Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [56,3,Mod(41,56)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(56, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("56.41");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.c (of order \(2\), degree \(1\), 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: | \(1.52588948042\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.1 | ||
Root | \(-1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 56.41 |
Dual form | 56.3.c.a.41.4 |
$q$-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 \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(29\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.69552i | − | 1.23184i | −0.787809 | − | 0.615920i | \(-0.788785\pi\) | ||
0.787809 | − | 0.615920i | \(-0.211215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.634051i | − | 0.126810i | −0.997988 | − | 0.0634051i | \(-0.979804\pi\) | ||
0.997988 | − | 0.0634051i | \(-0.0201960\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.82843 | − | 6.75699i | −0.261204 | − | 0.965284i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.65685 | −0.517428 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.3137 | 1.21034 | 0.605169 | − | 0.796097i | \(-0.293106\pi\) | ||||
0.605169 | + | 0.796097i | \(0.293106\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.5391i | 1.65685i | 0.560100 | + | 0.828425i | \(0.310763\pi\) | ||||
−0.560100 | + | 0.828425i | \(0.689237\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34315 | −0.156210 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.12293i | − | 0.360173i | −0.983651 | − | 0.180086i | \(-0.942362\pi\) | ||
0.983651 | − | 0.180086i | \(-0.0576377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.7457i | 1.03925i | 0.854395 | + | 0.519623i | \(0.173928\pi\) | ||||
−0.854395 | + | 0.519623i | \(0.826072\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −24.9706 | + | 6.75699i | −1.18907 | + | 0.321761i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.6274 | −1.24467 | −0.622335 | − | 0.782751i | \(-0.713816\pi\) | ||||
−0.622335 | + | 0.782751i | \(0.713816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.5980 | 0.983919 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 16.0502i | − | 0.594451i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.3137 | 1.28668 | 0.643340 | − | 0.765581i | \(-0.277548\pi\) | ||||
0.643340 | + | 0.765581i | \(0.277548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.9050i | 0.674355i | 0.941441 | + | 0.337178i | \(0.109472\pi\) | ||||
−0.941441 | + | 0.337178i | \(0.890528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 49.2011i | − | 1.49094i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.28427 | + | 1.15932i | −0.122408 | + | 0.0331233i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −23.9411 | −0.647057 | −0.323529 | − | 0.946218i | \(-0.604869\pi\) | ||||
−0.323529 | + | 0.946218i | \(0.604869\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 79.5980 | 2.04097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 70.1061i | − | 1.70990i | −0.518707 | − | 0.854952i | \(-0.673587\pi\) | ||
0.518707 | − | 0.854952i | \(-0.326413\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −46.0000 | −1.06977 | −0.534884 | − | 0.844926i | \(-0.679645\pi\) | ||||
−0.534884 | + | 0.844926i | \(0.679645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.95268i | 0.0656151i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.05053i | 0.0223517i | 0.999938 | + | 0.0111758i | \(0.00355746\pi\) | ||||
−0.999938 | + | 0.0111758i | \(0.996443\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −42.3137 | + | 24.7093i | −0.863545 | + | 0.504272i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.6274 | −0.443675 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −15.3726 | −0.290049 | −0.145024 | − | 0.989428i | \(-0.546326\pi\) | ||||
−0.145024 | + | 0.989428i | \(0.546326\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.44157i | − | 0.153483i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 72.9706 | 1.28019 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.8909i | 0.252387i | 0.992006 | + | 0.126194i | \(0.0402761\pi\) | ||||
−0.992006 | + | 0.126194i | \(0.959724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 86.7903i | 1.42279i | 0.702792 | + | 0.711396i | \(0.251937\pi\) | ||||
−0.702792 | + | 0.711396i | \(0.748063\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.51472 | + | 31.4663i | 0.135154 | + | 0.499465i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.6569 | 0.210105 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24.6274 | 0.367573 | 0.183787 | − | 0.982966i | \(-0.441164\pi\) | ||||
0.183787 | + | 0.982966i | \(0.441164\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 105.793i | 1.53323i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45.0294 | −0.634217 | −0.317109 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317109 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 51.7373i | 0.708730i | 0.935107 | + | 0.354365i | \(0.115303\pi\) | ||||
−0.935107 | + | 0.354365i | \(0.884697\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 90.9023i | − | 1.21203i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.3431 | − | 89.9605i | −0.316145 | − | 1.16832i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33.7157 | −0.426781 | −0.213391 | − | 0.976967i | \(-0.568451\pi\) | ||||
−0.213391 | + | 0.976967i | \(0.568451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.225 | −1.24970 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 77.3883i | 0.932389i | 0.884682 | + | 0.466195i | \(0.154375\pi\) | ||||
−0.884682 | + | 0.466195i | \(0.845625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.88225 | −0.0456735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 137.893i | − | 1.58498i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 78.7652i | 0.885002i | 0.896768 | + | 0.442501i | \(0.145909\pi\) | ||||
−0.896768 | + | 0.442501i | \(0.854091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 145.539 | − | 39.3826i | 1.59933 | − | 0.432776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 77.2548 | 0.830697 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.5198 | 0.131787 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 90.1781i | − | 0.929671i | −0.885397 | − | 0.464836i | \(-0.846113\pi\) | ||
0.885397 | − | 0.464836i | \(-0.153887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −62.0000 | −0.626263 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 129.651i | − | 1.28367i | −0.766842 | − | 0.641836i | \(-0.778173\pi\) | ||
0.766842 | − | 0.641836i | \(-0.221827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 34.4190i | − | 0.334165i | −0.985943 | − | 0.167082i | \(-0.946565\pi\) | ||
0.985943 | − | 0.167082i | \(-0.0534346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.28427 | + | 15.8326i | 0.0408026 | + | 0.150787i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 149.882 | 1.40077 | 0.700384 | − | 0.713766i | \(-0.253012\pi\) | ||||
0.700384 | + | 0.713766i | \(0.253012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −67.2548 | −0.617017 | −0.308508 | − | 0.951222i | \(-0.599830\pi\) | ||||
−0.308508 | + | 0.951222i | \(0.599830\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 88.4749i | 0.797071i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 70.2843 | 0.621985 | 0.310992 | − | 0.950412i | \(-0.399339\pi\) | ||||
0.310992 | + | 0.950412i | \(0.399339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.1512i | 0.157837i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 100.304i | − | 0.857301i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −41.3726 | + | 11.1953i | −0.347669 | + | 0.0940785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56.2548 | 0.464916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −259.078 | −2.10633 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 31.4476i | − | 0.251581i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −93.7645 | −0.738303 | −0.369152 | − | 0.929369i | \(-0.620352\pi\) | ||||
−0.369152 | + | 0.929369i | \(0.620352\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 169.994i | 1.31778i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 146.226i | 1.11623i | 0.829763 | + | 0.558116i | \(0.188475\pi\) | ||||
−0.829763 | + | 0.558116i | \(0.811525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 133.421 | − | 36.1036i | 1.00317 | − | 0.271455i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.1766 | −0.0753824 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −149.765 | −1.09317 | −0.546586 | − | 0.837403i | \(-0.684073\pi\) | ||||
−0.546586 | + | 0.837403i | \(0.684073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 120.249i | − | 0.865100i | −0.901610 | − | 0.432550i | \(-0.857614\pi\) | ||
0.901610 | − | 0.432550i | \(-0.142386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.88225 | 0.0275337 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 286.765i | 2.00535i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 23.6588i | − | 0.163164i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 91.3137 | + | 156.371i | 0.621182 | + | 1.06375i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 33.7645 | 0.226607 | 0.113304 | − | 0.993560i | \(-0.463857\pi\) | ||||
0.113304 | + | 0.993560i | \(0.463857\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 144.627 | 0.957797 | 0.478899 | − | 0.877870i | \(-0.341036\pi\) | ||||
0.478899 | + | 0.877870i | \(0.341036\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 28.5136i | 0.186363i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.2548 | 0.0855151 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 128.818i | − | 0.820496i | −0.911974 | − | 0.410248i | \(-0.865442\pi\) | ||
0.911974 | − | 0.410248i | \(-0.134558\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 56.8097i | 0.357293i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 52.3431 | + | 193.435i | 0.325113 | + | 1.20146i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 57.4315 | 0.352340 | 0.176170 | − | 0.984360i | \(-0.443629\pi\) | ||||
0.176170 | + | 0.984360i | \(0.443629\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −31.1960 | −0.189066 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 229.122i | − | 1.37199i | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||
0.727607 | − | 0.685994i | \(-0.240633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −294.931 | −1.74515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 91.9528i | − | 0.537736i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 123.310i | − | 0.712776i | −0.934338 | − | 0.356388i | \(-0.884008\pi\) | ||
0.934338 | − | 0.356388i | \(-0.115992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −44.9756 | − | 166.208i | −0.257004 | − | 0.949761i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 55.0294 | 0.310901 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −271.941 | −1.51922 | −0.759612 | − | 0.650376i | \(-0.774611\pi\) | ||||
−0.759612 | + | 0.650376i | \(0.774611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 30.6333i | − | 0.169245i | −0.996413 | − | 0.0846225i | \(-0.973032\pi\) | ||
0.996413 | − | 0.0846225i | \(-0.0269684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 320.735 | 1.75265 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.1799i | 0.0820534i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 81.5190i | − | 0.435930i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −108.451 | + | 29.3466i | −0.573814 | + | 0.155273i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −69.5980 | −0.364387 | −0.182194 | − | 0.983263i | \(-0.558320\pi\) | ||||
−0.182194 | + | 0.983263i | \(0.558320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 279.421 | 1.44778 | 0.723890 | − | 0.689916i | \(-0.242353\pi\) | ||||
0.723890 | + | 0.689916i | \(0.242353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 50.4692i | − | 0.258816i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 102.451 | 0.520055 | 0.260027 | − | 0.965601i | \(-0.416268\pi\) | ||||
0.260027 | + | 0.965601i | \(0.416268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 161.950i | − | 0.813820i | −0.913468 | − | 0.406910i | \(-0.866606\pi\) | ||
0.913468 | − | 0.406910i | \(-0.133394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 91.0111i | − | 0.452791i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −68.2254 | − | 252.128i | −0.336086 | − | 1.24201i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −44.4508 | −0.216833 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 133.314 | 0.644028 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 262.888i | 1.25784i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −51.0193 | −0.241798 | −0.120899 | − | 0.992665i | \(-0.538578\pi\) | ||||
−0.120899 | + | 0.992665i | \(0.538578\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 166.407i | 0.781254i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.1663i | 0.135657i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 141.255 | − | 38.2233i | 0.650944 | − | 0.176144i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 191.196 | 0.873041 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 131.882 | 0.596752 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 221.296i | 0.992358i | 0.868220 | + | 0.496179i | \(0.165264\pi\) | ||||
−0.868220 | + | 0.496179i | \(0.834736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −114.549 | −0.509108 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 101.047i | − | 0.445141i | −0.974917 | − | 0.222571i | \(-0.928555\pi\) | ||
0.974917 | − | 0.222571i | \(-0.0714448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 170.193i | 0.743200i | 0.928393 | + | 0.371600i | \(0.121191\pi\) | ||||
−0.928393 | + | 0.371600i | \(0.878809\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −332.451 | + | 89.9605i | −1.43918 | + | 0.389440i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −451.019 | −1.93571 | −0.967853 | − | 0.251518i | \(-0.919070\pi\) | ||||
−0.967853 | + | 0.251518i | \(0.919070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.666089 | 0.00283442 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 124.597i | 0.525726i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 219.137 | 0.916892 | 0.458446 | − | 0.888722i | \(-0.348406\pi\) | ||||
0.458446 | + | 0.888722i | \(0.348406\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 325.386i | − | 1.35015i | −0.737750 | − | 0.675074i | \(-0.764112\pi\) | ||
0.737750 | − | 0.675074i | \(-0.235888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 229.629i | 0.944974i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.6670 | + | 26.8290i | 0.0639468 | + | 0.109506i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −425.304 | −1.72188 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 285.990 | 1.14855 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 260.063i | 1.03611i | 0.855348 | + | 0.518054i | \(0.173343\pi\) | ||||
−0.855348 | + | 0.518054i | \(0.826657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −381.137 | −1.50647 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.3469i | 0.0562625i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 184.558i | 0.718126i | 0.933313 | + | 0.359063i | \(0.116904\pi\) | ||||
−0.933313 | + | 0.359063i | \(0.883096\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 43.7746 | + | 161.770i | 0.169014 | + | 0.624594i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −173.765 | −0.665764 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 246.853 | 0.938604 | 0.469302 | − | 0.883038i | \(-0.344506\pi\) | ||||
0.469302 | + | 0.883038i | \(0.344506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.74700i | 0.0367811i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 291.078 | 1.09018 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 105.159i | 0.390926i | 0.980711 | + | 0.195463i | \(0.0626210\pi\) | ||||
−0.980711 | + | 0.195463i | \(0.937379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 71.8093i | − | 0.264979i | −0.991184 | − | 0.132489i | \(-0.957703\pi\) | ||
0.991184 | − | 0.132489i | \(-0.0422971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −145.539 | − | 537.842i | −0.533110 | − | 1.97012i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 327.490 | 1.19087 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 402.098 | 1.45162 | 0.725808 | − | 0.687898i | \(-0.241466\pi\) | ||||
0.725808 | + | 0.687898i | \(0.241466\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 97.3516i | − | 0.348930i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 321.529 | 1.14423 | 0.572116 | − | 0.820173i | \(-0.306123\pi\) | ||||
0.572116 | + | 0.820173i | \(0.306123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 485.561i | 1.71576i | 0.513847 | + | 0.857882i | \(0.328220\pi\) | ||||
−0.513847 | + | 0.857882i | \(0.671780\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 46.2670i | − | 0.162340i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −473.706 | + | 128.184i | −1.65054 | + | 0.446634i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 251.510 | 0.870276 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −333.255 | −1.14521 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 480.218i | − | 1.63897i | −0.573100 | − | 0.819485i | \(-0.694259\pi\) | ||
0.573100 | − | 0.819485i | \(-0.305741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.44156 | 0.0320053 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 213.687i | − | 0.719486i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 616.608i | − | 2.06223i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 84.1076 | + | 310.821i | 0.279427 | + | 1.03263i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −479.127 | −1.58128 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 55.0294 | 0.180424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1876i | 0.0429564i | 0.999769 | + | 0.0214782i | \(0.00683725\pi\) | ||||
−0.999769 | + | 0.0214782i | \(0.993163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −127.196 | −0.411637 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 393.211i | − | 1.26434i | −0.774829 | − | 0.632171i | \(-0.782164\pi\) | ||
0.774829 | − | 0.632171i | \(-0.217836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 221.694i | − | 0.708287i | −0.935191 | − | 0.354143i | \(-0.884772\pi\) | ||
0.935191 | − | 0.354143i | \(-0.115228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19.9512 | − | 5.39876i | 0.0633372 | − | 0.0171389i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −94.5685 | −0.298323 | −0.149162 | − | 0.988813i | \(-0.547658\pi\) | ||||
−0.149162 | + | 0.988813i | \(0.547658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 496.784 | 1.55732 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 553.893i | − | 1.72552i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 120.902 | 0.374308 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 529.817i | 1.63021i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 248.541i | 0.760066i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.09841 | − | 1.92082i | 0.0215757 | − | 0.00583835i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −190.333 | −0.575024 | −0.287512 | − | 0.957777i | \(-0.592828\pi\) | ||||
−0.287512 | + | 0.957777i | \(0.592828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 111.490 | 0.334806 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 15.6150i | − | 0.0466120i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −430.735 | −1.27815 | −0.639073 | − | 0.769146i | \(-0.720682\pi\) | ||||
−0.639073 | + | 0.769146i | \(0.720682\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 259.737i | − | 0.766185i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 278.323i | 0.816197i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 244.328 | + | 240.734i | 0.712327 | + | 0.701848i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 67.0782 | 0.194430 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −251.255 | −0.724077 | −0.362039 | − | 0.932163i | \(-0.617919\pi\) | ||||
−0.362039 | + | 0.932163i | \(0.617919\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 78.3487i | − | 0.224495i | −0.993680 | − | 0.112247i | \(-0.964195\pi\) | ||
0.993680 | − | 0.112247i | \(-0.0358049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 345.706 | 0.984916 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 43.9111i | 0.124394i | 0.998064 | + | 0.0621970i | \(0.0198107\pi\) | ||||
−0.998064 | + | 0.0621970i | \(0.980189\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.5509i | 0.0804252i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 41.3726 | + | 152.893i | 0.115890 | + | 0.428272i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 546.431 | 1.52209 | 0.761045 | − | 0.648699i | \(-0.224686\pi\) | ||||
0.761045 | + | 0.648699i | \(0.224686\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −28.8924 | −0.0800342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 207.891i | − | 0.572702i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.8040 | 0.0898741 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 481.505i | 1.31200i | 0.754759 | + | 0.656002i | \(0.227754\pi\) | ||||
−0.754759 | + | 0.656002i | \(0.772246\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 326.474i | 0.884753i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.1076 | + | 103.872i | 0.0757619 | + | 0.279979i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −432.843 | −1.16044 | −0.580218 | − | 0.814461i | \(-0.697033\pi\) | ||||
−0.580218 | + | 0.814461i | \(0.697033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −116.215 | −0.309907 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 803.702i | 2.13184i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −512.607 | −1.35253 | −0.676263 | − | 0.736660i | \(-0.736402\pi\) | ||||
−0.676263 | + | 0.736660i | \(0.736402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 346.508i | 0.909471i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 651.897i | − | 1.70208i | −0.525100 | − | 0.851040i | \(-0.675972\pi\) | ||
0.525100 | − | 0.851040i | \(-0.324028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −57.0395 | + | 15.4348i | −0.148155 | + | 0.0400904i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 214.215 | 0.553528 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −523.352 | −1.34538 | −0.672689 | − | 0.739925i | \(-0.734861\pi\) | ||||
−0.672689 | + | 0.739925i | \(0.734861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 175.284i | 0.448296i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 540.382 | 1.37502 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.3775i | 0.0541202i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.8513i | 0.0399276i | 0.999801 | + | 0.0199638i | \(0.00635510\pi\) | ||||
−0.999801 | + | 0.0199638i | \(0.993645\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −133.421 | − | 493.061i | −0.334389 | − | 1.23574i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7746 | 0.0293631 | 0.0146816 | − | 0.999892i | \(-0.495327\pi\) | ||||
0.0146816 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −450.274 | −1.11731 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 64.1820i | 0.158474i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −318.745 | −0.783158 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 492.483i | − | 1.20411i | −0.798453 | − | 0.602057i | \(-0.794348\pi\) | ||
0.798453 | − | 0.602057i | \(-0.205652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 553.457i | 1.34661i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 100.617 | − | 27.2268i | 0.243625 | − | 0.0659246i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49.0681 | 0.118236 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −444.382 | −1.06566 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 276.946i | − | 0.660970i | −0.943811 | − | 0.330485i | \(-0.892788\pi\) | ||
0.943811 | − | 0.330485i | \(-0.107212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3532 | 0.0340932 | 0.0170466 | − | 0.999855i | \(-0.494574\pi\) | ||||
0.0170466 | + | 0.999855i | \(0.494574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.89216i | − | 0.0115654i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 150.612i | − | 0.354381i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 586.441 | − | 158.690i | 1.37340 | − | 0.371639i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1059.74 | 2.47027 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 250.471 | 0.581139 | 0.290570 | − | 0.956854i | \(-0.406155\pi\) | ||||
0.290570 | + | 0.956854i | \(0.406155\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 656.534i | 1.51625i | 0.652112 | + | 0.758123i | \(0.273883\pi\) | ||||
−0.652112 | + | 0.758123i | \(0.726117\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −87.4315 | −0.200992 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 565.268i | − | 1.29352i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 356.398i | 0.811841i | 0.913908 | + | 0.405921i | \(0.133049\pi\) | ||||
−0.913908 | + | 0.405921i | \(0.866951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 197.049 | − | 115.068i | 0.446823 | − | 0.260924i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 253.785 | 0.572877 | 0.286439 | − | 0.958099i | \(-0.407529\pi\) | ||||
0.286439 | + | 0.958099i | \(0.407529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 49.9411 | 0.112227 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 124.777i | − | 0.279144i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −107.921 | −0.240358 | −0.120179 | − | 0.992752i | \(-0.538347\pi\) | ||||
−0.120179 | + | 0.992752i | \(0.538347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 933.372i | − | 2.06956i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 534.473i | − | 1.17985i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.9706 | − | 92.2792i | −0.0548804 | − | 0.202811i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 143.990 | 0.315076 | 0.157538 | − | 0.987513i | \(-0.449644\pi\) | ||||
0.157538 | + | 0.987513i | \(0.449644\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −98.2742 | −0.214105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 380.728i | − | 0.825875i | −0.910759 | − | 0.412938i | \(-0.864503\pi\) | ||
0.910759 | − | 0.412938i | \(-0.135497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −227.990 | −0.492419 | −0.246209 | − | 0.969217i | \(-0.579185\pi\) | ||||
−0.246209 | + | 0.969217i | \(0.579185\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 48.9835i | − | 0.105341i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 502.917i | 1.07691i | 0.842654 | + | 0.538455i | \(0.180992\pi\) | ||||
−0.842654 | + | 0.538455i | \(0.819008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.0294 | − | 166.407i | −0.0960116 | − | 0.354813i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −476.049 | −1.01072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −612.431 | −1.29478 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 485.704i | 1.02254i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 71.5879 | 0.150079 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 212.637i | 0.443918i | 0.975056 | + | 0.221959i | \(0.0712451\pi\) | ||||
−0.975056 | + | 0.221959i | \(0.928755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 515.669i | − | 1.07208i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 714.843 | − | 193.435i | 1.48001 | − | 0.400487i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −57.1775 | −0.117892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −121.411 | −0.249304 | −0.124652 | − | 0.992200i | \(-0.539782\pi\) | ||||
−0.124652 | + | 0.992200i | \(0.539782\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 212.239i | − | 0.434027i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −130.353 | −0.265485 | −0.132743 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132743 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 228.469i | − | 0.463427i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 39.3111i | 0.0794164i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 82.3330 | + | 304.263i | 0.165660 | + | 0.612200i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 157.980 | 0.316593 | 0.158296 | − | 0.987392i | \(-0.449400\pi\) | ||||
0.158296 | + | 0.987392i | \(0.449400\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −846.725 | −1.69007 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 323.502i | 0.643146i | 0.946885 | + | 0.321573i | \(0.104212\pi\) | ||||
−0.946885 | + | 0.321573i | \(0.895788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −82.2052 | −0.162783 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1089.92i | 2.14975i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 505.723i | − | 0.993563i | −0.867876 | − | 0.496781i | \(-0.834515\pi\) | ||
0.867876 | − | 0.496781i | \(-0.165485\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 349.588 | − | 94.5978i | 0.684125 | − | 0.185123i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 316.922 | 0.617781 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.8234 | −0.0423755 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.9864i | 0.0270531i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −455.696 | −0.878026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 827.833i | 1.58893i | 0.607309 | + | 0.794466i | \(0.292249\pi\) | ||||
−0.607309 | + | 0.794466i | \(0.707751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 114.306i | − | 0.218559i | −0.994011 | − | 0.109279i | \(-0.965146\pi\) | ||
0.994011 | − | 0.109279i | \(-0.0348543\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −614.225 | + | 166.208i | −1.16995 | + | 0.316587i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 128.000 | 0.242884 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 290.529 | 0.549204 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 69.3446i | − | 0.130592i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1510.02 | 2.83306 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 95.0329i | − | 0.177632i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1004.96i | 1.87144i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −563.352 | + | 328.973i | −1.04518 | + | 0.610339i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 529.098 | 0.978001 | 0.489000 | − | 0.872284i | \(-0.337362\pi\) | ||||
0.489000 | + | 0.872284i | \(0.337362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −113.206 | −0.208483 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.6430i | 0.0782440i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −281.314 | −0.514285 | −0.257142 | − | 0.966374i | \(-0.582781\pi\) | ||||
−0.257142 | + | 0.966374i | \(0.582781\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 404.170i | − | 0.736193i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 736.785i | 1.33718i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61.6468 | + | 227.817i | 0.111477 | + | 0.411965i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 56.0975 | 0.101077 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −198.471 | −0.356321 | −0.178161 | − | 0.984001i | \(-0.557015\pi\) | ||||
−0.178161 | + | 0.984001i | \(0.557015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 990.797i | − | 1.77244i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −301.255 | −0.536996 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 98.2933i | 0.174588i | 0.996183 | + | 0.0872942i | \(0.0278220\pi\) | ||||
−0.996183 | + | 0.0872942i | \(0.972178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 44.5638i | − | 0.0788740i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 185.083 | + | 683.979i | 0.326426 | + | 1.20631i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −709.029 | −1.24610 | −0.623049 | − | 0.782183i | \(-0.714106\pi\) | ||||
−0.623049 | + | 0.782183i | \(0.714106\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 462.118 | 0.809313 | 0.404657 | − | 0.914469i | \(-0.367391\pi\) | ||||
0.404657 | + | 0.914469i | \(0.367391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 257.201i | 0.448867i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −704.177 | −1.22465 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 586.571i | 1.01659i | 0.861184 | + | 0.508294i | \(0.169724\pi\) | ||||
−0.861184 | + | 0.508294i | \(0.830276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1032.61i | − | 1.78343i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 522.912 | − | 141.499i | 0.900020 | − | 0.243544i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −204.666 | −0.351057 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −63.5980 | −0.108714 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 441.613i | − | 0.752322i | −0.926554 | − | 0.376161i | \(-0.877244\pi\) | ||
0.926554 | − | 0.376161i | \(-0.122756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −412.784 | −0.700821 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 378.609i | − | 0.640624i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 87.0265i | − | 0.146756i | −0.997304 | − | 0.0733782i | \(-0.976622\pi\) | ||
0.997304 | − | 0.0733782i | \(-0.0233780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.09841 | + | 26.2323i | 0.0119301 | + | 0.0440879i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −598.489 | −1.00249 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 484.108 | 0.808193 | 0.404097 | − | 0.914716i | \(-0.367586\pi\) | ||||
0.404097 | + | 0.914716i | \(0.367586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 904.895i | − | 1.50565i | −0.658221 | − | 0.752825i | \(-0.728691\pi\) | ||
0.658221 | − | 0.752825i | \(-0.271309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −114.686 | −0.190193 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 35.6684i | − | 0.0589561i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 940.980i | − | 1.55021i | −0.631830 | − | 0.775107i | \(-0.717696\pi\) | ||
0.631830 | − | 0.775107i | \(-0.282304\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −931.744 | + | 252.128i | −1.52996 | + | 0.414004i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.6274 | −0.0370334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 240.627 | 0.392541 | 0.196270 | − | 0.980550i | \(-0.437117\pi\) | ||||
0.196270 | + | 0.980550i | \(0.437117\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 164.269i | 0.267104i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 781.716 | 1.26696 | 0.633481 | − | 0.773758i | \(-0.281625\pi\) | ||||
0.633481 | + | 0.773758i | \(0.281625\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.99870i | 0.0161530i | 0.999967 | + | 0.00807649i | \(0.00257085\pi\) | ||||
−0.999967 | + | 0.00807649i | \(0.997429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 459.475i | 0.739895i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 532.215 | − | 144.016i | 0.854278 | − | 0.231166i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 595.010 | 0.952016 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 971.509 | 1.54946 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 146.590i | 0.233052i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 908.538 | 1.43984 | 0.719919 | − | 0.694058i | \(-0.244179\pi\) | ||||
0.719919 | + | 0.694058i | \(0.244179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 188.543i | 0.297856i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 59.4514i | 0.0936243i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −532.215 | − | 911.397i | −0.835503 | − | 1.43077i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 209.696 | 0.328162 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 193.460 | 0.301810 | 0.150905 | − | 0.988548i | \(-0.451781\pi\) | ||||
0.150905 | + | 0.988548i | \(0.451781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 362.412i | − | 0.563627i | −0.959469 | − | 0.281814i | \(-0.909064\pi\) | ||
0.959469 | − | 0.281814i | \(-0.0909360\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 107.785 | 0.167108 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 359.625i | − | 0.555834i | −0.960605 | − | 0.277917i | \(-0.910356\pi\) | ||
0.960605 | − | 0.277917i | \(-0.0896440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 198.253i | 0.305474i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −141.255 | − | 522.010i | −0.216981 | − | 0.801858i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −715.685 | −1.09600 | −0.547998 | − | 0.836480i | \(-0.684610\pi\) | ||||
−0.547998 | + | 0.836480i | \(0.684610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 92.7149 | 0.141549 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 240.933i | − | 0.366717i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −390.431 | −0.592459 | −0.296230 | − | 0.955117i | \(-0.595729\pi\) | ||||
−0.296230 | + | 0.955117i | \(0.595729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 350.474i | 0.530218i | 0.964218 | + | 0.265109i | \(0.0854080\pi\) | ||||
−0.964218 | + | 0.265109i | \(0.914592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 487.373i | − | 0.735103i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.8915 | − | 84.5959i | −0.0344233 | − | 0.127212i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1068.20 | −1.60149 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 817.803 | 1.22243 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1155.50i | 1.72206i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 487.214 | 0.723944 | 0.361972 | − | 0.932189i | \(-0.382104\pi\) | ||||
0.361972 | + | 0.932189i | \(0.382104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 394.802i | − | 0.584892i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 451.742i | 0.667271i | 0.942702 | + | 0.333635i | \(0.108275\pi\) | ||||
−0.942702 | + | 0.333635i | \(0.891725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −609.332 | + | 164.884i | −0.897396 | + | 0.242834i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −373.421 | −0.548343 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −224.745 | −0.329056 | −0.164528 | − | 0.986372i | \(-0.552610\pi\) | ||||
−0.164528 | + | 0.986372i | \(0.552610\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 94.9583i | 0.138625i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 628.950 | 0.915503 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 331.111i | − | 0.480567i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 56.0855i | − | 0.0811657i | −0.999176 | − | 0.0405828i | \(-0.987079\pi\) | ||
0.999176 | − | 0.0405828i | \(-0.0129215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 113.362 | + | 418.933i | 0.163582 | + | 0.604521i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −76.2439 | −0.109703 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −429.255 | −0.615861 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1666.75i | 2.38448i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −769.647 | −1.09793 | −0.548963 | − | 0.835846i | \(-0.684977\pi\) | ||||
−0.548963 | + | 0.835846i | \(0.684977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 472.734i | − | 0.672452i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.46154i | − | 0.00349155i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −876.049 | + | 237.057i | −1.23911 | + | 0.335300i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 465.960 | 0.657207 | 0.328603 | − | 0.944468i | \(-0.393422\pi\) | ||||
0.328603 | + | 0.944468i | \(0.393422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 157.009 | 0.220829 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 598.456i | − | 0.839350i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 181.823 | 0.254298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 809.825i | − | 1.12946i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1051.88i | 1.46298i | 0.681852 | + | 0.731490i | \(0.261175\pi\) | ||||
−0.681852 | + | 0.731490i | \(0.738825\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −232.569 | + | 62.9326i | −0.322564 | + | 0.0872852i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1202.47 | −1.66317 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 917.842 | 1.26599 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 161.080i | 0.221568i | 0.993845 | + | 0.110784i | \(0.0353361\pi\) | ||||
−0.993845 | + | 0.110784i | \(0.964664\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −62.4315 | −0.0856399 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 281.655i | 0.385301i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1438.70i | 1.96275i | 0.192097 | + | 0.981376i | \(0.438471\pi\) | ||||
−0.192097 | + | 0.981376i | \(0.561529\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 99.1472 | − | 57.8975i | 0.134894 | − | 0.0787721i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 327.882 | 0.444888 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1137.39 | 1.53909 | 0.769547 | − | 0.638590i | \(-0.220482\pi\) | ||||
0.769547 | + | 0.638590i | \(0.220482\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1571.72i | 2.12108i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −745.882 | −1.00388 | −0.501940 | − | 0.864903i | \(-0.667380\pi\) | ||||
−0.501940 | + | 0.864903i | \(0.667380\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 21.4084i | − | 0.0287361i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 360.386i | − | 0.482445i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −274.049 | − | 1012.75i | −0.365886 | − | 1.35214i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −153.882 | −0.204903 | −0.102452 | − | 0.994738i | \(-0.532669\pi\) | ||||
−0.102452 | + | 0.994738i | \(0.532669\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 961.068 | 1.27632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 91.7011i | − | 0.121458i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −119.137 | −0.157381 | −0.0786903 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786903 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1408.50i | 1.85573i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1385.20i | − | 1.82024i | −0.414348 | − | 0.910119i | \(-0.635990\pi\) | ||
0.414348 | − | 0.910119i | \(-0.364010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 122.971 | + | 454.440i | 0.161167 | + | 0.595596i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.0791 | 0.0236328 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −320.735 | −0.418168 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 55.9020i | − | 0.0726945i | −0.999339 | − | 0.0363472i | \(-0.988428\pi\) | ||
0.999339 | − | 0.0363472i | \(-0.0115722\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 682.039 | 0.884616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 179.759i | − | 0.232548i | −0.993217 | − | 0.116274i | \(-0.962905\pi\) | ||
0.993217 | − | 0.116274i | \(-0.0370950\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 514.221i | 0.663511i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 597.823 | − | 161.770i | 0.769399 | − | 0.208198i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1384.29 | 1.77701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −599.509 | −0.767617 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 598.892i | − | 0.764868i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −81.6771 | −0.104047 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 208.363i | − | 0.264756i | −0.991199 | − | 0.132378i | \(-0.957739\pi\) | ||
0.991199 | − | 0.132378i | \(-0.0422613\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 912.249i | − | 1.15621i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −128.510 | − | 474.910i | −0.162465 | − | 0.600392i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1869.38 | −2.35735 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36.0202 | 0.0453084 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 237.327i | 0.297776i | 0.988854 | + | 0.148888i | \(0.0475694\pi\) | ||||
−0.988854 | + | 0.148888i | \(0.952431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.43232 | 0.00805047 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 366.798i | − | 0.457925i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 688.815i | 0.857802i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 122.648 | − | 33.1882i | 0.152357 | − | 0.0412276i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 388.617 | 0.481558 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 513.793 | 0.635097 | 0.317548 | − | 0.948242i | \(-0.397140\pi\) | ||||
0.317548 | + | 0.948242i | \(0.397140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 452.373i | − | 0.557797i | −0.960321 | − | 0.278898i | \(-0.910031\pi\) | ||
0.960321 | − | 0.278898i | \(-0.0899692\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −265.373 | −0.326412 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 36.4145i | − | 0.0446803i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 908.302i | − | 1.11175i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −677.754 | + | 183.399i | −0.827539 | + | 0.223930i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1441.04 | −1.75522 | −0.877611 | − | 0.479373i | \(-0.840864\pi\) | ||||
−0.877611 | + | 0.479373i | \(0.840864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1603.66 | −1.94855 | −0.974275 | − | 0.225362i | \(-0.927644\pi\) | ||||
−0.974275 | + | 0.225362i | \(0.927644\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1210.25i | − | 1.46697i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 933.549 | 1.12884 | 0.564419 | − | 0.825488i | \(-0.309100\pi\) | ||||
0.564419 | + | 0.825488i | \(0.309100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 418.809i | 0.505198i | 0.967571 | + | 0.252599i | \(0.0812853\pi\) | ||||
−0.967571 | + | 0.252599i | \(0.918715\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1485.96i | − | 1.78816i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 151.294 | + | 259.084i | 0.181625 | + | 0.311025i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −145.275 | −0.173982 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 335.529 | 0.400871 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 995.689i | − | 1.18676i | −0.804924 | − | 0.593378i | \(-0.797794\pi\) | ||
0.804924 | − | 0.593378i | \(-0.202206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 551.313 | 0.655544 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1188.22i | − | 1.40951i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 187.001i | 0.221303i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −102.858 | − | 380.113i | −0.121438 | − | 0.448776i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1794.40 | 2.11355 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 685.373 | 0.805373 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 315.117i | 0.369422i | 0.982793 | + | 0.184711i | \(0.0591349\pi\) | ||||
−0.982793 | + | 0.184711i | \(0.940865\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −58.3027 | −0.0681903 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 218.287i | 0.254711i | 0.991857 | + | 0.127355i | \(0.0406489\pi\) | ||||
−0.991857 | + | 0.127355i | \(0.959351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1441.76i | 1.67842i | 0.543811 | + | 0.839208i | \(0.316981\pi\) | ||||
−0.543811 | + | 0.839208i | \(0.683019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 473.706 | + | 1750.59i | 0.550181 | + | 2.03320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 874.873 | 1.01376 | 0.506879 | − | 0.862017i | \(-0.330799\pi\) | ||||
0.506879 | + | 0.862017i | \(0.330799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −78.1850 | −0.0903873 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 929.459i | − | 1.07204i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −448.881 | −0.516549 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 530.451i | 0.609014i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 419.946i | 0.481038i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −212.491 | + | 57.4997i | −0.242847 | + | 0.0657139i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1702.65 | 1.94144 | 0.970722 | − | 0.240207i | \(-0.0772153\pi\) | ||||
0.970722 | + | 0.240207i | \(0.0772153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1774.66 | −2.01895 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1018.58i | − | 1.15617i | −0.815978 | − | 0.578083i | \(-0.803801\pi\) | ||
0.815978 | − | 0.578083i | \(-0.196199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1646.04 | 1.86414 | 0.932071 | − | 0.362276i | \(-0.118000\pi\) | ||||
0.932071 | + | 0.362276i | \(0.118000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 34.8915i | − | 0.0394254i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 688.597i | − | 0.776321i | −0.921592 | − | 0.388161i | \(-0.873111\pi\) | ||
0.921592 | − | 0.388161i | \(-0.126889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 171.442 | + | 633.565i | 0.192848 | + | 0.712672i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1347.69 | −1.51255 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.7434 | −0.0232289 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 172.424i | 0.192653i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2278.68 | −2.54034 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 780.043i | 0.867679i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 94.1253i | 0.104468i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1148.65 | − | 310.821i | 1.27203 | − | 0.344210i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.4231 | −0.0214620 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −212.018 | −0.233758 | −0.116879 | − | 0.993146i | \(-0.537289\pi\) | ||||
−0.116879 | + | 0.993146i | \(0.537289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 603.765i | 0.664208i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −601.882 | −0.660683 | −0.330342 | − | 0.943861i | \(-0.607164\pi\) | ||||
−0.330342 | + | 0.943861i | \(0.607164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1030.33i | 1.12851i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 203.362i | − | 0.222254i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 988.049 | − | 267.364i | 1.07748 | − | 0.291564i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1118.34 | 1.21691 | 0.608456 | − | 0.793588i | \(-0.291789\pi\) | ||||
0.608456 | + | 0.793588i | \(0.291789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.7351 | 0.0529154 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 969.892i | − | 1.05080i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −588.903 | −0.636652 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 160.284i | 0.172906i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 401.907i | 0.432623i | 0.976324 | + | 0.216312i | \(0.0694027\pi\) | ||||
−0.976324 | + | 0.216312i | \(0.930597\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −487.902 | − | 835.513i | −0.524063 | − | 0.897437i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1453.12 | −1.55747 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51.6872 | −0.0552804 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1597.84i | 1.70527i | 0.522507 | + | 0.852635i | \(0.324997\pi\) | ||||
−0.522507 | + | 0.852635i | \(0.675003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −819.273 | −0.872496 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1537.71i | 1.63413i | 0.576547 | + | 0.817064i | \(0.304400\pi\) | ||||
−0.576547 | + | 0.817064i | \(0.695600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2006.96i | 2.12827i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.6072 | + | 68.7633i | 0.0196902 | + | 0.0727654i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −320.274 | −0.338199 | −0.169099 | − | 0.985599i | \(-0.554086\pi\) | ||||
−0.169099 | + | 0.985599i | \(0.554086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1114.37 | −1.17426 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 349.480i | 0.367487i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −734.861 | −0.771103 | −0.385552 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385552 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.1286i | 0.0462080i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1835.87i | − | 1.91836i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 273.833 | + | 1011.96i | 0.285541 | + | 1.05522i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 523.981 | 0.545245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −697.980 | −0.724797 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 177.167i | − | 0.183593i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1446.98 | 1.49636 | 0.748179 | − | 0.663497i | \(-0.230928\pi\) | ||||
0.748179 | + | 0.663497i | \(0.230928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 446.794i | − | 0.461088i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 966.084i | − | 0.994937i | −0.867482 | − | 0.497469i | \(-0.834263\pi\) | ||
0.867482 | − | 0.497469i | \(-0.165737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −812.520 | + | 219.866i | −0.835067 | + | 0.225967i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1957.95 | 2.00815 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −609.606 | −0.623957 | −0.311979 | − | 0.950089i | \(-0.600992\pi\) | ||||
−0.311979 | + | 0.950089i | \(0.600992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1048.66i | 1.07115i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 313.196 | 0.319262 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1277.27i | − | 1.29936i | −0.760209 | − | 0.649679i | \(-0.774903\pi\) | ||
0.760209 | − | 0.649679i | \(-0.225097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 64.9590i | − | 0.0659482i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.09841 | − | 26.2323i | −0.00719191 | − | 0.0265778i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1316.86 | 1.33151 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1669.99 | −1.68515 | −0.842577 | − | 0.538575i | \(-0.818963\pi\) | ||||
−0.842577 | + | 0.538575i | \(0.818963\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 703.379i | 0.708338i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −102.685 | −0.103201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 789.952i | − | 0.792329i | −0.918180 | − | 0.396164i | \(-0.870341\pi\) | ||
0.918180 | − | 0.396164i | \(-0.129659\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 384.259i | 0.384644i |
(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 | 56.3.c.a.41.1 | ✓ | 4 | |
3.2 | odd | 2 | 504.3.f.a.433.3 | 4 | |||
4.3 | odd | 2 | 112.3.c.c.97.4 | 4 | |||
5.2 | odd | 4 | 1400.3.p.a.1049.1 | 8 | |||
5.3 | odd | 4 | 1400.3.p.a.1049.8 | 8 | |||
5.4 | even | 2 | 1400.3.f.a.601.4 | 4 | |||
7.2 | even | 3 | 392.3.o.b.129.4 | 8 | |||
7.3 | odd | 6 | 392.3.o.b.313.4 | 8 | |||
7.4 | even | 3 | 392.3.o.b.313.1 | 8 | |||
7.5 | odd | 6 | 392.3.o.b.129.1 | 8 | |||
7.6 | odd | 2 | inner | 56.3.c.a.41.4 | yes | 4 | |
8.3 | odd | 2 | 448.3.c.e.321.1 | 4 | |||
8.5 | even | 2 | 448.3.c.f.321.4 | 4 | |||
12.11 | even | 2 | 1008.3.f.h.433.3 | 4 | |||
21.20 | even | 2 | 504.3.f.a.433.2 | 4 | |||
28.3 | even | 6 | 784.3.s.f.705.1 | 8 | |||
28.11 | odd | 6 | 784.3.s.f.705.4 | 8 | |||
28.19 | even | 6 | 784.3.s.f.129.4 | 8 | |||
28.23 | odd | 6 | 784.3.s.f.129.1 | 8 | |||
28.27 | even | 2 | 112.3.c.c.97.1 | 4 | |||
35.13 | even | 4 | 1400.3.p.a.1049.2 | 8 | |||
35.27 | even | 4 | 1400.3.p.a.1049.7 | 8 | |||
35.34 | odd | 2 | 1400.3.f.a.601.1 | 4 | |||
56.13 | odd | 2 | 448.3.c.f.321.1 | 4 | |||
56.27 | even | 2 | 448.3.c.e.321.4 | 4 | |||
84.83 | odd | 2 | 1008.3.f.h.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.c.a.41.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
56.3.c.a.41.4 | yes | 4 | 7.6 | odd | 2 | inner | |
112.3.c.c.97.1 | 4 | 28.27 | even | 2 | |||
112.3.c.c.97.4 | 4 | 4.3 | odd | 2 | |||
392.3.o.b.129.1 | 8 | 7.5 | odd | 6 | |||
392.3.o.b.129.4 | 8 | 7.2 | even | 3 | |||
392.3.o.b.313.1 | 8 | 7.4 | even | 3 | |||
392.3.o.b.313.4 | 8 | 7.3 | odd | 6 | |||
448.3.c.e.321.1 | 4 | 8.3 | odd | 2 | |||
448.3.c.e.321.4 | 4 | 56.27 | even | 2 | |||
448.3.c.f.321.1 | 4 | 56.13 | odd | 2 | |||
448.3.c.f.321.4 | 4 | 8.5 | even | 2 | |||
504.3.f.a.433.2 | 4 | 21.20 | even | 2 | |||
504.3.f.a.433.3 | 4 | 3.2 | odd | 2 | |||
784.3.s.f.129.1 | 8 | 28.23 | odd | 6 | |||
784.3.s.f.129.4 | 8 | 28.19 | even | 6 | |||
784.3.s.f.705.1 | 8 | 28.3 | even | 6 | |||
784.3.s.f.705.4 | 8 | 28.11 | odd | 6 | |||
1008.3.f.h.433.2 | 4 | 84.83 | odd | 2 | |||
1008.3.f.h.433.3 | 4 | 12.11 | even | 2 | |||
1400.3.f.a.601.1 | 4 | 35.34 | odd | 2 | |||
1400.3.f.a.601.4 | 4 | 5.4 | even | 2 | |||
1400.3.p.a.1049.1 | 8 | 5.2 | odd | 4 | |||
1400.3.p.a.1049.2 | 8 | 35.13 | even | 4 | |||
1400.3.p.a.1049.7 | 8 | 35.27 | even | 4 | |||
1400.3.p.a.1049.8 | 8 | 5.3 | odd | 4 |