Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + \cdots + 69312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Root | \(-0.656794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.41 |
Dual form | 76.3.j.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.215056 | + | 0.590861i | 0.0716853 | + | 0.196954i | 0.970361 | − | 0.241660i | \(-0.0776919\pi\) |
−0.898676 | + | 0.438614i | \(0.855470\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.30596 | + | 7.40644i | −0.261191 | + | 1.48129i | 0.518475 | + | 0.855093i | \(0.326500\pi\) |
−0.779666 | + | 0.626196i | \(0.784611\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.03221 | + | 5.25195i | 0.433173 | + | 0.750278i | 0.997145 | − | 0.0755161i | \(-0.0240604\pi\) |
−0.563971 | + | 0.825795i | \(0.690727\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.59153 | − | 5.53095i | 0.732392 | − | 0.614550i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.46952 | − | 7.74143i | 0.406320 | − | 0.703766i | −0.588154 | − | 0.808749i | \(-0.700145\pi\) |
0.994474 | + | 0.104982i | \(0.0334786\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.31563 | + | 17.3521i | −0.485818 | + | 1.33477i | 0.418617 | + | 0.908163i | \(0.362515\pi\) |
−0.904435 | + | 0.426611i | \(0.859707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.65703 | + | 0.821160i | −0.310469 | + | 0.0547440i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.3773 | − | 12.9031i | −0.904547 | − | 0.759005i | 0.0665271 | − | 0.997785i | \(-0.478808\pi\) |
−0.971074 | + | 0.238780i | \(0.923253\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.8300 | − | 6.56436i | 0.938421 | − | 0.345493i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.45108 | + | 2.92108i | −0.116718 | + | 0.139099i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.31353 | − | 24.4632i | −0.187545 | − | 1.06362i | −0.922642 | − | 0.385657i | \(-0.873975\pi\) |
0.735097 | − | 0.677962i | \(-0.237136\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −29.6575 | − | 10.7945i | −1.18630 | − | 0.431778i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.58643 | + | 5.53473i | 0.355053 | + | 0.204990i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13.6106 | − | 16.2205i | −0.469332 | − | 0.559328i | 0.478504 | − | 0.878085i | \(-0.341179\pi\) |
−0.947836 | + | 0.318757i | \(0.896735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.7238 | − | 20.0478i | 1.12012 | − | 0.646704i | 0.178691 | − | 0.983905i | \(-0.442814\pi\) |
0.941432 | + | 0.337202i | \(0.109480\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.53530 | + | 0.976023i | 0.167736 | + | 0.0295765i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −42.8582 | + | 15.5991i | −1.22452 | + | 0.445689i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.8707i | 0.401912i | 0.979600 | + | 0.200956i | \(0.0644048\pi\) | ||||
−0.979600 | + | 0.200956i | \(0.935595\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.6109 | −0.297714 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19.0165 | + | 52.2475i | 0.463818 | + | 1.27433i | 0.922592 | + | 0.385776i | \(0.126066\pi\) |
−0.458775 | + | 0.888553i | \(0.651712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.72062 | − | 38.1145i | 0.156294 | − | 0.886385i | −0.801300 | − | 0.598263i | \(-0.795858\pi\) |
0.957594 | − | 0.288122i | \(-0.0930309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 32.3564 | + | 56.0430i | 0.719032 | + | 1.24540i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.10558 | − | 0.927693i | 0.0235230 | − | 0.0197382i | −0.630950 | − | 0.775823i | \(-0.717335\pi\) |
0.654473 | + | 0.756085i | \(0.272890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.11135 | − | 10.5852i | 0.124721 | − | 0.216024i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.31695 | − | 11.8607i | 0.0846461 | − | 0.232563i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23.5326 | − | 4.14943i | 0.444011 | − | 0.0782911i | 0.0528270 | − | 0.998604i | \(-0.483177\pi\) |
0.391184 | + | 0.920313i | \(0.372066\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 51.4995 | + | 43.2132i | 0.936354 | + | 0.785694i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.71307 | + | 9.12335i | 0.135317 | + | 0.160059i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34.9963 | + | 41.7070i | −0.593158 | + | 0.706898i | −0.976210 | − | 0.216829i | \(-0.930429\pi\) |
0.383052 | + | 0.923727i | \(0.374873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.501142 | − | 2.84212i | −0.00821544 | − | 0.0465921i | 0.980424 | − | 0.196896i | \(-0.0630860\pi\) |
−0.988640 | + | 0.150304i | \(0.951975\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 49.0352 | + | 17.8474i | 0.778337 | + | 0.283291i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −120.269 | − | 69.4374i | −1.85029 | − | 1.06827i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 71.6504 | + | 85.3896i | 1.06941 | + | 1.27447i | 0.959857 | + | 0.280490i | \(0.0904971\pi\) |
0.109552 | + | 0.993981i | \(0.465058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.5267 | − | 7.80966i | 0.196039 | − | 0.113183i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −114.429 | − | 20.1770i | −1.61168 | − | 0.284183i | −0.706022 | − | 0.708190i | \(-0.749512\pi\) |
−0.905659 | + | 0.424007i | \(0.860623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −42.9373 | + | 15.6279i | −0.588182 | + | 0.214081i | −0.618930 | − | 0.785446i | \(-0.712433\pi\) |
0.0307476 | + | 0.999527i | \(0.490211\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 19.8449i | − | 0.264599i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 54.2101 | 0.704028 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.39352 | − | 14.8186i | −0.0682725 | − | 0.187577i | 0.900864 | − | 0.434101i | \(-0.142934\pi\) |
−0.969137 | + | 0.246524i | \(0.920712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 12.2390 | − | 69.4107i | 0.151098 | − | 0.856922i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −38.7171 | − | 67.0600i | −0.466472 | − | 0.807952i | 0.532795 | − | 0.846244i | \(-0.321142\pi\) |
−0.999267 | + | 0.0382919i | \(0.987808\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 115.648 | − | 97.0402i | 1.36056 | − | 1.14165i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.65702 | − | 11.5303i | 0.0765175 | − | 0.132532i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 49.3453 | − | 135.575i | 0.554441 | − | 1.52331i | −0.273143 | − | 0.961973i | \(-0.588063\pi\) |
0.827584 | − | 0.561342i | \(-0.189715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −110.282 | + | 19.4458i | −1.21190 | + | 0.213690i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.3130 | + | 16.2056i | 0.207667 | + | 0.174253i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 25.3334 | + | 140.630i | 0.266667 | + | 1.48031i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −110.468 | + | 131.651i | −1.13885 | + | 1.35722i | −0.214020 | + | 0.976829i | \(0.568656\pi\) |
−0.924825 | + | 0.380394i | \(0.875789\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.3565 | − | 75.7486i | −0.134914 | − | 0.765137i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −31.0298 | − | 11.2939i | −0.307225 | − | 0.111821i | 0.183807 | − | 0.982962i | \(-0.441158\pi\) |
−0.491032 | + | 0.871142i | \(0.663380\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −162.740 | − | 93.9582i | −1.58000 | − | 0.912215i | −0.994857 | − | 0.101287i | \(-0.967704\pi\) |
−0.585146 | − | 0.810928i | \(-0.698963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.4338 | − | 21.9686i | −0.175560 | − | 0.209224i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −55.5976 | + | 32.0993i | −0.519604 | + | 0.299994i | −0.736773 | − | 0.676141i | \(-0.763651\pi\) |
0.217169 | + | 0.976134i | \(0.430318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 116.313 | + | 20.5091i | 1.06709 | + | 0.188157i | 0.679501 | − | 0.733675i | \(-0.262196\pi\) |
0.387590 | + | 0.921832i | \(0.373308\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.78654 | + | 3.19804i | −0.0791580 | + | 0.0288112i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 49.2047i | − | 0.435440i | −0.976011 | − | 0.217720i | \(-0.930138\pi\) | ||
0.976011 | − | 0.217720i | \(-0.0698619\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 186.819 | 1.62451 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 54.3437 | + | 149.308i | 0.464476 | + | 1.27614i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.1391 | − | 119.886i | 0.177639 | − | 1.00744i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.5468 | + | 35.5882i | 0.169809 | + | 0.294117i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.7814 | + | 22.4722i | −0.217735 | + | 0.182701i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.6713 | − | 42.7319i | 0.197370 | − | 0.341855i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −46.1499 | + | 126.796i | −0.363385 | + | 0.998392i | 0.614439 | + | 0.788964i | \(0.289382\pi\) |
−0.977824 | + | 0.209428i | \(0.932840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.9657 | − | 4.22580i | 0.185781 | − | 0.0327581i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 146.715 | + | 123.109i | 1.11996 | + | 0.939761i | 0.998603 | − | 0.0528470i | \(-0.0168295\pi\) |
0.121361 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 88.5401 | + | 73.7377i | 0.665715 | + | 0.554419i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −53.5121 | + | 63.7732i | −0.396386 | + | 0.472394i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.91656 | − | 39.2258i | −0.0504858 | − | 0.286319i | 0.949104 | − | 0.314963i | \(-0.101992\pi\) |
−0.999590 | + | 0.0286439i | \(0.990881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −185.193 | − | 67.4049i | −1.33233 | − | 0.484927i | −0.424939 | − | 0.905222i | \(-0.639704\pi\) |
−0.907388 | + | 0.420295i | \(0.861927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.785899 | + | 0.453739i | 0.00557375 | + | 0.00321801i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 106.102 | + | 126.447i | 0.741971 | + | 0.884247i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 137.911 | − | 79.6231i | 0.951112 | − | 0.549125i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.56865 | + | 1.33456i | 0.0514874 | + | 0.00907862i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −204.136 | + | 74.2993i | −1.37004 | + | 0.498653i | −0.919143 | − | 0.393924i | \(-0.871117\pi\) |
−0.450895 | + | 0.892577i | \(0.648895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 30.3509i | − | 0.201000i | −0.994937 | − | 0.100500i | \(-0.967956\pi\) | ||
0.994937 | − | 0.100500i | \(-0.0320442\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −172.726 | −1.12893 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 103.135 | + | 283.362i | 0.665388 | + | 1.82814i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.72805 | + | 55.1705i | −0.0619621 | + | 0.351405i | 0.938026 | + | 0.346564i | \(0.112652\pi\) |
−0.999988 | + | 0.00484024i | \(0.998459\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.51255 | + | 13.0121i | 0.0472487 | + | 0.0818372i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 115.400 | − | 96.8322i | 0.716771 | − | 0.601442i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 103.169 | − | 178.693i | 0.632936 | − | 1.09628i | −0.354012 | − | 0.935241i | \(-0.615183\pi\) |
0.986948 | − | 0.161037i | \(-0.0514838\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.4577 | + | 39.7223i | −0.0876226 | + | 0.240741i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 168.167 | − | 29.6524i | 1.00699 | − | 0.177559i | 0.354257 | − | 0.935148i | \(-0.384734\pi\) |
0.652732 | + | 0.757589i | \(0.273623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −131.745 | − | 110.547i | −0.779557 | − | 0.654126i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 81.2199 | − | 141.886i | 0.474970 | − | 0.829743i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.6636 | + | 18.6671i | −0.0905410 | + | 0.107903i | −0.809413 | − | 0.587240i | \(-0.800214\pi\) |
0.718872 | + | 0.695143i | \(0.244659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33.2361 | − | 188.491i | −0.189920 | − | 1.07709i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32.1692 | − | 11.7086i | −0.181747 | − | 0.0661504i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −147.021 | − | 84.8825i | −0.821346 | − | 0.474204i | 0.0295346 | − | 0.999564i | \(-0.490597\pi\) |
−0.850880 | + | 0.525360i | \(0.823931\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −69.4091 | − | 82.7185i | −0.383476 | − | 0.457009i | 0.539432 | − | 0.842029i | \(-0.318639\pi\) |
−0.922908 | + | 0.385020i | \(0.874194\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.57152 | − | 0.907318i | 0.00858755 | − | 0.00495802i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −110.139 | − | 19.4205i | −0.595347 | − | 0.104976i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −168.617 | + | 61.3717i | −0.901697 | + | 0.328191i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 67.1299i | 0.355185i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −152.732 | −0.799642 | −0.399821 | − | 0.916593i | \(-0.630928\pi\) | ||||
−0.399821 | + | 0.916593i | \(0.630928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.21211 | − | 19.8151i | −0.0373685 | − | 0.102669i | 0.919605 | − | 0.392844i | \(-0.128509\pi\) |
−0.956974 | + | 0.290175i | \(0.906287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.1633 | − | 85.9952i | 0.0777604 | − | 0.441001i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 174.804 | + | 302.769i | 0.887329 | + | 1.53690i | 0.843021 | + | 0.537881i | \(0.180775\pi\) |
0.0443078 | + | 0.999018i | \(0.485892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 224.125 | − | 188.063i | 1.12626 | − | 0.945041i | 0.127352 | − | 0.991858i | \(-0.459352\pi\) |
0.998903 | + | 0.0468167i | \(0.0149077\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −35.0445 | + | 60.6989i | −0.174351 | + | 0.301985i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 43.9190 | − | 120.666i | 0.216350 | − | 0.594416i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −411.803 | + | 72.6119i | −2.00879 | + | 0.354204i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −163.738 | − | 137.392i | −0.791004 | − | 0.663731i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.8740 | − | 167.369i | 0.138153 | − | 0.800810i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.6261 | − | 15.0472i | 0.0598394 | − | 0.0713138i | −0.735294 | − | 0.677748i | \(-0.762956\pi\) |
0.795134 | + | 0.606434i | \(0.207401\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.6869 | − | 71.9510i | −0.0595629 | − | 0.337798i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 273.516 | + | 99.5518i | 1.27217 | + | 0.463032i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 210.580 | + | 121.579i | 0.970415 | + | 0.560270i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.4678 | − | 22.0091i | −0.0843280 | − | 0.100498i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 321.012 | − | 185.337i | 1.45254 | − | 0.838627i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −106.283 | − | 18.7405i | −0.476603 | − | 0.0840380i | −0.0698139 | − | 0.997560i | \(-0.522241\pi\) |
−0.406789 | + | 0.913522i | \(0.633352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −255.192 | + | 92.8824i | −1.13419 | + | 0.412811i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 72.2905i | − | 0.318460i | −0.987241 | − | 0.159230i | \(-0.949099\pi\) | ||
0.987241 | − | 0.159230i | \(-0.0509012\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 63.8810 | 0.278956 | 0.139478 | − | 0.990225i | \(-0.455458\pi\) | ||||
0.139478 | + | 0.990225i | \(0.455458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.6582 | + | 32.0306i | 0.0504684 | + | 0.138661i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.64695 | − | 54.7105i | 0.0414032 | − | 0.234809i | −0.957083 | − | 0.289814i | \(-0.906406\pi\) |
0.998486 | + | 0.0550052i | \(0.0175175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.42707 | + | 9.39995i | 0.0230939 | + | 0.0399998i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.59581 | − | 6.37364i | 0.0320498 | − | 0.0268930i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3703 | + | 40.4785i | −0.0977835 | + | 0.169366i | −0.910767 | − | 0.412921i | \(-0.864509\pi\) |
0.812983 | + | 0.582287i | \(0.197842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −156.442 | + | 429.821i | −0.649138 | + | 1.78349i | −0.0282383 | + | 0.999601i | \(0.508990\pi\) |
−0.620900 | + | 0.783890i | \(0.713233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 141.756 | − | 24.9954i | 0.583357 | − | 0.102862i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 70.4173 | + | 59.0871i | 0.287418 | + | 0.241172i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.29737 | + | 350.845i | 0.00525252 | + | 1.42043i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.2968 | − | 37.2981i | 0.125690 | − | 0.149792i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 40.4570 | + | 229.443i | 0.161183 | + | 0.914115i | 0.952913 | + | 0.303244i | \(0.0980697\pi\) |
−0.791730 | + | 0.610872i | \(0.790819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −208.660 | − | 75.9460i | −0.824742 | − | 0.300182i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 82.2080 | + | 47.4628i | 0.322384 | + | 0.186129i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 134.459 | + | 160.241i | 0.523185 | + | 0.623508i | 0.961331 | − | 0.275396i | \(-0.0888091\pi\) |
−0.438146 | + | 0.898904i | \(0.644365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −78.1004 | + | 45.0913i | −0.301546 | + | 0.174098i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −179.430 | − | 31.6383i | −0.687471 | − | 0.121220i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 407.312 | − | 148.249i | 1.54872 | − | 0.563686i | 0.580599 | − | 0.814189i | \(-0.302818\pi\) |
0.968116 | + | 0.250503i | \(0.0805960\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 179.712i | 0.678157i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 90.7180 | 0.339768 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −45.8847 | − | 126.067i | −0.170575 | − | 0.468651i | 0.824720 | − | 0.565541i | \(-0.191333\pi\) |
−0.995295 | + | 0.0968902i | \(0.969110\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.79532 | + | 55.5520i | −0.0361451 | + | 0.204989i | −0.997532 | − | 0.0702106i | \(-0.977633\pi\) |
0.961387 | + | 0.275200i | \(0.0887440\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −35.2066 | − | 60.9797i | −0.128962 | − | 0.223369i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −216.119 | + | 181.346i | −0.785889 | + | 0.659439i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 75.3401 | − | 130.493i | 0.271986 | − | 0.471094i | −0.697384 | − | 0.716697i | \(-0.745653\pi\) |
0.969370 | + | 0.245604i | \(0.0789862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 118.000 | − | 324.202i | 0.422938 | − | 1.16201i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 233.857 | − | 41.2352i | 0.832230 | − | 0.146745i | 0.258729 | − | 0.965950i | \(-0.416696\pi\) |
0.573500 | + | 0.819205i | \(0.305585\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 307.886 | + | 258.347i | 1.08794 | + | 0.912887i | 0.996555 | − | 0.0829295i | \(-0.0264276\pi\) |
0.0913804 | + | 0.995816i | \(0.470872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −77.6445 | + | 45.2117i | −0.272437 | + | 0.158638i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −216.739 | + | 258.299i | −0.755188 | + | 0.899998i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.7873 | + | 112.219i | 0.0684682 | + | 0.388303i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −101.544 | − | 36.9590i | −0.348948 | − | 0.127007i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −136.838 | − | 79.0034i | −0.467024 | − | 0.269636i | 0.247969 | − | 0.968768i | \(-0.420237\pi\) |
−0.714993 | + | 0.699132i | \(0.753570\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −263.197 | − | 313.666i | −0.892192 | − | 1.06327i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 85.6935 | − | 49.4751i | 0.288530 | − | 0.166583i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 451.730 | + | 79.6522i | 1.51080 | + | 0.266395i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 220.554 | − | 80.2751i | 0.732738 | − | 0.266695i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 20.7631i | − | 0.0685250i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.7044 | 0.0711621 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −176.325 | − | 484.450i | −0.574349 | − | 1.57801i | −0.797559 | − | 0.603241i | \(-0.793876\pi\) |
0.223209 | − | 0.974771i | \(-0.428347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.5180 | − | 116.363i | 0.0664012 | − | 0.376580i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −133.065 | − | 230.476i | −0.427863 | − | 0.741081i | 0.568820 | − | 0.822462i | \(-0.307400\pi\) |
−0.996683 | + | 0.0813813i | \(0.974067\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −143.393 | + | 120.321i | −0.458123 | + | 0.384411i | −0.842440 | − | 0.538790i | \(-0.818882\pi\) |
0.384317 | + | 0.923201i | \(0.374437\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −196.223 | + | 339.869i | −0.622931 | + | 1.07895i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −49.3857 | + | 135.686i | −0.155791 | + | 0.428032i | −0.992892 | − | 0.119016i | \(-0.962026\pi\) |
0.837101 | + | 0.547048i | \(0.184248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −186.403 | + | 32.8679i | −0.584335 | + | 0.103034i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.9228 | − | 25.9473i | −0.0963328 | − | 0.0808328i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −358.878 | − | 129.120i | −1.11108 | − | 0.399752i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 374.612 | − | 446.445i | 1.15265 | − | 1.37368i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.8957 | + | 73.1354i | 0.0394365 | + | 0.223656i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.22456 | + | 2.99349i | 0.0249987 | + | 0.00909877i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −365.183 | − | 210.839i | −1.10327 | − | 0.636975i | −0.166194 | − | 0.986093i | \(-0.553148\pi\) |
−0.937079 | + | 0.349118i | \(0.886481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 82.2493 | + | 98.0209i | 0.246995 | + | 0.294357i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −726.005 | + | 419.159i | −2.16718 | + | 1.25122i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 66.7912 | + | 11.7771i | 0.198193 | + | 0.0349468i | 0.271863 | − | 0.962336i | \(-0.412360\pi\) |
−0.0736701 | + | 0.997283i | \(0.523471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.0731 | − | 10.5818i | 0.0857615 | − | 0.0312146i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 358.416i | − | 1.05107i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 371.281 | 1.08245 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 40.1765 | + | 110.384i | 0.116454 | + | 0.319953i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −49.7258 | + | 282.009i | −0.143302 | + | 0.812705i | 0.825413 | + | 0.564529i | \(0.190942\pi\) |
−0.968715 | + | 0.248176i | \(0.920169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −236.860 | − | 410.253i | −0.678681 | − | 1.17551i | −0.975378 | − | 0.220538i | \(-0.929219\pi\) |
0.296698 | − | 0.954971i | \(-0.404115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −156.583 | + | 131.389i | −0.446106 | + | 0.374328i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 106.688 | − | 184.789i | 0.302233 | − | 0.523483i | −0.674408 | − | 0.738358i | \(-0.735601\pi\) |
0.976641 | + | 0.214876i | \(0.0689346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 298.879 | − | 821.164i | 0.841914 | − | 2.31314i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 75.3818 | − | 13.2919i | 0.211154 | − | 0.0372321i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −41.4292 | − | 34.7632i | −0.115402 | − | 0.0968334i | 0.583261 | − | 0.812285i | \(-0.301777\pi\) |
−0.698662 | + | 0.715452i | \(0.746221\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 274.818 | − | 234.085i | 0.761270 | − | 0.648435i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.6089 | + | 19.7938i | −0.0457546 | + | 0.0545283i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −59.6729 | − | 338.422i | −0.163487 | − | 0.927183i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 414.996 | + | 151.046i | 1.13078 | + | 0.411570i | 0.838575 | − | 0.544786i | \(-0.183389\pi\) |
0.292204 | + | 0.956356i | \(0.405611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 414.326 | + | 239.211i | 1.12284 | + | 0.648269i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 93.1483 | + | 111.010i | 0.251074 | + | 0.299218i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −463.827 | + | 267.791i | −1.24350 | + | 0.717937i | −0.969806 | − | 0.243878i | \(-0.921580\pi\) |
−0.273698 | + | 0.961816i | \(0.588247\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.5543 | + | 5.38754i | 0.0814781 | + | 0.0143668i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 367.419 | − | 133.730i | 0.974586 | − | 0.354720i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 638.979i | 1.68596i | 0.537946 | + | 0.842980i | \(0.319201\pi\) | ||||
−0.537946 | + | 0.842980i | \(0.680799\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −84.8435 | −0.222686 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −52.7059 | − | 144.808i | −0.137613 | − | 0.378089i | 0.851674 | − | 0.524072i | \(-0.175588\pi\) |
−0.989287 | + | 0.145983i | \(0.953366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −70.7960 | + | 401.504i | −0.183886 | + | 1.04287i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −166.511 | − | 288.405i | −0.430260 | − | 0.745232i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −437.089 | + | 366.761i | −1.12362 | + | 0.942830i | −0.998782 | − | 0.0493469i | \(-0.984286\pi\) |
−0.124839 | + | 0.992177i | \(0.539842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −249.321 | + | 431.836i | −0.637649 | + | 1.10444i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −41.1882 | + | 113.164i | −0.104805 | + | 0.287948i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 116.797 | − | 20.5944i | 0.295688 | − | 0.0521377i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −389.565 | − | 326.883i | −0.981271 | − | 0.823384i | 0.00300971 | − | 0.999995i | \(-0.499042\pi\) |
−0.984281 | + | 0.176611i | \(0.943486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −24.5277 | + | 68.1726i | −0.0614729 | + | 0.170859i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 205.447 | − | 244.843i | 0.512338 | − | 0.610580i | −0.446413 | − | 0.894827i | \(-0.647299\pi\) |
0.958751 | + | 0.284246i | \(0.0917434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 128.568 | + | 729.144i | 0.319027 | + | 1.80929i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 498.103 | + | 181.294i | 1.22988 | + | 0.447641i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 115.121 | + | 66.4650i | 0.282852 | + | 0.163305i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 94.1956 | + | 112.258i | 0.230307 | + | 0.274469i | 0.868805 | − | 0.495154i | \(-0.164888\pi\) |
−0.638498 | + | 0.769623i | \(0.720444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.6895 | − | 12.5225i | 0.0527726 | − | 0.0304683i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −325.159 | − | 57.3343i | −0.787310 | − | 0.138824i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 547.239 | − | 199.179i | 1.31865 | − | 0.479949i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 123.919i | − | 0.297169i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −271.782 | −0.648644 | −0.324322 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324322 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.8085 | − | 65.4132i | −0.0565522 | − | 0.155376i | 0.908200 | − | 0.418537i | \(-0.137457\pi\) |
−0.964752 | + | 0.263161i | \(0.915235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.15645 | − | 12.2298i | 0.00509799 | − | 0.0289122i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 316.771 | + | 548.663i | 0.745343 | + | 1.29097i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4071 | − | 11.2499i | 0.0313983 | − | 0.0263463i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −51.8950 | + | 89.8847i | −0.120967 | + | 0.209521i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −90.9398 | + | 249.855i | −0.210997 | + | 0.579710i | −0.999370 | − | 0.0354877i | \(-0.988702\pi\) |
0.788373 | + | 0.615198i | \(0.210924\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 434.577 | − | 76.6277i | 1.00364 | − | 0.176969i | 0.352408 | − | 0.935846i | \(-0.385363\pi\) |
0.651234 | + | 0.758877i | \(0.274252\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 76.7047 | + | 64.3629i | 0.176333 | + | 0.147961i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −237.496 | − | 407.864i | −0.543468 | − | 0.933328i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.7798 | + | 41.4489i | −0.0792250 | + | 0.0944167i | −0.804201 | − | 0.594357i | \(-0.797406\pi\) |
0.724976 | + | 0.688774i | \(0.241851\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.2629 | − | 103.574i | −0.0414125 | − | 0.234862i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −218.537 | − | 79.5408i | −0.493311 | − | 0.179550i | 0.0833723 | − | 0.996518i | \(-0.473431\pi\) |
−0.576683 | + | 0.816968i | \(0.695653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 939.686 | + | 542.528i | 2.11165 | + | 1.21916i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −87.8011 | − | 104.637i | −0.196423 | − | 0.234088i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 343.201 | − | 198.147i | 0.764368 | − | 0.441308i | −0.0664938 | − | 0.997787i | \(-0.521181\pi\) |
0.830862 | + | 0.556479i | \(0.187848\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 489.465 | + | 86.3059i | 1.08529 | + | 0.191366i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.9332 | − | 6.52714i | 0.0395876 | − | 0.0144087i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 842.196i | − | 1.85098i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −660.306 | −1.44487 | −0.722435 | − | 0.691439i | \(-0.756977\pi\) | ||||
−0.722435 | + | 0.691439i | \(0.756977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −75.9983 | − | 208.804i | −0.165574 | − | 0.454910i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −120.280 | + | 682.139i | −0.260910 | + | 1.47969i | 0.519524 | + | 0.854456i | \(0.326109\pi\) |
−0.780434 | + | 0.625238i | \(0.785002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −53.6664 | − | 92.9529i | −0.115910 | − | 0.200762i | 0.802233 | − | 0.597011i | \(-0.203645\pi\) |
−0.918143 | + | 0.396249i | \(0.870312\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −145.247 | + | 121.877i | −0.312360 | + | 0.262101i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −104.758 | + | 181.446i | −0.224320 | + | 0.388534i | −0.956115 | − | 0.292991i | \(-0.905350\pi\) |
0.731795 | + | 0.681525i | \(0.238683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −231.203 | + | 635.224i | −0.492969 | + | 1.35442i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.6902 | + | 6.11682i | −0.0736522 | + | 0.0129869i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −265.023 | − | 222.381i | −0.560303 | − | 0.470150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −599.653 | + | 2.21742i | −1.26243 | + | 0.00466826i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 132.165 | − | 157.509i | 0.277076 | − | 0.330207i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 58.0466 | + | 329.198i | 0.121183 | + | 0.687262i | 0.983502 | + | 0.180897i | \(0.0579000\pi\) |
−0.862319 | + | 0.506365i | \(0.830989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −258.038 | − | 93.9181i | −0.536461 | − | 0.195256i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 82.0318 | + | 47.3611i | 0.169838 | + | 0.0980561i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −830.796 | − | 990.104i | −1.71298 | − | 2.04145i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 282.361 | − | 163.021i | 0.579797 | − | 0.334746i | −0.181256 | − | 0.983436i | \(-0.558016\pi\) |
0.761053 | + | 0.648690i | \(0.224683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 127.770 | + | 22.5293i | 0.261288 | + | 0.0460721i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −123.021 | + | 44.7760i | −0.250552 | + | 0.0911935i | −0.464243 | − | 0.885708i | \(-0.653674\pi\) |
0.213691 | + | 0.976901i | \(0.431451\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 425.047i | 0.862164i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 578.470 | 1.16863 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −241.006 | − | 662.158i | −0.484921 | − | 1.33231i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 89.2488 | − | 506.155i | 0.178855 | − | 1.01434i | −0.754744 | − | 0.656020i | \(-0.772239\pi\) |
0.933599 | − | 0.358319i | \(-0.116650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.6857 | + | 92.9864i | 0.107157 | + | 0.185602i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −101.395 | + | 85.0803i | −0.201580 | + | 0.169146i | −0.737990 | − | 0.674812i | \(-0.764225\pi\) |
0.536410 | + | 0.843958i | \(0.319780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 124.171 | − | 215.071i | 0.245883 | − | 0.425883i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 36.9855 | − | 101.617i | 0.0729497 | − | 0.200428i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −87.0041 | + | 15.3412i | −0.170931 | + | 0.0301398i | −0.258459 | − | 0.966022i | \(-0.583215\pi\) |
0.0875273 | + | 0.996162i | \(0.472103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −212.272 | − | 178.117i | −0.415405 | − | 0.348566i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 207.258 | + | 35.7555i | 0.404012 | + | 0.0696988i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 908.427 | − | 1082.62i | 1.76394 | − | 2.10218i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.24026 | − | 12.7051i | −0.00433318 | − | 0.0245747i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.3982 | − | 5.24053i | −0.0277423 | − | 0.0100974i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 638.201 | + | 368.465i | 1.22495 | + | 0.707227i | 0.965970 | − | 0.258654i | \(-0.0832790\pi\) |
0.258984 | + | 0.965882i | \(0.416612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −59.1609 | − | 70.5052i | −0.113118 | − | 0.134809i | 0.706514 | − | 0.707699i | \(-0.250267\pi\) |
−0.819632 | + | 0.572890i | \(0.805822\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 104.224 | − | 60.1740i | 0.198523 | − | 0.114617i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −792.637 | − | 139.763i | −1.50405 | − | 0.265205i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −82.7460 | + | 30.1171i | −0.156420 | + | 0.0569321i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 468.476i | 0.882252i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1026.70 | −1.92627 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −165.134 | − | 453.701i | −0.308661 | − | 0.848039i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.5361 | − | 105.123i | 0.0345179 | − | 0.195760i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −54.6296 | − | 94.6212i | −0.101354 | − | 0.175550i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 151.780 | − | 127.358i | 0.280554 | − | 0.235413i | −0.491642 | − | 0.870798i | \(-0.663603\pi\) |
0.772196 | + | 0.635385i | \(0.219159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.9483 | − | 58.8002i | 0.0625199 | − | 0.108288i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −303.799 | + | 834.681i | −0.557429 | + | 1.53152i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −174.568 | + | 30.7810i | −0.319137 | + | 0.0562725i | −0.330922 | − | 0.943658i | \(-0.607360\pi\) |
0.0117850 | + | 0.999931i | \(0.496249\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.0229 | − | 15.9621i | −0.0346501 | − | 0.0290749i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −349.155 | − | 199.867i | −0.633675 | − | 0.362735i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61.4721 | − | 73.2596i | 0.111161 | − | 0.132477i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.2113 | − | 69.2535i | −0.0220023 | − | 0.124781i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −473.669 | − | 172.401i | −0.850393 | − | 0.309518i | −0.120192 | − | 0.992751i | \(-0.538351\pi\) |
−0.730201 | + | 0.683233i | \(0.760573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 618.921 | + | 357.334i | 1.10719 | + | 0.639238i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −72.5243 | − | 86.4311i | −0.129277 | − | 0.154066i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 187.639 | − | 108.334i | 0.333285 | − | 0.192422i | −0.324014 | − | 0.946052i | \(-0.605032\pi\) |
0.657299 | + | 0.753630i | \(0.271699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 364.432 | + | 64.2592i | 0.645012 | + | 0.113733i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 401.653 | − | 146.190i | 0.708382 | − | 0.257830i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 865.434i | 1.52097i | 0.649353 | + | 0.760487i | \(0.275040\pi\) | ||||
−0.649353 | + | 0.760487i | \(0.724960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.6175 | −0.0483668 | −0.0241834 | − | 0.999708i | \(-0.507699\pi\) | ||||
−0.0241834 | + | 0.999708i | \(0.507699\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.8458 | − | 90.2432i | −0.0573226 | − | 0.157492i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −136.139 | + | 772.082i | −0.236763 | + | 1.34275i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −100.195 | − | 173.544i | −0.173649 | − | 0.300769i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342019i | \(0.888889\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.1570 | − | 8.52271i | 0.0175423 | − | 0.0147197i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 234.797 | − | 406.681i | 0.404126 | − | 0.699967i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 73.0567 | − | 200.722i | 0.125312 | − | 0.344291i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1176.81 | + | 207.504i | −2.01164 | + | 0.354707i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 172.908 | + | 145.087i | 0.294563 | + | 0.247168i | 0.778077 | − | 0.628169i | \(-0.216195\pi\) |
−0.483514 | + | 0.875337i | \(0.660640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 487.525 | − | 585.392i | 0.827717 | − | 0.993875i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −141.302 | + | 168.397i | −0.239089 | + | 0.284936i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 174.512 | + | 989.709i | 0.294287 | + | 1.66899i | 0.670084 | + | 0.742285i | \(0.266258\pi\) |
−0.375797 | + | 0.926702i | \(0.622631\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 860.319 | + | 313.131i | 1.44592 | + | 0.526270i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 159.318 | + | 91.9826i | 0.266865 | + | 0.154075i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 699.578 | + | 833.725i | 1.16791 | + | 1.39186i | 0.904119 | + | 0.427281i | \(0.140529\pi\) |
0.263791 | + | 0.964580i | \(0.415027\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −373.969 | + | 215.911i | −0.622245 | + | 0.359253i | −0.777743 | − | 0.628583i | \(-0.783635\pi\) |
0.155498 | + | 0.987836i | \(0.450302\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 944.572 | + | 166.553i | 1.56645 | + | 0.276208i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −290.415 | + | 105.702i | −0.480025 | + | 0.174715i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 693.123i | − | 1.14188i | −0.820991 | − | 0.570942i | \(-0.806578\pi\) | ||
0.820991 | − | 0.570942i | \(-0.193422\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 80.7421 | 0.132581 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.11494 | + | 25.0431i | 0.0149181 | + | 0.0409870i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.2820 | + | 80.9973i | −0.0232986 | + | 0.132133i | −0.994238 | − | 0.107191i | \(-0.965814\pi\) |
0.970940 | + | 0.239323i | \(0.0769256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −131.464 | − | 227.702i | −0.213763 | − | 0.370248i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 541.872 | − | 454.684i | 0.878236 | − | 0.736927i | −0.0875797 | − | 0.996158i | \(-0.527913\pi\) |
0.965816 | + | 0.259230i | \(0.0834688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −467.426 | + | 809.606i | −0.755131 | + | 1.30792i | 0.190178 | + | 0.981750i | \(0.439093\pi\) |
−0.945309 | + | 0.326175i | \(0.894240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 94.0461 | − | 258.389i | 0.151443 | − | 0.416086i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 861.659 | − | 151.934i | 1.38308 | − | 0.243874i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −320.155 | − | 268.642i | −0.512248 | − | 0.429827i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 105.101 | − | 18.9332i | 0.167626 | − | 0.0301965i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 191.878 | − | 228.672i | 0.305053 | − | 0.363548i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4137 | − | 149.800i | −0.0418601 | − | 0.237400i | 0.956698 | − | 0.291082i | \(-0.0940154\pi\) |
−0.998558 | + | 0.0536820i | \(0.982904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.6061 | + | 4.22429i | 0.0183351 | + | 0.00667344i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −878.836 | − | 507.396i | −1.38399 | − | 0.799049i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 145.077 | + | 172.897i | 0.227751 | + | 0.271423i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −865.863 | + | 499.906i | −1.35503 | + | 0.782326i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 175.672 | + | 30.9757i | 0.274060 | + | 0.0483241i | 0.308989 | − | 0.951066i | \(-0.400009\pi\) |
−0.0349292 | + | 0.999390i | \(0.511121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 415.509 | − | 151.233i | 0.646203 | − | 0.235199i | 0.00193485 | − | 0.999998i | \(-0.499384\pi\) |
0.644269 | + | 0.764799i | \(0.277162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 183.019i | 0.283751i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 340.919 | 0.526922 | 0.263461 | − | 0.964670i | \(-0.415136\pi\) | ||||
0.263461 | + | 0.964670i | \(0.415136\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 166.455 | + | 457.332i | 0.256479 | + | 0.704671i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.5495 | + | 150.570i | −0.0407827 | + | 0.231290i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 319.221 | + | 552.907i | 0.488853 | + | 0.846719i | 0.999918 | − | 0.0128237i | \(-0.00408202\pi\) |
−0.511065 | + | 0.859542i | \(0.670749\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1103.40 | + | 925.864i | −1.68458 | + | 1.41353i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −196.585 | + | 340.496i | −0.299217 | + | 0.518259i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 101.557 | − | 279.024i | 0.154107 | − | 0.423406i | −0.838481 | − | 0.544930i | \(-0.816556\pi\) |
0.992588 | + | 0.121525i | \(0.0387783\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 629.130 | − | 110.933i | 0.951786 | − | 0.167825i | 0.323865 | − | 0.946103i | \(-0.395017\pi\) |
0.627920 | + | 0.778278i | \(0.283906\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 178.544 | + | 149.816i | 0.269297 | + | 0.225967i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −661.764 | + | 559.469i | −0.995133 | + | 0.841306i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −338.096 | + | 402.928i | −0.506891 | + | 0.604090i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.7837 | − | 66.8284i | −0.0176138 | − | 0.0998930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.2419 | − | 8.82333i | −0.0361280 | − | 0.0131495i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −343.422 | − | 198.275i | −0.510286 | − | 0.294614i | 0.222665 | − | 0.974895i | \(-0.428524\pi\) |
−0.732951 | + | 0.680281i | \(0.761858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −224.566 | − | 267.627i | −0.332690 | − | 0.396484i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 589.512 | − | 340.355i | 0.870771 | − | 0.502740i | 0.00316684 | − | 0.999995i | \(-0.498992\pi\) |
0.867604 | + | 0.497255i | \(0.165659\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1026.38 | − | 180.979i | −1.51161 | − | 0.266538i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.7136 | − | 15.5465i | 0.0627219 | − | 0.0228289i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 687.614i | − | 1.00676i | −0.864066 | − | 0.503378i | \(-0.832090\pi\) | ||
0.864066 | − | 0.503378i | \(-0.167910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 299.556 | 0.437308 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.7380 | + | 37.7448i | 0.0199971 | + | 0.0549414i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −76.6219 | + | 434.545i | −0.111207 | + | 0.630689i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −340.133 | − | 589.127i | −0.492233 | − | 0.852572i | 0.507727 | − | 0.861518i | \(-0.330486\pi\) |
−0.999960 | + | 0.00894577i | \(0.997152\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 357.328 | − | 299.834i | 0.515625 | − | 0.432660i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 741.084 | − | 1283.60i | 1.06631 | − | 1.84690i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 381.731 | − | 1048.80i | 0.547677 | − | 1.50473i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.4010 | − | 6.06582i | 0.0492145 | − | 0.00867785i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 53.0747 | + | 44.5350i | 0.0757129 | + | 0.0635306i | 0.679859 | − | 0.733343i | \(-0.262041\pi\) |
−0.604146 | + | 0.796874i | \(0.706486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 97.6169 | + | 265.145i | 0.138858 | + | 0.377163i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.38694 | + | 5.22815i | −0.00622261 | + | 0.00741582i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.7738 | − | 197.212i | −0.0491851 | − | 0.278942i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 527.372 | + | 191.948i | 0.743826 | + | 0.270730i | 0.686005 | − | 0.727597i | \(-0.259363\pi\) |
0.0578204 | + | 0.998327i | \(0.481585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −117.512 | − | 67.8459i | −0.165278 | − | 0.0954232i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −640.216 | − | 762.980i | −0.897919 | − | 1.07010i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1075.09 | + | 620.703i | −1.50362 | + | 0.868116i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.9431 | − | 5.10344i | −0.0403669 | − | 0.00711777i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 558.183 | − | 203.162i | 0.776332 | − | 0.282562i | 0.0766895 | − | 0.997055i | \(-0.475565\pi\) |
0.699642 | + | 0.714493i | \(0.253343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1139.61i | − | 1.58059i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −287.608 | −0.397799 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 228.566 | + | 627.980i | 0.315264 | + | 0.866179i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 172.775 | − | 979.857i | 0.237655 | − | 1.34781i | −0.599294 | − | 0.800529i | \(-0.704552\pi\) |
0.836949 | − | 0.547280i | \(-0.184337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −271.912 | − | 470.966i | −0.372994 | − | 0.646044i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −595.140 | + | 499.382i | −0.814145 | + | 0.683149i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −639.935 | + | 1108.40i | −0.873035 | + | 1.51214i | −0.0141944 | + | 0.999899i | \(0.504518\pi\) |
−0.858841 | + | 0.512242i | \(0.828815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.7686 | + | 54.3139i | −0.0268961 | + | 0.0738964i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 981.280 | − | 173.026i | 1.33145 | − | 0.234771i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 288.561 | + | 242.131i | 0.390475 | + | 0.327647i | 0.816798 | − | 0.576924i | \(-0.195747\pi\) |
−0.426323 | + | 0.904571i | \(0.640191\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −207.022 | + | 76.2179i | −0.279382 | + | 0.102858i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −410.971 | + | 489.776i | −0.553123 | + | 0.659187i | −0.968076 | − | 0.250656i | \(-0.919354\pi\) |
0.414953 | + | 0.909843i | \(0.363798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −283.701 | − | 1608.95i | −0.380807 | − | 2.15967i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −626.111 | − | 227.886i | −0.838168 | − | 0.305068i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −337.168 | − | 194.664i | −0.450157 | − | 0.259898i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 823.889 | + | 981.873i | 1.09706 | + | 1.30742i | 0.947886 | + | 0.318608i | \(0.103216\pi\) |
0.149169 | + | 0.988812i | \(0.452340\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −126.868 | + | 73.2475i | −0.168484 | + | 0.0972742i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 224.792 | + | 39.6370i | 0.297738 | + | 0.0524993i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −246.078 | + | 89.5649i | −0.325069 | + | 0.118316i | −0.499400 | − | 0.866372i | \(-0.666446\pi\) |
0.174330 | + | 0.984687i | \(0.444224\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 139.622i | − | 0.183955i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1028.82 | 1.35193 | 0.675966 | − | 0.736933i | \(-0.263727\pi\) | ||||
0.675966 | + | 0.736933i | \(0.263727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 244.973 | + | 673.058i | 0.321065 | + | 0.882120i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 225.573 | − | 1279.29i | 0.294866 | − | 1.67227i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −502.678 | − | 870.664i | −0.655382 | − | 1.13515i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1673 | − | 10.2095i | 0.0158222 | − | 0.0132764i | −0.634842 | − | 0.772642i | \(-0.718935\pi\) |
0.650664 | + | 0.759365i | \(0.274490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.7643 | + | 113.907i | −0.0852974 | + | 0.147739i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −136.685 | + | 375.540i | −0.176825 | + | 0.485822i | −0.996166 | − | 0.0874845i | \(-0.972117\pi\) |
0.819341 | + | 0.573306i | \(0.194339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1246.23 | + | 219.744i | −1.60804 | + | 0.283540i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.4386 | − | 36.4493i | −0.0559055 | − | 0.0469103i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 682.036 | + | 806.741i | 0.875528 | + | 1.03561i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −667.643 | + | 795.666i | −0.854856 | + | 1.01878i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40.7012 | − | 230.828i | −0.0519811 | − | 0.294800i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −395.913 | − | 144.101i | −0.504348 | − | 0.183568i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −344.910 | − | 199.134i | −0.438260 | − | 0.253029i | 0.264599 | − | 0.964358i | \(-0.414760\pi\) |
−0.702859 | + | 0.711329i | \(0.748094\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 175.190 | + | 208.783i | 0.222040 | + | 0.264617i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 258.421 | − | 149.199i | 0.326701 | − | 0.188621i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.4816 | + | 9.25392i | 0.0661810 | + | 0.0116695i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −106.185 | + | 38.6480i | −0.133565 | + | 0.0486138i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 259.704i | 0.325852i | 0.986638 | + | 0.162926i | \(0.0520932\pi\) | ||||
−0.986638 | + | 0.162926i | \(0.947907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.9710 | −0.0362590 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −424.598 | − | 1166.57i | −0.530085 | − | 1.45640i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −70.9267 | + | 402.245i | −0.0883271 | + | 0.500928i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 566.475 | + | 981.163i | 0.703695 | + | 1.21884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 64.6203 | − | 54.2229i | 0.0800748 | − | 0.0671907i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 223.197 | − | 386.589i | 0.275893 | − | 0.477861i | −0.694467 | − | 0.719524i | \(-0.744360\pi\) |
0.970360 | + | 0.241664i | \(0.0776931\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 358.279 | − | 984.364i | 0.441774 | − | 1.21377i | −0.496550 | − | 0.868008i | \(-0.665400\pi\) |
0.938324 | − | 0.345757i | \(-0.112378\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.9301 | + | 6.15911i | −0.0429644 | + | 0.00757579i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1188.75 | + | 997.478i | 1.45859 | + | 1.22390i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −130.369 | − | 723.699i | −0.159570 | − | 0.885801i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −619.377 | + | 738.144i | −0.756260 | + | 0.901275i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 255.736 | + | 1450.35i | 0.311493 | + | 1.76656i | 0.591246 | + | 0.806491i | \(0.298636\pi\) |
−0.279754 | + | 0.960072i | \(0.590253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 686.983 | + | 250.041i | 0.834730 | + | 0.303817i | 0.723799 | − | 0.690011i | \(-0.242394\pi\) |
0.110931 | + | 0.993828i | \(0.464617\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −153.628 | − | 88.6971i | −0.186216 | − | 0.107512i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2850 | + | 44.4345i | 0.0450846 | + | 0.0537298i | 0.788116 | − | 0.615527i | \(-0.211057\pi\) |
−0.743031 | + | 0.669257i | \(0.766612\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 936.414 | − | 540.639i | 1.12957 | − | 0.652158i | 0.185743 | − | 0.982598i | \(-0.440531\pi\) |
0.943827 | + | 0.330441i | \(0.107197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 93.3055 | + | 16.4523i | 0.112281 | + | 0.0197982i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −230.557 | + | 83.9160i | −0.276780 | + | 0.100740i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1284.24i | 1.53802i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 443.837 | 0.530271 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.00431 | − | 13.7492i | −0.00596461 | − | 0.0163876i | 0.936675 | − | 0.350201i | \(-0.113887\pi\) |
−0.942639 | + | 0.333813i | \(0.891664\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 68.1822 | − | 386.680i | 0.0810728 | − | 0.459787i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 74.6565 | + | 129.309i | 0.0885605 | + | 0.153391i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 990.815 | − | 831.393i | 1.17256 | − | 0.983897i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −124.605 | + | 215.822i | −0.147113 | + | 0.254807i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −86.4344 | + | 237.477i | −0.101807 | + | 0.279713i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 363.786 | − | 64.1453i | 0.427481 | − | 0.0753764i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −326.273 | − | 273.776i | −0.382501 | − | 0.320956i | 0.431182 | − | 0.902265i | \(-0.358097\pi\) |
−0.813683 | + | 0.581308i | \(0.802541\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 944.802 | + | 786.847i | 1.10503 | + | 0.920289i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 172.163 | − | 205.176i | 0.200891 | − | 0.239412i | −0.656188 | − | 0.754597i | \(-0.727832\pi\) |
0.857079 | + | 0.515185i | \(0.172277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.38084 | − | 19.1737i | −0.00393578 | − | 0.0223209i | 0.982777 | − | 0.184797i | \(-0.0591629\pi\) |
−0.986712 | + | 0.162477i | \(0.948052\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −199.230 | − | 72.5138i | −0.231394 | − | 0.0842204i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −933.120 | − | 538.737i | −1.08125 | − | 0.624261i | −0.150018 | − | 0.988683i | \(-0.547933\pi\) |
−0.931234 | + | 0.364422i | \(0.881267\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −117.801 | − | 140.390i | −0.136186 | − | 0.162300i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −62.0507 | + | 35.8250i | −0.0715694 | + | 0.0413206i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −138.824 | − | 24.4783i | −0.159751 | − | 0.0281684i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1934.20 | + | 703.992i | −2.22067 | + | 0.808257i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1478.77i | 1.69390i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 299.234 | 0.341982 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 458.351 | + | 1259.31i | 0.522635 | + | 1.43593i | 0.867576 | + | 0.497304i | \(0.165677\pi\) |
−0.344941 | + | 0.938624i | \(0.612101\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.2522 | − | 97.8424i | 0.0196271 | − | 0.111311i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 768.865 | + | 1331.71i | 0.872718 | + | 1.51159i | 0.859174 | + | 0.511684i | \(0.170978\pi\) |
0.0135448 | + | 0.999908i | \(0.495688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1133.53 | − | 951.148i | 1.28373 | − | 1.07718i | 0.291012 | − | 0.956719i | \(-0.406008\pi\) |
0.992718 | − | 0.120458i | \(-0.0384363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 128.731 | − | 222.968i | 0.145458 | − | 0.251941i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −455.735 | + | 1252.12i | −0.513794 | + | 1.41164i | 0.363460 | + | 0.931610i | \(0.381595\pi\) |
−0.877254 | + | 0.480027i | \(0.840627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −805.861 | + | 142.095i | −0.906481 | + | 0.159837i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −482.636 | − | 404.979i | −0.541679 | − | 0.454522i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.6228 | − | 23.7982i | 0.0152551 | − | 0.0266497i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 820.680 | − | 978.049i | 0.916961 | − | 1.09279i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50.0838 | + | 284.039i | 0.0558348 | + | 0.316655i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −797.799 | − | 290.375i | −0.887429 | − | 0.322998i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −415.407 | − | 239.836i | −0.461052 | − | 0.266188i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 94.8628 | + | 113.053i | 0.105053 | + | 0.125197i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 703.295 | − | 406.048i | 0.777122 | − | 0.448672i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −363.404 | − | 64.0779i | −0.400666 | − | 0.0706482i | −0.0303155 | − | 0.999540i | \(-0.509651\pi\) |
−0.370350 | + | 0.928892i | \(0.620762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −267.000 | + | 97.1799i | −0.293729 | + | 0.106909i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 345.867i | − | 0.379657i | −0.981817 | − | 0.189828i | \(-0.939207\pi\) | ||
0.981817 | − | 0.189828i | \(-0.0607931\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −692.188 | −0.758146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.66766 | + | 12.8243i | 0.00510127 | + | 0.0140156i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −201.689 | + | 1143.83i | −0.219944 | + | 1.24736i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 186.618 | + | 323.232i | 0.203067 | + | 0.351722i | 0.949515 | − | 0.313722i | \(-0.101576\pi\) |
−0.746448 | + | 0.665443i | \(0.768243\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 248.323 | − | 208.367i | 0.269623 | − | 0.226240i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1072.81 | − | 1858.15i | 1.16230 | − | 2.01317i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 160.522 | − | 441.029i | 0.173537 | − | 0.476789i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1592.39 | + | 280.781i | −1.71778 | + | 0.302892i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 440.859 | + | 369.925i | 0.474552 | + | 0.398197i | 0.848452 | − | 0.529272i | \(-0.177535\pi\) |
−0.373900 | + | 0.927469i | \(0.621980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39.4806 | − | 228.851i | 0.0424066 | − | 0.245812i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 107.563 | − | 128.188i | 0.115287 | − | 0.137394i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −234.339 | − | 1329.00i | −0.250630 | − | 1.42139i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −459.523 | − | 167.253i | −0.490419 | − | 0.178498i | 0.0849605 | − | 0.996384i | \(-0.472924\pi\) |
−0.575380 | + | 0.817886i | \(0.695146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −101.930 | − | 58.8494i | −0.108552 | − | 0.0626724i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 897.696 | + | 1069.83i | 0.953981 | + | 1.13691i | 0.990491 | + | 0.137577i | \(0.0439314\pi\) |
−0.0365101 | + | 0.999333i | \(0.511624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1196.11 | − | 690.577i | 1.26841 | − | 0.732319i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −497.194 | − | 87.6687i | −0.526131 | − | 0.0927711i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 618.662 | − | 225.175i | 0.653286 | − | 0.237777i | 0.00595130 | − | 0.999982i | \(-0.498106\pi\) |
0.647335 | + | 0.762205i | \(0.275883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 843.750i | − | 0.889094i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −90.7923 | −0.0954704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 94.4822 | + | 259.588i | 0.0991418 | + | 0.272390i | 0.979341 | − | 0.202214i | \(-0.0648136\pi\) |
−0.880200 | + | 0.474604i | \(0.842591\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 199.461 | − | 1131.20i | 0.208859 | − | 1.18450i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −59.5074 | − | 103.070i | −0.0621812 | − | 0.107701i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 185.039 | − | 155.266i | 0.192950 | − | 0.161904i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 323.329 | − | 560.023i | 0.336451 | − | 0.582750i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −188.934 | + | 519.092i | −0.196193 | + | 0.539036i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 156.178 | − | 27.5384i | 0.161843 | − | 0.0285372i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 333.973 | + | 280.237i | 0.345370 | + | 0.289800i | 0.798928 | − | 0.601427i | \(-0.205401\pi\) |
−0.453557 | + | 0.891227i | \(0.649845\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.886798 | − | 239.815i | −0.000915168 | − | 0.247487i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −803.245 | + | 957.270i | −0.827235 | + | 0.985860i | 0.172765 | + | 0.984963i | \(0.444730\pi\) |
−1.00000 | 0.000896801i | \(0.999715\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −207.539 | − | 1177.01i | −0.213298 | − | 1.20967i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 344.350 | + | 125.333i | 0.353179 | + | 0.128547i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1274.02 | − | 735.558i | −1.30402 | − | 0.752874i | −0.322926 | − | 0.946424i | \(-0.604667\pi\) |
−0.981090 | + | 0.193550i | \(0.938000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −828.995 | − | 987.958i | −0.846777 | − | 1.00915i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 880.115 | − | 508.135i | 0.897162 | − | 0.517976i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1422.51 | − | 250.827i | −1.44711 | − | 0.255165i | −0.605759 | − | 0.795648i | \(-0.707131\pi\) |
−0.841355 | + | 0.540483i | \(0.818242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2470.73 | + | 899.271i | −2.50835 | + | 0.912966i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.50334i | 0.00557582i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −961.395 | −0.972088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.4988 | + | 108.522i | 0.0398576 | + | 0.109508i | 0.958025 | − | 0.286685i | \(-0.0925534\pi\) |
−0.918167 | + | 0.396193i | \(0.870331\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 46.0416 | − | 261.115i | 0.0463661 | − | 0.262955i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1100.18 | + | 1905.57i | 1.10571 | + | 1.91515i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −411.248 | + | 345.078i | −0.412486 | + | 0.346116i | −0.825296 | − | 0.564701i | \(-0.808992\pi\) |
0.412810 | + | 0.910817i | \(0.364547\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −82.3055 | + | 142.557i | −0.0823879 | + | 0.142700i |
(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 | 76.3.j.a.41.2 | yes | 18 | |
4.3 | odd | 2 | 304.3.z.b.193.2 | 18 | |||
19.5 | even | 9 | 1444.3.c.c.721.9 | 18 | |||
19.13 | odd | 18 | inner | 76.3.j.a.13.2 | ✓ | 18 | |
19.14 | odd | 18 | 1444.3.c.c.721.10 | 18 | |||
76.51 | even | 18 | 304.3.z.b.241.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.j.a.13.2 | ✓ | 18 | 19.13 | odd | 18 | inner | |
76.3.j.a.41.2 | yes | 18 | 1.1 | even | 1 | trivial | |
304.3.z.b.193.2 | 18 | 4.3 | odd | 2 | |||
304.3.z.b.241.2 | 18 | 76.51 | even | 18 | |||
1444.3.c.c.721.9 | 18 | 19.5 | even | 9 | |||
1444.3.c.c.721.10 | 18 | 19.14 | odd | 18 |