Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), 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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.7 | ||
Character | \(\chi\) | \(=\) | 1008.593 |
Dual form | 1008.4.bt.d.17.7 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00025 | + | 8.66069i | −0.447236 | + | 0.774636i | −0.998205 | − | 0.0598902i | \(-0.980925\pi\) |
0.550969 | + | 0.834526i | \(0.314258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56940 | − | 18.4536i | −0.0847395 | − | 0.996403i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.94164 | + | 5.16246i | −0.245092 | + | 0.141504i | −0.617515 | − | 0.786559i | \(-0.711860\pi\) |
0.372423 | + | 0.928063i | \(0.378527\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.4866i | 1.11978i | 0.828567 | + | 0.559891i | \(0.189157\pi\) | ||||
−0.828567 | + | 0.559891i | \(0.810843\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.584477 | + | 1.01234i | 0.00833862 | + | 0.0144429i | 0.870165 | − | 0.492761i | \(-0.164012\pi\) |
−0.861826 | + | 0.507204i | \(0.830679\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 86.7124 | + | 50.0634i | 1.04701 | + | 0.604491i | 0.921811 | − | 0.387640i | \(-0.126710\pi\) |
0.125199 | + | 0.992132i | \(0.460043\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −90.1373 | − | 52.0408i | −0.817171 | − | 0.471794i | 0.0322689 | − | 0.999479i | \(-0.489727\pi\) |
−0.849440 | + | 0.527685i | \(0.823060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.4950 | + | 21.6419i | 0.0999598 | + | 0.173135i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 187.555i | − | 1.20097i | −0.799636 | − | 0.600485i | \(-0.794974\pi\) | ||
0.799636 | − | 0.600485i | \(-0.205026\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 107.524 | − | 62.0789i | 0.622963 | − | 0.359668i | −0.155059 | − | 0.987905i | \(-0.549557\pi\) |
0.778022 | + | 0.628238i | \(0.216223\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 167.669 | + | 78.6808i | 0.809748 | + | 0.379985i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.0459 | − | 27.7922i | 0.0712952 | − | 0.123487i | −0.828174 | − | 0.560471i | \(-0.810620\pi\) |
0.899469 | + | 0.436984i | \(0.143953\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −415.597 | −1.58306 | −0.791528 | − | 0.611133i | \(-0.790714\pi\) | ||||
−0.791528 | + | 0.611133i | \(0.790714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 193.264 | 0.685407 | 0.342703 | − | 0.939444i | \(-0.388657\pi\) | ||||
0.342703 | + | 0.939444i | \(0.388657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −196.466 | + | 340.289i | −0.609735 | + | 1.05609i | 0.381549 | + | 0.924348i | \(0.375391\pi\) |
−0.991284 | + | 0.131743i | \(0.957943\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −338.074 | + | 57.9222i | −0.985638 | + | 0.168869i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −74.7758 | + | 43.1718i | −0.193797 | + | 0.111889i | −0.593759 | − | 0.804643i | \(-0.702357\pi\) |
0.399962 | + | 0.916532i | \(0.369023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 103.254i | − | 0.253142i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 102.286 | + | 177.165i | 0.225704 | + | 0.390931i | 0.956531 | − | 0.291632i | \(-0.0941983\pi\) |
−0.730826 | + | 0.682564i | \(0.760865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −183.527 | − | 105.959i | −0.385217 | − | 0.222405i | 0.294869 | − | 0.955538i | \(-0.404724\pi\) |
−0.680086 | + | 0.733133i | \(0.738057\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −454.570 | − | 262.446i | −0.867422 | − | 0.500806i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −364.857 | − | 631.951i | −0.665290 | − | 1.15232i | −0.979207 | − | 0.202865i | \(-0.934975\pi\) |
0.313917 | − | 0.949450i | \(-0.398359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 315.022i | 0.526566i | 0.964719 | + | 0.263283i | \(0.0848053\pi\) | ||||
−0.964719 | + | 0.263283i | \(0.915195\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −899.220 | + | 519.165i | −1.44172 | + | 0.832379i | −0.997965 | − | 0.0637680i | \(-0.979688\pi\) |
−0.443758 | + | 0.896147i | \(0.646355\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 109.299 | + | 156.904i | 0.161764 | + | 0.232219i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 607.787 | − | 1052.72i | 0.865587 | − | 1.49924i | −0.000876764 | − | 1.00000i | \(-0.500279\pi\) |
0.866463 | − | 0.499241i | \(-0.166388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 333.797 | 0.441434 | 0.220717 | − | 0.975338i | \(-0.429160\pi\) | ||||
0.220717 | + | 0.975338i | \(0.429160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6901 | −0.0149173 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −168.355 | + | 291.599i | −0.200512 | + | 0.347297i | −0.948693 | − | 0.316197i | \(-0.897594\pi\) |
0.748182 | + | 0.663494i | \(0.230927\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 968.568 | − | 82.3723i | 1.11575 | − | 0.0948897i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −867.167 | + | 500.659i | −0.936521 | + | 0.540701i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 893.179i | − | 0.934934i | −0.884011 | − | 0.467467i | \(-0.845167\pi\) | ||
0.884011 | − | 0.467467i | \(-0.154833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −463.543 | − | 802.881i | −0.456676 | − | 0.790986i | 0.542107 | − | 0.840310i | \(-0.317627\pi\) |
−0.998783 | + | 0.0493234i | \(0.984293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −487.361 | − | 281.378i | −0.466224 | − | 0.269175i | 0.248434 | − | 0.968649i | \(-0.420084\pi\) |
−0.714658 | + | 0.699474i | \(0.753418\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1290.34 | − | 744.979i | −1.16581 | − | 0.673082i | −0.213123 | − | 0.977025i | \(-0.568363\pi\) |
−0.952690 | + | 0.303943i | \(0.901697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −726.305 | − | 1258.00i | −0.638233 | − | 1.10545i | −0.985820 | − | 0.167804i | \(-0.946332\pi\) |
0.347587 | − | 0.937648i | \(-0.387001\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1761.48i | − | 1.46642i | −0.680001 | − | 0.733211i | \(-0.738021\pi\) | ||
0.680001 | − | 0.733211i | \(-0.261979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 901.419 | − | 520.434i | 0.730937 | − | 0.422007i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.7642 | − | 12.3745i | 0.0136844 | − | 0.00953251i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −612.198 | + | 1060.36i | −0.459953 | + | 0.796663i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1499.97 | −1.07329 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −68.3256 | −0.0477395 | −0.0238697 | − | 0.999715i | \(-0.507599\pi\) | ||||
−0.0238697 | + | 0.999715i | \(0.507599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 242.249 | − | 419.588i | 0.161568 | − | 0.279844i | −0.773863 | − | 0.633353i | \(-0.781678\pi\) |
0.935431 | + | 0.353509i | \(0.115012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 787.766 | − | 1678.73i | 0.513594 | − | 1.09447i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1247.91 | + | 720.479i | −0.778217 | + | 0.449304i | −0.835798 | − | 0.549037i | \(-0.814995\pi\) |
0.0575809 | + | 0.998341i | \(0.481661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1445.47i | − | 0.882035i | −0.897499 | − | 0.441017i | \(-0.854618\pi\) | ||
0.897499 | − | 0.441017i | \(-0.145382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −270.960 | − | 469.316i | −0.158453 | − | 0.274449i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1624.36 | + | 937.824i | 0.930314 | + | 0.537117i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −846.151 | − | 488.526i | −0.465231 | − | 0.268601i | 0.249010 | − | 0.968501i | \(-0.419895\pi\) |
−0.714241 | + | 0.699900i | \(0.753228\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −667.146 | − | 1155.53i | −0.359547 | − | 0.622753i | 0.628338 | − | 0.777940i | \(-0.283735\pi\) |
−0.987885 | + | 0.155187i | \(0.950402\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1241.64i | 0.643425i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1296.09 | − | 748.295i | 0.658846 | − | 0.380385i | −0.132991 | − | 0.991117i | \(-0.542458\pi\) |
0.791837 | + | 0.610732i | \(0.209125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −818.881 | + | 1745.04i | −0.400850 | + | 0.854211i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1894.73 | + | 3281.76i | −0.910469 | + | 1.57698i | −0.0970652 | + | 0.995278i | \(0.530946\pi\) |
−0.813403 | + | 0.581700i | \(0.802388\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1202.66 | −0.557273 | −0.278637 | − | 0.960397i | \(-0.589883\pi\) | ||||
−0.278637 | + | 0.960397i | \(0.589883\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −557.839 | −0.253910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −765.529 | + | 1325.94i | −0.336428 | + | 0.582711i | −0.983758 | − | 0.179499i | \(-0.942552\pi\) |
0.647330 | + | 0.762210i | \(0.275886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 379.763 | − | 264.543i | 0.164042 | − | 0.114272i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1595.31 | + | 921.053i | −0.666141 | + | 0.384596i | −0.794613 | − | 0.607117i | \(-0.792326\pi\) |
0.128472 | + | 0.991713i | \(0.458993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 325.049i | − | 0.133485i | −0.997770 | − | 0.0667423i | \(-0.978739\pi\) | ||
0.997770 | − | 0.0667423i | \(-0.0212605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 160.467 | + | 277.936i | 0.0637716 | + | 0.110456i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.4524 | − | 6.03468i | −0.00408745 | − | 0.00235989i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3045.91 | − | 1758.56i | −1.15390 | − | 0.666203i | −0.204063 | − | 0.978958i | \(-0.565415\pi\) |
−0.949834 | + | 0.312755i | \(0.898748\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −502.491 | − | 870.339i | −0.187410 | − | 0.324603i | 0.756976 | − | 0.653442i | \(-0.226676\pi\) |
−0.944386 | + | 0.328839i | \(0.893343\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2808.91i | 1.01587i | 0.861395 | + | 0.507935i | \(0.169591\pi\) | ||||
−0.861395 | + | 0.507935i | \(0.830409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 210.249 | − | 121.387i | 0.0748954 | − | 0.0432409i | −0.462085 | − | 0.886836i | \(-0.652898\pi\) |
0.536980 | + | 0.843595i | \(0.319565\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3461.08 | + | 294.349i | −1.19665 | + | 0.101770i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2078.09 | − | 3599.35i | 0.707999 | − | 1.22629i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1033.80 | −0.342151 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2238.46 | −0.730342 | −0.365171 | − | 0.930940i | \(-0.618989\pi\) | ||||
−0.365171 | + | 0.930940i | \(0.618989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −966.369 | + | 1673.80i | −0.306539 | + | 0.530941i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1314.33 | − | 1886.78i | −0.411164 | − | 0.590244i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −53.1345 | + | 30.6772i | −0.0161729 | + | 0.00933743i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 724.158i | 0.217458i | 0.994071 | + | 0.108729i | \(0.0346781\pi\) | ||||
−0.994071 | + | 0.108729i | \(0.965322\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1234.34 | − | 2137.94i | −0.360908 | − | 0.625111i | 0.627202 | − | 0.778856i | \(-0.284200\pi\) |
−0.988111 | + | 0.153745i | \(0.950867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3595.98 | + | 2076.14i | 1.03768 | + | 0.599106i | 0.919176 | − | 0.393847i | \(-0.128856\pi\) |
0.118507 | + | 0.992953i | \(0.462189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5140.63 | + | 2967.94i | 1.44538 | + | 0.834492i | 0.998201 | − | 0.0599522i | \(-0.0190948\pi\) |
0.447180 | + | 0.894444i | \(0.352428\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1964.76 | − | 3403.06i | −0.545391 | − | 0.944644i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4306.49i | − | 1.16554i | −0.812638 | − | 0.582769i | \(-0.801969\pi\) | ||
0.812638 | − | 0.582769i | \(-0.198031\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 674.728 | − | 389.554i | 0.180345 | − | 0.104122i | −0.407110 | − | 0.913379i | \(-0.633463\pi\) |
0.587455 | + | 0.809257i | \(0.300130\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1188.81 | − | 3217.58i | 0.310001 | − | 0.839035i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2627.66 | + | 4551.23i | −0.676898 | + | 1.17242i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −804.927 | −0.202416 | −0.101208 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101208 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1074.63 | 0.267042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2967.92 | + | 5140.59i | −0.720365 | + | 1.24771i | 0.240489 | + | 0.970652i | \(0.422692\pi\) |
−0.960854 | + | 0.277057i | \(0.910641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −538.050 | − | 252.487i | −0.129084 | − | 0.0605745i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6468.89 | − | 3734.82i | 1.51669 | − | 0.875660i | 0.516880 | − | 0.856058i | \(-0.327093\pi\) |
0.999808 | − | 0.0196026i | \(-0.00624010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 863.480i | − | 0.200163i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3714.97 | − | 6434.52i | −0.842029 | − | 1.45844i | −0.888176 | − | 0.459503i | \(-0.848028\pi\) |
0.0461472 | − | 0.998935i | \(-0.485306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1076.21 | − | 621.349i | −0.241236 | − | 0.139278i | 0.374509 | − | 0.927223i | \(-0.377811\pi\) |
−0.615745 | + | 0.787946i | \(0.711145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −223.451 | − | 129.010i | −0.0489986 | − | 0.0282894i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −339.471 | − | 587.980i | −0.0736347 | − | 0.127539i | 0.826857 | − | 0.562412i | \(-0.190127\pi\) |
−0.900492 | + | 0.434873i | \(0.856793\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2157.54i | 0.458036i | 0.973422 | + | 0.229018i | \(0.0735515\pi\) | ||||
−0.973422 | + | 0.229018i | \(0.926449\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 843.962 | − | 487.262i | 0.177273 | − | 0.102349i | −0.408738 | − | 0.912652i | \(-0.634031\pi\) |
0.586011 | + | 0.810303i | \(0.300698\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 652.236 | + | 7669.27i | 0.134147 | + | 1.57736i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2455.82 | − | 4253.60i | 0.499861 | − | 0.865785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6457.16 | 1.28748 | 0.643740 | − | 0.765245i | \(-0.277382\pi\) | ||||
0.643740 | + | 0.765245i | \(0.277382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2045.83 | −0.403773 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2731.44 | − | 4731.00i | 0.528306 | − | 0.915053i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −303.308 | − | 3566.43i | −0.0580810 | − | 0.682942i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1835.36 | − | 1059.65i | 0.344566 | − | 0.198935i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4133.66i | − | 0.768471i | −0.923235 | − | 0.384235i | \(-0.874465\pi\) | ||
0.923235 | − | 0.384235i | \(-0.125535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1222.12 | − | 2116.77i | −0.222829 | − | 0.385952i | 0.732837 | − | 0.680405i | \(-0.238196\pi\) |
−0.955666 | + | 0.294453i | \(0.904863\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3072.40 | + | 1773.85i | 0.554831 | + | 0.320332i | 0.751068 | − | 0.660225i | \(-0.229539\pi\) |
−0.196237 | + | 0.980556i | \(0.562872\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6357.24 | − | 3670.36i | −1.12637 | − | 0.650308i | −0.183348 | − | 0.983048i | \(-0.558694\pi\) |
−0.943019 | + | 0.332740i | \(0.892027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 968.247 | + | 1677.05i | 0.169942 | + | 0.294348i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 117.044i | 0.0201625i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1135.91 | + | 655.818i | −0.193874 | + | 0.111933i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6587.91 | + | 3091.47i | 1.10396 | + | 0.518049i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2815.66 | + | 4876.87i | −0.467561 | + | 0.809840i | −0.999313 | − | 0.0370602i | \(-0.988201\pi\) |
0.531752 | + | 0.846900i | \(0.321534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7297.51 | 1.19017 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9281.97 | −1.50036 | −0.750180 | − | 0.661234i | \(-0.770033\pi\) | ||||
−0.750180 | + | 0.661234i | \(0.770033\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −640.960 | + | 1110.17i | −0.101789 | + | 0.176303i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1599.45 | + | 6147.79i | 0.251784 | + | 0.967783i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4441.01 | + | 2564.02i | −0.687049 | + | 0.396668i | −0.802506 | − | 0.596644i | \(-0.796500\pi\) |
0.115456 | + | 0.993313i | \(0.463167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11096.5i | 1.70196i | 0.525199 | + | 0.850980i | \(0.323991\pi\) | ||||
−0.525199 | + | 0.850980i | \(0.676009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −401.521 | − | 695.454i | −0.0605405 | − | 0.104859i | 0.834167 | − | 0.551512i | \(-0.185949\pi\) |
−0.894707 | + | 0.446653i | \(0.852616\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2728.30 | − | 1575.19i | −0.407897 | − | 0.235499i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1596.45 | − | 921.712i | −0.234701 | − | 0.135504i | 0.378038 | − | 0.925790i | \(-0.376599\pi\) |
−0.612739 | + | 0.790286i | \(0.709932\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1583.19 | + | 2742.16i | 0.230819 | + | 0.399791i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10383.8i | − | 1.48908i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10118.6 | − | 5841.98i | 1.43920 | − | 0.830924i | 0.441408 | − | 0.897307i | \(-0.354479\pi\) |
0.997794 | + | 0.0663827i | \(0.0211458\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 914.030 | + | 1312.13i | 0.127909 | + | 0.183619i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 541.327 | − | 937.606i | 0.0751444 | − | 0.130154i | −0.826005 | − | 0.563663i | \(-0.809392\pi\) |
0.901149 | + | 0.433509i | \(0.142725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9844.13 | 1.34482 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13929.3 | 1.88786 | 0.943929 | − | 0.330148i | \(-0.107099\pi\) | ||||
0.943929 | + | 0.330148i | \(0.107099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1693.36 | − | 2932.98i | 0.225918 | − | 0.391301i | −0.730677 | − | 0.682724i | \(-0.760795\pi\) |
0.956594 | + | 0.291423i | \(0.0941286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1905.42 | + | 162.047i | −0.252232 | + | 0.0214511i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6652.61 | + | 3840.89i | −0.867097 | + | 0.500619i | −0.866382 | − | 0.499381i | \(-0.833561\pi\) |
−0.000714618 | 1.00000i | \(0.500227\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 121.667i | − | 0.0157364i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6078.17 | + | 10527.7i | 0.774243 | + | 1.34103i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8528.01 | + | 4923.65i | 1.07811 | + | 0.622446i | 0.930385 | − | 0.366583i | \(-0.119472\pi\) |
0.147722 | + | 0.989029i | \(0.452806\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11009.5 | + | 6356.33i | 1.37104 | + | 0.791571i | 0.991059 | − | 0.133423i | \(-0.0425969\pi\) |
0.379982 | + | 0.924994i | \(0.375930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3258.31 | + | 5643.55i | 0.402749 | + | 0.697582i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 331.344i | 0.0403541i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13544.0 | + | 7819.64i | −1.63743 | + | 0.945370i | −0.655715 | + | 0.755009i | \(0.727633\pi\) |
−0.981714 | + | 0.190362i | \(0.939034\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3108.82 | − | 2165.60i | 0.370399 | − | 0.258020i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1669.07 | + | 2890.91i | −0.197425 | + | 0.341950i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10568.3 | 1.23221 | 0.616105 | − | 0.787664i | \(-0.288710\pi\) | ||||
0.616105 | + | 0.787664i | \(0.288710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3890.36 | −0.450367 | −0.225184 | − | 0.974316i | \(-0.572298\pi\) | ||||
−0.225184 | + | 0.974316i | \(0.572298\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.6061 | + | 25.2984i | −0.00166705 | + | 0.00288742i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1667.31 | + | 3553.04i | −0.188962 | + | 0.402678i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2554.42 | + | 1474.79i | −0.285480 | + | 0.164822i | −0.635902 | − | 0.771770i | \(-0.719372\pi\) |
0.350422 | + | 0.936592i | \(0.386038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14292.9i | 1.58632i | 0.609017 | + | 0.793158i | \(0.291564\pi\) | ||||
−0.609017 | + | 0.793158i | \(0.708436\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5210.68 | − | 9025.17i | −0.570391 | − | 0.987946i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10289.2 | − | 5940.50i | −1.11863 | − | 0.645842i | −0.177580 | − | 0.984106i | \(-0.556827\pi\) |
−0.941051 | + | 0.338265i | \(0.890160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8000.43 | + | 4619.05i | 0.858040 | + | 0.495390i | 0.863356 | − | 0.504596i | \(-0.168359\pi\) |
−0.00531517 | + | 0.999986i | \(0.501692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1683.63 | − | 2916.14i | −0.179352 | − | 0.310647i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5478.22i | 0.575798i | 0.957661 | + | 0.287899i | \(0.0929568\pi\) | ||||
−0.957661 | + | 0.287899i | \(0.907043\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3716.12 | − | 2145.50i | 0.387994 | − | 0.224008i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4129.68 | + | 8800.35i | −0.425500 | + | 0.906740i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4423.49 | + | 7661.71i | −0.452784 | + | 0.784244i | −0.998558 | − | 0.0536880i | \(-0.982902\pi\) |
0.545774 | + | 0.837932i | \(0.316236\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15927.8 | −1.60917 | −0.804587 | − | 0.593834i | \(-0.797614\pi\) | ||||
−0.804587 | + | 0.593834i | \(0.797614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10491.3 | 1.05307 | 0.526535 | − | 0.850153i | \(-0.323491\pi\) | ||||
0.526535 | + | 0.850153i | \(0.323491\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7862.95 | − | 13619.0i | 0.779130 | − | 1.34949i | −0.153313 | − | 0.988178i | \(-0.548994\pi\) |
0.932444 | − | 0.361316i | \(-0.117672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11089.2 | + | 7724.73i | −1.09179 | + | 0.760543i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1728.10 | + | 997.718i | −0.167987 | + | 0.0969876i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2502.16i | 0.241699i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8758.87 | + | 15170.8i | 0.835496 | + | 1.44712i | 0.893626 | + | 0.448813i | \(0.148153\pi\) |
−0.0581291 | + | 0.998309i | \(0.518513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1458.72 | + | 842.192i | 0.138278 | + | 0.0798350i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7735.54 | + | 4466.12i | 0.724233 | + | 0.418136i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7026.77 | − | 12170.7i | −0.653826 | − | 1.13246i | −0.982187 | − | 0.187908i | \(-0.939829\pi\) |
0.328360 | − | 0.944553i | \(-0.393504\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9854.09i | 0.905720i | 0.891582 | + | 0.452860i | \(0.149596\pi\) | ||||
−0.891582 | + | 0.452860i | \(0.850404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 189.871 | − | 109.622i | 0.0173455 | − | 0.0100144i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5813.30 | − | 494.394i | 0.524672 | − | 0.0446209i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6290.14 | + | 10894.8i | −0.564300 | + | 0.977396i | 0.432815 | + | 0.901483i | \(0.357520\pi\) |
−0.997114 | + | 0.0759128i | \(0.975813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2545.29 | 0.225624 | 0.112812 | − | 0.993616i | \(-0.464014\pi\) | ||||
0.112812 | + | 0.993616i | \(0.464014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9271.33 | 0.816968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7388.51 | − | 12797.3i | 0.643399 | − | 1.11440i | −0.341270 | − | 0.939965i | \(-0.610857\pi\) |
0.984669 | − | 0.174434i | \(-0.0558097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10991.7 | + | 15779.1i | 0.951556 | + | 1.36600i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4873.85 | − | 2813.92i | 0.417025 | − | 0.240769i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4056.99i | − | 0.345119i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4037 | + | 44.0005i | 0.00213619 | + | 0.00369999i | 0.867092 | − | 0.498149i | \(-0.165987\pi\) |
−0.864955 | + | 0.501849i | \(0.832653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12714.2 | + | 7340.56i | 1.06301 | + | 0.613729i | 0.926263 | − | 0.376877i | \(-0.123002\pi\) |
0.136746 | + | 0.990606i | \(0.456335\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 125.690 | + | 72.5674i | 0.0103893 | + | 0.00599827i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −667.006 | − | 1155.29i | −0.0548209 | − | 0.0949526i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21813.2i | − | 1.77268i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12904.1 | − | 7450.16i | 1.04279 | − | 0.602053i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2723.92 | − | 2263.21i | 0.217676 | − | 0.180860i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8294.42 | − | 14366.4i | 0.659159 | − | 1.14170i | −0.321675 | − | 0.946850i | \(-0.604246\pi\) |
0.980834 | − | 0.194846i | \(-0.0624208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14526.8 | 1.14176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2029.96 | −0.158674 | −0.0793371 | − | 0.996848i | \(-0.525280\pi\) | ||||
−0.0793371 | + | 0.996848i | \(0.525280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9389.66 | − | 16263.4i | 0.725976 | − | 1.25743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20380.3 | − | 9563.75i | −1.56720 | − | 0.735428i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2597.94 | + | 1499.92i | −0.197627 | + | 0.114100i | −0.595548 | − | 0.803320i | \(-0.703065\pi\) |
0.397921 | + | 0.917420i | \(0.369732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10143.8i | 0.767506i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8333.02 | − | 14433.2i | −0.623792 | − | 1.08044i | −0.988773 | − | 0.149424i | \(-0.952258\pi\) |
0.364981 | − | 0.931015i | \(-0.381075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15255.6 | + | 8807.82i | 1.13594 | + | 0.655837i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16427.3 | + | 9484.30i | 1.21031 | + | 0.698774i | 0.962827 | − | 0.270118i | \(-0.0870627\pi\) |
0.247485 | + | 0.968892i | \(0.420396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7667.11 | − | 13279.8i | −0.561924 | − | 0.973281i | −0.997329 | − | 0.0730460i | \(-0.976728\pi\) |
0.435405 | − | 0.900235i | \(-0.356605\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2601.00i | − | 0.188642i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10576.2 | + | 6106.20i | −0.763076 | + | 0.440562i | −0.830399 | − | 0.557169i | \(-0.811887\pi\) |
0.0673231 | + | 0.997731i | \(0.478554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −523.861 | − | 6159.78i | −0.0374069 | − | 0.439846i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 445.746 | − | 772.054i | 0.0316653 | − | 0.0548460i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23173.7 | 1.62944 | 0.814718 | − | 0.579857i | \(-0.196892\pi\) | ||||
0.814718 | + | 0.579857i | \(0.196892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12431.5 | 0.869664 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1894.64 | − | 3281.61i | 0.131203 | − | 0.227251i | −0.792937 | − | 0.609303i | \(-0.791449\pi\) |
0.924141 | + | 0.382052i | \(0.124783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.3465 | + | 215.726i | 0.00126409 | + | 0.0148637i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13663.6 | + | 7888.67i | −0.932018 | + | 0.538101i | −0.887449 | − | 0.460906i | \(-0.847525\pi\) |
−0.0445687 | + | 0.999006i | \(0.514191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23750.2i | 1.61197i | 0.591939 | + | 0.805983i | \(0.298362\pi\) | ||||
−0.591939 | + | 0.805983i | \(0.701638\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6122.29 | − | 10604.1i | −0.411416 | − | 0.712593i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21418.8 | − | 12366.1i | −1.43223 | − | 0.826897i | −0.434937 | − | 0.900461i | \(-0.643229\pi\) |
−0.997290 | + | 0.0735641i | \(0.976563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17860.6 | − | 10311.8i | −1.18259 | − | 0.682769i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4659.04 | + | 8069.69i | 0.306977 | + | 0.531700i | 0.977700 | − | 0.210009i | \(-0.0673492\pi\) |
−0.670723 | + | 0.741708i | \(0.734016\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16544.3i | 1.07949i | 0.841828 | + | 0.539746i | \(0.181480\pi\) | ||||
−0.841828 | + | 0.539746i | \(0.818520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8835.49 | − | 5101.18i | 0.573713 | − | 0.331234i | −0.184918 | − | 0.982754i | \(-0.559202\pi\) |
0.758631 | + | 0.651520i | \(0.225869\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5645.28 | + | 2649.12i | 0.363039 | + | 0.170361i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5938.38 | − | 10285.6i | 0.380056 | − | 0.658277i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37.5137 | 0.00237801 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14729.3 | −0.929259 | −0.464630 | − | 0.885505i | \(-0.653813\pi\) | ||||
−0.464630 | + | 0.885505i | \(0.653813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 341.645 | − | 591.746i | 0.0213508 | − | 0.0369807i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3040.14 | − | 17744.3i | −0.189097 | − | 1.10370i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25503.6 | + | 14724.5i | −1.57150 | + | 0.907304i | −0.575511 | + | 0.817794i | \(0.695197\pi\) |
−0.995986 | + | 0.0895107i | \(0.971470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4194.07i | − | 0.257228i | −0.991695 | − | 0.128614i | \(-0.958947\pi\) | ||
0.991695 | − | 0.128614i | \(-0.0410529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10732.4 | − | 18589.0i | −0.652137 | − | 1.12953i | −0.982603 | − | 0.185717i | \(-0.940539\pi\) |
0.330466 | − | 0.943818i | \(-0.392794\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1829.22 | − | 1056.10i | −0.110636 | − | 0.0638760i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28232.5 | + | 16300.1i | 1.69192 | + | 0.976832i | 0.952966 | + | 0.303078i | \(0.0980143\pi\) |
0.738956 | + | 0.673753i | \(0.235319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2422.61 | + | 4196.09i | 0.144518 | + | 0.250313i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5931.69i | 0.350631i | 0.984512 | + | 0.175315i | \(0.0560945\pi\) | ||||
−0.984512 | + | 0.175315i | \(0.943905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16409.5 | − | 9474.01i | 0.965589 | − | 0.557483i | 0.0677004 | − | 0.997706i | \(-0.478434\pi\) |
0.897889 | + | 0.440223i | \(0.145100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10599.9 | + | 15216.7i | 0.618116 | + | 0.887334i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9760.53 | + | 16905.7i | −0.566611 | + | 0.981398i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2188.05 | 0.125885 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19463.2 | −1.11479 | −0.557394 | − | 0.830248i | \(-0.688199\pi\) | ||||
−0.557394 | + | 0.830248i | \(0.688199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7010.82 | + | 12143.1i | −0.398003 | + | 0.689361i | −0.993479 | − | 0.114012i | \(-0.963630\pi\) |
0.595477 | + | 0.803373i | \(0.296963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16482.4 | + | 1401.75i | −0.931571 | + | 0.0792258i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24229.0 | + | 13988.6i | −1.35739 | + | 0.783688i | −0.989271 | − | 0.146091i | \(-0.953331\pi\) |
−0.368117 | + | 0.929780i | \(0.619997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14410.3i | − | 0.803780i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2265.94 | − | 3924.72i | −0.125291 | − | 0.217010i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22352.5 | − | 12905.2i | −1.23058 | − | 0.710475i | −0.263429 | − | 0.964679i | \(-0.584853\pi\) |
−0.967151 | + | 0.254203i | \(0.918187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12518.7 | + | 7227.69i | 0.683255 | + | 0.394478i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −242.907 | − | 420.727i | −0.0132005 | − | 0.0228639i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15653.8i | − | 0.843420i | −0.906731 | − | 0.421710i | \(-0.861430\pi\) | ||
0.906731 | − | 0.421710i | \(-0.138570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2782.75 | − | 1606.62i | 0.149293 | − | 0.0861946i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14088.6 | + | 9814.10i | −0.749443 | + | 0.522061i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16769.6 | − | 29045.8i | 0.888286 | − | 1.53856i | 0.0463856 | − | 0.998924i | \(-0.485230\pi\) |
0.841900 | − | 0.539633i | \(-0.181437\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12922.5 | −0.678756 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5419.47 | 0.283464 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6620.60 | − | 11467.2i | 0.343403 | − | 0.594791i | −0.641659 | − | 0.766990i | \(-0.721754\pi\) |
0.985062 | + | 0.172198i | \(0.0550870\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4427.58 | + | 9435.18i | −0.228699 | + | 0.487357i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4059.06 | − | 2343.50i | 0.207931 | − | 0.120049i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33618.0i | 1.71502i | 0.514464 | + | 0.857512i | \(0.327991\pi\) | ||||
−0.514464 | + | 0.857512i | \(0.672009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 112.958 | + | 195.650i | 0.00571535 | + | 0.00989927i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3921.55 | + | 2264.11i | 0.197607 | + | 0.114088i | 0.595539 | − | 0.803327i | \(-0.296939\pi\) |
−0.397932 | + | 0.917415i | \(0.630272\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6524.85 | + | 3767.12i | 0.326114 | + | 0.188282i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8723.03 | + | 15108.7i | 0.434211 | + | 0.752075i | 0.997231 | − | 0.0743682i | \(-0.0236940\pi\) |
−0.563020 | + | 0.826443i | \(0.690361\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5516.23i | 0.272370i | 0.990683 | + | 0.136185i | \(0.0434842\pi\) | ||||
−0.990683 | + | 0.136185i | \(0.956516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8461.94 | − | 4885.50i | 0.416136 | − | 0.240256i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11722.5 | + | 24980.7i | −0.571871 | + | 1.21866i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1743.07 | − | 3019.09i | 0.0846947 | − | 0.146695i | −0.820566 | − | 0.571551i | \(-0.806342\pi\) |
0.905261 | + | 0.424856i | \(0.139675\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13343.6 | 0.643209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28650.9 | 1.37561 | 0.687805 | − | 0.725896i | \(-0.258575\pi\) | ||||
0.687805 | + | 0.725896i | \(0.258575\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9804.44 | + | 16981.8i | −0.467031 | + | 0.808922i | −0.999291 | − | 0.0376594i | \(-0.988010\pi\) |
0.532259 | + | 0.846581i | \(0.321343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22074.8 | + | 15377.3i | −1.04739 | + | 0.729613i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9298.80 | + | 5368.66i | −0.437758 | + | 0.252739i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6180.49i | 0.289823i | 0.989445 | + | 0.144912i | \(0.0462898\pi\) | ||||
−0.989445 | + | 0.144912i | \(0.953710\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18600.6 | − | 32217.2i | −0.865483 | − | 1.49906i | −0.866567 | − | 0.499060i | \(-0.833679\pi\) |
0.00108453 | − | 0.999999i | \(-0.499655\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2687.01 | + | 1551.35i | 0.124542 | + | 0.0719046i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36037.4 | − | 20806.2i | −1.65747 | − | 0.956943i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1626.29 | − | 2816.81i | −0.0745110 | − | 0.129057i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14966.7i | 0.680488i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4876.40 | − | 2815.39i | 0.220870 | − | 0.127519i | −0.385483 | − | 0.922715i | \(-0.625965\pi\) |
0.606353 | + | 0.795196i | \(0.292632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32505.6 | + | 2764.45i | −1.46115 | + | 0.124264i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5561.45 | − | 9632.71i | 0.249045 | − | 0.431359i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −482.766 | −0.0214560 | −0.0107280 | − | 0.999942i | \(-0.503415\pi\) | ||||
−0.0107280 | + | 0.999942i | \(0.503415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −459.320 | −0.0203374 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5360.34 | − | 9284.38i | 0.235569 | − | 0.408018i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11018.6 | − | 15817.7i | −0.482428 | − | 0.692547i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6666.35 | + | 3848.82i | −0.289711 | + | 0.167265i | −0.637812 | − | 0.770192i | \(-0.720160\pi\) |
0.348100 | + | 0.937457i | \(0.386827\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17872.8i | − | 0.773858i | −0.922110 | − | 0.386929i | \(-0.873536\pi\) | ||
0.922110 | − | 0.386929i | \(-0.126464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18948.2 | − | 32819.3i | −0.814389 | − | 1.41056i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16758.4 | + | 9675.46i | 0.717628 | + | 0.414322i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30510.4 | − | 17615.2i | −1.29698 | − | 0.748811i | −0.317097 | − | 0.948393i | \(-0.602708\pi\) |
−0.979881 | + | 0.199582i | \(0.936042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10049.0 | − | 17405.3i | −0.425619 | − | 0.737194i | 0.570859 | − | 0.821048i | \(-0.306610\pi\) |
−0.996478 | + | 0.0838543i | \(0.973277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4666.09i | 0.196198i | 0.995177 | + | 0.0980990i | \(0.0312762\pi\) | ||||
−0.995177 | + | 0.0980990i | \(0.968724\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25975.9 | − | 14997.2i | 1.08828 | − | 0.628317i | 0.155159 | − | 0.987889i | \(-0.450411\pi\) |
0.933117 | + | 0.359573i | \(0.117078\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −256.234 | − | 308.393i | −0.0106578 | − | 0.0128274i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6013.60 | − | 10415.9i | 0.249233 | − | 0.431684i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13935.9 | −0.573446 | −0.286723 | − | 0.958014i | \(-0.592566\pi\) | ||||
−0.286723 | + | 0.958014i | \(0.592566\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10788.0 | −0.442330 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2789.34 | − | 4831.27i | 0.113558 | − | 0.196687i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20528.3 | + | 9633.16i | 0.832773 | + | 0.390790i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2892.66 | + | 1670.08i | −0.116521 | + | 0.0672733i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1372.58i | 0.0550952i | 0.999620 | + | 0.0275476i | \(0.00876979\pi\) | ||||
−0.999620 | + | 0.0275476i | \(0.991230\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5619.68 | − | 9733.57i | −0.223996 | − | 0.387973i | 0.732022 | − | 0.681281i | \(-0.238577\pi\) |
−0.956018 | + | 0.293309i | \(0.905244\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37877.1 | − | 21868.4i | −1.50448 | − | 0.868613i | −0.999986 | − | 0.00519912i | \(-0.998345\pi\) |
−0.504496 | − | 0.863414i | \(-0.668322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17076.7 | + | 9859.22i | 0.673577 | + | 0.388890i | 0.797430 | − | 0.603411i | \(-0.206192\pi\) |
−0.123854 | + | 0.992300i | \(0.539525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7655.68 | − | 13260.0i | −0.300926 | − | 0.521219i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12550.7i | 0.489935i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33168.9 | − | 19150.1i | 1.29034 | − | 0.744979i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2354.06 | + | 27680.0i | 0.0909504 | + | 1.06943i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11293.8 | + | 19561.4i | −0.434850 | + | 0.753183i | −0.997283 | − | 0.0736598i | \(-0.976532\pi\) |
0.562433 | + | 0.826843i | \(0.309865\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39105.2 | 1.49545 | 0.747723 | − | 0.664011i | \(-0.231147\pi\) | ||||
0.747723 | + | 0.664011i | \(0.231147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37839.6 | 1.44213 | 0.721066 | − | 0.692866i | \(-0.243652\pi\) | ||||
0.721066 | + | 0.692866i | \(0.243652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8185.69 | + | 14178.0i | −0.309863 | + | 0.536698i | −0.978332 | − | 0.207041i | \(-0.933616\pi\) |
0.668469 | + | 0.743740i | \(0.266950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 107.230 | + | 1260.86i | 0.00404542 | + | 0.0475678i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34072.1 | + | 19671.5i | −1.27680 | + | 0.737158i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18422.0i | − | 0.688022i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11643.2 | − | 20166.7i | −0.431950 | − | 0.748160i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −87.4095 | − | 50.4659i | −0.00323200 | − | 0.00186600i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2815.15 | + | 1625.33i | 0.103402 | + | 0.0596991i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13419.7 | − | 23243.6i | −0.491283 | − | 0.850927i | 0.508667 | − | 0.860964i | \(-0.330139\pi\) |
−0.999950 | + | 0.0100365i | \(0.996805\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45173.3i | − | 1.64287i | −0.570300 | − | 0.821437i | \(-0.693173\pi\) | ||
0.570300 | − | 0.821437i | \(-0.306827\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2984.70 | + | 1723.22i | −0.108192 | + | 0.0624645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8123.11 | − | 3811.88i | −0.292529 | − | 0.137273i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10893.7 | + | 18868.4i | −0.391022 | + | 0.677270i | −0.992585 | − | 0.121556i | \(-0.961212\pi\) |
0.601563 | + | 0.798826i | \(0.294545\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16534.4 | −0.589639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 801.970 | 0.0285066 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5860.89 | + | 10151.4i | −0.206985 | + | 0.358509i | −0.950763 | − | 0.309917i | \(-0.899699\pi\) |
0.743778 | + | 0.668427i | \(0.233032\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32215.0 | − | 11902.6i | −1.13405 | − | 0.419002i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 104.529 | − | 60.3499i | 0.00365611 | − | 0.00211086i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9781.37i | 0.341028i | 0.985355 | + | 0.170514i | \(0.0545429\pi\) | ||||
−0.985355 | + | 0.170514i | \(0.945457\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14914.6 | − | 25832.9i | −0.516687 | − | 0.894928i | −0.999812 | − | 0.0193766i | \(-0.993832\pi\) |
0.483125 | − | 0.875551i | \(-0.339501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37460.8 | + | 21628.0i | 1.29363 | + | 0.746876i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1073.64 | + | 619.868i | 0.0368413 | + | 0.0212703i | 0.518308 | − | 0.855194i | \(-0.326562\pi\) |
−0.481466 | + | 0.876465i | \(0.659896\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27249.2 | − | 47197.0i | −0.932082 | − | 1.61441i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35161.2i | − | 1.19516i | −0.801810 | − | 0.597578i | \(-0.796130\pi\) | ||
0.801810 | − | 0.597578i | \(-0.203870\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30460.6 | − | 17586.5i | 1.03213 | − | 0.595900i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15253.9 | + | 21897.7i | 0.513634 | + | 0.737344i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7187.92 | + | 12449.8i | −0.241278 | + | 0.417906i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10050.3 | 0.335265 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38907.9 | −1.29389 | −0.646946 | − | 0.762536i | \(-0.723954\pi\) | ||||
−0.646946 | + | 0.762536i | \(0.723954\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2540.26 | + | 4399.87i | −0.0839557 | + | 0.145415i | −0.904946 | − | 0.425527i | \(-0.860089\pi\) |
0.820990 | + | 0.570942i | \(0.193422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26674.1 | + | 2268.51i | −0.878862 | + | 0.0747432i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13364.5 | + | 7715.98i | −0.437633 | + | 0.252667i | −0.702593 | − | 0.711592i | \(-0.747974\pi\) |
0.264960 | + | 0.964259i | \(0.414641\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3476.50i | − | 0.113493i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16878.9 | + | 29235.2i | 0.547665 | + | 0.948584i | 0.998434 | + | 0.0559429i | \(0.0178165\pi\) |
−0.450769 | + | 0.892641i | \(0.648850\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24327.1 | − | 14045.2i | −0.786929 | − | 0.454334i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17420.3 | − | 10057.6i | −0.560095 | − | 0.323371i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26259.7 | − | 45483.2i | −0.841743 | − | 1.45794i | −0.888420 | − | 0.459032i | \(-0.848196\pi\) |
0.0466765 | − | 0.998910i | \(-0.485137\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2427.87i | 0.0773555i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3156.68 | − | 1822.51i | 0.100274 | − | 0.0578931i | −0.449025 | − | 0.893519i | \(-0.648228\pi\) |
0.549298 | + | 0.835626i | \(0.314895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1008.4.bt.d.593.7 | 48 | ||
3.2 | odd | 2 | inner | 1008.4.bt.d.593.18 | 48 | ||
4.3 | odd | 2 | 504.4.bl.a.89.7 | yes | 48 | ||
7.3 | odd | 6 | inner | 1008.4.bt.d.17.18 | 48 | ||
12.11 | even | 2 | 504.4.bl.a.89.18 | yes | 48 | ||
21.17 | even | 6 | inner | 1008.4.bt.d.17.7 | 48 | ||
28.3 | even | 6 | 504.4.bl.a.17.18 | yes | 48 | ||
84.59 | odd | 6 | 504.4.bl.a.17.7 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.bl.a.17.7 | ✓ | 48 | 84.59 | odd | 6 | ||
504.4.bl.a.17.18 | yes | 48 | 28.3 | even | 6 | ||
504.4.bl.a.89.7 | yes | 48 | 4.3 | odd | 2 | ||
504.4.bl.a.89.18 | yes | 48 | 12.11 | even | 2 | ||
1008.4.bt.d.17.7 | 48 | 21.17 | even | 6 | inner | ||
1008.4.bt.d.17.18 | 48 | 7.3 | odd | 6 | inner | ||
1008.4.bt.d.593.7 | 48 | 1.1 | even | 1 | trivial | ||
1008.4.bt.d.593.18 | 48 | 3.2 | odd | 2 | inner |