Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,3,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.17166513675\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 20x^{4} + 121x^{2} + 214 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.1 | ||
Root | \(-3.18991i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.3.b.b.42.6 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.18991i | − | 1.59496i | −0.603348 | − | 0.797478i | \(-0.706167\pi\) | ||
0.603348 | − | 0.797478i | \(-0.293833\pi\) | |||||||
\(3\) | 0.724539i | 0.241513i | 0.992682 | + | 0.120757i | \(0.0385320\pi\) | ||||
−0.992682 | + | 0.120757i | \(0.961468\pi\) | |||||||
\(4\) | −6.17554 | −1.54389 | ||||||||
\(5\) | − | 7.66434i | − | 1.53287i | −0.642324 | − | 0.766434i | \(-0.722029\pi\) | ||
0.642324 | − | 0.766434i | \(-0.277971\pi\) | |||||||
\(6\) | 2.31122 | 0.385203 | ||||||||
\(7\) | 10.1297i | 1.44710i | 0.690271 | + | 0.723551i | \(0.257491\pi\) | ||||
−0.690271 | + | 0.723551i | \(0.742509\pi\) | |||||||
\(8\) | 6.93980i | 0.867475i | ||||||||
\(9\) | 8.47504 | 0.941671 | ||||||||
\(10\) | −24.4486 | −2.44486 | ||||||||
\(11\) | −2.43517 | −0.221379 | −0.110690 | − | 0.993855i | \(-0.535306\pi\) | ||||
−0.110690 | + | 0.993855i | \(0.535306\pi\) | |||||||
\(12\) | − | 4.47442i | − | 0.372869i | ||||||
\(13\) | 18.1491 | 1.39608 | 0.698041 | − | 0.716058i | \(-0.254055\pi\) | ||||
0.698041 | + | 0.716058i | \(0.254055\pi\) | |||||||
\(14\) | 32.3129 | 2.30806 | ||||||||
\(15\) | 5.55311 | 0.370207 | ||||||||
\(16\) | −2.56483 | −0.160302 | ||||||||
\(17\) | −1.13567 | −0.0668042 | −0.0334021 | − | 0.999442i | \(-0.510634\pi\) | ||||
−0.0334021 | + | 0.999442i | \(0.510634\pi\) | |||||||
\(18\) | − | 27.0346i | − | 1.50192i | ||||||
\(19\) | 12.3269i | 0.648783i | 0.945923 | + | 0.324391i | \(0.105159\pi\) | ||||
−0.945923 | + | 0.324391i | \(0.894841\pi\) | |||||||
\(20\) | 47.3314i | 2.36657i | ||||||||
\(21\) | −7.33937 | −0.349494 | ||||||||
\(22\) | 7.76798i | 0.353090i | ||||||||
\(23\) | −24.2847 | −1.05586 | −0.527929 | − | 0.849288i | \(-0.677031\pi\) | ||||
−0.527929 | + | 0.849288i | \(0.677031\pi\) | |||||||
\(24\) | −5.02815 | −0.209506 | ||||||||
\(25\) | −33.7420 | −1.34968 | ||||||||
\(26\) | − | 57.8939i | − | 2.22669i | ||||||
\(27\) | 12.6614i | 0.468939i | ||||||||
\(28\) | − | 62.5565i | − | 2.23416i | ||||||
\(29\) | 35.5218i | 1.22489i | 0.790513 | + | 0.612445i | \(0.209814\pi\) | ||||
−0.790513 | + | 0.612445i | \(0.790186\pi\) | |||||||
\(30\) | − | 17.7139i | − | 0.590465i | ||||||
\(31\) | −12.9823 | −0.418783 | −0.209391 | − | 0.977832i | \(-0.567148\pi\) | ||||
−0.209391 | + | 0.977832i | \(0.567148\pi\) | |||||||
\(32\) | 35.9408i | 1.12315i | ||||||||
\(33\) | − | 1.76438i | − | 0.0534660i | ||||||
\(34\) | 3.62270i | 0.106550i | ||||||||
\(35\) | 77.6375 | 2.21821 | ||||||||
\(36\) | −52.3380 | −1.45383 | ||||||||
\(37\) | − | 41.5116i | − | 1.12193i | −0.827838 | − | 0.560967i | \(-0.810429\pi\) | ||
0.827838 | − | 0.560967i | \(-0.189571\pi\) | |||||||
\(38\) | 39.3216 | 1.03478 | ||||||||
\(39\) | 13.1497i | 0.337172i | ||||||||
\(40\) | 53.1889 | 1.32972 | ||||||||
\(41\) | −65.0667 | −1.58699 | −0.793496 | − | 0.608576i | \(-0.791741\pi\) | ||||
−0.793496 | + | 0.608576i | \(0.791741\pi\) | |||||||
\(42\) | 23.4120i | 0.557427i | ||||||||
\(43\) | 23.6064 | − | 35.9408i | 0.548986 | − | 0.835832i | ||||
\(44\) | 15.0385 | 0.341784 | ||||||||
\(45\) | − | 64.9556i | − | 1.44346i | ||||||
\(46\) | 77.4662i | 1.68405i | ||||||||
\(47\) | 51.0402 | 1.08596 | 0.542981 | − | 0.839745i | \(-0.317296\pi\) | ||||
0.542981 | + | 0.839745i | \(0.317296\pi\) | |||||||
\(48\) | − | 1.85832i | − | 0.0387150i | ||||||
\(49\) | −53.6110 | −1.09410 | ||||||||
\(50\) | 107.634i | 2.15268i | ||||||||
\(51\) | − | 0.822839i | − | 0.0161341i | ||||||
\(52\) | −112.080 | −2.15539 | ||||||||
\(53\) | 56.2026 | 1.06043 | 0.530214 | − | 0.847864i | \(-0.322112\pi\) | ||||
0.530214 | + | 0.847864i | \(0.322112\pi\) | |||||||
\(54\) | 40.3886 | 0.747937 | ||||||||
\(55\) | 18.6640i | 0.339345i | ||||||||
\(56\) | −70.2981 | −1.25532 | ||||||||
\(57\) | −8.93130 | −0.156689 | ||||||||
\(58\) | 113.312 | 1.95365 | ||||||||
\(59\) | −88.8355 | −1.50569 | −0.752843 | − | 0.658200i | \(-0.771318\pi\) | ||||
−0.752843 | + | 0.658200i | \(0.771318\pi\) | |||||||
\(60\) | −34.2935 | −0.571558 | ||||||||
\(61\) | 65.1393i | 1.06786i | 0.845529 | + | 0.533929i | \(0.179285\pi\) | ||||
−0.845529 | + | 0.533929i | \(0.820715\pi\) | |||||||
\(62\) | 41.4123i | 0.667940i | ||||||||
\(63\) | 85.8497i | 1.36269i | ||||||||
\(64\) | 104.389 | 1.63107 | ||||||||
\(65\) | − | 139.101i | − | 2.14001i | ||||||
\(66\) | −5.62821 | −0.0852759 | ||||||||
\(67\) | 45.3618 | 0.677042 | 0.338521 | − | 0.940959i | \(-0.390073\pi\) | ||||
0.338521 | + | 0.940959i | \(0.390073\pi\) | |||||||
\(68\) | 7.01339 | 0.103138 | ||||||||
\(69\) | − | 17.5952i | − | 0.255004i | ||||||
\(70\) | − | 247.657i | − | 3.53796i | ||||||
\(71\) | − | 63.7983i | − | 0.898567i | −0.893389 | − | 0.449284i | \(-0.851679\pi\) | ||
0.893389 | − | 0.449284i | \(-0.148321\pi\) | |||||||
\(72\) | 58.8151i | 0.816876i | ||||||||
\(73\) | − | 8.80247i | − | 0.120582i | −0.998181 | − | 0.0602909i | \(-0.980797\pi\) | ||
0.998181 | − | 0.0602909i | \(-0.0192028\pi\) | |||||||
\(74\) | −132.418 | −1.78944 | ||||||||
\(75\) | − | 24.4474i | − | 0.325966i | ||||||
\(76\) | − | 76.1251i | − | 1.00165i | ||||||
\(77\) | − | 24.6676i | − | 0.320358i | ||||||
\(78\) | 41.9464 | 0.537775 | ||||||||
\(79\) | 31.8496 | 0.403159 | 0.201580 | − | 0.979472i | \(-0.435393\pi\) | ||||
0.201580 | + | 0.979472i | \(0.435393\pi\) | |||||||
\(80\) | 19.6577i | 0.245721i | ||||||||
\(81\) | 67.1017 | 0.828417 | ||||||||
\(82\) | 207.557i | 2.53118i | ||||||||
\(83\) | −68.4740 | −0.824988 | −0.412494 | − | 0.910960i | \(-0.635342\pi\) | ||||
−0.412494 | + | 0.910960i | \(0.635342\pi\) | |||||||
\(84\) | 45.3246 | 0.539579 | ||||||||
\(85\) | 8.70417i | 0.102402i | ||||||||
\(86\) | −114.648 | − | 75.3023i | −1.33312 | − | 0.875608i | ||||
\(87\) | −25.7370 | −0.295827 | ||||||||
\(88\) | − | 16.8996i | − | 0.192041i | ||||||
\(89\) | 5.90432i | 0.0663406i | 0.999450 | + | 0.0331703i | \(0.0105604\pi\) | ||||
−0.999450 | + | 0.0331703i | \(0.989440\pi\) | |||||||
\(90\) | −207.203 | −2.30225 | ||||||||
\(91\) | 183.845i | 2.02027i | ||||||||
\(92\) | 149.971 | 1.63012 | ||||||||
\(93\) | − | 9.40616i | − | 0.101142i | ||||||
\(94\) | − | 162.814i | − | 1.73206i | ||||||
\(95\) | 94.4773 | 0.994498 | ||||||||
\(96\) | −26.0405 | −0.271255 | ||||||||
\(97\) | −100.657 | −1.03770 | −0.518849 | − | 0.854866i | \(-0.673639\pi\) | ||||
−0.518849 | + | 0.854866i | \(0.673639\pi\) | |||||||
\(98\) | 171.015i | 1.74505i | ||||||||
\(99\) | −20.6382 | −0.208466 | ||||||||
\(100\) | 208.376 | 2.08376 | ||||||||
\(101\) | 13.7062 | 0.135705 | 0.0678525 | − | 0.997695i | \(-0.478385\pi\) | ||||
0.0678525 | + | 0.997695i | \(0.478385\pi\) | |||||||
\(102\) | −2.62478 | −0.0257332 | ||||||||
\(103\) | −96.0402 | −0.932429 | −0.466214 | − | 0.884672i | \(-0.654382\pi\) | ||||
−0.466214 | + | 0.884672i | \(0.654382\pi\) | |||||||
\(104\) | 125.951i | 1.21107i | ||||||||
\(105\) | 56.2514i | 0.535728i | ||||||||
\(106\) | − | 179.282i | − | 1.69134i | ||||||
\(107\) | −2.08036 | −0.0194427 | −0.00972133 | − | 0.999953i | \(-0.503094\pi\) | ||||
−0.00972133 | + | 0.999953i | \(0.503094\pi\) | |||||||
\(108\) | − | 78.1907i | − | 0.723988i | ||||||
\(109\) | −53.1078 | −0.487228 | −0.243614 | − | 0.969872i | \(-0.578333\pi\) | ||||
−0.243614 | + | 0.969872i | \(0.578333\pi\) | |||||||
\(110\) | 59.5364 | 0.541240 | ||||||||
\(111\) | 30.0768 | 0.270962 | ||||||||
\(112\) | − | 25.9810i | − | 0.231973i | ||||||
\(113\) | 28.8791i | 0.255568i | 0.991802 | + | 0.127784i | \(0.0407864\pi\) | ||||
−0.991802 | + | 0.127784i | \(0.959214\pi\) | |||||||
\(114\) | 28.4901i | 0.249913i | ||||||||
\(115\) | 186.126i | 1.61849i | ||||||||
\(116\) | − | 219.367i | − | 1.89109i | ||||||
\(117\) | 153.814 | 1.31465 | ||||||||
\(118\) | 283.378i | 2.40150i | ||||||||
\(119\) | − | 11.5040i | − | 0.0966725i | ||||||
\(120\) | 38.5375i | 0.321146i | ||||||||
\(121\) | −115.070 | −0.950991 | ||||||||
\(122\) | 207.789 | 1.70319 | ||||||||
\(123\) | − | 47.1433i | − | 0.383279i | ||||||
\(124\) | 80.1726 | 0.646553 | ||||||||
\(125\) | 67.0020i | 0.536016i | ||||||||
\(126\) | 273.853 | 2.17344 | ||||||||
\(127\) | 148.673 | 1.17066 | 0.585328 | − | 0.810797i | \(-0.300966\pi\) | ||||
0.585328 | + | 0.810797i | \(0.300966\pi\) | |||||||
\(128\) | − | 189.227i | − | 1.47834i | ||||||
\(129\) | 26.0405 | + | 17.1037i | 0.201864 | + | 0.132587i | ||||
\(130\) | −443.719 | −3.41322 | ||||||||
\(131\) | − | 157.214i | − | 1.20011i | −0.799960 | − | 0.600054i | \(-0.795146\pi\) | ||
0.799960 | − | 0.600054i | \(-0.204854\pi\) | |||||||
\(132\) | 10.8960i | 0.0825453i | ||||||||
\(133\) | −124.868 | −0.938854 | ||||||||
\(134\) | − | 144.700i | − | 1.07985i | ||||||
\(135\) | 97.0409 | 0.718821 | ||||||||
\(136\) | − | 7.88133i | − | 0.0579510i | ||||||
\(137\) | − | 121.604i | − | 0.887618i | −0.896122 | − | 0.443809i | \(-0.853627\pi\) | ||
0.896122 | − | 0.443809i | \(-0.146373\pi\) | |||||||
\(138\) | −56.1273 | −0.406719 | ||||||||
\(139\) | −27.8992 | −0.200714 | −0.100357 | − | 0.994952i | \(-0.531998\pi\) | ||||
−0.100357 | + | 0.994952i | \(0.531998\pi\) | |||||||
\(140\) | −479.454 | −3.42467 | ||||||||
\(141\) | 36.9806i | 0.262274i | ||||||||
\(142\) | −203.511 | −1.43318 | ||||||||
\(143\) | −44.1961 | −0.309063 | ||||||||
\(144\) | −21.7370 | −0.150952 | ||||||||
\(145\) | 272.251 | 1.87759 | ||||||||
\(146\) | −28.0791 | −0.192323 | ||||||||
\(147\) | − | 38.8433i | − | 0.264240i | ||||||
\(148\) | 256.357i | 1.73214i | ||||||||
\(149\) | 212.121i | 1.42363i | 0.702366 | + | 0.711816i | \(0.252127\pi\) | ||||
−0.702366 | + | 0.711816i | \(0.747873\pi\) | |||||||
\(150\) | −77.9852 | −0.519901 | ||||||||
\(151\) | − | 108.847i | − | 0.720842i | −0.932790 | − | 0.360421i | \(-0.882633\pi\) | ||
0.932790 | − | 0.360421i | \(-0.117367\pi\) | |||||||
\(152\) | −85.5460 | −0.562802 | ||||||||
\(153\) | −9.62487 | −0.0629077 | ||||||||
\(154\) | −78.6874 | −0.510957 | ||||||||
\(155\) | 99.5005i | 0.641938i | ||||||||
\(156\) | − | 81.2066i | − | 0.520555i | ||||||
\(157\) | 106.772i | 0.680075i | 0.940412 | + | 0.340038i | \(0.110440\pi\) | ||||
−0.940412 | + | 0.340038i | \(0.889560\pi\) | |||||||
\(158\) | − | 101.597i | − | 0.643021i | ||||||
\(159\) | 40.7210i | 0.256107i | ||||||||
\(160\) | 275.462 | 1.72164 | ||||||||
\(161\) | − | 245.997i | − | 1.52793i | ||||||
\(162\) | − | 214.049i | − | 1.32129i | ||||||
\(163\) | − | 202.231i | − | 1.24068i | −0.784334 | − | 0.620339i | \(-0.786995\pi\) | ||
0.784334 | − | 0.620339i | \(-0.213005\pi\) | |||||||
\(164\) | 401.822 | 2.45013 | ||||||||
\(165\) | −13.5228 | −0.0819562 | ||||||||
\(166\) | 218.426i | 1.31582i | ||||||||
\(167\) | −41.0703 | −0.245930 | −0.122965 | − | 0.992411i | \(-0.539240\pi\) | ||||
−0.122965 | + | 0.992411i | \(0.539240\pi\) | |||||||
\(168\) | − | 50.9337i | − | 0.303177i | ||||||
\(169\) | 160.389 | 0.949045 | ||||||||
\(170\) | 27.7656 | 0.163327 | ||||||||
\(171\) | 104.471i | 0.610940i | ||||||||
\(172\) | −145.782 | + | 221.954i | −0.847571 | + | 1.29043i | ||||
\(173\) | −24.1006 | −0.139310 | −0.0696549 | − | 0.997571i | \(-0.522190\pi\) | ||||
−0.0696549 | + | 0.997571i | \(0.522190\pi\) | |||||||
\(174\) | 82.0986i | 0.471831i | ||||||||
\(175\) | − | 341.797i | − | 1.95313i | ||||||
\(176\) | 6.24580 | 0.0354875 | ||||||||
\(177\) | − | 64.3648i | − | 0.363643i | ||||||
\(178\) | 18.8343 | 0.105810 | ||||||||
\(179\) | 83.0659i | 0.464055i | 0.972709 | + | 0.232028i | \(0.0745360\pi\) | ||||
−0.972709 | + | 0.232028i | \(0.925464\pi\) | |||||||
\(180\) | 401.136i | 2.22853i | ||||||||
\(181\) | −112.273 | −0.620291 | −0.310145 | − | 0.950689i | \(-0.600378\pi\) | ||||
−0.310145 | + | 0.950689i | \(0.600378\pi\) | |||||||
\(182\) | 586.449 | 3.22225 | ||||||||
\(183\) | −47.1960 | −0.257902 | ||||||||
\(184\) | − | 168.531i | − | 0.915930i | ||||||
\(185\) | −318.159 | −1.71978 | ||||||||
\(186\) | −30.0048 | −0.161316 | ||||||||
\(187\) | 2.76556 | 0.0147891 | ||||||||
\(188\) | −315.201 | −1.67660 | ||||||||
\(189\) | −128.256 | −0.678602 | ||||||||
\(190\) | − | 301.374i | − | 1.58618i | ||||||
\(191\) | − | 43.7078i | − | 0.228836i | −0.993433 | − | 0.114418i | \(-0.963500\pi\) | ||
0.993433 | − | 0.114418i | \(-0.0365004\pi\) | |||||||
\(192\) | 75.6336i | 0.393925i | ||||||||
\(193\) | 236.100 | 1.22332 | 0.611659 | − | 0.791122i | \(-0.290503\pi\) | ||||
0.611659 | + | 0.791122i | \(0.290503\pi\) | |||||||
\(194\) | 321.086i | 1.65508i | ||||||||
\(195\) | 100.784 | 0.516840 | ||||||||
\(196\) | 331.077 | 1.68917 | ||||||||
\(197\) | 350.134 | 1.77733 | 0.888665 | − | 0.458557i | \(-0.151634\pi\) | ||||
0.888665 | + | 0.458557i | \(0.151634\pi\) | |||||||
\(198\) | 65.8340i | 0.332495i | ||||||||
\(199\) | 353.573i | 1.77675i | 0.459122 | + | 0.888373i | \(0.348164\pi\) | ||||
−0.459122 | + | 0.888373i | \(0.651836\pi\) | |||||||
\(200\) | − | 234.163i | − | 1.17081i | ||||||
\(201\) | 32.8664i | 0.163514i | ||||||||
\(202\) | − | 43.7216i | − | 0.216444i | ||||||
\(203\) | −359.826 | −1.77254 | ||||||||
\(204\) | 5.08148i | 0.0249092i | ||||||||
\(205\) | 498.693i | 2.43265i | ||||||||
\(206\) | 306.360i | 1.48718i | ||||||||
\(207\) | −205.814 | −0.994272 | ||||||||
\(208\) | −46.5493 | −0.223794 | ||||||||
\(209\) | − | 30.0180i | − | 0.143627i | ||||||
\(210\) | 179.437 | 0.854462 | ||||||||
\(211\) | − | 281.519i | − | 1.33421i | −0.744962 | − | 0.667107i | \(-0.767532\pi\) | ||
0.744962 | − | 0.667107i | \(-0.232468\pi\) | |||||||
\(212\) | −347.082 | −1.63718 | ||||||||
\(213\) | 46.2243 | 0.217016 | ||||||||
\(214\) | 6.63618i | 0.0310102i | ||||||||
\(215\) | −275.462 | − | 180.927i | −1.28122 | − | 0.841522i | ||||
\(216\) | −87.8672 | −0.406793 | ||||||||
\(217\) | − | 131.507i | − | 0.606021i | ||||||
\(218\) | 169.409i | 0.777107i | ||||||||
\(219\) | 6.37774 | 0.0291221 | ||||||||
\(220\) | − | 115.260i | − | 0.523910i | ||||||
\(221\) | −20.6114 | −0.0932642 | ||||||||
\(222\) | − | 95.9423i | − | 0.432172i | ||||||
\(223\) | − | 95.1942i | − | 0.426880i | −0.976956 | − | 0.213440i | \(-0.931533\pi\) | ||
0.976956 | − | 0.213440i | \(-0.0684668\pi\) | |||||||
\(224\) | −364.070 | −1.62531 | ||||||||
\(225\) | −285.965 | −1.27096 | ||||||||
\(226\) | 92.1219 | 0.407619 | ||||||||
\(227\) | − | 106.481i | − | 0.469079i | −0.972107 | − | 0.234540i | \(-0.924642\pi\) | ||
0.972107 | − | 0.234540i | \(-0.0753583\pi\) | |||||||
\(228\) | 55.1556 | 0.241911 | ||||||||
\(229\) | 170.352 | 0.743896 | 0.371948 | − | 0.928254i | \(-0.378690\pi\) | ||||
0.371948 | + | 0.928254i | \(0.378690\pi\) | |||||||
\(230\) | 593.727 | 2.58142 | ||||||||
\(231\) | 17.8726 | 0.0773707 | ||||||||
\(232\) | −246.514 | −1.06256 | ||||||||
\(233\) | − | 55.4970i | − | 0.238184i | −0.992883 | − | 0.119092i | \(-0.962002\pi\) | ||
0.992883 | − | 0.119092i | \(-0.0379984\pi\) | |||||||
\(234\) | − | 490.654i | − | 2.09681i | ||||||
\(235\) | − | 391.189i | − | 1.66463i | ||||||
\(236\) | 548.608 | 2.32461 | ||||||||
\(237\) | 23.0763i | 0.0973682i | ||||||||
\(238\) | −36.6969 | −0.154188 | ||||||||
\(239\) | −20.7695 | −0.0869017 | −0.0434509 | − | 0.999056i | \(-0.513835\pi\) | ||||
−0.0434509 | + | 0.999056i | \(0.513835\pi\) | |||||||
\(240\) | −14.2428 | −0.0593449 | ||||||||
\(241\) | − | 303.282i | − | 1.25843i | −0.777231 | − | 0.629216i | \(-0.783376\pi\) | ||
0.777231 | − | 0.629216i | \(-0.216624\pi\) | |||||||
\(242\) | 367.063i | 1.51679i | ||||||||
\(243\) | 162.570i | 0.669012i | ||||||||
\(244\) | − | 402.271i | − | 1.64865i | ||||||
\(245\) | 410.893i | 1.67711i | ||||||||
\(246\) | −150.383 | −0.611314 | ||||||||
\(247\) | 223.721i | 0.905754i | ||||||||
\(248\) | − | 90.0943i | − | 0.363283i | ||||||
\(249\) | − | 49.6121i | − | 0.199245i | ||||||
\(250\) | 213.731 | 0.854922 | ||||||||
\(251\) | −7.25467 | −0.0289031 | −0.0144515 | − | 0.999896i | \(-0.504600\pi\) | ||||
−0.0144515 | + | 0.999896i | \(0.504600\pi\) | |||||||
\(252\) | − | 530.169i | − | 2.10384i | ||||||
\(253\) | 59.1375 | 0.233745 | ||||||||
\(254\) | − | 474.255i | − | 1.86715i | ||||||
\(255\) | −6.30651 | −0.0247314 | ||||||||
\(256\) | −186.065 | −0.726816 | ||||||||
\(257\) | 316.956i | 1.23329i | 0.787241 | + | 0.616645i | \(0.211509\pi\) | ||||
−0.787241 | + | 0.616645i | \(0.788491\pi\) | |||||||
\(258\) | 54.5595 | − | 83.0669i | 0.211471 | − | 0.321965i | ||||
\(259\) | 420.500 | 1.62355 | ||||||||
\(260\) | 859.022i | 3.30393i | ||||||||
\(261\) | 301.049i | 1.15344i | ||||||||
\(262\) | −501.499 | −1.91412 | ||||||||
\(263\) | 229.845i | 0.873934i | 0.899478 | + | 0.436967i | \(0.143947\pi\) | ||||
−0.899478 | + | 0.436967i | \(0.856053\pi\) | |||||||
\(264\) | 12.2444 | 0.0463804 | ||||||||
\(265\) | − | 430.756i | − | 1.62549i | ||||||
\(266\) | 398.317i | 1.49743i | ||||||||
\(267\) | −4.27791 | −0.0160221 | ||||||||
\(268\) | −280.134 | −1.04528 | ||||||||
\(269\) | 285.119 | 1.05992 | 0.529961 | − | 0.848022i | \(-0.322206\pi\) | ||||
0.529961 | + | 0.848022i | \(0.322206\pi\) | |||||||
\(270\) | − | 309.552i | − | 1.14649i | ||||||
\(271\) | 78.3270 | 0.289030 | 0.144515 | − | 0.989503i | \(-0.453838\pi\) | ||||
0.144515 | + | 0.989503i | \(0.453838\pi\) | |||||||
\(272\) | 2.91281 | 0.0107088 | ||||||||
\(273\) | −133.203 | −0.487922 | ||||||||
\(274\) | −387.905 | −1.41571 | ||||||||
\(275\) | 82.1677 | 0.298791 | ||||||||
\(276\) | 108.660i | 0.393696i | ||||||||
\(277\) | − | 119.631i | − | 0.431880i | −0.976407 | − | 0.215940i | \(-0.930718\pi\) | ||
0.976407 | − | 0.215940i | \(-0.0692815\pi\) | |||||||
\(278\) | 88.9960i | 0.320129i | ||||||||
\(279\) | −110.025 | −0.394356 | ||||||||
\(280\) | 538.789i | 1.92424i | ||||||||
\(281\) | −150.423 | −0.535314 | −0.267657 | − | 0.963514i | \(-0.586249\pi\) | ||||
−0.267657 | + | 0.963514i | \(0.586249\pi\) | |||||||
\(282\) | 117.965 | 0.418315 | ||||||||
\(283\) | −261.144 | −0.922771 | −0.461385 | − | 0.887200i | \(-0.652647\pi\) | ||||
−0.461385 | + | 0.887200i | \(0.652647\pi\) | |||||||
\(284\) | 393.989i | 1.38729i | ||||||||
\(285\) | 68.4525i | 0.240184i | ||||||||
\(286\) | 140.982i | 0.492943i | ||||||||
\(287\) | − | 659.106i | − | 2.29654i | ||||||
\(288\) | 304.600i | 1.05764i | ||||||||
\(289\) | −287.710 | −0.995537 | ||||||||
\(290\) | − | 868.458i | − | 2.99468i | ||||||
\(291\) | − | 72.9297i | − | 0.250618i | ||||||
\(292\) | 54.3601i | 0.186165i | ||||||||
\(293\) | 358.409 | 1.22324 | 0.611619 | − | 0.791152i | \(-0.290518\pi\) | ||||
0.611619 | + | 0.791152i | \(0.290518\pi\) | |||||||
\(294\) | −123.907 | −0.421451 | ||||||||
\(295\) | 680.865i | 2.30802i | ||||||||
\(296\) | 288.082 | 0.973250 | ||||||||
\(297\) | − | 30.8326i | − | 0.103813i | ||||||
\(298\) | 676.648 | 2.27063 | ||||||||
\(299\) | −440.745 | −1.47406 | ||||||||
\(300\) | 150.976i | 0.503254i | ||||||||
\(301\) | 364.070 | + | 239.126i | 1.20953 | + | 0.794438i | ||||
\(302\) | −347.213 | −1.14971 | ||||||||
\(303\) | 9.93068i | 0.0327745i | ||||||||
\(304\) | − | 31.6163i | − | 0.104001i | ||||||
\(305\) | 499.250 | 1.63688 | ||||||||
\(306\) | 30.7025i | 0.100335i | ||||||||
\(307\) | 509.730 | 1.66036 | 0.830180 | − | 0.557496i | \(-0.188238\pi\) | ||||
0.830180 | + | 0.557496i | \(0.188238\pi\) | |||||||
\(308\) | 152.336i | 0.494596i | ||||||||
\(309\) | − | 69.5849i | − | 0.225194i | ||||||
\(310\) | 317.398 | 1.02386 | ||||||||
\(311\) | −27.7820 | −0.0893312 | −0.0446656 | − | 0.999002i | \(-0.514222\pi\) | ||||
−0.0446656 | + | 0.999002i | \(0.514222\pi\) | |||||||
\(312\) | −91.2563 | −0.292488 | ||||||||
\(313\) | − | 38.5686i | − | 0.123222i | −0.998100 | − | 0.0616111i | \(-0.980376\pi\) | ||
0.998100 | − | 0.0616111i | \(-0.0196239\pi\) | |||||||
\(314\) | 340.593 | 1.08469 | ||||||||
\(315\) | 657.981 | 2.08883 | ||||||||
\(316\) | −196.688 | −0.622432 | ||||||||
\(317\) | 85.8945 | 0.270961 | 0.135480 | − | 0.990780i | \(-0.456742\pi\) | ||||
0.135480 | + | 0.990780i | \(0.456742\pi\) | |||||||
\(318\) | 129.896 | 0.408480 | ||||||||
\(319\) | − | 86.5017i | − | 0.271165i | ||||||
\(320\) | − | 800.069i | − | 2.50022i | ||||||
\(321\) | − | 1.50731i | − | 0.00469566i | ||||||
\(322\) | −784.710 | −2.43699 | ||||||||
\(323\) | − | 13.9993i | − | 0.0433414i | ||||||
\(324\) | −414.390 | −1.27898 | ||||||||
\(325\) | −612.387 | −1.88427 | ||||||||
\(326\) | −645.098 | −1.97883 | ||||||||
\(327\) | − | 38.4787i | − | 0.117672i | ||||||
\(328\) | − | 451.549i | − | 1.37668i | ||||||
\(329\) | 517.022i | 1.57150i | ||||||||
\(330\) | 43.1365i | 0.130717i | ||||||||
\(331\) | 363.666i | 1.09869i | 0.835596 | + | 0.549345i | \(0.185123\pi\) | ||||
−0.835596 | + | 0.549345i | \(0.814877\pi\) | |||||||
\(332\) | 422.864 | 1.27369 | ||||||||
\(333\) | − | 351.813i | − | 1.05649i | ||||||
\(334\) | 131.011i | 0.392247i | ||||||||
\(335\) | − | 347.668i | − | 1.03782i | ||||||
\(336\) | 18.8242 | 0.0560245 | ||||||||
\(337\) | 8.64293 | 0.0256467 | 0.0128233 | − | 0.999918i | \(-0.495918\pi\) | ||||
0.0128233 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(338\) | − | 511.626i | − | 1.51369i | ||||||
\(339\) | −20.9241 | −0.0617229 | ||||||||
\(340\) | − | 53.7530i | − | 0.158097i | ||||||
\(341\) | 31.6140 | 0.0927098 | ||||||||
\(342\) | 333.253 | 0.974423 | ||||||||
\(343\) | − | 46.7084i | − | 0.136176i | ||||||
\(344\) | 249.422 | + | 163.823i | 0.725063 | + | 0.476231i | ||||
\(345\) | −134.856 | −0.390887 | ||||||||
\(346\) | 76.8788i | 0.222193i | ||||||||
\(347\) | − | 278.736i | − | 0.803273i | −0.915799 | − | 0.401636i | \(-0.868442\pi\) | ||
0.915799 | − | 0.401636i | \(-0.131558\pi\) | |||||||
\(348\) | 158.940 | 0.456723 | ||||||||
\(349\) | − | 169.755i | − | 0.486403i | −0.969976 | − | 0.243201i | \(-0.921802\pi\) | ||
0.969976 | − | 0.243201i | \(-0.0781976\pi\) | |||||||
\(350\) | −1090.30 | −3.11515 | ||||||||
\(351\) | 229.792i | 0.654677i | ||||||||
\(352\) | − | 87.5219i | − | 0.248642i | ||||||
\(353\) | 26.8357 | 0.0760219 | 0.0380109 | − | 0.999277i | \(-0.487898\pi\) | ||||
0.0380109 | + | 0.999277i | \(0.487898\pi\) | |||||||
\(354\) | −205.318 | −0.579995 | ||||||||
\(355\) | −488.971 | −1.37738 | ||||||||
\(356\) | − | 36.4624i | − | 0.102422i | ||||||
\(357\) | 8.33512 | 0.0233477 | ||||||||
\(358\) | 264.973 | 0.740148 | ||||||||
\(359\) | 169.169 | 0.471223 | 0.235611 | − | 0.971847i | \(-0.424291\pi\) | ||||
0.235611 | + | 0.971847i | \(0.424291\pi\) | |||||||
\(360\) | 450.779 | 1.25216 | ||||||||
\(361\) | 209.048 | 0.579081 | ||||||||
\(362\) | 358.140i | 0.989336i | ||||||||
\(363\) | − | 83.3727i | − | 0.229677i | ||||||
\(364\) | − | 1135.34i | − | 3.11907i | ||||||
\(365\) | −67.4651 | −0.184836 | ||||||||
\(366\) | 150.551i | 0.411342i | ||||||||
\(367\) | −540.524 | −1.47282 | −0.736409 | − | 0.676536i | \(-0.763480\pi\) | ||||
−0.736409 | + | 0.676536i | \(0.763480\pi\) | |||||||
\(368\) | 62.2862 | 0.169256 | ||||||||
\(369\) | −551.443 | −1.49442 | ||||||||
\(370\) | 1014.90i | 2.74297i | ||||||||
\(371\) | 569.316i | 1.53455i | ||||||||
\(372\) | 58.0882i | 0.156151i | ||||||||
\(373\) | 26.7152i | 0.0716226i | 0.999359 | + | 0.0358113i | \(0.0114015\pi\) | ||||
−0.999359 | + | 0.0358113i | \(0.988598\pi\) | |||||||
\(374\) | − | 8.82188i | − | 0.0235879i | ||||||
\(375\) | −48.5456 | −0.129455 | ||||||||
\(376\) | 354.209i | 0.942044i | ||||||||
\(377\) | 644.688i | 1.71005i | ||||||||
\(378\) | 409.125i | 1.08234i | ||||||||
\(379\) | 315.193 | 0.831644 | 0.415822 | − | 0.909446i | \(-0.363494\pi\) | ||||
0.415822 | + | 0.909446i | \(0.363494\pi\) | |||||||
\(380\) | −583.449 | −1.53539 | ||||||||
\(381\) | 107.720i | 0.282729i | ||||||||
\(382\) | −139.424 | −0.364984 | ||||||||
\(383\) | 131.099i | 0.342295i | 0.985245 | + | 0.171148i | \(0.0547475\pi\) | ||||
−0.985245 | + | 0.171148i | \(0.945252\pi\) | |||||||
\(384\) | 137.103 | 0.357038 | ||||||||
\(385\) | −189.061 | −0.491066 | ||||||||
\(386\) | − | 753.139i | − | 1.95114i | ||||||
\(387\) | 200.065 | − | 304.600i | 0.516964 | − | 0.787079i | ||||
\(388\) | 621.610 | 1.60209 | ||||||||
\(389\) | 110.050i | 0.282904i | 0.989945 | + | 0.141452i | \(0.0451771\pi\) | ||||
−0.989945 | + | 0.141452i | \(0.954823\pi\) | |||||||
\(390\) | − | 321.491i | − | 0.824337i | ||||||
\(391\) | 27.5795 | 0.0705358 | ||||||||
\(392\) | − | 372.050i | − | 0.949106i | ||||||
\(393\) | 113.908 | 0.289841 | ||||||||
\(394\) | − | 1116.90i | − | 2.83476i | ||||||
\(395\) | − | 244.106i | − | 0.617989i | ||||||
\(396\) | 127.452 | 0.321848 | ||||||||
\(397\) | 68.3215 | 0.172094 | 0.0860472 | − | 0.996291i | \(-0.472576\pi\) | ||||
0.0860472 | + | 0.996291i | \(0.472576\pi\) | |||||||
\(398\) | 1127.87 | 2.83383 | ||||||||
\(399\) | − | 90.4715i | − | 0.226746i | ||||||
\(400\) | 86.5426 | 0.216356 | ||||||||
\(401\) | −675.508 | −1.68456 | −0.842279 | − | 0.539042i | \(-0.818787\pi\) | ||||
−0.842279 | + | 0.539042i | \(0.818787\pi\) | |||||||
\(402\) | 104.841 | 0.260798 | ||||||||
\(403\) | −235.616 | −0.584655 | ||||||||
\(404\) | −84.6433 | −0.209513 | ||||||||
\(405\) | − | 514.290i | − | 1.26985i | ||||||
\(406\) | 1147.81i | 2.82713i | ||||||||
\(407\) | 101.088i | 0.248373i | ||||||||
\(408\) | 5.71034 | 0.0139959 | ||||||||
\(409\) | 1.76834i | 0.00432356i | 0.999998 | + | 0.00216178i | \(0.000688116\pi\) | ||||
−0.999998 | + | 0.00216178i | \(0.999312\pi\) | |||||||
\(410\) | 1590.79 | 3.87997 | ||||||||
\(411\) | 88.1066 | 0.214371 | ||||||||
\(412\) | 593.100 | 1.43956 | ||||||||
\(413\) | − | 899.878i | − | 2.17888i | ||||||
\(414\) | 656.529i | 1.58582i | ||||||||
\(415\) | 524.808i | 1.26460i | ||||||||
\(416\) | 652.291i | 1.56801i | ||||||||
\(417\) | − | 20.2141i | − | 0.0484749i | ||||||
\(418\) | −95.7549 | −0.229079 | ||||||||
\(419\) | 444.028i | 1.05973i | 0.848081 | + | 0.529867i | \(0.177758\pi\) | ||||
−0.848081 | + | 0.529867i | \(0.822242\pi\) | |||||||
\(420\) | − | 347.383i | − | 0.827103i | ||||||
\(421\) | − | 141.195i | − | 0.335381i | −0.985840 | − | 0.167690i | \(-0.946369\pi\) | ||
0.985840 | − | 0.167690i | \(-0.0536309\pi\) | |||||||
\(422\) | −898.022 | −2.12801 | ||||||||
\(423\) | 432.568 | 1.02262 | ||||||||
\(424\) | 390.035i | 0.919894i | ||||||||
\(425\) | 38.3199 | 0.0901645 | ||||||||
\(426\) | − | 147.452i | − | 0.346131i | ||||||
\(427\) | −659.843 | −1.54530 | ||||||||
\(428\) | 12.8474 | 0.0300173 | ||||||||
\(429\) | − | 32.0218i | − | 0.0746429i | ||||||
\(430\) | −577.142 | + | 878.700i | −1.34219 | + | 2.04349i | ||||
\(431\) | 302.066 | 0.700849 | 0.350424 | − | 0.936591i | \(-0.386037\pi\) | ||||
0.350424 | + | 0.936591i | \(0.386037\pi\) | |||||||
\(432\) | − | 32.4742i | − | 0.0751718i | ||||||
\(433\) | − | 380.497i | − | 0.878747i | −0.898304 | − | 0.439374i | \(-0.855200\pi\) | ||
0.898304 | − | 0.439374i | \(-0.144800\pi\) | |||||||
\(434\) | −419.495 | −0.966578 | ||||||||
\(435\) | 197.257i | 0.453464i | ||||||||
\(436\) | 327.970 | 0.752224 | ||||||||
\(437\) | − | 299.355i | − | 0.685022i | ||||||
\(438\) | − | 20.3444i | − | 0.0464485i | ||||||
\(439\) | 558.769 | 1.27282 | 0.636412 | − | 0.771350i | \(-0.280418\pi\) | ||||
0.636412 | + | 0.771350i | \(0.280418\pi\) | |||||||
\(440\) | −129.524 | −0.294373 | ||||||||
\(441\) | −454.356 | −1.03029 | ||||||||
\(442\) | 65.7485i | 0.148752i | ||||||||
\(443\) | −346.462 | −0.782082 | −0.391041 | − | 0.920373i | \(-0.627885\pi\) | ||||
−0.391041 | + | 0.920373i | \(0.627885\pi\) | |||||||
\(444\) | −185.740 | −0.418334 | ||||||||
\(445\) | 45.2527 | 0.101691 | ||||||||
\(446\) | −303.661 | −0.680855 | ||||||||
\(447\) | −153.690 | −0.343826 | ||||||||
\(448\) | 1057.43i | 2.36033i | ||||||||
\(449\) | − | 250.699i | − | 0.558350i | −0.960240 | − | 0.279175i | \(-0.909939\pi\) | ||
0.960240 | − | 0.279175i | \(-0.0900609\pi\) | |||||||
\(450\) | 912.204i | 2.02712i | ||||||||
\(451\) | 158.448 | 0.351327 | ||||||||
\(452\) | − | 178.344i | − | 0.394567i | ||||||
\(453\) | 78.8640 | 0.174093 | ||||||||
\(454\) | −339.665 | −0.748161 | ||||||||
\(455\) | 1409.05 | 3.09681 | ||||||||
\(456\) | − | 61.9814i | − | 0.135924i | ||||||
\(457\) | − | 745.356i | − | 1.63098i | −0.578773 | − | 0.815488i | \(-0.696468\pi\) | ||
0.578773 | − | 0.815488i | \(-0.303532\pi\) | |||||||
\(458\) | − | 543.408i | − | 1.18648i | ||||||
\(459\) | − | 14.3791i | − | 0.0313271i | ||||||
\(460\) | − | 1149.43i | − | 2.49876i | ||||||
\(461\) | 6.73204 | 0.0146031 | 0.00730156 | − | 0.999973i | \(-0.497676\pi\) | ||||
0.00730156 | + | 0.999973i | \(0.497676\pi\) | |||||||
\(462\) | − | 57.0121i | − | 0.123403i | ||||||
\(463\) | − | 448.198i | − | 0.968031i | −0.875059 | − | 0.484016i | \(-0.839178\pi\) | ||
0.875059 | − | 0.484016i | \(-0.160822\pi\) | |||||||
\(464\) | − | 91.1074i | − | 0.196352i | ||||||
\(465\) | −72.0920 | −0.155037 | ||||||||
\(466\) | −177.031 | −0.379894 | ||||||||
\(467\) | 506.048i | 1.08361i | 0.840503 | + | 0.541807i | \(0.182260\pi\) | ||||
−0.840503 | + | 0.541807i | \(0.817740\pi\) | |||||||
\(468\) | −949.886 | −2.02967 | ||||||||
\(469\) | 459.502i | 0.979749i | ||||||||
\(470\) | −1247.86 | −2.65502 | ||||||||
\(471\) | −77.3603 | −0.164247 | ||||||||
\(472\) | − | 616.500i | − | 1.30614i | ||||||
\(473\) | −57.4856 | + | 87.5219i | −0.121534 | + | 0.185036i | ||||
\(474\) | 73.6112 | 0.155298 | ||||||||
\(475\) | − | 415.934i | − | 0.875650i | ||||||
\(476\) | 71.0436i | 0.149251i | ||||||||
\(477\) | 476.320 | 0.998574 | ||||||||
\(478\) | 66.2529i | 0.138604i | ||||||||
\(479\) | −772.714 | −1.61318 | −0.806591 | − | 0.591110i | \(-0.798690\pi\) | ||||
−0.806591 | + | 0.591110i | \(0.798690\pi\) | |||||||
\(480\) | 199.583i | 0.415798i | ||||||||
\(481\) | − | 753.397i | − | 1.56631i | ||||||
\(482\) | −967.443 | −2.00714 | ||||||||
\(483\) | 178.235 | 0.369016 | ||||||||
\(484\) | 710.620 | 1.46822 | ||||||||
\(485\) | 771.467i | 1.59065i | ||||||||
\(486\) | 518.584 | 1.06705 | ||||||||
\(487\) | −762.454 | −1.56561 | −0.782807 | − | 0.622265i | \(-0.786213\pi\) | ||||
−0.782807 | + | 0.622265i | \(0.786213\pi\) | |||||||
\(488\) | −452.054 | −0.926340 | ||||||||
\(489\) | 146.524 | 0.299640 | ||||||||
\(490\) | 1310.71 | 2.67492 | ||||||||
\(491\) | − | 928.398i | − | 1.89083i | −0.325868 | − | 0.945415i | \(-0.605657\pi\) | ||
0.325868 | − | 0.945415i | \(-0.394343\pi\) | |||||||
\(492\) | 291.136i | 0.591739i | ||||||||
\(493\) | − | 40.3411i | − | 0.0818279i | ||||||
\(494\) | 713.651 | 1.44464 | ||||||||
\(495\) | 158.178i | 0.319551i | ||||||||
\(496\) | 33.2973 | 0.0671317 | ||||||||
\(497\) | 646.258 | 1.30032 | ||||||||
\(498\) | −158.258 | −0.317788 | ||||||||
\(499\) | 669.978i | 1.34264i | 0.741167 | + | 0.671320i | \(0.234272\pi\) | ||||
−0.741167 | + | 0.671320i | \(0.765728\pi\) | |||||||
\(500\) | − | 413.774i | − | 0.827548i | ||||||
\(501\) | − | 29.7570i | − | 0.0593952i | ||||||
\(502\) | 23.1418i | 0.0460991i | ||||||||
\(503\) | − | 274.168i | − | 0.545065i | −0.962147 | − | 0.272532i | \(-0.912139\pi\) | ||
0.962147 | − | 0.272532i | \(-0.0878612\pi\) | |||||||
\(504\) | −595.780 | −1.18210 | ||||||||
\(505\) | − | 105.049i | − | 0.208018i | ||||||
\(506\) | − | 188.643i | − | 0.372813i | ||||||
\(507\) | 116.208i | 0.229207i | ||||||||
\(508\) | −918.139 | −1.80736 | ||||||||
\(509\) | 703.988 | 1.38308 | 0.691540 | − | 0.722338i | \(-0.256933\pi\) | ||||
0.691540 | + | 0.722338i | \(0.256933\pi\) | |||||||
\(510\) | 20.1172i | 0.0394456i | ||||||||
\(511\) | 89.1665 | 0.174494 | ||||||||
\(512\) | − | 163.380i | − | 0.319101i | ||||||
\(513\) | −156.075 | −0.304239 | ||||||||
\(514\) | 1011.06 | 1.96704 | ||||||||
\(515\) | 736.084i | 1.42929i | ||||||||
\(516\) | −160.814 | − | 105.625i | −0.311655 | − | 0.204699i | ||||
\(517\) | −124.292 | −0.240409 | ||||||||
\(518\) | − | 1341.36i | − | 2.58950i | ||||||
\(519\) | − | 17.4618i | − | 0.0336451i | ||||||
\(520\) | 965.330 | 1.85640 | ||||||||
\(521\) | − | 588.189i | − | 1.12896i | −0.825446 | − | 0.564480i | \(-0.809077\pi\) | ||
0.825446 | − | 0.564480i | \(-0.190923\pi\) | |||||||
\(522\) | 960.320 | 1.83969 | ||||||||
\(523\) | 743.907i | 1.42238i | 0.702998 | + | 0.711192i | \(0.251844\pi\) | ||||
−0.702998 | + | 0.711192i | \(0.748156\pi\) | |||||||
\(524\) | 970.882i | 1.85283i | ||||||||
\(525\) | 247.645 | 0.471706 | ||||||||
\(526\) | 733.184 | 1.39389 | ||||||||
\(527\) | 14.7436 | 0.0279765 | ||||||||
\(528\) | 4.52532i | 0.00857069i | ||||||||
\(529\) | 60.7485 | 0.114837 | ||||||||
\(530\) | −1374.07 | −2.59259 | ||||||||
\(531\) | −752.885 | −1.41786 | ||||||||
\(532\) | 771.125 | 1.44948 | ||||||||
\(533\) | −1180.90 | −2.21557 | ||||||||
\(534\) | 13.6462i | 0.0255546i | ||||||||
\(535\) | 15.9446i | 0.0298030i | ||||||||
\(536\) | 314.802i | 0.587317i | ||||||||
\(537\) | −60.1845 | −0.112075 | ||||||||
\(538\) | − | 909.506i | − | 1.69053i | ||||||
\(539\) | 130.552 | 0.242212 | ||||||||
\(540\) | −599.280 | −1.10978 | ||||||||
\(541\) | −2.77685 | −0.00513282 | −0.00256641 | − | 0.999997i | \(-0.500817\pi\) | ||||
−0.00256641 | + | 0.999997i | \(0.500817\pi\) | |||||||
\(542\) | − | 249.856i | − | 0.460990i | ||||||
\(543\) | − | 81.3459i | − | 0.149808i | ||||||
\(544\) | − | 40.8169i | − | 0.0750311i | ||||||
\(545\) | 407.036i | 0.746856i | ||||||||
\(546\) | 424.905i | 0.778214i | ||||||||
\(547\) | 700.748 | 1.28108 | 0.640538 | − | 0.767927i | \(-0.278711\pi\) | ||||
0.640538 | + | 0.767927i | \(0.278711\pi\) | |||||||
\(548\) | 750.968i | 1.37038i | ||||||||
\(549\) | 552.059i | 1.00557i | ||||||||
\(550\) | − | 262.108i | − | 0.476559i | ||||||
\(551\) | −437.873 | −0.794688 | ||||||||
\(552\) | 122.107 | 0.221209 | ||||||||
\(553\) | 322.627i | 0.583412i | ||||||||
\(554\) | −381.612 | −0.688830 | ||||||||
\(555\) | − | 230.518i | − | 0.415349i | ||||||
\(556\) | 172.293 | 0.309879 | ||||||||
\(557\) | −590.822 | −1.06072 | −0.530361 | − | 0.847772i | \(-0.677944\pi\) | ||||
−0.530361 | + | 0.847772i | \(0.677944\pi\) | |||||||
\(558\) | 350.971i | 0.628980i | ||||||||
\(559\) | 428.434 | − | 652.291i | 0.766429 | − | 1.16689i | ||||
\(560\) | −199.127 | −0.355584 | ||||||||
\(561\) | 2.00375i | 0.00357175i | ||||||||
\(562\) | 479.837i | 0.853803i | ||||||||
\(563\) | −306.648 | −0.544668 | −0.272334 | − | 0.962203i | \(-0.587795\pi\) | ||||
−0.272334 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(564\) | − | 228.375i | − | 0.404921i | ||||||
\(565\) | 221.339 | 0.391751 | ||||||||
\(566\) | 833.027i | 1.47178i | ||||||||
\(567\) | 679.721i | 1.19880i | ||||||||
\(568\) | 442.747 | 0.779484 | ||||||||
\(569\) | −5.67367 | −0.00997130 | −0.00498565 | − | 0.999988i | \(-0.501587\pi\) | ||||
−0.00498565 | + | 0.999988i | \(0.501587\pi\) | |||||||
\(570\) | 218.357 | 0.383083 | ||||||||
\(571\) | 811.264i | 1.42078i | 0.703810 | + | 0.710389i | \(0.251481\pi\) | ||||
−0.703810 | + | 0.710389i | \(0.748519\pi\) | |||||||
\(572\) | 272.935 | 0.477159 | ||||||||
\(573\) | 31.6680 | 0.0552670 | ||||||||
\(574\) | −2102.49 | −3.66288 | ||||||||
\(575\) | 819.417 | 1.42507 | ||||||||
\(576\) | 884.698 | 1.53593 | ||||||||
\(577\) | 976.820i | 1.69293i | 0.532445 | + | 0.846464i | \(0.321273\pi\) | ||||
−0.532445 | + | 0.846464i | \(0.678727\pi\) | |||||||
\(578\) | 917.771i | 1.58784i | ||||||||
\(579\) | 171.064i | 0.295447i | ||||||||
\(580\) | −1681.30 | −2.89879 | ||||||||
\(581\) | − | 693.622i | − | 1.19384i | ||||||
\(582\) | −232.639 | −0.399724 | ||||||||
\(583\) | −136.863 | −0.234757 | ||||||||
\(584\) | 61.0874 | 0.104602 | ||||||||
\(585\) | − | 1178.88i | − | 2.01518i | ||||||
\(586\) | − | 1143.29i | − | 1.95101i | ||||||
\(587\) | − | 681.557i | − | 1.16109i | −0.814230 | − | 0.580543i | \(-0.802840\pi\) | ||
0.814230 | − | 0.580543i | \(-0.197160\pi\) | |||||||
\(588\) | 239.878i | 0.407957i | ||||||||
\(589\) | − | 160.031i | − | 0.271699i | ||||||
\(590\) | 2171.90 | 3.68119 | ||||||||
\(591\) | 253.686i | 0.429248i | ||||||||
\(592\) | 106.470i | 0.179848i | ||||||||
\(593\) | 1030.13i | 1.73715i | 0.495561 | + | 0.868573i | \(0.334962\pi\) | ||||
−0.495561 | + | 0.868573i | \(0.665038\pi\) | |||||||
\(594\) | −98.3532 | −0.165578 | ||||||||
\(595\) | −88.1708 | −0.148186 | ||||||||
\(596\) | − | 1309.96i | − | 2.19793i | ||||||
\(597\) | −256.177 | −0.429107 | ||||||||
\(598\) | 1405.94i | 2.35107i | ||||||||
\(599\) | 1028.30 | 1.71669 | 0.858345 | − | 0.513073i | \(-0.171493\pi\) | ||||
0.858345 | + | 0.513073i | \(0.171493\pi\) | |||||||
\(600\) | 169.660 | 0.282767 | ||||||||
\(601\) | − | 655.529i | − | 1.09073i | −0.838198 | − | 0.545365i | \(-0.816391\pi\) | ||
0.838198 | − | 0.545365i | \(-0.183609\pi\) | |||||||
\(602\) | 762.790 | − | 1161.35i | 1.26709 | − | 1.92915i | ||||
\(603\) | 384.443 | 0.637551 | ||||||||
\(604\) | 672.190i | 1.11290i | ||||||||
\(605\) | 881.935i | 1.45774i | ||||||||
\(606\) | 31.6780 | 0.0522739 | ||||||||
\(607\) | 1016.42i | 1.67450i | 0.546822 | + | 0.837249i | \(0.315837\pi\) | ||||
−0.546822 | + | 0.837249i | \(0.684163\pi\) | |||||||
\(608\) | −443.037 | −0.728680 | ||||||||
\(609\) | − | 260.708i | − | 0.428092i | ||||||
\(610\) | − | 1592.56i | − | 2.61076i | ||||||
\(611\) | 926.332 | 1.51609 | ||||||||
\(612\) | 59.4388 | 0.0971223 | ||||||||
\(613\) | −1029.51 | −1.67946 | −0.839728 | − | 0.543007i | \(-0.817286\pi\) | ||||
−0.839728 | + | 0.543007i | \(0.817286\pi\) | |||||||
\(614\) | − | 1626.00i | − | 2.64820i | ||||||
\(615\) | −361.322 | −0.587516 | ||||||||
\(616\) | 171.188 | 0.277903 | ||||||||
\(617\) | 426.603 | 0.691415 | 0.345708 | − | 0.938342i | \(-0.387639\pi\) | ||||
0.345708 | + | 0.938342i | \(0.387639\pi\) | |||||||
\(618\) | −221.970 | −0.359174 | ||||||||
\(619\) | −503.515 | −0.813432 | −0.406716 | − | 0.913555i | \(-0.633326\pi\) | ||||
−0.406716 | + | 0.913555i | \(0.633326\pi\) | |||||||
\(620\) | − | 614.470i | − | 0.991080i | ||||||
\(621\) | − | 307.478i | − | 0.495133i | ||||||
\(622\) | 88.6222i | 0.142479i | ||||||||
\(623\) | −59.8090 | −0.0960016 | ||||||||
\(624\) | − | 33.7268i | − | 0.0540493i | ||||||
\(625\) | −330.025 | −0.528041 | ||||||||
\(626\) | −123.030 | −0.196534 | ||||||||
\(627\) | 21.7492 | 0.0346878 | ||||||||
\(628\) | − | 659.374i | − | 1.04996i | ||||||
\(629\) | 47.1436i | 0.0749500i | ||||||||
\(630\) | − | 2098.90i | − | 3.33159i | ||||||
\(631\) | 299.884i | 0.475252i | 0.971357 | + | 0.237626i | \(0.0763692\pi\) | ||||
−0.971357 | + | 0.237626i | \(0.923631\pi\) | |||||||
\(632\) | 221.030i | 0.349730i | ||||||||
\(633\) | 203.972 | 0.322230 | ||||||||
\(634\) | − | 273.996i | − | 0.432170i | ||||||
\(635\) | − | 1139.48i | − | 1.79446i | ||||||
\(636\) | − | 251.474i | − | 0.395400i | ||||||
\(637\) | −972.990 | −1.52746 | ||||||||
\(638\) | −275.933 | −0.432497 | ||||||||
\(639\) | − | 540.693i | − | 0.846155i | ||||||
\(640\) | −1450.30 | −2.26610 | ||||||||
\(641\) | 724.346i | 1.13002i | 0.825082 | + | 0.565012i | \(0.191129\pi\) | ||||
−0.825082 | + | 0.565012i | \(0.808871\pi\) | |||||||
\(642\) | −4.80817 | −0.00748937 | ||||||||
\(643\) | 743.353 | 1.15607 | 0.578035 | − | 0.816012i | \(-0.303820\pi\) | ||||
0.578035 | + | 0.816012i | \(0.303820\pi\) | |||||||
\(644\) | 1519.17i | 2.35896i | ||||||||
\(645\) | 131.089 | − | 199.583i | 0.203239 | − | 0.309431i | ||||
\(646\) | −44.6565 | −0.0691277 | ||||||||
\(647\) | 61.7177i | 0.0953905i | 0.998862 | + | 0.0476953i | \(0.0151876\pi\) | ||||
−0.998862 | + | 0.0476953i | \(0.984812\pi\) | |||||||
\(648\) | 465.672i | 0.718630i | ||||||||
\(649\) | 216.330 | 0.333328 | ||||||||
\(650\) | 1953.46i | 3.00532i | ||||||||
\(651\) | 95.2817 | 0.146362 | ||||||||
\(652\) | 1248.88i | 1.91547i | ||||||||
\(653\) | 422.488i | 0.646996i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(654\) | −122.744 | −0.187681 | ||||||||
\(655\) | −1204.94 | −1.83960 | ||||||||
\(656\) | 166.885 | 0.254398 | ||||||||
\(657\) | − | 74.6013i | − | 0.113548i | ||||||
\(658\) | 1649.26 | 2.50647 | ||||||||
\(659\) | −620.921 | −0.942217 | −0.471108 | − | 0.882075i | \(-0.656146\pi\) | ||||
−0.471108 | + | 0.882075i | \(0.656146\pi\) | |||||||
\(660\) | 83.5105 | 0.126531 | ||||||||
\(661\) | 496.134 | 0.750581 | 0.375291 | − | 0.926907i | \(-0.377543\pi\) | ||||
0.375291 | + | 0.926907i | \(0.377543\pi\) | |||||||
\(662\) | 1160.06 | 1.75236 | ||||||||
\(663\) | − | 14.9338i | − | 0.0225245i | ||||||
\(664\) | − | 475.196i | − | 0.715656i | ||||||
\(665\) | 957.027i | 1.43914i | ||||||||
\(666\) | −1122.25 | −1.68506 | ||||||||
\(667\) | − | 862.638i | − | 1.29331i | ||||||
\(668\) | 253.631 | 0.379687 | ||||||||
\(669\) | 68.9719 | 0.103097 | ||||||||
\(670\) | −1109.03 | −1.65527 | ||||||||
\(671\) | − | 158.625i | − | 0.236402i | ||||||
\(672\) | − | 263.783i | − | 0.392534i | ||||||
\(673\) | 453.069i | 0.673209i | 0.941646 | + | 0.336604i | \(0.109278\pi\) | ||||
−0.941646 | + | 0.336604i | \(0.890722\pi\) | |||||||
\(674\) | − | 27.5702i | − | 0.0409053i | ||||||
\(675\) | − | 427.220i | − | 0.632918i | ||||||
\(676\) | −990.487 | −1.46522 | ||||||||
\(677\) | 233.751i | 0.345275i | 0.984985 | + | 0.172638i | \(0.0552289\pi\) | ||||
−0.984985 | + | 0.172638i | \(0.944771\pi\) | |||||||
\(678\) | 66.7459i | 0.0984453i | ||||||||
\(679\) | − | 1019.62i | − | 1.50165i | ||||||
\(680\) | −60.4052 | −0.0888312 | ||||||||
\(681\) | 77.1497 | 0.113289 | ||||||||
\(682\) | − | 100.846i | − | 0.147868i | ||||||
\(683\) | 578.370 | 0.846808 | 0.423404 | − | 0.905941i | \(-0.360835\pi\) | ||||
0.423404 | + | 0.905941i | \(0.360835\pi\) | |||||||
\(684\) | − | 645.164i | − | 0.943222i | ||||||
\(685\) | −932.011 | −1.36060 | ||||||||
\(686\) | −148.996 | −0.217195 | ||||||||
\(687\) | 123.427i | 0.179660i | ||||||||
\(688\) | −60.5463 | + | 92.1819i | −0.0880034 | + | 0.133985i | ||||
\(689\) | 1020.03 | 1.48044 | ||||||||
\(690\) | 430.178i | 0.623447i | ||||||||
\(691\) | − | 127.474i | − | 0.184477i | −0.995737 | − | 0.0922387i | \(-0.970598\pi\) | ||
0.995737 | − | 0.0922387i | \(-0.0294023\pi\) | |||||||
\(692\) | 148.834 | 0.215078 | ||||||||
\(693\) | − | 209.059i | − | 0.301672i | ||||||
\(694\) | −889.142 | −1.28118 | ||||||||
\(695\) | 213.829i | 0.307667i | ||||||||
\(696\) | − | 178.609i | − | 0.256622i | ||||||
\(697\) | 73.8944 | 0.106018 | ||||||||
\(698\) | −541.502 | −0.775791 | ||||||||
\(699\) | 40.2097 | 0.0575247 | ||||||||
\(700\) | 2110.78i | 3.01541i | ||||||||
\(701\) | 126.686 | 0.180721 | 0.0903606 | − | 0.995909i | \(-0.471198\pi\) | ||||
0.0903606 | + | 0.995909i | \(0.471198\pi\) | |||||||
\(702\) | 733.016 | 1.04418 | ||||||||
\(703\) | 511.708 | 0.727892 | ||||||||
\(704\) | −254.204 | −0.361085 | ||||||||
\(705\) | 283.432 | 0.402031 | ||||||||
\(706\) | − | 85.6036i | − | 0.121252i | ||||||
\(707\) | 138.840i | 0.196379i | ||||||||
\(708\) | 397.488i | 0.561423i | ||||||||
\(709\) | 733.535 | 1.03461 | 0.517303 | − | 0.855803i | \(-0.326936\pi\) | ||||
0.517303 | + | 0.855803i | \(0.326936\pi\) | |||||||
\(710\) | 1559.78i | 2.19687i | ||||||||
\(711\) | 269.926 | 0.379643 | ||||||||
\(712\) | −40.9748 | −0.0575488 | ||||||||
\(713\) | 315.271 | 0.442175 | ||||||||
\(714\) | − | 26.5883i | − | 0.0372385i | ||||||
\(715\) | 338.734i | 0.473753i | ||||||||
\(716\) | − | 512.977i | − | 0.716449i | ||||||
\(717\) | − | 15.0483i | − | 0.0209879i | ||||||
\(718\) | − | 539.634i | − | 0.751580i | ||||||
\(719\) | −885.641 | −1.23177 | −0.615884 | − | 0.787837i | \(-0.711201\pi\) | ||||
−0.615884 | + | 0.787837i | \(0.711201\pi\) | |||||||
\(720\) | 166.600i | 0.231389i | ||||||||
\(721\) | − | 972.859i | − | 1.34932i | ||||||
\(722\) | − | 666.846i | − | 0.923609i | ||||||
\(723\) | 219.740 | 0.303928 | ||||||||
\(724\) | 693.344 | 0.957658 | ||||||||
\(725\) | − | 1198.58i | − | 1.65321i | ||||||
\(726\) | −265.952 | −0.366324 | ||||||||
\(727\) | 244.282i | 0.336014i | 0.985786 | + | 0.168007i | \(0.0537331\pi\) | ||||
−0.985786 | + | 0.168007i | \(0.946267\pi\) | |||||||
\(728\) | −1275.85 | −1.75253 | ||||||||
\(729\) | 486.127 | 0.666841 | ||||||||
\(730\) | 215.208i | 0.294805i | ||||||||
\(731\) | −26.8091 | + | 40.8169i | −0.0366746 | + | 0.0558371i | ||||
\(732\) | 291.461 | 0.398171 | ||||||||
\(733\) | − | 1317.81i | − | 1.79783i | −0.438120 | − | 0.898917i | \(-0.644355\pi\) | ||
0.438120 | − | 0.898917i | \(-0.355645\pi\) | |||||||
\(734\) | 1724.23i | 2.34908i | ||||||||
\(735\) | −297.708 | −0.405045 | ||||||||
\(736\) | − | 872.812i | − | 1.18589i | ||||||
\(737\) | −110.464 | −0.149883 | ||||||||
\(738\) | 1759.05i | 2.38354i | ||||||||
\(739\) | − | 126.907i | − | 0.171728i | −0.996307 | − | 0.0858641i | \(-0.972635\pi\) | ||
0.996307 | − | 0.0858641i | \(-0.0273651\pi\) | |||||||
\(740\) | 1964.80 | 2.65514 | ||||||||
\(741\) | −162.095 | −0.218751 | ||||||||
\(742\) | 1816.07 | 2.44753 | ||||||||
\(743\) | − | 483.885i | − | 0.651259i | −0.945497 | − | 0.325629i | \(-0.894424\pi\) | ||
0.945497 | − | 0.325629i | \(-0.105576\pi\) | |||||||
\(744\) | 65.2768 | 0.0877377 | ||||||||
\(745\) | 1625.77 | 2.18224 | ||||||||
\(746\) | 85.2192 | 0.114235 | ||||||||
\(747\) | −580.320 | −0.776867 | ||||||||
\(748\) | −17.0788 | −0.0228326 | ||||||||
\(749\) | − | 21.0735i | − | 0.0281355i | ||||||
\(750\) | 154.856i | 0.206475i | ||||||||
\(751\) | − | 11.4506i | − | 0.0152471i | −0.999971 | − | 0.00762354i | \(-0.997573\pi\) | ||
0.999971 | − | 0.00762354i | \(-0.00242667\pi\) | |||||||
\(752\) | −130.909 | −0.174082 | ||||||||
\(753\) | − | 5.25629i | − | 0.00698047i | ||||||
\(754\) | 2056.50 | 2.72745 | ||||||||
\(755\) | −834.241 | −1.10495 | ||||||||
\(756\) | 792.050 | 1.04768 | ||||||||
\(757\) | 995.145i | 1.31459i | 0.753633 | + | 0.657295i | \(0.228299\pi\) | ||||
−0.753633 | + | 0.657295i | \(0.771701\pi\) | |||||||
\(758\) | − | 1005.44i | − | 1.32644i | ||||||
\(759\) | 42.8474i | 0.0564525i | ||||||||
\(760\) | 655.653i | 0.862701i | ||||||||
\(761\) | 1067.64i | 1.40295i | 0.712695 | + | 0.701474i | \(0.247474\pi\) | ||||
−0.712695 | + | 0.701474i | \(0.752526\pi\) | |||||||
\(762\) | 343.616 | 0.450940 | ||||||||
\(763\) | − | 537.967i | − | 0.705068i | ||||||
\(764\) | 269.919i | 0.353297i | ||||||||
\(765\) | 73.7682i | 0.0964291i | ||||||||
\(766\) | 418.195 | 0.545946 | ||||||||
\(767\) | −1612.28 | −2.10206 | ||||||||
\(768\) | − | 134.811i | − | 0.175535i | ||||||
\(769\) | −361.976 | −0.470710 | −0.235355 | − | 0.971909i | \(-0.575625\pi\) | ||||
−0.235355 | + | 0.971909i | \(0.575625\pi\) | |||||||
\(770\) | 603.087i | 0.783230i | ||||||||
\(771\) | −229.647 | −0.297856 | ||||||||
\(772\) | −1458.05 | −1.88866 | ||||||||
\(773\) | − | 579.373i | − | 0.749513i | −0.927123 | − | 0.374756i | \(-0.877726\pi\) | ||
0.927123 | − | 0.374756i | \(-0.122274\pi\) | |||||||
\(774\) | −971.646 | − | 638.190i | −1.25536 | − | 0.824535i | ||||
\(775\) | 438.048 | 0.565224 | ||||||||
\(776\) | − | 698.537i | − | 0.900176i | ||||||
\(777\) | 304.669i | 0.392109i | ||||||||
\(778\) | 351.049 | 0.451220 | ||||||||
\(779\) | − | 802.068i | − | 1.02961i | ||||||
\(780\) | −622.395 | −0.797942 | ||||||||
\(781\) | 155.360i | 0.198924i | ||||||||
\(782\) | − | 87.9762i | − | 0.112502i | ||||||
\(783\) | −449.754 | −0.574399 | ||||||||
\(784\) | 137.503 | 0.175387 | ||||||||
\(785\) | 818.335 | 1.04246 | ||||||||
\(786\) | − | 363.356i | − | 0.462285i | ||||||
\(787\) | −1046.34 | −1.32954 | −0.664768 | − | 0.747050i | \(-0.731470\pi\) | ||||
−0.664768 | + | 0.747050i | \(0.731470\pi\) | |||||||
\(788\) | −2162.27 | −2.74399 | ||||||||
\(789\) | −166.531 | −0.211066 | ||||||||
\(790\) | −778.676 | −0.985666 | ||||||||
\(791\) | −292.537 | −0.369832 | ||||||||
\(792\) | − | 143.225i | − | 0.180839i | ||||||
\(793\) | 1182.22i | 1.49082i | ||||||||
\(794\) | − | 217.940i | − | 0.274483i | ||||||
\(795\) | 312.100 | 0.392578 | ||||||||
\(796\) | − | 2183.50i | − | 2.74309i | ||||||
\(797\) | −959.219 | −1.20354 | −0.601769 | − | 0.798670i | \(-0.705537\pi\) | ||||
−0.601769 | + | 0.798670i | \(0.705537\pi\) | |||||||
\(798\) | −288.596 | −0.361649 | ||||||||
\(799\) | −57.9649 | −0.0725468 | ||||||||
\(800\) | − | 1212.72i | − | 1.51589i | ||||||
\(801\) | 50.0393i | 0.0624711i | ||||||||
\(802\) | 2154.81i | 2.68680i | ||||||||
\(803\) | 21.4355i | 0.0266943i | ||||||||
\(804\) | − | 202.968i | − | 0.252448i | ||||||
\(805\) | −1885.41 | −2.34212 | ||||||||
\(806\) | 751.595i | 0.932500i | ||||||||
\(807\) | 206.580i | 0.255985i | ||||||||
\(808\) | 95.1183i | 0.117721i | ||||||||
\(809\) | 639.565 | 0.790562 | 0.395281 | − | 0.918560i | \(-0.370647\pi\) | ||||
0.395281 | + | 0.918560i | \(0.370647\pi\) | |||||||
\(810\) | −1640.54 | −2.02536 | ||||||||
\(811\) | 515.867i | 0.636087i | 0.948076 | + | 0.318044i | \(0.103026\pi\) | ||||
−0.948076 | + | 0.318044i | \(0.896974\pi\) | |||||||
\(812\) | 2222.12 | 2.73660 | ||||||||
\(813\) | 56.7510i | 0.0698044i | ||||||||
\(814\) | 322.461 | 0.396144 | ||||||||
\(815\) | −1549.96 | −1.90180 | ||||||||
\(816\) | 2.11044i | 0.00258632i | ||||||||
\(817\) | 443.037 | + | 290.993i | 0.542273 | + | 0.356172i | ||||
\(818\) | 5.64084 | 0.00689589 | ||||||||
\(819\) | 1558.09i | 1.90243i | ||||||||
\(820\) | − | 3079.70i | − | 3.75573i | ||||||
\(821\) | 1288.57 | 1.56951 | 0.784756 | − | 0.619805i | \(-0.212788\pi\) | ||||
0.784756 | + | 0.619805i | \(0.212788\pi\) | |||||||
\(822\) | − | 281.052i | − | 0.341913i | ||||||
\(823\) | 516.675 | 0.627795 | 0.313897 | − | 0.949457i | \(-0.398365\pi\) | ||||
0.313897 | + | 0.949457i | \(0.398365\pi\) | |||||||
\(824\) | − | 666.499i | − | 0.808858i | ||||||
\(825\) | 59.5337i | 0.0721620i | ||||||||
\(826\) | −2870.53 | −3.47522 | ||||||||
\(827\) | 35.6545 | 0.0431131 | 0.0215565 | − | 0.999768i | \(-0.493138\pi\) | ||||
0.0215565 | + | 0.999768i | \(0.493138\pi\) | |||||||
\(828\) | 1271.01 | 1.53504 | ||||||||
\(829\) | − | 617.780i | − | 0.745212i | −0.927990 | − | 0.372606i | \(-0.878464\pi\) | ||
0.927990 | − | 0.372606i | \(-0.121536\pi\) | |||||||
\(830\) | 1674.09 | 2.01698 | ||||||||
\(831\) | 86.6771 | 0.104305 | ||||||||
\(832\) | 1894.56 | 2.27711 | ||||||||
\(833\) | 60.8846 | 0.0730907 | ||||||||
\(834\) | −64.4811 | −0.0773154 | ||||||||
\(835\) | 314.776i | 0.376978i | ||||||||
\(836\) | 185.378i | 0.221744i | ||||||||
\(837\) | − | 164.373i | − | 0.196384i | ||||||
\(838\) | 1416.41 | 1.69023 | ||||||||
\(839\) | 98.1185i | 0.116947i | 0.998289 | + | 0.0584735i | \(0.0186233\pi\) | ||||
−0.998289 | + | 0.0584735i | \(0.981377\pi\) | |||||||
\(840\) | −390.373 | −0.464730 | ||||||||
\(841\) | −420.800 | −0.500357 | ||||||||
\(842\) | −450.401 | −0.534918 | ||||||||
\(843\) | − | 108.988i | − | 0.129285i | ||||||
\(844\) | 1738.53i | 2.05987i | ||||||||
\(845\) | − | 1229.27i | − | 1.45476i | ||||||
\(846\) | − | 1379.85i | − | 1.63103i | ||||||
\(847\) | − | 1165.63i | − | 1.37618i | ||||||
\(848\) | −144.150 | −0.169988 | ||||||||
\(849\) | − | 189.209i | − | 0.222861i | ||||||
\(850\) | − | 122.237i | − | 0.143808i | ||||||
\(851\) | 1008.10i | 1.18460i | ||||||||
\(852\) | −285.460 | −0.335047 | ||||||||
\(853\) | 564.129 | 0.661347 | 0.330674 | − | 0.943745i | \(-0.392724\pi\) | ||||
0.330674 | + | 0.943745i | \(0.392724\pi\) | |||||||
\(854\) | 2104.84i | 2.46468i | ||||||||
\(855\) | 800.699 | 0.936490 | ||||||||
\(856\) | − | 14.4373i | − | 0.0168660i | ||||||
\(857\) | −699.603 | −0.816340 | −0.408170 | − | 0.912906i | \(-0.633833\pi\) | ||||
−0.408170 | + | 0.912906i | \(0.633833\pi\) | |||||||
\(858\) | −102.147 | −0.119052 | ||||||||
\(859\) | − | 1395.67i | − | 1.62476i | −0.583128 | − | 0.812380i | \(-0.698171\pi\) | ||
0.583128 | − | 0.812380i | \(-0.301829\pi\) | |||||||
\(860\) | 1701.13 | + | 1117.32i | 1.97806 | + | 1.29921i | ||||
\(861\) | 477.548 | 0.554644 | ||||||||
\(862\) | − | 963.564i | − | 1.11782i | ||||||
\(863\) | − | 768.514i | − | 0.890515i | −0.895403 | − | 0.445257i | \(-0.853112\pi\) | ||
0.895403 | − | 0.445257i | \(-0.146888\pi\) | |||||||
\(864\) | −455.059 | −0.526688 | ||||||||
\(865\) | 184.715i | 0.213543i | ||||||||
\(866\) | −1213.75 | −1.40156 | ||||||||
\(867\) | − | 208.457i | − | 0.240435i | ||||||
\(868\) | 812.125i | 0.935628i | ||||||||
\(869\) | −77.5591 | −0.0892510 | ||||||||
\(870\) | 629.232 | 0.723255 | ||||||||
\(871\) | 823.275 | 0.945206 | ||||||||
\(872\) | − | 368.558i | − | 0.422658i | ||||||
\(873\) | −853.070 | −0.977170 | ||||||||
\(874\) | −954.916 | −1.09258 | ||||||||
\(875\) | −678.711 | −0.775670 | ||||||||
\(876\) | −39.3860 | −0.0449612 | ||||||||
\(877\) | 1318.08 | 1.50294 | 0.751470 | − | 0.659767i | \(-0.229345\pi\) | ||||
0.751470 | + | 0.659767i | \(0.229345\pi\) | |||||||
\(878\) | − | 1782.43i | − | 2.03010i | ||||||
\(879\) | 259.681i | 0.295428i | ||||||||
\(880\) | − | 47.8699i | − | 0.0543976i | ||||||
\(881\) | −691.467 | −0.784867 | −0.392433 | − | 0.919780i | \(-0.628367\pi\) | ||||
−0.392433 | + | 0.919780i | \(0.628367\pi\) | |||||||
\(882\) | 1449.36i | 1.64326i | ||||||||
\(883\) | −173.332 | −0.196299 | −0.0981493 | − | 0.995172i | \(-0.531292\pi\) | ||||
−0.0981493 | + | 0.995172i | \(0.531292\pi\) | |||||||
\(884\) | 127.287 | 0.143989 | ||||||||
\(885\) | −493.313 | −0.557416 | ||||||||
\(886\) | 1105.19i | 1.24739i | ||||||||
\(887\) | − | 142.316i | − | 0.160446i | −0.996777 | − | 0.0802232i | \(-0.974437\pi\) | ||
0.996777 | − | 0.0802232i | \(-0.0255633\pi\) | |||||||
\(888\) | 208.727i | 0.235053i | ||||||||
\(889\) | 1506.02i | 1.69406i | ||||||||
\(890\) | − | 144.352i | − | 0.162193i | ||||||
\(891\) | −163.404 | −0.183394 | ||||||||
\(892\) | 587.876i | 0.659054i | ||||||||
\(893\) | 629.166i | 0.704553i | ||||||||
\(894\) | 490.258i | 0.548387i | ||||||||
\(895\) | 636.645 | 0.711335 | ||||||||
\(896\) | 1916.82 | 2.13931 | ||||||||
\(897\) | − | 319.337i | − | 0.356006i | ||||||
\(898\) | −799.708 | −0.890543 | ||||||||
\(899\) | − | 461.154i | − | 0.512963i | ||||||
\(900\) | 1765.99 | 1.96221 | ||||||||
\(901\) | −63.8278 | −0.0708410 | ||||||||
\(902\) | − | 505.437i | − | 0.560351i | ||||||
\(903\) | −173.256 | + | 263.783i | −0.191867 | + | 0.292118i | ||||
\(904\) | −200.415 | −0.221698 | ||||||||
\(905\) | 860.495i | 0.950823i | ||||||||
\(906\) | − | 251.569i | − | 0.277670i | ||||||
\(907\) | 1795.52 | 1.97963 | 0.989814 | − | 0.142370i | \(-0.0454721\pi\) | ||||
0.989814 | + | 0.142370i | \(0.0454721\pi\) | |||||||
\(908\) | 657.578i | 0.724205i | ||||||||
\(909\) | 116.161 | 0.127790 | ||||||||
\(910\) | − | 4494.74i | − | 4.93928i | ||||||
\(911\) | 365.632i | 0.401353i | 0.979658 | + | 0.200676i | \(0.0643140\pi\) | ||||
−0.979658 | + | 0.200676i | \(0.935686\pi\) | |||||||
\(912\) | 22.9073 | 0.0251176 | ||||||||
\(913\) | 166.746 | 0.182635 | ||||||||
\(914\) | −2377.62 | −2.60134 | ||||||||
\(915\) | 361.726i | 0.395329i | ||||||||
\(916\) | −1052.02 | −1.14849 | ||||||||
\(917\) | 1592.53 | 1.73668 | ||||||||
\(918\) | −45.8682 | −0.0499654 | ||||||||
\(919\) | 1083.62 | 1.17913 | 0.589566 | − | 0.807720i | \(-0.299299\pi\) | ||||
0.589566 | + | 0.807720i | \(0.299299\pi\) | |||||||
\(920\) | −1291.68 | −1.40400 | ||||||||
\(921\) | 369.320i | 0.400998i | ||||||||
\(922\) | − | 21.4746i | − | 0.0232913i | ||||||
\(923\) | − | 1157.88i | − | 1.25447i | ||||||
\(924\) | −110.373 | −0.119451 | ||||||||
\(925\) | 1400.69i | 1.51426i | ||||||||
\(926\) | −1429.71 | −1.54397 | ||||||||
\(927\) | −813.945 | −0.878042 | ||||||||
\(928\) | −1276.68 | −1.37573 | ||||||||
\(929\) | 1400.56i | 1.50760i | 0.657105 | + | 0.753799i | \(0.271781\pi\) | ||||
−0.657105 | + | 0.753799i | \(0.728219\pi\) | |||||||
\(930\) | 229.967i | 0.247276i | ||||||||
\(931\) | − | 660.856i | − | 0.709835i | ||||||
\(932\) | 342.724i | 0.367730i | ||||||||
\(933\) | − | 20.1292i | − | 0.0215747i | ||||||
\(934\) | 1614.25 | 1.72832 | ||||||||
\(935\) | − | 21.1962i | − | 0.0226697i | ||||||
\(936\) | 1067.44i | 1.14043i | ||||||||
\(937\) | 846.473i | 0.903387i | 0.892173 | + | 0.451693i | \(0.149180\pi\) | ||||
−0.892173 | + | 0.451693i | \(0.850820\pi\) | |||||||
\(938\) | 1465.77 | 1.56266 | ||||||||
\(939\) | 27.9444 | 0.0297598 | ||||||||
\(940\) | 2415.81i | 2.57001i | ||||||||
\(941\) | −1354.63 | −1.43956 | −0.719780 | − | 0.694203i | \(-0.755757\pi\) | ||||
−0.719780 | + | 0.694203i | \(0.755757\pi\) | |||||||
\(942\) | 246.773i | 0.261967i | ||||||||
\(943\) | 1580.13 | 1.67564 | ||||||||
\(944\) | 227.848 | 0.241364 | ||||||||
\(945\) | 982.996i | 1.04021i | ||||||||
\(946\) | 279.187 | + | 183.374i | 0.295124 | + | 0.193841i | ||||
\(947\) | −209.288 | −0.221001 | −0.110501 | − | 0.993876i | \(-0.535245\pi\) | ||||
−0.110501 | + | 0.993876i | \(0.535245\pi\) | |||||||
\(948\) | − | 142.508i | − | 0.150325i | ||||||
\(949\) | − | 159.757i | − | 0.168342i | ||||||
\(950\) | −1326.79 | −1.39662 | ||||||||
\(951\) | 62.2339i | 0.0654405i | ||||||||
\(952\) | 79.8356 | 0.0838610 | ||||||||
\(953\) | 293.406i | 0.307876i | 0.988080 | + | 0.153938i | \(0.0491957\pi\) | ||||
−0.988080 | + | 0.153938i | \(0.950804\pi\) | |||||||
\(954\) | − | 1519.42i | − | 1.59268i | ||||||
\(955\) | −334.991 | −0.350776 | ||||||||
\(956\) | 128.263 | 0.134166 | ||||||||
\(957\) | 62.6739 | 0.0654899 | ||||||||
\(958\) | 2464.89i | 2.57295i | ||||||||
\(959\) | 1231.81 | 1.28447 | ||||||||
\(960\) | 579.682 | 0.603835 | ||||||||
\(961\) | −792.461 | −0.824621 | ||||||||
\(962\) | −2403.27 | −2.49820 | ||||||||
\(963\) | −17.6312 | −0.0183086 | ||||||||
\(964\) | 1872.93i | 1.94288i | ||||||||
\(965\) | − | 1809.55i | − | 1.87518i | ||||||
\(966\) | − | 568.553i | − | 0.588564i | ||||||
\(967\) | −1028.49 | −1.06359 | −0.531794 | − | 0.846874i | \(-0.678482\pi\) | ||||
−0.531794 | + | 0.846874i | \(0.678482\pi\) | |||||||
\(968\) | − | 798.562i | − | 0.824961i | ||||||
\(969\) | 10.1430 | 0.0104675 | ||||||||
\(970\) | 2460.91 | 2.53702 | ||||||||
\(971\) | −438.558 | −0.451656 | −0.225828 | − | 0.974167i | \(-0.572509\pi\) | ||||
−0.225828 | + | 0.974167i | \(0.572509\pi\) | |||||||
\(972\) | − | 1003.96i | − | 1.03288i | ||||||
\(973\) | − | 282.611i | − | 0.290453i | ||||||
\(974\) | 2432.16i | 2.49709i | ||||||||
\(975\) | − | 443.698i | − | 0.455075i | ||||||
\(976\) | − | 167.071i | − | 0.171180i | ||||||
\(977\) | −626.212 | −0.640954 | −0.320477 | − | 0.947256i | \(-0.603843\pi\) | ||||
−0.320477 | + | 0.947256i | \(0.603843\pi\) | |||||||
\(978\) | − | 467.399i | − | 0.477913i | ||||||
\(979\) | − | 14.3780i | − | 0.0146864i | ||||||
\(980\) | − | 2537.49i | − | 2.58927i | ||||||
\(981\) | −450.091 | −0.458808 | ||||||||
\(982\) | −2961.51 | −3.01579 | ||||||||
\(983\) | − | 1720.98i | − | 1.75074i | −0.483454 | − | 0.875370i | \(-0.660618\pi\) | ||
0.483454 | − | 0.875370i | \(-0.339382\pi\) | |||||||
\(984\) | 327.165 | 0.332485 | ||||||||
\(985\) | − | 2683.54i | − | 2.72441i | ||||||
\(986\) | −128.685 | −0.130512 | ||||||||
\(987\) | −374.603 | −0.379537 | ||||||||
\(988\) | − | 1381.60i | − | 1.39838i | ||||||
\(989\) | −573.275 | + | 872.812i | −0.579651 | + | 0.882520i | ||||
\(990\) | 504.574 | 0.509671 | ||||||||
\(991\) | − | 753.187i | − | 0.760027i | −0.924981 | − | 0.380014i | \(-0.875919\pi\) | ||
0.924981 | − | 0.380014i | \(-0.124081\pi\) | |||||||
\(992\) | − | 466.593i | − | 0.470356i | ||||||
\(993\) | −263.490 | −0.265348 | ||||||||
\(994\) | − | 2061.51i | − | 2.07395i | ||||||
\(995\) | 2709.90 | 2.72352 | ||||||||
\(996\) | 306.382i | 0.307612i | ||||||||
\(997\) | 533.031i | 0.534635i | 0.963609 | + | 0.267317i | \(0.0861372\pi\) | ||||
−0.963609 | + | 0.267317i | \(0.913863\pi\) | |||||||
\(998\) | 2137.17 | 2.14145 | ||||||||
\(999\) | 525.593 | 0.526119 |
(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 | 43.3.b.b.42.1 | ✓ | 6 | |
3.2 | odd | 2 | 387.3.b.c.343.6 | 6 | |||
4.3 | odd | 2 | 688.3.b.e.257.3 | 6 | |||
43.42 | odd | 2 | inner | 43.3.b.b.42.6 | yes | 6 | |
129.128 | even | 2 | 387.3.b.c.343.1 | 6 | |||
172.171 | even | 2 | 688.3.b.e.257.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.b.b.42.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
43.3.b.b.42.6 | yes | 6 | 43.42 | odd | 2 | inner | |
387.3.b.c.343.1 | 6 | 129.128 | even | 2 | |||
387.3.b.c.343.6 | 6 | 3.2 | odd | 2 | |||
688.3.b.e.257.3 | 6 | 4.3 | odd | 2 | |||
688.3.b.e.257.4 | 6 | 172.171 | even | 2 |