Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,3,Mod(257,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("688.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.7466421880\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(3.18991i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.257 |
Dual form | 688.3.b.e.257.4 |
$q$-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 \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 0.724539i | − | 0.241513i | −0.992682 | − | 0.120757i | \(-0.961468\pi\) | ||
0.992682 | − | 0.120757i | \(-0.0385320\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 7.66434i | − | 1.53287i | −0.642324 | − | 0.766434i | \(-0.722029\pi\) | ||
0.642324 | − | 0.766434i | \(-0.277971\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 10.1297i | − | 1.44710i | −0.690271 | − | 0.723551i | \(-0.742509\pi\) | ||
0.690271 | − | 0.723551i | \(-0.257491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.47504 | 0.941671 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.43517 | 0.221379 | 0.110690 | − | 0.993855i | \(-0.464694\pi\) | ||||
0.110690 | + | 0.993855i | \(0.464694\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.1491 | 1.39608 | 0.698041 | − | 0.716058i | \(-0.254055\pi\) | ||||
0.698041 | + | 0.716058i | \(0.254055\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.55311 | −0.370207 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.13567 | −0.0668042 | −0.0334021 | − | 0.999442i | \(-0.510634\pi\) | ||||
−0.0334021 | + | 0.999442i | \(0.510634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 12.3269i | − | 0.648783i | −0.945923 | − | 0.324391i | \(-0.894841\pi\) | ||
0.945923 | − | 0.324391i | \(-0.105159\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.33937 | −0.349494 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.2847 | 1.05586 | 0.527929 | − | 0.849288i | \(-0.322969\pi\) | ||||
0.527929 | + | 0.849288i | \(0.322969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −33.7420 | −1.34968 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 12.6614i | − | 0.468939i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.5218i | 1.22489i | 0.790513 | + | 0.612445i | \(0.209814\pi\) | ||||
−0.790513 | + | 0.612445i | \(0.790186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.9823 | 0.418783 | 0.209391 | − | 0.977832i | \(-0.432852\pi\) | ||||
0.209391 | + | 0.977832i | \(0.432852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.76438i | − | 0.0534660i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −77.6375 | −2.21821 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 41.5116i | − | 1.12193i | −0.827838 | − | 0.560967i | \(-0.810429\pi\) | ||
0.827838 | − | 0.560967i | \(-0.189571\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 13.1497i | − | 0.337172i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −65.0667 | −1.58699 | −0.793496 | − | 0.608576i | \(-0.791741\pi\) | ||||
−0.793496 | + | 0.608576i | \(0.791741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −23.6064 | + | 35.9408i | −0.548986 | + | 0.835832i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 64.9556i | − | 1.44346i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −51.0402 | −1.08596 | −0.542981 | − | 0.839745i | \(-0.682704\pi\) | ||||
−0.542981 | + | 0.839745i | \(0.682704\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −53.6110 | −1.09410 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.822839i | 0.0161341i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 56.2026 | 1.06043 | 0.530214 | − | 0.847864i | \(-0.322112\pi\) | ||||
0.530214 | + | 0.847864i | \(0.322112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 18.6640i | − | 0.339345i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.93130 | −0.156689 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 88.8355 | 1.50569 | 0.752843 | − | 0.658200i | \(-0.228682\pi\) | ||||
0.752843 | + | 0.658200i | \(0.228682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 65.1393i | 1.06786i | 0.845529 | + | 0.533929i | \(0.179285\pi\) | ||||
−0.845529 | + | 0.533929i | \(0.820715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 85.8497i | − | 1.36269i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 139.101i | − | 2.14001i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −45.3618 | −0.677042 | −0.338521 | − | 0.940959i | \(-0.609927\pi\) | ||||
−0.338521 | + | 0.940959i | \(0.609927\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 17.5952i | − | 0.255004i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 63.7983i | 0.898567i | 0.893389 | + | 0.449284i | \(0.148321\pi\) | ||||
−0.893389 | + | 0.449284i | \(0.851679\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.80247i | − | 0.120582i | −0.998181 | − | 0.0602909i | \(-0.980797\pi\) | ||
0.998181 | − | 0.0602909i | \(-0.0192028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 24.4474i | 0.325966i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 24.6676i | − | 0.320358i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31.8496 | −0.403159 | −0.201580 | − | 0.979472i | \(-0.564607\pi\) | ||||
−0.201580 | + | 0.979472i | \(0.564607\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 67.1017 | 0.828417 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 68.4740 | 0.824988 | 0.412494 | − | 0.910960i | \(-0.364658\pi\) | ||||
0.412494 | + | 0.910960i | \(0.364658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.70417i | 0.102402i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25.7370 | 0.295827 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.90432i | 0.0663406i | 0.999450 | + | 0.0331703i | \(0.0105604\pi\) | ||||
−0.999450 | + | 0.0331703i | \(0.989440\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 183.845i | − | 2.02027i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.40616i | − | 0.101142i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −94.4773 | −0.994498 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −100.657 | −1.03770 | −0.518849 | − | 0.854866i | \(-0.673639\pi\) | ||||
−0.518849 | + | 0.854866i | \(0.673639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.6382 | 0.208466 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7062 | 0.135705 | 0.0678525 | − | 0.997695i | \(-0.478385\pi\) | ||||
0.0678525 | + | 0.997695i | \(0.478385\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 96.0402 | 0.932429 | 0.466214 | − | 0.884672i | \(-0.345618\pi\) | ||||
0.466214 | + | 0.884672i | \(0.345618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 56.2514i | 0.535728i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.08036 | 0.0194427 | 0.00972133 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972133 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −53.1078 | −0.487228 | −0.243614 | − | 0.969872i | \(-0.578333\pi\) | ||||
−0.243614 | + | 0.969872i | \(0.578333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.0768 | −0.270962 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 28.8791i | 0.255568i | 0.991802 | + | 0.127784i | \(0.0407864\pi\) | ||||
−0.991802 | + | 0.127784i | \(0.959214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 186.126i | − | 1.61849i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 153.814 | 1.31465 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5040i | 0.0966725i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −115.070 | −0.950991 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 47.1433i | 0.383279i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 67.0020i | 0.536016i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −148.673 | −1.17066 | −0.585328 | − | 0.810797i | \(-0.699034\pi\) | ||||
−0.585328 | + | 0.810797i | \(0.699034\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.0405 | + | 17.1037i | 0.201864 | + | 0.132587i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 157.214i | 1.20011i | 0.799960 | + | 0.600054i | \(0.204854\pi\) | ||||
−0.799960 | + | 0.600054i | \(0.795146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −124.868 | −0.938854 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −97.0409 | −0.718821 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 121.604i | − | 0.887618i | −0.896122 | − | 0.443809i | \(-0.853627\pi\) | ||
0.896122 | − | 0.443809i | \(-0.146373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 27.8992 | 0.200714 | 0.100357 | − | 0.994952i | \(-0.468002\pi\) | ||||
0.100357 | + | 0.994952i | \(0.468002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.9806i | 0.262274i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 44.1961 | 0.309063 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 272.251 | 1.87759 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 38.8433i | 0.264240i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 212.121i | 1.42363i | 0.702366 | + | 0.711816i | \(0.252127\pi\) | ||||
−0.702366 | + | 0.711816i | \(0.747873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 108.847i | 0.720842i | 0.932790 | + | 0.360421i | \(0.117367\pi\) | ||||
−0.932790 | + | 0.360421i | \(0.882633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.62487 | −0.0629077 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 99.5005i | − | 0.641938i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 106.772i | 0.680075i | 0.940412 | + | 0.340038i | \(0.110440\pi\) | ||||
−0.940412 | + | 0.340038i | \(0.889560\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 40.7210i | − | 0.256107i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 245.997i | − | 1.52793i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 202.231i | 1.24068i | 0.784334 | + | 0.620339i | \(0.213005\pi\) | ||||
−0.784334 | + | 0.620339i | \(0.786995\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.5228 | −0.0819562 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 41.0703 | 0.245930 | 0.122965 | − | 0.992411i | \(-0.460760\pi\) | ||||
0.122965 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 160.389 | 0.949045 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 104.471i | − | 0.610940i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.1006 | −0.139310 | −0.0696549 | − | 0.997571i | \(-0.522190\pi\) | ||||
−0.0696549 | + | 0.997571i | \(0.522190\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 341.797i | 1.95313i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 64.3648i | − | 0.363643i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 83.0659i | − | 0.464055i | −0.972709 | − | 0.232028i | \(-0.925464\pi\) | ||
0.972709 | − | 0.232028i | \(-0.0745360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −112.273 | −0.620291 | −0.310145 | − | 0.950689i | \(-0.600378\pi\) | ||||
−0.310145 | + | 0.950689i | \(0.600378\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 47.1960 | 0.257902 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −318.159 | −1.71978 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.76556 | −0.0147891 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −128.256 | −0.678602 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 43.7078i | 0.228836i | 0.993433 | + | 0.114418i | \(0.0365004\pi\) | ||||
−0.993433 | + | 0.114418i | \(0.963500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 236.100 | 1.22332 | 0.611659 | − | 0.791122i | \(-0.290503\pi\) | ||||
0.611659 | + | 0.791122i | \(0.290503\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −100.784 | −0.516840 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 350.134 | 1.77733 | 0.888665 | − | 0.458557i | \(-0.151634\pi\) | ||||
0.888665 | + | 0.458557i | \(0.151634\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 353.573i | − | 1.77675i | −0.459122 | − | 0.888373i | \(-0.651836\pi\) | ||
0.459122 | − | 0.888373i | \(-0.348164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.8664i | 0.163514i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 359.826 | 1.77254 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 498.693i | 2.43265i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 205.814 | 0.994272 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 30.0180i | − | 0.143627i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 281.519i | 1.33421i | 0.744962 | + | 0.667107i | \(0.232468\pi\) | ||||
−0.744962 | + | 0.667107i | \(0.767532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 46.2243 | 0.217016 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 275.462 | + | 180.927i | 1.28122 | + | 0.841522i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 131.507i | − | 0.606021i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.37774 | −0.0291221 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.6114 | −0.0932642 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 95.1942i | 0.426880i | 0.976956 | + | 0.213440i | \(0.0684668\pi\) | ||||
−0.976956 | + | 0.213440i | \(0.931533\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −285.965 | −1.27096 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 106.481i | 0.469079i | 0.972107 | + | 0.234540i | \(0.0753583\pi\) | ||||
−0.972107 | + | 0.234540i | \(0.924642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 170.352 | 0.743896 | 0.371948 | − | 0.928254i | \(-0.378690\pi\) | ||||
0.371948 | + | 0.928254i | \(0.378690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.8726 | −0.0773707 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 55.4970i | − | 0.238184i | −0.992883 | − | 0.119092i | \(-0.962002\pi\) | ||
0.992883 | − | 0.119092i | \(-0.0379984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 391.189i | 1.66463i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.0763i | 0.0973682i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.7695 | 0.0869017 | 0.0434509 | − | 0.999056i | \(-0.486165\pi\) | ||||
0.0434509 | + | 0.999056i | \(0.486165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 303.282i | − | 1.25843i | −0.777231 | − | 0.629216i | \(-0.783376\pi\) | ||
0.777231 | − | 0.629216i | \(-0.216624\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 162.570i | − | 0.669012i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 410.893i | 1.67711i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 223.721i | − | 0.905754i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 49.6121i | − | 0.199245i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.25467 | 0.0289031 | 0.0144515 | − | 0.999896i | \(-0.495400\pi\) | ||||
0.0144515 | + | 0.999896i | \(0.495400\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 59.1375 | 0.233745 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.30651 | 0.0247314 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 316.956i | 1.23329i | 0.787241 | + | 0.616645i | \(0.211509\pi\) | ||||
−0.787241 | + | 0.616645i | \(0.788491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −420.500 | −1.62355 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 301.049i | 1.15344i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 229.845i | − | 0.873934i | −0.899478 | − | 0.436967i | \(-0.856053\pi\) | ||
0.899478 | − | 0.436967i | \(-0.143947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 430.756i | − | 1.62549i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.27791 | 0.0160221 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 285.119 | 1.05992 | 0.529961 | − | 0.848022i | \(-0.322206\pi\) | ||||
0.529961 | + | 0.848022i | \(0.322206\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −78.3270 | −0.289030 | −0.144515 | − | 0.989503i | \(-0.546162\pi\) | ||||
−0.144515 | + | 0.989503i | \(0.546162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −133.203 | −0.487922 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −82.1677 | −0.298791 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 119.631i | − | 0.431880i | −0.976407 | − | 0.215940i | \(-0.930718\pi\) | ||
0.976407 | − | 0.215940i | \(-0.0692815\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 110.025 | 0.394356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −150.423 | −0.535314 | −0.267657 | − | 0.963514i | \(-0.586249\pi\) | ||||
−0.267657 | + | 0.963514i | \(0.586249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 261.144 | 0.922771 | 0.461385 | − | 0.887200i | \(-0.347353\pi\) | ||||
0.461385 | + | 0.887200i | \(0.347353\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 68.4525i | 0.240184i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 659.106i | 2.29654i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −287.710 | −0.995537 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 72.9297i | 0.250618i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 358.409 | 1.22324 | 0.611619 | − | 0.791152i | \(-0.290518\pi\) | ||||
0.611619 | + | 0.791152i | \(0.290518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 680.865i | − | 2.30802i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 30.8326i | − | 0.103813i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 440.745 | 1.47406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 364.070 | + | 239.126i | 1.20953 | + | 0.794438i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.93068i | − | 0.0327745i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 499.250 | 1.63688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −509.730 | −1.66036 | −0.830180 | − | 0.557496i | \(-0.811762\pi\) | ||||
−0.830180 | + | 0.557496i | \(0.811762\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 69.5849i | − | 0.225194i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.7820 | 0.0893312 | 0.0446656 | − | 0.999002i | \(-0.485778\pi\) | ||||
0.0446656 | + | 0.999002i | \(0.485778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 38.5686i | − | 0.123222i | −0.998100 | − | 0.0616111i | \(-0.980376\pi\) | ||
0.998100 | − | 0.0616111i | \(-0.0196239\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −657.981 | −2.08883 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 85.8945 | 0.270961 | 0.135480 | − | 0.990780i | \(-0.456742\pi\) | ||||
0.135480 | + | 0.990780i | \(0.456742\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 86.5017i | 0.271165i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.50731i | − | 0.00469566i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9993i | 0.0433414i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −612.387 | −1.88427 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 38.4787i | 0.117672i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 517.022i | 1.57150i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 363.666i | − | 1.09869i | −0.835596 | − | 0.549345i | \(-0.814877\pi\) | ||
0.835596 | − | 0.549345i | \(-0.185123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 351.813i | − | 1.05649i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 347.668i | 1.03782i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.64293 | 0.0256467 | 0.0128233 | − | 0.999918i | \(-0.495918\pi\) | ||||
0.0128233 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.9241 | 0.0617229 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.6140 | 0.0927098 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 46.7084i | 0.136176i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −134.856 | −0.390887 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 278.736i | 0.803273i | 0.915799 | + | 0.401636i | \(0.131558\pi\) | ||||
−0.915799 | + | 0.401636i | \(0.868442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 169.755i | − | 0.486403i | −0.969976 | − | 0.243201i | \(-0.921802\pi\) | ||
0.969976 | − | 0.243201i | \(-0.0781976\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 229.792i | − | 0.654677i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.8357 | 0.0760219 | 0.0380109 | − | 0.999277i | \(-0.487898\pi\) | ||||
0.0380109 | + | 0.999277i | \(0.487898\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 488.971 | 1.37738 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.33512 | 0.0233477 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −169.169 | −0.471223 | −0.235611 | − | 0.971847i | \(-0.575709\pi\) | ||||
−0.235611 | + | 0.971847i | \(0.575709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 209.048 | 0.579081 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 83.3727i | 0.229677i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −67.4651 | −0.184836 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 540.524 | 1.47282 | 0.736409 | − | 0.676536i | \(-0.236520\pi\) | ||||
0.736409 | + | 0.676536i | \(0.236520\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −551.443 | −1.49442 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 569.316i | − | 1.53455i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.7152i | 0.0716226i | 0.999359 | + | 0.0358113i | \(0.0114015\pi\) | ||||
−0.999359 | + | 0.0358113i | \(0.988598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 48.5456 | 0.129455 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 644.688i | 1.71005i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −315.193 | −0.831644 | −0.415822 | − | 0.909446i | \(-0.636506\pi\) | ||||
−0.415822 | + | 0.909446i | \(0.636506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 107.720i | 0.282729i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 131.099i | − | 0.342295i | −0.985245 | − | 0.171148i | \(-0.945252\pi\) | ||
0.985245 | − | 0.171148i | \(-0.0547475\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −189.061 | −0.491066 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −200.065 | + | 304.600i | −0.516964 | + | 0.787079i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 110.050i | 0.282904i | 0.989945 | + | 0.141452i | \(0.0451771\pi\) | ||||
−0.989945 | + | 0.141452i | \(0.954823\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.5795 | −0.0705358 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 113.908 | 0.289841 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 244.106i | 0.617989i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 68.3215 | 0.172094 | 0.0860472 | − | 0.996291i | \(-0.472576\pi\) | ||||
0.0860472 | + | 0.996291i | \(0.472576\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 90.4715i | 0.226746i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −675.508 | −1.68456 | −0.842279 | − | 0.539042i | \(-0.818787\pi\) | ||||
−0.842279 | + | 0.539042i | \(0.818787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 235.616 | 0.584655 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 514.290i | − | 1.26985i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 101.088i | − | 0.248373i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.76834i | 0.00432356i | 0.999998 | + | 0.00216178i | \(0.000688116\pi\) | ||||
−0.999998 | + | 0.00216178i | \(0.999312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −88.1066 | −0.214371 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 899.878i | − | 2.17888i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 524.808i | − | 1.26460i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 20.2141i | − | 0.0484749i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 444.028i | − | 1.05973i | −0.848081 | − | 0.529867i | \(-0.822242\pi\) | ||
0.848081 | − | 0.529867i | \(-0.177758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 141.195i | − | 0.335381i | −0.985840 | − | 0.167690i | \(-0.946369\pi\) | ||
0.985840 | − | 0.167690i | \(-0.0536309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −432.568 | −1.02262 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.3199 | 0.0901645 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 659.843 | 1.54530 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 32.0218i | − | 0.0746429i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −302.066 | −0.700849 | −0.350424 | − | 0.936591i | \(-0.613963\pi\) | ||||
−0.350424 | + | 0.936591i | \(0.613963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 380.497i | − | 0.878747i | −0.898304 | − | 0.439374i | \(-0.855200\pi\) | ||
0.898304 | − | 0.439374i | \(-0.144800\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 197.257i | − | 0.453464i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 299.355i | − | 0.685022i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −558.769 | −1.27282 | −0.636412 | − | 0.771350i | \(-0.719582\pi\) | ||||
−0.636412 | + | 0.771350i | \(0.719582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −454.356 | −1.03029 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 346.462 | 0.782082 | 0.391041 | − | 0.920373i | \(-0.372115\pi\) | ||||
0.391041 | + | 0.920373i | \(0.372115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.2527 | 0.101691 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 153.690 | 0.343826 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 250.699i | − | 0.558350i | −0.960240 | − | 0.279175i | \(-0.909939\pi\) | ||
0.960240 | − | 0.279175i | \(-0.0900609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −158.448 | −0.351327 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 78.8640 | 0.174093 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1409.05 | −3.09681 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 745.356i | − | 1.63098i | −0.578773 | − | 0.815488i | \(-0.696468\pi\) | ||
0.578773 | − | 0.815488i | \(-0.303532\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.3791i | 0.0313271i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.73204 | 0.0146031 | 0.00730156 | − | 0.999973i | \(-0.497676\pi\) | ||||
0.00730156 | + | 0.999973i | \(0.497676\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 448.198i | 0.968031i | 0.875059 | + | 0.484016i | \(0.160822\pi\) | ||||
−0.875059 | + | 0.484016i | \(0.839178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −72.0920 | −0.155037 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 506.048i | − | 1.08361i | −0.840503 | − | 0.541807i | \(-0.817740\pi\) | ||
0.840503 | − | 0.541807i | \(-0.182260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 459.502i | 0.979749i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 77.3603 | 0.164247 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −57.4856 | + | 87.5219i | −0.121534 | + | 0.185036i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 415.934i | 0.875650i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 476.320 | 0.998574 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 772.714 | 1.61318 | 0.806591 | − | 0.591110i | \(-0.201310\pi\) | ||||
0.806591 | + | 0.591110i | \(0.201310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 753.397i | − | 1.56631i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −178.235 | −0.369016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 771.467i | 1.59065i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 762.454 | 1.56561 | 0.782807 | − | 0.622265i | \(-0.213787\pi\) | ||||
0.782807 | + | 0.622265i | \(0.213787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 146.524 | 0.299640 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 928.398i | 1.89083i | 0.325868 | + | 0.945415i | \(0.394343\pi\) | ||||
−0.325868 | + | 0.945415i | \(0.605657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 40.3411i | − | 0.0818279i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 158.178i | − | 0.319551i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 646.258 | 1.30032 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 669.978i | − | 1.34264i | −0.741167 | − | 0.671320i | \(-0.765728\pi\) | ||
0.741167 | − | 0.671320i | \(-0.234272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 29.7570i | − | 0.0593952i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 274.168i | 0.545065i | 0.962147 | + | 0.272532i | \(0.0878612\pi\) | ||||
−0.962147 | + | 0.272532i | \(0.912139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 105.049i | − | 0.208018i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 116.208i | − | 0.229207i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 703.988 | 1.38308 | 0.691540 | − | 0.722338i | \(-0.256933\pi\) | ||||
0.691540 | + | 0.722338i | \(0.256933\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −89.1665 | −0.174494 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −156.075 | −0.304239 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 736.084i | − | 1.42929i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −124.292 | −0.240409 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.4618i | 0.0336451i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 588.189i | − | 1.12896i | −0.825446 | − | 0.564480i | \(-0.809077\pi\) | ||
0.825446 | − | 0.564480i | \(-0.190923\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 743.907i | − | 1.42238i | −0.702998 | − | 0.711192i | \(-0.748156\pi\) | ||
0.702998 | − | 0.711192i | \(-0.251844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 247.645 | 0.471706 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.7436 | −0.0279765 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.7485 | 0.114837 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 752.885 | 1.41786 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1180.90 | −2.21557 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 15.9446i | − | 0.0298030i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −60.1845 | −0.112075 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −130.552 | −0.242212 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.77685 | −0.00513282 | −0.00256641 | − | 0.999997i | \(-0.500817\pi\) | ||||
−0.00256641 | + | 0.999997i | \(0.500817\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 81.3459i | 0.149808i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 407.036i | 0.746856i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −700.748 | −1.28108 | −0.640538 | − | 0.767927i | \(-0.721289\pi\) | ||||
−0.640538 | + | 0.767927i | \(0.721289\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 552.059i | 1.00557i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 437.873 | 0.794688 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 322.627i | 0.583412i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 230.518i | 0.415349i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −590.822 | −1.06072 | −0.530361 | − | 0.847772i | \(-0.677944\pi\) | ||||
−0.530361 | + | 0.847772i | \(0.677944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −428.434 | + | 652.291i | −0.766429 | + | 1.16689i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.00375i | 0.00357175i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 306.648 | 0.544668 | 0.272334 | − | 0.962203i | \(-0.412205\pi\) | ||||
0.272334 | + | 0.962203i | \(0.412205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 221.339 | 0.391751 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 679.721i | − | 1.19880i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.67367 | −0.00997130 | −0.00498565 | − | 0.999988i | \(-0.501587\pi\) | ||||
−0.00498565 | + | 0.999988i | \(0.501587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 811.264i | − | 1.42078i | −0.703810 | − | 0.710389i | \(-0.748519\pi\) | ||
0.703810 | − | 0.710389i | \(-0.251481\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.6680 | 0.0552670 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −819.417 | −1.42507 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 976.820i | 1.69293i | 0.532445 | + | 0.846464i | \(0.321273\pi\) | ||||
−0.532445 | + | 0.846464i | \(0.678727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 171.064i | − | 0.295447i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 693.622i | − | 1.19384i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 136.863 | 0.234757 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 1178.88i | − | 2.01518i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 681.557i | 1.16109i | 0.814230 | + | 0.580543i | \(0.197160\pi\) | ||||
−0.814230 | + | 0.580543i | \(0.802840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 160.031i | − | 0.271699i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 253.686i | − | 0.429248i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1030.13i | 1.73715i | 0.495561 | + | 0.868573i | \(0.334962\pi\) | ||||
−0.495561 | + | 0.868573i | \(0.665038\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 88.1708 | 0.148186 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −256.177 | −0.429107 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1028.30 | −1.71669 | −0.858345 | − | 0.513073i | \(-0.828507\pi\) | ||||
−0.858345 | + | 0.513073i | \(0.828507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 655.529i | − | 1.09073i | −0.838198 | − | 0.545365i | \(-0.816391\pi\) | ||
0.838198 | − | 0.545365i | \(-0.183609\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −384.443 | −0.637551 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 881.935i | 1.45774i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1016.42i | − | 1.67450i | −0.546822 | − | 0.837249i | \(-0.684163\pi\) | ||
0.546822 | − | 0.837249i | \(-0.315837\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 260.708i | − | 0.428092i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −926.332 | −1.51609 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1029.51 | −1.67946 | −0.839728 | − | 0.543007i | \(-0.817286\pi\) | ||||
−0.839728 | + | 0.543007i | \(0.817286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 361.322 | 0.587516 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 426.603 | 0.691415 | 0.345708 | − | 0.938342i | \(-0.387639\pi\) | ||||
0.345708 | + | 0.938342i | \(0.387639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 503.515 | 0.813432 | 0.406716 | − | 0.913555i | \(-0.366674\pi\) | ||||
0.406716 | + | 0.913555i | \(0.366674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 307.478i | − | 0.495133i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 59.8090 | 0.0960016 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −330.025 | −0.528041 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.7492 | −0.0346878 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.1436i | 0.0749500i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 299.884i | − | 0.475252i | −0.971357 | − | 0.237626i | \(-0.923631\pi\) | ||
0.971357 | − | 0.237626i | \(-0.0763692\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 203.972 | 0.322230 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1139.48i | 1.79446i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −972.990 | −1.52746 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 540.693i | 0.846155i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 724.346i | 1.13002i | 0.825082 | + | 0.565012i | \(0.191129\pi\) | ||||
−0.825082 | + | 0.565012i | \(0.808871\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −743.353 | −1.15607 | −0.578035 | − | 0.816012i | \(-0.696180\pi\) | ||||
−0.578035 | + | 0.816012i | \(0.696180\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 131.089 | − | 199.583i | 0.203239 | − | 0.309431i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 61.7177i | − | 0.0953905i | −0.998862 | − | 0.0476953i | \(-0.984812\pi\) | ||
0.998862 | − | 0.0476953i | \(-0.0151876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 216.330 | 0.333328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −95.2817 | −0.146362 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 422.488i | 0.646996i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1204.94 | 1.83960 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 74.6013i | − | 0.113548i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 620.921 | 0.942217 | 0.471108 | − | 0.882075i | \(-0.343854\pi\) | ||||
0.471108 | + | 0.882075i | \(0.343854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 496.134 | 0.750581 | 0.375291 | − | 0.926907i | \(-0.377543\pi\) | ||||
0.375291 | + | 0.926907i | \(0.377543\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.9338i | 0.0225245i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 957.027i | 1.43914i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 862.638i | 1.29331i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68.9719 | 0.103097 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 158.625i | 0.236402i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 453.069i | 0.673209i | 0.941646 | + | 0.336604i | \(0.109278\pi\) | ||||
−0.941646 | + | 0.336604i | \(0.890722\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 427.220i | 0.632918i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 233.751i | 0.345275i | 0.984985 | + | 0.172638i | \(0.0552289\pi\) | ||||
−0.984985 | + | 0.172638i | \(0.944771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1019.62i | 1.50165i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 77.1497 | 0.113289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −578.370 | −0.846808 | −0.423404 | − | 0.905941i | \(-0.639165\pi\) | ||||
−0.423404 | + | 0.905941i | \(0.639165\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −932.011 | −1.36060 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 123.427i | − | 0.179660i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1020.03 | 1.48044 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 127.474i | 0.184477i | 0.995737 | + | 0.0922387i | \(0.0294023\pi\) | ||||
−0.995737 | + | 0.0922387i | \(0.970598\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 209.059i | − | 0.301672i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 213.829i | − | 0.307667i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 73.8944 | 0.106018 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −40.2097 | −0.0575247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 126.686 | 0.180721 | 0.0903606 | − | 0.995909i | \(-0.471198\pi\) | ||||
0.0903606 | + | 0.995909i | \(0.471198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −511.708 | −0.727892 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 283.432 | 0.402031 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 138.840i | − | 0.196379i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 733.535 | 1.03461 | 0.517303 | − | 0.855803i | \(-0.326936\pi\) | ||||
0.517303 | + | 0.855803i | \(0.326936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −269.926 | −0.379643 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 315.271 | 0.442175 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 338.734i | − | 0.473753i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 15.0483i | − | 0.0209879i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 885.641 | 1.23177 | 0.615884 | − | 0.787837i | \(-0.288799\pi\) | ||||
0.615884 | + | 0.787837i | \(0.288799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 972.859i | − | 1.34932i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −219.740 | −0.303928 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1198.58i | − | 1.65321i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 244.282i | − | 0.336014i | −0.985786 | − | 0.168007i | \(-0.946267\pi\) | ||
0.985786 | − | 0.168007i | \(-0.0537331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 486.127 | 0.666841 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.8091 | − | 40.8169i | 0.0366746 | − | 0.0558371i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1317.81i | − | 1.79783i | −0.438120 | − | 0.898917i | \(-0.644355\pi\) | ||
0.438120 | − | 0.898917i | \(-0.355645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 297.708 | 0.405045 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −110.464 | −0.149883 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 126.907i | 0.171728i | 0.996307 | + | 0.0858641i | \(0.0273651\pi\) | ||||
−0.996307 | + | 0.0858641i | \(0.972635\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −162.095 | −0.218751 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 483.885i | 0.651259i | 0.945497 | + | 0.325629i | \(0.105576\pi\) | ||||
−0.945497 | + | 0.325629i | \(0.894424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1625.77 | 2.18224 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 580.320 | 0.776867 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 21.0735i | − | 0.0281355i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4506i | 0.0152471i | 0.999971 | + | 0.00762354i | \(0.00242667\pi\) | ||||
−0.999971 | + | 0.00762354i | \(0.997573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.25629i | − | 0.00698047i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 834.241 | 1.10495 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 995.145i | 1.31459i | 0.753633 | + | 0.657295i | \(0.228299\pi\) | ||||
−0.753633 | + | 0.657295i | \(0.771701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 42.8474i | − | 0.0564525i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1067.64i | 1.40295i | 0.712695 | + | 0.701474i | \(0.247474\pi\) | ||||
−0.712695 | + | 0.701474i | \(0.752526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 537.967i | 0.705068i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 73.7682i | 0.0964291i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1612.28 | 2.10206 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −361.976 | −0.470710 | −0.235355 | − | 0.971909i | \(-0.575625\pi\) | ||||
−0.235355 | + | 0.971909i | \(0.575625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 229.647 | 0.297856 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 579.373i | − | 0.749513i | −0.927123 | − | 0.374756i | \(-0.877726\pi\) | ||
0.927123 | − | 0.374756i | \(-0.122274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −438.048 | −0.565224 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 304.669i | 0.392109i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 802.068i | 1.02961i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 155.360i | 0.198924i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 449.754 | 0.574399 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 818.335 | 1.04246 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1046.34 | 1.32954 | 0.664768 | − | 0.747050i | \(-0.268530\pi\) | ||||
0.664768 | + | 0.747050i | \(0.268530\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −166.531 | −0.211066 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 292.537 | 0.369832 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1182.22i | 1.49082i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −312.100 | −0.392578 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −959.219 | −1.20354 | −0.601769 | − | 0.798670i | \(-0.705537\pi\) | ||||
−0.601769 | + | 0.798670i | \(0.705537\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 57.9649 | 0.0725468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 50.0393i | 0.0624711i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 21.4355i | − | 0.0266943i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1885.41 | −2.34212 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 206.580i | − | 0.255985i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 639.565 | 0.790562 | 0.395281 | − | 0.918560i | \(-0.370647\pi\) | ||||
0.395281 | + | 0.918560i | \(0.370647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 515.867i | − | 0.636087i | −0.948076 | − | 0.318044i | \(-0.896974\pi\) | ||
0.948076 | − | 0.318044i | \(-0.103026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.7510i | 0.0698044i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1549.96 | 1.90180 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 443.037 | + | 290.993i | 0.542273 | + | 0.356172i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1558.09i | − | 1.90243i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1288.57 | 1.56951 | 0.784756 | − | 0.619805i | \(-0.212788\pi\) | ||||
0.784756 | + | 0.619805i | \(0.212788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −516.675 | −0.627795 | −0.313897 | − | 0.949457i | \(-0.601635\pi\) | ||||
−0.313897 | + | 0.949457i | \(0.601635\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 59.5337i | 0.0721620i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.6545 | −0.0431131 | −0.0215565 | − | 0.999768i | \(-0.506862\pi\) | ||||
−0.0215565 | + | 0.999768i | \(0.506862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 617.780i | − | 0.745212i | −0.927990 | − | 0.372606i | \(-0.878464\pi\) | ||
0.927990 | − | 0.372606i | \(-0.121536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −86.6771 | −0.104305 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 60.8846 | 0.0730907 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 314.776i | − | 0.376978i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 164.373i | − | 0.196384i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 98.1185i | − | 0.116947i | −0.998289 | − | 0.0584735i | \(-0.981377\pi\) | ||
0.998289 | − | 0.0584735i | \(-0.0186233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420.800 | −0.500357 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 108.988i | 0.129285i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1229.27i | − | 1.45476i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1165.63i | 1.37618i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 189.209i | − | 0.222861i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1008.10i | − | 1.18460i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 564.129 | 0.661347 | 0.330674 | − | 0.943745i | \(-0.392724\pi\) | ||||
0.330674 | + | 0.943745i | \(0.392724\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −800.699 | −0.936490 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −699.603 | −0.816340 | −0.408170 | − | 0.912906i | \(-0.633833\pi\) | ||||
−0.408170 | + | 0.912906i | \(0.633833\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1395.67i | 1.62476i | 0.583128 | + | 0.812380i | \(0.301829\pi\) | ||||
−0.583128 | + | 0.812380i | \(0.698171\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 477.548 | 0.554644 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 768.514i | 0.890515i | 0.895403 | + | 0.445257i | \(0.146888\pi\) | ||||
−0.895403 | + | 0.445257i | \(0.853112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 184.715i | 0.213543i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 208.457i | 0.240435i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −77.5591 | −0.0892510 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −823.275 | −0.945206 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −853.070 | −0.977170 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 678.711 | 0.775670 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1318.08 | 1.50294 | 0.751470 | − | 0.659767i | \(-0.229345\pi\) | ||||
0.751470 | + | 0.659767i | \(0.229345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 259.681i | − | 0.295428i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −691.467 | −0.784867 | −0.392433 | − | 0.919780i | \(-0.628367\pi\) | ||||
−0.392433 | + | 0.919780i | \(0.628367\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 173.332 | 0.196299 | 0.0981493 | − | 0.995172i | \(-0.468708\pi\) | ||||
0.0981493 | + | 0.995172i | \(0.468708\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −493.313 | −0.557416 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 142.316i | 0.160446i | 0.996777 | + | 0.0802232i | \(0.0255633\pi\) | ||||
−0.996777 | + | 0.0802232i | \(0.974437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1506.02i | 1.69406i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 163.404 | 0.183394 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 629.166i | 0.704553i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −636.645 | −0.711335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 319.337i | − | 0.356006i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 461.154i | 0.512963i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63.8278 | −0.0708410 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 173.256 | − | 263.783i | 0.191867 | − | 0.292118i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 860.495i | 0.950823i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1795.52 | −1.97963 | −0.989814 | − | 0.142370i | \(-0.954528\pi\) | ||||
−0.989814 | + | 0.142370i | \(0.954528\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 116.161 | 0.127790 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 365.632i | − | 0.401353i | −0.979658 | − | 0.200676i | \(-0.935686\pi\) | ||
0.979658 | − | 0.200676i | \(-0.0643140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 166.746 | 0.182635 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 361.726i | − | 0.395329i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1592.53 | 1.73668 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1083.62 | −1.17913 | −0.589566 | − | 0.807720i | \(-0.700701\pi\) | ||||
−0.589566 | + | 0.807720i | \(0.700701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 369.320i | 0.400998i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1157.88i | 1.25447i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1400.69i | 1.51426i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 813.945 | 0.878042 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1400.56i | 1.50760i | 0.657105 | + | 0.753799i | \(0.271781\pi\) | ||||
−0.657105 | + | 0.753799i | \(0.728219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 660.856i | 0.709835i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 20.1292i | − | 0.0215747i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.1962i | 0.0226697i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 846.473i | 0.903387i | 0.892173 | + | 0.451693i | \(0.149180\pi\) | ||||
−0.892173 | + | 0.451693i | \(0.850820\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.9444 | −0.0297598 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1354.63 | −1.43956 | −0.719780 | − | 0.694203i | \(-0.755757\pi\) | ||||
−0.719780 | + | 0.694203i | \(0.755757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1580.13 | −1.67564 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 982.996i | 1.04021i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 209.288 | 0.221001 | 0.110501 | − | 0.993876i | \(-0.464755\pi\) | ||||
0.110501 | + | 0.993876i | \(0.464755\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 159.757i | − | 0.168342i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 62.2339i | − | 0.0654405i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 293.406i | 0.307876i | 0.988080 | + | 0.153938i | \(0.0491957\pi\) | ||||
−0.988080 | + | 0.153938i | \(0.950804\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 334.991 | 0.350776 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 62.6739 | 0.0654899 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1231.81 | −1.28447 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −792.461 | −0.824621 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.6312 | 0.0183086 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1809.55i | − | 1.87518i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1028.49 | 1.06359 | 0.531794 | − | 0.846874i | \(-0.321518\pi\) | ||||
0.531794 | + | 0.846874i | \(0.321518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.1430 | 0.0104675 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 438.558 | 0.451656 | 0.225828 | − | 0.974167i | \(-0.427491\pi\) | ||||
0.225828 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 282.611i | − | 0.290453i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 443.698i | 0.455075i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −626.212 | −0.640954 | −0.320477 | − | 0.947256i | \(-0.603843\pi\) | ||||
−0.320477 | + | 0.947256i | \(0.603843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.3780i | 0.0146864i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −450.091 | −0.458808 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1720.98i | 1.75074i | 0.483454 | + | 0.875370i | \(0.339382\pi\) | ||||
−0.483454 | + | 0.875370i | \(0.660618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2683.54i | − | 2.72441i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 374.603 | 0.379537 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −573.275 | + | 872.812i | −0.579651 | + | 0.882520i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 753.187i | 0.760027i | 0.924981 | + | 0.380014i | \(0.124081\pi\) | ||||
−0.924981 | + | 0.380014i | \(0.875919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −263.490 | −0.265348 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2709.90 | −2.72352 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 533.031i | 0.534635i | 0.963609 | + | 0.267317i | \(0.0861372\pi\) | ||||
−0.963609 | + | 0.267317i | \(0.913863\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 688.3.b.e.257.3 | 6 | ||
4.3 | odd | 2 | 43.3.b.b.42.1 | ✓ | 6 | ||
12.11 | even | 2 | 387.3.b.c.343.6 | 6 | |||
43.42 | odd | 2 | inner | 688.3.b.e.257.4 | 6 | ||
172.171 | even | 2 | 43.3.b.b.42.6 | yes | 6 | ||
516.515 | odd | 2 | 387.3.b.c.343.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.b.b.42.1 | ✓ | 6 | 4.3 | odd | 2 | ||
43.3.b.b.42.6 | yes | 6 | 172.171 | even | 2 | ||
387.3.b.c.343.1 | 6 | 516.515 | odd | 2 | |||
387.3.b.c.343.6 | 6 | 12.11 | even | 2 | |||
688.3.b.e.257.3 | 6 | 1.1 | even | 1 | trivial | ||
688.3.b.e.257.4 | 6 | 43.42 | odd | 2 | inner |