Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.27793984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{3} + 49x^{2} - 14x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.2 | ||
Root | \(0.143705 + 0.143705i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.b.288.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.67129 | −1.65155 | −0.825775 | − | 0.564000i | \(-0.809262\pi\) | ||||
−0.825775 | + | 0.564000i | \(0.809262\pi\) | |||||||
\(3\) | 7.62999i | 1.46839i | 0.678938 | + | 0.734196i | \(0.262441\pi\) | ||||
−0.678938 | + | 0.734196i | \(0.737559\pi\) | |||||||
\(4\) | 13.8209 | 1.72762 | ||||||||
\(5\) | 11.9174i | 1.06592i | 0.846139 | + | 0.532962i | \(0.178921\pi\) | ||||
−0.846139 | + | 0.532962i | \(0.821079\pi\) | |||||||
\(6\) | − 35.6419i | − 2.42512i | ||||||||
\(7\) | 26.1222i | 1.41047i | 0.708975 | + | 0.705233i | \(0.249158\pi\) | ||||
−0.708975 | + | 0.705233i | \(0.750842\pi\) | |||||||
\(8\) | −27.1912 | −1.20169 | ||||||||
\(9\) | −31.2167 | −1.15617 | ||||||||
\(10\) | − 55.6696i | − 1.76043i | ||||||||
\(11\) | − 3.24412i | − 0.0889216i | −0.999011 | − | 0.0444608i | \(-0.985843\pi\) | ||||
0.999011 | − | 0.0444608i | \(-0.0141570\pi\) | |||||||
\(12\) | 105.453i | 2.53682i | ||||||||
\(13\) | −20.0515 | −0.427790 | −0.213895 | − | 0.976857i | \(-0.568615\pi\) | ||||
−0.213895 | + | 0.976857i | \(0.568615\pi\) | |||||||
\(14\) | − 122.024i | − 2.32945i | ||||||||
\(15\) | −90.9296 | −1.56519 | ||||||||
\(16\) | 16.4506 | 0.257041 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 145.822 | 1.90948 | ||||||||
\(19\) | −57.3466 | −0.692432 | −0.346216 | − | 0.938155i | \(-0.612534\pi\) | ||||
−0.346216 | + | 0.938155i | \(0.612534\pi\) | |||||||
\(20\) | 164.709i | 1.84151i | ||||||||
\(21\) | −199.312 | −2.07112 | ||||||||
\(22\) | 15.1542i | 0.146858i | ||||||||
\(23\) | 77.0438i | 0.698467i | 0.937036 | + | 0.349233i | \(0.113558\pi\) | ||||
−0.937036 | + | 0.349233i | \(0.886442\pi\) | |||||||
\(24\) | − 207.469i | − 1.76456i | ||||||||
\(25\) | −17.0243 | −0.136195 | ||||||||
\(26\) | 93.6662 | 0.706517 | ||||||||
\(27\) | − 32.1732i | − 0.229323i | ||||||||
\(28\) | 361.033i | 2.43674i | ||||||||
\(29\) | 286.162i | 1.83238i | 0.400744 | + | 0.916190i | \(0.368752\pi\) | ||||
−0.400744 | + | 0.916190i | \(0.631248\pi\) | |||||||
\(30\) | 424.758 | 2.58500 | ||||||||
\(31\) | 8.54816i | 0.0495256i | 0.999693 | + | 0.0247628i | \(0.00788305\pi\) | ||||
−0.999693 | + | 0.0247628i | \(0.992117\pi\) | |||||||
\(32\) | 140.684 | 0.777178 | ||||||||
\(33\) | 24.7526 | 0.130572 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −311.309 | −1.50345 | ||||||||
\(36\) | −431.443 | −1.99742 | ||||||||
\(37\) | − 357.982i | − 1.59059i | −0.606221 | − | 0.795296i | \(-0.707315\pi\) | ||||
0.606221 | − | 0.795296i | \(-0.292685\pi\) | |||||||
\(38\) | 267.882 | 1.14359 | ||||||||
\(39\) | − 152.992i | − 0.628164i | ||||||||
\(40\) | − 324.049i | − 1.28091i | ||||||||
\(41\) | 194.467i | 0.740748i | 0.928883 | + | 0.370374i | \(0.120770\pi\) | ||||
−0.928883 | + | 0.370374i | \(0.879230\pi\) | |||||||
\(42\) | 931.044 | 3.42055 | ||||||||
\(43\) | 74.2619 | 0.263368 | 0.131684 | − | 0.991292i | \(-0.457962\pi\) | ||||
0.131684 | + | 0.991292i | \(0.457962\pi\) | |||||||
\(44\) | − 44.8367i | − 0.153622i | ||||||||
\(45\) | − 372.021i | − 1.23239i | ||||||||
\(46\) | − 359.894i | − 1.15355i | ||||||||
\(47\) | 23.6130 | 0.0732831 | 0.0366416 | − | 0.999328i | \(-0.488334\pi\) | ||||
0.0366416 | + | 0.999328i | \(0.488334\pi\) | |||||||
\(48\) | 125.518i | 0.377437i | ||||||||
\(49\) | −339.369 | −0.989415 | ||||||||
\(50\) | 79.5255 | 0.224932 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −277.130 | −0.739058 | ||||||||
\(53\) | −104.330 | −0.270393 | −0.135197 | − | 0.990819i | \(-0.543167\pi\) | ||||
−0.135197 | + | 0.990819i | \(0.543167\pi\) | |||||||
\(54\) | 150.290i | 0.378739i | ||||||||
\(55\) | 38.6614 | 0.0947837 | ||||||||
\(56\) | − 710.295i | − 1.69495i | ||||||||
\(57\) | − 437.553i | − 1.01676i | ||||||||
\(58\) | − 1336.75i | − 3.02627i | ||||||||
\(59\) | −249.363 | −0.550243 | −0.275122 | − | 0.961409i | \(-0.588718\pi\) | ||||
−0.275122 | + | 0.961409i | \(0.588718\pi\) | |||||||
\(60\) | −1256.73 | −2.70405 | ||||||||
\(61\) | − 370.384i | − 0.777424i | −0.921359 | − | 0.388712i | \(-0.872920\pi\) | ||||
0.921359 | − | 0.388712i | \(-0.127080\pi\) | |||||||
\(62\) | − 39.9309i | − 0.0817940i | ||||||||
\(63\) | − 815.448i | − 1.63074i | ||||||||
\(64\) | −788.781 | −1.54059 | ||||||||
\(65\) | − 238.961i | − 0.455992i | ||||||||
\(66\) | −115.626 | −0.215646 | ||||||||
\(67\) | 939.650 | 1.71338 | 0.856691 | − | 0.515830i | \(-0.172517\pi\) | ||||
0.856691 | + | 0.515830i | \(0.172517\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −587.843 | −1.02562 | ||||||||
\(70\) | 1454.21 | 2.48302 | ||||||||
\(71\) | 520.197i | 0.869522i | 0.900546 | + | 0.434761i | \(0.143167\pi\) | ||||
−0.900546 | + | 0.434761i | \(0.856833\pi\) | |||||||
\(72\) | 848.820 | 1.38937 | ||||||||
\(73\) | − 348.741i | − 0.559137i | −0.960126 | − | 0.279568i | \(-0.909809\pi\) | ||||
0.960126 | − | 0.279568i | \(-0.0901914\pi\) | |||||||
\(74\) | 1672.24i | 2.62694i | ||||||||
\(75\) | − 129.895i | − 0.199987i | ||||||||
\(76\) | −792.583 | −1.19626 | ||||||||
\(77\) | 84.7434 | 0.125421 | ||||||||
\(78\) | 714.672i | 1.03744i | ||||||||
\(79\) | − 953.827i | − 1.35840i | −0.733951 | − | 0.679202i | \(-0.762326\pi\) | ||||
0.733951 | − | 0.679202i | \(-0.237674\pi\) | |||||||
\(80\) | 196.049i | 0.273986i | ||||||||
\(81\) | −597.369 | −0.819437 | ||||||||
\(82\) | − 908.412i | − 1.22338i | ||||||||
\(83\) | 1414.28 | 1.87033 | 0.935166 | − | 0.354211i | \(-0.115250\pi\) | ||||
0.935166 | + | 0.354211i | \(0.115250\pi\) | |||||||
\(84\) | −2754.68 | −3.57809 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −346.899 | −0.434966 | ||||||||
\(87\) | −2183.41 | −2.69065 | ||||||||
\(88\) | 88.2115i | 0.106857i | ||||||||
\(89\) | −486.132 | −0.578987 | −0.289493 | − | 0.957180i | \(-0.593487\pi\) | ||||
−0.289493 | + | 0.957180i | \(0.593487\pi\) | |||||||
\(90\) | 1737.82i | 2.03536i | ||||||||
\(91\) | − 523.788i | − 0.603384i | ||||||||
\(92\) | 1064.82i | 1.20668i | ||||||||
\(93\) | −65.2223 | −0.0727230 | ||||||||
\(94\) | −110.303 | −0.121031 | ||||||||
\(95\) | − 683.422i | − 0.738080i | ||||||||
\(96\) | 1073.42i | 1.14120i | ||||||||
\(97\) | 685.281i | 0.717317i | 0.933469 | + | 0.358659i | \(0.116766\pi\) | ||||
−0.933469 | + | 0.358659i | \(0.883234\pi\) | |||||||
\(98\) | 1585.29 | 1.63407 | ||||||||
\(99\) | 101.271i | 0.102809i | ||||||||
\(100\) | −235.292 | −0.235292 | ||||||||
\(101\) | 864.755 | 0.851944 | 0.425972 | − | 0.904736i | \(-0.359932\pi\) | ||||
0.425972 | + | 0.904736i | \(0.359932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1880.91 | 1.79933 | 0.899665 | − | 0.436580i | \(-0.143810\pi\) | ||||
0.899665 | + | 0.436580i | \(0.143810\pi\) | |||||||
\(104\) | 545.224 | 0.514073 | ||||||||
\(105\) | − 2375.28i | − 2.20765i | ||||||||
\(106\) | 487.355 | 0.446567 | ||||||||
\(107\) | 32.8149i | 0.0296480i | 0.999890 | + | 0.0148240i | \(0.00471880\pi\) | ||||
−0.999890 | + | 0.0148240i | \(0.995281\pi\) | |||||||
\(108\) | − 444.663i | − 0.396183i | ||||||||
\(109\) | 528.727i | 0.464613i | 0.972643 | + | 0.232307i | \(0.0746273\pi\) | ||||
−0.972643 | + | 0.232307i | \(0.925373\pi\) | |||||||
\(110\) | −180.599 | −0.156540 | ||||||||
\(111\) | 2731.40 | 2.33561 | ||||||||
\(112\) | 429.727i | 0.362548i | ||||||||
\(113\) | 414.691i | 0.345229i | 0.984989 | + | 0.172614i | \(0.0552215\pi\) | ||||
−0.984989 | + | 0.172614i | \(0.944779\pi\) | |||||||
\(114\) | 2043.94i | 1.67923i | ||||||||
\(115\) | −918.161 | −0.744513 | ||||||||
\(116\) | 3955.03i | 3.16565i | ||||||||
\(117\) | 625.940 | 0.494600 | ||||||||
\(118\) | 1164.85 | 0.908754 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2472.49 | 1.88088 | ||||||||
\(121\) | 1320.48 | 0.992093 | ||||||||
\(122\) | 1730.17i | 1.28395i | ||||||||
\(123\) | −1483.78 | −1.08771 | ||||||||
\(124\) | 118.143i | 0.0855613i | ||||||||
\(125\) | 1286.79i | 0.920751i | ||||||||
\(126\) | 3809.19i | 2.69325i | ||||||||
\(127\) | −596.093 | −0.416494 | −0.208247 | − | 0.978076i | \(-0.566776\pi\) | ||||
−0.208247 | + | 0.978076i | \(0.566776\pi\) | |||||||
\(128\) | 2559.15 | 1.76718 | ||||||||
\(129\) | 566.617i | 0.386728i | ||||||||
\(130\) | 1116.26i | 0.753094i | ||||||||
\(131\) | − 121.819i | − 0.0812472i | −0.999175 | − | 0.0406236i | \(-0.987066\pi\) | ||||
0.999175 | − | 0.0406236i | \(-0.0129344\pi\) | |||||||
\(132\) | 342.103 | 0.225578 | ||||||||
\(133\) | − 1498.02i | − 0.976652i | ||||||||
\(134\) | −4389.38 | −2.82973 | ||||||||
\(135\) | 383.420 | 0.244441 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −897.365 | −0.559614 | −0.279807 | − | 0.960056i | \(-0.590270\pi\) | ||||
−0.279807 | + | 0.960056i | \(0.590270\pi\) | |||||||
\(138\) | 2745.98 | 1.69387 | ||||||||
\(139\) | 2113.61i | 1.28974i | 0.764292 | + | 0.644871i | \(0.223089\pi\) | ||||
−0.764292 | + | 0.644871i | \(0.776911\pi\) | |||||||
\(140\) | −4302.57 | −2.59738 | ||||||||
\(141\) | 180.167i | 0.107608i | ||||||||
\(142\) | − 2429.99i | − 1.43606i | ||||||||
\(143\) | 65.0493i | 0.0380398i | ||||||||
\(144\) | −513.534 | −0.297184 | ||||||||
\(145\) | −3410.31 | −1.95318 | ||||||||
\(146\) | 1629.07i | 0.923442i | ||||||||
\(147\) | − 2589.38i | − 1.45285i | ||||||||
\(148\) | − 4947.65i | − 2.74793i | ||||||||
\(149\) | 2580.76 | 1.41895 | 0.709476 | − | 0.704729i | \(-0.248932\pi\) | ||||
0.709476 | + | 0.704729i | \(0.248932\pi\) | |||||||
\(150\) | 606.778i | 0.330288i | ||||||||
\(151\) | −1342.77 | −0.723662 | −0.361831 | − | 0.932244i | \(-0.617848\pi\) | ||||
−0.361831 | + | 0.932244i | \(0.617848\pi\) | |||||||
\(152\) | 1559.32 | 0.832091 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −395.861 | −0.207139 | ||||||||
\(155\) | −101.872 | −0.0527906 | ||||||||
\(156\) | − 2114.50i | − 1.08523i | ||||||||
\(157\) | −2495.82 | −1.26871 | −0.634357 | − | 0.773041i | \(-0.718735\pi\) | ||||
−0.634357 | + | 0.773041i | \(0.718735\pi\) | |||||||
\(158\) | 4455.60i | 2.24347i | ||||||||
\(159\) | − 796.036i | − 0.397043i | ||||||||
\(160\) | 1676.59i | 0.828413i | ||||||||
\(161\) | −2012.55 | −0.985164 | ||||||||
\(162\) | 2790.48 | 1.35334 | ||||||||
\(163\) | 1961.58i | 0.942595i | 0.881974 | + | 0.471297i | \(0.156214\pi\) | ||||
−0.881974 | + | 0.471297i | \(0.843786\pi\) | |||||||
\(164\) | 2687.72i | 1.27973i | ||||||||
\(165\) | 294.986i | 0.139180i | ||||||||
\(166\) | −6606.51 | −3.08894 | ||||||||
\(167\) | − 2179.24i | − 1.00979i | −0.863182 | − | 0.504894i | \(-0.831532\pi\) | ||||
0.863182 | − | 0.504894i | \(-0.168468\pi\) | |||||||
\(168\) | 5419.54 | 2.48885 | ||||||||
\(169\) | −1794.94 | −0.816995 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1790.17 | 0.800571 | ||||||||
\(172\) | 1026.37 | 0.454999 | ||||||||
\(173\) | − 3111.45i | − 1.36739i | −0.729766 | − | 0.683697i | \(-0.760371\pi\) | ||||
0.729766 | − | 0.683697i | \(-0.239629\pi\) | |||||||
\(174\) | 10199.4 | 4.44374 | ||||||||
\(175\) | − 444.713i | − 0.192098i | ||||||||
\(176\) | − 53.3677i | − 0.0228565i | ||||||||
\(177\) | − 1902.64i | − 0.807972i | ||||||||
\(178\) | 2270.86 | 0.956226 | ||||||||
\(179\) | −810.106 | −0.338269 | −0.169135 | − | 0.985593i | \(-0.554097\pi\) | ||||
−0.169135 | + | 0.985593i | \(0.554097\pi\) | |||||||
\(180\) | − 5141.68i | − 2.12910i | ||||||||
\(181\) | − 3356.23i | − 1.37827i | −0.724634 | − | 0.689134i | \(-0.757991\pi\) | ||||
0.724634 | − | 0.689134i | \(-0.242009\pi\) | |||||||
\(182\) | 2446.77i | 0.996519i | ||||||||
\(183\) | 2826.03 | 1.14156 | ||||||||
\(184\) | − 2094.92i | − 0.839343i | ||||||||
\(185\) | 4266.22 | 1.69545 | ||||||||
\(186\) | 304.672 | 0.120106 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 326.353 | 0.126605 | ||||||||
\(189\) | 840.434 | 0.323453 | ||||||||
\(190\) | 3192.46i | 1.21898i | ||||||||
\(191\) | 1338.41 | 0.507038 | 0.253519 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253519 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(192\) | − 6018.39i | − 2.26219i | ||||||||
\(193\) | − 227.465i | − 0.0848358i | −0.999100 | − | 0.0424179i | \(-0.986494\pi\) | ||||
0.999100 | − | 0.0424179i | \(-0.0135061\pi\) | |||||||
\(194\) | − 3201.15i | − 1.18468i | ||||||||
\(195\) | 1823.27 | 0.669575 | ||||||||
\(196\) | −4690.40 | −1.70933 | ||||||||
\(197\) | 815.549i | 0.294952i | 0.989066 | + | 0.147476i | \(0.0471148\pi\) | ||||
−0.989066 | + | 0.147476i | \(0.952885\pi\) | |||||||
\(198\) | − 473.064i | − 0.169794i | ||||||||
\(199\) | − 1866.90i | − 0.665030i | −0.943098 | − | 0.332515i | \(-0.892103\pi\) | ||||
0.943098 | − | 0.332515i | \(-0.107897\pi\) | |||||||
\(200\) | 462.912 | 0.163664 | ||||||||
\(201\) | 7169.52i | 2.51591i | ||||||||
\(202\) | −4039.52 | −1.40703 | ||||||||
\(203\) | −7475.19 | −2.58451 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2317.54 | −0.789581 | ||||||||
\(206\) | −8786.25 | −2.97168 | ||||||||
\(207\) | − 2405.05i | − 0.807549i | ||||||||
\(208\) | −329.859 | −0.109960 | ||||||||
\(209\) | 186.039i | 0.0615721i | ||||||||
\(210\) | 11095.6i | 3.64605i | ||||||||
\(211\) | − 1102.88i | − 0.359836i | −0.983682 | − | 0.179918i | \(-0.942417\pi\) | ||||
0.983682 | − | 0.179918i | \(-0.0575833\pi\) | |||||||
\(212\) | −1441.94 | −0.467135 | ||||||||
\(213\) | −3969.10 | −1.27680 | ||||||||
\(214\) | − 153.288i | − 0.0489651i | ||||||||
\(215\) | 885.008i | 0.280731i | ||||||||
\(216\) | 874.828i | 0.275576i | ||||||||
\(217\) | −223.297 | −0.0698542 | ||||||||
\(218\) | − 2469.84i | − 0.767332i | ||||||||
\(219\) | 2660.89 | 0.821032 | ||||||||
\(220\) | 534.337 | 0.163750 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −12759.2 | −3.85738 | ||||||||
\(223\) | 568.848 | 0.170820 | 0.0854100 | − | 0.996346i | \(-0.472780\pi\) | ||||
0.0854100 | + | 0.996346i | \(0.472780\pi\) | |||||||
\(224\) | 3674.98i | 1.09618i | ||||||||
\(225\) | 531.442 | 0.157464 | ||||||||
\(226\) | − 1937.14i | − 0.570163i | ||||||||
\(227\) | 2106.99i | 0.616061i | 0.951377 | + | 0.308030i | \(0.0996698\pi\) | ||||
−0.951377 | + | 0.308030i | \(0.900330\pi\) | |||||||
\(228\) | − 6047.39i | − 1.75657i | ||||||||
\(229\) | −4336.30 | −1.25131 | −0.625656 | − | 0.780099i | \(-0.715169\pi\) | ||||
−0.625656 | + | 0.780099i | \(0.715169\pi\) | |||||||
\(230\) | 4289.00 | 1.22960 | ||||||||
\(231\) | 646.591i | 0.184167i | ||||||||
\(232\) | − 7781.11i | − 2.20196i | ||||||||
\(233\) | 4517.39i | 1.27014i | 0.772453 | + | 0.635072i | \(0.219030\pi\) | ||||
−0.772453 | + | 0.635072i | \(0.780970\pi\) | |||||||
\(234\) | −2923.95 | −0.816856 | ||||||||
\(235\) | 281.405i | 0.0781143i | ||||||||
\(236\) | −3446.43 | −0.950609 | ||||||||
\(237\) | 7277.69 | 1.99467 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5300.88 | 1.43467 | 0.717333 | − | 0.696731i | \(-0.245363\pi\) | ||||
0.717333 | + | 0.696731i | \(0.245363\pi\) | |||||||
\(240\) | −1495.85 | −0.402319 | ||||||||
\(241\) | 1368.82i | 0.365864i | 0.983126 | + | 0.182932i | \(0.0585588\pi\) | ||||
−0.983126 | + | 0.182932i | \(0.941441\pi\) | |||||||
\(242\) | −6168.32 | −1.63849 | ||||||||
\(243\) | − 5426.60i | − 1.43258i | ||||||||
\(244\) | − 5119.05i | − 1.34309i | ||||||||
\(245\) | − 4044.40i | − 1.05464i | ||||||||
\(246\) | 6931.17 | 1.79640 | ||||||||
\(247\) | 1149.88 | 0.296216 | ||||||||
\(248\) | − 232.435i | − 0.0595146i | ||||||||
\(249\) | 10790.9i | 2.74638i | ||||||||
\(250\) | − 6010.96i | − 1.52067i | ||||||||
\(251\) | −5547.63 | −1.39507 | −0.697536 | − | 0.716549i | \(-0.745720\pi\) | ||||
−0.697536 | + | 0.716549i | \(0.745720\pi\) | |||||||
\(252\) | − 11270.3i | − 2.81730i | ||||||||
\(253\) | 249.939 | 0.0621088 | ||||||||
\(254\) | 2784.52 | 0.687860 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5644.28 | −1.37800 | ||||||||
\(257\) | 193.949 | 0.0470748 | 0.0235374 | − | 0.999723i | \(-0.492507\pi\) | ||||
0.0235374 | + | 0.999723i | \(0.492507\pi\) | |||||||
\(258\) | − 2646.83i | − 0.638700i | ||||||||
\(259\) | 9351.29 | 2.24348 | ||||||||
\(260\) | − 3302.67i | − 0.787780i | ||||||||
\(261\) | − 8933.04i | − 2.11855i | ||||||||
\(262\) | 569.052i | 0.134184i | ||||||||
\(263\) | 1345.63 | 0.315494 | 0.157747 | − | 0.987480i | \(-0.449577\pi\) | ||||
0.157747 | + | 0.987480i | \(0.449577\pi\) | |||||||
\(264\) | −673.052 | −0.156907 | ||||||||
\(265\) | − 1243.34i | − 0.288218i | ||||||||
\(266\) | 6997.67i | 1.61299i | ||||||||
\(267\) | − 3709.18i | − 0.850180i | ||||||||
\(268\) | 12986.8 | 2.96007 | ||||||||
\(269\) | 3083.04i | 0.698797i | 0.936974 | + | 0.349398i | \(0.113614\pi\) | ||||
−0.936974 | + | 0.349398i | \(0.886386\pi\) | |||||||
\(270\) | −1791.07 | −0.403707 | ||||||||
\(271\) | −422.163 | −0.0946294 | −0.0473147 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473147 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3996.50 | 0.886004 | ||||||||
\(274\) | 4191.85 | 0.924230 | ||||||||
\(275\) | 55.2288i | 0.0121106i | ||||||||
\(276\) | −8124.54 | −1.77188 | ||||||||
\(277\) | 8260.00i | 1.79168i | 0.444377 | + | 0.895840i | \(0.353425\pi\) | ||||
−0.444377 | + | 0.895840i | \(0.646575\pi\) | |||||||
\(278\) | − 9873.28i | − 2.13007i | ||||||||
\(279\) | − 266.845i | − 0.0572602i | ||||||||
\(280\) | 8464.86 | 1.80669 | ||||||||
\(281\) | −3321.91 | −0.705226 | −0.352613 | − | 0.935769i | \(-0.614707\pi\) | ||||
−0.352613 | + | 0.935769i | \(0.614707\pi\) | |||||||
\(282\) | − 841.611i | − 0.177721i | ||||||||
\(283\) | − 7954.43i | − 1.67082i | −0.549629 | − | 0.835409i | \(-0.685231\pi\) | ||||
0.549629 | − | 0.835409i | \(-0.314769\pi\) | |||||||
\(284\) | 7189.61i | 1.50220i | ||||||||
\(285\) | 5214.50 | 1.08379 | ||||||||
\(286\) | − 303.864i | − 0.0628246i | ||||||||
\(287\) | −5079.91 | −1.04480 | ||||||||
\(288\) | −4391.69 | −0.898552 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 15930.5 | 3.22577 | ||||||||
\(291\) | −5228.69 | −1.05330 | ||||||||
\(292\) | − 4819.92i | − 0.965974i | ||||||||
\(293\) | −1171.99 | −0.233681 | −0.116841 | − | 0.993151i | \(-0.537277\pi\) | ||||
−0.116841 | + | 0.993151i | \(0.537277\pi\) | |||||||
\(294\) | 12095.8i | 2.39945i | ||||||||
\(295\) | − 2971.76i | − 0.586517i | ||||||||
\(296\) | 9733.98i | 1.91141i | ||||||||
\(297\) | −104.374 | −0.0203918 | ||||||||
\(298\) | −12055.5 | −2.34347 | ||||||||
\(299\) | − 1544.84i | − 0.298798i | ||||||||
\(300\) | − 1795.27i | − 0.345500i | ||||||||
\(301\) | 1939.88i | 0.371472i | ||||||||
\(302\) | 6272.46 | 1.19516 | ||||||||
\(303\) | 6598.07i | 1.25099i | ||||||||
\(304\) | −943.387 | −0.177983 | ||||||||
\(305\) | 4414.01 | 0.828675 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 865.763 | 0.160950 | 0.0804751 | − | 0.996757i | \(-0.474356\pi\) | ||||
0.0804751 | + | 0.996757i | \(0.474356\pi\) | |||||||
\(308\) | 1171.23 | 0.216679 | ||||||||
\(309\) | 14351.3i | 2.64212i | ||||||||
\(310\) | 475.872 | 0.0871862 | ||||||||
\(311\) | − 6994.83i | − 1.27537i | −0.770297 | − | 0.637685i | \(-0.779892\pi\) | ||||
0.770297 | − | 0.637685i | \(-0.220108\pi\) | |||||||
\(312\) | 4160.05i | 0.754861i | ||||||||
\(313\) | 3442.33i | 0.621635i | 0.950470 | + | 0.310818i | \(0.100603\pi\) | ||||
−0.950470 | + | 0.310818i | \(0.899397\pi\) | |||||||
\(314\) | 11658.7 | 2.09534 | ||||||||
\(315\) | 9718.02 | 1.73825 | ||||||||
\(316\) | − 13182.8i | − 2.34680i | ||||||||
\(317\) | 2066.15i | 0.366078i | 0.983106 | + | 0.183039i | \(0.0585935\pi\) | ||||
−0.983106 | + | 0.183039i | \(0.941407\pi\) | |||||||
\(318\) | 3718.52i | 0.655736i | ||||||||
\(319\) | 928.344 | 0.162938 | ||||||||
\(320\) | − 9400.22i | − 1.64215i | ||||||||
\(321\) | −250.377 | −0.0435349 | ||||||||
\(322\) | 9401.21 | 1.62705 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −8256.20 | −1.41567 | ||||||||
\(325\) | 341.362 | 0.0582627 | ||||||||
\(326\) | − 9163.11i | − 1.55674i | ||||||||
\(327\) | −4034.18 | −0.682234 | ||||||||
\(328\) | − 5287.80i | − 0.890152i | ||||||||
\(329\) | 616.823i | 0.103363i | ||||||||
\(330\) | − 1377.96i | − 0.229862i | ||||||||
\(331\) | −9027.44 | −1.49907 | −0.749536 | − | 0.661964i | \(-0.769723\pi\) | ||||
−0.749536 | + | 0.661964i | \(0.769723\pi\) | |||||||
\(332\) | 19546.7 | 3.23121 | ||||||||
\(333\) | 11175.0i | 1.83900i | ||||||||
\(334\) | 10179.8i | 1.66771i | ||||||||
\(335\) | 11198.2i | 1.82633i | ||||||||
\(336\) | −3278.81 | −0.532362 | ||||||||
\(337\) | − 204.309i | − 0.0330250i | −0.999864 | − | 0.0165125i | \(-0.994744\pi\) | ||||
0.999864 | − | 0.0165125i | \(-0.00525633\pi\) | |||||||
\(338\) | 8384.67 | 1.34931 | ||||||||
\(339\) | −3164.09 | −0.506931 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.7312 | 0.00440390 | ||||||||
\(342\) | −8362.39 | −1.32218 | ||||||||
\(343\) | 94.8397i | 0.0149296i | ||||||||
\(344\) | −2019.27 | −0.316488 | ||||||||
\(345\) | − 7005.56i | − 1.09324i | ||||||||
\(346\) | 14534.5i | 2.25832i | ||||||||
\(347\) | 143.063i | 0.0221326i | 0.999939 | + | 0.0110663i | \(0.00352259\pi\) | ||||
−0.999939 | + | 0.0110663i | \(0.996477\pi\) | |||||||
\(348\) | −30176.8 | −4.64841 | ||||||||
\(349\) | 3998.42 | 0.613268 | 0.306634 | − | 0.951828i | \(-0.400797\pi\) | ||||
0.306634 | + | 0.951828i | \(0.400797\pi\) | |||||||
\(350\) | 2077.38i | 0.317259i | ||||||||
\(351\) | 645.119i | 0.0981024i | ||||||||
\(352\) | − 456.396i | − 0.0691079i | ||||||||
\(353\) | −5809.57 | −0.875956 | −0.437978 | − | 0.898986i | \(-0.644305\pi\) | ||||
−0.437978 | + | 0.898986i | \(0.644305\pi\) | |||||||
\(354\) | 8887.77i | 1.33441i | ||||||||
\(355\) | −6199.39 | −0.926844 | ||||||||
\(356\) | −6718.79 | −1.00027 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3784.24 | 0.558668 | ||||||||
\(359\) | 4895.37 | 0.719687 | 0.359844 | − | 0.933013i | \(-0.382830\pi\) | ||||
0.359844 | + | 0.933013i | \(0.382830\pi\) | |||||||
\(360\) | 10115.7i | 1.48096i | ||||||||
\(361\) | −3570.37 | −0.520538 | ||||||||
\(362\) | 15677.9i | 2.27628i | ||||||||
\(363\) | 10075.2i | 1.45678i | ||||||||
\(364\) | − 7239.24i | − 1.04242i | ||||||||
\(365\) | 4156.08 | 0.595998 | ||||||||
\(366\) | −13201.2 | −1.88535 | ||||||||
\(367\) | 528.151i | 0.0751206i | 0.999294 | + | 0.0375603i | \(0.0119586\pi\) | ||||
−0.999294 | + | 0.0375603i | \(0.988041\pi\) | |||||||
\(368\) | 1267.42i | 0.179535i | ||||||||
\(369\) | − 6070.62i | − 0.856433i | ||||||||
\(370\) | −19928.7 | −2.80012 | ||||||||
\(371\) | − 2725.33i | − 0.381380i | ||||||||
\(372\) | −901.433 | −0.125637 | ||||||||
\(373\) | −10113.5 | −1.40390 | −0.701950 | − | 0.712226i | \(-0.747687\pi\) | ||||
−0.701950 | + | 0.712226i | \(0.747687\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9818.18 | −1.35202 | ||||||||
\(376\) | −642.066 | −0.0880639 | ||||||||
\(377\) | − 5737.98i | − 0.783875i | ||||||||
\(378\) | −3925.91 | −0.534198 | ||||||||
\(379\) | − 729.385i | − 0.0988548i | −0.998778 | − | 0.0494274i | \(-0.984260\pi\) | ||||
0.998778 | − | 0.0494274i | \(-0.0157396\pi\) | |||||||
\(380\) | − 9445.52i | − 1.27512i | ||||||||
\(381\) | − 4548.18i | − 0.611576i | ||||||||
\(382\) | −6252.12 | −0.837399 | ||||||||
\(383\) | 1608.08 | 0.214540 | 0.107270 | − | 0.994230i | \(-0.465789\pi\) | ||||
0.107270 | + | 0.994230i | \(0.465789\pi\) | |||||||
\(384\) | 19526.3i | 2.59491i | ||||||||
\(385\) | 1009.92i | 0.133689i | ||||||||
\(386\) | 1062.56i | 0.140111i | ||||||||
\(387\) | −2318.21 | −0.304499 | ||||||||
\(388\) | 9471.22i | 1.23925i | ||||||||
\(389\) | −9824.09 | −1.28047 | −0.640233 | − | 0.768181i | \(-0.721162\pi\) | ||||
−0.640233 | + | 0.768181i | \(0.721162\pi\) | |||||||
\(390\) | −8517.02 | −1.10584 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 9227.87 | 1.18897 | ||||||||
\(393\) | 929.478 | 0.119303 | ||||||||
\(394\) | − 3809.66i | − 0.487127i | ||||||||
\(395\) | 11367.1 | 1.44796 | ||||||||
\(396\) | 1399.65i | 0.177614i | ||||||||
\(397\) | 2876.88i | 0.363694i | 0.983327 | + | 0.181847i | \(0.0582076\pi\) | ||||
−0.983327 | + | 0.181847i | \(0.941792\pi\) | |||||||
\(398\) | 8720.82i | 1.09833i | ||||||||
\(399\) | 11429.9 | 1.43411 | ||||||||
\(400\) | −280.061 | −0.0350076 | ||||||||
\(401\) | − 6515.91i | − 0.811444i | −0.913996 | − | 0.405722i | \(-0.867020\pi\) | ||||
0.913996 | − | 0.405722i | \(-0.132980\pi\) | |||||||
\(402\) | − 33490.9i | − 4.15516i | ||||||||
\(403\) | − 171.403i | − 0.0211866i | ||||||||
\(404\) | 11951.7 | 1.47183 | ||||||||
\(405\) | − 7119.09i | − 0.873457i | ||||||||
\(406\) | 34918.8 | 4.26845 | ||||||||
\(407\) | −1161.34 | −0.141438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8870.10 | −1.07237 | −0.536183 | − | 0.844101i | \(-0.680134\pi\) | ||||
−0.536183 | + | 0.844101i | \(0.680134\pi\) | |||||||
\(410\) | 10825.9 | 1.30403 | ||||||||
\(411\) | − 6846.89i | − 0.821732i | ||||||||
\(412\) | 25995.9 | 3.10855 | ||||||||
\(413\) | − 6513.92i | − 0.776099i | ||||||||
\(414\) | 11234.7i | 1.33371i | ||||||||
\(415\) | 16854.5i | 1.99363i | ||||||||
\(416\) | −2820.93 | −0.332469 | ||||||||
\(417\) | −16126.8 | −1.89385 | ||||||||
\(418\) | − 869.041i | − 0.101689i | ||||||||
\(419\) | − 1009.53i | − 0.117706i | −0.998267 | − | 0.0588531i | \(-0.981256\pi\) | ||||
0.998267 | − | 0.0588531i | \(-0.0187443\pi\) | |||||||
\(420\) | − 32828.6i | − 3.81398i | ||||||||
\(421\) | −3253.60 | −0.376652 | −0.188326 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188326 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(422\) | 5151.87i | 0.594287i | ||||||||
\(423\) | −737.119 | −0.0847280 | ||||||||
\(424\) | 2836.86 | 0.324930 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18540.8 | 2.10870 | ||||||||
\(427\) | 9675.25 | 1.09653 | ||||||||
\(428\) | 453.532i | 0.0512203i | ||||||||
\(429\) | −496.325 | −0.0558573 | ||||||||
\(430\) | − 4134.13i | − 0.463640i | ||||||||
\(431\) | − 2352.51i | − 0.262915i | −0.991322 | − | 0.131457i | \(-0.958034\pi\) | ||||
0.991322 | − | 0.131457i | \(-0.0419656\pi\) | |||||||
\(432\) | − 529.269i | − 0.0589455i | ||||||||
\(433\) | 5860.51 | 0.650434 | 0.325217 | − | 0.945639i | \(-0.394563\pi\) | ||||
0.325217 | + | 0.945639i | \(0.394563\pi\) | |||||||
\(434\) | 1043.08 | 0.115368 | ||||||||
\(435\) | − 26020.6i | − 2.86803i | ||||||||
\(436\) | 7307.50i | 0.802674i | ||||||||
\(437\) | − 4418.20i | − 0.483641i | ||||||||
\(438\) | −12429.8 | −1.35597 | ||||||||
\(439\) | − 2894.17i | − 0.314650i | −0.987547 | − | 0.157325i | \(-0.949713\pi\) | ||||
0.987547 | − | 0.157325i | \(-0.0502870\pi\) | |||||||
\(440\) | −1051.25 | −0.113901 | ||||||||
\(441\) | 10594.0 | 1.14394 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8256.85 | −0.885541 | −0.442771 | − | 0.896635i | \(-0.646004\pi\) | ||||
−0.442771 | + | 0.896635i | \(0.646004\pi\) | |||||||
\(444\) | 37750.5 | 4.03504 | ||||||||
\(445\) | − 5793.42i | − 0.617156i | ||||||||
\(446\) | −2657.25 | −0.282118 | ||||||||
\(447\) | 19691.1i | 2.08358i | ||||||||
\(448\) | − 20604.7i | − 2.17295i | ||||||||
\(449\) | 15487.1i | 1.62779i | 0.581009 | + | 0.813897i | \(0.302658\pi\) | ||||
−0.581009 | + | 0.813897i | \(0.697342\pi\) | |||||||
\(450\) | −2482.52 | −0.260060 | ||||||||
\(451\) | 630.874 | 0.0658685 | ||||||||
\(452\) | 5731.42i | 0.596423i | ||||||||
\(453\) | − 10245.3i | − 1.06262i | ||||||||
\(454\) | − 9842.35i | − 1.01745i | ||||||||
\(455\) | 6242.19 | 0.643162 | ||||||||
\(456\) | 11897.6i | 1.22184i | ||||||||
\(457\) | 16055.6 | 1.64343 | 0.821716 | − | 0.569897i | \(-0.193017\pi\) | ||||
0.821716 | + | 0.569897i | \(0.193017\pi\) | |||||||
\(458\) | 20256.1 | 2.06661 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12689.8 | −1.28623 | ||||||||
\(461\) | −14064.0 | −1.42088 | −0.710440 | − | 0.703758i | \(-0.751504\pi\) | ||||
−0.710440 | + | 0.703758i | \(0.751504\pi\) | |||||||
\(462\) | − 3020.41i | − 0.304161i | ||||||||
\(463\) | −8071.30 | −0.810162 | −0.405081 | − | 0.914281i | \(-0.632757\pi\) | ||||
−0.405081 | + | 0.914281i | \(0.632757\pi\) | |||||||
\(464\) | 4707.55i | 0.470997i | ||||||||
\(465\) | − 777.280i | − 0.0775172i | ||||||||
\(466\) | − 21102.0i | − 2.09771i | ||||||||
\(467\) | −8582.41 | −0.850421 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(468\) | 8651.07 | 0.854479 | ||||||||
\(469\) | 24545.7i | 2.41667i | ||||||||
\(470\) | − 1314.53i | − 0.129010i | ||||||||
\(471\) | − 19043.1i | − 1.86297i | ||||||||
\(472\) | 6780.49 | 0.661224 | ||||||||
\(473\) | − 240.914i | − 0.0234191i | ||||||||
\(474\) | −33996.2 | −3.29429 | ||||||||
\(475\) | 976.286 | 0.0943054 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3256.84 | 0.312621 | ||||||||
\(478\) | −24761.9 | −2.36942 | ||||||||
\(479\) | 6320.96i | 0.602948i | 0.953474 | + | 0.301474i | \(0.0974787\pi\) | ||||
−0.953474 | + | 0.301474i | \(0.902521\pi\) | |||||||
\(480\) | −12792.4 | −1.21643 | ||||||||
\(481\) | 7178.07i | 0.680441i | ||||||||
\(482\) | − 6394.13i | − 0.604242i | ||||||||
\(483\) | − 15355.8i | − 1.44661i | ||||||||
\(484\) | 18250.2 | 1.71396 | ||||||||
\(485\) | −8166.77 | −0.764606 | ||||||||
\(486\) | 25349.2i | 2.36597i | ||||||||
\(487\) | 7336.47i | 0.682643i | 0.939947 | + | 0.341321i | \(0.110874\pi\) | ||||
−0.939947 | + | 0.341321i | \(0.889126\pi\) | |||||||
\(488\) | 10071.2i | 0.934225i | ||||||||
\(489\) | −14966.8 | −1.38410 | ||||||||
\(490\) | 18892.6i | 1.74179i | ||||||||
\(491\) | −6672.53 | −0.613294 | −0.306647 | − | 0.951823i | \(-0.599207\pi\) | ||||
−0.306647 | + | 0.951823i | \(0.599207\pi\) | |||||||
\(492\) | −20507.2 | −1.87914 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −5371.43 | −0.489215 | ||||||||
\(495\) | −1206.88 | −0.109586 | ||||||||
\(496\) | 140.623i | 0.0127301i | ||||||||
\(497\) | −13588.7 | −1.22643 | ||||||||
\(498\) | − 50407.6i | − 4.53578i | ||||||||
\(499\) | 17920.9i | 1.60772i | 0.594821 | + | 0.803858i | \(0.297223\pi\) | ||||
−0.594821 | + | 0.803858i | \(0.702777\pi\) | |||||||
\(500\) | 17784.6i | 1.59070i | ||||||||
\(501\) | 16627.6 | 1.48276 | ||||||||
\(502\) | 25914.6 | 2.30403 | ||||||||
\(503\) | − 11325.3i | − 1.00392i | −0.864891 | − | 0.501959i | \(-0.832613\pi\) | ||||
0.864891 | − | 0.501959i | \(-0.167387\pi\) | |||||||
\(504\) | 22173.0i | 1.95965i | ||||||||
\(505\) | 10305.6i | 0.908108i | ||||||||
\(506\) | −1167.54 | −0.102576 | ||||||||
\(507\) | − 13695.4i | − 1.19967i | ||||||||
\(508\) | −8238.56 | −0.719541 | ||||||||
\(509\) | −8313.78 | −0.723972 | −0.361986 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361986 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9109.87 | 0.788644 | ||||||||
\(512\) | 5892.85 | 0.508651 | ||||||||
\(513\) | 1845.02i | 0.158791i | ||||||||
\(514\) | −905.993 | −0.0777464 | ||||||||
\(515\) | 22415.5i | 1.91795i | ||||||||
\(516\) | 7831.17i | 0.668117i | ||||||||
\(517\) | − 76.6033i | − 0.00651646i | ||||||||
\(518\) | −43682.6 | −3.70521 | ||||||||
\(519\) | 23740.3 | 2.00787 | ||||||||
\(520\) | 6497.65i | 0.547963i | ||||||||
\(521\) | 5121.64i | 0.430677i | 0.976539 | + | 0.215339i | \(0.0690856\pi\) | ||||
−0.976539 | + | 0.215339i | \(0.930914\pi\) | |||||||
\(522\) | 41728.8i | 3.49889i | ||||||||
\(523\) | 13378.5 | 1.11855 | 0.559275 | − | 0.828982i | \(-0.311080\pi\) | ||||
0.559275 | + | 0.828982i | \(0.311080\pi\) | |||||||
\(524\) | − 1683.65i | − 0.140364i | ||||||||
\(525\) | 3393.15 | 0.282075 | ||||||||
\(526\) | −6285.81 | −0.521054 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 407.195 | 0.0335623 | ||||||||
\(529\) | 6231.26 | 0.512144 | ||||||||
\(530\) | 5808.01i | 0.476007i | ||||||||
\(531\) | 7784.29 | 0.636176 | ||||||||
\(532\) | − 20704.0i | − 1.68728i | ||||||||
\(533\) | − 3899.35i | − 0.316885i | ||||||||
\(534\) | 17326.6i | 1.40411i | ||||||||
\(535\) | −391.068 | −0.0316025 | ||||||||
\(536\) | −25550.2 | −2.05896 | ||||||||
\(537\) | − 6181.10i | − 0.496712i | ||||||||
\(538\) | − 14401.8i | − 1.15410i | ||||||||
\(539\) | 1100.95i | 0.0879804i | ||||||||
\(540\) | 5299.23 | 0.422301 | ||||||||
\(541\) | − 9906.81i | − 0.787296i | −0.919261 | − | 0.393648i | \(-0.871213\pi\) | ||||
0.919261 | − | 0.393648i | \(-0.128787\pi\) | |||||||
\(542\) | 1972.04 | 0.156285 | ||||||||
\(543\) | 25608.0 | 2.02384 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6301.05 | −0.495243 | ||||||||
\(546\) | −18668.8 | −1.46328 | ||||||||
\(547\) | − 16399.6i | − 1.28189i | −0.767585 | − | 0.640947i | \(-0.778542\pi\) | ||||
0.767585 | − | 0.640947i | \(-0.221458\pi\) | |||||||
\(548\) | −12402.4 | −0.966798 | ||||||||
\(549\) | 11562.2i | 0.898836i | ||||||||
\(550\) | − 257.990i | − 0.0200013i | ||||||||
\(551\) | − 16410.4i | − 1.26880i | ||||||||
\(552\) | 15984.2 | 1.23248 | ||||||||
\(553\) | 24916.1 | 1.91598 | ||||||||
\(554\) | − 38584.8i | − 2.95905i | ||||||||
\(555\) | 32551.2i | 2.48959i | ||||||||
\(556\) | 29212.0i | 2.22818i | ||||||||
\(557\) | 22044.3 | 1.67692 | 0.838461 | − | 0.544962i | \(-0.183456\pi\) | ||||
0.838461 | + | 0.544962i | \(0.183456\pi\) | |||||||
\(558\) | 1246.51i | 0.0945681i | ||||||||
\(559\) | −1489.06 | −0.112666 | ||||||||
\(560\) | −5121.22 | −0.386448 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15517.6 | 1.16472 | ||||||||
\(563\) | −12048.8 | −0.901947 | −0.450973 | − | 0.892537i | \(-0.648923\pi\) | ||||
−0.450973 | + | 0.892537i | \(0.648923\pi\) | |||||||
\(564\) | 2490.07i | 0.185906i | ||||||||
\(565\) | −4942.04 | −0.367988 | ||||||||
\(566\) | 37157.4i | 2.75944i | ||||||||
\(567\) | − 15604.6i | − 1.15579i | ||||||||
\(568\) | − 14144.8i | − 1.04490i | ||||||||
\(569\) | 23785.4 | 1.75243 | 0.876217 | − | 0.481916i | \(-0.160059\pi\) | ||||
0.876217 | + | 0.481916i | \(0.160059\pi\) | |||||||
\(570\) | −24358.4 | −1.78993 | ||||||||
\(571\) | − 10878.3i | − 0.797271i | −0.917110 | − | 0.398635i | \(-0.869484\pi\) | ||||
0.917110 | − | 0.398635i | \(-0.130516\pi\) | |||||||
\(572\) | 899.041i | 0.0657182i | ||||||||
\(573\) | 10212.1i | 0.744531i | ||||||||
\(574\) | 23729.7 | 1.72554 | ||||||||
\(575\) | − 1311.62i | − 0.0951274i | ||||||||
\(576\) | 24623.1 | 1.78119 | ||||||||
\(577\) | 6315.86 | 0.455689 | 0.227845 | − | 0.973698i | \(-0.426832\pi\) | ||||
0.227845 | + | 0.973698i | \(0.426832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1735.56 | 0.124572 | ||||||||
\(580\) | −47133.7 | −3.37434 | ||||||||
\(581\) | 36944.1i | 2.63804i | ||||||||
\(582\) | 24424.7 | 1.73958 | ||||||||
\(583\) | 338.459i | 0.0240438i | ||||||||
\(584\) | 9482.69i | 0.671912i | ||||||||
\(585\) | 7459.58i | 0.527206i | ||||||||
\(586\) | 5474.72 | 0.385936 | ||||||||
\(587\) | −18192.1 | −1.27916 | −0.639581 | − | 0.768724i | \(-0.720892\pi\) | ||||
−0.639581 | + | 0.768724i | \(0.720892\pi\) | |||||||
\(588\) | − 35787.7i | − 2.50996i | ||||||||
\(589\) | − 490.207i | − 0.0342931i | ||||||||
\(590\) | 13882.0i | 0.968663i | ||||||||
\(591\) | −6222.63 | −0.433104 | ||||||||
\(592\) | − 5889.03i | − 0.408848i | ||||||||
\(593\) | 9828.72 | 0.680636 | 0.340318 | − | 0.940310i | \(-0.389465\pi\) | ||||
0.340318 | + | 0.940310i | \(0.389465\pi\) | |||||||
\(594\) | 487.559 | 0.0336781 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 35668.5 | 2.45140 | ||||||||
\(597\) | 14244.4 | 0.976524 | ||||||||
\(598\) | 7216.40i | 0.493479i | ||||||||
\(599\) | 4662.57 | 0.318043 | 0.159021 | − | 0.987275i | \(-0.449166\pi\) | ||||
0.159021 | + | 0.987275i | \(0.449166\pi\) | |||||||
\(600\) | 3532.01i | 0.240323i | ||||||||
\(601\) | 21658.6i | 1.47000i | 0.678066 | + | 0.735001i | \(0.262818\pi\) | ||||
−0.678066 | + | 0.735001i | \(0.737182\pi\) | |||||||
\(602\) | − 9061.76i | − 0.613504i | ||||||||
\(603\) | −29332.8 | −1.98097 | ||||||||
\(604\) | −18558.3 | −1.25021 | ||||||||
\(605\) | 15736.6i | 1.05750i | ||||||||
\(606\) | − 30821.5i | − 2.06607i | ||||||||
\(607\) | − 25764.7i | − 1.72283i | −0.507902 | − | 0.861415i | \(-0.669579\pi\) | ||||
0.507902 | − | 0.861415i | \(-0.330421\pi\) | |||||||
\(608\) | −8067.76 | −0.538143 | ||||||||
\(609\) | − 57035.6i | − 3.79507i | ||||||||
\(610\) | −20619.1 | −1.36860 | ||||||||
\(611\) | −473.475 | −0.0313498 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16018.1 | 1.05541 | 0.527705 | − | 0.849428i | \(-0.323053\pi\) | ||||
0.527705 | + | 0.849428i | \(0.323053\pi\) | |||||||
\(614\) | −4044.23 | −0.265817 | ||||||||
\(615\) | − 17682.8i | − 1.15941i | ||||||||
\(616\) | −2304.28 | −0.150718 | ||||||||
\(617\) | − 22250.3i | − 1.45180i | −0.687798 | − | 0.725902i | \(-0.741422\pi\) | ||||
0.687798 | − | 0.725902i | \(-0.258578\pi\) | |||||||
\(618\) | − 67038.9i | − 4.36360i | ||||||||
\(619\) | − 3765.95i | − 0.244534i | −0.992497 | − | 0.122267i | \(-0.960984\pi\) | ||||
0.992497 | − | 0.122267i | \(-0.0390164\pi\) | |||||||
\(620\) | −1407.96 | −0.0912018 | ||||||||
\(621\) | 2478.74 | 0.160175 | ||||||||
\(622\) | 32674.9i | 2.10634i | ||||||||
\(623\) | − 12698.8i | − 0.816642i | ||||||||
\(624\) | − 2516.82i | − 0.161464i | ||||||||
\(625\) | −17463.2 | −1.11765 | ||||||||
\(626\) | − 16080.1i | − 1.02666i | ||||||||
\(627\) | −1419.47 | −0.0904120 | ||||||||
\(628\) | −34494.5 | −2.19185 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −45395.7 | −2.87080 | ||||||||
\(631\) | 20806.5 | 1.31267 | 0.656334 | − | 0.754470i | \(-0.272106\pi\) | ||||
0.656334 | + | 0.754470i | \(0.272106\pi\) | |||||||
\(632\) | 25935.7i | 1.63239i | ||||||||
\(633\) | 8414.96 | 0.528380 | ||||||||
\(634\) | − 9651.60i | − 0.604596i | ||||||||
\(635\) | − 7103.88i | − 0.443951i | ||||||||
\(636\) | − 11002.0i | − 0.685937i | ||||||||
\(637\) | 6804.85 | 0.423262 | ||||||||
\(638\) | −4336.56 | −0.269100 | ||||||||
\(639\) | − 16238.8i | − 1.00532i | ||||||||
\(640\) | 30498.4i | 1.88368i | ||||||||
\(641\) | − 2439.58i | − 0.150324i | −0.997171 | − | 0.0751620i | \(-0.976053\pi\) | ||||
0.997171 | − | 0.0751620i | \(-0.0239474\pi\) | |||||||
\(642\) | 1169.58 | 0.0719000 | ||||||||
\(643\) | 19320.1i | 1.18493i | 0.805595 | + | 0.592466i | \(0.201846\pi\) | ||||
−0.805595 | + | 0.592466i | \(0.798154\pi\) | |||||||
\(644\) | −27815.4 | −1.70199 | ||||||||
\(645\) | −6752.60 | −0.412222 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14067.1 | −0.854766 | −0.427383 | − | 0.904071i | \(-0.640564\pi\) | ||||
−0.427383 | + | 0.904071i | \(0.640564\pi\) | |||||||
\(648\) | 16243.2 | 0.984712 | ||||||||
\(649\) | 808.963i | 0.0489285i | ||||||||
\(650\) | −1594.60 | −0.0962238 | ||||||||
\(651\) | − 1703.75i | − 0.102573i | ||||||||
\(652\) | 27110.9i | 1.62844i | ||||||||
\(653\) | 15893.7i | 0.952478i | 0.879316 | + | 0.476239i | \(0.158000\pi\) | ||||
−0.879316 | + | 0.476239i | \(0.842000\pi\) | |||||||
\(654\) | 18844.8 | 1.12674 | ||||||||
\(655\) | 1451.77 | 0.0866033 | ||||||||
\(656\) | 3199.11i | 0.190403i | ||||||||
\(657\) | 10886.5i | 0.646459i | ||||||||
\(658\) | − 2881.36i | − 0.170710i | ||||||||
\(659\) | −9653.54 | −0.570635 | −0.285318 | − | 0.958433i | \(-0.592099\pi\) | ||||
−0.285318 | + | 0.958433i | \(0.592099\pi\) | |||||||
\(660\) | 4076.98i | 0.240449i | ||||||||
\(661\) | −5389.06 | −0.317111 | −0.158555 | − | 0.987350i | \(-0.550684\pi\) | ||||
−0.158555 | + | 0.987350i | \(0.550684\pi\) | |||||||
\(662\) | 42169.7 | 2.47579 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38456.0 | −2.24757 | ||||||||
\(665\) | 17852.5 | 1.04104 | ||||||||
\(666\) | − 52201.7i | − 3.03720i | ||||||||
\(667\) | −22047.0 | −1.27986 | ||||||||
\(668\) | − 30119.1i | − 1.74453i | ||||||||
\(669\) | 4340.30i | 0.250831i | ||||||||
\(670\) | − 52309.9i | − 3.01628i | ||||||||
\(671\) | −1201.57 | −0.0691297 | ||||||||
\(672\) | −28040.1 | −1.60963 | ||||||||
\(673\) | − 3032.18i | − 0.173673i | −0.996223 | − | 0.0868366i | \(-0.972324\pi\) | ||||
0.996223 | − | 0.0868366i | \(-0.0276758\pi\) | |||||||
\(674\) | 954.386i | 0.0545424i | ||||||||
\(675\) | 547.726i | 0.0312326i | ||||||||
\(676\) | −24807.7 | −1.41145 | ||||||||
\(677\) | 22029.2i | 1.25059i | 0.780388 | + | 0.625295i | \(0.215021\pi\) | ||||
−0.780388 | + | 0.625295i | \(0.784979\pi\) | |||||||
\(678\) | 14780.4 | 0.837222 | ||||||||
\(679\) | −17901.1 | −1.01175 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16076.3 | −0.904618 | ||||||||
\(682\) | −129.540 | −0.00727326 | ||||||||
\(683\) | 9040.72i | 0.506491i | 0.967402 | + | 0.253246i | \(0.0814980\pi\) | ||||
−0.967402 | + | 0.253246i | \(0.918502\pi\) | |||||||
\(684\) | 24741.8 | 1.38308 | ||||||||
\(685\) | − 10694.3i | − 0.596506i | ||||||||
\(686\) | − 443.023i | − 0.0246570i | ||||||||
\(687\) | − 33085.9i | − 1.83742i | ||||||||
\(688\) | 1221.65 | 0.0676964 | ||||||||
\(689\) | 2091.97 | 0.115672 | ||||||||
\(690\) | 32725.0i | 1.80553i | ||||||||
\(691\) | − 22863.5i | − 1.25871i | −0.777118 | − | 0.629355i | \(-0.783319\pi\) | ||||
0.777118 | − | 0.629355i | \(-0.216681\pi\) | |||||||
\(692\) | − 43003.1i | − 2.36233i | ||||||||
\(693\) | −2645.41 | −0.145008 | ||||||||
\(694\) | − 668.288i | − 0.0365531i | ||||||||
\(695\) | −25188.7 | −1.37477 | ||||||||
\(696\) | 59369.7 | 3.23334 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −18677.8 | −1.01284 | ||||||||
\(699\) | −34467.6 | −1.86507 | ||||||||
\(700\) | − 6146.34i | − 0.331871i | ||||||||
\(701\) | 1753.00 | 0.0944507 | 0.0472253 | − | 0.998884i | \(-0.484962\pi\) | ||||
0.0472253 | + | 0.998884i | \(0.484962\pi\) | |||||||
\(702\) | − 3013.54i | − 0.162021i | ||||||||
\(703\) | 20529.1i | 1.10138i | ||||||||
\(704\) | 2558.90i | 0.136992i | ||||||||
\(705\) | −2147.12 | −0.114702 | ||||||||
\(706\) | 27138.2 | 1.44668 | ||||||||
\(707\) | 22589.3i | 1.20164i | ||||||||
\(708\) | − 26296.2i | − 1.39587i | ||||||||
\(709\) | − 11547.0i | − 0.611645i | −0.952089 | − | 0.305823i | \(-0.901069\pi\) | ||||
0.952089 | − | 0.305823i | \(-0.0989315\pi\) | |||||||
\(710\) | 28959.2 | 1.53073 | ||||||||
\(711\) | 29775.3i | 1.57055i | ||||||||
\(712\) | 13218.5 | 0.695765 | ||||||||
\(713\) | −658.582 | −0.0345920 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −775.218 | −0.0405476 | ||||||||
\(716\) | −11196.4 | −0.584399 | ||||||||
\(717\) | 40445.6i | 2.10665i | ||||||||
\(718\) | −22867.7 | −1.18860 | ||||||||
\(719\) | 10289.8i | 0.533720i | 0.963735 | + | 0.266860i | \(0.0859861\pi\) | ||||
−0.963735 | + | 0.266860i | \(0.914014\pi\) | |||||||
\(720\) | − 6119.99i | − 0.316776i | ||||||||
\(721\) | 49133.4i | 2.53790i | ||||||||
\(722\) | 16678.2 | 0.859695 | ||||||||
\(723\) | −10444.0 | −0.537231 | ||||||||
\(724\) | − 46386.2i | − 2.38112i | ||||||||
\(725\) | − 4871.72i | − 0.249560i | ||||||||
\(726\) | − 47064.2i | − 2.40595i | ||||||||
\(727\) | 2950.10 | 0.150499 | 0.0752497 | − | 0.997165i | \(-0.476025\pi\) | ||||
0.0752497 | + | 0.997165i | \(0.476025\pi\) | |||||||
\(728\) | 14242.5i | 0.725083i | ||||||||
\(729\) | 25275.9 | 1.28415 | ||||||||
\(730\) | −19414.2 | −0.984320 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 39058.3 | 1.97218 | ||||||||
\(733\) | −24348.2 | −1.22691 | −0.613453 | − | 0.789731i | \(-0.710220\pi\) | ||||
−0.613453 | + | 0.789731i | \(0.710220\pi\) | |||||||
\(734\) | − 2467.15i | − 0.124065i | ||||||||
\(735\) | 30858.7 | 1.54863 | ||||||||
\(736\) | 10838.8i | 0.542833i | ||||||||
\(737\) | − 3048.33i | − 0.152357i | ||||||||
\(738\) | 28357.6i | 1.41444i | ||||||||
\(739\) | 29233.5 | 1.45517 | 0.727585 | − | 0.686017i | \(-0.240642\pi\) | ||||
0.727585 | + | 0.686017i | \(0.240642\pi\) | |||||||
\(740\) | 58963.1 | 2.92909 | ||||||||
\(741\) | 8773.59i | 0.434961i | ||||||||
\(742\) | 12730.8i | 0.629868i | ||||||||
\(743\) | − 15340.6i | − 0.757457i | −0.925508 | − | 0.378729i | \(-0.876361\pi\) | ||||
0.925508 | − | 0.378729i | \(-0.123639\pi\) | |||||||
\(744\) | 1773.47 | 0.0873908 | ||||||||
\(745\) | 30755.9i | 1.51250i | ||||||||
\(746\) | 47242.9 | 2.31861 | ||||||||
\(747\) | −44149.2 | −2.16243 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −857.197 | −0.0418175 | ||||||||
\(750\) | 45863.5 | 2.23293 | ||||||||
\(751\) | − 39862.6i | − 1.93689i | −0.249223 | − | 0.968446i | \(-0.580175\pi\) | ||||
0.249223 | − | 0.968446i | \(-0.419825\pi\) | |||||||
\(752\) | 388.448 | 0.0188368 | ||||||||
\(753\) | − 42328.3i | − 2.04851i | ||||||||
\(754\) | 26803.7i | 1.29461i | ||||||||
\(755\) | − 16002.3i | − 0.771369i | ||||||||
\(756\) | 11615.6 | 0.558802 | ||||||||
\(757\) | −26375.1 | −1.26634 | −0.633169 | − | 0.774013i | \(-0.718246\pi\) | ||||
−0.633169 | + | 0.774013i | \(0.718246\pi\) | |||||||
\(758\) | 3407.17i | 0.163264i | ||||||||
\(759\) | 1907.03i | 0.0912000i | ||||||||
\(760\) | 18583.1i | 0.886946i | ||||||||
\(761\) | 7848.63 | 0.373867 | 0.186933 | − | 0.982373i | \(-0.440145\pi\) | ||||
0.186933 | + | 0.982373i | \(0.440145\pi\) | |||||||
\(762\) | 21245.9i | 1.01005i | ||||||||
\(763\) | −13811.5 | −0.655322 | ||||||||
\(764\) | 18498.1 | 0.875967 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7511.78 | −0.354323 | ||||||||
\(767\) | 5000.10 | 0.235389 | ||||||||
\(768\) | − 43065.8i | − 2.02344i | ||||||||
\(769\) | 31818.9 | 1.49209 | 0.746046 | − | 0.665895i | \(-0.231950\pi\) | ||||
0.746046 | + | 0.665895i | \(0.231950\pi\) | |||||||
\(770\) | − 4717.63i | − 0.220794i | ||||||||
\(771\) | 1479.83i | 0.0691242i | ||||||||
\(772\) | − 3143.78i | − 0.146564i | ||||||||
\(773\) | 29559.8 | 1.37541 | 0.687706 | − | 0.725990i | \(-0.258618\pi\) | ||||
0.687706 | + | 0.725990i | \(0.258618\pi\) | |||||||
\(774\) | 10829.0 | 0.502896 | ||||||||
\(775\) | − 145.527i | − 0.00674512i | ||||||||
\(776\) | − 18633.6i | − 0.861996i | ||||||||
\(777\) | 71350.2i | 3.29430i | ||||||||
\(778\) | 45891.2 | 2.11475 | ||||||||
\(779\) | − 11152.0i | − 0.512917i | ||||||||
\(780\) | 25199.3 | 1.15677 | ||||||||
\(781\) | 1687.58 | 0.0773193 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9206.75 | 0.420208 | ||||||||
\(784\) | −5582.84 | −0.254320 | ||||||||
\(785\) | − 29743.6i | − 1.35235i | ||||||||
\(786\) | −4341.86 | −0.197034 | ||||||||
\(787\) | 28038.7i | 1.26998i | 0.772521 | + | 0.634989i | \(0.218995\pi\) | ||||
−0.772521 | + | 0.634989i | \(0.781005\pi\) | |||||||
\(788\) | 11271.6i | 0.509563i | ||||||||
\(789\) | 10267.1i | 0.463269i | ||||||||
\(790\) | −53099.2 | −2.39137 | ||||||||
\(791\) | −10832.6 | −0.486934 | ||||||||
\(792\) | − 2753.67i | − 0.123545i | ||||||||
\(793\) | 7426.75i | 0.332574i | ||||||||
\(794\) | − 13438.7i | − 0.600659i | ||||||||
\(795\) | 9486.68 | 0.423217 | ||||||||
\(796\) | − 25802.3i | − 1.14892i | ||||||||
\(797\) | −5320.45 | −0.236462 | −0.118231 | − | 0.992986i | \(-0.537722\pi\) | ||||
−0.118231 | + | 0.992986i | \(0.537722\pi\) | |||||||
\(798\) | −53392.2 | −2.36850 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2395.05 | −0.105847 | ||||||||
\(801\) | 15175.4 | 0.669409 | ||||||||
\(802\) | 30437.7i | 1.34014i | ||||||||
\(803\) | −1131.35 | −0.0497194 | ||||||||
\(804\) | 99089.4i | 4.34653i | ||||||||
\(805\) | − 23984.4i | − 1.05011i | ||||||||
\(806\) | 800.673i | 0.0349907i | ||||||||
\(807\) | −23523.6 | −1.02611 | ||||||||
\(808\) | −23513.8 | −1.02378 | ||||||||
\(809\) | 30934.0i | 1.34435i | 0.740390 | + | 0.672177i | \(0.234641\pi\) | ||||
−0.740390 | + | 0.672177i | \(0.765359\pi\) | |||||||
\(810\) | 33255.3i | 1.44256i | ||||||||
\(811\) | 40364.5i | 1.74771i | 0.486189 | + | 0.873854i | \(0.338387\pi\) | ||||
−0.486189 | + | 0.873854i | \(0.661613\pi\) | |||||||
\(812\) | −103314. | −4.46504 | ||||||||
\(813\) | − 3221.10i | − 0.138953i | ||||||||
\(814\) | 5424.94 | 0.233592 | ||||||||
\(815\) | −23376.9 | −1.00473 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4258.66 | −0.182364 | ||||||||
\(818\) | 41434.8 | 1.77107 | ||||||||
\(819\) | 16350.9i | 0.697616i | ||||||||
\(820\) | −32030.6 | −1.36409 | ||||||||
\(821\) | − 19799.7i | − 0.841672i | −0.907137 | − | 0.420836i | \(-0.861737\pi\) | ||||
0.907137 | − | 0.420836i | \(-0.138263\pi\) | |||||||
\(822\) | 31983.8i | 1.35713i | ||||||||
\(823\) | 18756.4i | 0.794419i | 0.917728 | + | 0.397210i | \(0.130021\pi\) | ||||
−0.917728 | + | 0.397210i | \(0.869979\pi\) | |||||||
\(824\) | −51144.1 | −2.16225 | ||||||||
\(825\) | −421.395 | −0.0177832 | ||||||||
\(826\) | 30428.4i | 1.28177i | ||||||||
\(827\) | 20958.0i | 0.881234i | 0.897695 | + | 0.440617i | \(0.145240\pi\) | ||||
−0.897695 | + | 0.440617i | \(0.854760\pi\) | |||||||
\(828\) | − 33240.0i | − 1.39513i | ||||||||
\(829\) | −31320.3 | −1.31218 | −0.656091 | − | 0.754682i | \(-0.727791\pi\) | ||||
−0.656091 | + | 0.754682i | \(0.727791\pi\) | |||||||
\(830\) | − 78732.4i | − 3.29258i | ||||||||
\(831\) | −63023.7 | −2.63089 | ||||||||
\(832\) | 15816.2 | 0.659049 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 75333.0 | 3.12778 | ||||||||
\(835\) | 25970.8 | 1.07636 | ||||||||
\(836\) | 2571.23i | 0.106373i | ||||||||
\(837\) | 275.021 | 0.0113574 | ||||||||
\(838\) | 4715.82i | 0.194398i | ||||||||
\(839\) | − 30290.6i | − 1.24642i | −0.782053 | − | 0.623212i | \(-0.785827\pi\) | ||||
0.782053 | − | 0.623212i | \(-0.214173\pi\) | |||||||
\(840\) | 64586.8i | 2.65292i | ||||||||
\(841\) | −57499.9 | −2.35762 | ||||||||
\(842\) | 15198.5 | 0.622060 | ||||||||
\(843\) | − 25346.1i | − 1.03555i | ||||||||
\(844\) | − 15242.8i | − 0.621659i | ||||||||
\(845\) | − 21391.0i | − 0.870855i | ||||||||
\(846\) | 3443.29 | 0.139933 | ||||||||
\(847\) | 34493.7i | 1.39931i | ||||||||
\(848\) | −1716.29 | −0.0695021 | ||||||||
\(849\) | 60692.2 | 2.45342 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27580.3 | 1.11098 | ||||||||
\(852\) | −54856.6 | −2.20582 | ||||||||
\(853\) | 21111.8i | 0.847425i | 0.905797 | + | 0.423712i | \(0.139273\pi\) | ||||
−0.905797 | + | 0.423712i | \(0.860727\pi\) | |||||||
\(854\) | −45195.9 | −1.81097 | ||||||||
\(855\) | 21334.2i | 0.853348i | ||||||||
\(856\) | − 892.277i | − 0.0356278i | ||||||||
\(857\) | − 39983.0i | − 1.59369i | −0.604184 | − | 0.796845i | \(-0.706501\pi\) | ||||
0.604184 | − | 0.796845i | \(-0.293499\pi\) | |||||||
\(858\) | 2318.48 | 0.0922512 | ||||||||
\(859\) | 39503.3 | 1.56907 | 0.784537 | − | 0.620082i | \(-0.212901\pi\) | ||||
0.784537 | + | 0.620082i | \(0.212901\pi\) | |||||||
\(860\) | 12231.6i | 0.484995i | ||||||||
\(861\) | − 38759.6i | − 1.53418i | ||||||||
\(862\) | 10989.2i | 0.434217i | ||||||||
\(863\) | 26019.9 | 1.02634 | 0.513168 | − | 0.858288i | \(-0.328472\pi\) | ||||
0.513168 | + | 0.858288i | \(0.328472\pi\) | |||||||
\(864\) | − 4526.26i | − 0.178225i | ||||||||
\(865\) | 37080.4 | 1.45754 | ||||||||
\(866\) | −27376.1 | −1.07422 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3086.17 | −0.120681 | ||||||||
\(869\) | −3094.33 | −0.120791 | ||||||||
\(870\) | 121550.i | 4.73669i | ||||||||
\(871\) | −18841.4 | −0.732968 | ||||||||
\(872\) | − 14376.7i | − 0.558323i | ||||||||
\(873\) | − 21392.2i | − 0.829343i | ||||||||
\(874\) | 20638.7i | 0.798757i | ||||||||
\(875\) | −33613.8 | −1.29869 | ||||||||
\(876\) | 36775.9 | 1.41843 | ||||||||
\(877\) | 15038.3i | 0.579027i | 0.957174 | + | 0.289514i | \(0.0934935\pi\) | ||||
−0.957174 | + | 0.289514i | \(0.906506\pi\) | |||||||
\(878\) | 13519.5i | 0.519660i | ||||||||
\(879\) | − 8942.30i | − 0.343136i | ||||||||
\(880\) | 636.004 | 0.0243633 | ||||||||
\(881\) | 18334.3i | 0.701133i | 0.936538 | + | 0.350567i | \(0.114011\pi\) | ||||
−0.936538 | + | 0.350567i | \(0.885989\pi\) | |||||||
\(882\) | −49487.5 | −1.88927 | ||||||||
\(883\) | 26659.5 | 1.01604 | 0.508020 | − | 0.861345i | \(-0.330378\pi\) | ||||
0.508020 | + | 0.861345i | \(0.330378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22674.5 | 0.861237 | ||||||||
\(886\) | 38570.1 | 1.46251 | ||||||||
\(887\) | − 11473.7i | − 0.434327i | −0.976135 | − | 0.217163i | \(-0.930320\pi\) | ||||
0.976135 | − | 0.217163i | \(-0.0696804\pi\) | |||||||
\(888\) | −74270.1 | −2.80669 | ||||||||
\(889\) | − 15571.3i | − 0.587450i | ||||||||
\(890\) | 27062.7i | 1.01926i | ||||||||
\(891\) | 1937.94i | 0.0728656i | ||||||||
\(892\) | 7862.01 | 0.295111 | ||||||||
\(893\) | −1354.12 | −0.0507436 | ||||||||
\(894\) | − 91983.0i | − 3.44113i | ||||||||
\(895\) | − 9654.36i | − 0.360569i | ||||||||
\(896\) | 66850.7i | 2.49255i | ||||||||
\(897\) | 11787.1 | 0.438752 | ||||||||
\(898\) | − 72344.6i | − 2.68838i | ||||||||
\(899\) | −2446.16 | −0.0907498 | ||||||||
\(900\) | 7345.03 | 0.272038 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −2946.99 | −0.108785 | ||||||||
\(903\) | −14801.3 | −0.545466 | ||||||||
\(904\) | − 11276.0i | − 0.414860i | ||||||||
\(905\) | 39997.5 | 1.46913 | ||||||||
\(906\) | 47858.8i | 1.75497i | ||||||||
\(907\) | − 20361.6i | − 0.745421i | −0.927948 | − | 0.372710i | \(-0.878429\pi\) | ||||
0.927948 | − | 0.372710i | \(-0.121571\pi\) | |||||||
\(908\) | 29120.5i | 1.06432i | ||||||||
\(909\) | −26994.8 | −0.984995 | ||||||||
\(910\) | −29159.1 | −1.06221 | ||||||||
\(911\) | − 19261.9i | − 0.700523i | −0.936652 | − | 0.350262i | \(-0.886093\pi\) | ||||
0.936652 | − | 0.350262i | \(-0.113907\pi\) | |||||||
\(912\) | − 7198.03i | − 0.261349i | ||||||||
\(913\) | − 4588.09i | − 0.166313i | ||||||||
\(914\) | −75000.3 | −2.71421 | ||||||||
\(915\) | 33678.9i | 1.21682i | ||||||||
\(916\) | −59931.7 | −2.16179 | ||||||||
\(917\) | 3182.18 | 0.114596 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21191.8 | −0.760666 | −0.380333 | − | 0.924850i | \(-0.624191\pi\) | ||||
−0.380333 | + | 0.924850i | \(0.624191\pi\) | |||||||
\(920\) | 24965.9 | 0.894677 | ||||||||
\(921\) | 6605.76i | 0.236338i | ||||||||
\(922\) | 65697.0 | 2.34665 | ||||||||
\(923\) | − 10430.7i | − 0.371973i | ||||||||
\(924\) | 8936.49i | 0.318170i | ||||||||
\(925\) | 6094.40i | 0.216630i | ||||||||
\(926\) | 37703.4 | 1.33802 | ||||||||
\(927\) | −58715.6 | −2.08034 | ||||||||
\(928\) | 40258.5i | 1.42409i | ||||||||
\(929\) | 40815.0i | 1.44144i | 0.693227 | + | 0.720719i | \(0.256188\pi\) | ||||
−0.693227 | + | 0.720719i | \(0.743812\pi\) | |||||||
\(930\) | 3630.90i | 0.128024i | ||||||||
\(931\) | 19461.7 | 0.685102 | ||||||||
\(932\) | 62434.5i | 2.19432i | ||||||||
\(933\) | 53370.4 | 1.87274 | ||||||||
\(934\) | 40090.9 | 1.40451 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −17020.1 | −0.594358 | ||||||||
\(937\) | 38439.1 | 1.34018 | 0.670092 | − | 0.742278i | \(-0.266255\pi\) | ||||
0.670092 | + | 0.742278i | \(0.266255\pi\) | |||||||
\(938\) | − 114660.i | − 3.99124i | ||||||||
\(939\) | −26264.9 | −0.912804 | ||||||||
\(940\) | 3889.28i | 0.134951i | ||||||||
\(941\) | − 2244.08i | − 0.0777415i | −0.999244 | − | 0.0388708i | \(-0.987624\pi\) | ||||
0.999244 | − | 0.0388708i | \(-0.0123761\pi\) | |||||||
\(942\) | 88955.6i | 3.07678i | ||||||||
\(943\) | −14982.5 | −0.517388 | ||||||||
\(944\) | −4102.18 | −0.141435 | ||||||||
\(945\) | 10015.8i | 0.344776i | ||||||||
\(946\) | 1125.38i | 0.0386778i | ||||||||
\(947\) | 42289.0i | 1.45112i | 0.688160 | + | 0.725559i | \(0.258419\pi\) | ||||
−0.688160 | + | 0.725559i | \(0.741581\pi\) | |||||||
\(948\) | 100584. | 3.44602 | ||||||||
\(949\) | 6992.76i | 0.239193i | ||||||||
\(950\) | −4560.51 | −0.155750 | ||||||||
\(951\) | −15764.7 | −0.537546 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37426.2 | 1.27214 | 0.636072 | − | 0.771629i | \(-0.280558\pi\) | ||||
0.636072 | + | 0.771629i | \(0.280558\pi\) | |||||||
\(954\) | −15213.6 | −0.516309 | ||||||||
\(955\) | 15950.4i | 0.540464i | ||||||||
\(956\) | 73263.0 | 2.47855 | ||||||||
\(957\) | 7083.25i | 0.239257i | ||||||||
\(958\) | − 29527.0i | − 0.995799i | ||||||||
\(959\) | − 23441.2i | − 0.789317i | ||||||||
\(960\) | 71723.5 | 2.41132 | ||||||||
\(961\) | 29717.9 | 0.997547 | ||||||||
\(962\) | − 33530.8i | − 1.12378i | ||||||||
\(963\) | − 1024.37i | − 0.0342782i | ||||||||
\(964\) | 18918.3i | 0.632072i | ||||||||
\(965\) | 2710.80 | 0.0904286 | ||||||||
\(966\) | 71731.1i | 2.38914i | ||||||||
\(967\) | −1088.56 | −0.0362003 | −0.0181001 | − | 0.999836i | \(-0.505762\pi\) | ||||
−0.0181001 | + | 0.999836i | \(0.505762\pi\) | |||||||
\(968\) | −35905.4 | −1.19219 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38149.3 | 1.26278 | ||||||||
\(971\) | −39506.5 | −1.30569 | −0.652845 | − | 0.757491i | \(-0.726425\pi\) | ||||
−0.652845 | + | 0.757491i | \(0.726425\pi\) | |||||||
\(972\) | − 75000.6i | − 2.47494i | ||||||||
\(973\) | −55212.1 | −1.81914 | ||||||||
\(974\) | − 34270.8i | − 1.12742i | ||||||||
\(975\) | 2604.59i | 0.0855525i | ||||||||
\(976\) | − 6093.05i | − 0.199830i | ||||||||
\(977\) | 43326.8 | 1.41878 | 0.709389 | − | 0.704817i | \(-0.248971\pi\) | ||||
0.709389 | + | 0.704817i | \(0.248971\pi\) | |||||||
\(978\) | 69914.4 | 2.28591 | ||||||||
\(979\) | 1577.07i | 0.0514845i | ||||||||
\(980\) | − 55897.3i | − 1.82202i | ||||||||
\(981\) | − 16505.1i | − 0.537174i | ||||||||
\(982\) | 31169.3 | 1.01288 | ||||||||
\(983\) | − 10664.1i | − 0.346014i | −0.984921 | − | 0.173007i | \(-0.944652\pi\) | ||||
0.984921 | − | 0.173007i | \(-0.0553483\pi\) | |||||||
\(984\) | 40345.9 | 1.30709 | ||||||||
\(985\) | −9719.22 | −0.314396 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4706.35 | −0.151778 | ||||||||
\(988\) | 15892.4 | 0.511747 | ||||||||
\(989\) | 5721.42i | 0.183954i | ||||||||
\(990\) | 5637.69 | 0.180987 | ||||||||
\(991\) | − 15461.4i | − 0.495609i | −0.968810 | − | 0.247804i | \(-0.920291\pi\) | ||||
0.968810 | − | 0.247804i | \(-0.0797090\pi\) | |||||||
\(992\) | 1202.59i | 0.0384902i | ||||||||
\(993\) | − 68879.2i | − 2.20122i | ||||||||
\(994\) | 63476.7 | 2.02551 | ||||||||
\(995\) | 22248.6 | 0.708871 | ||||||||
\(996\) | 149141.i | 4.74469i | ||||||||
\(997\) | 46061.1i | 1.46316i | 0.681756 | + | 0.731579i | \(0.261216\pi\) | ||||
−0.681756 | + | 0.731579i | \(0.738784\pi\) | |||||||
\(998\) | − 83713.7i | − 2.65522i | ||||||||
\(999\) | −11517.4 | −0.364760 |
(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 | 289.4.b.b.288.2 | 6 | ||
17.4 | even | 4 | 289.4.a.b.1.3 | 3 | |||
17.13 | even | 4 | 17.4.a.b.1.3 | ✓ | 3 | ||
17.16 | even | 2 | inner | 289.4.b.b.288.1 | 6 | ||
51.47 | odd | 4 | 153.4.a.g.1.1 | 3 | |||
68.47 | odd | 4 | 272.4.a.h.1.3 | 3 | |||
85.13 | odd | 4 | 425.4.b.f.324.2 | 6 | |||
85.47 | odd | 4 | 425.4.b.f.324.5 | 6 | |||
85.64 | even | 4 | 425.4.a.g.1.1 | 3 | |||
119.13 | odd | 4 | 833.4.a.d.1.3 | 3 | |||
136.13 | even | 4 | 1088.4.a.v.1.3 | 3 | |||
136.115 | odd | 4 | 1088.4.a.x.1.1 | 3 | |||
187.98 | odd | 4 | 2057.4.a.e.1.1 | 3 | |||
204.47 | even | 4 | 2448.4.a.bi.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.3 | ✓ | 3 | 17.13 | even | 4 | ||
153.4.a.g.1.1 | 3 | 51.47 | odd | 4 | |||
272.4.a.h.1.3 | 3 | 68.47 | odd | 4 | |||
289.4.a.b.1.3 | 3 | 17.4 | even | 4 | |||
289.4.b.b.288.1 | 6 | 17.16 | even | 2 | inner | ||
289.4.b.b.288.2 | 6 | 1.1 | even | 1 | trivial | ||
425.4.a.g.1.1 | 3 | 85.64 | even | 4 | |||
425.4.b.f.324.2 | 6 | 85.13 | odd | 4 | |||
425.4.b.f.324.5 | 6 | 85.47 | odd | 4 | |||
833.4.a.d.1.3 | 3 | 119.13 | odd | 4 | |||
1088.4.a.v.1.3 | 3 | 136.13 | even | 4 | |||
1088.4.a.x.1.1 | 3 | 136.115 | odd | 4 | |||
2057.4.a.e.1.1 | 3 | 187.98 | odd | 4 | |||
2448.4.a.bi.1.3 | 3 | 204.47 | even | 4 |