0.728411 | − | 0.685141i | \(-0.240259\pi\) | ||||
0.728411 | + | 0.685141i | \(0.240259\pi\) | |||||||
\(108\) | −767.987 | −0.684256 | ||||||||
\(109\) | −682.057 | −0.599351 | −0.299675 | − | 0.954041i | \(-0.596878\pi\) | ||||
−0.299675 | + | 0.954041i | \(0.596878\pi\) | |||||||
\(110\) | −200.968 | −0.174196 | ||||||||
\(111\) | −357.267 | −0.305498 | ||||||||
\(112\) | 106.524 | 0.0898709 | ||||||||
\(113\) | 7.28207 | 0.00606230 | 0.00303115 | − | 0.999995i | \(-0.499035\pi\) | ||||
0.00303115 | + | 0.999995i | \(0.499035\pi\) | |||||||
\(114\) | −233.276 | −0.191651 | ||||||||
\(115\) | 629.270 | 0.510258 | ||||||||
\(116\) | −1308.88 | −1.04764 | ||||||||
\(117\) | 1123.52 | 0.887769 | ||||||||
\(118\) | −2241.53 | −1.74872 | ||||||||
\(119\) | −76.1817 | −0.0586855 | ||||||||
\(120\) | −162.587 | −0.123684 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −463.740 | −0.344140 | ||||||||
\(123\) | −1757.40 | −1.28829 | ||||||||
\(124\) | 317.072 | 0.229628 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 78.2209 | 0.0553053 | ||||||||
\(127\) | −1785.00 | −1.24719 | −0.623596 | − | 0.781747i | \(-0.714329\pi\) | ||||
−0.623596 | + | 0.781747i | \(0.714329\pi\) | |||||||
\(128\) | 1170.84 | 0.808505 | ||||||||
\(129\) | 963.613 | 0.657685 | ||||||||
\(130\) | −1306.60 | −0.881512 | ||||||||
\(131\) | −1291.33 | −0.861254 | −0.430627 | − | 0.902530i | \(-0.641707\pi\) | ||||
−0.430627 | + | 0.902530i | \(0.641707\pi\) | |||||||
\(132\) | −197.797 | −0.130424 | ||||||||
\(133\) | 25.8905 | 0.0168796 | ||||||||
\(134\) | 2138.79 | 1.37883 | ||||||||
\(135\) | −717.544 | −0.457454 | ||||||||
\(136\) | −541.039 | −0.341130 | ||||||||
\(137\) | −434.352 | −0.270870 | −0.135435 | − | 0.990786i | \(-0.543243\pi\) | ||||
−0.135435 | + | 0.990786i | \(0.543243\pi\) | |||||||
\(138\) | 1545.19 | 0.953156 | ||||||||
\(139\) | 1899.56 | 1.15913 | 0.579565 | − | 0.814926i | \(-0.303223\pi\) | ||||
0.579565 | + | 0.814926i | \(0.303223\pi\) | |||||||
\(140\) | −36.4613 | −0.0220110 | ||||||||
\(141\) | −1469.61 | −0.877755 | ||||||||
\(142\) | 2694.56 | 1.59241 | ||||||||
\(143\) | 786.685 | 0.460041 | ||||||||
\(144\) | 1228.09 | 0.710700 | ||||||||
\(145\) | −1222.91 | −0.700392 | ||||||||
\(146\) | 555.415 | 0.314839 | ||||||||
\(147\) | −1146.27 | −0.643149 | ||||||||
\(148\) | −569.008 | −0.316028 | ||||||||
\(149\) | 486.320 | 0.267389 | 0.133694 | − | 0.991023i | \(-0.457316\pi\) | ||||
0.133694 | + | 0.991023i | \(0.457316\pi\) | |||||||
\(150\) | 306.942 | 0.167078 | ||||||||
\(151\) | −1846.25 | −0.995005 | −0.497503 | − | 0.867462i | \(-0.665750\pi\) | ||||
−0.497503 | + | 0.867462i | \(0.665750\pi\) | |||||||
\(152\) | 183.873 | 0.0981189 | ||||||||
\(153\) | −878.284 | −0.464085 | ||||||||
\(154\) | 54.7702 | 0.0286592 | ||||||||
\(155\) | 296.246 | 0.153516 | ||||||||
\(156\) | −1285.98 | −0.660006 | ||||||||
\(157\) | −1380.31 | −0.701660 | −0.350830 | − | 0.936439i | \(-0.614100\pi\) | ||||
−0.350830 | + | 0.936439i | \(0.614100\pi\) | |||||||
\(158\) | 1672.76 | 0.842261 | ||||||||
\(159\) | 790.158 | 0.394111 | ||||||||
\(160\) | −1041.12 | −0.514422 | ||||||||
\(161\) | −171.496 | −0.0839489 | ||||||||
\(162\) | −212.067 | −0.102849 | ||||||||
\(163\) | 3201.15 | 1.53824 | 0.769121 | − | 0.639103i | \(-0.220694\pi\) | ||||
0.769121 | + | 0.639103i | \(0.220694\pi\) | |||||||
\(164\) | −2798.96 | −1.33270 | ||||||||
\(165\) | −184.805 | −0.0871942 | ||||||||
\(166\) | 4728.04 | 2.21064 | ||||||||
\(167\) | 1727.66 | 0.800541 | 0.400270 | − | 0.916397i | \(-0.368916\pi\) | ||||
0.400270 | + | 0.916397i | \(0.368916\pi\) | |||||||
\(168\) | 44.3100 | 0.0203488 | ||||||||
\(169\) | 2917.66 | 1.32802 | ||||||||
\(170\) | 1021.41 | 0.460814 | ||||||||
\(171\) | 298.486 | 0.133484 | ||||||||
\(172\) | 1534.71 | 0.680354 | ||||||||
\(173\) | −1366.74 | −0.600645 | −0.300322 | − | 0.953838i | \(-0.597094\pi\) | ||||
−0.300322 | + | 0.953838i | \(0.597094\pi\) | |||||||
\(174\) | −3002.89 | −1.30832 | ||||||||
\(175\) | −34.0665 | −0.0147153 | ||||||||
\(176\) | 859.908 | 0.368284 | ||||||||
\(177\) | −2061.24 | −0.875325 | ||||||||
\(178\) | −3985.64 | −1.67829 | ||||||||
\(179\) | −4087.07 | −1.70660 | −0.853301 | − | 0.521418i | \(-0.825403\pi\) | ||||
−0.853301 | + | 0.521418i | \(0.825403\pi\) | |||||||
\(180\) | −420.355 | −0.174064 | ||||||||
\(181\) | −3149.66 | −1.29344 | −0.646720 | − | 0.762728i | \(-0.723860\pi\) | ||||
−0.646720 | + | 0.762728i | \(0.723860\pi\) | |||||||
\(182\) | 356.090 | 0.145028 | ||||||||
\(183\) | −426.443 | −0.172260 | ||||||||
\(184\) | −1217.96 | −0.487983 | ||||||||
\(185\) | −531.633 | −0.211278 | ||||||||
\(186\) | 727.441 | 0.286767 | ||||||||
\(187\) | −614.974 | −0.240488 | ||||||||
\(188\) | −2340.60 | −0.908009 | ||||||||
\(189\) | 195.553 | 0.0752614 | ||||||||
\(190\) | −347.127 | −0.132543 | ||||||||
\(191\) | 341.566 | 0.129397 | 0.0646985 | − | 0.997905i | \(-0.479391\pi\) | ||||
0.0646985 | + | 0.997905i | \(0.479391\pi\) | |||||||
\(192\) | −455.138 | −0.171077 | ||||||||
\(193\) | −2888.68 | −1.07737 | −0.538683 | − | 0.842509i | \(-0.681078\pi\) | ||||
−0.538683 | + | 0.842509i | \(0.681078\pi\) | |||||||
\(194\) | −3827.06 | −1.41633 | ||||||||
\(195\) | −1201.51 | −0.441242 | ||||||||
\(196\) | −1825.63 | −0.665317 | ||||||||
\(197\) | 1031.47 | 0.373041 | 0.186521 | − | 0.982451i | \(-0.440279\pi\) | ||||
0.186521 | + | 0.982451i | \(0.440279\pi\) | |||||||
\(198\) | 631.435 | 0.226637 | ||||||||
\(199\) | −1249.43 | −0.445075 | −0.222537 | − | 0.974924i | \(-0.571434\pi\) | ||||
−0.222537 | + | 0.974924i | \(0.571434\pi\) | |||||||
\(200\) | −241.938 | −0.0855381 | ||||||||
\(201\) | 1966.77 | 0.690176 | ||||||||
\(202\) | 5612.70 | 1.95499 | ||||||||
\(203\) | 333.280 | 0.115230 | ||||||||
\(204\) | 1005.29 | 0.345021 | ||||||||
\(205\) | −2615.12 | −0.890964 | ||||||||
\(206\) | −3464.55 | −1.17178 | ||||||||
\(207\) | −1977.14 | −0.663868 | ||||||||
\(208\) | 5590.72 | 1.86368 | ||||||||
\(209\) | 209.000 | 0.0691714 | ||||||||
\(210\) | −83.6513 | −0.0274880 | ||||||||
\(211\) | 1117.74 | 0.364686 | 0.182343 | − | 0.983235i | \(-0.441632\pi\) | ||||
0.182343 | + | 0.983235i | \(0.441632\pi\) | |||||||
\(212\) | 1258.46 | 0.407695 | ||||||||
\(213\) | 2477.84 | 0.797083 | ||||||||
\(214\) | 5891.79 | 1.88203 | ||||||||
\(215\) | 1433.91 | 0.454846 | ||||||||
\(216\) | 1388.81 | 0.437484 | ||||||||
\(217\) | −80.7363 | −0.0252569 | ||||||||
\(218\) | −2492.22 | −0.774285 | ||||||||
\(219\) | 510.744 | 0.157593 | ||||||||
\(220\) | −294.333 | −0.0901996 | ||||||||
\(221\) | −3998.27 | −1.21698 | ||||||||
\(222\) | −1305.44 | −0.394665 | ||||||||
\(223\) | −670.642 | −0.201388 | −0.100694 | − | 0.994917i | \(-0.532106\pi\) | ||||
−0.100694 | + | 0.994917i | \(0.532106\pi\) | |||||||
\(224\) | 283.737 | 0.0846338 | ||||||||
\(225\) | −392.745 | −0.116369 | ||||||||
\(226\) | 26.6085 | 0.00783172 | ||||||||
\(227\) | 3463.91 | 1.01281 | 0.506405 | − | 0.862296i | \(-0.330974\pi\) | ||||
0.506405 | + | 0.862296i | \(0.330974\pi\) | |||||||
\(228\) | −341.649 | −0.0992380 | ||||||||
\(229\) | 3244.29 | 0.936196 | 0.468098 | − | 0.883677i | \(-0.344939\pi\) | ||||
0.468098 | + | 0.883677i | \(0.344939\pi\) | |||||||
\(230\) | 2299.33 | 0.659189 | ||||||||
\(231\) | 50.3652 | 0.0143454 | ||||||||
\(232\) | 2366.94 | 0.669816 | ||||||||
\(233\) | −2702.97 | −0.759989 | −0.379995 | − | 0.924989i | \(-0.624074\pi\) | ||||
−0.379995 | + | 0.924989i | \(0.624074\pi\) | |||||||
\(234\) | 4105.29 | 1.14689 | ||||||||
\(235\) | −2186.86 | −0.607043 | ||||||||
\(236\) | −3282.88 | −0.905496 | ||||||||
\(237\) | 1538.22 | 0.421595 | ||||||||
\(238\) | −278.366 | −0.0758142 | ||||||||
\(239\) | −707.108 | −0.191377 | −0.0956883 | − | 0.995411i | \(-0.530505\pi\) | ||||
−0.0956883 | + | 0.995411i | \(0.530505\pi\) | |||||||
\(240\) | −1313.35 | −0.353234 | ||||||||
\(241\) | 4070.10 | 1.08788 | 0.543938 | − | 0.839125i | \(-0.316933\pi\) | ||||
0.543938 | + | 0.839125i | \(0.316933\pi\) | |||||||
\(242\) | 442.130 | 0.117443 | ||||||||
\(243\) | 3679.73 | 0.971418 | ||||||||
\(244\) | −679.181 | −0.178197 | ||||||||
\(245\) | −1705.72 | −0.444793 | ||||||||
\(246\) | −6421.50 | −1.66431 | ||||||||
\(247\) | 1358.82 | 0.350039 | ||||||||
\(248\) | −573.386 | −0.146815 | ||||||||
\(249\) | 4347.77 | 1.10654 | ||||||||
\(250\) | 456.746 | 0.115549 | ||||||||
\(251\) | 1491.47 | 0.375063 | 0.187532 | − | 0.982259i | \(-0.439951\pi\) | ||||
0.187532 | + | 0.982259i | \(0.439951\pi\) | |||||||
\(252\) | 114.560 | 0.0286373 | ||||||||
\(253\) | −1384.39 | −0.344016 | ||||||||
\(254\) | −6522.35 | −1.61121 | ||||||||
\(255\) | 939.258 | 0.230661 | ||||||||
\(256\) | 5361.85 | 1.30905 | ||||||||
\(257\) | −74.6875 | −0.0181279 | −0.00906397 | − | 0.999959i | \(-0.502885\pi\) | ||||
−0.00906397 | + | 0.999959i | \(0.502885\pi\) | |||||||
\(258\) | 3521.01 | 0.849646 | ||||||||
\(259\) | 144.887 | 0.0347600 | ||||||||
\(260\) | −1913.61 | −0.456451 | ||||||||
\(261\) | 3842.32 | 0.911240 | ||||||||
\(262\) | −4718.49 | −1.11263 | ||||||||
\(263\) | 2587.90 | 0.606757 | 0.303378 | − | 0.952870i | \(-0.401885\pi\) | ||||
0.303378 | + | 0.952870i | \(0.401885\pi\) | |||||||
\(264\) | 357.691 | 0.0833877 | ||||||||
\(265\) | 1175.80 | 0.272561 | ||||||||
\(266\) | 94.6031 | 0.0218064 | ||||||||
\(267\) | −3665.08 | −0.840073 | ||||||||
\(268\) | 3132.41 | 0.713965 | ||||||||
\(269\) | −1584.76 | −0.359198 | −0.179599 | − | 0.983740i | \(-0.557480\pi\) | ||||
−0.179599 | + | 0.983740i | \(0.557480\pi\) | |||||||
\(270\) | −2621.88 | −0.590973 | ||||||||
\(271\) | 342.084 | 0.0766794 | 0.0383397 | − | 0.999265i | \(-0.487793\pi\) | ||||
0.0383397 | + | 0.999265i | \(0.487793\pi\) | |||||||
\(272\) | −4370.42 | −0.974249 | ||||||||
\(273\) | 327.451 | 0.0725942 | ||||||||
\(274\) | −1587.11 | −0.349930 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 2263.05 | 0.493548 | ||||||||
\(277\) | 5532.84 | 1.20013 | 0.600065 | − | 0.799951i | \(-0.295141\pi\) | ||||
0.600065 | + | 0.799951i | \(0.295141\pi\) | |||||||
\(278\) | 6940.95 | 1.49745 | ||||||||
\(279\) | −930.793 | −0.199732 | ||||||||
\(280\) | 65.9358 | 0.0140729 | ||||||||
\(281\) | 1455.87 | 0.309075 | 0.154538 | − | 0.987987i | \(-0.450611\pi\) | ||||
0.154538 | + | 0.987987i | \(0.450611\pi\) | |||||||
\(282\) | −5369.91 | −1.13395 | ||||||||
\(283\) | 1808.30 | 0.379831 | 0.189915 | − | 0.981800i | \(-0.439179\pi\) | ||||
0.189915 | + | 0.981800i | \(0.439179\pi\) | |||||||
\(284\) | 3946.37 | 0.824556 | ||||||||
\(285\) | −319.208 | −0.0663448 | ||||||||
\(286\) | 2874.52 | 0.594315 | ||||||||
\(287\) | 712.702 | 0.146583 | ||||||||
\(288\) | 3271.15 | 0.669285 | ||||||||
\(289\) | −1787.44 | −0.363818 | ||||||||
\(290\) | −4468.46 | −0.904817 | ||||||||
\(291\) | −3519.26 | −0.708944 | ||||||||
\(292\) | 813.446 | 0.163025 | ||||||||
\(293\) | −235.695 | −0.0469947 | −0.0234973 | − | 0.999724i | \(-0.507480\pi\) | ||||
−0.0234973 | + | 0.999724i | \(0.507480\pi\) | |||||||
\(294\) | −4188.44 | −0.830867 | ||||||||
\(295\) | −3067.25 | −0.605363 | ||||||||
\(296\) | 1028.98 | 0.202055 | ||||||||
\(297\) | 1578.60 | 0.308416 | ||||||||
\(298\) | 1777.00 | 0.345433 | ||||||||
\(299\) | −9000.67 | −1.74088 | ||||||||
\(300\) | 449.538 | 0.0865137 | ||||||||
\(301\) | −390.786 | −0.0748323 | ||||||||
\(302\) | −6746.15 | −1.28542 | ||||||||
\(303\) | 5161.28 | 0.978574 | ||||||||
\(304\) | 1485.30 | 0.280222 | ||||||||
\(305\) | −634.571 | −0.119132 | ||||||||
\(306\) | −3209.22 | −0.599539 | ||||||||
\(307\) | −2540.46 | −0.472285 | −0.236142 | − | 0.971718i | \(-0.575883\pi\) | ||||
−0.236142 | + | 0.971718i | \(0.575883\pi\) | |||||||
\(308\) | 80.2150 | 0.0148398 | ||||||||
\(309\) | −3185.90 | −0.586536 | ||||||||
\(310\) | 1082.47 | 0.198324 | ||||||||
\(311\) | 7147.77 | 1.30326 | 0.651628 | − | 0.758538i | \(-0.274086\pi\) | ||||
0.651628 | + | 0.758538i | \(0.274086\pi\) | |||||||
\(312\) | 2325.54 | 0.421980 | ||||||||
\(313\) | 4302.99 | 0.777058 | 0.388529 | − | 0.921436i | \(-0.372983\pi\) | ||||
0.388529 | + | 0.921436i | \(0.372983\pi\) | |||||||
\(314\) | −5043.60 | −0.906456 | ||||||||
\(315\) | 107.035 | 0.0191453 | ||||||||
\(316\) | 2449.87 | 0.436126 | ||||||||
\(317\) | 4858.80 | 0.860875 | 0.430438 | − | 0.902620i | \(-0.358359\pi\) | ||||
0.430438 | + | 0.902620i | \(0.358359\pi\) | |||||||
\(318\) | 2887.21 | 0.509141 | ||||||||
\(319\) | 2690.39 | 0.472204 | ||||||||
\(320\) | −677.270 | −0.118314 | ||||||||
\(321\) | 5417.92 | 0.942053 | ||||||||
\(322\) | −626.641 | −0.108451 | ||||||||
\(323\) | −1062.23 | −0.182984 | ||||||||
\(324\) | −310.587 | −0.0532557 | ||||||||
\(325\) | −1787.92 | −0.305157 | ||||||||
\(326\) | 11696.9 | 1.98721 | ||||||||
\(327\) | −2291.77 | −0.387570 | ||||||||
\(328\) | 5061.57 | 0.852069 | ||||||||
\(329\) | 595.989 | 0.0998722 | ||||||||
\(330\) | −675.272 | −0.112644 | ||||||||
\(331\) | −3944.03 | −0.654935 | −0.327468 | − | 0.944862i | \(-0.606195\pi\) | ||||
−0.327468 | + | 0.944862i | \(0.606195\pi\) | |||||||
\(332\) | 6924.55 | 1.14468 | ||||||||
\(333\) | 1670.37 | 0.274882 | ||||||||
\(334\) | 6312.82 | 1.03420 | ||||||||
\(335\) | 2926.67 | 0.477316 | ||||||||
\(336\) | 357.929 | 0.0581150 | ||||||||
\(337\) | −4567.58 | −0.738315 | −0.369157 | − | 0.929367i | \(-0.620354\pi\) | ||||
−0.369157 | + | 0.929367i | \(0.620354\pi\) | |||||||
\(338\) | 10661.0 | 1.71563 | ||||||||
\(339\) | 24.4684 | 0.00392018 | ||||||||
\(340\) | 1495.92 | 0.238612 | ||||||||
\(341\) | −651.741 | −0.103501 | ||||||||
\(342\) | 1090.66 | 0.172445 | ||||||||
\(343\) | 932.253 | 0.146755 | ||||||||
\(344\) | −2775.34 | −0.434989 | ||||||||
\(345\) | 2114.40 | 0.329958 | ||||||||
\(346\) | −4994.04 | −0.775957 | ||||||||
\(347\) | 3717.49 | 0.575117 | 0.287558 | − | 0.957763i | \(-0.407156\pi\) | ||||
0.287558 | + | 0.957763i | \(0.407156\pi\) | |||||||
\(348\) | −4397.94 | −0.677455 | ||||||||
\(349\) | −11402.2 | −1.74884 | −0.874418 | − | 0.485173i | \(-0.838757\pi\) | ||||
−0.874418 | + | 0.485173i | \(0.838757\pi\) | |||||||
\(350\) | −124.478 | −0.0190103 | ||||||||
\(351\) | 10263.3 | 1.56072 | ||||||||
\(352\) | 2290.46 | 0.346823 | ||||||||
\(353\) | −5994.36 | −0.903817 | −0.451909 | − | 0.892064i | \(-0.649257\pi\) | ||||
−0.451909 | + | 0.892064i | \(0.649257\pi\) | |||||||
\(354\) | −7531.72 | −1.13081 | ||||||||
\(355\) | 3687.16 | 0.551251 | ||||||||
\(356\) | −5837.26 | −0.869028 | ||||||||
\(357\) | −255.977 | −0.0379489 | ||||||||
\(358\) | −14934.0 | −2.20472 | ||||||||
\(359\) | 2837.37 | 0.417132 | 0.208566 | − | 0.978008i | \(-0.433120\pi\) | ||||
0.208566 | + | 0.978008i | \(0.433120\pi\) | |||||||
\(360\) | 760.161 | 0.111289 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −11508.8 | −1.67096 | ||||||||
\(363\) | 406.571 | 0.0587863 | ||||||||
\(364\) | 521.520 | 0.0750964 | ||||||||
\(365\) | 760.016 | 0.108989 | ||||||||
\(366\) | −1558.21 | −0.222538 | ||||||||
\(367\) | −8558.98 | −1.21737 | −0.608685 | − | 0.793412i | \(-0.708303\pi\) | ||||
−0.608685 | + | 0.793412i | \(0.708303\pi\) | |||||||
\(368\) | −9838.43 | −1.39365 | ||||||||
\(369\) | 8216.59 | 1.15918 | ||||||||
\(370\) | −1942.57 | −0.272945 | ||||||||
\(371\) | −320.443 | −0.0448424 | ||||||||
\(372\) | 1065.39 | 0.148489 | ||||||||
\(373\) | −2255.02 | −0.313031 | −0.156515 | − | 0.987676i | \(-0.550026\pi\) | ||||
−0.156515 | + | 0.987676i | \(0.550026\pi\) | |||||||
\(374\) | −2247.10 | −0.310681 | ||||||||
\(375\) | 420.011 | 0.0578381 | ||||||||
\(376\) | 4232.68 | 0.580543 | ||||||||
\(377\) | 17491.7 | 2.38957 | ||||||||
\(378\) | 714.546 | 0.0972283 | ||||||||
\(379\) | −9184.01 | −1.24472 | −0.622362 | − | 0.782729i | \(-0.713827\pi\) | ||||
−0.622362 | + | 0.782729i | \(0.713827\pi\) | |||||||
\(380\) | −508.393 | −0.0686316 | ||||||||
\(381\) | −5997.77 | −0.806496 | ||||||||
\(382\) | 1248.07 | 0.167165 | ||||||||
\(383\) | 6361.02 | 0.848649 | 0.424325 | − | 0.905510i | \(-0.360512\pi\) | ||||
0.424325 | + | 0.905510i | \(0.360512\pi\) | |||||||
\(384\) | 3934.13 | 0.522819 | ||||||||
\(385\) | 74.9462 | 0.00992107 | ||||||||
\(386\) | −10555.1 | −1.39182 | ||||||||
\(387\) | −4505.29 | −0.591774 | ||||||||
\(388\) | −5605.01 | −0.733380 | ||||||||
\(389\) | 2334.60 | 0.304291 | 0.152145 | − | 0.988358i | \(-0.451382\pi\) | ||||
0.152145 | + | 0.988358i | \(0.451382\pi\) | |||||||
\(390\) | −4390.30 | −0.570029 | ||||||||
\(391\) | 7036.08 | 0.910051 | ||||||||
\(392\) | 3301.42 | 0.425375 | ||||||||
\(393\) | −4338.99 | −0.556929 | ||||||||
\(394\) | 3768.96 | 0.481922 | ||||||||
\(395\) | 2288.96 | 0.291569 | ||||||||
\(396\) | 924.782 | 0.117354 | ||||||||
\(397\) | −2294.44 | −0.290062 | −0.145031 | − | 0.989427i | \(-0.546328\pi\) | ||||
−0.145031 | + | 0.989427i | \(0.546328\pi\) | |||||||
\(398\) | −4565.39 | −0.574981 | ||||||||
\(399\) | 86.9944 | 0.0109152 | ||||||||
\(400\) | −1954.34 | −0.244292 | ||||||||
\(401\) | −12131.7 | −1.51080 | −0.755399 | − | 0.655265i | \(-0.772557\pi\) | ||||
−0.755399 | + | 0.655265i | \(0.772557\pi\) | |||||||
\(402\) | 7186.52 | 0.891620 | ||||||||
\(403\) | −4237.31 | −0.523761 | ||||||||
\(404\) | 8220.21 | 1.01230 | ||||||||
\(405\) | −290.187 | −0.0356037 | ||||||||
\(406\) | 1217.80 | 0.148863 | ||||||||
\(407\) | 1169.59 | 0.142444 | ||||||||
\(408\) | −1817.94 | −0.220592 | ||||||||
\(409\) | −12437.7 | −1.50368 | −0.751841 | − | 0.659344i | \(-0.770834\pi\) | ||||
−0.751841 | + | 0.659344i | \(0.770834\pi\) | |||||||
\(410\) | −9555.56 | −1.15101 | ||||||||
\(411\) | −1459.46 | −0.175158 | ||||||||
\(412\) | −5074.08 | −0.606753 | ||||||||
\(413\) | 835.921 | 0.0995957 | ||||||||
\(414\) | −7224.41 | −0.857634 | ||||||||
\(415\) | 6469.73 | 0.765269 | ||||||||
\(416\) | 14891.5 | 1.75508 | ||||||||
\(417\) | 6382.71 | 0.749550 | ||||||||
\(418\) | 763.680 | 0.0893608 | ||||||||
\(419\) | 3450.77 | 0.402341 | 0.201171 | − | 0.979556i | \(-0.435525\pi\) | ||||
0.201171 | + | 0.979556i | \(0.435525\pi\) | |||||||
\(420\) | −122.513 | −0.0142334 | ||||||||
\(421\) | −13085.9 | −1.51489 | −0.757445 | − | 0.652900i | \(-0.773552\pi\) | ||||
−0.757445 | + | 0.652900i | \(0.773552\pi\) | |||||||
\(422\) | 4084.20 | 0.471128 | ||||||||
\(423\) | 6871.03 | 0.789790 | ||||||||
\(424\) | −2275.77 | −0.260663 | ||||||||
\(425\) | 1397.67 | 0.159522 | ||||||||
\(426\) | 9053.95 | 1.02973 | ||||||||
\(427\) | 172.941 | 0.0196000 | ||||||||
\(428\) | 8628.95 | 0.974523 | ||||||||
\(429\) | 2643.33 | 0.297485 | ||||||||
\(430\) | 5239.46 | 0.587603 | ||||||||
\(431\) | 10086.0 | 1.12721 | 0.563603 | − | 0.826046i | \(-0.309415\pi\) | ||||
0.563603 | + | 0.826046i | \(0.309415\pi\) | |||||||
\(432\) | 11218.6 | 1.24943 | ||||||||
\(433\) | −4373.45 | −0.485391 | −0.242696 | − | 0.970102i | \(-0.578032\pi\) | ||||
−0.242696 | + | 0.970102i | \(0.578032\pi\) | |||||||
\(434\) | −295.008 | −0.0326287 | ||||||||
\(435\) | −4109.07 | −0.452908 | ||||||||
\(436\) | −3650.03 | −0.400928 | ||||||||
\(437\) | −2391.22 | −0.261757 | ||||||||
\(438\) | 1866.24 | 0.203590 | ||||||||
\(439\) | −15007.0 | −1.63153 | −0.815766 | − | 0.578382i | \(-0.803684\pi\) | ||||
−0.815766 | + | 0.578382i | \(0.803684\pi\) | |||||||
\(440\) | 532.264 | 0.0576698 | ||||||||
\(441\) | 5359.29 | 0.578695 | ||||||||
\(442\) | −14609.6 | −1.57219 | ||||||||
\(443\) | 7440.33 | 0.797970 | 0.398985 | − | 0.916957i | \(-0.369362\pi\) | ||||
0.398985 | + | 0.916957i | \(0.369362\pi\) | |||||||
\(444\) | −1911.92 | −0.204359 | ||||||||
\(445\) | −5453.85 | −0.580983 | ||||||||
\(446\) | −2450.51 | −0.260168 | ||||||||
\(447\) | 1634.08 | 0.172907 | ||||||||
\(448\) | 184.578 | 0.0194653 | ||||||||
\(449\) | −11130.0 | −1.16984 | −0.584919 | − | 0.811092i | \(-0.698874\pi\) | ||||
−0.584919 | + | 0.811092i | \(0.698874\pi\) | |||||||
\(450\) | −1435.08 | −0.150334 | ||||||||
\(451\) | 5753.25 | 0.600688 | ||||||||
\(452\) | 38.9700 | 0.00405530 | ||||||||
\(453\) | −6203.57 | −0.643420 | ||||||||
\(454\) | 12657.0 | 1.30842 | ||||||||
\(455\) | 487.265 | 0.0502051 | ||||||||
\(456\) | 617.830 | 0.0634485 | ||||||||
\(457\) | 14831.3 | 1.51812 | 0.759060 | − | 0.651021i | \(-0.225659\pi\) | ||||
0.759060 | + | 0.651021i | \(0.225659\pi\) | |||||||
\(458\) | 11854.5 | 1.20945 | ||||||||
\(459\) | −8023.10 | −0.815874 | ||||||||
\(460\) | 3367.54 | 0.341331 | ||||||||
\(461\) | 4929.97 | 0.498073 | 0.249037 | − | 0.968494i | \(-0.419886\pi\) | ||||
0.249037 | + | 0.968494i | \(0.419886\pi\) | |||||||
\(462\) | 184.033 | 0.0185324 | ||||||||
\(463\) | 15879.4 | 1.59390 | 0.796951 | − | 0.604044i | \(-0.206445\pi\) | ||||
0.796951 | + | 0.604044i | \(0.206445\pi\) | |||||||
\(464\) | 19119.7 | 1.91296 | ||||||||
\(465\) | 995.412 | 0.0992713 | ||||||||
\(466\) | −9876.57 | −0.981810 | ||||||||
\(467\) | −2221.50 | −0.220126 | −0.110063 | − | 0.993925i | \(-0.535105\pi\) | ||||
−0.110063 | + | 0.993925i | \(0.535105\pi\) | |||||||
\(468\) | 6012.50 | 0.593863 | ||||||||
\(469\) | −797.609 | −0.0785291 | ||||||||
\(470\) | −7990.73 | −0.784223 | ||||||||
\(471\) | −4637.96 | −0.453728 | ||||||||
\(472\) | 5936.67 | 0.578935 | ||||||||
\(473\) | −3154.60 | −0.306657 | ||||||||
\(474\) | 5620.61 | 0.544648 | ||||||||
\(475\) | −475.000 | −0.0458831 | ||||||||
\(476\) | −407.687 | −0.0392569 | ||||||||
\(477\) | −3694.32 | −0.354614 | ||||||||
\(478\) | −2583.75 | −0.247234 | ||||||||
\(479\) | −16649.9 | −1.58821 | −0.794105 | − | 0.607780i | \(-0.792060\pi\) | ||||
−0.794105 | + | 0.607780i | \(0.792060\pi\) | |||||||
\(480\) | −3498.24 | −0.332650 | ||||||||
\(481\) | 7604.15 | 0.720830 | ||||||||
\(482\) | 14872.0 | 1.40540 | ||||||||
\(483\) | −576.241 | −0.0542855 | ||||||||
\(484\) | 647.532 | 0.0608125 | ||||||||
\(485\) | −5236.86 | −0.490296 | ||||||||
\(486\) | 13445.6 | 1.25495 | ||||||||
\(487\) | 14791.8 | 1.37634 | 0.688171 | − | 0.725548i | \(-0.258414\pi\) | ||||
0.688171 | + | 0.725548i | \(0.258414\pi\) | |||||||
\(488\) | 1228.22 | 0.113932 | ||||||||
\(489\) | 10756.1 | 0.994703 | ||||||||
\(490\) | −6232.64 | −0.574616 | ||||||||
\(491\) | −16308.1 | −1.49893 | −0.749463 | − | 0.662046i | \(-0.769688\pi\) | ||||
−0.749463 | + | 0.662046i | \(0.769688\pi\) | |||||||
\(492\) | −9404.75 | −0.861787 | ||||||||
\(493\) | −13673.7 | −1.24916 | ||||||||
\(494\) | 4965.09 | 0.452206 | ||||||||
\(495\) | 864.039 | 0.0784559 | ||||||||
\(496\) | −4631.71 | −0.419294 | ||||||||
\(497\) | −1004.87 | −0.0906931 | ||||||||
\(498\) | 15886.6 | 1.42951 | ||||||||
\(499\) | −15279.2 | −1.37073 | −0.685363 | − | 0.728201i | \(-0.740357\pi\) | ||||
−0.685363 | + | 0.728201i | \(0.740357\pi\) | |||||||
\(500\) | 668.938 | 0.0598316 | ||||||||
\(501\) | 5805.09 | 0.517669 | ||||||||
\(502\) | 5449.79 | 0.484534 | ||||||||
\(503\) | −11335.4 | −1.00481 | −0.502406 | − | 0.864632i | \(-0.667552\pi\) | ||||
−0.502406 | + | 0.864632i | \(0.667552\pi\) | |||||||
\(504\) | −207.168 | −0.0183095 | ||||||||
\(505\) | 7680.28 | 0.676768 | ||||||||
\(506\) | −5058.53 | −0.444425 | ||||||||
\(507\) | 9803.59 | 0.858762 | ||||||||
\(508\) | −9552.45 | −0.834294 | ||||||||
\(509\) | 3200.91 | 0.278739 | 0.139369 | − | 0.990240i | \(-0.455492\pi\) | ||||
0.139369 | + | 0.990240i | \(0.455492\pi\) | |||||||
\(510\) | 3432.02 | 0.297985 | ||||||||
\(511\) | −207.128 | −0.0179312 | ||||||||
\(512\) | 10225.3 | 0.882616 | ||||||||
\(513\) | 2726.67 | 0.234669 | ||||||||
\(514\) | −272.906 | −0.0234190 | ||||||||
\(515\) | −4740.80 | −0.405640 | ||||||||
\(516\) | 5156.78 | 0.439951 | ||||||||
\(517\) | 4811.10 | 0.409268 | ||||||||
\(518\) | 529.413 | 0.0449055 | ||||||||
\(519\) | −4592.38 | −0.388407 | ||||||||
\(520\) | 3460.53 | 0.291835 | ||||||||
\(521\) | −10054.9 | −0.845515 | −0.422757 | − | 0.906243i | \(-0.638938\pi\) | ||||
−0.422757 | + | 0.906243i | \(0.638938\pi\) | |||||||
\(522\) | 14039.7 | 1.17721 | ||||||||
\(523\) | −796.139 | −0.0665635 | −0.0332818 | − | 0.999446i | \(-0.510596\pi\) | ||||
−0.0332818 | + | 0.999446i | \(0.510596\pi\) | |||||||
\(524\) | −6910.57 | −0.576125 | ||||||||
\(525\) | −114.466 | −0.00951566 | ||||||||
\(526\) | 9456.13 | 0.783853 | ||||||||
\(527\) | 3312.43 | 0.273798 | ||||||||
\(528\) | 2889.37 | 0.238151 | ||||||||
\(529\) | 3672.21 | 0.301817 | ||||||||
\(530\) | 4296.34 | 0.352115 | ||||||||
\(531\) | 9637.17 | 0.787603 | ||||||||
\(532\) | 138.553 | 0.0112914 | ||||||||
\(533\) | 37405.0 | 3.03975 | ||||||||
\(534\) | −13392.1 | −1.08527 | ||||||||
\(535\) | 8062.17 | 0.651510 | ||||||||
\(536\) | −5664.58 | −0.456479 | ||||||||
\(537\) | −13732.9 | −1.10357 | ||||||||
\(538\) | −5790.65 | −0.464039 | ||||||||
\(539\) | 3752.57 | 0.299879 | ||||||||
\(540\) | −3839.94 | −0.306008 | ||||||||
\(541\) | 4488.02 | 0.356664 | 0.178332 | − | 0.983970i | \(-0.442930\pi\) | ||||
0.178332 | + | 0.983970i | \(0.442930\pi\) | |||||||
\(542\) | 1249.96 | 0.0990600 | ||||||||
\(543\) | −10583.1 | −0.836402 | ||||||||
\(544\) | −11641.1 | −0.917476 | ||||||||
\(545\) | −3410.29 | −0.268038 | ||||||||
\(546\) | 1196.50 | 0.0937825 | ||||||||
\(547\) | −6865.40 | −0.536642 | −0.268321 | − | 0.963330i | \(-0.586469\pi\) | ||||
−0.268321 | + | 0.963330i | \(0.586469\pi\) | |||||||
\(548\) | −2324.44 | −0.181195 | ||||||||
\(549\) | 1993.80 | 0.154997 | ||||||||
\(550\) | −1004.84 | −0.0779029 | ||||||||
\(551\) | 4647.04 | 0.359293 | ||||||||
\(552\) | −4092.44 | −0.315554 | ||||||||
\(553\) | −623.813 | −0.0479696 | ||||||||
\(554\) | 20216.8 | 1.55042 | ||||||||
\(555\) | −1786.34 | −0.136623 | ||||||||
\(556\) | 10165.5 | 0.775385 | ||||||||
\(557\) | −4135.45 | −0.314587 | −0.157293 | − | 0.987552i | \(-0.550277\pi\) | ||||
−0.157293 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(558\) | −3401.09 | −0.258028 | ||||||||
\(559\) | −20509.7 | −1.55182 | ||||||||
\(560\) | 532.618 | 0.0401915 | ||||||||
\(561\) | −2066.37 | −0.155512 | ||||||||
\(562\) | 5319.72 | 0.399286 | ||||||||
\(563\) | −13134.9 | −0.983252 | −0.491626 | − | 0.870806i | \(-0.663597\pi\) | ||||
−0.491626 | + | 0.870806i | \(0.663597\pi\) | |||||||
\(564\) | −7864.62 | −0.587164 | ||||||||
\(565\) | 36.4104 | 0.00271114 | ||||||||
\(566\) | 6607.46 | 0.490693 | ||||||||
\(567\) | 79.0851 | 0.00585760 | ||||||||
\(568\) | −7136.52 | −0.527186 | ||||||||
\(569\) | 10883.7 | 0.801881 | 0.400940 | − | 0.916104i | \(-0.368683\pi\) | ||||
0.400940 | + | 0.916104i | \(0.368683\pi\) | |||||||
\(570\) | −1166.38 | −0.0857091 | ||||||||
\(571\) | 5834.56 | 0.427616 | 0.213808 | − | 0.976876i | \(-0.431413\pi\) | ||||
0.213808 | + | 0.976876i | \(0.431413\pi\) | |||||||
\(572\) | 4209.95 | 0.307739 | ||||||||
\(573\) | 1147.69 | 0.0836745 | ||||||||
\(574\) | 2604.19 | 0.189367 | ||||||||
\(575\) | 3146.35 | 0.228194 | ||||||||
\(576\) | 2127.96 | 0.153932 | ||||||||
\(577\) | −5810.86 | −0.419254 | −0.209627 | − | 0.977781i | \(-0.567225\pi\) | ||||
−0.209627 | + | 0.977781i | \(0.567225\pi\) | |||||||
\(578\) | −6531.25 | −0.470007 | ||||||||
\(579\) | −9706.21 | −0.696678 | ||||||||
\(580\) | −6544.38 | −0.468518 | ||||||||
\(581\) | −1763.21 | −0.125904 | ||||||||
\(582\) | −12859.3 | −0.915866 | ||||||||
\(583\) | −2586.76 | −0.183761 | ||||||||
\(584\) | −1471.02 | −0.104231 | ||||||||
\(585\) | 5617.58 | 0.397023 | ||||||||
\(586\) | −861.222 | −0.0607112 | ||||||||
\(587\) | −10274.2 | −0.722419 | −0.361210 | − | 0.932485i | \(-0.617636\pi\) | ||||
−0.361210 | + | 0.932485i | \(0.617636\pi\) | |||||||
\(588\) | −6134.27 | −0.430227 | ||||||||
\(589\) | −1125.73 | −0.0787522 | ||||||||
\(590\) | −11207.6 | −0.782052 | ||||||||
\(591\) | 3465.83 | 0.241227 | ||||||||
\(592\) | 8311.92 | 0.577057 | ||||||||
\(593\) | 10956.6 | 0.758739 | 0.379369 | − | 0.925245i | \(-0.376141\pi\) | ||||
0.379369 | + | 0.925245i | \(0.376141\pi\) | |||||||
\(594\) | 5768.14 | 0.398434 | ||||||||
\(595\) | −380.909 | −0.0262449 | ||||||||
\(596\) | 2602.55 | 0.178866 | ||||||||
\(597\) | −4198.20 | −0.287807 | ||||||||
\(598\) | −32888.2 | −2.24899 | ||||||||
\(599\) | 12782.0 | 0.871882 | 0.435941 | − | 0.899975i | \(-0.356416\pi\) | ||||
0.435941 | + | 0.899975i | \(0.356416\pi\) | |||||||
\(600\) | −812.934 | −0.0553132 | ||||||||
\(601\) | 17715.9 | 1.20240 | 0.601202 | − | 0.799097i | \(-0.294689\pi\) | ||||
0.601202 | + | 0.799097i | \(0.294689\pi\) | |||||||
\(602\) | −1427.92 | −0.0966739 | ||||||||
\(603\) | −9195.47 | −0.621009 | ||||||||
\(604\) | −9880.22 | −0.665597 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 18859.2 | 1.26419 | ||||||||
\(607\) | 15691.8 | 1.04927 | 0.524637 | − | 0.851326i | \(-0.324201\pi\) | ||||
0.524637 | + | 0.851326i | \(0.324201\pi\) | |||||||
\(608\) | 3956.24 | 0.263893 | ||||||||
\(609\) | 1119.85 | 0.0745134 | ||||||||
\(610\) | −2318.70 | −0.153904 | ||||||||
\(611\) | 31279.5 | 2.07108 | ||||||||
\(612\) | −4700.14 | −0.310444 | ||||||||
\(613\) | −25998.7 | −1.71301 | −0.856507 | − | 0.516136i | \(-0.827370\pi\) | ||||
−0.856507 | + | 0.516136i | \(0.827370\pi\) | |||||||
\(614\) | −9282.75 | −0.610133 | ||||||||
\(615\) | −8787.02 | −0.576141 | ||||||||
\(616\) | −145.059 | −0.00948796 | ||||||||
\(617\) | −24067.6 | −1.57038 | −0.785191 | − | 0.619253i | \(-0.787435\pi\) | ||||
−0.785191 | + | 0.619253i | \(0.787435\pi\) | |||||||
\(618\) | −11641.2 | −0.757731 | ||||||||
\(619\) | 30.1848 | 0.00195998 | 0.000979991 | − | 1.00000i | \(-0.499688\pi\) | ||||
0.000979991 | 1.00000i | \(0.499688\pi\) | ||||||||
\(620\) | 1585.36 | 0.102693 | ||||||||
\(621\) | −18061.1 | −1.16710 | ||||||||
\(622\) | 26117.7 | 1.68364 | ||||||||
\(623\) | 1486.35 | 0.0955846 | ||||||||
\(624\) | 18785.3 | 1.20515 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 15723.0 | 1.00386 | ||||||||
\(627\) | 702.259 | 0.0447297 | ||||||||
\(628\) | −7386.72 | −0.469367 | ||||||||
\(629\) | −5944.38 | −0.376817 | ||||||||
\(630\) | 391.104 | 0.0247333 | ||||||||
\(631\) | −4316.76 | −0.272342 | −0.136171 | − | 0.990685i | \(-0.543480\pi\) | ||||
−0.136171 | + | 0.990685i | \(0.543480\pi\) | |||||||
\(632\) | −4430.29 | −0.278841 | ||||||||
\(633\) | 3755.72 | 0.235824 | ||||||||
\(634\) | 17753.9 | 1.11214 | ||||||||
\(635\) | −8925.01 | −0.557761 | ||||||||
\(636\) | 4228.53 | 0.263636 | ||||||||
\(637\) | 24397.5 | 1.51752 | ||||||||
\(638\) | 9830.61 | 0.610028 | ||||||||
\(639\) | −11584.9 | −0.717202 | ||||||||
\(640\) | 5854.20 | 0.361574 | ||||||||
\(641\) | 2087.70 | 0.128641 | 0.0643207 | − | 0.997929i | \(-0.479512\pi\) | ||||
0.0643207 | + | 0.997929i | \(0.479512\pi\) | |||||||
\(642\) | 19796.9 | 1.21701 | ||||||||
\(643\) | −11141.9 | −0.683350 | −0.341675 | − | 0.939818i | \(-0.610994\pi\) | ||||
−0.341675 | + | 0.939818i | \(0.610994\pi\) | |||||||
\(644\) | −917.761 | −0.0561566 | ||||||||
\(645\) | 4818.06 | 0.294126 | ||||||||
\(646\) | −3881.35 | −0.236393 | ||||||||
\(647\) | 3757.99 | 0.228349 | 0.114175 | − | 0.993461i | \(-0.463578\pi\) | ||||
0.114175 | + | 0.993461i | \(0.463578\pi\) | |||||||
\(648\) | 561.658 | 0.0340494 | ||||||||
\(649\) | 6747.94 | 0.408135 | ||||||||
\(650\) | −6533.01 | −0.394224 | ||||||||
\(651\) | −271.281 | −0.0163323 | ||||||||
\(652\) | 17131.0 | 1.02899 | ||||||||
\(653\) | 11744.3 | 0.703814 | 0.351907 | − | 0.936035i | \(-0.385533\pi\) | ||||
0.351907 | + | 0.936035i | \(0.385533\pi\) | |||||||
\(654\) | −8374.07 | −0.500691 | ||||||||
\(655\) | −6456.66 | −0.385164 | ||||||||
\(656\) | 40886.5 | 2.43346 | ||||||||
\(657\) | −2387.94 | −0.141800 | ||||||||
\(658\) | 2177.73 | 0.129022 | ||||||||
\(659\) | 15110.3 | 0.893194 | 0.446597 | − | 0.894735i | \(-0.352636\pi\) | ||||
0.446597 | + | 0.894735i | \(0.352636\pi\) | |||||||
\(660\) | −988.984 | −0.0583275 | ||||||||
\(661\) | −23918.2 | −1.40743 | −0.703714 | − | 0.710483i | \(-0.748476\pi\) | ||||
−0.703714 | + | 0.710483i | \(0.748476\pi\) | |||||||
\(662\) | −14411.4 | −0.846094 | ||||||||
\(663\) | −13434.5 | −0.786960 | ||||||||
\(664\) | −12522.2 | −0.731861 | ||||||||
\(665\) | 129.453 | 0.00754880 | ||||||||
\(666\) | 6103.49 | 0.355113 | ||||||||
\(667\) | −30781.5 | −1.78690 | ||||||||
\(668\) | 9245.58 | 0.535512 | ||||||||
\(669\) | −2253.42 | −0.130227 | ||||||||
\(670\) | 10693.9 | 0.616632 | ||||||||
\(671\) | 1396.06 | 0.0803191 | ||||||||
\(672\) | 953.382 | 0.0547284 | ||||||||
\(673\) | 19268.0 | 1.10360 | 0.551802 | − | 0.833975i | \(-0.313940\pi\) | ||||
0.551802 | + | 0.833975i | \(0.313940\pi\) | |||||||
\(674\) | −16689.8 | −0.953810 | ||||||||
\(675\) | −3587.72 | −0.204580 | ||||||||
\(676\) | 15613.8 | 0.888362 | ||||||||
\(677\) | 19433.3 | 1.10323 | 0.551613 | − | 0.834100i | \(-0.314013\pi\) | ||||
0.551613 | + | 0.834100i | \(0.314013\pi\) | |||||||
\(678\) | 89.4069 | 0.00506438 | ||||||||
\(679\) | 1427.21 | 0.0806646 | ||||||||
\(680\) | −2705.19 | −0.152558 | ||||||||
\(681\) | 11639.1 | 0.654933 | ||||||||
\(682\) | −2381.44 | −0.133710 | ||||||||
\(683\) | −30727.0 | −1.72143 | −0.860714 | − | 0.509089i | \(-0.829982\pi\) | ||||
−0.860714 | + | 0.509089i | \(0.829982\pi\) | |||||||
\(684\) | 1597.35 | 0.0892927 | ||||||||
\(685\) | −2171.76 | −0.121137 | ||||||||
\(686\) | 3406.43 | 0.189589 | ||||||||
\(687\) | 10901.1 | 0.605390 | ||||||||
\(688\) | −22418.7 | −1.24231 | ||||||||
\(689\) | −16817.9 | −0.929914 | ||||||||
\(690\) | 7725.96 | 0.426264 | ||||||||
\(691\) | 29310.7 | 1.61365 | 0.806823 | − | 0.590793i | \(-0.201185\pi\) | ||||
0.806823 | + | 0.590793i | \(0.201185\pi\) | |||||||
\(692\) | −7314.13 | −0.401794 | ||||||||
\(693\) | −235.478 | −0.0129077 | ||||||||
\(694\) | 13583.6 | 0.742978 | ||||||||
\(695\) | 9497.82 | 0.518378 | ||||||||
\(696\) | 7953.13 | 0.433136 | ||||||||
\(697\) | −29240.5 | −1.58904 | ||||||||
\(698\) | −41663.2 | −2.25928 | ||||||||
\(699\) | −9082.22 | −0.491446 | ||||||||
\(700\) | −182.307 | −0.00984364 | ||||||||
\(701\) | −10535.9 | −0.567671 | −0.283835 | − | 0.958873i | \(-0.591607\pi\) | ||||
−0.283835 | + | 0.958873i | \(0.591607\pi\) | |||||||
\(702\) | 37501.8 | 2.01626 | ||||||||
\(703\) | 2020.21 | 0.108383 | ||||||||
\(704\) | 1490.00 | 0.0797675 | ||||||||
\(705\) | −7348.05 | −0.392544 | ||||||||
\(706\) | −21903.2 | −1.16762 | ||||||||
\(707\) | −2093.12 | −0.111343 | ||||||||
\(708\) | −11030.8 | −0.585538 | ||||||||
\(709\) | 14295.1 | 0.757211 | 0.378605 | − | 0.925558i | \(-0.376404\pi\) | ||||
0.378605 | + | 0.925558i | \(0.376404\pi\) | |||||||
\(710\) | 13472.8 | 0.712147 | ||||||||
\(711\) | −7191.81 | −0.379344 | ||||||||
\(712\) | 10556.0 | 0.555620 | ||||||||
\(713\) | 7456.74 | 0.391665 | ||||||||
\(714\) | −935.334 | −0.0490252 | ||||||||
\(715\) | 3933.43 | 0.205737 | ||||||||
\(716\) | −21872.0 | −1.14161 | ||||||||
\(717\) | −2375.94 | −0.123753 | ||||||||
\(718\) | 10367.7 | 0.538882 | ||||||||
\(719\) | −13160.0 | −0.682595 | −0.341298 | − | 0.939955i | \(-0.610866\pi\) | ||||
−0.341298 | + | 0.939955i | \(0.610866\pi\) | |||||||
\(720\) | 6140.45 | 0.317835 | ||||||||
\(721\) | 1292.02 | 0.0667369 | ||||||||
\(722\) | 1319.08 | 0.0679934 | ||||||||
\(723\) | 13675.9 | 0.703475 | ||||||||
\(724\) | −16855.4 | −0.865231 | ||||||||
\(725\) | −6114.53 | −0.313225 | ||||||||
\(726\) | 1485.60 | 0.0759445 | ||||||||
\(727\) | −9955.26 | −0.507868 | −0.253934 | − | 0.967222i | \(-0.581725\pi\) | ||||
−0.253934 | + | 0.967222i | \(0.581725\pi\) | |||||||
\(728\) | −943.104 | −0.0480134 | ||||||||
\(729\) | 13931.2 | 0.707779 | ||||||||
\(730\) | 2777.08 | 0.140800 | ||||||||
\(731\) | 16033.0 | 0.811222 | ||||||||
\(732\) | −2282.11 | −0.115231 | ||||||||
\(733\) | 21132.8 | 1.06488 | 0.532440 | − | 0.846468i | \(-0.321275\pi\) | ||||
0.532440 | + | 0.846468i | \(0.321275\pi\) | |||||||
\(734\) | −31274.3 | −1.57269 | ||||||||
\(735\) | −5731.36 | −0.287625 | ||||||||
\(736\) | −26205.7 | −1.31244 | ||||||||
\(737\) | −6438.66 | −0.321806 | ||||||||
\(738\) | 30023.2 | 1.49752 | ||||||||
\(739\) | −30716.6 | −1.52900 | −0.764499 | − | 0.644624i | \(-0.777014\pi\) | ||||
−0.764499 | + | 0.644624i | \(0.777014\pi\) | |||||||
\(740\) | −2845.04 | −0.141332 | ||||||||
\(741\) | 4565.75 | 0.226352 | ||||||||
\(742\) | −1170.89 | −0.0579308 | ||||||||
\(743\) | −4970.27 | −0.245413 | −0.122706 | − | 0.992443i | \(-0.539157\pi\) | ||||
−0.122706 | + | 0.992443i | \(0.539157\pi\) | |||||||
\(744\) | −1926.63 | −0.0949376 | ||||||||
\(745\) | 2431.60 | 0.119580 | ||||||||
\(746\) | −8239.78 | −0.404396 | ||||||||
\(747\) | −20327.6 | −0.995648 | ||||||||
\(748\) | −3291.03 | −0.160872 | ||||||||
\(749\) | −2197.20 | −0.107188 | ||||||||
\(750\) | 1534.71 | 0.0747195 | ||||||||
\(751\) | 15535.1 | 0.754841 | 0.377420 | − | 0.926042i | \(-0.376811\pi\) | ||||
0.377420 | + | 0.926042i | \(0.376811\pi\) | |||||||
\(752\) | 34190.9 | 1.65800 | ||||||||
\(753\) | 5011.48 | 0.242534 | ||||||||
\(754\) | 63914.0 | 3.08702 | ||||||||
\(755\) | −9231.26 | −0.444980 | ||||||||
\(756\) | 1046.50 | 0.0503452 | ||||||||
\(757\) | 8452.81 | 0.405842 | 0.202921 | − | 0.979195i | \(-0.434956\pi\) | ||||
0.202921 | + | 0.979195i | \(0.434956\pi\) | |||||||
\(758\) | −33558.1 | −1.60803 | ||||||||
\(759\) | −4651.68 | −0.222458 | ||||||||
\(760\) | 919.365 | 0.0438801 | ||||||||
\(761\) | 20960.9 | 0.998463 | 0.499232 | − | 0.866469i | \(-0.333616\pi\) | ||||
0.499232 | + | 0.866469i | \(0.333616\pi\) | |||||||
\(762\) | −21915.7 | −1.04189 | ||||||||
\(763\) | 929.411 | 0.0440982 | ||||||||
\(764\) | 1827.89 | 0.0865586 | ||||||||
\(765\) | −4391.42 | −0.207545 | ||||||||
\(766\) | 23243.0 | 1.09635 | ||||||||
\(767\) | 43871.9 | 2.06535 | ||||||||
\(768\) | 18016.3 | 0.846493 | ||||||||
\(769\) | 32084.5 | 1.50455 | 0.752274 | − | 0.658850i | \(-0.228957\pi\) | ||||
0.752274 | + | 0.658850i | \(0.228957\pi\) | |||||||
\(770\) | 273.851 | 0.0128168 | ||||||||
\(771\) | −250.957 | −0.0117224 | ||||||||
\(772\) | −15458.8 | −0.720690 | ||||||||
\(773\) | −12955.7 | −0.602827 | −0.301413 | − | 0.953494i | \(-0.597458\pi\) | ||||
−0.301413 | + | 0.953494i | \(0.597458\pi\) | |||||||
\(774\) | −16462.2 | −0.764498 | ||||||||
\(775\) | 1481.23 | 0.0686546 | ||||||||
\(776\) | 10136.0 | 0.468892 | ||||||||
\(777\) | 486.833 | 0.0224775 | ||||||||
\(778\) | 8530.58 | 0.393105 | ||||||||
\(779\) | 9937.44 | 0.457055 | ||||||||
\(780\) | −6429.91 | −0.295164 | ||||||||
\(781\) | −8111.75 | −0.371653 | ||||||||
\(782\) | 25709.6 | 1.17567 | ||||||||
\(783\) | 35099.5 | 1.60199 | ||||||||
\(784\) | 26668.3 | 1.21485 | ||||||||
\(785\) | −6901.54 | −0.313792 | ||||||||
\(786\) | −15854.5 | −0.719482 | ||||||||
\(787\) | 15113.9 | 0.684565 | 0.342282 | − | 0.939597i | \(-0.388800\pi\) | ||||
0.342282 | + | 0.939597i | \(0.388800\pi\) | |||||||
\(788\) | 5519.91 | 0.249541 | ||||||||
\(789\) | 8695.59 | 0.392359 | ||||||||
\(790\) | 8363.78 | 0.376671 | ||||||||
\(791\) | −9.92297 | −0.000446043 0 | ||||||||
\(792\) | −1672.35 | −0.0750309 | ||||||||
\(793\) | 9076.49 | 0.406451 | ||||||||
\(794\) | −8383.81 | −0.374723 | ||||||||
\(795\) | 3950.79 | 0.176252 | ||||||||
\(796\) | −6686.34 | −0.297727 | ||||||||
\(797\) | −11456.2 | −0.509159 | −0.254580 | − | 0.967052i | \(-0.581937\pi\) | ||||
−0.254580 | + | 0.967052i | \(0.581937\pi\) | |||||||
\(798\) | 317.875 | 0.0141011 | ||||||||
\(799\) | −24452.1 | −1.08267 | ||||||||
\(800\) | −5205.58 | −0.230056 | ||||||||
\(801\) | 17135.8 | 0.755884 | ||||||||
\(802\) | −44329.0 | −1.95176 | ||||||||
\(803\) | −1672.04 | −0.0734805 | ||||||||
\(804\) | 10525.2 | 0.461685 | ||||||||
\(805\) | −857.479 | −0.0375431 | ||||||||
\(806\) | −15483.0 | −0.676633 | ||||||||
\(807\) | −5324.92 | −0.232275 | ||||||||
\(808\) | −14865.2 | −0.647224 | ||||||||
\(809\) | 11358.0 | 0.493603 | 0.246802 | − | 0.969066i | \(-0.420620\pi\) | ||||
0.246802 | + | 0.969066i | \(0.420620\pi\) | |||||||
\(810\) | −1060.33 | −0.0459955 | ||||||||
\(811\) | 31036.9 | 1.34384 | 0.671919 | − | 0.740625i | \(-0.265470\pi\) | ||||
0.671919 | + | 0.740625i | \(0.265470\pi\) | |||||||
\(812\) | 1783.55 | 0.0770817 | ||||||||
\(813\) | 1149.43 | 0.0495847 | ||||||||
\(814\) | 4273.66 | 0.184019 | ||||||||
\(815\) | 16005.8 | 0.687923 | ||||||||
\(816\) | −14685.0 | −0.629997 | ||||||||
\(817\) | −5448.86 | −0.233331 | ||||||||
\(818\) | −45447.1 | −1.94257 | ||||||||
\(819\) | −1530.97 | −0.0653191 | ||||||||
\(820\) | −13994.8 | −0.596000 | ||||||||
\(821\) | −8530.36 | −0.362621 | −0.181310 | − | 0.983426i | \(-0.558034\pi\) | ||||
−0.181310 | + | 0.983426i | \(0.558034\pi\) | |||||||
\(822\) | −5332.83 | −0.226282 | ||||||||
\(823\) | −25062.9 | −1.06153 | −0.530765 | − | 0.847519i | \(-0.678095\pi\) | ||||
−0.530765 | + | 0.847519i | \(0.678095\pi\) | |||||||
\(824\) | 9175.85 | 0.387932 | ||||||||
\(825\) | −924.024 | −0.0389944 | ||||||||
\(826\) | 3054.43 | 0.128665 | ||||||||
\(827\) | −40794.4 | −1.71531 | −0.857654 | − | 0.514228i | \(-0.828079\pi\) | ||||
−0.857654 | + | 0.514228i | \(0.828079\pi\) | |||||||
\(828\) | −10580.7 | −0.444087 | ||||||||
\(829\) | −46684.1 | −1.95586 | −0.977928 | − | 0.208942i | \(-0.932998\pi\) | ||||
−0.977928 | + | 0.208942i | \(0.932998\pi\) | |||||||
\(830\) | 23640.2 | 0.988630 | ||||||||
\(831\) | 18590.8 | 0.776063 | ||||||||
\(832\) | 9687.25 | 0.403660 | ||||||||
\(833\) | −19072.2 | −0.793292 | ||||||||
\(834\) | 23322.2 | 0.968324 | ||||||||
\(835\) | 8638.30 | 0.358013 | ||||||||
\(836\) | 1118.46 | 0.0462714 | ||||||||
\(837\) | −8502.77 | −0.351134 | ||||||||
\(838\) | 12609.0 | 0.519774 | ||||||||
\(839\) | −21987.6 | −0.904763 | −0.452382 | − | 0.891824i | \(-0.649426\pi\) | ||||
−0.452382 | + | 0.891824i | \(0.649426\pi\) | |||||||
\(840\) | 221.550 | 0.00910025 | ||||||||
\(841\) | 35430.9 | 1.45274 | ||||||||
\(842\) | −47815.5 | −1.95705 | ||||||||
\(843\) | 4891.86 | 0.199863 | ||||||||
\(844\) | 5981.61 | 0.243952 | ||||||||
\(845\) | 14588.3 | 0.593908 | ||||||||
\(846\) | 25106.6 | 1.02031 | ||||||||
\(847\) | −164.882 | −0.00668878 | ||||||||
\(848\) | −18383.3 | −0.744438 | ||||||||
\(849\) | 6076.04 | 0.245617 | ||||||||
\(850\) | 5107.04 | 0.206082 | ||||||||
\(851\) | −13381.6 | −0.539032 | ||||||||
\(852\) | 13260.2 | 0.533199 | ||||||||
\(853\) | −29157.5 | −1.17038 | −0.585191 | − | 0.810896i | \(-0.698980\pi\) | ||||
−0.585191 | + | 0.810896i | \(0.698980\pi\) | |||||||
\(854\) | 631.920 | 0.0253207 | ||||||||
\(855\) | 1492.43 | 0.0596960 | ||||||||
\(856\) | −15604.4 | −0.623069 | ||||||||
\(857\) | 1866.81 | 0.0744094 | 0.0372047 | − | 0.999308i | \(-0.488155\pi\) | ||||
0.0372047 | + | 0.999308i | \(0.488155\pi\) | |||||||
\(858\) | 9658.66 | 0.384314 | ||||||||
\(859\) | 3494.52 | 0.138803 | 0.0694013 | − | 0.997589i | \(-0.477891\pi\) | ||||
0.0694013 | + | 0.997589i | \(0.477891\pi\) | |||||||
\(860\) | 7673.57 | 0.304264 | ||||||||
\(861\) | 2394.74 | 0.0947881 | ||||||||
\(862\) | 36854.0 | 1.45621 | ||||||||
\(863\) | −5051.57 | −0.199255 | −0.0996276 | − | 0.995025i | \(-0.531765\pi\) | ||||
−0.0996276 | + | 0.995025i | \(0.531765\pi\) | |||||||
\(864\) | 29881.9 | 1.17662 | ||||||||
\(865\) | −6833.72 | −0.268617 | ||||||||
\(866\) | −15980.4 | −0.627064 | ||||||||
\(867\) | −6005.95 | −0.235263 | ||||||||
\(868\) | −432.061 | −0.0168953 | ||||||||
\(869\) | −5035.70 | −0.196576 | ||||||||
\(870\) | −15014.4 | −0.585100 | ||||||||
\(871\) | −41861.2 | −1.62849 | ||||||||
\(872\) | 6600.63 | 0.256337 | ||||||||
\(873\) | 16454.0 | 0.637896 | ||||||||
\(874\) | −8737.47 | −0.338157 | ||||||||
\(875\) | −170.332 | −0.00658089 | ||||||||
\(876\) | 2733.25 | 0.105420 | ||||||||
\(877\) | −13637.9 | −0.525107 | −0.262554 | − | 0.964917i | \(-0.584565\pi\) | ||||
−0.262554 | + | 0.964917i | \(0.584565\pi\) | |||||||
\(878\) | −54835.0 | −2.10773 | ||||||||
\(879\) | −791.955 | −0.0303891 | ||||||||
\(880\) | 4299.54 | 0.164702 | ||||||||
\(881\) | −2545.94 | −0.0973610 | −0.0486805 | − | 0.998814i | \(-0.515502\pi\) | ||||
−0.0486805 | + | 0.998814i | \(0.515502\pi\) | |||||||
\(882\) | 19582.7 | 0.747601 | ||||||||
\(883\) | 24253.3 | 0.924334 | 0.462167 | − | 0.886793i | \(-0.347072\pi\) | ||||
0.462167 | + | 0.886793i | \(0.347072\pi\) | |||||||
\(884\) | −21396.8 | −0.814085 | ||||||||
\(885\) | −10306.2 | −0.391457 | ||||||||
\(886\) | 27186.8 | 1.03088 | ||||||||
\(887\) | −23666.3 | −0.895870 | −0.447935 | − | 0.894066i | \(-0.647840\pi\) | ||||
−0.447935 | + | 0.894066i | \(0.647840\pi\) | |||||||
\(888\) | 3457.46 | 0.130659 | ||||||||
\(889\) | 2432.35 | 0.0917642 | ||||||||
\(890\) | −19928.2 | −0.750556 | ||||||||
\(891\) | 638.411 | 0.0240040 | ||||||||
\(892\) | −3588.94 | −0.134716 | ||||||||
\(893\) | 8310.08 | 0.311407 | ||||||||
\(894\) | 5970.88 | 0.223374 | ||||||||
\(895\) | −20435.3 | −0.763216 | ||||||||
\(896\) | −1595.46 | −0.0594871 | ||||||||
\(897\) | −30243.1 | −1.12574 | ||||||||
\(898\) | −40668.7 | −1.51128 | ||||||||
\(899\) | −14491.2 | −0.537608 | ||||||||
\(900\) | −2101.78 | −0.0778436 | ||||||||
\(901\) | 13147.0 | 0.486116 | ||||||||
\(902\) | 21022.2 | 0.776013 | ||||||||
\(903\) | −1313.07 | −0.0483903 | ||||||||
\(904\) | −70.4725 | −0.00259279 | ||||||||
\(905\) | −15748.3 | −0.578444 | ||||||||
\(906\) | −22667.7 | −0.831217 | ||||||||
\(907\) | −20165.2 | −0.738231 | −0.369116 | − | 0.929383i | \(-0.620339\pi\) | ||||
−0.369116 | + | 0.929383i | \(0.620339\pi\) | |||||||
\(908\) | 18537.1 | 0.677508 | ||||||||
\(909\) | −24131.1 | −0.880505 | ||||||||
\(910\) | 1780.45 | 0.0648587 | ||||||||
\(911\) | 44617.5 | 1.62266 | 0.811330 | − | 0.584589i | \(-0.198744\pi\) | ||||
0.811330 | + | 0.584589i | \(0.198744\pi\) | |||||||
\(912\) | 4990.72 | 0.181205 | ||||||||
\(913\) | −14233.4 | −0.515944 | ||||||||
\(914\) | 54193.3 | 1.96122 | ||||||||
\(915\) | −2132.21 | −0.0770369 | ||||||||
\(916\) | 17361.8 | 0.626257 | ||||||||
\(917\) | 1759.64 | 0.0633681 | ||||||||
\(918\) | −29316.2 | −1.05401 | ||||||||
\(919\) | 38351.8 | 1.37662 | 0.688308 | − | 0.725419i | \(-0.258354\pi\) | ||||
0.688308 | + | 0.725419i | \(0.258354\pi\) | |||||||
\(920\) | −6089.78 | −0.218233 | ||||||||
\(921\) | −8536.16 | −0.305403 | ||||||||
\(922\) | 18014.0 | 0.643447 | ||||||||
\(923\) | −52738.8 | −1.88074 | ||||||||
\(924\) | 269.529 | 0.00959618 | ||||||||
\(925\) | −2658.17 | −0.0944865 | ||||||||
\(926\) | 58022.7 | 2.05912 | ||||||||
\(927\) | 14895.4 | 0.527756 | ||||||||
\(928\) | 50927.5 | 1.80148 | ||||||||
\(929\) | −28949.1 | −1.02238 | −0.511190 | − | 0.859468i | \(-0.670795\pi\) | ||||
−0.511190 | + | 0.859468i | \(0.670795\pi\) | |||||||
\(930\) | 3637.21 | 0.128246 | ||||||||
\(931\) | 6481.72 | 0.228174 | ||||||||
\(932\) | −14465.0 | −0.508385 | ||||||||
\(933\) | 24017.1 | 0.842750 | ||||||||
\(934\) | −8117.31 | −0.284375 | ||||||||
\(935\) | −3074.87 | −0.107550 | ||||||||
\(936\) | −10872.9 | −0.379691 | ||||||||
\(937\) | 37002.9 | 1.29011 | 0.645054 | − | 0.764137i | \(-0.276835\pi\) | ||||
0.645054 | + | 0.764137i | \(0.276835\pi\) | |||||||
\(938\) | −2914.44 | −0.101450 | ||||||||
\(939\) | 14458.4 | 0.502484 | ||||||||
\(940\) | −11703.0 | −0.406074 | ||||||||
\(941\) | −43236.2 | −1.49783 | −0.748916 | − | 0.662665i | \(-0.769425\pi\) | ||||
−0.748916 | + | 0.662665i | \(0.769425\pi\) | |||||||
\(942\) | −16947.0 | −0.586159 | ||||||||
\(943\) | −65824.5 | −2.27311 | ||||||||
\(944\) | 47955.4 | 1.65341 | ||||||||
\(945\) | 977.767 | 0.0336579 | ||||||||
\(946\) | −11526.8 | −0.396162 | ||||||||
\(947\) | −13217.9 | −0.453562 | −0.226781 | − | 0.973946i | \(-0.572820\pi\) | ||||
−0.226781 | + | 0.973946i | \(0.572820\pi\) | |||||||
\(948\) | 8231.78 | 0.282021 | ||||||||
\(949\) | −10870.8 | −0.371845 | ||||||||
\(950\) | −1735.64 | −0.0592752 | ||||||||
\(951\) | 16326.0 | 0.556684 | ||||||||
\(952\) | 737.251 | 0.0250992 | ||||||||
\(953\) | −56255.5 | −1.91217 | −0.956083 | − | 0.293095i | \(-0.905315\pi\) | ||||
−0.956083 | + | 0.293095i | \(0.905315\pi\) | |||||||
\(954\) | −13498.9 | −0.458117 | ||||||||
\(955\) | 1707.83 | 0.0578681 | ||||||||
\(956\) | −3784.09 | −0.128019 | ||||||||
\(957\) | 9039.96 | 0.305350 | ||||||||
\(958\) | −60838.2 | −2.05177 | ||||||||
\(959\) | 591.873 | 0.0199297 | ||||||||
\(960\) | −2275.69 | −0.0765079 | ||||||||
\(961\) | −26280.5 | −0.882164 | ||||||||
\(962\) | 27785.3 | 0.931221 | ||||||||
\(963\) | −25331.0 | −0.847644 | ||||||||
\(964\) | 21781.2 | 0.727722 | ||||||||
\(965\) | −14443.4 | −0.481812 | ||||||||
\(966\) | −2105.57 | −0.0701300 | ||||||||
\(967\) | −4156.89 | −0.138239 | −0.0691193 | − | 0.997608i | \(-0.522019\pi\) | ||||
−0.0691193 | + | 0.997608i | \(0.522019\pi\) | |||||||
\(968\) | −1170.98 | −0.0388810 | ||||||||
\(969\) | −3569.18 | −0.118327 | ||||||||
\(970\) | −19135.3 | −0.633400 | ||||||||
\(971\) | 37468.6 | 1.23834 | 0.619169 | − | 0.785258i | \(-0.287470\pi\) | ||||
0.619169 | + | 0.785258i | \(0.287470\pi\) | |||||||
\(972\) | 19692.1 | 0.649818 | ||||||||
\(973\) | −2588.46 | −0.0852848 | ||||||||
\(974\) | 54048.7 | 1.77806 | ||||||||
\(975\) | −6007.57 | −0.197330 | ||||||||
\(976\) | 9921.31 | 0.325383 | ||||||||
\(977\) | 19520.5 | 0.639217 | 0.319609 | − | 0.947550i | \(-0.396449\pi\) | ||||
0.319609 | + | 0.947550i | \(0.396449\pi\) | |||||||
\(978\) | 39302.7 | 1.28503 | ||||||||
\(979\) | 11998.5 | 0.391698 | ||||||||
\(980\) | −9128.14 | −0.297539 | ||||||||
\(981\) | 10715.0 | 0.348729 | ||||||||
\(982\) | −59589.2 | −1.93642 | ||||||||
\(983\) | 22929.6 | 0.743988 | 0.371994 | − | 0.928235i | \(-0.378674\pi\) | ||||
0.371994 | + | 0.928235i | \(0.378674\pi\) | |||||||
\(984\) | 17007.3 | 0.550990 | ||||||||
\(985\) | 5157.35 | 0.166829 | ||||||||
\(986\) | −49963.4 | −1.61375 | ||||||||
\(987\) | 2002.58 | 0.0645823 | ||||||||
\(988\) | 7271.73 | 0.234154 | ||||||||
\(989\) | 36092.6 | 1.16044 | ||||||||
\(990\) | 3157.17 | 0.101355 | ||||||||
\(991\) | 38360.4 | 1.22962 | 0.614812 | − | 0.788673i | \(-0.289232\pi\) | ||||
0.614812 | + | 0.788673i | \(0.289232\pi\) | |||||||
\(992\) | −12337.1 | −0.394861 | ||||||||
\(993\) | −13252.3 | −0.423513 | ||||||||
\(994\) | −3671.76 | −0.117164 | ||||||||
\(995\) | −6247.16 | −0.199044 | ||||||||
\(996\) | 23267.1 | 0.740208 | ||||||||
\(997\) | −43460.8 | −1.38056 | −0.690280 | − | 0.723542i | \(-0.742513\pi\) | ||||
−0.690280 | + | 0.723542i | \(0.742513\pi\) | |||||||
\(998\) | −55829.9 | −1.77081 | ||||||||
\(999\) | 15258.8 | 0.483251 |
(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 | 1045.4.a.d.1.17 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.d.1.17 | ✓ | 22 | 1.1 | even | 1 | trivial |