Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,3,Mod(319,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.e (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: | \(17.4387369191\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{14} + 104x^{12} - 208x^{10} - 352x^{8} + 2312x^{6} + 2497x^{4} - 9072x^{2} + 5184 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{38} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.8 | ||
Root | \(-0.973371 + 0.130814i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.319 |
Dual form | 640.3.e.i.319.11 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 2.20837i | − | 0.736123i | −0.929801 | − | 0.368062i | \(-0.880022\pi\) | ||
0.929801 | − | 0.368062i | \(-0.119978\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.50932 | + | 3.56155i | 0.701864 | + | 0.712311i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.620058 | 0.0885797 | 0.0442899 | − | 0.999019i | \(-0.485897\pi\) | ||||
0.0442899 | + | 0.999019i | \(0.485897\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.12311 | 0.458123 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.6757 | 1.60689 | 0.803443 | − | 0.595382i | \(-0.202999\pi\) | ||||
0.803443 | + | 0.595382i | \(0.202999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.9786 | −1.38297 | −0.691486 | − | 0.722390i | \(-0.743043\pi\) | ||||
−0.691486 | + | 0.722390i | \(0.743043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.86522 | − | 7.74988i | 0.524348 | − | 0.516659i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.9600i | 0.644705i | 0.946620 | + | 0.322352i | \(0.104474\pi\) | ||||
−0.946620 | + | 0.322352i | \(0.895526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.17598 | 0.114525 | 0.0572627 | − | 0.998359i | \(-0.481763\pi\) | ||||
0.0572627 | + | 0.998359i | \(0.481763\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.36932i | − | 0.0652056i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.8703 | 0.603055 | 0.301528 | − | 0.953457i | \(-0.402503\pi\) | ||||
0.301528 | + | 0.953457i | \(0.402503\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.369317 | + | 24.9973i | −0.0147727 | + | 0.999891i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 28.9807i | − | 1.07336i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.7386i | 0.508229i | 0.967174 | + | 0.254114i | \(0.0817840\pi\) | ||||
−0.967174 | + | 0.254114i | \(0.918216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 55.2032i | 1.78075i | 0.455229 | + | 0.890374i | \(0.349557\pi\) | ||||
−0.455229 | + | 0.890374i | \(0.650443\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 39.0346i | − | 1.18287i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.17598 | + | 2.20837i | 0.0621709 | + | 0.0630963i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.01864 | 0.189693 | 0.0948465 | − | 0.995492i | \(-0.469764\pi\) | ||||
0.0948465 | + | 0.995492i | \(0.469764\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.7034i | 1.01804i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.3542 | 1.17937 | 0.589685 | − | 0.807633i | \(-0.299252\pi\) | ||||
0.589685 | + | 0.807633i | \(0.299252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 58.7769i | − | 1.36690i | −0.729995 | − | 0.683452i | \(-0.760478\pi\) | ||
0.729995 | − | 0.683452i | \(-0.239522\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.4693 | + | 14.6847i | 0.321540 | + | 0.326326i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 54.1646 | 1.15244 | 0.576220 | − | 0.817295i | \(-0.304527\pi\) | ||||
0.576220 | + | 0.817295i | \(0.304527\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.6155 | −0.992154 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24.2037 | 0.474582 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.94134 | 0.0743649 | 0.0371824 | − | 0.999308i | \(-0.488162\pi\) | ||||
0.0371824 | + | 0.999308i | \(0.488162\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 62.0299 | + | 62.9531i | 1.12782 | + | 1.14460i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.80537i | − | 0.0843048i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 72.8789 | 1.23524 | 0.617618 | − | 0.786478i | \(-0.288098\pi\) | ||||
0.617618 | + | 0.786478i | \(0.288098\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 79.3390i | − | 1.30064i | −0.759661 | − | 0.650320i | \(-0.774635\pi\) | ||
0.759661 | − | 0.650320i | \(-0.225365\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.55656 | 0.0405804 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −63.0928 | − | 64.0318i | −0.970658 | − | 0.985105i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 26.7723i | − | 0.399586i | −0.979838 | − | 0.199793i | \(-0.935973\pi\) | ||
0.979838 | − | 0.199793i | \(-0.0640270\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 30.6307i | − | 0.443923i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 46.4993i | − | 0.654919i | −0.944865 | − | 0.327460i | \(-0.893807\pi\) | ||
0.944865 | − | 0.327460i | \(-0.106193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 95.1837i | 1.30389i | 0.758268 | + | 0.651943i | \(0.226046\pi\) | ||||
−0.758268 | + | 0.651943i | \(0.773954\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 55.2032 | + | 0.815588i | 0.736043 | + | 0.0108745i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.9600 | 0.142337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.2037i | 0.306376i | 0.988197 | + | 0.153188i | \(0.0489540\pi\) | ||||
−0.988197 | + | 0.153188i | \(0.951046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −26.8920 | −0.332001 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 107.361i | − | 1.29351i | −0.762699 | − | 0.646753i | \(-0.776126\pi\) | ||
0.762699 | − | 0.646753i | \(-0.223874\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −39.0346 | + | 38.4621i | −0.459230 | + | 0.452495i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 32.5483 | 0.374119 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 44.2462 | 0.497148 | 0.248574 | − | 0.968613i | \(-0.420038\pi\) | ||||
0.248574 | + | 0.968613i | \(0.420038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.1478 | −0.122503 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 121.909 | 1.31085 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.63623 | + | 7.74988i | 0.0803813 | + | 0.0815777i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 123.258i | − | 1.27070i | −0.772223 | − | 0.635352i | \(-0.780855\pi\) | ||
0.772223 | − | 0.635352i | \(-0.219145\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 72.8789 | 0.736151 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 32.7083i | − | 0.323845i | −0.986803 | − | 0.161922i | \(-0.948231\pi\) | ||
0.986803 | − | 0.161922i | \(-0.0517694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −70.2862 | −0.682390 | −0.341195 | − | 0.939993i | \(-0.610832\pi\) | ||||
−0.341195 | + | 0.939993i | \(0.610832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.87689 | − | 4.80537i | 0.0464466 | − | 0.0457655i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 87.7576i | 0.820164i | 0.912049 | + | 0.410082i | \(0.134500\pi\) | ||||
−0.912049 | + | 0.410082i | \(0.865500\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 81.8617i | 0.751025i | 0.926817 | + | 0.375513i | \(0.122533\pi\) | ||||
−0.926817 | + | 0.375513i | \(0.877467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 15.4998i | − | 0.139637i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.3092i | − | 0.108931i | −0.998516 | − | 0.0544656i | \(-0.982654\pi\) | ||
0.998516 | − | 0.0544656i | \(-0.0173455\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 48.6753 | + | 49.3997i | 0.423263 | + | 0.429563i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −74.1278 | −0.633571 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.79583i | 0.0571078i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 191.432 | 1.58208 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 106.784i | − | 0.868161i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −90.3252 | + | 86.4081i | −0.722601 | + | 0.691265i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 175.897 | 1.38501 | 0.692507 | − | 0.721411i | \(-0.256506\pi\) | ||||
0.692507 | + | 0.721411i | \(0.256506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −129.801 | −1.00621 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.2319 | −0.116274 | −0.0581370 | − | 0.998309i | \(-0.518516\pi\) | ||||
−0.0581370 | + | 0.998309i | \(0.518516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.34924 | 0.0101446 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 103.216 | − | 101.702i | 0.764564 | − | 0.753352i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 249.973i | 1.82462i | 0.409502 | + | 0.912309i | \(0.365702\pi\) | ||||
−0.409502 | + | 0.912309i | \(0.634298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −225.433 | −1.62182 | −0.810909 | − | 0.585172i | \(-0.801027\pi\) | ||||
−0.810909 | + | 0.585172i | \(0.801027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 119.616i | − | 0.848337i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −317.786 | −2.22228 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −52.4924 | + | 51.7226i | −0.362017 | + | 0.356708i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 107.361i | 0.730347i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 77.3693i | 0.519257i | 0.965709 | + | 0.259629i | \(0.0836001\pi\) | ||||
−0.965709 | + | 0.259629i | \(0.916400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 163.702i | 1.08412i | 0.840341 | + | 0.542058i | \(0.182355\pi\) | ||||
−0.840341 | + | 0.542058i | \(0.817645\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 45.1892i | 0.295354i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −196.609 | + | 193.726i | −1.26845 | + | 1.24984i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −58.7413 | −0.374148 | −0.187074 | − | 0.982346i | \(-0.559900\pi\) | ||||
−0.187074 | + | 0.982346i | \(0.559900\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 8.70393i | − | 0.0547417i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.60037 | 0.0534185 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 112.560i | − | 0.690551i | −0.938501 | − | 0.345276i | \(-0.887785\pi\) | ||
0.938501 | − | 0.345276i | \(-0.112215\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 139.024 | − | 136.985i | 0.842568 | − | 0.830211i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −237.035 | −1.41937 | −0.709685 | − | 0.704519i | \(-0.751163\pi\) | ||||
−0.709685 | + | 0.704519i | \(0.751163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 154.231 | 0.912610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.97181 | 0.0524667 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −292.949 | −1.69334 | −0.846672 | − | 0.532115i | \(-0.821398\pi\) | ||||
−0.846672 | + | 0.532115i | \(0.821398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.228998 | + | 15.4998i | −0.00130856 | + | 0.0885700i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 160.944i | − | 0.909286i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −180.841 | −1.01029 | −0.505144 | − | 0.863035i | \(-0.668561\pi\) | ||||
−0.505144 | + | 0.863035i | \(0.668561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 259.231i | 1.43222i | 0.697990 | + | 0.716108i | \(0.254078\pi\) | ||||
−0.697990 | + | 0.716108i | \(0.745922\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −175.210 | −0.957431 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.6307 | + | 24.9973i | 0.133139 | + | 0.135120i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 193.726i | 1.03597i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 17.9697i | − | 0.0950777i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 269.220i | − | 1.40953i | −0.709441 | − | 0.704765i | \(-0.751052\pi\) | ||
0.709441 | − | 0.704765i | \(-0.248948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 145.178i | − | 0.752219i | −0.926575 | − | 0.376109i | \(-0.877262\pi\) | ||
0.926575 | − | 0.376109i | \(-0.122738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −141.406 | + | 139.332i | −0.725159 | + | 0.714524i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 272.378 | 1.38263 | 0.691314 | − | 0.722554i | \(-0.257032\pi\) | ||||
0.691314 | + | 0.722554i | \(0.257032\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 329.311i | − | 1.65483i | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||
0.561591 | − | 0.827415i | \(-0.310189\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −59.1231 | −0.294145 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.13881i | 0.0450188i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 169.690 | + | 172.216i | 0.827758 | + | 0.840078i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 57.1886 | 0.276273 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.4621 | 0.184029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.52795 | −0.0309381 | −0.0154691 | − | 0.999880i | \(-0.504924\pi\) | ||||
−0.0154691 | + | 0.999880i | \(0.504924\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −102.688 | −0.482101 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 209.337 | − | 206.267i | 0.973661 | − | 0.959382i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 34.2292i | 0.157738i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 210.201 | 0.959821 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 197.045i | − | 0.891608i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −365.597 | −1.63945 | −0.819724 | − | 0.572759i | \(-0.805873\pi\) | ||||
−0.819724 | + | 0.572759i | \(0.805873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.52273 | + | 103.066i | −0.00676770 | + | 0.458073i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 224.066i | 0.987074i | 0.869725 | + | 0.493537i | \(0.164296\pi\) | ||||
−0.869725 | + | 0.493537i | \(0.835704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 247.723i | − | 1.08176i | −0.841099 | − | 0.540881i | \(-0.818091\pi\) | ||
0.841099 | − | 0.540881i | \(-0.181909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 24.2037i | − | 0.104778i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 260.933i | − | 1.11988i | −0.828532 | − | 0.559941i | \(-0.810824\pi\) | ||
0.828532 | − | 0.559941i | \(-0.189176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 190.081 | + | 192.910i | 0.808856 | + | 0.820895i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 53.4507 | 0.225530 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 183.017i | − | 0.765764i | −0.923797 | − | 0.382882i | \(-0.874932\pi\) | ||
0.923797 | − | 0.382882i | \(-0.125068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −204.725 | −0.849483 | −0.424741 | − | 0.905315i | \(-0.639635\pi\) | ||||
−0.424741 | + | 0.905315i | \(0.639635\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 201.438i | − | 0.828965i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −170.608 | − | 173.147i | −0.696357 | − | 0.706722i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −39.1212 | −0.158385 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −237.093 | −0.952180 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −322.247 | −1.28385 | −0.641927 | − | 0.766766i | \(-0.721865\pi\) | ||||
−0.641927 | + | 0.766766i | \(0.721865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 245.167 | 0.969041 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 84.9385 | + | 86.2027i | 0.333092 | + | 0.338050i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 234.207i | 0.911313i | 0.890156 | + | 0.455656i | \(0.150595\pi\) | ||||
−0.890156 | + | 0.455656i | \(0.849405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.35197 | 0.0168030 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 60.7689i | 0.232831i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −448.361 | −1.70479 | −0.852397 | − | 0.522896i | \(-0.824852\pi\) | ||||
−0.852397 | + | 0.522896i | \(0.824852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.8314 | + | 14.0373i | 0.0521941 | + | 0.0529709i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 97.7120i | − | 0.365962i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6610i | 0.0619368i | 0.999520 | + | 0.0309684i | \(0.00985912\pi\) | ||||
−0.999520 | + | 0.0309684i | \(0.990141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 148.202i | − | 0.546870i | −0.961890 | − | 0.273435i | \(-0.911840\pi\) | ||
0.961890 | − | 0.273435i | \(-0.0881598\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.6184i | 0.0901774i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.52795 | + | 441.845i | −0.0237380 | + | 1.60671i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −373.716 | −1.34916 | −0.674578 | − | 0.738204i | \(-0.735674\pi\) | ||||
−0.674578 | + | 0.738204i | \(0.735674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 227.609i | 0.815802i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −250.756 | −0.892369 | −0.446184 | − | 0.894941i | \(-0.647217\pi\) | ||||
−0.446184 | + | 0.894941i | \(0.647217\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 463.657i | − | 1.63836i | −0.573533 | − | 0.819182i | \(-0.694428\pi\) | ||
0.573533 | − | 0.819182i | \(-0.305572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.1146 | − | 16.8636i | 0.0600512 | − | 0.0591705i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.9824 | 0.104468 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 168.879 | 0.584356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −272.200 | −0.935395 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 275.455 | 0.940120 | 0.470060 | − | 0.882634i | \(-0.344232\pi\) | ||||
0.470060 | + | 0.882634i | \(0.344232\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 255.756 | + | 259.562i | 0.866968 | + | 0.879872i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 512.255i | − | 1.72476i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −249.368 | −0.834008 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 36.4451i | − | 0.121080i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −72.2321 | −0.238390 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 282.570 | − | 278.426i | 0.926459 | − | 0.912873i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 131.620i | 0.428728i | 0.976754 | + | 0.214364i | \(0.0687679\pi\) | ||||
−0.976754 | + | 0.214364i | \(0.931232\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 155.218i | 0.502323i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 353.515i | − | 1.13670i | −0.822786 | − | 0.568352i | \(-0.807581\pi\) | ||
0.822786 | − | 0.568352i | \(-0.192419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 281.503i | 0.899372i | 0.893187 | + | 0.449686i | \(0.148464\pi\) | ||||
−0.893187 | + | 0.449686i | \(0.851536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.97181 | + | 9.10534i | 0.0284819 | + | 0.0289058i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 216.229 | 0.682110 | 0.341055 | − | 0.940043i | \(-0.389216\pi\) | ||||
0.341055 | + | 0.940043i | \(0.389216\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 260.516i | 0.816665i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 193.801 | 0.603742 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.8487i | 0.0738351i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.63981 | − | 449.417i | 0.0204302 | − | 1.38282i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 180.781 | 0.552847 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.5852 | 0.102083 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 333.395 | 1.00724 | 0.503618 | − | 0.863926i | \(-0.332002\pi\) | ||||
0.503618 | + | 0.863926i | \(0.332002\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 28.9386 | 0.0869027 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 95.3509 | − | 93.9526i | 0.284630 | − | 0.280456i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 243.818i | 0.723496i | 0.932276 | + | 0.361748i | \(0.117820\pi\) | ||||
−0.932276 | + | 0.361748i | \(0.882180\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.1833 | −0.0801867 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 975.758i | 2.86146i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −60.5273 | −0.176464 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 109.093 | − | 107.493i | 0.316211 | − | 0.311574i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 221.109i | 0.637201i | 0.947889 | + | 0.318601i | \(0.103213\pi\) | ||||
−0.947889 | + | 0.318601i | \(0.896787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 39.1704i | − | 0.112236i | −0.998424 | − | 0.0561181i | \(-0.982128\pi\) | ||
0.998424 | − | 0.0561181i | \(-0.0178723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 521.033i | 1.48442i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 646.473i | 1.83137i | 0.401899 | + | 0.915684i | \(0.368350\pi\) | ||||
−0.401899 | + | 0.915684i | \(0.631650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 165.610 | − | 163.181i | 0.466506 | − | 0.459665i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.0077 | 0.0420383 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 256.700i | 0.715042i | 0.933905 | + | 0.357521i | \(0.116378\pi\) | ||||
−0.933905 | + | 0.357521i | \(0.883622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −356.265 | −0.986884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 422.752i | − | 1.16461i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −339.002 | + | 334.030i | −0.928772 | + | 0.915152i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 551.424 | 1.50252 | 0.751259 | − | 0.660008i | \(-0.229447\pi\) | ||||
0.751259 | + | 0.660008i | \(0.229447\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 199.369 | 0.540296 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.44386 | 0.00658722 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −261.418 | −0.700852 | −0.350426 | − | 0.936590i | \(-0.613963\pi\) | ||||
−0.350426 | + | 0.936590i | \(0.613963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 190.821 | + | 199.471i | 0.508856 | + | 0.531923i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 264.980i | − | 0.702866i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 344.007 | 0.907671 | 0.453835 | − | 0.891086i | \(-0.350055\pi\) | ||||
0.453835 | + | 0.891086i | \(0.350055\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 388.445i | − | 1.01954i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −374.736 | −0.978422 | −0.489211 | − | 0.872165i | \(-0.662715\pi\) | ||||
−0.489211 | + | 0.872165i | \(0.662715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 38.4621 | + | 39.0346i | 0.0999016 | + | 0.101388i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 242.343i | − | 0.626210i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 692.358i | − | 1.77984i | −0.456116 | − | 0.889920i | \(-0.650760\pi\) | ||
0.456116 | − | 0.889920i | \(-0.349240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 152.018i | 0.388793i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.6376i | 0.0855919i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −86.2027 | + | 84.9385i | −0.218235 | + | 0.215034i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −427.546 | −1.07694 | −0.538471 | − | 0.842644i | \(-0.680998\pi\) | ||||
−0.538471 | + | 0.842644i | \(0.680998\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 2.97961i | − | 0.00746770i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 179.261 | 0.447036 | 0.223518 | − | 0.974700i | \(-0.428246\pi\) | ||||
0.223518 | + | 0.974700i | \(0.428246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 992.478i | − | 2.46272i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −94.3729 | − | 95.7775i | −0.233019 | − | 0.236488i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 124.060 | 0.304815 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −89.7368 | −0.219405 | −0.109703 | − | 0.993964i | \(-0.534990\pi\) | ||||
−0.109703 | + | 0.993964i | \(0.534990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 552.032 | 1.34314 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.1892 | 0.109417 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 382.372 | − | 376.764i | 0.921378 | − | 0.907866i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 497.839i | 1.19386i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 203.673 | 0.486093 | 0.243046 | − | 0.970015i | \(-0.421853\pi\) | ||||
0.243046 | + | 0.970015i | \(0.421853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 388.384i | 0.922528i | 0.887263 | + | 0.461264i | \(0.152604\pi\) | ||||
−0.887263 | + | 0.461264i | \(0.847396\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 223.327 | 0.527959 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −273.970 | − | 4.04771i | −0.644635 | − | 0.00952402i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 49.1948i | − | 0.115210i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 701.788i | 1.63587i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 617.011i | 1.43158i | 0.698316 | + | 0.715790i | \(0.253933\pi\) | ||||
−0.698316 | + | 0.715790i | \(0.746067\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 210.938i | − | 0.487155i | −0.969881 | − | 0.243578i | \(-0.921679\pi\) | ||
0.969881 | − | 0.243578i | \(-0.0783210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 114.223 | + | 115.923i | 0.262581 | + | 0.266489i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.1815 | 0.0690652 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 159.885i | − | 0.364203i | −0.983280 | − | 0.182102i | \(-0.941710\pi\) | ||
0.983280 | − | 0.182102i | \(-0.0582900\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −200.447 | −0.454528 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 121.460i | − | 0.274177i | −0.990559 | − | 0.137088i | \(-0.956226\pi\) | ||
0.990559 | − | 0.137088i | \(-0.0437744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 155.274 | + | 157.585i | 0.348931 | + | 0.354124i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 170.860 | 0.382237 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 533.002 | 1.18709 | 0.593543 | − | 0.804802i | \(-0.297729\pi\) | ||||
0.593543 | + | 0.804802i | \(0.297729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 854.696 | 1.89511 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 361.513 | 0.798043 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −39.1212 | − | 39.7034i | −0.0859806 | − | 0.0872603i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 103.445i | − | 0.226357i | −0.993575 | − | 0.113179i | \(-0.963897\pi\) | ||
0.993575 | − | 0.113179i | \(-0.0361032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 317.628 | 0.691999 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 420.337i | − | 0.911794i | −0.890032 | − | 0.455897i | \(-0.849318\pi\) | ||
0.890032 | − | 0.455897i | \(-0.150682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 63.3035 | 0.136725 | 0.0683623 | − | 0.997661i | \(-0.478223\pi\) | ||||
0.0683623 | + | 0.997661i | \(0.478223\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 427.818 | + | 434.186i | 0.920039 | + | 0.933732i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 129.206i | 0.276673i | 0.990385 | + | 0.138337i | \(0.0441756\pi\) | ||||
−0.990385 | + | 0.138337i | \(0.955824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.6004i | − | 0.0353953i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 129.722i | 0.275419i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1038.93i | − | 2.19646i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.803627 | + | 54.3936i | −0.00169185 | + | 0.114513i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.2506 | 0.0340683 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 517.216i | − | 1.07978i | −0.841734 | − | 0.539892i | \(-0.818465\pi\) | ||
0.841734 | − | 0.539892i | \(-0.181535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −126.186 | −0.262340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 18.9928i | − | 0.0393226i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 438.991 | − | 432.553i | 0.905136 | − | 0.891862i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 893.449 | 1.83460 | 0.917299 | − | 0.398199i | \(-0.130365\pi\) | ||||
0.917299 | + | 0.398199i | \(0.130365\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −248.574 | −0.508331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −506.336 | −1.03124 | −0.515618 | − | 0.856819i | \(-0.672437\pi\) | ||||
−0.515618 | + | 0.856819i | \(0.672437\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −161.535 | −0.327658 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 255.756 | + | 259.562i | 0.516678 | + | 0.524368i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 28.8322i | − | 0.0580126i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 512.596 | 1.02725 | 0.513624 | − | 0.858016i | \(-0.328303\pi\) | ||||
0.513624 | + | 0.858016i | \(0.328303\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 523.460i | 1.04483i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −389.856 | −0.775061 | −0.387530 | − | 0.921857i | \(-0.626672\pi\) | ||||
−0.387530 | + | 0.921857i | \(0.626672\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 116.492 | − | 114.784i | 0.230678 | − | 0.227295i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 340.599i | − | 0.671793i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 80.1553i | − | 0.157476i | −0.996895 | − | 0.0787380i | \(-0.974911\pi\) | ||
0.996895 | − | 0.0787380i | \(-0.0250891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.0194i | 0.115498i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 63.0614i | − | 0.122927i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −246.657 | − | 250.328i | −0.478945 | − | 0.486073i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 957.400 | 1.85184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 646.939i | 1.24651i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −417.076 | −0.800529 | −0.400265 | − | 0.916400i | \(-0.631082\pi\) | ||||
−0.400265 | + | 0.916400i | \(0.631082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.2320i | 0.0539809i | 0.999636 | + | 0.0269904i | \(0.00859237\pi\) | ||||
−0.999636 | + | 0.0269904i | \(0.991408\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 34.2292 | + | 0.505712i | 0.0651985 | + | 0.000963261i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −605.026 | −1.14806 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −336.616 | −0.636324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 300.488 | 0.565890 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −869.341 | −1.63103 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −312.553 | + | 307.970i | −0.584212 | + | 0.575644i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 399.365i | 0.743696i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −859.315 | −1.59428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 948.095i | − | 1.75249i | −0.481870 | − | 0.876243i | \(-0.660042\pi\) | ||
0.481870 | − | 0.876243i | \(-0.339958\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 572.478 | 1.05429 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −291.555 | + | 287.279i | −0.534963 | + | 0.527118i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 266.602i | − | 0.487389i | −0.969852 | − | 0.243695i | \(-0.921641\pi\) | ||
0.969852 | − | 0.243695i | \(-0.0783595\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 327.123i | − | 0.595853i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.0710i | 0.0582051i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.0077i | 0.0271387i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 55.2032 | − | 54.3936i | 0.0994652 | − | 0.0980066i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.5417 | 0.0422651 | 0.0211326 | − | 0.999777i | \(-0.493273\pi\) | ||||
0.0211326 | + | 0.999777i | \(0.493273\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1056.73i | 1.89039i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 427.818 | 0.762599 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 119.352i | − | 0.211993i | −0.994366 | − | 0.105997i | \(-0.966197\pi\) | ||
0.994366 | − | 0.105997i | \(-0.0338033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.8399 | − | 43.1970i | 0.0775928 | − | 0.0764549i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.6746 | −0.0294085 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −717.434 | −1.26087 | −0.630434 | − | 0.776243i | \(-0.717123\pi\) | ||||
−0.630434 | + | 0.776243i | \(0.717123\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −389.134 | −0.681496 | −0.340748 | − | 0.940155i | \(-0.610680\pi\) | ||||
−0.340748 | + | 0.940155i | \(0.610680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −594.538 | −1.03759 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.12253 | + | 346.719i | −0.00890874 | + | 0.602990i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 934.131i | − | 1.61894i | −0.587158 | − | 0.809472i | \(-0.699753\pi\) | ||
0.587158 | − | 0.809472i | \(-0.300247\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −320.607 | −0.553726 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 66.5701i | − | 0.114578i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 69.6661 | 0.119496 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −260.138 | − | 264.010i | −0.444681 | − | 0.451299i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 372.365i | 0.634353i | 0.948366 | + | 0.317177i | \(0.102735\pi\) | ||||
−0.948366 | + | 0.317177i | \(0.897265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 120.121i | 0.203941i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 601.511i | − | 1.01778i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 446.495i | 0.752942i | 0.926428 | + | 0.376471i | \(0.122863\pi\) | ||||
−0.926428 | + | 0.376471i | \(0.877137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.2037 | + | 23.8487i | −0.0406785 | + | 0.0400819i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −727.241 | −1.21816 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 677.938i | − | 1.13178i | −0.824480 | − | 0.565892i | \(-0.808532\pi\) | ||
0.824480 | − | 0.565892i | \(-0.191468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 696.941 | 1.15964 | 0.579818 | − | 0.814746i | \(-0.303124\pi\) | ||||
0.579818 | + | 0.814746i | \(0.303124\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 110.385i | − | 0.183060i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 671.796 | + | 681.794i | 1.11041 | + | 1.12693i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −372.628 | −0.613884 | −0.306942 | − | 0.951728i | \(-0.599306\pi\) | ||||
−0.306942 | + | 0.951728i | \(0.599306\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.1819 | 0.0331393 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −973.806 | −1.59379 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 569.647 | 0.929277 | 0.464638 | − | 0.885501i | \(-0.346184\pi\) | ||||
0.464638 | + | 0.885501i | \(0.346184\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 380.316 | − | 374.739i | 0.618400 | − | 0.609332i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 126.714i | 0.205372i | 0.994714 | + | 0.102686i | \(0.0327437\pi\) | ||||
−0.994714 | + | 0.102686i | \(0.967256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 771.205 | 1.24589 | 0.622944 | − | 0.782266i | \(-0.285936\pi\) | ||||
0.622944 | + | 0.782266i | \(0.285936\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 401.970i | − | 0.647294i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.4352 | 0.0440373 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −624.727 | − | 18.4638i | −0.999564 | − | 0.0295421i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 84.9385i | − | 0.135468i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 76.9242i | 0.122296i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 74.5192i | 0.118097i | 0.998255 | + | 0.0590485i | \(0.0188067\pi\) | ||||
−0.998255 | + | 0.0590485i | \(0.981193\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.4161i | 0.0227743i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 617.279 | + | 626.466i | 0.972092 | + | 0.986560i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 874.040 | 1.37212 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 191.721i | − | 0.300034i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.9072 | −0.0513373 | −0.0256686 | − | 0.999671i | \(-0.508171\pi\) | ||||
−0.0256686 | + | 0.999671i | \(0.508171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 900.609i | 1.40064i | 0.713831 | + | 0.700318i | \(0.246958\pi\) | ||||
−0.713831 | + | 0.700318i | \(0.753042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −455.514 | − | 462.294i | −0.706223 | − | 0.716734i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −571.419 | −0.883182 | −0.441591 | − | 0.897217i | \(-0.645586\pi\) | ||||
−0.441591 | + | 0.897217i | \(0.645586\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1288.19 | 1.98488 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 75.5907 | 0.116115 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1138.05 | 1.74280 | 0.871402 | − | 0.490570i | \(-0.163212\pi\) | ||||
0.871402 | + | 0.490570i | \(0.163212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.4536 | − | 54.2492i | −0.0816085 | − | 0.0828231i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 392.453i | 0.597340i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −260.248 | −0.394914 | −0.197457 | − | 0.980312i | \(-0.563268\pi\) | ||||
−0.197457 | + | 0.980312i | \(0.563268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1012.05i | 1.53109i | 0.643385 | + | 0.765543i | \(0.277529\pi\) | ||||
−0.643385 | + | 0.765543i | \(0.722471\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −435.149 | −0.656334 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.73490 | + | 4.80537i | 0.00712015 | + | 0.00722613i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 204.429i | 0.306490i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 807.373i | 1.20684i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1402.38i | − | 2.08998i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 597.070i | − | 0.887177i | −0.896231 | − | 0.443588i | \(-0.853705\pi\) | ||
0.896231 | − | 0.443588i | \(-0.146295\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 724.437 | + | 10.7030i | 1.07324 | + | 0.0158564i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1112.46 | −1.64322 | −0.821611 | − | 0.570048i | \(-0.806925\pi\) | ||||
−0.821611 | + | 0.570048i | \(0.806925\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 76.4273i | − | 0.112559i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 494.820 | 0.726608 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1089.31i | 1.59489i | 0.603394 | + | 0.797443i | \(0.293815\pi\) | ||||
−0.603394 | + | 0.797443i | \(0.706185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −890.291 | + | 877.235i | −1.29969 | + | 1.28063i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −547.065 | −0.796310 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −70.8599 | −0.102845 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −837.556 | −1.21209 | −0.606046 | − | 0.795430i | \(-0.707245\pi\) | ||||
−0.606046 | + | 0.795430i | \(0.707245\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 45.1892 | 0.0652080 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −791.116 | − | 802.890i | −1.13830 | − | 1.15524i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 529.961i | 0.760346i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −576.236 | −0.824372 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 969.714i | − | 1.38333i | −0.722219 | − | 0.691665i | \(-0.756878\pi\) | ||
0.722219 | − | 0.691665i | \(-0.243122\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2725 | 0.0217247 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 426.017 | − | 419.769i | 0.604279 | − | 0.595418i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 20.2811i | − | 0.0286861i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 636.769i | − | 0.898123i | −0.893501 | − | 0.449061i | \(-0.851758\pi\) | ||
0.893501 | − | 0.449061i | \(-0.148242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 99.7944i | 0.140358i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 765.684i | 1.07389i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1115.21 | − | 1131.81i | −1.55974 | − | 1.58295i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −404.170 | −0.563696 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 955.862i | − | 1.32943i | −0.747096 | − | 0.664717i | \(-0.768552\pi\) | ||
0.747096 | − | 0.664717i | \(-0.231448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.5815 | −0.0604459 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 452.109i | 0.625324i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −368.426 | − | 5.44323i | −0.508173 | − | 0.00750790i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 334.899 | 0.460659 | 0.230330 | − | 0.973113i | \(-0.426020\pi\) | ||||
0.230330 | + | 0.973113i | \(0.426020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −686.879 | −0.942221 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 644.194 | 0.881250 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −321.781 | −0.438992 | −0.219496 | − | 0.975613i | \(-0.570441\pi\) | ||||
−0.219496 | + | 0.975613i | \(0.570441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −382.372 | + | 376.764i | −0.520234 | + | 0.512605i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 473.220i | − | 0.642090i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −446.245 | −0.603850 | −0.301925 | − | 0.953332i | \(-0.597629\pi\) | ||||
−0.301925 | + | 0.953332i | \(0.597629\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 86.3940i | 0.116591i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 436.894 | 0.588014 | 0.294007 | − | 0.955803i | \(-0.405011\pi\) | ||||
0.294007 | + | 0.955803i | \(0.405011\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −275.555 | + | 271.514i | −0.369872 | + | 0.364448i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 442.661i | − | 0.592585i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.4148i | 0.0726499i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 273.036i | − | 0.363564i | −0.983339 | − | 0.181782i | \(-0.941814\pi\) | ||
0.983339 | − | 0.181782i | \(-0.0581865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 711.641i | 0.945075i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −583.032 | + | 574.481i | −0.772227 | + | 0.760902i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 265.844 | 0.351182 | 0.175591 | − | 0.984463i | \(-0.443816\pi\) | ||||
0.175591 | + | 0.984463i | \(0.443816\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 541.420i | − | 0.713333i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 475.322 | 0.624602 | 0.312301 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312301 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.7590i | 0.0665256i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −160.944 | + | 158.583i | −0.210384 | + | 0.207298i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1310.26 | −1.70830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −768.098 | −0.998828 | −0.499414 | − | 0.866364i | \(-0.666451\pi\) | ||||
−0.499414 | + | 0.866364i | \(0.666451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 517.216 | 0.670838 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 628.494 | 0.813059 | 0.406529 | − | 0.913638i | \(-0.366739\pi\) | ||||
0.406529 | + | 0.913638i | \(0.366739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1379.93 | − | 20.3875i | −1.78055 | − | 0.0263064i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.61075i | − | 0.0123690i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 105.218 | 0.135068 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 821.909i | − | 1.05238i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 427.135 | 0.545511 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −206.142 | − | 209.210i | −0.262601 | − | 0.266510i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1051.87i | 1.33655i | 0.743914 | + | 0.668275i | \(0.232967\pi\) | ||||
−0.743914 | + | 0.668275i | \(0.767033\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 990.146i | 1.25494i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.63243i | − | 0.00964909i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1426.41i | 1.79875i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 30.9995 | − | 30.5449i | 0.0389931 | − | 0.0384213i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −783.662 | −0.983265 | −0.491632 | − | 0.870803i | \(-0.663600\pi\) | ||||
−0.491632 | + | 0.870803i | \(0.663600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 593.644i | 0.742983i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 182.432 | 0.227755 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1682.44i | 2.09520i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.1815 | + | 30.6307i | 0.0374925 | + | 0.0380505i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.7936 | 0.0455931 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 860.712 | 1.06392 | 0.531960 | − | 0.846769i | \(-0.321455\pi\) | ||||
0.531960 | + | 0.846769i | \(0.321455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −489.765 | −0.603903 | −0.301951 | − | 0.953323i | \(-0.597638\pi\) | ||||
−0.301951 | + | 0.953323i | \(0.597638\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −327.284 | −0.402564 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 400.888 | − | 395.009i | 0.491887 | − | 0.484674i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 127.898i | − | 0.156545i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −45.9635 | −0.0561215 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 296.634i | − | 0.361309i | −0.983547 | − | 0.180654i | \(-0.942178\pi\) | ||
0.983547 | − | 0.180654i | \(-0.0578215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 544.661 | 0.661800 | 0.330900 | − | 0.943666i | \(-0.392648\pi\) | ||||
0.330900 | + | 0.943666i | \(0.392648\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 975.758 | + | 14.4161i | 1.18274 | + | 0.0174741i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 187.749i | − | 0.227024i | −0.993537 | − | 0.113512i | \(-0.963790\pi\) | ||
0.993537 | − | 0.113512i | \(-0.0362101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 153.430i | − | 0.185078i | −0.995709 | − | 0.0925392i | \(-0.970502\pi\) | ||
0.995709 | − | 0.0925392i | \(-0.0294983\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 825.303i | 0.993145i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 532.825i | − | 0.639646i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −831.831 | − | 844.212i | −0.996205 | − | 1.01103i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1599.83 | 1.91138 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 826.140i | − | 0.984672i | −0.870405 | − | 0.492336i | \(-0.836143\pi\) | ||
0.870405 | − | 0.492336i | \(-0.163857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 623.773 | 0.741704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 553.761i | 0.656893i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 541.246 | + | 549.302i | 0.640528 | + | 0.650062i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 118.699 | 0.140140 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1023.93 | −1.20604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 97.3505 | 0.114395 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −186.426 | −0.218553 | −0.109277 | − | 0.994011i | \(-0.534853\pi\) | ||||
−0.109277 | + | 0.994011i | \(0.534853\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.4850 | + | 31.9536i | 0.0368245 | + | 0.0373726i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1310.23i | − | 1.52885i | −0.644711 | − | 0.764426i | \(-0.723022\pi\) | ||
0.644711 | − | 0.764426i | \(-0.276978\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −655.375 | −0.762951 | −0.381475 | − | 0.924379i | \(-0.624584\pi\) | ||||
−0.381475 | + | 0.924379i | \(0.624584\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 66.2122i | − | 0.0769015i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 170.869 | 0.197995 | 0.0989973 | − | 0.995088i | \(-0.468436\pi\) | ||||
0.0989973 | + | 0.995088i | \(0.468436\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1028.05 | − | 1043.35i | −1.18850 | − | 1.20619i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 372.947i | − | 0.430158i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 427.818i | 0.492311i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 481.329i | 0.552617i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 508.207i | − | 0.582139i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −56.0068 | + | 53.5781i | −0.0640078 | + | 0.0612321i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −303.743 | −0.346343 | −0.173171 | − | 0.984892i | \(-0.555401\pi\) | ||||
−0.173171 | + | 0.984892i | \(0.555401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 608.307i | − | 0.692044i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.32385 | 0.00263774 | 0.00131887 | − | 0.999999i | \(-0.499580\pi\) | ||||
0.00131887 | + | 0.999999i | \(0.499580\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 260.688i | − | 0.295230i | −0.989045 | − | 0.147615i | \(-0.952840\pi\) | ||
0.989045 | − | 0.147615i | \(-0.0471596\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 573.209 | − | 564.803i | 0.647694 | − | 0.638195i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −452.710 | −0.510384 | −0.255192 | − | 0.966890i | \(-0.582139\pi\) | ||||
−0.255192 | + | 0.966890i | \(0.582139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 109.066 | 0.122684 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −475.337 | −0.533487 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 117.861 | 0.131984 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −634.631 | − | 644.077i | −0.709085 | − | 0.719639i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 550.698i | 0.613933i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −813.620 | −0.905028 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.1970i | 0.0479434i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −80.4842 | −0.0891298 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −923.265 | + | 909.725i | −1.02018 | + | 1.00522i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 417.248i | 0.460031i | 0.973187 | + | 0.230015i | \(0.0738777\pi\) | ||||
−0.973187 | + | 0.230015i | \(0.926122\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 134.860i | − | 0.148361i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 673.050i | 0.738804i | 0.929270 | + | 0.369402i | \(0.120437\pi\) | ||||
−0.929270 | + | 0.369402i | \(0.879563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1897.69i | − | 2.07852i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −614.868 | − | 624.019i | −0.671987 | − | 0.681988i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.44465 | −0.0102995 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1204.93i | 1.31113i | 0.755138 | + | 0.655566i | \(0.227570\pi\) | ||||
−0.755138 | + | 0.655566i | \(0.772430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 290.665 | 0.315597 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 835.993i | 0.905735i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.59210 | + | 175.447i | −0.00280227 | + | 0.189672i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −289.797 | −0.312618 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 658.790 | 0.709139 | 0.354569 | − | 0.935030i | \(-0.384628\pi\) | ||||
0.354569 | + | 0.935030i | \(0.384628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −105.787 | −0.113627 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −780.691 | −0.836754 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −689.965 | + | 679.846i | −0.737930 | + | 0.727108i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1690.80i | 1.80448i | 0.431237 | + | 0.902239i | \(0.358077\pi\) | ||||
−0.431237 | + | 0.902239i | \(0.641923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 621.664 | 0.662048 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 219.663i | 0.233436i | 0.993165 | + | 0.116718i | \(0.0372373\pi\) | ||||
−0.993165 | + | 0.116718i | \(0.962763\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 670.685 | 0.711225 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 64.0000 | − | 63.0614i | 0.0677249 | − | 0.0667317i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 552.774i | − | 0.583711i | −0.956462 | − | 0.291855i | \(-0.905727\pi\) | ||
0.956462 | − | 0.291855i | \(-0.0942726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1711.27i | − | 1.80324i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 477.513i | − | 0.502117i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.7654i | 0.0165429i | 0.999966 | + | 0.00827144i | \(0.00263291\pi\) | ||||
−0.999966 | + | 0.00827144i | \(0.997367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 958.842 | − | 944.780i | 1.00402 | − | 0.989299i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 575.316 | 0.601166 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 154.998i | 0.161624i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2086.39 | −2.17107 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 361.834i | 0.375736i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 517.060 | − | 509.477i | 0.535814 | − | 0.527956i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 308.027 | 0.318538 | 0.159269 | − | 0.987235i | \(-0.449086\pi\) | ||||
0.159269 | + | 0.987235i | \(0.449086\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 52.6668 | 0.0543517 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.8794 | 0.0431302 | 0.0215651 | − | 0.999767i | \(-0.493135\pi\) | ||||
0.0215651 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −139.781 | −0.143660 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −992.478 | − | 14.6632i | −1.01793 | − | 0.0150391i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 586.276i | − | 0.600078i | −0.953927 | − | 0.300039i | \(-0.903000\pi\) | ||
0.953927 | − | 0.300039i | \(-0.0969997\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 782.085 | 0.798861 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 337.525i | 0.344062i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1627.01 | 1.65515 | 0.827573 | − | 0.561358i | \(-0.189721\pi\) | ||||
0.827573 | + | 0.561358i | \(0.189721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 955.862 | + | 970.088i | 0.970418 | + | 0.984861i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 74.1686i | − | 0.0751455i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 815.252i | − | 0.824319i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 255.629i | 0.257950i | 0.991648 | + | 0.128975i | \(0.0411687\pi\) | ||||
−0.991648 | + | 0.128975i | \(0.958831\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 736.260i | − | 0.741450i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1172.86 | − | 1155.66i | 1.17875 | − | 1.16147i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1001.35 | −1.00436 | −0.502180 | − | 0.864763i | \(-0.667468\pi\) | ||||
−0.502180 | + | 0.864763i | \(0.667468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 203.405i | − | 0.203609i |
(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 | 640.3.e.i.319.8 | yes | 16 | |
4.3 | odd | 2 | inner | 640.3.e.i.319.12 | yes | 16 | |
5.4 | even | 2 | inner | 640.3.e.i.319.10 | yes | 16 | |
8.3 | odd | 2 | inner | 640.3.e.i.319.5 | ✓ | 16 | |
8.5 | even | 2 | inner | 640.3.e.i.319.9 | yes | 16 | |
16.3 | odd | 4 | 1280.3.h.l.1279.3 | 8 | |||
16.5 | even | 4 | 1280.3.h.h.1279.4 | 8 | |||
16.11 | odd | 4 | 1280.3.h.h.1279.6 | 8 | |||
16.13 | even | 4 | 1280.3.h.l.1279.5 | 8 | |||
20.19 | odd | 2 | inner | 640.3.e.i.319.6 | yes | 16 | |
40.19 | odd | 2 | inner | 640.3.e.i.319.11 | yes | 16 | |
40.29 | even | 2 | inner | 640.3.e.i.319.7 | yes | 16 | |
80.19 | odd | 4 | 1280.3.h.l.1279.6 | 8 | |||
80.29 | even | 4 | 1280.3.h.l.1279.4 | 8 | |||
80.59 | odd | 4 | 1280.3.h.h.1279.3 | 8 | |||
80.69 | even | 4 | 1280.3.h.h.1279.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.3.e.i.319.5 | ✓ | 16 | 8.3 | odd | 2 | inner | |
640.3.e.i.319.6 | yes | 16 | 20.19 | odd | 2 | inner | |
640.3.e.i.319.7 | yes | 16 | 40.29 | even | 2 | inner | |
640.3.e.i.319.8 | yes | 16 | 1.1 | even | 1 | trivial | |
640.3.e.i.319.9 | yes | 16 | 8.5 | even | 2 | inner | |
640.3.e.i.319.10 | yes | 16 | 5.4 | even | 2 | inner | |
640.3.e.i.319.11 | yes | 16 | 40.19 | odd | 2 | inner | |
640.3.e.i.319.12 | yes | 16 | 4.3 | odd | 2 | inner | |
1280.3.h.h.1279.3 | 8 | 80.59 | odd | 4 | |||
1280.3.h.h.1279.4 | 8 | 16.5 | even | 4 | |||
1280.3.h.h.1279.5 | 8 | 80.69 | even | 4 | |||
1280.3.h.h.1279.6 | 8 | 16.11 | odd | 4 | |||
1280.3.h.l.1279.3 | 8 | 16.3 | odd | 4 | |||
1280.3.h.l.1279.4 | 8 | 80.29 | even | 4 | |||
1280.3.h.l.1279.5 | 8 | 16.13 | even | 4 | |||
1280.3.h.l.1279.6 | 8 | 80.19 | odd | 4 |