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: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.55626 | 1.25733 | 0.628664 | − | 0.777677i | \(-0.283602\pi\) | ||||
0.628664 | + | 0.777677i | \(0.283602\pi\) | |||||||
\(3\) | −9.55461 | −1.83879 | −0.919393 | − | 0.393340i | \(-0.871320\pi\) | ||||
−0.919393 | + | 0.393340i | \(0.871320\pi\) | |||||||
\(4\) | 4.64698 | 0.580872 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −33.9787 | −2.31196 | ||||||||
\(7\) | −15.7816 | −0.852128 | −0.426064 | − | 0.904693i | \(-0.640100\pi\) | ||||
−0.426064 | + | 0.904693i | \(0.640100\pi\) | |||||||
\(8\) | −11.9242 | −0.526981 | ||||||||
\(9\) | 64.2906 | 2.38114 | ||||||||
\(10\) | −17.7813 | −0.562294 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −44.4001 | −1.06810 | ||||||||
\(13\) | 63.5848 | 1.35656 | 0.678279 | − | 0.734804i | \(-0.262726\pi\) | ||||
0.678279 | + | 0.734804i | \(0.262726\pi\) | |||||||
\(14\) | −56.1236 | −1.07140 | ||||||||
\(15\) | 47.7731 | 0.822330 | ||||||||
\(16\) | −79.5814 | −1.24346 | ||||||||
\(17\) | 82.1291 | 1.17172 | 0.585860 | − | 0.810412i | \(-0.300757\pi\) | ||||
0.585860 | + | 0.810412i | \(0.300757\pi\) | |||||||
\(18\) | 228.634 | 2.99387 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | −23.2349 | −0.259774 | ||||||||
\(21\) | 150.787 | 1.56688 | ||||||||
\(22\) | 39.1188 | 0.379098 | ||||||||
\(23\) | −51.7522 | −0.469177 | −0.234589 | − | 0.972095i | \(-0.575374\pi\) | ||||
−0.234589 | + | 0.972095i | \(0.575374\pi\) | |||||||
\(24\) | 113.931 | 0.969005 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 226.124 | 1.70564 | ||||||||
\(27\) | −356.298 | −2.53961 | ||||||||
\(28\) | −73.3369 | −0.494978 | ||||||||
\(29\) | −140.105 | −0.897132 | −0.448566 | − | 0.893750i | \(-0.648065\pi\) | ||||
−0.448566 | + | 0.893750i | \(0.648065\pi\) | |||||||
\(30\) | 169.893 | 1.03394 | ||||||||
\(31\) | 341.164 | 1.97661 | 0.988305 | − | 0.152489i | \(-0.0487288\pi\) | ||||
0.988305 | + | 0.152489i | \(0.0487288\pi\) | |||||||
\(32\) | −187.618 | −1.03646 | ||||||||
\(33\) | −105.101 | −0.554415 | ||||||||
\(34\) | 292.072 | 1.47324 | ||||||||
\(35\) | 78.9082 | 0.381083 | ||||||||
\(36\) | 298.757 | 1.38314 | ||||||||
\(37\) | 298.575 | 1.32663 | 0.663316 | − | 0.748339i | \(-0.269148\pi\) | ||||
0.663316 | + | 0.748339i | \(0.269148\pi\) | |||||||
\(38\) | −67.5689 | −0.288451 | ||||||||
\(39\) | −607.529 | −2.49442 | ||||||||
\(40\) | 59.6211 | 0.235673 | ||||||||
\(41\) | −380.297 | −1.44859 | −0.724297 | − | 0.689488i | \(-0.757836\pi\) | ||||
−0.724297 | + | 0.689488i | \(0.757836\pi\) | |||||||
\(42\) | 536.239 | 1.97008 | ||||||||
\(43\) | 544.593 | 1.93139 | 0.965693 | − | 0.259685i | \(-0.0836186\pi\) | ||||
0.965693 | + | 0.259685i | \(0.0836186\pi\) | |||||||
\(44\) | 51.1168 | 0.175140 | ||||||||
\(45\) | −321.453 | −1.06488 | ||||||||
\(46\) | −184.044 | −0.589909 | ||||||||
\(47\) | −327.869 | −1.01755 | −0.508773 | − | 0.860901i | \(-0.669901\pi\) | ||||
−0.508773 | + | 0.860901i | \(0.669901\pi\) | |||||||
\(48\) | 760.370 | 2.28646 | ||||||||
\(49\) | −93.9398 | −0.273877 | ||||||||
\(50\) | 88.9065 | 0.251465 | ||||||||
\(51\) | −784.712 | −2.15454 | ||||||||
\(52\) | 295.477 | 0.787987 | ||||||||
\(53\) | −570.774 | −1.47928 | −0.739640 | − | 0.673003i | \(-0.765004\pi\) | ||||
−0.739640 | + | 0.673003i | \(0.765004\pi\) | |||||||
\(54\) | −1267.09 | −3.19312 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 188.184 | 0.449055 | ||||||||
\(57\) | 181.538 | 0.421847 | ||||||||
\(58\) | −498.249 | −1.12799 | ||||||||
\(59\) | −766.062 | −1.69039 | −0.845193 | − | 0.534461i | \(-0.820514\pi\) | ||||
−0.845193 | + | 0.534461i | \(0.820514\pi\) | |||||||
\(60\) | 222.000 | 0.477669 | ||||||||
\(61\) | 703.612 | 1.47686 | 0.738428 | − | 0.674332i | \(-0.235568\pi\) | ||||
0.738428 | + | 0.674332i | \(0.235568\pi\) | |||||||
\(62\) | 1213.27 | 2.48525 | ||||||||
\(63\) | −1014.61 | −2.02903 | ||||||||
\(64\) | −30.5684 | −0.0597039 | ||||||||
\(65\) | −317.924 | −0.606671 | ||||||||
\(66\) | −373.766 | −0.697081 | ||||||||
\(67\) | −183.134 | −0.333930 | −0.166965 | − | 0.985963i | \(-0.553397\pi\) | ||||
−0.166965 | + | 0.985963i | \(0.553397\pi\) | |||||||
\(68\) | 381.652 | 0.680620 | ||||||||
\(69\) | 494.472 | 0.862716 | ||||||||
\(70\) | 280.618 | 0.479147 | ||||||||
\(71\) | −361.012 | −0.603439 | −0.301720 | − | 0.953397i | \(-0.597561\pi\) | ||||
−0.301720 | + | 0.953397i | \(0.597561\pi\) | |||||||
\(72\) | −766.615 | −1.25481 | ||||||||
\(73\) | 112.254 | 0.179977 | 0.0899884 | − | 0.995943i | \(-0.471317\pi\) | ||||
0.0899884 | + | 0.995943i | \(0.471317\pi\) | |||||||
\(74\) | 1061.81 | 1.66801 | ||||||||
\(75\) | −238.865 | −0.367757 | ||||||||
\(76\) | −88.2926 | −0.133261 | ||||||||
\(77\) | −173.598 | −0.256926 | ||||||||
\(78\) | −2160.53 | −3.13630 | ||||||||
\(79\) | −431.104 | −0.613962 | −0.306981 | − | 0.951716i | \(-0.599319\pi\) | ||||
−0.306981 | + | 0.951716i | \(0.599319\pi\) | |||||||
\(80\) | 397.907 | 0.556092 | ||||||||
\(81\) | 1668.44 | 2.28867 | ||||||||
\(82\) | −1352.43 | −1.82136 | ||||||||
\(83\) | −752.698 | −0.995414 | −0.497707 | − | 0.867345i | \(-0.665824\pi\) | ||||
−0.497707 | + | 0.867345i | \(0.665824\pi\) | |||||||
\(84\) | 700.706 | 0.910158 | ||||||||
\(85\) | −410.646 | −0.524009 | ||||||||
\(86\) | 1936.71 | 2.42839 | ||||||||
\(87\) | 1338.65 | 1.64963 | ||||||||
\(88\) | −131.166 | −0.158891 | ||||||||
\(89\) | −276.201 | −0.328958 | −0.164479 | − | 0.986381i | \(-0.552594\pi\) | ||||
−0.164479 | + | 0.986381i | \(0.552594\pi\) | |||||||
\(90\) | −1143.17 | −1.33890 | ||||||||
\(91\) | −1003.47 | −1.15596 | ||||||||
\(92\) | −240.491 | −0.272532 | ||||||||
\(93\) | −3259.69 | −3.63456 | ||||||||
\(94\) | −1165.99 | −1.27939 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | 1792.62 | 1.90582 | ||||||||
\(97\) | 273.694 | 0.286489 | 0.143245 | − | 0.989687i | \(-0.454246\pi\) | ||||
0.143245 | + | 0.989687i | \(0.454246\pi\) | |||||||
\(98\) | −334.074 | −0.344353 | ||||||||
\(99\) | 707.197 | 0.717939 | ||||||||
\(100\) | 116.174 | 0.116174 | ||||||||
\(101\) | 310.068 | 0.305475 | 0.152737 | − | 0.988267i | \(-0.451191\pi\) | ||||
0.152737 | + | 0.988267i | \(0.451191\pi\) | |||||||
\(102\) | −2790.64 | −2.70897 | ||||||||
\(103\) | −1400.13 | −1.33940 | −0.669701 | − | 0.742631i | \(-0.733578\pi\) | ||||
−0.669701 | + | 0.742631i | \(0.733578\pi\) | |||||||
\(104\) | −758.199 | −0.714880 | ||||||||
\(105\) | −753.937 | −0.700731 | ||||||||
\(106\) | −2029.82 | −1.85994 | ||||||||
\(107\) | 743.667 | 0.671897 | 0.335948 | − | 0.941880i | \(-0.390943\pi\) | ||||
0.335948 | + | 0.941880i | \(0.390943\pi\) | |||||||
\(108\) | −1655.71 | −1.47519 | ||||||||
\(109\) | 230.370 | 0.202435 | 0.101218 | − | 0.994864i | \(-0.467726\pi\) | ||||
0.101218 | + | 0.994864i | \(0.467726\pi\) | |||||||
\(110\) | −195.594 | −0.169538 | ||||||||
\(111\) | −2852.77 | −2.43939 | ||||||||
\(112\) | 1255.93 | 1.05959 | ||||||||
\(113\) | −248.240 | −0.206659 | −0.103329 | − | 0.994647i | \(-0.532950\pi\) | ||||
−0.103329 | + | 0.994647i | \(0.532950\pi\) | |||||||
\(114\) | 645.595 | 0.530399 | ||||||||
\(115\) | 258.761 | 0.209822 | ||||||||
\(116\) | −651.065 | −0.521119 | ||||||||
\(117\) | 4087.91 | 3.23015 | ||||||||
\(118\) | −2724.31 | −2.12537 | ||||||||
\(119\) | −1296.13 | −0.998456 | ||||||||
\(120\) | −569.656 | −0.433352 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 2502.23 | 1.85689 | ||||||||
\(123\) | 3633.59 | 2.66365 | ||||||||
\(124\) | 1585.38 | 1.14816 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −3608.22 | −2.55116 | ||||||||
\(127\) | 1531.01 | 1.06973 | 0.534863 | − | 0.844939i | \(-0.320363\pi\) | ||||
0.534863 | + | 0.844939i | \(0.320363\pi\) | |||||||
\(128\) | 1392.24 | 0.961388 | ||||||||
\(129\) | −5203.38 | −3.55141 | ||||||||
\(130\) | −1130.62 | −0.762785 | ||||||||
\(131\) | −2608.54 | −1.73977 | −0.869883 | − | 0.493258i | \(-0.835806\pi\) | ||||
−0.869883 | + | 0.493258i | \(0.835806\pi\) | |||||||
\(132\) | −488.401 | −0.322044 | ||||||||
\(133\) | 299.851 | 0.195492 | ||||||||
\(134\) | −651.271 | −0.419860 | ||||||||
\(135\) | 1781.49 | 1.13575 | ||||||||
\(136\) | −979.325 | −0.617474 | ||||||||
\(137\) | 480.774 | 0.299820 | 0.149910 | − | 0.988700i | \(-0.452102\pi\) | ||||
0.149910 | + | 0.988700i | \(0.452102\pi\) | |||||||
\(138\) | 1758.47 | 1.08472 | ||||||||
\(139\) | −392.957 | −0.239786 | −0.119893 | − | 0.992787i | \(-0.538255\pi\) | ||||
−0.119893 | + | 0.992787i | \(0.538255\pi\) | |||||||
\(140\) | 366.685 | 0.221361 | ||||||||
\(141\) | 3132.66 | 1.87105 | ||||||||
\(142\) | −1283.85 | −0.758721 | ||||||||
\(143\) | 699.433 | 0.409018 | ||||||||
\(144\) | −5116.34 | −2.96085 | ||||||||
\(145\) | 700.525 | 0.401210 | ||||||||
\(146\) | 399.203 | 0.226290 | ||||||||
\(147\) | 897.559 | 0.503601 | ||||||||
\(148\) | 1387.47 | 0.770604 | ||||||||
\(149\) | 2142.22 | 1.17784 | 0.588919 | − | 0.808192i | \(-0.299554\pi\) | ||||
0.588919 | + | 0.808192i | \(0.299554\pi\) | |||||||
\(150\) | −849.467 | −0.462391 | ||||||||
\(151\) | −675.336 | −0.363961 | −0.181980 | − | 0.983302i | \(-0.558251\pi\) | ||||
−0.181980 | + | 0.983302i | \(0.558251\pi\) | |||||||
\(152\) | 226.560 | 0.120898 | ||||||||
\(153\) | 5280.14 | 2.79002 | ||||||||
\(154\) | −617.360 | −0.323041 | ||||||||
\(155\) | −1705.82 | −0.883967 | ||||||||
\(156\) | −2823.17 | −1.44894 | ||||||||
\(157\) | −600.936 | −0.305477 | −0.152739 | − | 0.988267i | \(-0.548809\pi\) | ||||
−0.152739 | + | 0.988267i | \(0.548809\pi\) | |||||||
\(158\) | −1533.12 | −0.771952 | ||||||||
\(159\) | 5453.52 | 2.72008 | ||||||||
\(160\) | 938.092 | 0.463517 | ||||||||
\(161\) | 816.734 | 0.399799 | ||||||||
\(162\) | 5933.40 | 2.87761 | ||||||||
\(163\) | −184.371 | −0.0885956 | −0.0442978 | − | 0.999018i | \(-0.514105\pi\) | ||||
−0.0442978 | + | 0.999018i | \(0.514105\pi\) | |||||||
\(164\) | −1767.23 | −0.841448 | ||||||||
\(165\) | 525.504 | 0.247942 | ||||||||
\(166\) | −2676.79 | −1.25156 | ||||||||
\(167\) | 3600.99 | 1.66858 | 0.834290 | − | 0.551326i | \(-0.185878\pi\) | ||||
0.834290 | + | 0.551326i | \(0.185878\pi\) | |||||||
\(168\) | −1798.02 | −0.825717 | ||||||||
\(169\) | 1846.03 | 0.840251 | ||||||||
\(170\) | −1460.36 | −0.658851 | ||||||||
\(171\) | −1221.52 | −0.546270 | ||||||||
\(172\) | 2530.71 | 1.12189 | ||||||||
\(173\) | −1881.61 | −0.826912 | −0.413456 | − | 0.910524i | \(-0.635678\pi\) | ||||
−0.413456 | + | 0.910524i | \(0.635678\pi\) | |||||||
\(174\) | 4760.58 | 2.07413 | ||||||||
\(175\) | −394.541 | −0.170426 | ||||||||
\(176\) | −875.396 | −0.374917 | ||||||||
\(177\) | 7319.43 | 3.10826 | ||||||||
\(178\) | −982.242 | −0.413608 | ||||||||
\(179\) | −3120.71 | −1.30309 | −0.651543 | − | 0.758611i | \(-0.725878\pi\) | ||||
−0.651543 | + | 0.758611i | \(0.725878\pi\) | |||||||
\(180\) | −1493.79 | −0.618557 | ||||||||
\(181\) | 1735.82 | 0.712829 | 0.356415 | − | 0.934328i | \(-0.383999\pi\) | ||||
0.356415 | + | 0.934328i | \(0.383999\pi\) | |||||||
\(182\) | −3568.61 | −1.45342 | ||||||||
\(183\) | −6722.74 | −2.71562 | ||||||||
\(184\) | 617.104 | 0.247247 | ||||||||
\(185\) | −1492.87 | −0.593288 | ||||||||
\(186\) | −11592.3 | −4.56984 | ||||||||
\(187\) | 903.420 | 0.353287 | ||||||||
\(188\) | −1523.60 | −0.591064 | ||||||||
\(189\) | 5622.96 | 2.16408 | ||||||||
\(190\) | 337.845 | 0.128999 | ||||||||
\(191\) | −3171.49 | −1.20147 | −0.600736 | − | 0.799448i | \(-0.705126\pi\) | ||||
−0.600736 | + | 0.799448i | \(0.705126\pi\) | |||||||
\(192\) | 292.069 | 0.109783 | ||||||||
\(193\) | 2839.28 | 1.05894 | 0.529471 | − | 0.848328i | \(-0.322391\pi\) | ||||
0.529471 | + | 0.848328i | \(0.322391\pi\) | |||||||
\(194\) | 973.327 | 0.360210 | ||||||||
\(195\) | 3037.64 | 1.11554 | ||||||||
\(196\) | −436.536 | −0.159088 | ||||||||
\(197\) | −3002.12 | −1.08575 | −0.542873 | − | 0.839815i | \(-0.682664\pi\) | ||||
−0.542873 | + | 0.839815i | \(0.682664\pi\) | |||||||
\(198\) | 2514.98 | 0.902685 | ||||||||
\(199\) | −3715.16 | −1.32342 | −0.661711 | − | 0.749759i | \(-0.730169\pi\) | ||||
−0.661711 | + | 0.749759i | \(0.730169\pi\) | |||||||
\(200\) | −298.105 | −0.105396 | ||||||||
\(201\) | 1749.77 | 0.614027 | ||||||||
\(202\) | 1102.68 | 0.384082 | ||||||||
\(203\) | 2211.09 | 0.764472 | ||||||||
\(204\) | −3646.54 | −1.25151 | ||||||||
\(205\) | 1901.48 | 0.647831 | ||||||||
\(206\) | −4979.21 | −1.68407 | ||||||||
\(207\) | −3327.18 | −1.11717 | ||||||||
\(208\) | −5060.17 | −1.68683 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | −2681.20 | −0.881048 | ||||||||
\(211\) | −1142.70 | −0.372827 | −0.186413 | − | 0.982471i | \(-0.559686\pi\) | ||||
−0.186413 | + | 0.982471i | \(0.559686\pi\) | |||||||
\(212\) | −2652.37 | −0.859272 | ||||||||
\(213\) | 3449.33 | 1.10960 | ||||||||
\(214\) | 2644.67 | 0.844794 | ||||||||
\(215\) | −2722.96 | −0.863743 | ||||||||
\(216\) | 4248.57 | 1.33833 | ||||||||
\(217\) | −5384.13 | −1.68433 | ||||||||
\(218\) | 819.255 | 0.254527 | ||||||||
\(219\) | −1072.54 | −0.330939 | ||||||||
\(220\) | −255.584 | −0.0783248 | ||||||||
\(221\) | 5222.17 | 1.58951 | ||||||||
\(222\) | −10145.2 | −3.06712 | ||||||||
\(223\) | 2792.07 | 0.838435 | 0.419218 | − | 0.907886i | \(-0.362304\pi\) | ||||
0.419218 | + | 0.907886i | \(0.362304\pi\) | |||||||
\(224\) | 2960.93 | 0.883193 | ||||||||
\(225\) | 1607.27 | 0.476227 | ||||||||
\(226\) | −882.806 | −0.259838 | ||||||||
\(227\) | −1023.26 | −0.299190 | −0.149595 | − | 0.988747i | \(-0.547797\pi\) | ||||
−0.149595 | + | 0.988747i | \(0.547797\pi\) | |||||||
\(228\) | 843.602 | 0.245039 | ||||||||
\(229\) | −4438.45 | −1.28079 | −0.640395 | − | 0.768046i | \(-0.721229\pi\) | ||||
−0.640395 | + | 0.768046i | \(0.721229\pi\) | |||||||
\(230\) | 920.221 | 0.263815 | ||||||||
\(231\) | 1658.66 | 0.472433 | ||||||||
\(232\) | 1670.64 | 0.472771 | ||||||||
\(233\) | 566.920 | 0.159400 | 0.0796999 | − | 0.996819i | \(-0.474604\pi\) | ||||
0.0796999 | + | 0.996819i | \(0.474604\pi\) | |||||||
\(234\) | 14537.7 | 4.06136 | ||||||||
\(235\) | 1639.35 | 0.455060 | ||||||||
\(236\) | −3559.87 | −0.981898 | ||||||||
\(237\) | 4119.04 | 1.12895 | ||||||||
\(238\) | −4609.38 | −1.25539 | ||||||||
\(239\) | −5127.28 | −1.38768 | −0.693841 | − | 0.720128i | \(-0.744083\pi\) | ||||
−0.693841 | + | 0.720128i | \(0.744083\pi\) | |||||||
\(240\) | −3801.85 | −1.02253 | ||||||||
\(241\) | −2785.96 | −0.744645 | −0.372323 | − | 0.928103i | \(-0.621438\pi\) | ||||
−0.372323 | + | 0.928103i | \(0.621438\pi\) | |||||||
\(242\) | 430.307 | 0.114302 | ||||||||
\(243\) | −6321.26 | −1.66876 | ||||||||
\(244\) | 3269.67 | 0.857865 | ||||||||
\(245\) | 469.699 | 0.122482 | ||||||||
\(246\) | 12922.0 | 3.34909 | ||||||||
\(247\) | −1208.11 | −0.311216 | ||||||||
\(248\) | −4068.12 | −1.04164 | ||||||||
\(249\) | 7191.74 | 1.83035 | ||||||||
\(250\) | −444.532 | −0.112459 | ||||||||
\(251\) | −4187.44 | −1.05302 | −0.526512 | − | 0.850168i | \(-0.676500\pi\) | ||||
−0.526512 | + | 0.850168i | \(0.676500\pi\) | |||||||
\(252\) | −4714.88 | −1.17861 | ||||||||
\(253\) | −569.274 | −0.141462 | ||||||||
\(254\) | 5444.67 | 1.34499 | ||||||||
\(255\) | 3923.56 | 0.963541 | ||||||||
\(256\) | 5195.71 | 1.26848 | ||||||||
\(257\) | 5754.34 | 1.39668 | 0.698338 | − | 0.715768i | \(-0.253923\pi\) | ||||
0.698338 | + | 0.715768i | \(0.253923\pi\) | |||||||
\(258\) | −18504.5 | −4.46528 | ||||||||
\(259\) | −4712.00 | −1.13046 | ||||||||
\(260\) | −1477.39 | −0.352399 | ||||||||
\(261\) | −9007.44 | −2.13619 | ||||||||
\(262\) | −9276.65 | −2.18746 | ||||||||
\(263\) | −6386.37 | −1.49734 | −0.748670 | − | 0.662943i | \(-0.769307\pi\) | ||||
−0.748670 | + | 0.662943i | \(0.769307\pi\) | |||||||
\(264\) | 1253.24 | 0.292166 | ||||||||
\(265\) | 2853.87 | 0.661554 | ||||||||
\(266\) | 1066.35 | 0.245797 | ||||||||
\(267\) | 2638.99 | 0.604883 | ||||||||
\(268\) | −851.018 | −0.193971 | ||||||||
\(269\) | −8596.44 | −1.94846 | −0.974228 | − | 0.225567i | \(-0.927577\pi\) | ||||
−0.974228 | + | 0.225567i | \(0.927577\pi\) | |||||||
\(270\) | 6335.44 | 1.42801 | ||||||||
\(271\) | −5116.34 | −1.14685 | −0.573424 | − | 0.819259i | \(-0.694385\pi\) | ||||
−0.573424 | + | 0.819259i | \(0.694385\pi\) | |||||||
\(272\) | −6535.95 | −1.45699 | ||||||||
\(273\) | 9587.80 | 2.12557 | ||||||||
\(274\) | 1709.76 | 0.376972 | ||||||||
\(275\) | 275.000 | 0.0603023 | ||||||||
\(276\) | 2297.80 | 0.501128 | ||||||||
\(277\) | −2057.55 | −0.446304 | −0.223152 | − | 0.974784i | \(-0.571635\pi\) | ||||
−0.223152 | + | 0.974784i | \(0.571635\pi\) | |||||||
\(278\) | −1397.46 | −0.301489 | ||||||||
\(279\) | 21933.7 | 4.70658 | ||||||||
\(280\) | −940.918 | −0.200824 | ||||||||
\(281\) | 5042.93 | 1.07059 | 0.535295 | − | 0.844665i | \(-0.320201\pi\) | ||||
0.535295 | + | 0.844665i | \(0.320201\pi\) | |||||||
\(282\) | 11140.6 | 2.35252 | ||||||||
\(283\) | −2156.19 | −0.452904 | −0.226452 | − | 0.974022i | \(-0.572713\pi\) | ||||
−0.226452 | + | 0.974022i | \(0.572713\pi\) | |||||||
\(284\) | −1677.61 | −0.350521 | ||||||||
\(285\) | −907.688 | −0.188655 | ||||||||
\(286\) | 2487.37 | 0.514269 | ||||||||
\(287\) | 6001.70 | 1.23439 | ||||||||
\(288\) | −12062.1 | −2.46794 | ||||||||
\(289\) | 1832.19 | 0.372928 | ||||||||
\(290\) | 2491.25 | 0.504452 | ||||||||
\(291\) | −2615.04 | −0.526792 | ||||||||
\(292\) | 521.641 | 0.104544 | ||||||||
\(293\) | 4712.80 | 0.939674 | 0.469837 | − | 0.882753i | \(-0.344313\pi\) | ||||
0.469837 | + | 0.882753i | \(0.344313\pi\) | |||||||
\(294\) | 3191.95 | 0.633192 | ||||||||
\(295\) | 3830.31 | 0.755964 | ||||||||
\(296\) | −3560.27 | −0.699110 | ||||||||
\(297\) | −3919.28 | −0.765722 | ||||||||
\(298\) | 7618.30 | 1.48093 | ||||||||
\(299\) | −3290.65 | −0.636466 | ||||||||
\(300\) | −1110.00 | −0.213620 | ||||||||
\(301\) | −8594.57 | −1.64579 | ||||||||
\(302\) | −2401.67 | −0.457618 | ||||||||
\(303\) | −2962.58 | −0.561703 | ||||||||
\(304\) | 1512.05 | 0.285269 | ||||||||
\(305\) | −3518.06 | −0.660470 | ||||||||
\(306\) | 18777.5 | 3.50797 | ||||||||
\(307\) | −3284.79 | −0.610661 | −0.305331 | − | 0.952246i | \(-0.598767\pi\) | ||||
−0.305331 | + | 0.952246i | \(0.598767\pi\) | |||||||
\(308\) | −806.706 | −0.149241 | ||||||||
\(309\) | 13377.7 | 2.46287 | ||||||||
\(310\) | −6066.34 | −1.11144 | ||||||||
\(311\) | 5682.11 | 1.03602 | 0.518011 | − | 0.855374i | \(-0.326672\pi\) | ||||
0.518011 | + | 0.855374i | \(0.326672\pi\) | |||||||
\(312\) | 7244.30 | 1.31451 | ||||||||
\(313\) | 9225.31 | 1.66596 | 0.832980 | − | 0.553304i | \(-0.186633\pi\) | ||||
0.832980 | + | 0.553304i | \(0.186633\pi\) | |||||||
\(314\) | −2137.09 | −0.384085 | ||||||||
\(315\) | 5073.06 | 0.907411 | ||||||||
\(316\) | −2003.33 | −0.356634 | ||||||||
\(317\) | −2168.94 | −0.384290 | −0.192145 | − | 0.981367i | \(-0.561544\pi\) | ||||
−0.192145 | + | 0.981367i | \(0.561544\pi\) | |||||||
\(318\) | 19394.1 | 3.42003 | ||||||||
\(319\) | −1541.15 | −0.270496 | ||||||||
\(320\) | 152.842 | 0.0267004 | ||||||||
\(321\) | −7105.45 | −1.23547 | ||||||||
\(322\) | 2904.52 | 0.502678 | ||||||||
\(323\) | −1560.45 | −0.268811 | ||||||||
\(324\) | 7753.20 | 1.32942 | ||||||||
\(325\) | 1589.62 | 0.271312 | ||||||||
\(326\) | −655.672 | −0.111394 | ||||||||
\(327\) | −2201.10 | −0.372235 | ||||||||
\(328\) | 4534.74 | 0.763381 | ||||||||
\(329\) | 5174.31 | 0.867080 | ||||||||
\(330\) | 1868.83 | 0.311744 | ||||||||
\(331\) | 141.422 | 0.0234842 | 0.0117421 | − | 0.999931i | \(-0.496262\pi\) | ||||
0.0117421 | + | 0.999931i | \(0.496262\pi\) | |||||||
\(332\) | −3497.77 | −0.578208 | ||||||||
\(333\) | 19195.6 | 3.15889 | ||||||||
\(334\) | 12806.0 | 2.09795 | ||||||||
\(335\) | 915.669 | 0.149338 | ||||||||
\(336\) | −11999.9 | −1.94835 | ||||||||
\(337\) | −5247.39 | −0.848200 | −0.424100 | − | 0.905615i | \(-0.639409\pi\) | ||||
−0.424100 | + | 0.905615i | \(0.639409\pi\) | |||||||
\(338\) | 6564.97 | 1.05647 | ||||||||
\(339\) | 2371.84 | 0.380001 | ||||||||
\(340\) | −1908.26 | −0.304382 | ||||||||
\(341\) | 3752.81 | 0.595970 | ||||||||
\(342\) | −4344.05 | −0.686840 | ||||||||
\(343\) | 6895.63 | 1.08551 | ||||||||
\(344\) | −6493.84 | −1.01780 | ||||||||
\(345\) | −2472.36 | −0.385819 | ||||||||
\(346\) | −6691.48 | −1.03970 | ||||||||
\(347\) | 9012.15 | 1.39423 | 0.697115 | − | 0.716959i | \(-0.254467\pi\) | ||||
0.697115 | + | 0.716959i | \(0.254467\pi\) | |||||||
\(348\) | 6220.67 | 0.958227 | ||||||||
\(349\) | 5256.23 | 0.806188 | 0.403094 | − | 0.915159i | \(-0.367935\pi\) | ||||
0.403094 | + | 0.915159i | \(0.367935\pi\) | |||||||
\(350\) | −1403.09 | −0.214281 | ||||||||
\(351\) | −22655.1 | −3.44513 | ||||||||
\(352\) | −2063.80 | −0.312503 | ||||||||
\(353\) | −2126.07 | −0.320565 | −0.160282 | − | 0.987071i | \(-0.551240\pi\) | ||||
−0.160282 | + | 0.987071i | \(0.551240\pi\) | |||||||
\(354\) | 26029.8 | 3.90810 | ||||||||
\(355\) | 1805.06 | 0.269866 | ||||||||
\(356\) | −1283.50 | −0.191082 | ||||||||
\(357\) | 12384.0 | 1.83595 | ||||||||
\(358\) | −11098.0 | −1.63841 | ||||||||
\(359\) | 12471.5 | 1.83349 | 0.916744 | − | 0.399474i | \(-0.130807\pi\) | ||||
0.916744 | + | 0.399474i | \(0.130807\pi\) | |||||||
\(360\) | 3833.08 | 0.561169 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 6173.01 | 0.896260 | ||||||||
\(363\) | −1156.11 | −0.167162 | ||||||||
\(364\) | −4663.12 | −0.671466 | ||||||||
\(365\) | −561.269 | −0.0804880 | ||||||||
\(366\) | −23907.8 | −3.41443 | ||||||||
\(367\) | −3574.01 | −0.508342 | −0.254171 | − | 0.967159i | \(-0.581803\pi\) | ||||
−0.254171 | + | 0.967159i | \(0.581803\pi\) | |||||||
\(368\) | 4118.51 | 0.583403 | ||||||||
\(369\) | −24449.5 | −3.44930 | ||||||||
\(370\) | −5309.05 | −0.745957 | ||||||||
\(371\) | 9007.75 | 1.26054 | ||||||||
\(372\) | −15147.7 | −2.11122 | ||||||||
\(373\) | −4030.01 | −0.559427 | −0.279713 | − | 0.960084i | \(-0.590239\pi\) | ||||
−0.279713 | + | 0.960084i | \(0.590239\pi\) | |||||||
\(374\) | 3212.80 | 0.444197 | ||||||||
\(375\) | 1194.33 | 0.164466 | ||||||||
\(376\) | 3909.58 | 0.536227 | ||||||||
\(377\) | −8908.55 | −1.21701 | ||||||||
\(378\) | 19996.7 | 2.72095 | ||||||||
\(379\) | 6530.98 | 0.885155 | 0.442578 | − | 0.896730i | \(-0.354064\pi\) | ||||
0.442578 | + | 0.896730i | \(0.354064\pi\) | |||||||
\(380\) | 441.463 | 0.0595962 | ||||||||
\(381\) | −14628.2 | −1.96700 | ||||||||
\(382\) | −11278.6 | −1.51064 | ||||||||
\(383\) | −10114.6 | −1.34944 | −0.674718 | − | 0.738076i | \(-0.735735\pi\) | ||||
−0.674718 | + | 0.738076i | \(0.735735\pi\) | |||||||
\(384\) | −13302.3 | −1.76779 | ||||||||
\(385\) | 867.990 | 0.114901 | ||||||||
\(386\) | 10097.2 | 1.33144 | ||||||||
\(387\) | 35012.2 | 4.59889 | ||||||||
\(388\) | 1271.85 | 0.166414 | ||||||||
\(389\) | 8183.23 | 1.06660 | 0.533299 | − | 0.845927i | \(-0.320952\pi\) | ||||
0.533299 | + | 0.845927i | \(0.320952\pi\) | |||||||
\(390\) | 10802.6 | 1.40260 | ||||||||
\(391\) | −4250.36 | −0.549744 | ||||||||
\(392\) | 1120.16 | 0.144328 | ||||||||
\(393\) | 24923.6 | 3.19906 | ||||||||
\(394\) | −10676.3 | −1.36514 | ||||||||
\(395\) | 2155.52 | 0.274572 | ||||||||
\(396\) | 3286.33 | 0.417031 | ||||||||
\(397\) | −4617.19 | −0.583704 | −0.291852 | − | 0.956464i | \(-0.594271\pi\) | ||||
−0.291852 | + | 0.956464i | \(0.594271\pi\) | |||||||
\(398\) | −13212.1 | −1.66397 | ||||||||
\(399\) | −2864.96 | −0.359467 | ||||||||
\(400\) | −1989.54 | −0.248692 | ||||||||
\(401\) | 9493.37 | 1.18223 | 0.591117 | − | 0.806586i | \(-0.298687\pi\) | ||||
0.591117 | + | 0.806586i | \(0.298687\pi\) | |||||||
\(402\) | 6222.64 | 0.772033 | ||||||||
\(403\) | 21692.9 | 2.68139 | ||||||||
\(404\) | 1440.88 | 0.177442 | ||||||||
\(405\) | −8342.20 | −1.02352 | ||||||||
\(406\) | 7863.19 | 0.961191 | ||||||||
\(407\) | 3284.32 | 0.399995 | ||||||||
\(408\) | 9357.08 | 1.13540 | ||||||||
\(409\) | −823.193 | −0.0995214 | −0.0497607 | − | 0.998761i | \(-0.515846\pi\) | ||||
−0.0497607 | + | 0.998761i | \(0.515846\pi\) | |||||||
\(410\) | 6762.17 | 0.814536 | ||||||||
\(411\) | −4593.61 | −0.551305 | ||||||||
\(412\) | −6506.35 | −0.778022 | ||||||||
\(413\) | 12089.7 | 1.44043 | ||||||||
\(414\) | −11832.3 | −1.40465 | ||||||||
\(415\) | 3763.49 | 0.445163 | ||||||||
\(416\) | −11929.7 | −1.40601 | ||||||||
\(417\) | 3754.55 | 0.440914 | ||||||||
\(418\) | −743.258 | −0.0869712 | ||||||||
\(419\) | −4611.76 | −0.537707 | −0.268854 | − | 0.963181i | \(-0.586645\pi\) | ||||
−0.268854 | + | 0.963181i | \(0.586645\pi\) | |||||||
\(420\) | −3503.53 | −0.407035 | ||||||||
\(421\) | −13857.9 | −1.60425 | −0.802127 | − | 0.597154i | \(-0.796298\pi\) | ||||
−0.802127 | + | 0.597154i | \(0.796298\pi\) | |||||||
\(422\) | −4063.72 | −0.468765 | ||||||||
\(423\) | −21078.9 | −2.42291 | ||||||||
\(424\) | 6806.03 | 0.779552 | ||||||||
\(425\) | 2053.23 | 0.234344 | ||||||||
\(426\) | 12266.7 | 1.39513 | ||||||||
\(427\) | −11104.1 | −1.25847 | ||||||||
\(428\) | 3455.80 | 0.390286 | ||||||||
\(429\) | −6682.81 | −0.752096 | ||||||||
\(430\) | −9683.57 | −1.08601 | ||||||||
\(431\) | −9836.15 | −1.09928 | −0.549641 | − | 0.835401i | \(-0.685236\pi\) | ||||
−0.549641 | + | 0.835401i | \(0.685236\pi\) | |||||||
\(432\) | 28354.7 | 3.15791 | ||||||||
\(433\) | −15250.8 | −1.69262 | −0.846311 | − | 0.532688i | \(-0.821182\pi\) | ||||
−0.846311 | + | 0.532688i | \(0.821182\pi\) | |||||||
\(434\) | −19147.4 | −2.11775 | ||||||||
\(435\) | −6693.24 | −0.737739 | ||||||||
\(436\) | 1070.52 | 0.117589 | ||||||||
\(437\) | 983.291 | 0.107637 | ||||||||
\(438\) | −3814.23 | −0.416098 | ||||||||
\(439\) | −1098.00 | −0.119372 | −0.0596862 | − | 0.998217i | \(-0.519010\pi\) | ||||
−0.0596862 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(440\) | 655.832 | 0.0710581 | ||||||||
\(441\) | −6039.45 | −0.652138 | ||||||||
\(442\) | 18571.4 | 1.99853 | ||||||||
\(443\) | 13504.2 | 1.44831 | 0.724157 | − | 0.689635i | \(-0.242229\pi\) | ||||
0.724157 | + | 0.689635i | \(0.242229\pi\) | |||||||
\(444\) | −13256.7 | −1.41698 | ||||||||
\(445\) | 1381.00 | 0.147114 | ||||||||
\(446\) | 9929.33 | 1.05419 | ||||||||
\(447\) | −20468.1 | −2.16579 | ||||||||
\(448\) | 482.419 | 0.0508754 | ||||||||
\(449\) | −14196.1 | −1.49210 | −0.746051 | − | 0.665888i | \(-0.768053\pi\) | ||||
−0.746051 | + | 0.665888i | \(0.768053\pi\) | |||||||
\(450\) | 5715.86 | 0.598773 | ||||||||
\(451\) | −4183.26 | −0.436767 | ||||||||
\(452\) | −1153.57 | −0.120042 | ||||||||
\(453\) | 6452.57 | 0.669246 | ||||||||
\(454\) | −3638.98 | −0.376180 | ||||||||
\(455\) | 5017.37 | 0.516962 | ||||||||
\(456\) | −2164.69 | −0.222305 | ||||||||
\(457\) | 8889.24 | 0.909893 | 0.454947 | − | 0.890519i | \(-0.349658\pi\) | ||||
0.454947 | + | 0.890519i | \(0.349658\pi\) | |||||||
\(458\) | −15784.3 | −1.61037 | ||||||||
\(459\) | −29262.4 | −2.97571 | ||||||||
\(460\) | 1202.46 | 0.121880 | ||||||||
\(461\) | −16936.9 | −1.71113 | −0.855566 | − | 0.517695i | \(-0.826790\pi\) | ||||
−0.855566 | + | 0.517695i | \(0.826790\pi\) | |||||||
\(462\) | 5898.63 | 0.594003 | ||||||||
\(463\) | −1071.27 | −0.107530 | −0.0537649 | − | 0.998554i | \(-0.517122\pi\) | ||||
−0.0537649 | + | 0.998554i | \(0.517122\pi\) | |||||||
\(464\) | 11149.7 | 1.11555 | ||||||||
\(465\) | 16298.5 | 1.62543 | ||||||||
\(466\) | 2016.11 | 0.200418 | ||||||||
\(467\) | −10354.0 | −1.02597 | −0.512984 | − | 0.858398i | \(-0.671460\pi\) | ||||
−0.512984 | + | 0.858398i | \(0.671460\pi\) | |||||||
\(468\) | 18996.4 | 1.87630 | ||||||||
\(469\) | 2890.15 | 0.284552 | ||||||||
\(470\) | 5829.94 | 0.572160 | ||||||||
\(471\) | 5741.71 | 0.561707 | ||||||||
\(472\) | 9134.69 | 0.890801 | ||||||||
\(473\) | 5990.52 | 0.582335 | ||||||||
\(474\) | 14648.4 | 1.41945 | ||||||||
\(475\) | −475.000 | −0.0458831 | ||||||||
\(476\) | −6023.10 | −0.579975 | ||||||||
\(477\) | −36695.4 | −3.52236 | ||||||||
\(478\) | −18233.9 | −1.74477 | ||||||||
\(479\) | 1957.37 | 0.186711 | 0.0933554 | − | 0.995633i | \(-0.470241\pi\) | ||||
0.0933554 | + | 0.995633i | \(0.470241\pi\) | |||||||
\(480\) | −8963.11 | −0.852308 | ||||||||
\(481\) | 18984.8 | 1.79965 | ||||||||
\(482\) | −9907.60 | −0.936263 | ||||||||
\(483\) | −7803.58 | −0.735145 | ||||||||
\(484\) | 562.284 | 0.0528066 | ||||||||
\(485\) | −1368.47 | −0.128122 | ||||||||
\(486\) | −22480.0 | −2.09818 | ||||||||
\(487\) | −9116.55 | −0.848275 | −0.424138 | − | 0.905598i | \(-0.639423\pi\) | ||||
−0.424138 | + | 0.905598i | \(0.639423\pi\) | |||||||
\(488\) | −8390.02 | −0.778275 | ||||||||
\(489\) | 1761.60 | 0.162908 | ||||||||
\(490\) | 1670.37 | 0.153999 | ||||||||
\(491\) | −184.420 | −0.0169506 | −0.00847532 | − | 0.999964i | \(-0.502698\pi\) | ||||
−0.00847532 | + | 0.999964i | \(0.502698\pi\) | |||||||
\(492\) | 16885.2 | 1.54724 | ||||||||
\(493\) | −11506.7 | −1.05119 | ||||||||
\(494\) | −4296.36 | −0.391300 | ||||||||
\(495\) | −3535.99 | −0.321072 | ||||||||
\(496\) | −27150.3 | −2.45784 | ||||||||
\(497\) | 5697.35 | 0.514208 | ||||||||
\(498\) | 25575.7 | 2.30135 | ||||||||
\(499\) | 14600.0 | 1.30979 | 0.654896 | − | 0.755719i | \(-0.272713\pi\) | ||||
0.654896 | + | 0.755719i | \(0.272713\pi\) | |||||||
\(500\) | −580.872 | −0.0519548 | ||||||||
\(501\) | −34406.0 | −3.06816 | ||||||||
\(502\) | −14891.6 | −1.32400 | ||||||||
\(503\) | −22433.4 | −1.98858 | −0.994288 | − | 0.106731i | \(-0.965962\pi\) | ||||
−0.994288 | + | 0.106731i | \(0.965962\pi\) | |||||||
\(504\) | 12098.4 | 1.06926 | ||||||||
\(505\) | −1550.34 | −0.136612 | ||||||||
\(506\) | −2024.49 | −0.177864 | ||||||||
\(507\) | −17638.1 | −1.54504 | ||||||||
\(508\) | 7114.57 | 0.621374 | ||||||||
\(509\) | −15778.4 | −1.37400 | −0.687001 | − | 0.726657i | \(-0.741073\pi\) | ||||
−0.687001 | + | 0.726657i | \(0.741073\pi\) | |||||||
\(510\) | 13953.2 | 1.21149 | ||||||||
\(511\) | −1771.55 | −0.153363 | ||||||||
\(512\) | 7339.37 | 0.633511 | ||||||||
\(513\) | 6769.66 | 0.582627 | ||||||||
\(514\) | 20463.9 | 1.75608 | ||||||||
\(515\) | 7000.63 | 0.598999 | ||||||||
\(516\) | −24180.0 | −2.06291 | ||||||||
\(517\) | −3606.56 | −0.306802 | ||||||||
\(518\) | −16757.1 | −1.42136 | ||||||||
\(519\) | 17978.0 | 1.52051 | ||||||||
\(520\) | 3791.00 | 0.319704 | ||||||||
\(521\) | 7388.88 | 0.621329 | 0.310665 | − | 0.950520i | \(-0.399448\pi\) | ||||
0.310665 | + | 0.950520i | \(0.399448\pi\) | |||||||
\(522\) | −32032.8 | −2.68589 | ||||||||
\(523\) | −21072.4 | −1.76182 | −0.880909 | − | 0.473286i | \(-0.843068\pi\) | ||||
−0.880909 | + | 0.473286i | \(0.843068\pi\) | |||||||
\(524\) | −12121.8 | −1.01058 | ||||||||
\(525\) | 3769.69 | 0.313376 | ||||||||
\(526\) | −22711.6 | −1.88265 | ||||||||
\(527\) | 28019.5 | 2.31603 | ||||||||
\(528\) | 8364.07 | 0.689393 | ||||||||
\(529\) | −9488.71 | −0.779873 | ||||||||
\(530\) | 10149.1 | 0.831790 | ||||||||
\(531\) | −49250.6 | −4.02504 | ||||||||
\(532\) | 1393.40 | 0.113556 | ||||||||
\(533\) | −24181.1 | −1.96510 | ||||||||
\(534\) | 9384.95 | 0.760536 | ||||||||
\(535\) | −3718.33 | −0.300481 | ||||||||
\(536\) | 2183.73 | 0.175975 | ||||||||
\(537\) | 29817.1 | 2.39610 | ||||||||
\(538\) | −30571.2 | −2.44985 | ||||||||
\(539\) | −1033.34 | −0.0825770 | ||||||||
\(540\) | 8278.54 | 0.659725 | ||||||||
\(541\) | 7955.28 | 0.632207 | 0.316104 | − | 0.948725i | \(-0.397625\pi\) | ||||
0.316104 | + | 0.948725i | \(0.397625\pi\) | |||||||
\(542\) | −18195.0 | −1.44196 | ||||||||
\(543\) | −16585.0 | −1.31074 | ||||||||
\(544\) | −15408.9 | −1.21444 | ||||||||
\(545\) | −1151.85 | −0.0905317 | ||||||||
\(546\) | 34096.7 | 2.67253 | ||||||||
\(547\) | −1204.66 | −0.0941636 | −0.0470818 | − | 0.998891i | \(-0.514992\pi\) | ||||
−0.0470818 | + | 0.998891i | \(0.514992\pi\) | |||||||
\(548\) | 2234.15 | 0.174157 | ||||||||
\(549\) | 45235.7 | 3.51659 | ||||||||
\(550\) | 977.971 | 0.0758197 | ||||||||
\(551\) | 2661.99 | 0.205816 | ||||||||
\(552\) | −5896.19 | −0.454635 | ||||||||
\(553\) | 6803.53 | 0.523175 | ||||||||
\(554\) | −7317.18 | −0.561150 | ||||||||
\(555\) | 14263.8 | 1.09093 | ||||||||
\(556\) | −1826.06 | −0.139285 | ||||||||
\(557\) | 13218.3 | 1.00553 | 0.502763 | − | 0.864424i | \(-0.332317\pi\) | ||||
0.502763 | + | 0.864424i | \(0.332317\pi\) | |||||||
\(558\) | 78001.8 | 5.91771 | ||||||||
\(559\) | 34627.9 | 2.62004 | ||||||||
\(560\) | −6279.63 | −0.473862 | ||||||||
\(561\) | −8631.83 | −0.649619 | ||||||||
\(562\) | 17933.9 | 1.34608 | ||||||||
\(563\) | −4353.73 | −0.325911 | −0.162956 | − | 0.986633i | \(-0.552103\pi\) | ||||
−0.162956 | + | 0.986633i | \(0.552103\pi\) | |||||||
\(564\) | 14557.4 | 1.08684 | ||||||||
\(565\) | 1241.20 | 0.0924207 | ||||||||
\(566\) | −7667.95 | −0.569449 | ||||||||
\(567\) | −26330.7 | −1.95024 | ||||||||
\(568\) | 4304.78 | 0.318001 | ||||||||
\(569\) | −10725.2 | −0.790202 | −0.395101 | − | 0.918638i | \(-0.629290\pi\) | ||||
−0.395101 | + | 0.918638i | \(0.629290\pi\) | |||||||
\(570\) | −3227.97 | −0.237202 | ||||||||
\(571\) | −17478.1 | −1.28098 | −0.640488 | − | 0.767968i | \(-0.721268\pi\) | ||||
−0.640488 | + | 0.767968i | \(0.721268\pi\) | |||||||
\(572\) | 3250.25 | 0.237587 | ||||||||
\(573\) | 30302.4 | 2.20925 | ||||||||
\(574\) | 21343.6 | 1.55203 | ||||||||
\(575\) | −1293.80 | −0.0938354 | ||||||||
\(576\) | −1965.26 | −0.142163 | ||||||||
\(577\) | 25176.5 | 1.81649 | 0.908244 | − | 0.418441i | \(-0.137423\pi\) | ||||
0.908244 | + | 0.418441i | \(0.137423\pi\) | |||||||
\(578\) | 6515.76 | 0.468892 | ||||||||
\(579\) | −27128.2 | −1.94717 | ||||||||
\(580\) | 3255.32 | 0.233052 | ||||||||
\(581\) | 11878.8 | 0.848221 | ||||||||
\(582\) | −9299.77 | −0.662350 | ||||||||
\(583\) | −6278.51 | −0.446020 | ||||||||
\(584\) | −1338.54 | −0.0948443 | ||||||||
\(585\) | −20439.6 | −1.44457 | ||||||||
\(586\) | 16759.9 | 1.18148 | ||||||||
\(587\) | −10522.1 | −0.739854 | −0.369927 | − | 0.929061i | \(-0.620617\pi\) | ||||
−0.369927 | + | 0.929061i | \(0.620617\pi\) | |||||||
\(588\) | 4170.94 | 0.292528 | ||||||||
\(589\) | −6482.12 | −0.453466 | ||||||||
\(590\) | 13621.6 | 0.950494 | ||||||||
\(591\) | 28684.1 | 1.99645 | ||||||||
\(592\) | −23761.0 | −1.64961 | ||||||||
\(593\) | −12806.4 | −0.886837 | −0.443418 | − | 0.896315i | \(-0.646234\pi\) | ||||
−0.443418 | + | 0.896315i | \(0.646234\pi\) | |||||||
\(594\) | −13938.0 | −0.962763 | ||||||||
\(595\) | 6480.66 | 0.446523 | ||||||||
\(596\) | 9954.87 | 0.684173 | ||||||||
\(597\) | 35496.9 | 2.43349 | ||||||||
\(598\) | −11702.4 | −0.800246 | ||||||||
\(599\) | −13801.7 | −0.941440 | −0.470720 | − | 0.882283i | \(-0.656006\pi\) | ||||
−0.470720 | + | 0.882283i | \(0.656006\pi\) | |||||||
\(600\) | 2848.28 | 0.193801 | ||||||||
\(601\) | −10114.3 | −0.686472 | −0.343236 | − | 0.939249i | \(-0.611523\pi\) | ||||
−0.343236 | + | 0.939249i | \(0.611523\pi\) | |||||||
\(602\) | −30564.5 | −2.06930 | ||||||||
\(603\) | −11773.8 | −0.795134 | ||||||||
\(604\) | −3138.27 | −0.211415 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | −10535.7 | −0.706244 | ||||||||
\(607\) | 14070.1 | 0.940835 | 0.470417 | − | 0.882444i | \(-0.344103\pi\) | ||||
0.470417 | + | 0.882444i | \(0.344103\pi\) | |||||||
\(608\) | 3564.75 | 0.237779 | ||||||||
\(609\) | −21126.1 | −1.40570 | ||||||||
\(610\) | −12511.1 | −0.830427 | ||||||||
\(611\) | −20847.5 | −1.38036 | ||||||||
\(612\) | 24536.7 | 1.62065 | ||||||||
\(613\) | 12314.7 | 0.811396 | 0.405698 | − | 0.914007i | \(-0.367028\pi\) | ||||
0.405698 | + | 0.914007i | \(0.367028\pi\) | |||||||
\(614\) | −11681.6 | −0.767801 | ||||||||
\(615\) | −18167.9 | −1.19122 | ||||||||
\(616\) | 2070.02 | 0.135395 | ||||||||
\(617\) | −104.090 | −0.00679176 | −0.00339588 | − | 0.999994i | \(-0.501081\pi\) | ||||
−0.00339588 | + | 0.999994i | \(0.501081\pi\) | |||||||
\(618\) | 47574.4 | 3.09664 | ||||||||
\(619\) | 7499.08 | 0.486936 | 0.243468 | − | 0.969909i | \(-0.421715\pi\) | ||||
0.243468 | + | 0.969909i | \(0.421715\pi\) | |||||||
\(620\) | −7926.92 | −0.513472 | ||||||||
\(621\) | 18439.2 | 1.19153 | ||||||||
\(622\) | 20207.1 | 1.30262 | ||||||||
\(623\) | 4358.90 | 0.280314 | ||||||||
\(624\) | 48348.0 | 3.10171 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 32807.6 | 2.09466 | ||||||||
\(627\) | 1996.91 | 0.127192 | ||||||||
\(628\) | −2792.54 | −0.177443 | ||||||||
\(629\) | 24521.7 | 1.55444 | ||||||||
\(630\) | 18041.1 | 1.14091 | ||||||||
\(631\) | 7178.78 | 0.452904 | 0.226452 | − | 0.974022i | \(-0.427287\pi\) | ||||
0.226452 | + | 0.974022i | \(0.427287\pi\) | |||||||
\(632\) | 5140.58 | 0.323546 | ||||||||
\(633\) | 10918.0 | 0.685549 | ||||||||
\(634\) | −7713.32 | −0.483178 | ||||||||
\(635\) | −7655.05 | −0.478396 | ||||||||
\(636\) | 25342.4 | 1.58002 | ||||||||
\(637\) | −5973.15 | −0.371530 | ||||||||
\(638\) | −5480.74 | −0.340101 | ||||||||
\(639\) | −23209.7 | −1.43687 | ||||||||
\(640\) | −6961.19 | −0.429946 | ||||||||
\(641\) | 14085.2 | 0.867915 | 0.433958 | − | 0.900933i | \(-0.357117\pi\) | ||||
0.433958 | + | 0.900933i | \(0.357117\pi\) | |||||||
\(642\) | −25268.8 | −1.55340 | ||||||||
\(643\) | −13814.3 | −0.847249 | −0.423624 | − | 0.905838i | \(-0.639242\pi\) | ||||
−0.423624 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(644\) | 3795.35 | 0.232232 | ||||||||
\(645\) | 26016.9 | 1.58824 | ||||||||
\(646\) | −5549.38 | −0.337983 | ||||||||
\(647\) | −6237.19 | −0.378994 | −0.189497 | − | 0.981881i | \(-0.560686\pi\) | ||||
−0.189497 | + | 0.981881i | \(0.560686\pi\) | |||||||
\(648\) | −19894.8 | −1.20608 | ||||||||
\(649\) | −8426.68 | −0.509670 | ||||||||
\(650\) | 5653.10 | 0.341128 | ||||||||
\(651\) | 51443.3 | 3.09712 | ||||||||
\(652\) | −856.770 | −0.0514627 | ||||||||
\(653\) | −28608.0 | −1.71442 | −0.857212 | − | 0.514964i | \(-0.827805\pi\) | ||||
−0.857212 | + | 0.514964i | \(0.827805\pi\) | |||||||
\(654\) | −7827.66 | −0.468021 | ||||||||
\(655\) | 13042.7 | 0.778047 | ||||||||
\(656\) | 30264.5 | 1.80127 | ||||||||
\(657\) | 7216.86 | 0.428549 | ||||||||
\(658\) | 18401.2 | 1.09020 | ||||||||
\(659\) | 2255.66 | 0.133335 | 0.0666677 | − | 0.997775i | \(-0.478763\pi\) | ||||
0.0666677 | + | 0.997775i | \(0.478763\pi\) | |||||||
\(660\) | 2442.00 | 0.144023 | ||||||||
\(661\) | −12873.4 | −0.757517 | −0.378759 | − | 0.925496i | \(-0.623649\pi\) | ||||
−0.378759 | + | 0.925496i | \(0.623649\pi\) | |||||||
\(662\) | 502.935 | 0.0295274 | ||||||||
\(663\) | −49895.8 | −2.92276 | ||||||||
\(664\) | 8975.33 | 0.524564 | ||||||||
\(665\) | −1499.26 | −0.0874265 | ||||||||
\(666\) | 68264.4 | 3.97176 | ||||||||
\(667\) | 7250.73 | 0.420914 | ||||||||
\(668\) | 16733.7 | 0.969232 | ||||||||
\(669\) | −26677.2 | −1.54170 | ||||||||
\(670\) | 3256.35 | 0.187767 | ||||||||
\(671\) | 7739.73 | 0.445289 | ||||||||
\(672\) | −28290.5 | −1.62400 | ||||||||
\(673\) | −10154.3 | −0.581606 | −0.290803 | − | 0.956783i | \(-0.593922\pi\) | ||||
−0.290803 | + | 0.956783i | \(0.593922\pi\) | |||||||
\(674\) | −18661.1 | −1.06647 | ||||||||
\(675\) | −8907.44 | −0.507922 | ||||||||
\(676\) | 8578.47 | 0.488079 | ||||||||
\(677\) | −19891.8 | −1.12925 | −0.564626 | − | 0.825347i | \(-0.690980\pi\) | ||||
−0.564626 | + | 0.825347i | \(0.690980\pi\) | |||||||
\(678\) | 8434.87 | 0.477786 | ||||||||
\(679\) | −4319.34 | −0.244125 | ||||||||
\(680\) | 4896.63 | 0.276143 | ||||||||
\(681\) | 9776.85 | 0.550147 | ||||||||
\(682\) | 13346.0 | 0.749330 | ||||||||
\(683\) | −498.789 | −0.0279438 | −0.0139719 | − | 0.999902i | \(-0.504448\pi\) | ||||
−0.0139719 | + | 0.999902i | \(0.504448\pi\) | |||||||
\(684\) | −5676.39 | −0.317313 | ||||||||
\(685\) | −2403.87 | −0.134083 | ||||||||
\(686\) | 24522.6 | 1.36484 | ||||||||
\(687\) | 42407.7 | 2.35510 | ||||||||
\(688\) | −43339.5 | −2.40160 | ||||||||
\(689\) | −36292.6 | −2.00673 | ||||||||
\(690\) | −8792.35 | −0.485100 | ||||||||
\(691\) | −1697.97 | −0.0934787 | −0.0467394 | − | 0.998907i | \(-0.514883\pi\) | ||||
−0.0467394 | + | 0.998907i | \(0.514883\pi\) | |||||||
\(692\) | −8743.78 | −0.480330 | ||||||||
\(693\) | −11160.7 | −0.611776 | ||||||||
\(694\) | 32049.6 | 1.75300 | ||||||||
\(695\) | 1964.79 | 0.107235 | ||||||||
\(696\) | −15962.3 | −0.869325 | ||||||||
\(697\) | −31233.4 | −1.69735 | ||||||||
\(698\) | 18692.5 | 1.01364 | ||||||||
\(699\) | −5416.70 | −0.293102 | ||||||||
\(700\) | −1833.42 | −0.0989956 | ||||||||
\(701\) | −5049.07 | −0.272041 | −0.136020 | − | 0.990706i | \(-0.543431\pi\) | ||||
−0.136020 | + | 0.990706i | \(0.543431\pi\) | |||||||
\(702\) | −80567.5 | −4.33166 | ||||||||
\(703\) | −5672.92 | −0.304350 | ||||||||
\(704\) | −336.252 | −0.0180014 | ||||||||
\(705\) | −15663.3 | −0.836759 | ||||||||
\(706\) | −7560.86 | −0.403055 | ||||||||
\(707\) | −4893.38 | −0.260304 | ||||||||
\(708\) | 34013.2 | 1.80550 | ||||||||
\(709\) | −28098.4 | −1.48837 | −0.744186 | − | 0.667972i | \(-0.767163\pi\) | ||||
−0.744186 | + | 0.667972i | \(0.767163\pi\) | |||||||
\(710\) | 6419.25 | 0.339310 | ||||||||
\(711\) | −27716.0 | −1.46193 | ||||||||
\(712\) | 3293.48 | 0.173354 | ||||||||
\(713\) | −17656.0 | −0.927380 | ||||||||
\(714\) | 44040.9 | 2.30839 | ||||||||
\(715\) | −3497.17 | −0.182918 | ||||||||
\(716\) | −14501.9 | −0.756927 | ||||||||
\(717\) | 48989.2 | 2.55165 | ||||||||
\(718\) | 44352.0 | 2.30530 | ||||||||
\(719\) | 23561.7 | 1.22212 | 0.611059 | − | 0.791585i | \(-0.290744\pi\) | ||||
0.611059 | + | 0.791585i | \(0.290744\pi\) | |||||||
\(720\) | 25581.7 | 1.32413 | ||||||||
\(721\) | 22096.3 | 1.14134 | ||||||||
\(722\) | 1283.81 | 0.0661751 | ||||||||
\(723\) | 26618.8 | 1.36924 | ||||||||
\(724\) | 8066.30 | 0.414063 | ||||||||
\(725\) | −3502.62 | −0.179426 | ||||||||
\(726\) | −4111.42 | −0.210178 | ||||||||
\(727\) | −5103.57 | −0.260359 | −0.130179 | − | 0.991490i | \(-0.541555\pi\) | ||||
−0.130179 | + | 0.991490i | \(0.541555\pi\) | |||||||
\(728\) | 11965.6 | 0.609170 | ||||||||
\(729\) | 15349.3 | 0.779827 | ||||||||
\(730\) | −1996.02 | −0.101200 | ||||||||
\(731\) | 44726.9 | 2.26304 | ||||||||
\(732\) | −31240.4 | −1.57743 | ||||||||
\(733\) | −16522.7 | −0.832580 | −0.416290 | − | 0.909232i | \(-0.636670\pi\) | ||||
−0.416290 | + | 0.909232i | \(0.636670\pi\) | |||||||
\(734\) | −12710.1 | −0.639153 | ||||||||
\(735\) | −4487.79 | −0.225217 | ||||||||
\(736\) | 9709.66 | 0.486281 | ||||||||
\(737\) | −2014.47 | −0.100684 | ||||||||
\(738\) | −86948.8 | −4.33690 | ||||||||
\(739\) | 4168.34 | 0.207490 | 0.103745 | − | 0.994604i | \(-0.466917\pi\) | ||||
0.103745 | + | 0.994604i | \(0.466917\pi\) | |||||||
\(740\) | −6937.35 | −0.344625 | ||||||||
\(741\) | 11543.0 | 0.572259 | ||||||||
\(742\) | 32033.9 | 1.58491 | ||||||||
\(743\) | 32527.1 | 1.60606 | 0.803032 | − | 0.595937i | \(-0.203219\pi\) | ||||
0.803032 | + | 0.595937i | \(0.203219\pi\) | |||||||
\(744\) | 38869.3 | 1.91535 | ||||||||
\(745\) | −10711.1 | −0.526745 | ||||||||
\(746\) | −14331.8 | −0.703382 | ||||||||
\(747\) | −48391.5 | −2.37022 | ||||||||
\(748\) | 4198.18 | 0.205215 | ||||||||
\(749\) | −11736.3 | −0.572542 | ||||||||
\(750\) | 4247.34 | 0.206788 | ||||||||
\(751\) | −16121.8 | −0.783346 | −0.391673 | − | 0.920104i | \(-0.628104\pi\) | ||||
−0.391673 | + | 0.920104i | \(0.628104\pi\) | |||||||
\(752\) | 26092.3 | 1.26528 | ||||||||
\(753\) | 40009.4 | 1.93629 | ||||||||
\(754\) | −31681.1 | −1.53018 | ||||||||
\(755\) | 3376.68 | 0.162768 | ||||||||
\(756\) | 26129.8 | 1.25705 | ||||||||
\(757\) | −1959.32 | −0.0940722 | −0.0470361 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470361 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(758\) | 23225.9 | 1.11293 | ||||||||
\(759\) | 5439.19 | 0.260119 | ||||||||
\(760\) | −1132.80 | −0.0540671 | ||||||||
\(761\) | 4037.12 | 0.192307 | 0.0961534 | − | 0.995367i | \(-0.469346\pi\) | ||||
0.0961534 | + | 0.995367i | \(0.469346\pi\) | |||||||
\(762\) | −52021.7 | −2.47316 | ||||||||
\(763\) | −3635.61 | −0.172501 | ||||||||
\(764\) | −14737.8 | −0.697901 | ||||||||
\(765\) | −26400.7 | −1.24774 | ||||||||
\(766\) | −35970.3 | −1.69668 | ||||||||
\(767\) | −48709.9 | −2.29311 | ||||||||
\(768\) | −49643.0 | −2.33247 | ||||||||
\(769\) | −20471.7 | −0.959985 | −0.479993 | − | 0.877272i | \(-0.659361\pi\) | ||||
−0.479993 | + | 0.877272i | \(0.659361\pi\) | |||||||
\(770\) | 3086.80 | 0.144468 | ||||||||
\(771\) | −54980.5 | −2.56819 | ||||||||
\(772\) | 13194.1 | 0.615110 | ||||||||
\(773\) | 11032.7 | 0.513347 | 0.256673 | − | 0.966498i | \(-0.417374\pi\) | ||||
0.256673 | + | 0.966498i | \(0.417374\pi\) | |||||||
\(774\) | 124513. | 5.78231 | ||||||||
\(775\) | 8529.11 | 0.395322 | ||||||||
\(776\) | −3263.59 | −0.150974 | ||||||||
\(777\) | 45021.3 | 2.07868 | ||||||||
\(778\) | 29101.7 | 1.34106 | ||||||||
\(779\) | 7225.64 | 0.332330 | ||||||||
\(780\) | 14115.9 | 0.647986 | ||||||||
\(781\) | −3971.13 | −0.181944 | ||||||||
\(782\) | −15115.4 | −0.691208 | ||||||||
\(783\) | 49919.1 | 2.27837 | ||||||||
\(784\) | 7475.87 | 0.340555 | ||||||||
\(785\) | 3004.68 | 0.136614 | ||||||||
\(786\) | 88634.8 | 4.02226 | ||||||||
\(787\) | −11394.8 | −0.516111 | −0.258056 | − | 0.966130i | \(-0.583082\pi\) | ||||
−0.258056 | + | 0.966130i | \(0.583082\pi\) | |||||||
\(788\) | −13950.8 | −0.630680 | ||||||||
\(789\) | 61019.3 | 2.75329 | ||||||||
\(790\) | 7665.59 | 0.345227 | ||||||||
\(791\) | 3917.63 | 0.176100 | ||||||||
\(792\) | −8432.77 | −0.378340 | ||||||||
\(793\) | 44739.0 | 2.00344 | ||||||||
\(794\) | −16419.9 | −0.733906 | ||||||||
\(795\) | −27267.6 | −1.21646 | ||||||||
\(796\) | −17264.3 | −0.768739 | ||||||||
\(797\) | −19693.0 | −0.875236 | −0.437618 | − | 0.899161i | \(-0.644178\pi\) | ||||
−0.437618 | + | 0.899161i | \(0.644178\pi\) | |||||||
\(798\) | −10188.5 | −0.451968 | ||||||||
\(799\) | −26927.6 | −1.19228 | ||||||||
\(800\) | −4690.46 | −0.207291 | ||||||||
\(801\) | −17757.1 | −0.783293 | ||||||||
\(802\) | 33760.9 | 1.48646 | ||||||||
\(803\) | 1234.79 | 0.0542650 | ||||||||
\(804\) | 8131.15 | 0.356671 | ||||||||
\(805\) | −4083.67 | −0.178796 | ||||||||
\(806\) | 77145.5 | 3.37138 | ||||||||
\(807\) | 82135.7 | 3.58279 | ||||||||
\(808\) | −3697.32 | −0.160979 | ||||||||
\(809\) | 24939.6 | 1.08384 | 0.541921 | − | 0.840429i | \(-0.317697\pi\) | ||||
0.541921 | + | 0.840429i | \(0.317697\pi\) | |||||||
\(810\) | −29667.0 | −1.28690 | ||||||||
\(811\) | 9789.67 | 0.423874 | 0.211937 | − | 0.977283i | \(-0.432023\pi\) | ||||
0.211937 | + | 0.977283i | \(0.432023\pi\) | |||||||
\(812\) | 10274.9 | 0.444060 | ||||||||
\(813\) | 48884.7 | 2.10881 | ||||||||
\(814\) | 11679.9 | 0.502924 | ||||||||
\(815\) | 921.857 | 0.0396211 | ||||||||
\(816\) | 62448.5 | 2.67909 | ||||||||
\(817\) | −10347.3 | −0.443091 | ||||||||
\(818\) | −2927.49 | −0.125131 | ||||||||
\(819\) | −64513.9 | −2.75250 | ||||||||
\(820\) | 8836.15 | 0.376307 | ||||||||
\(821\) | 6187.91 | 0.263045 | 0.131522 | − | 0.991313i | \(-0.458014\pi\) | ||||
0.131522 | + | 0.991313i | \(0.458014\pi\) | |||||||
\(822\) | −16336.1 | −0.693170 | ||||||||
\(823\) | 34354.7 | 1.45508 | 0.727538 | − | 0.686067i | \(-0.240664\pi\) | ||||
0.727538 | + | 0.686067i | \(0.240664\pi\) | |||||||
\(824\) | 16695.4 | 0.705839 | ||||||||
\(825\) | −2627.52 | −0.110883 | ||||||||
\(826\) | 42994.2 | 1.81109 | ||||||||
\(827\) | 20640.7 | 0.867894 | 0.433947 | − | 0.900938i | \(-0.357121\pi\) | ||||
0.433947 | + | 0.900938i | \(0.357121\pi\) | |||||||
\(828\) | −15461.3 | −0.648935 | ||||||||
\(829\) | −35471.4 | −1.48610 | −0.743048 | − | 0.669238i | \(-0.766621\pi\) | ||||
−0.743048 | + | 0.669238i | \(0.766621\pi\) | |||||||
\(830\) | 13383.9 | 0.559715 | ||||||||
\(831\) | 19659.1 | 0.820657 | ||||||||
\(832\) | −1943.69 | −0.0809918 | ||||||||
\(833\) | −7715.20 | −0.320907 | ||||||||
\(834\) | 13352.2 | 0.554374 | ||||||||
\(835\) | −18004.9 | −0.746211 | ||||||||
\(836\) | −971.218 | −0.0401798 | ||||||||
\(837\) | −121556. | −5.01982 | ||||||||
\(838\) | −16400.6 | −0.676074 | ||||||||
\(839\) | −12387.4 | −0.509727 | −0.254864 | − | 0.966977i | \(-0.582031\pi\) | ||||
−0.254864 | + | 0.966977i | \(0.582031\pi\) | |||||||
\(840\) | 8990.11 | 0.369272 | ||||||||
\(841\) | −4759.61 | −0.195154 | ||||||||
\(842\) | −49282.1 | −2.01707 | ||||||||
\(843\) | −48183.2 | −1.96859 | ||||||||
\(844\) | −5310.08 | −0.216565 | ||||||||
\(845\) | −9230.16 | −0.375772 | ||||||||
\(846\) | −74962.1 | −3.04640 | ||||||||
\(847\) | −1909.58 | −0.0774662 | ||||||||
\(848\) | 45423.0 | 1.83942 | ||||||||
\(849\) | 20601.5 | 0.832794 | ||||||||
\(850\) | 7301.81 | 0.294647 | ||||||||
\(851\) | −15451.9 | −0.622426 | ||||||||
\(852\) | 16028.9 | 0.644534 | ||||||||
\(853\) | 13430.3 | 0.539093 | 0.269546 | − | 0.962987i | \(-0.413126\pi\) | ||||
0.269546 | + | 0.962987i | \(0.413126\pi\) | |||||||
\(854\) | −39489.2 | −1.58231 | ||||||||
\(855\) | 6107.61 | 0.244299 | ||||||||
\(856\) | −8867.64 | −0.354077 | ||||||||
\(857\) | 33098.6 | 1.31929 | 0.659643 | − | 0.751579i | \(-0.270708\pi\) | ||||
0.659643 | + | 0.751579i | \(0.270708\pi\) | |||||||
\(858\) | −23765.8 | −0.945631 | ||||||||
\(859\) | −34099.5 | −1.35443 | −0.677217 | − | 0.735783i | \(-0.736814\pi\) | ||||
−0.677217 | + | 0.735783i | \(0.736814\pi\) | |||||||
\(860\) | −12653.6 | −0.501724 | ||||||||
\(861\) | −57344.0 | −2.26978 | ||||||||
\(862\) | −34979.9 | −1.38216 | ||||||||
\(863\) | −5836.94 | −0.230234 | −0.115117 | − | 0.993352i | \(-0.536724\pi\) | ||||
−0.115117 | + | 0.993352i | \(0.536724\pi\) | |||||||
\(864\) | 66848.0 | 2.63219 | ||||||||
\(865\) | 9408.03 | 0.369806 | ||||||||
\(866\) | −54235.7 | −2.12818 | ||||||||
\(867\) | −17505.9 | −0.685735 | ||||||||
\(868\) | −25019.9 | −0.978378 | ||||||||
\(869\) | −4742.15 | −0.185117 | ||||||||
\(870\) | −23802.9 | −0.927579 | ||||||||
\(871\) | −11644.5 | −0.452996 | ||||||||
\(872\) | −2746.98 | −0.106679 | ||||||||
\(873\) | 17596.0 | 0.682169 | ||||||||
\(874\) | 3496.84 | 0.135334 | ||||||||
\(875\) | 1972.71 | 0.0762167 | ||||||||
\(876\) | −4984.07 | −0.192233 | ||||||||
\(877\) | 23603.5 | 0.908816 | 0.454408 | − | 0.890794i | \(-0.349851\pi\) | ||||
0.454408 | + | 0.890794i | \(0.349851\pi\) | |||||||
\(878\) | −3904.76 | −0.150090 | ||||||||
\(879\) | −45029.0 | −1.72786 | ||||||||
\(880\) | 4376.98 | 0.167668 | ||||||||
\(881\) | 2235.23 | 0.0854788 | 0.0427394 | − | 0.999086i | \(-0.486391\pi\) | ||||
0.0427394 | + | 0.999086i | \(0.486391\pi\) | |||||||
\(882\) | −21477.9 | −0.819951 | ||||||||
\(883\) | 20886.0 | 0.796004 | 0.398002 | − | 0.917385i | \(-0.369704\pi\) | ||||
0.398002 | + | 0.917385i | \(0.369704\pi\) | |||||||
\(884\) | 24267.3 | 0.923300 | ||||||||
\(885\) | −36597.1 | −1.39006 | ||||||||
\(886\) | 48024.4 | 1.82101 | ||||||||
\(887\) | 37757.7 | 1.42929 | 0.714644 | − | 0.699489i | \(-0.246589\pi\) | ||||
0.714644 | + | 0.699489i | \(0.246589\pi\) | |||||||
\(888\) | 34017.0 | 1.28551 | ||||||||
\(889\) | −24161.8 | −0.911543 | ||||||||
\(890\) | 4911.21 | 0.184971 | ||||||||
\(891\) | 18352.8 | 0.690060 | ||||||||
\(892\) | 12974.7 | 0.487024 | ||||||||
\(893\) | 6229.52 | 0.233441 | ||||||||
\(894\) | −72790.0 | −2.72311 | ||||||||
\(895\) | 15603.5 | 0.582758 | ||||||||
\(896\) | −21971.8 | −0.819226 | ||||||||
\(897\) | 31440.9 | 1.17033 | ||||||||
\(898\) | −50484.9 | −1.87606 | ||||||||
\(899\) | −47798.8 | −1.77328 | ||||||||
\(900\) | 7468.93 | 0.276627 | ||||||||
\(901\) | −46877.2 | −1.73330 | ||||||||
\(902\) | −14876.8 | −0.549160 | ||||||||
\(903\) | 82117.8 | 3.02626 | ||||||||
\(904\) | 2960.07 | 0.108905 | ||||||||
\(905\) | −8679.08 | −0.318787 | ||||||||
\(906\) | 22947.0 | 0.841461 | ||||||||
\(907\) | −36817.6 | −1.34786 | −0.673930 | − | 0.738795i | \(-0.735395\pi\) | ||||
−0.673930 | + | 0.738795i | \(0.735395\pi\) | |||||||
\(908\) | −4755.07 | −0.173791 | ||||||||
\(909\) | 19934.5 | 0.727376 | ||||||||
\(910\) | 17843.0 | 0.649990 | ||||||||
\(911\) | 7864.91 | 0.286033 | 0.143017 | − | 0.989720i | \(-0.454320\pi\) | ||||
0.143017 | + | 0.989720i | \(0.454320\pi\) | |||||||
\(912\) | −14447.0 | −0.524549 | ||||||||
\(913\) | −8279.68 | −0.300129 | ||||||||
\(914\) | 31612.5 | 1.14403 | ||||||||
\(915\) | 33613.7 | 1.21446 | ||||||||
\(916\) | −20625.4 | −0.743975 | ||||||||
\(917\) | 41167.1 | 1.48250 | ||||||||
\(918\) | −104065. | −3.74145 | ||||||||
\(919\) | 37629.1 | 1.35067 | 0.675337 | − | 0.737509i | \(-0.263998\pi\) | ||||
0.675337 | + | 0.737509i | \(0.263998\pi\) | |||||||
\(920\) | −3085.52 | −0.110572 | ||||||||
\(921\) | 31384.9 | 1.12288 | ||||||||
\(922\) | −60232.1 | −2.15145 | ||||||||
\(923\) | −22954.9 | −0.818601 | ||||||||
\(924\) | 7707.77 | 0.274423 | ||||||||
\(925\) | 7464.37 | 0.265326 | ||||||||
\(926\) | −3809.73 | −0.135200 | ||||||||
\(927\) | −90015.0 | −3.18930 | ||||||||
\(928\) | 26286.3 | 0.929837 | ||||||||
\(929\) | 34809.4 | 1.22934 | 0.614672 | − | 0.788783i | \(-0.289289\pi\) | ||||
0.614672 | + | 0.788783i | \(0.289289\pi\) | |||||||
\(930\) | 57961.6 | 2.04369 | ||||||||
\(931\) | 1784.86 | 0.0628317 | ||||||||
\(932\) | 2634.46 | 0.0925909 | ||||||||
\(933\) | −54290.4 | −1.90502 | ||||||||
\(934\) | −36821.6 | −1.28998 | ||||||||
\(935\) | −4517.10 | −0.157995 | ||||||||
\(936\) | −48745.1 | −1.70223 | ||||||||
\(937\) | −33947.7 | −1.18359 | −0.591795 | − | 0.806088i | \(-0.701581\pi\) | ||||
−0.591795 | + | 0.806088i | \(0.701581\pi\) | |||||||
\(938\) | 10278.1 | 0.357775 | ||||||||
\(939\) | −88144.3 | −3.06334 | ||||||||
\(940\) | 7618.01 | 0.264332 | ||||||||
\(941\) | 13691.9 | 0.474328 | 0.237164 | − | 0.971470i | \(-0.423782\pi\) | ||||
0.237164 | + | 0.971470i | \(0.423782\pi\) | |||||||
\(942\) | 20419.0 | 0.706250 | ||||||||
\(943\) | 19681.2 | 0.679647 | ||||||||
\(944\) | 60964.3 | 2.10193 | ||||||||
\(945\) | −28114.8 | −0.967804 | ||||||||
\(946\) | 21303.8 | 0.732186 | ||||||||
\(947\) | 12598.2 | 0.432298 | 0.216149 | − | 0.976360i | \(-0.430650\pi\) | ||||
0.216149 | + | 0.976360i | \(0.430650\pi\) | |||||||
\(948\) | 19141.1 | 0.655773 | ||||||||
\(949\) | 7137.63 | 0.244149 | ||||||||
\(950\) | −1689.22 | −0.0576901 | ||||||||
\(951\) | 20723.4 | 0.706627 | ||||||||
\(952\) | 15455.4 | 0.526167 | ||||||||
\(953\) | −13647.4 | −0.463884 | −0.231942 | − | 0.972730i | \(-0.574508\pi\) | ||||
−0.231942 | + | 0.972730i | \(0.574508\pi\) | |||||||
\(954\) | −130498. | −4.42877 | ||||||||
\(955\) | 15857.5 | 0.537314 | ||||||||
\(956\) | −23826.4 | −0.806066 | ||||||||
\(957\) | 14725.1 | 0.497383 | ||||||||
\(958\) | 6960.91 | 0.234757 | ||||||||
\(959\) | −7587.41 | −0.255485 | ||||||||
\(960\) | −1460.35 | −0.0490963 | ||||||||
\(961\) | 86602.1 | 2.90699 | ||||||||
\(962\) | 67515.0 | 2.26276 | ||||||||
\(963\) | 47810.8 | 1.59988 | ||||||||
\(964\) | −12946.3 | −0.432544 | ||||||||
\(965\) | −14196.4 | −0.473573 | ||||||||
\(966\) | −27751.5 | −0.924318 | ||||||||
\(967\) | 33723.7 | 1.12149 | 0.560745 | − | 0.827988i | \(-0.310515\pi\) | ||||
0.560745 | + | 0.827988i | \(0.310515\pi\) | |||||||
\(968\) | −1442.83 | −0.0479073 | ||||||||
\(969\) | 14909.5 | 0.494286 | ||||||||
\(970\) | −4866.64 | −0.161091 | ||||||||
\(971\) | 5738.59 | 0.189660 | 0.0948301 | − | 0.995493i | \(-0.469769\pi\) | ||||
0.0948301 | + | 0.995493i | \(0.469769\pi\) | |||||||
\(972\) | −29374.8 | −0.969337 | ||||||||
\(973\) | 6201.51 | 0.204328 | ||||||||
\(974\) | −32420.8 | −1.06656 | ||||||||
\(975\) | −15188.2 | −0.498884 | ||||||||
\(976\) | −55994.4 | −1.83641 | ||||||||
\(977\) | 4949.31 | 0.162070 | 0.0810351 | − | 0.996711i | \(-0.474177\pi\) | ||||
0.0810351 | + | 0.996711i | \(0.474177\pi\) | |||||||
\(978\) | 6264.70 | 0.204829 | ||||||||
\(979\) | −3038.21 | −0.0991845 | ||||||||
\(980\) | 2182.68 | 0.0711461 | ||||||||
\(981\) | 14810.6 | 0.482025 | ||||||||
\(982\) | −655.846 | −0.0213125 | ||||||||
\(983\) | 8112.37 | 0.263219 | 0.131610 | − | 0.991302i | \(-0.457985\pi\) | ||||
0.131610 | + | 0.991302i | \(0.457985\pi\) | |||||||
\(984\) | −43327.7 | −1.40369 | ||||||||
\(985\) | 15010.6 | 0.485560 | ||||||||
\(986\) | −40920.8 | −1.32169 | ||||||||
\(987\) | −49438.6 | −1.59437 | ||||||||
\(988\) | −5614.07 | −0.180777 | ||||||||
\(989\) | −28183.9 | −0.906163 | ||||||||
\(990\) | −12574.9 | −0.403693 | ||||||||
\(991\) | 5787.92 | 0.185529 | 0.0927646 | − | 0.995688i | \(-0.470430\pi\) | ||||
0.0927646 | + | 0.995688i | \(0.470430\pi\) | |||||||
\(992\) | −64008.7 | −2.04867 | ||||||||
\(993\) | −1351.24 | −0.0431825 | ||||||||
\(994\) | 20261.3 | 0.646528 | ||||||||
\(995\) | 18575.8 | 0.591852 | ||||||||
\(996\) | 33419.9 | 1.06320 | ||||||||
\(997\) | 37407.4 | 1.18827 | 0.594135 | − | 0.804365i | \(-0.297494\pi\) | ||||
0.594135 | + | 0.804365i | \(0.297494\pi\) | |||||||
\(998\) | 51921.4 | 1.64684 | ||||||||
\(999\) | −106382. | −3.36913 |
(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.f.1.19 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.f.1.19 | ✓ | 23 | 1.1 | even | 1 | trivial |