Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(64,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 15x^{6} + 67x^{4} + 77x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(-2.60520i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.64 |
Dual form | 273.2.c.c.64.8 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.60520i | − | 1.84215i | −0.389381 | − | 0.921077i | \(-0.627311\pi\) | ||
0.389381 | − | 0.921077i | \(-0.372689\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −4.78706 | −2.39353 | ||||||||
\(5\) | 3.78706i | 1.69362i | 0.531892 | + | 0.846812i | \(0.321481\pi\) | ||||
−0.531892 | + | 0.846812i | \(0.678519\pi\) | |||||||
\(6\) | 2.60520i | 1.06357i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 7.26084i | 2.56709i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.86604 | 3.11992 | ||||||||
\(11\) | − | 2.55475i | − | 0.770287i | −0.922857 | − | 0.385144i | \(-0.874152\pi\) | ||
0.922857 | − | 0.385144i | \(-0.125848\pi\) | |||||||
\(12\) | 4.78706 | 1.38190 | ||||||||
\(13\) | 0.0504439 | + | 3.60520i | 0.0139906 | + | 0.999902i | ||||
\(14\) | 2.60520 | 0.696269 | ||||||||
\(15\) | − | 3.78706i | − | 0.977814i | ||||||
\(16\) | 9.34181 | 2.33545 | ||||||||
\(17\) | −3.21040 | −0.778636 | −0.389318 | − | 0.921103i | \(-0.627289\pi\) | ||||
−0.389318 | + | 0.921103i | \(0.627289\pi\) | |||||||
\(18\) | − | 2.60520i | − | 0.614051i | ||||||
\(19\) | 8.44270i | 1.93689i | 0.249230 | + | 0.968444i | \(0.419822\pi\) | ||||
−0.249230 | + | 0.968444i | \(0.580178\pi\) | |||||||
\(20\) | − | 18.1289i | − | 4.05374i | ||||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | −6.65564 | −1.41899 | ||||||||
\(23\) | 3.97809 | 0.829490 | 0.414745 | − | 0.909938i | \(-0.363871\pi\) | ||||
0.414745 | + | 0.909938i | \(0.363871\pi\) | |||||||
\(24\) | − | 7.26084i | − | 1.48211i | ||||||
\(25\) | −9.34181 | −1.86836 | ||||||||
\(26\) | 9.39226 | − | 0.131416i | 1.84197 | − | 0.0257729i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − | 4.78706i | − | 0.904669i | ||||||
\(29\) | −2.86858 | −0.532683 | −0.266341 | − | 0.963879i | \(-0.585815\pi\) | ||||
−0.266341 | + | 0.963879i | \(0.585815\pi\) | |||||||
\(30\) | −9.86604 | −1.80128 | ||||||||
\(31\) | − | 0.868584i | − | 0.156002i | −0.996953 | − | 0.0780011i | \(-0.975146\pi\) | ||
0.996953 | − | 0.0780011i | \(-0.0248538\pi\) | |||||||
\(32\) | − | 9.81560i | − | 1.73517i | ||||||
\(33\) | 2.55475i | 0.444726i | ||||||||
\(34\) | 8.36372i | 1.43437i | ||||||||
\(35\) | −3.78706 | −0.640130 | ||||||||
\(36\) | −4.78706 | −0.797843 | ||||||||
\(37\) | 5.10951i | 0.839998i | 0.907525 | + | 0.419999i | \(0.137970\pi\) | ||||
−0.907525 | + | 0.419999i | \(0.862030\pi\) | |||||||
\(38\) | 21.9949 | 3.56805 | ||||||||
\(39\) | −0.0504439 | − | 3.60520i | −0.00807749 | − | 0.577294i | ||||
\(40\) | −27.4972 | −4.34769 | ||||||||
\(41\) | 3.34436i | 0.522301i | 0.965298 | + | 0.261150i | \(0.0841019\pi\) | ||||
−0.965298 | + | 0.261150i | \(0.915898\pi\) | |||||||
\(42\) | −2.60520 | −0.401991 | ||||||||
\(43\) | 4.86858 | 0.742452 | 0.371226 | − | 0.928543i | \(-0.378938\pi\) | ||||
0.371226 | + | 0.928543i | \(0.378938\pi\) | |||||||
\(44\) | 12.2298i | 1.84371i | ||||||||
\(45\) | 3.78706i | 0.564541i | ||||||||
\(46\) | − | 10.3637i | − | 1.52805i | ||||||
\(47\) | − | 11.0983i | − | 1.61886i | −0.587217 | − | 0.809430i | \(-0.699776\pi\) | ||
0.587217 | − | 0.809430i | \(-0.300224\pi\) | |||||||
\(48\) | −9.34181 | −1.34837 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 24.3373i | 3.44181i | ||||||||
\(51\) | 3.21040 | 0.449545 | ||||||||
\(52\) | −0.241478 | − | 17.2583i | −0.0334870 | − | 2.39330i | ||||
\(53\) | 1.33319 | 0.183128 | 0.0915640 | − | 0.995799i | \(-0.470813\pi\) | ||||
0.0915640 | + | 0.995799i | \(0.470813\pi\) | |||||||
\(54\) | 2.60520i | 0.354523i | ||||||||
\(55\) | 9.67501 | 1.30458 | ||||||||
\(56\) | −7.26084 | −0.970271 | ||||||||
\(57\) | − | 8.44270i | − | 1.11826i | ||||||
\(58\) | 7.47323i | 0.981283i | ||||||||
\(59\) | − | 10.6556i | − | 1.38725i | −0.720338 | − | 0.693623i | \(-0.756013\pi\) | ||
0.720338 | − | 0.693623i | \(-0.243987\pi\) | |||||||
\(60\) | 18.1289i | 2.34043i | ||||||||
\(61\) | −4.10089 | −0.525065 | −0.262532 | − | 0.964923i | \(-0.584558\pi\) | ||||
−0.262532 | + | 0.964923i | \(0.584558\pi\) | |||||||
\(62\) | −2.26283 | −0.287380 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | −6.88795 | −0.860993 | ||||||||
\(65\) | −13.6531 | + | 0.191034i | −1.69346 | + | 0.0236949i | ||||
\(66\) | 6.65564 | 0.819253 | ||||||||
\(67\) | 10.8467i | 1.32513i | 0.749003 | + | 0.662566i | \(0.230533\pi\) | ||||
−0.749003 | + | 0.662566i | \(0.769467\pi\) | |||||||
\(68\) | 15.3684 | 1.86369 | ||||||||
\(69\) | −3.97809 | −0.478906 | ||||||||
\(70\) | 9.86604i | 1.17922i | ||||||||
\(71\) | 2.55475i | 0.303194i | 0.988442 | + | 0.151597i | \(0.0484415\pi\) | ||||
−0.988442 | + | 0.151597i | \(0.951558\pi\) | |||||||
\(72\) | 7.26084i | 0.855698i | ||||||||
\(73\) | 6.76770i | 0.792099i | 0.918229 | + | 0.396049i | \(0.129619\pi\) | ||||
−0.918229 | + | 0.396049i | \(0.870381\pi\) | |||||||
\(74\) | 13.3113 | 1.54741 | ||||||||
\(75\) | 9.34181 | 1.07870 | ||||||||
\(76\) | − | 40.4157i | − | 4.63600i | ||||||
\(77\) | 2.55475 | 0.291141 | ||||||||
\(78\) | −9.39226 | + | 0.131416i | −1.06346 | + | 0.0148800i | ||||
\(79\) | −1.23230 | −0.138645 | −0.0693225 | − | 0.997594i | \(-0.522084\pi\) | ||||
−0.0693225 | + | 0.997594i | \(0.522084\pi\) | |||||||
\(80\) | 35.3780i | 3.95538i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.71272 | 0.962158 | ||||||||
\(83\) | 11.0983i | 1.21820i | 0.793093 | + | 0.609101i | \(0.208469\pi\) | ||||
−0.793093 | + | 0.609101i | \(0.791531\pi\) | |||||||
\(84\) | 4.78706i | 0.522311i | ||||||||
\(85\) | − | 12.1580i | − | 1.31872i | ||||||
\(86\) | − | 12.6836i | − | 1.36771i | ||||||
\(87\) | 2.86858 | 0.307544 | ||||||||
\(88\) | 18.5497 | 1.97740 | ||||||||
\(89\) | − | 5.52423i | − | 0.585567i | −0.956179 | − | 0.292783i | \(-0.905419\pi\) | ||
0.956179 | − | 0.292783i | \(-0.0945815\pi\) | |||||||
\(90\) | 9.86604 | 1.03997 | ||||||||
\(91\) | −3.60520 | + | 0.0504439i | −0.377927 | + | 0.00528796i | ||||
\(92\) | −19.0434 | −1.98541 | ||||||||
\(93\) | 0.868584i | 0.0900679i | ||||||||
\(94\) | −28.9134 | −2.98219 | ||||||||
\(95\) | −31.9730 | −3.28036 | ||||||||
\(96\) | 9.81560i | 1.00180i | ||||||||
\(97\) | − | 5.65819i | − | 0.574502i | −0.957855 | − | 0.287251i | \(-0.907259\pi\) | ||
0.957855 | − | 0.287251i | \(-0.0927414\pi\) | |||||||
\(98\) | 2.60520i | 0.263165i | ||||||||
\(99\) | − | 2.55475i | − | 0.256762i | ||||||
\(100\) | 44.7198 | 4.47198 | ||||||||
\(101\) | −8.94756 | −0.890316 | −0.445158 | − | 0.895452i | \(-0.646852\pi\) | ||||
−0.445158 | + | 0.895452i | \(0.646852\pi\) | |||||||
\(102\) | − | 8.36372i | − | 0.828132i | ||||||
\(103\) | −1.67501 | −0.165043 | −0.0825216 | − | 0.996589i | \(-0.526297\pi\) | ||||
−0.0825216 | + | 0.996589i | \(0.526297\pi\) | |||||||
\(104\) | −26.1768 | + | 0.366265i | −2.56684 | + | 0.0359152i | ||||
\(105\) | 3.78706 | 0.369579 | ||||||||
\(106\) | − | 3.47323i | − | 0.337350i | ||||||
\(107\) | −0.846676 | −0.0818513 | −0.0409256 | − | 0.999162i | \(-0.513031\pi\) | ||||
−0.0409256 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(108\) | 4.78706 | 0.460635 | ||||||||
\(109\) | − | 17.9949i | − | 1.72360i | −0.507248 | − | 0.861800i | \(-0.669337\pi\) | ||
0.507248 | − | 0.861800i | \(-0.330663\pi\) | |||||||
\(110\) | − | 25.2053i | − | 2.40323i | ||||||
\(111\) | − | 5.10951i | − | 0.484973i | ||||||
\(112\) | 9.34181i | 0.882718i | ||||||||
\(113\) | 2.86858 | 0.269854 | 0.134927 | − | 0.990856i | \(-0.456920\pi\) | ||||
0.134927 | + | 0.990856i | \(0.456920\pi\) | |||||||
\(114\) | −21.9949 | −2.06001 | ||||||||
\(115\) | 15.0653i | 1.40484i | ||||||||
\(116\) | 13.7321 | 1.27499 | ||||||||
\(117\) | 0.0504439 | + | 3.60520i | 0.00466354 | + | 0.333301i | ||||
\(118\) | −27.7601 | −2.55552 | ||||||||
\(119\) | − | 3.21040i | − | 0.294297i | ||||||
\(120\) | 27.4972 | 2.51014 | ||||||||
\(121\) | 4.47323 | 0.406657 | ||||||||
\(122\) | 10.6836i | 0.967250i | ||||||||
\(123\) | − | 3.34436i | − | 0.301551i | ||||||
\(124\) | 4.15796i | 0.373396i | ||||||||
\(125\) | − | 16.4427i | − | 1.47068i | ||||||
\(126\) | 2.60520 | 0.232090 | ||||||||
\(127\) | 17.2053 | 1.52672 | 0.763362 | − | 0.645971i | \(-0.223547\pi\) | ||||
0.763362 | + | 0.645971i | \(0.223547\pi\) | |||||||
\(128\) | − | 1.68672i | − | 0.149087i | ||||||
\(129\) | −4.86858 | −0.428655 | ||||||||
\(130\) | 0.497681 | + | 35.5690i | 0.0436496 | + | 3.11961i | ||||
\(131\) | 16.6836 | 1.45766 | 0.728828 | − | 0.684697i | \(-0.240066\pi\) | ||||
0.728828 | + | 0.684697i | \(0.240066\pi\) | |||||||
\(132\) | − | 12.2298i | − | 1.06446i | ||||||
\(133\) | −8.44270 | −0.732075 | ||||||||
\(134\) | 28.2577 | 2.44110 | ||||||||
\(135\) | − | 3.78706i | − | 0.325938i | ||||||
\(136\) | − | 23.3102i | − | 1.99883i | ||||||
\(137\) | 18.9134i | 1.61588i | 0.589265 | + | 0.807940i | \(0.299417\pi\) | ||||
−0.589265 | + | 0.807940i | \(0.700583\pi\) | |||||||
\(138\) | 10.3637i | 0.882218i | ||||||||
\(139\) | 5.67501 | 0.481348 | 0.240674 | − | 0.970606i | \(-0.422632\pi\) | ||||
0.240674 | + | 0.970606i | \(0.422632\pi\) | |||||||
\(140\) | 18.1289 | 1.53217 | ||||||||
\(141\) | 11.0983i | 0.934649i | ||||||||
\(142\) | 6.65564 | 0.558529 | ||||||||
\(143\) | 9.21040 | − | 0.128872i | 0.770212 | − | 0.0107768i | ||||
\(144\) | 9.34181 | 0.778484 | ||||||||
\(145\) | − | 10.8635i | − | 0.902164i | ||||||
\(146\) | 17.6312 | 1.45917 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | − | 24.4595i | − | 2.01056i | ||||||
\(149\) | − | 8.49259i | − | 0.695740i | −0.937543 | − | 0.347870i | \(-0.886905\pi\) | ||
0.937543 | − | 0.347870i | \(-0.113095\pi\) | |||||||
\(150\) | − | 24.3373i | − | 1.98713i | ||||||
\(151\) | − | 14.2190i | − | 1.15713i | −0.815637 | − | 0.578564i | \(-0.803613\pi\) | ||
0.815637 | − | 0.578564i | \(-0.196387\pi\) | |||||||
\(152\) | −61.3011 | −4.97218 | ||||||||
\(153\) | −3.21040 | −0.259545 | ||||||||
\(154\) | − | 6.65564i | − | 0.536327i | ||||||
\(155\) | 3.28938 | 0.264209 | ||||||||
\(156\) | 0.241478 | + | 17.2583i | 0.0193337 | + | 1.38177i | ||||
\(157\) | 8.42079 | 0.672052 | 0.336026 | − | 0.941853i | \(-0.390917\pi\) | ||||
0.336026 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(158\) | 3.21040i | 0.255405i | ||||||||
\(159\) | −1.33319 | −0.105729 | ||||||||
\(160\) | 37.1722 | 2.93872 | ||||||||
\(161\) | 3.97809i | 0.313518i | ||||||||
\(162\) | − | 2.60520i | − | 0.204684i | ||||||
\(163\) | 3.77589i | 0.295751i | 0.989006 | + | 0.147875i | \(0.0472435\pi\) | ||||
−0.989006 | + | 0.147875i | \(0.952757\pi\) | |||||||
\(164\) | − | 16.0096i | − | 1.25014i | ||||||
\(165\) | −9.67501 | −0.753198 | ||||||||
\(166\) | 28.9134 | 2.24411 | ||||||||
\(167\) | − | 8.83551i | − | 0.683712i | −0.939752 | − | 0.341856i | \(-0.888944\pi\) | ||
0.939752 | − | 0.341856i | \(-0.111056\pi\) | |||||||
\(168\) | 7.26084 | 0.560186 | ||||||||
\(169\) | −12.9949 | + | 0.363721i | −0.999609 | + | 0.0279785i | ||||
\(170\) | −31.6739 | −2.42928 | ||||||||
\(171\) | 8.44270i | 0.645629i | ||||||||
\(172\) | −23.3062 | −1.77708 | ||||||||
\(173\) | 17.6750 | 1.34381 | 0.671903 | − | 0.740639i | \(-0.265477\pi\) | ||||
0.671903 | + | 0.740639i | \(0.265477\pi\) | |||||||
\(174\) | − | 7.47323i | − | 0.566544i | ||||||
\(175\) | − | 9.34181i | − | 0.706175i | ||||||
\(176\) | − | 23.8660i | − | 1.79897i | ||||||
\(177\) | 10.6556i | 0.800927i | ||||||||
\(178\) | −14.3917 | −1.07870 | ||||||||
\(179\) | 16.9073 | 1.26371 | 0.631856 | − | 0.775086i | \(-0.282293\pi\) | ||||
0.631856 | + | 0.775086i | \(0.282293\pi\) | |||||||
\(180\) | − | 18.1289i | − | 1.35125i | ||||||
\(181\) | 7.73717 | 0.575099 | 0.287550 | − | 0.957766i | \(-0.407159\pi\) | ||||
0.287550 | + | 0.957766i | \(0.407159\pi\) | |||||||
\(182\) | 0.131416 | + | 9.39226i | 0.00974123 | + | 0.696200i | ||||
\(183\) | 4.10089 | 0.303146 | ||||||||
\(184\) | 28.8843i | 2.12938i | ||||||||
\(185\) | −19.3500 | −1.42264 | ||||||||
\(186\) | 2.26283 | 0.165919 | ||||||||
\(187\) | 8.20178i | 0.599773i | ||||||||
\(188\) | 53.1284i | 3.87479i | ||||||||
\(189\) | − | 1.00000i | − | 0.0727393i | ||||||
\(190\) | 83.2960i | 6.04293i | ||||||||
\(191\) | 5.57412 | 0.403329 | 0.201664 | − | 0.979455i | \(-0.435365\pi\) | ||||
0.201664 | + | 0.979455i | \(0.435365\pi\) | |||||||
\(192\) | 6.88795 | 0.497095 | ||||||||
\(193\) | 7.57412i | 0.545197i | 0.962128 | + | 0.272598i | \(0.0878830\pi\) | ||||
−0.962128 | + | 0.272598i | \(0.912117\pi\) | |||||||
\(194\) | −14.7407 | −1.05832 | ||||||||
\(195\) | 13.6531 | − | 0.191034i | 0.977719 | − | 0.0136802i | ||||
\(196\) | 4.78706 | 0.341933 | ||||||||
\(197\) | 13.3444i | 0.950746i | 0.879784 | + | 0.475373i | \(0.157687\pi\) | ||||
−0.879784 | + | 0.475373i | \(0.842313\pi\) | |||||||
\(198\) | −6.65564 | −0.472996 | ||||||||
\(199\) | −16.8854 | −1.19697 | −0.598487 | − | 0.801132i | \(-0.704231\pi\) | ||||
−0.598487 | + | 0.801132i | \(0.704231\pi\) | |||||||
\(200\) | − | 67.8294i | − | 4.79626i | ||||||
\(201\) | − | 10.8467i | − | 0.765066i | ||||||
\(202\) | 23.3102i | 1.64010i | ||||||||
\(203\) | − | 2.86858i | − | 0.201335i | ||||||
\(204\) | −15.3684 | −1.07600 | ||||||||
\(205\) | −12.6653 | −0.884581 | ||||||||
\(206\) | 4.36372i | 0.304035i | ||||||||
\(207\) | 3.97809 | 0.276497 | ||||||||
\(208\) | 0.471237 | + | 33.6791i | 0.0326744 | + | 2.33522i | ||||
\(209\) | 21.5690 | 1.49196 | ||||||||
\(210\) | − | 9.86604i | − | 0.680821i | ||||||
\(211\) | 11.6969 | 0.805249 | 0.402624 | − | 0.915365i | \(-0.368098\pi\) | ||||
0.402624 | + | 0.915365i | \(0.368098\pi\) | |||||||
\(212\) | −6.38207 | −0.438322 | ||||||||
\(213\) | − | 2.55475i | − | 0.175049i | ||||||
\(214\) | 2.20576i | 0.150783i | ||||||||
\(215\) | 18.4376i | 1.25743i | ||||||||
\(216\) | − | 7.26084i | − | 0.494038i | ||||||
\(217\) | 0.868584 | 0.0589633 | ||||||||
\(218\) | −46.8803 | −3.17514 | ||||||||
\(219\) | − | 6.76770i | − | 0.457319i | ||||||
\(220\) | −46.3148 | −3.12254 | ||||||||
\(221\) | −0.161945 | − | 11.5741i | −0.0108936 | − | 0.778559i | ||||
\(222\) | −13.3113 | −0.893395 | ||||||||
\(223\) | − | 4.24093i | − | 0.283993i | −0.989867 | − | 0.141997i | \(-0.954648\pi\) | ||
0.989867 | − | 0.141997i | \(-0.0453522\pi\) | |||||||
\(224\) | 9.81560 | 0.655832 | ||||||||
\(225\) | −9.34181 | −0.622788 | ||||||||
\(226\) | − | 7.47323i | − | 0.497112i | ||||||
\(227\) | 1.72643i | 0.114587i | 0.998357 | + | 0.0572934i | \(0.0182471\pi\) | ||||
−0.998357 | + | 0.0572934i | \(0.981753\pi\) | |||||||
\(228\) | 40.4157i | 2.67660i | ||||||||
\(229\) | − | 6.82833i | − | 0.451229i | −0.974217 | − | 0.225614i | \(-0.927561\pi\) | ||
0.974217 | − | 0.225614i | \(-0.0724389\pi\) | |||||||
\(230\) | 39.2480 | 2.58794 | ||||||||
\(231\) | −2.55475 | −0.168091 | ||||||||
\(232\) | − | 20.8283i | − | 1.36745i | ||||||
\(233\) | −1.33319 | −0.0873403 | −0.0436702 | − | 0.999046i | \(-0.513905\pi\) | ||||
−0.0436702 | + | 0.999046i | \(0.513905\pi\) | |||||||
\(234\) | 9.39226 | − | 0.131416i | 0.613991 | − | 0.00859096i | ||||
\(235\) | 42.0301 | 2.74174 | ||||||||
\(236\) | 51.0092i | 3.32042i | ||||||||
\(237\) | 1.23230 | 0.0800468 | ||||||||
\(238\) | −8.36372 | −0.542139 | ||||||||
\(239\) | − | 3.90985i | − | 0.252907i | −0.991973 | − | 0.126454i | \(-0.959640\pi\) | ||
0.991973 | − | 0.126454i | \(-0.0403595\pi\) | |||||||
\(240\) | − | 35.3780i | − | 2.28364i | ||||||
\(241\) | 25.3903i | 1.63553i | 0.575552 | + | 0.817765i | \(0.304787\pi\) | ||||
−0.575552 | + | 0.817765i | \(0.695213\pi\) | |||||||
\(242\) | − | 11.6537i | − | 0.749125i | ||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 19.6312 | 1.25676 | ||||||||
\(245\) | − | 3.78706i | − | 0.241946i | ||||||
\(246\) | −8.71272 | −0.555502 | ||||||||
\(247\) | −30.4376 | + | 0.425883i | −1.93670 | + | 0.0270983i | ||||
\(248\) | 6.30665 | 0.400473 | ||||||||
\(249\) | − | 11.0983i | − | 0.703329i | ||||||
\(250\) | −42.8365 | −2.70922 | ||||||||
\(251\) | −25.7708 | −1.62664 | −0.813319 | − | 0.581818i | \(-0.802342\pi\) | ||||
−0.813319 | + | 0.581818i | \(0.802342\pi\) | |||||||
\(252\) | − | 4.78706i | − | 0.301556i | ||||||
\(253\) | − | 10.1631i | − | 0.638945i | ||||||
\(254\) | − | 44.8232i | − | 2.81246i | ||||||
\(255\) | 12.1580i | 0.761361i | ||||||||
\(256\) | −18.1701 | −1.13563 | ||||||||
\(257\) | 5.87678 | 0.366584 | 0.183292 | − | 0.983059i | \(-0.441325\pi\) | ||||
0.183292 | + | 0.983059i | \(0.441325\pi\) | |||||||
\(258\) | 12.6836i | 0.789648i | ||||||||
\(259\) | −5.10951 | −0.317489 | ||||||||
\(260\) | 65.3582 | − | 0.914491i | 4.05334 | − | 0.0567143i | ||||
\(261\) | −2.86858 | −0.177561 | ||||||||
\(262\) | − | 43.4642i | − | 2.68522i | ||||||
\(263\) | −10.2409 | −0.631483 | −0.315741 | − | 0.948845i | \(-0.602253\pi\) | ||||
−0.315741 | + | 0.948845i | \(0.602253\pi\) | |||||||
\(264\) | −18.5497 | −1.14165 | ||||||||
\(265\) | 5.04888i | 0.310150i | ||||||||
\(266\) | 21.9949i | 1.34859i | ||||||||
\(267\) | 5.52423i | 0.338077i | ||||||||
\(268\) | − | 51.9237i | − | 3.17174i | ||||||
\(269\) | −16.1396 | −0.984050 | −0.492025 | − | 0.870581i | \(-0.663743\pi\) | ||||
−0.492025 | + | 0.870581i | \(0.663743\pi\) | |||||||
\(270\) | −9.86604 | −0.600428 | ||||||||
\(271\) | 12.2577i | 0.744605i | 0.928111 | + | 0.372302i | \(0.121432\pi\) | ||||
−0.928111 | + | 0.372302i | \(0.878568\pi\) | |||||||
\(272\) | −29.9909 | −1.81847 | ||||||||
\(273\) | 3.60520 | − | 0.0504439i | 0.218197 | − | 0.00305300i | ||||
\(274\) | 49.2731 | 2.97670 | ||||||||
\(275\) | 23.8660i | 1.43918i | ||||||||
\(276\) | 19.0434 | 1.14628 | ||||||||
\(277\) | 9.81504 | 0.589729 | 0.294864 | − | 0.955539i | \(-0.404726\pi\) | ||||
0.294864 | + | 0.955539i | \(0.404726\pi\) | |||||||
\(278\) | − | 14.7845i | − | 0.886716i | ||||||
\(279\) | − | 0.868584i | − | 0.0520007i | ||||||
\(280\) | − | 27.4972i | − | 1.64327i | ||||||
\(281\) | − | 16.1910i | − | 0.965876i | −0.875655 | − | 0.482938i | \(-0.839570\pi\) | ||
0.875655 | − | 0.482938i | \(-0.160430\pi\) | |||||||
\(282\) | 28.9134 | 1.72177 | ||||||||
\(283\) | 19.1482 | 1.13824 | 0.569122 | − | 0.822253i | \(-0.307283\pi\) | ||||
0.569122 | + | 0.822253i | \(0.307283\pi\) | |||||||
\(284\) | − | 12.2298i | − | 0.725703i | ||||||
\(285\) | 31.9730 | 1.89392 | ||||||||
\(286\) | −0.335737 | − | 23.9949i | −0.0198525 | − | 1.41885i | ||||
\(287\) | −3.34436 | −0.197411 | ||||||||
\(288\) | − | 9.81560i | − | 0.578389i | ||||||
\(289\) | −6.69335 | −0.393727 | ||||||||
\(290\) | −28.3016 | −1.66192 | ||||||||
\(291\) | 5.65819i | 0.331689i | ||||||||
\(292\) | − | 32.3974i | − | 1.89591i | ||||||
\(293\) | 24.6725i | 1.44138i | 0.693257 | + | 0.720690i | \(0.256175\pi\) | ||||
−0.693257 | + | 0.720690i | \(0.743825\pi\) | |||||||
\(294\) | − | 2.60520i | − | 0.151938i | ||||||
\(295\) | 40.3535 | 2.34947 | ||||||||
\(296\) | −37.0993 | −2.15635 | ||||||||
\(297\) | 2.55475i | 0.148242i | ||||||||
\(298\) | −22.1249 | −1.28166 | ||||||||
\(299\) | 0.200670 | + | 14.3418i | 0.0116051 | + | 0.829408i | ||||
\(300\) | −44.7198 | −2.58190 | ||||||||
\(301\) | 4.86858i | 0.280620i | ||||||||
\(302\) | −37.0434 | −2.13161 | ||||||||
\(303\) | 8.94756 | 0.514024 | ||||||||
\(304\) | 78.8701i | 4.52351i | ||||||||
\(305\) | − | 15.5303i | − | 0.889263i | ||||||
\(306\) | 8.36372i | 0.478122i | ||||||||
\(307\) | 13.7540i | 0.784981i | 0.919756 | + | 0.392491i | \(0.128386\pi\) | ||||
−0.919756 | + | 0.392491i | \(0.871614\pi\) | |||||||
\(308\) | −12.2298 | −0.696855 | ||||||||
\(309\) | 1.67501 | 0.0952877 | ||||||||
\(310\) | − | 8.56948i | − | 0.486714i | ||||||
\(311\) | 12.1580 | 0.689415 | 0.344707 | − | 0.938710i | \(-0.387978\pi\) | ||||
0.344707 | + | 0.938710i | \(0.387978\pi\) | |||||||
\(312\) | 26.1768 | − | 0.366265i | 1.48197 | − | 0.0207357i | ||||
\(313\) | 21.6699 | 1.22486 | 0.612428 | − | 0.790526i | \(-0.290193\pi\) | ||||
0.612428 | + | 0.790526i | \(0.290193\pi\) | |||||||
\(314\) | − | 21.9378i | − | 1.23802i | ||||||
\(315\) | −3.78706 | −0.213377 | ||||||||
\(316\) | 5.89911 | 0.331851 | ||||||||
\(317\) | 29.3780i | 1.65003i | 0.565109 | + | 0.825016i | \(0.308834\pi\) | ||||
−0.565109 | + | 0.825016i | \(0.691166\pi\) | |||||||
\(318\) | 3.47323i | 0.194769i | ||||||||
\(319\) | 7.32853i | 0.410319i | ||||||||
\(320\) | − | 26.0851i | − | 1.45820i | ||||||
\(321\) | 0.846676 | 0.0472569 | ||||||||
\(322\) | 10.3637 | 0.577548 | ||||||||
\(323\) | − | 27.1044i | − | 1.50813i | ||||||
\(324\) | −4.78706 | −0.265948 | ||||||||
\(325\) | −0.471237 | − | 33.6791i | −0.0261396 | − | 1.86818i | ||||
\(326\) | 9.83695 | 0.544818 | ||||||||
\(327\) | 17.9949i | 0.995121i | ||||||||
\(328\) | −24.2828 | −1.34080 | ||||||||
\(329\) | 11.0983 | 0.611871 | ||||||||
\(330\) | 25.2053i | 1.38751i | ||||||||
\(331\) | − | 23.9124i | − | 1.31434i | −0.753741 | − | 0.657171i | \(-0.771753\pi\) | ||
0.753741 | − | 0.657171i | \(-0.228247\pi\) | |||||||
\(332\) | − | 53.1284i | − | 2.91580i | ||||||
\(333\) | 5.10951i | 0.279999i | ||||||||
\(334\) | −23.0183 | −1.25950 | ||||||||
\(335\) | −41.0770 | −2.24428 | ||||||||
\(336\) | − | 9.34181i | − | 0.509638i | ||||||
\(337\) | −15.5706 | −0.848182 | −0.424091 | − | 0.905620i | \(-0.639406\pi\) | ||||
−0.424091 | + | 0.905620i | \(0.639406\pi\) | |||||||
\(338\) | 0.947564 | + | 33.8543i | 0.0515407 | + | 1.84143i | ||||
\(339\) | −2.86858 | −0.155800 | ||||||||
\(340\) | 58.2009i | 3.15639i | ||||||||
\(341\) | −2.21902 | −0.120167 | ||||||||
\(342\) | 21.9949 | 1.18935 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 35.3500i | 1.90594i | ||||||||
\(345\) | − | 15.0653i | − | 0.811087i | ||||||
\(346\) | − | 46.0469i | − | 2.47550i | ||||||
\(347\) | 1.04845 | 0.0562838 | 0.0281419 | − | 0.999604i | \(-0.491041\pi\) | ||||
0.0281419 | + | 0.999604i | \(0.491041\pi\) | |||||||
\(348\) | −13.7321 | −0.736117 | ||||||||
\(349\) | − | 13.8721i | − | 0.742557i | −0.928521 | − | 0.371279i | \(-0.878919\pi\) | ||
0.928521 | − | 0.371279i | \(-0.121081\pi\) | |||||||
\(350\) | −24.3373 | −1.30088 | ||||||||
\(351\) | −0.0504439 | − | 3.60520i | −0.00269250 | − | 0.192431i | ||||
\(352\) | −25.0764 | −1.33658 | ||||||||
\(353\) | 9.96693i | 0.530486i | 0.964182 | + | 0.265243i | \(0.0854522\pi\) | ||||
−0.964182 | + | 0.265243i | \(0.914548\pi\) | |||||||
\(354\) | 27.7601 | 1.47543 | ||||||||
\(355\) | −9.67501 | −0.513496 | ||||||||
\(356\) | 26.4448i | 1.40157i | ||||||||
\(357\) | 3.21040i | 0.169912i | ||||||||
\(358\) | − | 44.0469i | − | 2.32795i | ||||||
\(359\) | 18.9705i | 1.00122i | 0.865672 | + | 0.500611i | \(0.166891\pi\) | ||||
−0.865672 | + | 0.500611i | \(0.833109\pi\) | |||||||
\(360\) | −27.4972 | −1.44923 | ||||||||
\(361\) | −52.2792 | −2.75154 | ||||||||
\(362\) | − | 20.1569i | − | 1.05942i | ||||||
\(363\) | −4.47323 | −0.234784 | ||||||||
\(364\) | 17.2583 | − | 0.241478i | 0.904581 | − | 0.0126569i | ||||
\(365\) | −25.6297 | −1.34152 | ||||||||
\(366\) | − | 10.6836i | − | 0.558442i | ||||||
\(367\) | 22.3586 | 1.16711 | 0.583556 | − | 0.812073i | \(-0.301661\pi\) | ||||
0.583556 | + | 0.812073i | \(0.301661\pi\) | |||||||
\(368\) | 37.1626 | 1.93723 | ||||||||
\(369\) | 3.34436i | 0.174100i | ||||||||
\(370\) | 50.4106i | 2.62072i | ||||||||
\(371\) | 1.33319i | 0.0692159i | ||||||||
\(372\) | − | 4.15796i | − | 0.215580i | ||||||
\(373\) | 26.0958 | 1.35119 | 0.675595 | − | 0.737273i | \(-0.263887\pi\) | ||||
0.675595 | + | 0.737273i | \(0.263887\pi\) | |||||||
\(374\) | 21.3673 | 1.10487 | ||||||||
\(375\) | 16.4427i | 0.849097i | ||||||||
\(376\) | 80.5833 | 4.15577 | ||||||||
\(377\) | −0.144703 | − | 10.3418i | −0.00745256 | − | 0.532630i | ||||
\(378\) | −2.60520 | −0.133997 | ||||||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | 153.057 | 7.85164 | ||||||||
\(381\) | −17.2053 | −0.881455 | ||||||||
\(382\) | − | 14.5217i | − | 0.742994i | ||||||
\(383\) | 4.96229i | 0.253561i | 0.991931 | + | 0.126781i | \(0.0404644\pi\) | ||||
−0.991931 | + | 0.126781i | \(0.959536\pi\) | |||||||
\(384\) | 1.68672i | 0.0860752i | ||||||||
\(385\) | 9.67501i | 0.493084i | ||||||||
\(386\) | 19.7321 | 1.00434 | ||||||||
\(387\) | 4.86858 | 0.247484 | ||||||||
\(388\) | 27.0861i | 1.37509i | ||||||||
\(389\) | 17.8757 | 0.906333 | 0.453166 | − | 0.891426i | \(-0.350294\pi\) | ||||
0.453166 | + | 0.891426i | \(0.350294\pi\) | |||||||
\(390\) | −0.497681 | − | 35.5690i | −0.0252011 | − | 1.80111i | ||||
\(391\) | −12.7713 | −0.645870 | ||||||||
\(392\) | − | 7.26084i | − | 0.366728i | ||||||
\(393\) | −16.6836 | −0.841578 | ||||||||
\(394\) | 34.7647 | 1.75142 | ||||||||
\(395\) | − | 4.66681i | − | 0.234813i | ||||||
\(396\) | 12.2298i | 0.614569i | ||||||||
\(397\) | − | 7.06925i | − | 0.354796i | −0.984139 | − | 0.177398i | \(-0.943232\pi\) | ||
0.984139 | − | 0.177398i | \(-0.0567679\pi\) | |||||||
\(398\) | 43.9898i | 2.20501i | ||||||||
\(399\) | 8.44270 | 0.422664 | ||||||||
\(400\) | −87.2695 | −4.36347 | ||||||||
\(401\) | 9.12025i | 0.455444i | 0.973726 | + | 0.227722i | \(0.0731277\pi\) | ||||
−0.973726 | + | 0.227722i | \(0.926872\pi\) | |||||||
\(402\) | −28.2577 | −1.40937 | ||||||||
\(403\) | 3.13142 | − | 0.0438147i | 0.155987 | − | 0.00218257i | ||||
\(404\) | 42.8325 | 2.13100 | ||||||||
\(405\) | 3.78706i | 0.188180i | ||||||||
\(406\) | −7.47323 | −0.370890 | ||||||||
\(407\) | 13.0535 | 0.647040 | ||||||||
\(408\) | 23.3102i | 1.15403i | ||||||||
\(409\) | 18.2542i | 0.902611i | 0.892369 | + | 0.451306i | \(0.149042\pi\) | ||||
−0.892369 | + | 0.451306i | \(0.850958\pi\) | |||||||
\(410\) | 32.9956i | 1.62953i | ||||||||
\(411\) | − | 18.9134i | − | 0.932929i | ||||||
\(412\) | 8.01835 | 0.395036 | ||||||||
\(413\) | 10.6556 | 0.524330 | ||||||||
\(414\) | − | 10.3637i | − | 0.509349i | ||||||
\(415\) | −42.0301 | −2.06318 | ||||||||
\(416\) | 35.3872 | − | 0.495137i | 1.73500 | − | 0.0242761i | ||||
\(417\) | −5.67501 | −0.277906 | ||||||||
\(418\) | − | 56.1916i | − | 2.74842i | ||||||
\(419\) | 13.6934 | 0.668964 | 0.334482 | − | 0.942402i | \(-0.391439\pi\) | ||||
0.334482 | + | 0.942402i | \(0.391439\pi\) | |||||||
\(420\) | −18.1289 | −0.884598 | ||||||||
\(421\) | 33.8146i | 1.64802i | 0.566573 | + | 0.824012i | \(0.308269\pi\) | ||||
−0.566573 | + | 0.824012i | \(0.691731\pi\) | |||||||
\(422\) | − | 30.4728i | − | 1.48339i | ||||||
\(423\) | − | 11.0983i | − | 0.539620i | ||||||
\(424\) | 9.68009i | 0.470107i | ||||||||
\(425\) | 29.9909 | 1.45477 | ||||||||
\(426\) | −6.65564 | −0.322467 | ||||||||
\(427\) | − | 4.10089i | − | 0.198456i | ||||||
\(428\) | 4.05309 | 0.195913 | ||||||||
\(429\) | −9.21040 | + | 0.128872i | −0.444682 | + | 0.00622199i | ||||
\(430\) | 48.0336 | 2.31639 | ||||||||
\(431\) | − | 20.3256i | − | 0.979048i | −0.871990 | − | 0.489524i | \(-0.837171\pi\) | ||
0.871990 | − | 0.489524i | \(-0.162829\pi\) | |||||||
\(432\) | −9.34181 | −0.449458 | ||||||||
\(433\) | −17.1106 | −0.822284 | −0.411142 | − | 0.911571i | \(-0.634870\pi\) | ||||
−0.411142 | + | 0.911571i | \(0.634870\pi\) | |||||||
\(434\) | − | 2.26283i | − | 0.108619i | ||||||
\(435\) | 10.8635i | 0.520865i | ||||||||
\(436\) | 86.1427i | 4.12549i | ||||||||
\(437\) | 33.5858i | 1.60663i | ||||||||
\(438\) | −17.6312 | −0.842451 | ||||||||
\(439\) | −1.67501 | −0.0799436 | −0.0399718 | − | 0.999201i | \(-0.512727\pi\) | ||||
−0.0399718 | + | 0.999201i | \(0.512727\pi\) | |||||||
\(440\) | 70.2487i | 3.34897i | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −30.1529 | + | 0.421899i | −1.43423 | + | 0.0200677i | ||||
\(443\) | −12.9073 | −0.613245 | −0.306622 | − | 0.951831i | \(-0.599199\pi\) | ||||
−0.306622 | + | 0.951831i | \(0.599199\pi\) | |||||||
\(444\) | 24.4595i | 1.16080i | ||||||||
\(445\) | 20.9206 | 0.991730 | ||||||||
\(446\) | −11.0485 | −0.523159 | ||||||||
\(447\) | 8.49259i | 0.401686i | ||||||||
\(448\) | − | 6.88795i | − | 0.325425i | ||||||
\(449\) | − | 21.1762i | − | 0.999368i | −0.866208 | − | 0.499684i | \(-0.833450\pi\) | ||
0.866208 | − | 0.499684i | \(-0.166550\pi\) | |||||||
\(450\) | 24.3373i | 1.14727i | ||||||||
\(451\) | 8.54401 | 0.402322 | ||||||||
\(452\) | −13.7321 | −0.645903 | ||||||||
\(453\) | 14.2190i | 0.668068i | ||||||||
\(454\) | 4.49768 | 0.211087 | ||||||||
\(455\) | −0.191034 | − | 13.6531i | −0.00895581 | − | 0.640067i | ||||
\(456\) | 61.3011 | 2.87069 | ||||||||
\(457\) | 8.41570i | 0.393670i | 0.980437 | + | 0.196835i | \(0.0630663\pi\) | ||||
−0.980437 | + | 0.196835i | \(0.936934\pi\) | |||||||
\(458\) | −17.7892 | −0.831232 | ||||||||
\(459\) | 3.21040 | 0.149848 | ||||||||
\(460\) | − | 72.1183i | − | 3.36253i | ||||||
\(461\) | − | 1.76515i | − | 0.0822113i | −0.999155 | − | 0.0411056i | \(-0.986912\pi\) | ||
0.999155 | − | 0.0411056i | \(-0.0130880\pi\) | |||||||
\(462\) | 6.65564i | 0.309649i | ||||||||
\(463\) | − | 38.9241i | − | 1.80896i | −0.426519 | − | 0.904479i | \(-0.640260\pi\) | ||
0.426519 | − | 0.904479i | \(-0.359740\pi\) | |||||||
\(464\) | −26.7978 | −1.24406 | ||||||||
\(465\) | −3.28938 | −0.152541 | ||||||||
\(466\) | 3.47323i | 0.160894i | ||||||||
\(467\) | −30.4544 | −1.40926 | −0.704631 | − | 0.709573i | \(-0.748888\pi\) | ||||
−0.704631 | + | 0.709573i | \(0.748888\pi\) | |||||||
\(468\) | −0.241478 | − | 17.2583i | −0.0111623 | − | 0.797765i | ||||
\(469\) | −10.8467 | −0.500853 | ||||||||
\(470\) | − | 109.497i | − | 5.05071i | ||||||
\(471\) | −8.42079 | −0.388010 | ||||||||
\(472\) | 77.3689 | 3.56119 | ||||||||
\(473\) | − | 12.4380i | − | 0.571902i | ||||||
\(474\) | − | 3.21040i | − | 0.147458i | ||||||
\(475\) | − | 78.8701i | − | 3.61881i | ||||||
\(476\) | 15.3684i | 0.704408i | ||||||||
\(477\) | 1.33319 | 0.0610427 | ||||||||
\(478\) | −10.1859 | −0.465894 | ||||||||
\(479\) | 3.54656i | 0.162046i | 0.996712 | + | 0.0810232i | \(0.0258188\pi\) | ||||
−0.996712 | + | 0.0810232i | \(0.974181\pi\) | |||||||
\(480\) | −37.1722 | −1.69667 | ||||||||
\(481\) | −18.4208 | + | 0.257744i | −0.839916 | + | 0.0117521i | ||||
\(482\) | 66.1467 | 3.01290 | ||||||||
\(483\) | − | 3.97809i | − | 0.181009i | ||||||
\(484\) | −21.4136 | −0.973346 | ||||||||
\(485\) | 21.4279 | 0.972990 | ||||||||
\(486\) | 2.60520i | 0.118174i | ||||||||
\(487\) | − | 39.9898i | − | 1.81211i | −0.423158 | − | 0.906056i | \(-0.639078\pi\) | ||
0.423158 | − | 0.906056i | \(-0.360922\pi\) | |||||||
\(488\) | − | 29.7759i | − | 1.34789i | ||||||
\(489\) | − | 3.77589i | − | 0.170752i | ||||||
\(490\) | −9.86604 | −0.445702 | ||||||||
\(491\) | −9.69844 | −0.437685 | −0.218842 | − | 0.975760i | \(-0.570228\pi\) | ||||
−0.218842 | + | 0.975760i | \(0.570228\pi\) | |||||||
\(492\) | 16.0096i | 0.721770i | ||||||||
\(493\) | 9.20929 | 0.414766 | ||||||||
\(494\) | 1.10951 | + | 79.2960i | 0.0499192 | + | 3.56770i | ||||
\(495\) | 9.67501 | 0.434859 | ||||||||
\(496\) | − | 8.11415i | − | 0.364336i | ||||||
\(497\) | −2.55475 | −0.114596 | ||||||||
\(498\) | −28.9134 | −1.29564 | ||||||||
\(499\) | − | 24.0336i | − | 1.07589i | −0.842979 | − | 0.537947i | \(-0.819200\pi\) | ||
0.842979 | − | 0.537947i | \(-0.180800\pi\) | |||||||
\(500\) | 78.7122i | 3.52012i | ||||||||
\(501\) | 8.83551i | 0.394741i | ||||||||
\(502\) | 67.1381i | 2.99652i | ||||||||
\(503\) | 3.67390 | 0.163811 | 0.0819056 | − | 0.996640i | \(-0.473899\pi\) | ||||
0.0819056 | + | 0.996640i | \(0.473899\pi\) | |||||||
\(504\) | −7.26084 | −0.323424 | ||||||||
\(505\) | − | 33.8849i | − | 1.50786i | ||||||
\(506\) | −26.4768 | −1.17704 | ||||||||
\(507\) | 12.9949 | − | 0.363721i | 0.577124 | − | 0.0161534i | ||||
\(508\) | −82.3628 | −3.65426 | ||||||||
\(509\) | − | 19.3612i | − | 0.858169i | −0.903264 | − | 0.429085i | \(-0.858836\pi\) | ||
0.903264 | − | 0.429085i | \(-0.141164\pi\) | |||||||
\(510\) | 31.6739 | 1.40254 | ||||||||
\(511\) | −6.76770 | −0.299385 | ||||||||
\(512\) | 43.9634i | 1.94293i | ||||||||
\(513\) | − | 8.44270i | − | 0.372754i | ||||||
\(514\) | − | 15.3102i | − | 0.675303i | ||||||
\(515\) | − | 6.34334i | − | 0.279521i | ||||||
\(516\) | 23.3062 | 1.02600 | ||||||||
\(517\) | −28.3535 | −1.24699 | ||||||||
\(518\) | 13.3113i | 0.584864i | ||||||||
\(519\) | −17.6750 | −0.775847 | ||||||||
\(520\) | −1.38707 | − | 99.1330i | −0.0608269 | − | 4.34727i | ||||
\(521\) | 34.1130 | 1.49452 | 0.747260 | − | 0.664532i | \(-0.231369\pi\) | ||||
0.747260 | + | 0.664532i | \(0.231369\pi\) | |||||||
\(522\) | 7.47323i | 0.327094i | ||||||||
\(523\) | −33.0250 | −1.44408 | −0.722042 | − | 0.691850i | \(-0.756796\pi\) | ||||
−0.722042 | + | 0.691850i | \(0.756796\pi\) | |||||||
\(524\) | −79.8655 | −3.48894 | ||||||||
\(525\) | 9.34181i | 0.407710i | ||||||||
\(526\) | 26.6796i | 1.16329i | ||||||||
\(527\) | 2.78850i | 0.121469i | ||||||||
\(528\) | 23.8660i | 1.03864i | ||||||||
\(529\) | −7.17478 | −0.311947 | ||||||||
\(530\) | 13.1533 | 0.571344 | ||||||||
\(531\) | − | 10.6556i | − | 0.462415i | ||||||
\(532\) | 40.4157 | 1.75224 | ||||||||
\(533\) | −12.0571 | + | 0.168702i | −0.522250 | + | 0.00730731i | ||||
\(534\) | 14.3917 | 0.622790 | ||||||||
\(535\) | − | 3.20641i | − | 0.138625i | ||||||
\(536\) | −78.7560 | −3.40174 | ||||||||
\(537\) | −16.9073 | −0.729604 | ||||||||
\(538\) | 42.0469i | 1.81277i | ||||||||
\(539\) | 2.55475i | 0.110041i | ||||||||
\(540\) | 18.1289i | 0.780142i | ||||||||
\(541\) | 24.8416i | 1.06802i | 0.845477 | + | 0.534012i | \(0.179316\pi\) | ||||
−0.845477 | + | 0.534012i | \(0.820684\pi\) | |||||||
\(542\) | 31.9339 | 1.37168 | ||||||||
\(543\) | −7.73717 | −0.332034 | ||||||||
\(544\) | 31.5120i | 1.35106i | ||||||||
\(545\) | 68.1478 | 2.91913 | ||||||||
\(546\) | −0.131416 | − | 9.39226i | −0.00562410 | − | 0.401951i | ||||
\(547\) | 8.14114 | 0.348090 | 0.174045 | − | 0.984738i | \(-0.444316\pi\) | ||||
0.174045 | + | 0.984738i | \(0.444316\pi\) | |||||||
\(548\) | − | 90.5395i | − | 3.86766i | ||||||
\(549\) | −4.10089 | −0.175022 | ||||||||
\(550\) | 62.1758 | 2.65118 | ||||||||
\(551\) | − | 24.2186i | − | 1.03175i | ||||||
\(552\) | − | 28.8843i | − | 1.22940i | ||||||
\(553\) | − | 1.23230i | − | 0.0524029i | ||||||
\(554\) | − | 25.5701i | − | 1.08637i | ||||||
\(555\) | 19.3500 | 0.821362 | ||||||||
\(556\) | −27.1666 | −1.15212 | ||||||||
\(557\) | − | 8.11052i | − | 0.343654i | −0.985127 | − | 0.171827i | \(-0.945033\pi\) | ||
0.985127 | − | 0.171827i | \(-0.0549670\pi\) | |||||||
\(558\) | −2.26283 | −0.0957933 | ||||||||
\(559\) | 0.245590 | + | 17.5522i | 0.0103874 | + | 0.742379i | ||||
\(560\) | −35.3780 | −1.49499 | ||||||||
\(561\) | − | 8.20178i | − | 0.346279i | ||||||
\(562\) | −42.1809 | −1.77929 | ||||||||
\(563\) | 11.1044 | 0.467995 | 0.233998 | − | 0.972237i | \(-0.424819\pi\) | ||||
0.233998 | + | 0.972237i | \(0.424819\pi\) | |||||||
\(564\) | − | 53.1284i | − | 2.23711i | ||||||
\(565\) | 10.8635i | 0.457031i | ||||||||
\(566\) | − | 49.8849i | − | 2.09682i | ||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | −18.5497 | −0.778327 | ||||||||
\(569\) | 2.86858 | 0.120257 | 0.0601286 | − | 0.998191i | \(-0.480849\pi\) | ||||
0.0601286 | + | 0.998191i | \(0.480849\pi\) | |||||||
\(570\) | − | 83.2960i | − | 3.48889i | ||||||
\(571\) | 32.4947 | 1.35986 | 0.679930 | − | 0.733277i | \(-0.262010\pi\) | ||||
0.679930 | + | 0.733277i | \(0.262010\pi\) | |||||||
\(572\) | −44.0907 | + | 0.616917i | −1.84353 | + | 0.0257946i | ||||
\(573\) | −5.57412 | −0.232862 | ||||||||
\(574\) | 8.71272i | 0.363662i | ||||||||
\(575\) | −37.1626 | −1.54979 | ||||||||
\(576\) | −6.88795 | −0.286998 | ||||||||
\(577\) | 24.3759i | 1.01478i | 0.861716 | + | 0.507390i | \(0.169390\pi\) | ||||
−0.861716 | + | 0.507390i | \(0.830610\pi\) | |||||||
\(578\) | 17.4375i | 0.725305i | ||||||||
\(579\) | − | 7.57412i | − | 0.314770i | ||||||
\(580\) | 52.0042i | 2.15936i | ||||||||
\(581\) | −11.0983 | −0.460437 | ||||||||
\(582\) | 14.7407 | 0.611022 | ||||||||
\(583\) | − | 3.40598i | − | 0.141061i | ||||||
\(584\) | −49.1392 | −2.03339 | ||||||||
\(585\) | −13.6531 | + | 0.191034i | −0.564486 | + | 0.00789828i | ||||
\(586\) | 64.2767 | 2.65524 | ||||||||
\(587\) | 11.7483i | 0.484906i | 0.970163 | + | 0.242453i | \(0.0779520\pi\) | ||||
−0.970163 | + | 0.242453i | \(0.922048\pi\) | |||||||
\(588\) | −4.78706 | −0.197415 | ||||||||
\(589\) | 7.33319 | 0.302159 | ||||||||
\(590\) | − | 105.129i | − | 4.32809i | ||||||
\(591\) | − | 13.3444i | − | 0.548914i | ||||||
\(592\) | 47.7321i | 1.96178i | ||||||||
\(593\) | − | 46.6459i | − | 1.91552i | −0.287574 | − | 0.957759i | \(-0.592849\pi\) | ||
0.287574 | − | 0.957759i | \(-0.407151\pi\) | |||||||
\(594\) | 6.65564 | 0.273084 | ||||||||
\(595\) | 12.1580 | 0.498428 | ||||||||
\(596\) | 40.6545i | 1.66527i | ||||||||
\(597\) | 16.8854 | 0.691073 | ||||||||
\(598\) | 37.3633 | − | 0.522786i | 1.52790 | − | 0.0213783i | ||||
\(599\) | −20.8197 | −0.850669 | −0.425335 | − | 0.905036i | \(-0.639844\pi\) | ||||
−0.425335 | + | 0.905036i | \(0.639844\pi\) | |||||||
\(600\) | 67.8294i | 2.76912i | ||||||||
\(601\) | 24.2588 | 0.989539 | 0.494770 | − | 0.869024i | \(-0.335252\pi\) | ||||
0.494770 | + | 0.869024i | \(0.335252\pi\) | |||||||
\(602\) | 12.6836 | 0.516946 | ||||||||
\(603\) | 10.8467i | 0.441711i | ||||||||
\(604\) | 68.0673i | 2.76962i | ||||||||
\(605\) | 16.9404i | 0.688724i | ||||||||
\(606\) | − | 23.3102i | − | 0.946911i | ||||||
\(607\) | 6.20067 | 0.251677 | 0.125839 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125839 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(608\) | 82.8701 | 3.36083 | ||||||||
\(609\) | 2.86858i | 0.116241i | ||||||||
\(610\) | −40.4595 | −1.63816 | ||||||||
\(611\) | 40.0117 | − | 0.559844i | 1.61870 | − | 0.0226489i | ||||
\(612\) | 15.3684 | 0.621229 | ||||||||
\(613\) | 14.9026i | 0.601912i | 0.953638 | + | 0.300956i | \(0.0973058\pi\) | ||||
−0.953638 | + | 0.300956i | \(0.902694\pi\) | |||||||
\(614\) | 35.8319 | 1.44606 | ||||||||
\(615\) | 12.6653 | 0.510713 | ||||||||
\(616\) | 18.5497i | 0.747387i | ||||||||
\(617\) | 24.1472i | 0.972130i | 0.873923 | + | 0.486065i | \(0.161568\pi\) | ||||
−0.873923 | + | 0.486065i | \(0.838432\pi\) | |||||||
\(618\) | − | 4.36372i | − | 0.175535i | ||||||
\(619\) | − | 43.9339i | − | 1.76585i | −0.469513 | − | 0.882925i | \(-0.655571\pi\) | ||
0.469513 | − | 0.882925i | \(-0.344429\pi\) | |||||||
\(620\) | −15.7464 | −0.632392 | ||||||||
\(621\) | −3.97809 | −0.159635 | ||||||||
\(622\) | − | 31.6739i | − | 1.27001i | ||||||
\(623\) | 5.52423 | 0.221323 | ||||||||
\(624\) | −0.471237 | − | 33.6791i | −0.0188646 | − | 1.34824i | ||||
\(625\) | 15.5604 | 0.622416 | ||||||||
\(626\) | − | 56.4544i | − | 2.25637i | ||||||
\(627\) | −21.5690 | −0.861384 | ||||||||
\(628\) | −40.3108 | −1.60858 | ||||||||
\(629\) | − | 16.4036i | − | 0.654052i | ||||||
\(630\) | 9.86604i | 0.393072i | ||||||||
\(631\) | 25.9511i | 1.03310i | 0.856258 | + | 0.516548i | \(0.172783\pi\) | ||||
−0.856258 | + | 0.516548i | \(0.827217\pi\) | |||||||
\(632\) | − | 8.94756i | − | 0.355915i | ||||||
\(633\) | −11.6969 | −0.464911 | ||||||||
\(634\) | 76.5355 | 3.03961 | ||||||||
\(635\) | 65.1575i | 2.58570i | ||||||||
\(636\) | 6.38207 | 0.253065 | ||||||||
\(637\) | −0.0504439 | − | 3.60520i | −0.00199866 | − | 0.142843i | ||||
\(638\) | 19.0923 | 0.755870 | ||||||||
\(639\) | 2.55475i | 0.101065i | ||||||||
\(640\) | 6.38772 | 0.252497 | ||||||||
\(641\) | −39.5858 | −1.56355 | −0.781773 | − | 0.623563i | \(-0.785685\pi\) | ||||
−0.781773 | + | 0.623563i | \(0.785685\pi\) | |||||||
\(642\) | − | 2.20576i | − | 0.0870544i | ||||||
\(643\) | 17.0434i | 0.672125i | 0.941840 | + | 0.336062i | \(0.109095\pi\) | ||||
−0.941840 | + | 0.336062i | \(0.890905\pi\) | |||||||
\(644\) | − | 19.0434i | − | 0.750414i | ||||||
\(645\) | − | 18.4376i | − | 0.725980i | ||||||
\(646\) | −70.6124 | −2.77821 | ||||||||
\(647\) | −27.7544 | −1.09114 | −0.545569 | − | 0.838066i | \(-0.683687\pi\) | ||||
−0.545569 | + | 0.838066i | \(0.683687\pi\) | |||||||
\(648\) | 7.26084i | 0.285233i | ||||||||
\(649\) | −27.2225 | −1.06858 | ||||||||
\(650\) | −87.7407 | + | 1.22767i | −3.44147 | + | 0.0481531i | ||||
\(651\) | −0.868584 | −0.0340425 | ||||||||
\(652\) | − | 18.0754i | − | 0.707888i | ||||||
\(653\) | −7.77080 | −0.304095 | −0.152048 | − | 0.988373i | \(-0.548587\pi\) | ||||
−0.152048 | + | 0.988373i | \(0.548587\pi\) | |||||||
\(654\) | 46.8803 | 1.83317 | ||||||||
\(655\) | 63.1819i | 2.46872i | ||||||||
\(656\) | 31.2424i | 1.21981i | ||||||||
\(657\) | 6.76770i | 0.264033i | ||||||||
\(658\) | − | 28.9134i | − | 1.12716i | ||||||
\(659\) | −4.74935 | −0.185008 | −0.0925042 | − | 0.995712i | \(-0.529487\pi\) | ||||
−0.0925042 | + | 0.995712i | \(0.529487\pi\) | |||||||
\(660\) | 46.3148 | 1.80280 | ||||||||
\(661\) | 38.0301i | 1.47920i | 0.673047 | + | 0.739599i | \(0.264985\pi\) | ||||
−0.673047 | + | 0.739599i | \(0.735015\pi\) | |||||||
\(662\) | −62.2965 | −2.42122 | ||||||||
\(663\) | 0.161945 | + | 11.5741i | 0.00628942 | + | 0.449501i | ||||
\(664\) | −80.5833 | −3.12724 | ||||||||
\(665\) | − | 31.9730i | − | 1.23986i | ||||||
\(666\) | 13.3113 | 0.515802 | ||||||||
\(667\) | −11.4115 | −0.441855 | ||||||||
\(668\) | 42.2961i | 1.63649i | ||||||||
\(669\) | 4.24093i | 0.163964i | ||||||||
\(670\) | 107.014i | 4.13430i | ||||||||
\(671\) | 10.4768i | 0.404451i | ||||||||
\(672\) | −9.81560 | −0.378645 | ||||||||
\(673\) | 23.0602 | 0.888905 | 0.444452 | − | 0.895803i | \(-0.353398\pi\) | ||||
0.444452 | + | 0.895803i | \(0.353398\pi\) | |||||||
\(674\) | 40.5644i | 1.56248i | ||||||||
\(675\) | 9.34181 | 0.359567 | ||||||||
\(676\) | 62.2074 | − | 1.74115i | 2.39259 | − | 0.0669674i | ||||
\(677\) | −44.3759 | −1.70550 | −0.852752 | − | 0.522317i | \(-0.825068\pi\) | ||||
−0.852752 | + | 0.522317i | \(0.825068\pi\) | |||||||
\(678\) | 7.47323i | 0.287008i | ||||||||
\(679\) | 5.65819 | 0.217141 | ||||||||
\(680\) | 88.2770 | 3.38527 | ||||||||
\(681\) | − | 1.72643i | − | 0.0661568i | ||||||
\(682\) | 5.78098i | 0.221365i | ||||||||
\(683\) | − | 5.91494i | − | 0.226329i | −0.993576 | − | 0.113165i | \(-0.963901\pi\) | ||
0.993576 | − | 0.113165i | \(-0.0360987\pi\) | |||||||
\(684\) | − | 40.4157i | − | 1.54533i | ||||||
\(685\) | −71.6261 | −2.73669 | ||||||||
\(686\) | −2.60520 | −0.0994669 | ||||||||
\(687\) | 6.82833i | 0.260517i | ||||||||
\(688\) | 45.4814 | 1.73396 | ||||||||
\(689\) | 0.0672514 | + | 4.80642i | 0.00256207 | + | 0.183110i | ||||
\(690\) | −39.2480 | −1.49415 | ||||||||
\(691\) | 12.6883i | 0.482685i | 0.970440 | + | 0.241343i | \(0.0775878\pi\) | ||||
−0.970440 | + | 0.241343i | \(0.922412\pi\) | |||||||
\(692\) | −84.6113 | −3.21644 | ||||||||
\(693\) | 2.55475 | 0.0970471 | ||||||||
\(694\) | − | 2.73143i | − | 0.103683i | ||||||
\(695\) | 21.4916i | 0.815222i | ||||||||
\(696\) | 20.8283i | 0.789496i | ||||||||
\(697\) | − | 10.7367i | − | 0.406682i | ||||||
\(698\) | −36.1396 | −1.36790 | ||||||||
\(699\) | 1.33319 | 0.0504260 | ||||||||
\(700\) | 44.7198i | 1.69025i | ||||||||
\(701\) | 25.8487 | 0.976291 | 0.488146 | − | 0.872762i | \(-0.337674\pi\) | ||||
0.488146 | + | 0.872762i | \(0.337674\pi\) | |||||||
\(702\) | −9.39226 | + | 0.131416i | −0.354488 | + | 0.00495999i | ||||
\(703\) | −43.1381 | −1.62698 | ||||||||
\(704\) | 17.5970i | 0.663212i | ||||||||
\(705\) | −42.0301 | −1.58294 | ||||||||
\(706\) | 25.9658 | 0.977237 | ||||||||
\(707\) | − | 8.94756i | − | 0.336508i | ||||||
\(708\) | − | 51.0092i | − | 1.91704i | ||||||
\(709\) | − | 18.8803i | − | 0.709065i | −0.935044 | − | 0.354533i | \(-0.884640\pi\) | ||
0.935044 | − | 0.354533i | \(-0.115360\pi\) | |||||||
\(710\) | 25.2053i | 0.945938i | ||||||||
\(711\) | −1.23230 | −0.0462150 | ||||||||
\(712\) | 40.1105 | 1.50321 | ||||||||
\(713\) | − | 3.45531i | − | 0.129402i | ||||||
\(714\) | 8.36372 | 0.313004 | ||||||||
\(715\) | 0.488045 | + | 34.8803i | 0.0182518 | + | 1.30445i | ||||
\(716\) | −80.9363 | −3.02473 | ||||||||
\(717\) | 3.90985i | 0.146016i | ||||||||
\(718\) | 49.4218 | 1.84441 | ||||||||
\(719\) | −40.1580 | −1.49764 | −0.748820 | − | 0.662774i | \(-0.769379\pi\) | ||||
−0.748820 | + | 0.662774i | \(0.769379\pi\) | |||||||
\(720\) | 35.3780i | 1.31846i | ||||||||
\(721\) | − | 1.67501i | − | 0.0623804i | ||||||
\(722\) | 136.198i | 5.06875i | ||||||||
\(723\) | − | 25.3903i | − | 0.944274i | ||||||
\(724\) | −37.0383 | −1.37652 | ||||||||
\(725\) | 26.7978 | 0.995244 | ||||||||
\(726\) | 11.6537i | 0.432508i | ||||||||
\(727\) | −32.0336 | −1.18806 | −0.594031 | − | 0.804442i | \(-0.702464\pi\) | ||||
−0.594031 | + | 0.804442i | \(0.702464\pi\) | |||||||
\(728\) | −0.366265 | − | 26.1768i | −0.0135747 | − | 0.970176i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 66.7704i | 2.47128i | ||||||||
\(731\) | −15.6301 | −0.578100 | ||||||||
\(732\) | −19.6312 | −0.725590 | ||||||||
\(733\) | − | 48.3265i | − | 1.78498i | −0.451066 | − | 0.892491i | \(-0.648956\pi\) | ||
0.451066 | − | 0.892491i | \(-0.351044\pi\) | |||||||
\(734\) | − | 58.2487i | − | 2.15000i | ||||||
\(735\) | 3.78706i | 0.139688i | ||||||||
\(736\) | − | 39.0473i | − | 1.43930i | ||||||
\(737\) | 27.7106 | 1.02073 | ||||||||
\(738\) | 8.71272 | 0.320719 | ||||||||
\(739\) | − | 35.7321i | − | 1.31443i | −0.753705 | − | 0.657213i | \(-0.771735\pi\) | ||
0.753705 | − | 0.657213i | \(-0.228265\pi\) | |||||||
\(740\) | 92.6296 | 3.40513 | ||||||||
\(741\) | 30.4376 | − | 0.425883i | 1.11815 | − | 0.0156452i | ||||
\(742\) | 3.47323 | 0.127506 | ||||||||
\(743\) | 45.0092i | 1.65123i | 0.564236 | + | 0.825613i | \(0.309171\pi\) | ||||
−0.564236 | + | 0.825613i | \(0.690829\pi\) | |||||||
\(744\) | −6.30665 | −0.231213 | ||||||||
\(745\) | 32.1619 | 1.17832 | ||||||||
\(746\) | − | 67.9847i | − | 2.48910i | ||||||
\(747\) | 11.0983i | 0.406067i | ||||||||
\(748\) | − | 39.2624i | − | 1.43557i | ||||||
\(749\) | − | 0.846676i | − | 0.0309369i | ||||||
\(750\) | 42.8365 | 1.56417 | ||||||||
\(751\) | 5.39425 | 0.196839 | 0.0984195 | − | 0.995145i | \(-0.468621\pi\) | ||||
0.0984195 | + | 0.995145i | \(0.468621\pi\) | |||||||
\(752\) | − | 103.679i | − | 3.78077i | ||||||
\(753\) | 25.7708 | 0.939140 | ||||||||
\(754\) | −26.9425 | + | 0.376979i | −0.981187 | + | 0.0137288i | ||||
\(755\) | 53.8483 | 1.95974 | ||||||||
\(756\) | 4.78706i | 0.174104i | ||||||||
\(757\) | 13.7896 | 0.501191 | 0.250595 | − | 0.968092i | \(-0.419374\pi\) | ||||
0.250595 | + | 0.968092i | \(0.419374\pi\) | |||||||
\(758\) | 31.2624 | 1.13550 | ||||||||
\(759\) | 10.1631i | 0.368895i | ||||||||
\(760\) | − | 232.151i | − | 8.42100i | ||||||
\(761\) | − | 30.6674i | − | 1.11169i | −0.831286 | − | 0.555846i | \(-0.812395\pi\) | ||
0.831286 | − | 0.555846i | \(-0.187605\pi\) | |||||||
\(762\) | 44.8232i | 1.62377i | ||||||||
\(763\) | 17.9949 | 0.651460 | ||||||||
\(764\) | −26.6836 | −0.965380 | ||||||||
\(765\) | − | 12.1580i | − | 0.439572i | ||||||
\(766\) | 12.9277 | 0.467099 | ||||||||
\(767\) | 38.4157 | − | 0.537512i | 1.38711 | − | 0.0194084i | ||||
\(768\) | 18.1701 | 0.655659 | ||||||||
\(769\) | 48.6160i | 1.75314i | 0.481278 | + | 0.876568i | \(0.340173\pi\) | ||||
−0.481278 | + | 0.876568i | \(0.659827\pi\) | |||||||
\(770\) | 25.2053 | 0.908336 | ||||||||
\(771\) | −5.87678 | −0.211647 | ||||||||
\(772\) | − | 36.2577i | − | 1.30494i | ||||||
\(773\) | − | 18.6729i | − | 0.671617i | −0.941930 | − | 0.335808i | \(-0.890991\pi\) | ||
0.941930 | − | 0.335808i | \(-0.109009\pi\) | |||||||
\(774\) | − | 12.6836i | − | 0.455904i | ||||||
\(775\) | 8.11415i | 0.291469i | ||||||||
\(776\) | 41.0832 | 1.47480 | ||||||||
\(777\) | 5.10951 | 0.183303 | ||||||||
\(778\) | − | 46.5697i | − | 1.66960i | ||||||
\(779\) | −28.2354 | −1.01164 | ||||||||
\(780\) | −65.3582 | + | 0.914491i | −2.34020 | + | 0.0327440i | ||||
\(781\) | 6.52677 | 0.233546 | ||||||||
\(782\) | 33.2717i | 1.18979i | ||||||||
\(783\) | 2.86858 | 0.102515 | ||||||||
\(784\) | −9.34181 | −0.333636 | ||||||||
\(785\) | 31.8900i | 1.13820i | ||||||||
\(786\) | 43.4642i | 1.55032i | ||||||||
\(787\) | 9.61751i | 0.342827i | 0.985199 | + | 0.171414i | \(0.0548334\pi\) | ||||
−0.985199 | + | 0.171414i | \(0.945167\pi\) | |||||||
\(788\) | − | 63.8802i | − | 2.27564i | ||||||
\(789\) | 10.2409 | 0.364587 | ||||||||
\(790\) | −12.1580 | −0.432561 | ||||||||
\(791\) | 2.86858i | 0.101995i | ||||||||
\(792\) | 18.5497 | 0.659134 | ||||||||
\(793\) | −0.206865 | − | 14.7845i | −0.00734598 | − | 0.525013i | ||||
\(794\) | −18.4168 | −0.653588 | ||||||||
\(795\) | − | 5.04888i | − | 0.179065i | ||||||
\(796\) | 80.8314 | 2.86499 | ||||||||
\(797\) | −3.73606 | −0.132338 | −0.0661691 | − | 0.997808i | \(-0.521078\pi\) | ||||
−0.0661691 | + | 0.997808i | \(0.521078\pi\) | |||||||
\(798\) | − | 21.9949i | − | 0.778611i | ||||||
\(799\) | 35.6301i | 1.26050i | ||||||||
\(800\) | 91.6955i | 3.24192i | ||||||||
\(801\) | − | 5.52423i | − | 0.195189i | ||||||
\(802\) | 23.7601 | 0.838997 | ||||||||
\(803\) | 17.2898 | 0.610144 | ||||||||
\(804\) | 51.9237i | 1.83121i | ||||||||
\(805\) | −15.0653 | −0.530981 | ||||||||
\(806\) | −0.114146 | − | 8.15796i | −0.00402062 | − | 0.287352i | ||||
\(807\) | 16.1396 | 0.568141 | ||||||||
\(808\) | − | 64.9668i | − | 2.28553i | ||||||
\(809\) | −10.1850 | −0.358084 | −0.179042 | − | 0.983841i | \(-0.557300\pi\) | ||||
−0.179042 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(810\) | 9.86604 | 0.346657 | ||||||||
\(811\) | − | 6.21902i | − | 0.218379i | −0.994021 | − | 0.109190i | \(-0.965174\pi\) | ||
0.994021 | − | 0.109190i | \(-0.0348256\pi\) | |||||||
\(812\) | 13.7321i | 0.481901i | ||||||||
\(813\) | − | 12.2577i | − | 0.429898i | ||||||
\(814\) | − | 34.0071i | − | 1.19195i | ||||||
\(815\) | −14.2995 | −0.500891 | ||||||||
\(816\) | 29.9909 | 1.04989 | ||||||||
\(817\) | 41.1040i | 1.43805i | ||||||||
\(818\) | 47.5558 | 1.66275 | ||||||||
\(819\) | −3.60520 | + | 0.0504439i | −0.125976 | + | 0.00176265i | ||||
\(820\) | 60.6294 | 2.11727 | ||||||||
\(821\) | 55.4534i | 1.93534i | 0.252224 | + | 0.967669i | \(0.418838\pi\) | ||||
−0.252224 | + | 0.967669i | \(0.581162\pi\) | |||||||
\(822\) | −49.2731 | −1.71860 | ||||||||
\(823\) | −20.4380 | −0.712425 | −0.356213 | − | 0.934405i | \(-0.615932\pi\) | ||||
−0.356213 | + | 0.934405i | \(0.615932\pi\) | |||||||
\(824\) | − | 12.1619i | − | 0.423681i | ||||||
\(825\) | − | 23.8660i | − | 0.830909i | ||||||
\(826\) | − | 27.7601i | − | 0.965896i | ||||||
\(827\) | 14.1289i | 0.491309i | 0.969357 | + | 0.245655i | \(0.0790029\pi\) | ||||
−0.969357 | + | 0.245655i | \(0.920997\pi\) | |||||||
\(828\) | −19.0434 | −0.661803 | ||||||||
\(829\) | 34.9159 | 1.21268 | 0.606340 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606340 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(830\) | 109.497i | 3.80069i | ||||||||
\(831\) | −9.81504 | −0.340480 | ||||||||
\(832\) | −0.347455 | − | 24.8324i | −0.0120458 | − | 0.860909i | ||||
\(833\) | 3.21040 | 0.111234 | ||||||||
\(834\) | 14.7845i | 0.511946i | ||||||||
\(835\) | 33.4606 | 1.15795 | ||||||||
\(836\) | −103.252 | −3.57105 | ||||||||
\(837\) | 0.868584i | 0.0300226i | ||||||||
\(838\) | − | 35.6739i | − | 1.23233i | ||||||
\(839\) | − | 46.4437i | − | 1.60341i | −0.597717 | − | 0.801707i | \(-0.703925\pi\) | ||
0.597717 | − | 0.801707i | \(-0.296075\pi\) | |||||||
\(840\) | 27.4972i | 0.948745i | ||||||||
\(841\) | −20.7712 | −0.716249 | ||||||||
\(842\) | 88.0938 | 3.03591 | ||||||||
\(843\) | 16.1910i | 0.557649i | ||||||||
\(844\) | −55.9938 | −1.92739 | ||||||||
\(845\) | −1.37743 | − | 49.2125i | −0.0473851 | − | 1.69296i | ||||
\(846\) | −28.9134 | −0.994063 | ||||||||
\(847\) | 4.47323i | 0.153702i | ||||||||
\(848\) | 12.4544 | 0.427687 | ||||||||
\(849\) | −19.1482 | −0.657166 | ||||||||
\(850\) | − | 78.1323i | − | 2.67992i | ||||||
\(851\) | 20.3261i | 0.696770i | ||||||||
\(852\) | 12.2298i | 0.418985i | ||||||||
\(853\) | − | 41.4462i | − | 1.41909i | −0.704659 | − | 0.709546i | \(-0.748900\pi\) | ||
0.704659 | − | 0.709546i | \(-0.251100\pi\) | |||||||
\(854\) | −10.6836 | −0.365586 | ||||||||
\(855\) | −31.9730 | −1.09345 | ||||||||
\(856\) | − | 6.14758i | − | 0.210120i | ||||||
\(857\) | 33.8666 | 1.15686 | 0.578431 | − | 0.815732i | \(-0.303665\pi\) | ||||
0.578431 | + | 0.815732i | \(0.303665\pi\) | |||||||
\(858\) | 0.335737 | + | 23.9949i | 0.0114619 | + | 0.819173i | ||||
\(859\) | −37.2890 | −1.27228 | −0.636141 | − | 0.771573i | \(-0.719470\pi\) | ||||
−0.636141 | + | 0.771573i | \(0.719470\pi\) | |||||||
\(860\) | − | 88.2619i | − | 3.00971i | ||||||
\(861\) | 3.34436 | 0.113975 | ||||||||
\(862\) | −52.9521 | −1.80356 | ||||||||
\(863\) | − | 38.7464i | − | 1.31894i | −0.751730 | − | 0.659471i | \(-0.770781\pi\) | ||
0.751730 | − | 0.659471i | \(-0.229219\pi\) | |||||||
\(864\) | 9.81560i | 0.333933i | ||||||||
\(865\) | 66.9363i | 2.27590i | ||||||||
\(866\) | 44.5765i | 1.51477i | ||||||||
\(867\) | 6.69335 | 0.227318 | ||||||||
\(868\) | −4.15796 | −0.141130 | ||||||||
\(869\) | 3.14823i | 0.106797i | ||||||||
\(870\) | 28.3016 | 0.959513 | ||||||||
\(871\) | −39.1044 | + | 0.547149i | −1.32500 | + | 0.0185394i | ||||
\(872\) | 130.658 | 4.42464 | ||||||||
\(873\) | − | 5.65819i | − | 0.191501i | ||||||
\(874\) | 87.4978 | 2.95966 | ||||||||
\(875\) | 16.4427 | 0.555865 | ||||||||
\(876\) | 32.3974i | 1.09461i | ||||||||
\(877\) | − | 51.8319i | − | 1.75024i | −0.483908 | − | 0.875119i | \(-0.660783\pi\) | ||
0.483908 | − | 0.875119i | \(-0.339217\pi\) | |||||||
\(878\) | 4.36372i | 0.147268i | ||||||||
\(879\) | − | 24.6725i | − | 0.832181i | ||||||
\(880\) | 90.3821 | 3.04678 | ||||||||
\(881\) | 20.7896 | 0.700420 | 0.350210 | − | 0.936671i | \(-0.386110\pi\) | ||||
0.350210 | + | 0.936671i | \(0.386110\pi\) | |||||||
\(882\) | 2.60520i | 0.0877216i | ||||||||
\(883\) | 17.5292 | 0.589904 | 0.294952 | − | 0.955512i | \(-0.404696\pi\) | ||||
0.294952 | + | 0.955512i | \(0.404696\pi\) | |||||||
\(884\) | 0.775240 | + | 55.4060i | 0.0260741 | + | 1.86350i | ||||
\(885\) | −40.3535 | −1.35647 | ||||||||
\(886\) | 33.6261i | 1.12969i | ||||||||
\(887\) | 9.53539 | 0.320167 | 0.160084 | − | 0.987103i | \(-0.448824\pi\) | ||||
0.160084 | + | 0.987103i | \(0.448824\pi\) | |||||||
\(888\) | 37.0993 | 1.24497 | ||||||||
\(889\) | 17.2053i | 0.577047i | ||||||||
\(890\) | − | 54.5022i | − | 1.82692i | ||||||
\(891\) | − | 2.55475i | − | 0.0855875i | ||||||
\(892\) | 20.3016i | 0.679746i | ||||||||
\(893\) | 93.7000 | 3.13555 | ||||||||
\(894\) | 22.1249 | 0.739967 | ||||||||
\(895\) | 64.0290i | 2.14025i | ||||||||
\(896\) | 1.68672 | 0.0563495 | ||||||||
\(897\) | −0.200670 | − | 14.3418i | −0.00670019 | − | 0.478859i | ||||
\(898\) | −55.1683 | −1.84099 | ||||||||
\(899\) | 2.49160i | 0.0830997i | ||||||||
\(900\) | 44.7198 | 1.49066 | ||||||||
\(901\) | −4.28008 | −0.142590 | ||||||||
\(902\) | − | 22.2588i | − | 0.741139i | ||||||
\(903\) | − | 4.86858i | − | 0.162016i | ||||||
\(904\) | 20.8283i | 0.692740i | ||||||||
\(905\) | 29.3011i | 0.974002i | ||||||||
\(906\) | 37.0434 | 1.23068 | ||||||||
\(907\) | 27.3270 | 0.907378 | 0.453689 | − | 0.891160i | \(-0.350108\pi\) | ||||
0.453689 | + | 0.891160i | \(0.350108\pi\) | |||||||
\(908\) | − | 8.26450i | − | 0.274267i | ||||||
\(909\) | −8.94756 | −0.296772 | ||||||||
\(910\) | −35.5690 | + | 0.497681i | −1.17910 | + | 0.0164980i | ||||
\(911\) | −38.9582 | −1.29074 | −0.645371 | − | 0.763869i | \(-0.723297\pi\) | ||||
−0.645371 | + | 0.763869i | \(0.723297\pi\) | |||||||
\(912\) | − | 78.8701i | − | 2.61165i | ||||||
\(913\) | 28.3535 | 0.938365 | ||||||||
\(914\) | 21.9246 | 0.725201 | ||||||||
\(915\) | 15.5303i | 0.513416i | ||||||||
\(916\) | 32.6876i | 1.08003i | ||||||||
\(917\) | 16.6836i | 0.550942i | ||||||||
\(918\) | − | 8.36372i | − | 0.276044i | ||||||
\(919\) | 9.94293 | 0.327987 | 0.163993 | − | 0.986461i | \(-0.447562\pi\) | ||||
0.163993 | + | 0.986461i | \(0.447562\pi\) | |||||||
\(920\) | −109.387 | −3.60637 | ||||||||
\(921\) | − | 13.7540i | − | 0.453209i | ||||||
\(922\) | −4.59857 | −0.151446 | ||||||||
\(923\) | −9.21040 | + | 0.128872i | −0.303164 | + | 0.00424187i | ||||
\(924\) | 12.2298 | 0.402330 | ||||||||
\(925\) | − | 47.7321i | − | 1.56942i | ||||||
\(926\) | −101.405 | −3.33238 | ||||||||
\(927\) | −1.67501 | −0.0550144 | ||||||||
\(928\) | 28.1569i | 0.924294i | ||||||||
\(929\) | 7.80854i | 0.256190i | 0.991762 | + | 0.128095i | \(0.0408862\pi\) | ||||
−0.991762 | + | 0.128095i | \(0.959114\pi\) | |||||||
\(930\) | 8.56948i | 0.281004i | ||||||||
\(931\) | − | 8.44270i | − | 0.276698i | ||||||
\(932\) | 6.38207 | 0.209052 | ||||||||
\(933\) | −12.1580 | −0.398034 | ||||||||
\(934\) | 79.3398i | 2.59608i | ||||||||
\(935\) | −31.0606 | −1.01579 | ||||||||
\(936\) | −26.1768 | + | 0.366265i | −0.855615 | + | 0.0119717i | ||||
\(937\) | −9.59246 | −0.313372 | −0.156686 | − | 0.987648i | \(-0.550081\pi\) | ||||
−0.156686 | + | 0.987648i | \(0.550081\pi\) | |||||||
\(938\) | 28.2577i | 0.922648i | ||||||||
\(939\) | −21.6699 | −0.707171 | ||||||||
\(940\) | −201.200 | −6.56243 | ||||||||
\(941\) | − | 28.5043i | − | 0.929214i | −0.885517 | − | 0.464607i | \(-0.846196\pi\) | ||
0.885517 | − | 0.464607i | \(-0.153804\pi\) | |||||||
\(942\) | 21.9378i | 0.714773i | ||||||||
\(943\) | 13.3042i | 0.433243i | ||||||||
\(944\) | − | 99.5430i | − | 3.23985i | ||||||
\(945\) | 3.78706 | 0.123193 | ||||||||
\(946\) | −32.4036 | −1.05353 | ||||||||
\(947\) | − | 47.8997i | − | 1.55653i | −0.627936 | − | 0.778265i | \(-0.716100\pi\) | ||
0.627936 | − | 0.778265i | \(-0.283900\pi\) | |||||||
\(948\) | −5.89911 | −0.191594 | ||||||||
\(949\) | −24.3989 | + | 0.341389i | −0.792021 | + | 0.0110820i | ||||
\(950\) | −205.472 | −6.66640 | ||||||||
\(951\) | − | 29.3780i | − | 0.952647i | ||||||
\(952\) | 23.3102 | 0.755487 | ||||||||
\(953\) | 32.5181 | 1.05337 | 0.526683 | − | 0.850062i | \(-0.323436\pi\) | ||||
0.526683 | + | 0.850062i | \(0.323436\pi\) | |||||||
\(954\) | − | 3.47323i | − | 0.112450i | ||||||
\(955\) | 21.1095i | 0.683088i | ||||||||
\(956\) | 18.7167i | 0.605341i | ||||||||
\(957\) | − | 7.32853i | − | 0.236898i | ||||||
\(958\) | 9.23949 | 0.298514 | ||||||||
\(959\) | −18.9134 | −0.610745 | ||||||||
\(960\) | 26.0851i | 0.841892i | ||||||||
\(961\) | 30.2456 | 0.975663 | ||||||||
\(962\) | 0.671473 | + | 47.9898i | 0.0216492 | + | 1.54725i | ||||
\(963\) | −0.846676 | −0.0272838 | ||||||||
\(964\) | − | 121.545i | − | 3.91469i | ||||||
\(965\) | −28.6836 | −0.923359 | ||||||||
\(966\) | −10.3637 | −0.333447 | ||||||||
\(967\) | − | 18.0387i | − | 0.580086i | −0.957014 | − | 0.290043i | \(-0.906330\pi\) | ||
0.957014 | − | 0.290043i | \(-0.0936697\pi\) | |||||||
\(968\) | 32.4794i | 1.04393i | ||||||||
\(969\) | 27.1044i | 0.870719i | ||||||||
\(970\) | − | 55.8239i | − | 1.79240i | ||||||
\(971\) | 30.2190 | 0.969774 | 0.484887 | − | 0.874577i | \(-0.338861\pi\) | ||||
0.484887 | + | 0.874577i | \(0.338861\pi\) | |||||||
\(972\) | 4.78706 | 0.153545 | ||||||||
\(973\) | 5.67501i | 0.181932i | ||||||||
\(974\) | −104.181 | −3.33819 | ||||||||
\(975\) | 0.471237 | + | 33.6791i | 0.0150917 | + | 1.07859i | ||||
\(976\) | −38.3097 | −1.22626 | ||||||||
\(977\) | 38.4652i | 1.23061i | 0.788289 | + | 0.615305i | \(0.210967\pi\) | ||||
−0.788289 | + | 0.615305i | \(0.789033\pi\) | |||||||
\(978\) | −9.83695 | −0.314551 | ||||||||
\(979\) | −14.1130 | −0.451055 | ||||||||
\(980\) | 18.1289i | 0.579106i | ||||||||
\(981\) | − | 17.9949i | − | 0.574533i | ||||||
\(982\) | 25.2664i | 0.806282i | ||||||||
\(983\) | − | 12.1742i | − | 0.388297i | −0.980972 | − | 0.194149i | \(-0.937806\pi\) | ||
0.980972 | − | 0.194149i | \(-0.0621944\pi\) | |||||||
\(984\) | 24.2828 | 0.774109 | ||||||||
\(985\) | −50.5359 | −1.61021 | ||||||||
\(986\) | − | 23.9920i | − | 0.764062i | ||||||
\(987\) | −11.0983 | −0.353264 | ||||||||
\(988\) | 145.707 | − | 2.03873i | 4.63555 | − | 0.0648605i | ||||
\(989\) | 19.3677 | 0.615856 | ||||||||
\(990\) | − | 25.2053i | − | 0.801077i | ||||||
\(991\) | 14.4982 | 0.460552 | 0.230276 | − | 0.973125i | \(-0.426037\pi\) | ||||
0.230276 | + | 0.973125i | \(0.426037\pi\) | |||||||
\(992\) | −8.52567 | −0.270690 | ||||||||
\(993\) | 23.9124i | 0.758836i | ||||||||
\(994\) | 6.65564i | 0.211104i | ||||||||
\(995\) | − | 63.9460i | − | 2.02722i | ||||||
\(996\) | 53.1284i | 1.68344i | ||||||||
\(997\) | −9.35086 | −0.296145 | −0.148072 | − | 0.988977i | \(-0.547307\pi\) | ||||
−0.148072 | + | 0.988977i | \(0.547307\pi\) | |||||||
\(998\) | −62.6124 | −1.98196 | ||||||||
\(999\) | − | 5.10951i | − | 0.161658i |
(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 | 273.2.c.c.64.1 | ✓ | 8 | |
3.2 | odd | 2 | 819.2.c.d.64.8 | 8 | |||
4.3 | odd | 2 | 4368.2.h.q.337.8 | 8 | |||
7.6 | odd | 2 | 1911.2.c.l.883.1 | 8 | |||
13.5 | odd | 4 | 3549.2.a.x.1.1 | 4 | |||
13.8 | odd | 4 | 3549.2.a.v.1.4 | 4 | |||
13.12 | even | 2 | inner | 273.2.c.c.64.8 | yes | 8 | |
39.38 | odd | 2 | 819.2.c.d.64.1 | 8 | |||
52.51 | odd | 2 | 4368.2.h.q.337.1 | 8 | |||
91.90 | odd | 2 | 1911.2.c.l.883.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.c.c.64.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
273.2.c.c.64.8 | yes | 8 | 13.12 | even | 2 | inner | |
819.2.c.d.64.1 | 8 | 39.38 | odd | 2 | |||
819.2.c.d.64.8 | 8 | 3.2 | odd | 2 | |||
1911.2.c.l.883.1 | 8 | 7.6 | odd | 2 | |||
1911.2.c.l.883.8 | 8 | 91.90 | odd | 2 | |||
3549.2.a.v.1.4 | 4 | 13.8 | odd | 4 | |||
3549.2.a.x.1.1 | 4 | 13.5 | odd | 4 | |||
4368.2.h.q.337.1 | 8 | 52.51 | odd | 2 | |||
4368.2.h.q.337.8 | 8 | 4.3 | odd | 2 |