Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), degree \(2\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 484.2 | ||
Root | \(0.222521 + 0.385418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.484 |
Dual form | 507.2.e.j.22.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.222521 | − | 0.385418i | −0.157346 | − | 0.272531i | 0.776565 | − | 0.630037i | \(-0.216960\pi\) |
−0.933911 | + | 0.357506i | \(0.883627\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.900969 | − | 1.56052i | 0.450484 | − | 0.780262i | ||||
\(5\) | −0.246980 | −0.110453 | −0.0552263 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552263 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(6\) | −0.222521 | + | 0.385418i | −0.0908438 | + | 0.157346i | ||||
\(7\) | −0.876510 | + | 1.51816i | −0.331290 | + | 0.573811i | −0.982765 | − | 0.184859i | \(-0.940817\pi\) |
0.651475 | + | 0.758670i | \(0.274150\pi\) | |||||||
\(8\) | −1.69202 | −0.598220 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.0549581 | + | 0.0951903i | 0.0173793 | + | 0.0301018i | ||||
\(11\) | −2.82640 | − | 4.89546i | −0.852191 | − | 1.47604i | −0.879227 | − | 0.476403i | \(-0.841940\pi\) |
0.0270365 | − | 0.999634i | \(-0.491393\pi\) | |||||||
\(12\) | −1.80194 | −0.520175 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.780167 | 0.208509 | ||||||||
\(15\) | 0.123490 | + | 0.213891i | 0.0318849 | + | 0.0552263i | ||||
\(16\) | −1.42543 | − | 2.46891i | −0.356357 | − | 0.617228i | ||||
\(17\) | 1.90097 | − | 3.29257i | 0.461053 | − | 0.798567i | −0.537961 | − | 0.842970i | \(-0.680805\pi\) |
0.999014 | + | 0.0444031i | \(0.0141386\pi\) | |||||||
\(18\) | 0.445042 | 0.104897 | ||||||||
\(19\) | −2.79105 | + | 4.83424i | −0.640311 | + | 1.10905i | 0.345052 | + | 0.938584i | \(0.387861\pi\) |
−0.985363 | + | 0.170468i | \(0.945472\pi\) | |||||||
\(20\) | −0.222521 | + | 0.385418i | −0.0497572 | + | 0.0861820i | ||||
\(21\) | 1.75302 | 0.382540 | ||||||||
\(22\) | −1.25786 | + | 2.17869i | −0.268178 | + | 0.464497i | ||||
\(23\) | −4.17241 | − | 7.22682i | −0.870007 | − | 1.50690i | −0.861988 | − | 0.506929i | \(-0.830781\pi\) |
−0.00801894 | − | 0.999968i | \(-0.502553\pi\) | |||||||
\(24\) | 0.846011 | + | 1.46533i | 0.172691 | + | 0.299110i | ||||
\(25\) | −4.93900 | −0.987800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.57942 | + | 2.73563i | 0.298482 | + | 0.516986i | ||||
\(29\) | 2.96950 | + | 5.14333i | 0.551422 | + | 0.955092i | 0.998172 | + | 0.0604327i | \(0.0192481\pi\) |
−0.446750 | + | 0.894659i | \(0.647419\pi\) | |||||||
\(30\) | 0.0549581 | − | 0.0951903i | 0.0100339 | − | 0.0173793i | ||||
\(31\) | 5.26875 | 0.946295 | 0.473148 | − | 0.880983i | \(-0.343118\pi\) | ||||
0.473148 | + | 0.880983i | \(0.343118\pi\) | |||||||
\(32\) | −2.32640 | + | 4.02944i | −0.411253 | + | 0.712311i | ||||
\(33\) | −2.82640 | + | 4.89546i | −0.492012 | + | 0.852191i | ||||
\(34\) | −1.69202 | −0.290179 | ||||||||
\(35\) | 0.216480 | − | 0.374955i | 0.0365918 | − | 0.0633789i | ||||
\(36\) | 0.900969 | + | 1.56052i | 0.150161 | + | 0.260087i | ||||
\(37\) | −1.59903 | − | 2.76960i | −0.262879 | − | 0.455320i | 0.704127 | − | 0.710074i | \(-0.251339\pi\) |
−0.967006 | + | 0.254754i | \(0.918005\pi\) | |||||||
\(38\) | 2.48427 | 0.403002 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.417895 | 0.0660750 | ||||||||
\(41\) | −0.222521 | − | 0.385418i | −0.0347519 | − | 0.0601921i | 0.848126 | − | 0.529794i | \(-0.177731\pi\) |
−0.882878 | + | 0.469602i | \(0.844397\pi\) | |||||||
\(42\) | −0.390084 | − | 0.675645i | −0.0601912 | − | 0.104254i | ||||
\(43\) | −0.856896 | + | 1.48419i | −0.130675 | + | 0.226336i | −0.923937 | − | 0.382544i | \(-0.875048\pi\) |
0.793262 | + | 0.608881i | \(0.208381\pi\) | |||||||
\(44\) | −10.1860 | −1.53559 | ||||||||
\(45\) | 0.123490 | − | 0.213891i | 0.0184088 | − | 0.0318849i | ||||
\(46\) | −1.85690 | + | 3.21624i | −0.273784 | + | 0.474208i | ||||
\(47\) | −6.73556 | −0.982483 | −0.491241 | − | 0.871024i | \(-0.663457\pi\) | ||||
−0.491241 | + | 0.871024i | \(0.663457\pi\) | |||||||
\(48\) | −1.42543 | + | 2.46891i | −0.205743 | + | 0.356357i | ||||
\(49\) | 1.96346 | + | 3.40081i | 0.280494 | + | 0.485830i | ||||
\(50\) | 1.09903 | + | 1.90358i | 0.155426 | + | 0.269207i | ||||
\(51\) | −3.80194 | −0.532378 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.06100 | −0.145739 | −0.0728697 | − | 0.997341i | \(-0.523216\pi\) | ||||
−0.0728697 | + | 0.997341i | \(0.523216\pi\) | |||||||
\(54\) | −0.222521 | − | 0.385418i | −0.0302813 | − | 0.0524487i | ||||
\(55\) | 0.698062 | + | 1.20908i | 0.0941267 | + | 0.163032i | ||||
\(56\) | 1.48307 | − | 2.56876i | 0.198184 | − | 0.343265i | ||||
\(57\) | 5.58211 | 0.739368 | ||||||||
\(58\) | 1.32155 | − | 2.28900i | 0.173528 | − | 0.300560i | ||||
\(59\) | 6.85086 | − | 11.8660i | 0.891905 | − | 1.54483i | 0.0543169 | − | 0.998524i | \(-0.482702\pi\) |
0.837589 | − | 0.546302i | \(-0.183965\pi\) | |||||||
\(60\) | 0.445042 | 0.0574547 | ||||||||
\(61\) | 4.25786 | − | 7.37484i | 0.545164 | − | 0.944251i | −0.453433 | − | 0.891290i | \(-0.649801\pi\) |
0.998597 | − | 0.0529608i | \(-0.0168658\pi\) | |||||||
\(62\) | −1.17241 | − | 2.03067i | −0.148896 | − | 0.257895i | ||||
\(63\) | −0.876510 | − | 1.51816i | −0.110430 | − | 0.191270i | ||||
\(64\) | −3.63102 | −0.453878 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.51573 | 0.309665 | ||||||||
\(67\) | −2.98039 | − | 5.16218i | −0.364112 | − | 0.630661i | 0.624521 | − | 0.781008i | \(-0.285294\pi\) |
−0.988633 | + | 0.150347i | \(0.951961\pi\) | |||||||
\(68\) | −3.42543 | − | 5.93301i | −0.415394 | − | 0.719484i | ||||
\(69\) | −4.17241 | + | 7.22682i | −0.502299 | + | 0.870007i | ||||
\(70\) | −0.192685 | −0.0230303 | ||||||||
\(71\) | 2.85958 | − | 4.95295i | 0.339370 | − | 0.587806i | −0.644944 | − | 0.764230i | \(-0.723119\pi\) |
0.984314 | + | 0.176423i | \(0.0564527\pi\) | |||||||
\(72\) | 0.846011 | − | 1.46533i | 0.0997033 | − | 0.172691i | ||||
\(73\) | 7.35690 | 0.861060 | 0.430530 | − | 0.902576i | \(-0.358327\pi\) | ||||
0.430530 | + | 0.902576i | \(0.358327\pi\) | |||||||
\(74\) | −0.711636 | + | 1.23259i | −0.0827260 | + | 0.143286i | ||||
\(75\) | 2.46950 | + | 4.27730i | 0.285153 | + | 0.493900i | ||||
\(76\) | 5.02930 | + | 8.71101i | 0.576901 | + | 0.999221i | ||||
\(77\) | 9.90946 | 1.12929 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.45473 | 0.501196 | 0.250598 | − | 0.968091i | \(-0.419373\pi\) | ||||
0.250598 | + | 0.968091i | \(0.419373\pi\) | |||||||
\(80\) | 0.352052 | + | 0.609771i | 0.0393606 | + | 0.0681745i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.0990311 | + | 0.171527i | −0.0109362 | + | 0.0189420i | ||||
\(83\) | −10.1860 | −1.11806 | −0.559028 | − | 0.829149i | \(-0.688826\pi\) | ||||
−0.559028 | + | 0.829149i | \(0.688826\pi\) | |||||||
\(84\) | 1.57942 | − | 2.73563i | 0.172329 | − | 0.298482i | ||||
\(85\) | −0.469501 | + | 0.813199i | −0.0509245 | + | 0.0882038i | ||||
\(86\) | 0.762709 | 0.0822450 | ||||||||
\(87\) | 2.96950 | − | 5.14333i | 0.318364 | − | 0.551422i | ||||
\(88\) | 4.78232 | + | 8.28323i | 0.509797 | + | 0.882995i | ||||
\(89\) | −0.0685317 | − | 0.118700i | −0.00726434 | − | 0.0125822i | 0.862370 | − | 0.506278i | \(-0.168979\pi\) |
−0.869635 | + | 0.493696i | \(0.835646\pi\) | |||||||
\(90\) | −0.109916 | −0.0115862 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −15.0368 | −1.56770 | ||||||||
\(93\) | −2.63437 | − | 4.56287i | −0.273172 | − | 0.473148i | ||||
\(94\) | 1.49880 | + | 2.59600i | 0.154590 | + | 0.267757i | ||||
\(95\) | 0.689333 | − | 1.19396i | 0.0707241 | − | 0.122498i | ||||
\(96\) | 4.65279 | 0.474874 | ||||||||
\(97\) | 6.84481 | − | 11.8556i | 0.694986 | − | 1.20375i | −0.275200 | − | 0.961387i | \(-0.588744\pi\) |
0.970186 | − | 0.242363i | \(-0.0779226\pi\) | |||||||
\(98\) | 0.873822 | − | 1.51350i | 0.0882693 | − | 0.152887i | ||||
\(99\) | 5.65279 | 0.568127 | ||||||||
\(100\) | −4.44989 | + | 7.70743i | −0.444989 | + | 0.770743i | ||||
\(101\) | 2.70560 | + | 4.68623i | 0.269217 | + | 0.466297i | 0.968660 | − | 0.248391i | \(-0.0799019\pi\) |
−0.699443 | + | 0.714688i | \(0.746569\pi\) | |||||||
\(102\) | 0.846011 | + | 1.46533i | 0.0837675 | + | 0.145090i | ||||
\(103\) | 13.7560 | 1.35542 | 0.677710 | − | 0.735330i | \(-0.262973\pi\) | ||||
0.677710 | + | 0.735330i | \(0.262973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.432960 | −0.0422526 | ||||||||
\(106\) | 0.236094 | + | 0.408928i | 0.0229315 | + | 0.0397186i | ||||
\(107\) | 6.40850 | + | 11.0999i | 0.619533 | + | 1.07306i | 0.989571 | + | 0.144046i | \(0.0460114\pi\) |
−0.370038 | + | 0.929017i | \(0.620655\pi\) | |||||||
\(108\) | 0.900969 | − | 1.56052i | 0.0866958 | − | 0.150161i | ||||
\(109\) | 12.1468 | 1.16345 | 0.581724 | − | 0.813386i | \(-0.302378\pi\) | ||||
0.581724 | + | 0.813386i | \(0.302378\pi\) | |||||||
\(110\) | 0.310667 | − | 0.538091i | 0.0296209 | − | 0.0513050i | ||||
\(111\) | −1.59903 | + | 2.76960i | −0.151773 | + | 0.262879i | ||||
\(112\) | 4.99761 | 0.472229 | ||||||||
\(113\) | 0.818864 | − | 1.41831i | 0.0770322 | − | 0.133424i | −0.824936 | − | 0.565226i | \(-0.808789\pi\) |
0.901968 | + | 0.431802i | \(0.142122\pi\) | |||||||
\(114\) | −1.24214 | − | 2.15144i | −0.116337 | − | 0.201501i | ||||
\(115\) | 1.03050 | + | 1.78488i | 0.0960946 | + | 0.166441i | ||||
\(116\) | 10.7017 | 0.993629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.09783 | −0.561351 | ||||||||
\(119\) | 3.33244 | + | 5.77195i | 0.305484 | + | 0.529114i | ||||
\(120\) | −0.208947 | − | 0.361908i | −0.0190742 | − | 0.0330375i | ||||
\(121\) | −10.4770 | + | 18.1468i | −0.952458 | + | 1.64970i | ||||
\(122\) | −3.78986 | −0.343117 | ||||||||
\(123\) | −0.222521 | + | 0.385418i | −0.0200640 | + | 0.0347519i | ||||
\(124\) | 4.74698 | − | 8.22201i | 0.426291 | − | 0.738358i | ||||
\(125\) | 2.45473 | 0.219558 | ||||||||
\(126\) | −0.390084 | + | 0.675645i | −0.0347514 | + | 0.0601912i | ||||
\(127\) | −5.39977 | − | 9.35268i | −0.479152 | − | 0.829916i | 0.520562 | − | 0.853824i | \(-0.325723\pi\) |
−0.999714 | + | 0.0239078i | \(0.992389\pi\) | |||||||
\(128\) | 5.46077 | + | 9.45833i | 0.482669 | + | 0.836006i | ||||
\(129\) | 1.71379 | 0.150891 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.907542 | 0.0792923 | 0.0396462 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396462 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(132\) | 5.09299 | + | 8.82132i | 0.443288 | + | 0.767797i | ||||
\(133\) | −4.89277 | − | 8.47453i | −0.424257 | − | 0.734835i | ||||
\(134\) | −1.32640 | + | 2.29739i | −0.114583 | + | 0.198464i | ||||
\(135\) | −0.246980 | −0.0212566 | ||||||||
\(136\) | −3.21648 | + | 5.57111i | −0.275811 | + | 0.477718i | ||||
\(137\) | 4.77413 | − | 8.26903i | 0.407881 | − | 0.706471i | −0.586771 | − | 0.809753i | \(-0.699601\pi\) |
0.994652 | + | 0.103282i | \(0.0329344\pi\) | |||||||
\(138\) | 3.71379 | 0.316139 | ||||||||
\(139\) | 2.04623 | − | 3.54417i | 0.173559 | − | 0.300613i | −0.766103 | − | 0.642718i | \(-0.777807\pi\) |
0.939662 | + | 0.342105i | \(0.111140\pi\) | |||||||
\(140\) | −0.390084 | − | 0.675645i | −0.0329681 | − | 0.0571024i | ||||
\(141\) | 3.36778 | + | 5.83317i | 0.283618 | + | 0.491241i | ||||
\(142\) | −2.54527 | −0.213594 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.85086 | 0.237571 | ||||||||
\(145\) | −0.733406 | − | 1.27030i | −0.0609061 | − | 0.105492i | ||||
\(146\) | −1.63706 | − | 2.83548i | −0.135484 | − | 0.234666i | ||||
\(147\) | 1.96346 | − | 3.40081i | 0.161943 | − | 0.280494i | ||||
\(148\) | −5.76271 | −0.473692 | ||||||||
\(149\) | 7.69418 | − | 13.3267i | 0.630332 | − | 1.09177i | −0.357152 | − | 0.934046i | \(-0.616252\pi\) |
0.987484 | − | 0.157720i | \(-0.0504144\pi\) | |||||||
\(150\) | 1.09903 | − | 1.90358i | 0.0897355 | − | 0.155426i | ||||
\(151\) | −3.67456 | −0.299032 | −0.149516 | − | 0.988759i | \(-0.547772\pi\) | ||||
−0.149516 | + | 0.988759i | \(0.547772\pi\) | |||||||
\(152\) | 4.72252 | − | 8.17965i | 0.383047 | − | 0.663457i | ||||
\(153\) | 1.90097 | + | 3.29257i | 0.153684 | + | 0.266189i | ||||
\(154\) | −2.20506 | − | 3.81928i | −0.177689 | − | 0.307766i | ||||
\(155\) | −1.30127 | −0.104521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.87800 | −0.389307 | −0.194653 | − | 0.980872i | \(-0.562358\pi\) | ||||
−0.194653 | + | 0.980872i | \(0.562358\pi\) | |||||||
\(158\) | −0.991271 | − | 1.71693i | −0.0788613 | − | 0.136592i | ||||
\(159\) | 0.530499 | + | 0.918852i | 0.0420713 | + | 0.0728697i | ||||
\(160\) | 0.574572 | − | 0.995189i | 0.0454239 | − | 0.0786766i | ||||
\(161\) | 14.6286 | 1.15290 | ||||||||
\(162\) | −0.222521 | + | 0.385418i | −0.0174829 | + | 0.0302813i | ||||
\(163\) | −4.31551 | + | 7.47468i | −0.338017 | + | 0.585462i | −0.984060 | − | 0.177839i | \(-0.943089\pi\) |
0.646043 | + | 0.763301i | \(0.276423\pi\) | |||||||
\(164\) | −0.801938 | −0.0626208 | ||||||||
\(165\) | 0.698062 | − | 1.20908i | 0.0543441 | − | 0.0941267i | ||||
\(166\) | 2.26659 | + | 3.92586i | 0.175922 | + | 0.304706i | ||||
\(167\) | −4.73490 | − | 8.20108i | −0.366397 | − | 0.634619i | 0.622602 | − | 0.782539i | \(-0.286076\pi\) |
−0.988999 | + | 0.147920i | \(0.952742\pi\) | |||||||
\(168\) | −2.96615 | −0.228843 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.417895 | 0.0320511 | ||||||||
\(171\) | −2.79105 | − | 4.83424i | −0.213437 | − | 0.369684i | ||||
\(172\) | 1.54407 | + | 2.67441i | 0.117734 | + | 0.203922i | ||||
\(173\) | −2.38740 | + | 4.13509i | −0.181510 | + | 0.314385i | −0.942395 | − | 0.334502i | \(-0.891432\pi\) |
0.760885 | + | 0.648887i | \(0.224765\pi\) | |||||||
\(174\) | −2.64310 | −0.200373 | ||||||||
\(175\) | 4.32908 | − | 7.49819i | 0.327248 | − | 0.566810i | ||||
\(176\) | −8.05765 | + | 13.9563i | −0.607368 | + | 1.05199i | ||||
\(177\) | −13.7017 | −1.02988 | ||||||||
\(178\) | −0.0304995 | + | 0.0528266i | −0.00228603 | + | 0.00395952i | ||||
\(179\) | −1.71768 | − | 2.97510i | −0.128385 | − | 0.222370i | 0.794666 | − | 0.607047i | \(-0.207646\pi\) |
−0.923051 | + | 0.384677i | \(0.874313\pi\) | |||||||
\(180\) | −0.222521 | − | 0.385418i | −0.0165857 | − | 0.0287273i | ||||
\(181\) | −13.4862 | −1.00242 | −0.501210 | − | 0.865326i | \(-0.667112\pi\) | ||||
−0.501210 | + | 0.865326i | \(0.667112\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.51573 | −0.629501 | ||||||||
\(184\) | 7.05980 | + | 12.2279i | 0.520456 | + | 0.901455i | ||||
\(185\) | 0.394928 | + | 0.684035i | 0.0290357 | + | 0.0502913i | ||||
\(186\) | −1.17241 | + | 2.03067i | −0.0859651 | + | 0.148896i | ||||
\(187\) | −21.4916 | −1.57162 | ||||||||
\(188\) | −6.06853 | + | 10.5110i | −0.442593 | + | 0.766594i | ||||
\(189\) | −0.876510 | + | 1.51816i | −0.0637567 | + | 0.110430i | ||||
\(190\) | −0.613564 | −0.0445126 | ||||||||
\(191\) | 0.650637 | − | 1.12694i | 0.0470784 | − | 0.0815422i | −0.841526 | − | 0.540217i | \(-0.818342\pi\) |
0.888604 | + | 0.458674i | \(0.151676\pi\) | |||||||
\(192\) | 1.81551 | + | 3.14456i | 0.131023 | + | 0.226939i | ||||
\(193\) | 4.59783 | + | 7.96368i | 0.330959 | + | 0.573238i | 0.982700 | − | 0.185203i | \(-0.0592944\pi\) |
−0.651741 | + | 0.758442i | \(0.725961\pi\) | |||||||
\(194\) | −6.09246 | −0.437413 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.07606 | 0.505433 | ||||||||
\(197\) | −2.05615 | − | 3.56136i | −0.146495 | − | 0.253737i | 0.783435 | − | 0.621474i | \(-0.213466\pi\) |
−0.929930 | + | 0.367737i | \(0.880133\pi\) | |||||||
\(198\) | −1.25786 | − | 2.17869i | −0.0893926 | − | 0.154832i | ||||
\(199\) | 12.3862 | − | 21.4535i | 0.878034 | − | 1.52080i | 0.0245395 | − | 0.999699i | \(-0.492188\pi\) |
0.853495 | − | 0.521101i | \(-0.174479\pi\) | |||||||
\(200\) | 8.35690 | 0.590922 | ||||||||
\(201\) | −2.98039 | + | 5.16218i | −0.210220 | + | 0.364112i | ||||
\(202\) | 1.20410 | − | 2.08557i | 0.0847204 | − | 0.146740i | ||||
\(203\) | −10.4112 | −0.730722 | ||||||||
\(204\) | −3.42543 | + | 5.93301i | −0.239828 | + | 0.415394i | ||||
\(205\) | 0.0549581 | + | 0.0951903i | 0.00383844 | + | 0.00664838i | ||||
\(206\) | −3.06100 | − | 5.30181i | −0.213270 | − | 0.369394i | ||||
\(207\) | 8.34481 | 0.580005 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.5545 | 2.18267 | ||||||||
\(210\) | 0.0963427 | + | 0.166870i | 0.00664828 | + | 0.0115152i | ||||
\(211\) | 2.96950 | + | 5.14333i | 0.204429 | + | 0.354081i | 0.949951 | − | 0.312400i | \(-0.101133\pi\) |
−0.745522 | + | 0.666481i | \(0.767800\pi\) | |||||||
\(212\) | −0.955927 | + | 1.65571i | −0.0656533 | + | 0.113715i | ||||
\(213\) | −5.71917 | −0.391871 | ||||||||
\(214\) | 2.85205 | − | 4.93990i | 0.194962 | − | 0.337684i | ||||
\(215\) | 0.211636 | − | 0.366564i | 0.0144334 | − | 0.0249995i | ||||
\(216\) | −1.69202 | −0.115127 | ||||||||
\(217\) | −4.61811 | + | 7.99881i | −0.313498 | + | 0.542994i | ||||
\(218\) | −2.70291 | − | 4.68157i | −0.183064 | − | 0.317076i | ||||
\(219\) | −3.67845 | − | 6.37126i | −0.248566 | − | 0.430530i | ||||
\(220\) | 2.51573 | 0.169610 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.42327 | 0.0955237 | ||||||||
\(223\) | −7.10052 | − | 12.2985i | −0.475486 | − | 0.823566i | 0.524120 | − | 0.851645i | \(-0.324395\pi\) |
−0.999606 | + | 0.0280785i | \(0.991061\pi\) | |||||||
\(224\) | −4.07822 | − | 7.06368i | −0.272488 | − | 0.471962i | ||||
\(225\) | 2.46950 | − | 4.27730i | 0.164633 | − | 0.285153i | ||||
\(226\) | −0.728857 | −0.0484829 | ||||||||
\(227\) | −8.00365 | + | 13.8627i | −0.531221 | + | 0.920101i | 0.468115 | + | 0.883667i | \(0.344933\pi\) |
−0.999336 | + | 0.0364340i | \(0.988400\pi\) | |||||||
\(228\) | 5.02930 | − | 8.71101i | 0.333074 | − | 0.576901i | ||||
\(229\) | 1.84117 | 0.121668 | 0.0608339 | − | 0.998148i | \(-0.480624\pi\) | ||||
0.0608339 | + | 0.998148i | \(0.480624\pi\) | |||||||
\(230\) | 0.458615 | − | 0.794345i | 0.0302402 | − | 0.0523776i | ||||
\(231\) | −4.95473 | − | 8.58185i | −0.325997 | − | 0.564644i | ||||
\(232\) | −5.02446 | − | 8.70262i | −0.329872 | − | 0.571355i | ||||
\(233\) | −23.4252 | −1.53464 | −0.767318 | − | 0.641267i | \(-0.778409\pi\) | ||||
−0.767318 | + | 0.641267i | \(0.778409\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.66355 | 0.108518 | ||||||||
\(236\) | −12.3448 | − | 21.3818i | −0.803579 | − | 1.39184i | ||||
\(237\) | −2.22737 | − | 3.85791i | −0.144683 | − | 0.250598i | ||||
\(238\) | 1.48307 | − | 2.56876i | 0.0961334 | − | 0.166508i | ||||
\(239\) | 14.6015 | 0.944491 | 0.472246 | − | 0.881467i | \(-0.343444\pi\) | ||||
0.472246 | + | 0.881467i | \(0.343444\pi\) | |||||||
\(240\) | 0.352052 | − | 0.609771i | 0.0227248 | − | 0.0393606i | ||||
\(241\) | −4.31551 | + | 7.47468i | −0.277987 | + | 0.481487i | −0.970884 | − | 0.239549i | \(-0.923000\pi\) |
0.692898 | + | 0.721036i | \(0.256334\pi\) | |||||||
\(242\) | 9.32544 | 0.599462 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −7.67241 | − | 13.2890i | −0.491176 | − | 0.850741i | ||||
\(245\) | −0.484935 | − | 0.839931i | −0.0309813 | − | 0.0536612i | ||||
\(246\) | 0.198062 | 0.0126280 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.91484 | −0.566093 | ||||||||
\(249\) | 5.09299 | + | 8.82132i | 0.322755 | + | 0.559028i | ||||
\(250\) | −0.546229 | − | 0.946096i | −0.0345466 | − | 0.0598364i | ||||
\(251\) | 1.90097 | − | 3.29257i | 0.119988 | − | 0.207825i | −0.799775 | − | 0.600300i | \(-0.795048\pi\) |
0.919763 | + | 0.392475i | \(0.128381\pi\) | |||||||
\(252\) | −3.15883 | −0.198988 | ||||||||
\(253\) | −23.5858 | + | 40.8517i | −1.48282 | + | 2.56833i | ||||
\(254\) | −2.40312 | + | 4.16233i | −0.150785 | + | 0.261168i | ||||
\(255\) | 0.939001 | 0.0588025 | ||||||||
\(256\) | −1.20075 | + | 2.07976i | −0.0750469 | + | 0.129985i | ||||
\(257\) | 10.2981 | + | 17.8368i | 0.642375 | + | 1.11263i | 0.984901 | + | 0.173118i | \(0.0553841\pi\) |
−0.342526 | + | 0.939508i | \(0.611283\pi\) | |||||||
\(258\) | −0.381355 | − | 0.660525i | −0.0237421 | − | 0.0411225i | ||||
\(259\) | 5.60627 | 0.348357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.93900 | −0.367615 | ||||||||
\(262\) | −0.201947 | − | 0.349783i | −0.0124763 | − | 0.0216096i | ||||
\(263\) | −0.166366 | − | 0.288155i | −0.0102586 | − | 0.0177684i | 0.860851 | − | 0.508858i | \(-0.169932\pi\) |
−0.871109 | + | 0.491089i | \(0.836599\pi\) | |||||||
\(264\) | 4.78232 | − | 8.28323i | 0.294332 | − | 0.509797i | ||||
\(265\) | 0.262045 | 0.0160973 | ||||||||
\(266\) | −2.17749 | + | 3.77152i | −0.133510 | + | 0.231247i | ||||
\(267\) | −0.0685317 | + | 0.118700i | −0.00419407 | + | 0.00726434i | ||||
\(268\) | −10.7409 | −0.656107 | ||||||||
\(269\) | −13.6516 | + | 23.6453i | −0.832353 | + | 1.44168i | 0.0638154 | + | 0.997962i | \(0.479673\pi\) |
−0.896168 | + | 0.443715i | \(0.853660\pi\) | |||||||
\(270\) | 0.0549581 | + | 0.0951903i | 0.00334465 | + | 0.00579310i | ||||
\(271\) | −13.9928 | − | 24.2362i | −0.850000 | − | 1.47224i | −0.881207 | − | 0.472730i | \(-0.843269\pi\) |
0.0312076 | − | 0.999513i | \(-0.490065\pi\) | |||||||
\(272\) | −10.8388 | −0.657197 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.24937 | −0.256714 | ||||||||
\(275\) | 13.9596 | + | 24.1787i | 0.841794 | + | 1.45803i | ||||
\(276\) | 7.51842 | + | 13.0223i | 0.452556 | + | 0.783849i | ||||
\(277\) | 1.05161 | − | 1.82143i | 0.0631849 | − | 0.109439i | −0.832703 | − | 0.553721i | \(-0.813208\pi\) |
0.895887 | + | 0.444281i | \(0.146541\pi\) | |||||||
\(278\) | −1.82132 | −0.109235 | ||||||||
\(279\) | −2.63437 | + | 4.56287i | −0.157716 | + | 0.273172i | ||||
\(280\) | −0.366289 | + | 0.634431i | −0.0218900 | + | 0.0379145i | ||||
\(281\) | 27.2349 | 1.62470 | 0.812349 | − | 0.583172i | \(-0.198189\pi\) | ||||
0.812349 | + | 0.583172i | \(0.198189\pi\) | |||||||
\(282\) | 1.49880 | − | 2.59600i | 0.0892525 | − | 0.154590i | ||||
\(283\) | −2.64191 | − | 4.57592i | −0.157045 | − | 0.272010i | 0.776757 | − | 0.629801i | \(-0.216863\pi\) |
−0.933802 | + | 0.357791i | \(0.883530\pi\) | |||||||
\(284\) | −5.15279 | − | 8.92490i | −0.305762 | − | 0.529595i | ||||
\(285\) | −1.37867 | −0.0816651 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.780167 | 0.0460518 | ||||||||
\(288\) | −2.32640 | − | 4.02944i | −0.137084 | − | 0.237437i | ||||
\(289\) | 1.27263 | + | 2.20427i | 0.0748609 | + | 0.129663i | ||||
\(290\) | −0.326396 | + | 0.565335i | −0.0191667 | + | 0.0331976i | ||||
\(291\) | −13.6896 | −0.802500 | ||||||||
\(292\) | 6.62833 | − | 11.4806i | 0.387894 | − | 0.671852i | ||||
\(293\) | −16.3312 | + | 28.2865i | −0.954081 | + | 1.65252i | −0.217625 | + | 0.976033i | \(0.569831\pi\) |
−0.736457 | + | 0.676485i | \(0.763502\pi\) | |||||||
\(294\) | −1.74764 | −0.101925 | ||||||||
\(295\) | −1.69202 | + | 2.93067i | −0.0985133 | + | 0.170630i | ||||
\(296\) | 2.70560 | + | 4.68623i | 0.157260 | + | 0.272381i | ||||
\(297\) | −2.82640 | − | 4.89546i | −0.164004 | − | 0.284064i | ||||
\(298\) | −6.84846 | −0.396721 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 8.89977 | 0.513829 | ||||||||
\(301\) | −1.50216 | − | 2.60181i | −0.0865828 | − | 0.149966i | ||||
\(302\) | 0.817667 | + | 1.41624i | 0.0470515 | + | 0.0814955i | ||||
\(303\) | 2.70560 | − | 4.68623i | 0.155432 | − | 0.269217i | ||||
\(304\) | 15.9138 | 0.912717 | ||||||||
\(305\) | −1.05161 | + | 1.82143i | −0.0602148 | + | 0.104295i | ||||
\(306\) | 0.846011 | − | 1.46533i | 0.0483632 | − | 0.0837675i | ||||
\(307\) | −20.7614 | −1.18491 | −0.592457 | − | 0.805602i | \(-0.701842\pi\) | ||||
−0.592457 | + | 0.805602i | \(0.701842\pi\) | |||||||
\(308\) | 8.92812 | − | 15.4640i | 0.508727 | − | 0.881140i | ||||
\(309\) | −6.87800 | − | 11.9130i | −0.391276 | − | 0.677710i | ||||
\(310\) | 0.289561 | + | 0.501534i | 0.0164459 | + | 0.0284852i | ||||
\(311\) | −11.3013 | −0.640836 | −0.320418 | − | 0.947276i | \(-0.603823\pi\) | ||||
−0.320418 | + | 0.947276i | \(0.603823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.27173 | −0.241453 | −0.120726 | − | 0.992686i | \(-0.538522\pi\) | ||||
−0.120726 | + | 0.992686i | \(0.538522\pi\) | |||||||
\(314\) | 1.08546 | + | 1.88007i | 0.0612559 | + | 0.106098i | ||||
\(315\) | 0.216480 | + | 0.374955i | 0.0121973 | + | 0.0211263i | ||||
\(316\) | 4.01357 | − | 6.95171i | 0.225781 | − | 0.391064i | ||||
\(317\) | 15.4776 | 0.869307 | 0.434653 | − | 0.900598i | \(-0.356871\pi\) | ||||
0.434653 | + | 0.900598i | \(0.356871\pi\) | |||||||
\(318\) | 0.236094 | − | 0.408928i | 0.0132395 | − | 0.0229315i | ||||
\(319\) | 16.7860 | − | 29.0742i | 0.939834 | − | 1.62784i | ||||
\(320\) | 0.896789 | 0.0501320 | ||||||||
\(321\) | 6.40850 | − | 11.0999i | 0.357688 | − | 0.619533i | ||||
\(322\) | −3.25518 | − | 5.63813i | −0.181404 | − | 0.314201i | ||||
\(323\) | 10.6114 | + | 18.3795i | 0.590435 | + | 1.02266i | ||||
\(324\) | −1.80194 | −0.100108 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.84117 | 0.212743 | ||||||||
\(327\) | −6.07338 | − | 10.5194i | −0.335858 | − | 0.581724i | ||||
\(328\) | 0.376510 | + | 0.652135i | 0.0207893 | + | 0.0360081i | ||||
\(329\) | 5.90379 | − | 10.2257i | 0.325486 | − | 0.563759i | ||||
\(330\) | −0.621334 | −0.0342033 | ||||||||
\(331\) | −3.03415 | + | 5.25530i | −0.166772 | + | 0.288857i | −0.937283 | − | 0.348569i | \(-0.886668\pi\) |
0.770511 | + | 0.637426i | \(0.220001\pi\) | |||||||
\(332\) | −9.17725 | + | 15.8955i | −0.503667 | + | 0.872377i | ||||
\(333\) | 3.19806 | 0.175253 | ||||||||
\(334\) | −2.10723 | + | 3.64983i | −0.115302 | + | 0.199710i | ||||
\(335\) | 0.736094 | + | 1.27495i | 0.0402171 | + | 0.0696581i | ||||
\(336\) | −2.49880 | − | 4.32805i | −0.136321 | − | 0.236115i | ||||
\(337\) | 12.1239 | 0.660432 | 0.330216 | − | 0.943905i | \(-0.392878\pi\) | ||||
0.330216 | + | 0.943905i | \(0.392878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.63773 | −0.0889491 | ||||||||
\(340\) | 0.846011 | + | 1.46533i | 0.0458814 | + | 0.0794689i | ||||
\(341\) | −14.8916 | − | 25.7930i | −0.806424 | − | 1.39677i | ||||
\(342\) | −1.24214 | + | 2.15144i | −0.0671670 | + | 0.116337i | ||||
\(343\) | −19.1551 | −1.03428 | ||||||||
\(344\) | 1.44989 | − | 2.51128i | 0.0781726 | − | 0.135399i | ||||
\(345\) | 1.03050 | − | 1.78488i | 0.0554802 | − | 0.0960946i | ||||
\(346\) | 2.12498 | 0.114240 | ||||||||
\(347\) | −11.5749 | + | 20.0483i | −0.621371 | + | 1.07625i | 0.367859 | + | 0.929882i | \(0.380091\pi\) |
−0.989231 | + | 0.146365i | \(0.953242\pi\) | |||||||
\(348\) | −5.35086 | − | 9.26795i | −0.286836 | − | 0.496814i | ||||
\(349\) | 11.0978 | + | 19.2220i | 0.594053 | + | 1.02893i | 0.993680 | + | 0.112253i | \(0.0358066\pi\) |
−0.399626 | + | 0.916678i | \(0.630860\pi\) | |||||||
\(350\) | −3.85325 | −0.205965 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.3013 | 1.40186 | ||||||||
\(353\) | 2.53534 | + | 4.39134i | 0.134943 | + | 0.233728i | 0.925576 | − | 0.378563i | \(-0.123582\pi\) |
−0.790633 | + | 0.612291i | \(0.790248\pi\) | |||||||
\(354\) | 3.04892 | + | 5.28088i | 0.162048 | + | 0.280676i | ||||
\(355\) | −0.706259 | + | 1.22328i | −0.0374843 | + | 0.0649248i | ||||
\(356\) | −0.246980 | −0.0130899 | ||||||||
\(357\) | 3.33244 | − | 5.77195i | 0.176371 | − | 0.305484i | ||||
\(358\) | −0.764438 | + | 1.32405i | −0.0404018 | + | 0.0699780i | ||||
\(359\) | −16.6746 | −0.880050 | −0.440025 | − | 0.897986i | \(-0.645030\pi\) | ||||
−0.440025 | + | 0.897986i | \(0.645030\pi\) | |||||||
\(360\) | −0.208947 | + | 0.361908i | −0.0110125 | + | 0.0190742i | ||||
\(361\) | −6.07995 | − | 10.5308i | −0.319997 | − | 0.554252i | ||||
\(362\) | 3.00096 | + | 5.19781i | 0.157727 | + | 0.273191i | ||||
\(363\) | 20.9541 | 1.09980 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.81700 | −0.0951063 | ||||||||
\(366\) | 1.89493 | + | 3.28211i | 0.0990495 | + | 0.171559i | ||||
\(367\) | 0.589638 | + | 1.02128i | 0.0307789 | + | 0.0533105i | 0.881005 | − | 0.473108i | \(-0.156868\pi\) |
−0.850226 | + | 0.526418i | \(0.823535\pi\) | |||||||
\(368\) | −11.8949 | + | 20.6026i | −0.620066 | + | 1.07399i | ||||
\(369\) | 0.445042 | 0.0231680 | ||||||||
\(370\) | 0.175760 | − | 0.304424i | 0.00913730 | − | 0.0158263i | ||||
\(371\) | 0.929976 | − | 1.61077i | 0.0482820 | − | 0.0836268i | ||||
\(372\) | −9.49396 | −0.492239 | ||||||||
\(373\) | 15.0462 | − | 26.0608i | 0.779064 | − | 1.34938i | −0.153417 | − | 0.988161i | \(-0.549028\pi\) |
0.932482 | − | 0.361217i | \(-0.117639\pi\) | |||||||
\(374\) | 4.78232 | + | 8.28323i | 0.247288 | + | 0.428315i | ||||
\(375\) | −1.22737 | − | 2.12586i | −0.0633809 | − | 0.109779i | ||||
\(376\) | 11.3967 | 0.587741 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.780167 | 0.0401275 | ||||||||
\(379\) | 9.58157 | + | 16.5958i | 0.492172 | + | 0.852467i | 0.999959 | − | 0.00901515i | \(-0.00286965\pi\) |
−0.507787 | + | 0.861483i | \(0.669536\pi\) | |||||||
\(380\) | −1.24214 | − | 2.15144i | −0.0637202 | − | 0.110367i | ||||
\(381\) | −5.39977 | + | 9.35268i | −0.276639 | + | 0.479152i | ||||
\(382\) | −0.579121 | −0.0296304 | ||||||||
\(383\) | 7.69418 | − | 13.3267i | 0.393154 | − | 0.680963i | −0.599710 | − | 0.800218i | \(-0.704717\pi\) |
0.992864 | + | 0.119255i | \(0.0380506\pi\) | |||||||
\(384\) | 5.46077 | − | 9.45833i | 0.278669 | − | 0.482669i | ||||
\(385\) | −2.44743 | −0.124733 | ||||||||
\(386\) | 2.04623 | − | 3.54417i | 0.104150 | − | 0.180394i | ||||
\(387\) | −0.856896 | − | 1.48419i | −0.0435585 | − | 0.0754455i | ||||
\(388\) | −12.3339 | − | 21.3630i | −0.626160 | − | 1.08454i | ||||
\(389\) | −24.0315 | −1.21844 | −0.609222 | − | 0.793000i | \(-0.708518\pi\) | ||||
−0.609222 | + | 0.793000i | \(0.708518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.7265 | −1.60448 | ||||||||
\(392\) | −3.32222 | − | 5.75425i | −0.167797 | − | 0.290633i | ||||
\(393\) | −0.453771 | − | 0.785955i | −0.0228897 | − | 0.0396462i | ||||
\(394\) | −0.915075 | + | 1.58496i | −0.0461008 | + | 0.0798489i | ||||
\(395\) | −1.10023 | −0.0553585 | ||||||||
\(396\) | 5.09299 | − | 8.82132i | 0.255932 | − | 0.443288i | ||||
\(397\) | −14.8007 | + | 25.6356i | −0.742828 | + | 1.28662i | 0.208375 | + | 0.978049i | \(0.433183\pi\) |
−0.951203 | + | 0.308567i | \(0.900151\pi\) | |||||||
\(398\) | −11.0248 | −0.552621 | ||||||||
\(399\) | −4.89277 | + | 8.47453i | −0.244945 | + | 0.424257i | ||||
\(400\) | 7.04019 | + | 12.1940i | 0.352009 | + | 0.609698i | ||||
\(401\) | 10.5516 | + | 18.2759i | 0.526922 | + | 0.912656i | 0.999508 | + | 0.0313711i | \(0.00998736\pi\) |
−0.472586 | + | 0.881285i | \(0.656679\pi\) | |||||||
\(402\) | 2.65279 | 0.132309 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9.75063 | 0.485112 | ||||||||
\(405\) | 0.123490 | + | 0.213891i | 0.00613626 | + | 0.0106283i | ||||
\(406\) | 2.31671 | + | 4.01266i | 0.114976 | + | 0.199145i | ||||
\(407\) | −9.03899 | + | 15.6560i | −0.448046 | + | 0.776039i | ||||
\(408\) | 6.43296 | 0.318479 | ||||||||
\(409\) | 18.0112 | − | 31.1963i | 0.890596 | − | 1.54256i | 0.0514328 | − | 0.998676i | \(-0.483621\pi\) |
0.839163 | − | 0.543880i | \(-0.183045\pi\) | |||||||
\(410\) | 0.0244587 | − | 0.0423637i | 0.00120793 | − | 0.00209219i | ||||
\(411\) | −9.54825 | −0.470981 | ||||||||
\(412\) | 12.3937 | − | 21.4666i | 0.610595 | − | 1.05758i | ||||
\(413\) | 12.0097 | + | 20.8014i | 0.590958 | + | 1.02357i | ||||
\(414\) | −1.85690 | − | 3.21624i | −0.0912615 | − | 0.158069i | ||||
\(415\) | 2.51573 | 0.123492 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.09246 | −0.200409 | ||||||||
\(418\) | −7.02153 | − | 12.1617i | −0.343434 | − | 0.594846i | ||||
\(419\) | −2.98427 | − | 5.16891i | −0.145791 | − | 0.252518i | 0.783877 | − | 0.620917i | \(-0.213239\pi\) |
−0.929668 | + | 0.368399i | \(0.879906\pi\) | |||||||
\(420\) | −0.390084 | + | 0.675645i | −0.0190341 | + | 0.0329681i | ||||
\(421\) | −2.09544 | −0.102126 | −0.0510628 | − | 0.998695i | \(-0.516261\pi\) | ||||
−0.0510628 | + | 0.998695i | \(0.516261\pi\) | |||||||
\(422\) | 1.32155 | − | 2.28900i | 0.0643321 | − | 0.111427i | ||||
\(423\) | 3.36778 | − | 5.83317i | 0.163747 | − | 0.283618i | ||||
\(424\) | 1.79523 | 0.0871842 | ||||||||
\(425\) | −9.38889 | + | 16.2620i | −0.455428 | + | 0.788824i | ||||
\(426\) | 1.27263 | + | 2.20427i | 0.0616594 | + | 0.106797i | ||||
\(427\) | 7.46412 | + | 12.9282i | 0.361214 | + | 0.625641i | ||||
\(428\) | 23.0954 | 1.11636 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.188374 | −0.00908418 | ||||||||
\(431\) | 1.44289 | + | 2.49915i | 0.0695014 | + | 0.120380i | 0.898682 | − | 0.438601i | \(-0.144526\pi\) |
−0.829181 | + | 0.558981i | \(0.811193\pi\) | |||||||
\(432\) | −1.42543 | − | 2.46891i | −0.0685809 | − | 0.118786i | ||||
\(433\) | 6.32424 | − | 10.9539i | 0.303924 | − | 0.526411i | −0.673097 | − | 0.739554i | \(-0.735037\pi\) |
0.977021 | + | 0.213143i | \(0.0683699\pi\) | |||||||
\(434\) | 4.11051 | 0.197311 | ||||||||
\(435\) | −0.733406 | + | 1.27030i | −0.0351641 | + | 0.0609061i | ||||
\(436\) | 10.9438 | − | 18.9553i | 0.524115 | − | 0.907794i | ||||
\(437\) | 46.5816 | 2.22830 | ||||||||
\(438\) | −1.63706 | + | 2.83548i | −0.0782219 | + | 0.135484i | ||||
\(439\) | 5.46346 | + | 9.46299i | 0.260757 | + | 0.451644i | 0.966443 | − | 0.256880i | \(-0.0826946\pi\) |
−0.705687 | + | 0.708524i | \(0.749361\pi\) | |||||||
\(440\) | −1.18114 | − | 2.04579i | −0.0563085 | − | 0.0975291i | ||||
\(441\) | −3.92692 | −0.186996 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.2403 | −0.914133 | −0.457067 | − | 0.889433i | \(-0.651100\pi\) | ||||
−0.457067 | + | 0.889433i | \(0.651100\pi\) | |||||||
\(444\) | 2.88135 | + | 4.99065i | 0.136743 | + | 0.236846i | ||||
\(445\) | 0.0169259 | + | 0.0293166i | 0.000802366 | + | 0.00138974i | ||||
\(446\) | −3.16003 | + | 5.47333i | −0.149632 | + | 0.259170i | ||||
\(447\) | −15.3884 | −0.727844 | ||||||||
\(448\) | 3.18263 | − | 5.51247i | 0.150365 | − | 0.260440i | ||||
\(449\) | 14.4100 | − | 24.9588i | 0.680050 | − | 1.17788i | −0.294916 | − | 0.955523i | \(-0.595292\pi\) |
0.974965 | − | 0.222357i | \(-0.0713751\pi\) | |||||||
\(450\) | −2.19806 | −0.103618 | ||||||||
\(451\) | −1.25786 | + | 2.17869i | −0.0592305 | + | 0.102590i | ||||
\(452\) | −1.47554 | − | 2.55571i | −0.0694036 | − | 0.120211i | ||||
\(453\) | 1.83728 | + | 3.18226i | 0.0863230 | + | 0.149516i | ||||
\(454\) | 7.12392 | 0.334342 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.44504 | −0.442305 | ||||||||
\(457\) | 9.03534 | + | 15.6497i | 0.422656 | + | 0.732061i | 0.996198 | − | 0.0871147i | \(-0.0277647\pi\) |
−0.573543 | + | 0.819176i | \(0.694431\pi\) | |||||||
\(458\) | −0.409698 | − | 0.709618i | −0.0191439 | − | 0.0331583i | ||||
\(459\) | 1.90097 | − | 3.29257i | 0.0887296 | − | 0.153684i | ||||
\(460\) | 3.71379 | 0.173156 | ||||||||
\(461\) | 3.78382 | − | 6.55376i | 0.176230 | − | 0.305239i | −0.764356 | − | 0.644794i | \(-0.776943\pi\) |
0.940586 | + | 0.339555i | \(0.110276\pi\) | |||||||
\(462\) | −2.20506 | + | 3.81928i | −0.102589 | + | 0.177689i | ||||
\(463\) | 35.3551 | 1.64309 | 0.821545 | − | 0.570143i | \(-0.193112\pi\) | ||||
0.821545 | + | 0.570143i | \(0.193112\pi\) | |||||||
\(464\) | 8.46562 | − | 14.6629i | 0.393006 | − | 0.680707i | ||||
\(465\) | 0.650637 | + | 1.12694i | 0.0301726 | + | 0.0522604i | ||||
\(466\) | 5.21260 | + | 9.02848i | 0.241469 | + | 0.418236i | ||||
\(467\) | 13.0000 | 0.601568 | 0.300784 | − | 0.953692i | \(-0.402752\pi\) | ||||
0.300784 | + | 0.953692i | \(0.402752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4494 | 0.482506 | ||||||||
\(470\) | −0.370174 | − | 0.641160i | −0.0170748 | − | 0.0295745i | ||||
\(471\) | 2.43900 | + | 4.22447i | 0.112383 | + | 0.194653i | ||||
\(472\) | −11.5918 | + | 20.0776i | −0.533556 | + | 0.924145i | ||||
\(473\) | 9.68771 | 0.445441 | ||||||||
\(474\) | −0.991271 | + | 1.71693i | −0.0455306 | + | 0.0788613i | ||||
\(475\) | 13.7850 | − | 23.8763i | 0.632500 | − | 1.09552i | ||||
\(476\) | 12.0097 | 0.550463 | ||||||||
\(477\) | 0.530499 | − | 0.918852i | 0.0242899 | − | 0.0420713i | ||||
\(478\) | −3.24914 | − | 5.62767i | −0.148612 | − | 0.257404i | ||||
\(479\) | 12.7632 | + | 22.1066i | 0.583167 | + | 1.01008i | 0.995101 | + | 0.0988618i | \(0.0315202\pi\) |
−0.411934 | + | 0.911214i | \(0.635147\pi\) | |||||||
\(480\) | −1.14914 | −0.0524510 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.84117 | 0.174960 | ||||||||
\(483\) | −7.31431 | − | 12.6688i | −0.332813 | − | 0.576449i | ||||
\(484\) | 18.8790 | + | 32.6993i | 0.858135 | + | 1.48633i | ||||
\(485\) | −1.69053 | + | 2.92808i | −0.0767630 | + | 0.132957i | ||||
\(486\) | 0.445042 | 0.0201875 | ||||||||
\(487\) | −8.00365 | + | 13.8627i | −0.362680 | + | 0.628180i | −0.988401 | − | 0.151867i | \(-0.951471\pi\) |
0.625721 | + | 0.780047i | \(0.284805\pi\) | |||||||
\(488\) | −7.20440 | + | 12.4784i | −0.326128 | + | 0.564870i | ||||
\(489\) | 8.63102 | 0.390308 | ||||||||
\(490\) | −0.215816 | + | 0.373805i | −0.00974958 | + | 0.0168868i | ||||
\(491\) | −10.3693 | − | 17.9601i | −0.467959 | − | 0.810528i | 0.531371 | − | 0.847139i | \(-0.321677\pi\) |
−0.999330 | + | 0.0366110i | \(0.988344\pi\) | |||||||
\(492\) | 0.400969 | + | 0.694498i | 0.0180771 | + | 0.0313104i | ||||
\(493\) | 22.5797 | 1.01694 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.39612 | −0.0627511 | ||||||||
\(496\) | −7.51022 | − | 13.0081i | −0.337219 | − | 0.584080i | ||||
\(497\) | 5.01291 | + | 8.68261i | 0.224860 | + | 0.389468i | ||||
\(498\) | 2.26659 | − | 3.92586i | 0.101569 | − | 0.175922i | ||||
\(499\) | −8.06770 | −0.361160 | −0.180580 | − | 0.983560i | \(-0.557797\pi\) | ||||
−0.180580 | + | 0.983560i | \(0.557797\pi\) | |||||||
\(500\) | 2.21164 | − | 3.83067i | 0.0989074 | − | 0.171313i | ||||
\(501\) | −4.73490 | + | 8.20108i | −0.211540 | + | 0.366397i | ||||
\(502\) | −1.69202 | −0.0755186 | ||||||||
\(503\) | 15.1211 | − | 26.1905i | 0.674216 | − | 1.16778i | −0.302481 | − | 0.953155i | \(-0.597815\pi\) |
0.976697 | − | 0.214622i | \(-0.0688518\pi\) | |||||||
\(504\) | 1.48307 | + | 2.56876i | 0.0660614 | + | 0.114422i | ||||
\(505\) | −0.668227 | − | 1.15740i | −0.0297357 | − | 0.0515037i | ||||
\(506\) | 20.9933 | 0.933266 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.4601 | −0.863403 | ||||||||
\(509\) | −8.02475 | − | 13.8993i | −0.355691 | − | 0.616075i | 0.631545 | − | 0.775339i | \(-0.282421\pi\) |
−0.987236 | + | 0.159264i | \(0.949088\pi\) | |||||||
\(510\) | −0.208947 | − | 0.361908i | −0.00925235 | − | 0.0160255i | ||||
\(511\) | −6.44839 | + | 11.1689i | −0.285260 | + | 0.494085i | ||||
\(512\) | 22.9119 | 1.01257 | ||||||||
\(513\) | −2.79105 | + | 4.83424i | −0.123228 | + | 0.213437i | ||||
\(514\) | 4.58306 | − | 7.93810i | 0.202150 | − | 0.350135i | ||||
\(515\) | −3.39745 | −0.149710 | ||||||||
\(516\) | 1.54407 | − | 2.67441i | 0.0679740 | − | 0.117734i | ||||
\(517\) | 19.0374 | + | 32.9737i | 0.837262 | + | 1.45018i | ||||
\(518\) | −1.24751 | − | 2.16075i | −0.0548125 | − | 0.0949381i | ||||
\(519\) | 4.77479 | 0.209590 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.69309 | −0.117986 | −0.0589931 | − | 0.998258i | \(-0.518789\pi\) | ||||
−0.0589931 | + | 0.998258i | \(0.518789\pi\) | |||||||
\(522\) | 1.32155 | + | 2.28900i | 0.0578428 | + | 0.100187i | ||||
\(523\) | −17.6978 | − | 30.6535i | −0.773872 | − | 1.34039i | −0.935426 | − | 0.353522i | \(-0.884984\pi\) |
0.161554 | − | 0.986864i | \(-0.448349\pi\) | |||||||
\(524\) | 0.817667 | − | 1.41624i | 0.0357200 | − | 0.0618688i | ||||
\(525\) | −8.65817 | −0.377874 | ||||||||
\(526\) | −0.0740400 | + | 0.128241i | −0.00322830 | + | 0.00559157i | ||||
\(527\) | 10.0157 | − | 17.3478i | 0.436292 | − | 0.755680i | ||||
\(528\) | 16.1153 | 0.701328 | ||||||||
\(529\) | −23.3180 | + | 40.3879i | −1.01382 | + | 1.75600i | ||||
\(530\) | −0.0583105 | − | 0.100997i | −0.00253285 | − | 0.00438702i | ||||
\(531\) | 6.85086 | + | 11.8660i | 0.297302 | + | 0.514942i | ||||
\(532\) | −17.6329 | −0.764485 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.0609989 | 0.00263968 | ||||||||
\(535\) | −1.58277 | − | 2.74144i | −0.0684291 | − | 0.118523i | ||||
\(536\) | 5.04288 | + | 8.73452i | 0.217819 | + | 0.377274i | ||||
\(537\) | −1.71768 | + | 2.97510i | −0.0741232 | + | 0.128385i | ||||
\(538\) | 12.1511 | 0.523870 | ||||||||
\(539\) | 11.0990 | − | 19.2241i | 0.478069 | − | 0.828040i | ||||
\(540\) | −0.222521 | + | 0.385418i | −0.00957578 | + | 0.0165857i | ||||
\(541\) | −34.7338 | −1.49332 | −0.746660 | − | 0.665205i | \(-0.768344\pi\) | ||||
−0.746660 | + | 0.665205i | \(0.768344\pi\) | |||||||
\(542\) | −6.22737 | + | 10.7861i | −0.267488 | + | 0.463303i | ||||
\(543\) | 6.74309 | + | 11.6794i | 0.289374 | + | 0.501210i | ||||
\(544\) | 8.84481 | + | 15.3197i | 0.379218 | + | 0.656825i | ||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1183 | −1.11674 | −0.558368 | − | 0.829593i | \(-0.688572\pi\) | ||||
−0.558368 | + | 0.829593i | \(0.688572\pi\) | |||||||
\(548\) | −8.60268 | − | 14.9003i | −0.367488 | − | 0.636508i | ||||
\(549\) | 4.25786 | + | 7.37484i | 0.181721 | + | 0.314750i | ||||
\(550\) | 6.21260 | − | 10.7605i | 0.264906 | − | 0.458831i | ||||
\(551\) | −33.1521 | −1.41233 | ||||||||
\(552\) | 7.05980 | − | 12.2279i | 0.300485 | − | 0.520456i | ||||
\(553\) | −3.90462 | + | 6.76299i | −0.166041 | + | 0.287592i | ||||
\(554\) | −0.936017 | −0.0397676 | ||||||||
\(555\) | 0.394928 | − | 0.684035i | 0.0167638 | − | 0.0290357i | ||||
\(556\) | −3.68718 | − | 6.38638i | −0.156371 | − | 0.270843i | ||||
\(557\) | −12.3874 | − | 21.4556i | −0.524871 | − | 0.909103i | −0.999581 | − | 0.0289605i | \(-0.990780\pi\) |
0.474710 | − | 0.880142i | \(-0.342553\pi\) | |||||||
\(558\) | 2.34481 | 0.0992639 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.23431 | −0.0521590 | ||||||||
\(561\) | 10.7458 | + | 18.6122i | 0.453687 | + | 0.785809i | ||||
\(562\) | −6.06033 | − | 10.4968i | −0.255640 | − | 0.442781i | ||||
\(563\) | −2.63049 | + | 4.55614i | −0.110862 | + | 0.192019i | −0.916118 | − | 0.400909i | \(-0.868694\pi\) |
0.805256 | + | 0.592927i | \(0.202028\pi\) | |||||||
\(564\) | 12.1371 | 0.511063 | ||||||||
\(565\) | −0.202243 | + | 0.350294i | −0.00850841 | + | 0.0147370i | ||||
\(566\) | −1.17576 | + | 2.03648i | −0.0494209 | + | 0.0855994i | ||||
\(567\) | 1.75302 | 0.0736199 | ||||||||
\(568\) | −4.83848 | + | 8.38049i | −0.203018 | + | 0.351638i | ||||
\(569\) | 16.8729 | + | 29.2248i | 0.707350 | + | 1.22517i | 0.965837 | + | 0.259151i | \(0.0834427\pi\) |
−0.258487 | + | 0.966015i | \(0.583224\pi\) | |||||||
\(570\) | 0.306782 | + | 0.531362i | 0.0128497 | + | 0.0222563i | ||||
\(571\) | 23.0887 | 0.966234 | 0.483117 | − | 0.875556i | \(-0.339505\pi\) | ||||
0.483117 | + | 0.875556i | \(0.339505\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.30127 | −0.0543615 | ||||||||
\(574\) | −0.173604 | − | 0.300690i | −0.00724607 | − | 0.0125506i | ||||
\(575\) | 20.6075 | + | 35.6933i | 0.859393 | + | 1.48851i | ||||
\(576\) | 1.81551 | − | 3.14456i | 0.0756463 | − | 0.131023i | ||||
\(577\) | 3.57002 | 0.148622 | 0.0743110 | − | 0.997235i | \(-0.476324\pi\) | ||||
0.0743110 | + | 0.997235i | \(0.476324\pi\) | |||||||
\(578\) | 0.566376 | − | 0.980992i | 0.0235581 | − | 0.0408039i | ||||
\(579\) | 4.59783 | − | 7.96368i | 0.191079 | − | 0.330959i | ||||
\(580\) | −2.64310 | −0.109749 | ||||||||
\(581\) | 8.92812 | − | 15.4640i | 0.370401 | − | 0.641553i | ||||
\(582\) | 3.04623 | + | 5.27622i | 0.126270 | + | 0.218706i | ||||
\(583\) | 2.99880 | + | 5.19408i | 0.124198 | + | 0.215117i | ||||
\(584\) | −12.4480 | −0.515103 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5362 | 0.600484 | ||||||||
\(587\) | 5.73125 | + | 9.92682i | 0.236554 | + | 0.409724i | 0.959723 | − | 0.280947i | \(-0.0906486\pi\) |
−0.723169 | + | 0.690671i | \(0.757315\pi\) | |||||||
\(588\) | −3.53803 | − | 6.12805i | −0.145906 | − | 0.252717i | ||||
\(589\) | −14.7054 | + | 25.4704i | −0.605924 | + | 1.04949i | ||||
\(590\) | 1.50604 | 0.0620027 | ||||||||
\(591\) | −2.05615 | + | 3.56136i | −0.0845789 | + | 0.146495i | ||||
\(592\) | −4.55861 | + | 7.89574i | −0.187358 | + | 0.324513i | ||||
\(593\) | −21.8538 | −0.897430 | −0.448715 | − | 0.893675i | \(-0.648118\pi\) | ||||
−0.448715 | + | 0.893675i | \(0.648118\pi\) | |||||||
\(594\) | −1.25786 | + | 2.17869i | −0.0516108 | + | 0.0893926i | ||||
\(595\) | −0.823044 | − | 1.42555i | −0.0337415 | − | 0.0584420i | ||||
\(596\) | −13.8644 | − | 24.0139i | −0.567909 | − | 0.983647i | ||||
\(597\) | −24.7724 | −1.01387 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.0573 | 1.10553 | 0.552765 | − | 0.833337i | \(-0.313573\pi\) | ||||
0.552765 | + | 0.833337i | \(0.313573\pi\) | |||||||
\(600\) | −4.17845 | − | 7.23728i | −0.170584 | − | 0.295461i | ||||
\(601\) | −5.43900 | − | 9.42063i | −0.221861 | − | 0.384275i | 0.733512 | − | 0.679677i | \(-0.237880\pi\) |
−0.955373 | + | 0.295401i | \(0.904547\pi\) | |||||||
\(602\) | −0.668522 | + | 1.15791i | −0.0272469 | + | 0.0471931i | ||||
\(603\) | 5.96077 | 0.242741 | ||||||||
\(604\) | −3.31067 | + | 5.73424i | −0.134709 | + | 0.233323i | ||||
\(605\) | 2.58761 | − | 4.48188i | 0.105201 | − | 0.182214i | ||||
\(606\) | −2.40821 | −0.0978267 | ||||||||
\(607\) | 14.8180 | − | 25.6655i | 0.601443 | − | 1.04173i | −0.391160 | − | 0.920323i | \(-0.627926\pi\) |
0.992603 | − | 0.121407i | \(-0.0387405\pi\) | |||||||
\(608\) | −12.9862 | − | 22.4927i | −0.526660 | − | 0.912201i | ||||
\(609\) | 5.20560 | + | 9.01636i | 0.210941 | + | 0.365361i | ||||
\(610\) | 0.936017 | 0.0378982 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.85086 | 0.276929 | ||||||||
\(613\) | −5.11715 | − | 8.86317i | −0.206680 | − | 0.357980i | 0.743987 | − | 0.668194i | \(-0.232933\pi\) |
−0.950667 | + | 0.310214i | \(0.899599\pi\) | |||||||
\(614\) | 4.61984 | + | 8.00180i | 0.186442 | + | 0.322926i | ||||
\(615\) | 0.0549581 | − | 0.0951903i | 0.00221613 | − | 0.00383844i | ||||
\(616\) | −16.7670 | −0.675563 | ||||||||
\(617\) | −13.1414 | + | 22.7615i | −0.529052 | + | 0.916345i | 0.470374 | + | 0.882467i | \(0.344119\pi\) |
−0.999426 | + | 0.0338776i | \(0.989214\pi\) | |||||||
\(618\) | −3.06100 | + | 5.30181i | −0.123131 | + | 0.213270i | ||||
\(619\) | 29.0834 | 1.16896 | 0.584479 | − | 0.811408i | \(-0.301299\pi\) | ||||
0.584479 | + | 0.811408i | \(0.301299\pi\) | |||||||
\(620\) | −1.17241 | + | 2.03067i | −0.0470850 | + | 0.0815536i | ||||
\(621\) | −4.17241 | − | 7.22682i | −0.167433 | − | 0.290002i | ||||
\(622\) | 2.51477 | + | 4.35571i | 0.100833 | + | 0.174648i | ||||
\(623\) | 0.240275 | 0.00962641 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0887 | 0.963549 | ||||||||
\(626\) | 0.950550 | + | 1.64640i | 0.0379916 | + | 0.0658034i | ||||
\(627\) | −15.7772 | − | 27.3270i | −0.630082 | − | 1.09133i | ||||
\(628\) | −4.39493 | + | 7.61224i | −0.175377 | + | 0.303761i | ||||
\(629\) | −12.1588 | −0.484804 | ||||||||
\(630\) | 0.0963427 | − | 0.166870i | 0.00383839 | − | 0.00664828i | ||||
\(631\) | −12.7240 | + | 22.0386i | −0.506535 | + | 0.877344i | 0.493436 | + | 0.869782i | \(0.335741\pi\) |
−0.999971 | + | 0.00756243i | \(0.997593\pi\) | |||||||
\(632\) | −7.53750 | −0.299826 | ||||||||
\(633\) | 2.96950 | − | 5.14333i | 0.118027 | − | 0.204429i | ||||
\(634\) | −3.44408 | − | 5.96533i | −0.136782 | − | 0.236913i | ||||
\(635\) | 1.33363 | + | 2.30992i | 0.0529236 | + | 0.0916664i | ||||
\(636\) | 1.91185 | 0.0758099 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.9409 | −0.591517 | ||||||||
\(639\) | 2.85958 | + | 4.95295i | 0.113123 | + | 0.195935i | ||||
\(640\) | −1.34870 | − | 2.33602i | −0.0533120 | − | 0.0923391i | ||||
\(641\) | 13.3705 | − | 23.1583i | 0.528102 | − | 0.914699i | −0.471361 | − | 0.881940i | \(-0.656237\pi\) |
0.999463 | − | 0.0327590i | \(-0.0104294\pi\) | |||||||
\(642\) | −5.70410 | −0.225123 | ||||||||
\(643\) | 16.4807 | − | 28.5454i | 0.649935 | − | 1.12572i | −0.333203 | − | 0.942855i | \(-0.608130\pi\) |
0.983138 | − | 0.182865i | \(-0.0585371\pi\) | |||||||
\(644\) | 13.1799 | − | 22.8283i | 0.519362 | − | 0.899562i | ||||
\(645\) | −0.423272 | −0.0166663 | ||||||||
\(646\) | 4.72252 | − | 8.17965i | 0.185805 | − | 0.321824i | ||||
\(647\) | −17.2473 | − | 29.8732i | −0.678060 | − | 1.17443i | −0.975564 | − | 0.219714i | \(-0.929487\pi\) |
0.297504 | − | 0.954721i | \(-0.403846\pi\) | |||||||
\(648\) | 0.846011 | + | 1.46533i | 0.0332344 | + | 0.0575637i | ||||
\(649\) | −77.4529 | −3.04029 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.23623 | 0.361996 | ||||||||
\(652\) | 7.77628 | + | 13.4689i | 0.304543 | + | 0.527483i | ||||
\(653\) | −18.0758 | − | 31.3083i | −0.707362 | − | 1.22519i | −0.965832 | − | 0.259167i | \(-0.916552\pi\) |
0.258471 | − | 0.966019i | \(-0.416781\pi\) | |||||||
\(654\) | −2.70291 | + | 4.68157i | −0.105692 | + | 0.183064i | ||||
\(655\) | −0.224144 | −0.00875805 | ||||||||
\(656\) | −0.634375 | + | 1.09877i | −0.0247682 | + | 0.0428997i | ||||
\(657\) | −3.67845 | + | 6.37126i | −0.143510 | + | 0.248566i | ||||
\(658\) | −5.25487 | −0.204856 | ||||||||
\(659\) | 3.40850 | − | 5.90370i | 0.132776 | − | 0.229975i | −0.791969 | − | 0.610561i | \(-0.790944\pi\) |
0.924746 | + | 0.380585i | \(0.124277\pi\) | |||||||
\(660\) | −1.25786 | − | 2.17869i | −0.0489623 | − | 0.0848052i | ||||
\(661\) | 5.44720 | + | 9.43482i | 0.211871 | + | 0.366972i | 0.952300 | − | 0.305163i | \(-0.0987109\pi\) |
−0.740429 | + | 0.672135i | \(0.765378\pi\) | |||||||
\(662\) | 2.70065 | 0.104964 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.2349 | 0.668844 | ||||||||
\(665\) | 1.20841 | + | 2.09304i | 0.0468603 | + | 0.0811645i | ||||
\(666\) | −0.711636 | − | 1.23259i | −0.0275753 | − | 0.0477619i | ||||
\(667\) | 24.7799 | − | 42.9201i | 0.959483 | − | 1.66187i | ||||
\(668\) | −17.0640 | −0.660225 | ||||||||
\(669\) | −7.10052 | + | 12.2985i | −0.274522 | + | 0.475486i | ||||
\(670\) | 0.327593 | − | 0.567407i | 0.0126560 | − | 0.0219209i | ||||
\(671\) | −48.1377 | −1.85833 | ||||||||
\(672\) | −4.07822 | + | 7.06368i | −0.157321 | + | 0.272488i | ||||
\(673\) | −10.3693 | − | 17.9601i | −0.399706 | − | 0.692311i | 0.593983 | − | 0.804477i | \(-0.297554\pi\) |
−0.993689 | + | 0.112166i | \(0.964221\pi\) | |||||||
\(674\) | −2.69783 | − | 4.67277i | −0.103916 | − | 0.179988i | ||||
\(675\) | −4.93900 | −0.190102 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5786 | −0.983067 | −0.491534 | − | 0.870859i | \(-0.663564\pi\) | ||||
−0.491534 | + | 0.870859i | \(0.663564\pi\) | |||||||
\(678\) | 0.364429 | + | 0.631209i | 0.0139958 | + | 0.0242414i | ||||
\(679\) | 11.9991 | + | 20.7830i | 0.460483 | + | 0.797580i | ||||
\(680\) | 0.794405 | − | 1.37595i | 0.0304640 | − | 0.0527653i | ||||
\(681\) | 16.0073 | 0.613401 | ||||||||
\(682\) | −6.62737 | + | 11.4789i | −0.253775 | + | 0.439552i | ||||
\(683\) | −10.8155 | + | 18.7330i | −0.413844 | + | 0.716799i | −0.995306 | − | 0.0967744i | \(-0.969147\pi\) |
0.581462 | + | 0.813573i | \(0.302481\pi\) | |||||||
\(684\) | −10.0586 | −0.384600 | ||||||||
\(685\) | −1.17911 | + | 2.04228i | −0.0450516 | + | 0.0780316i | ||||
\(686\) | 4.26241 | + | 7.38272i | 0.162740 | + | 0.281873i | ||||
\(687\) | −0.920583 | − | 1.59450i | −0.0351224 | − | 0.0608339i | ||||
\(688\) | 4.88577 | 0.186268 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.917231 | −0.0349184 | ||||||||
\(691\) | −1.31498 | − | 2.27761i | −0.0500242 | − | 0.0866444i | 0.839929 | − | 0.542696i | \(-0.182596\pi\) |
−0.889953 | + | 0.456052i | \(0.849263\pi\) | |||||||
\(692\) | 4.30194 | + | 7.45117i | 0.163535 | + | 0.283251i | ||||
\(693\) | −4.95473 | + | 8.58185i | −0.188215 | + | 0.325997i | ||||
\(694\) | 10.3026 | 0.391081 | ||||||||
\(695\) | −0.505377 | + | 0.875338i | −0.0191700 | + | 0.0332035i | ||||
\(696\) | −5.02446 | + | 8.70262i | −0.190452 | + | 0.329872i | ||||
\(697\) | −1.69202 | −0.0640899 | ||||||||
\(698\) | 4.93900 | − | 8.55460i | 0.186944 | − | 0.323796i | ||||
\(699\) | 11.7126 | + | 20.2868i | 0.443011 | + | 0.767318i | ||||
\(700\) | −7.80074 | − | 13.5113i | −0.294840 | − | 0.510678i | ||||
\(701\) | 40.0925 | 1.51427 | 0.757136 | − | 0.653258i | \(-0.226598\pi\) | ||||
0.757136 | + | 0.653258i | \(0.226598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.8519 | 0.673298 | ||||||||
\(704\) | 10.2627 | + | 17.7755i | 0.386790 | + | 0.669941i | ||||
\(705\) | −0.831773 | − | 1.44067i | −0.0313264 | − | 0.0542589i | ||||
\(706\) | 1.12833 | − | 1.95433i | 0.0424654 | − | 0.0735523i | ||||
\(707\) | −9.48593 | −0.356755 | ||||||||
\(708\) | −12.3448 | + | 21.3818i | −0.463947 | + | 0.803579i | ||||
\(709\) | −11.6048 | + | 20.1002i | −0.435829 | + | 0.754877i | −0.997363 | − | 0.0725761i | \(-0.976878\pi\) |
0.561534 | + | 0.827454i | \(0.310211\pi\) | |||||||
\(710\) | 0.628630 | 0.0235921 | ||||||||
\(711\) | −2.22737 | + | 3.85791i | −0.0835327 | + | 0.144683i | ||||
\(712\) | 0.115957 | + | 0.200844i | 0.00434567 | + | 0.00752693i | ||||
\(713\) | −21.9834 | − | 38.0763i | −0.823284 | − | 1.42597i | ||||
\(714\) | −2.96615 | −0.111005 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.19029 | −0.231342 | ||||||||
\(717\) | −7.30074 | − | 12.6453i | −0.272651 | − | 0.472246i | ||||
\(718\) | 3.71044 | + | 6.42667i | 0.138472 | + | 0.239841i | ||||
\(719\) | 13.0073 | − | 22.5293i | 0.485090 | − | 0.840201i | −0.514763 | − | 0.857333i | \(-0.672120\pi\) |
0.999853 | + | 0.0171315i | \(0.00545340\pi\) | |||||||
\(720\) | −0.704103 | −0.0262404 | ||||||||
\(721\) | −12.0573 | + | 20.8838i | −0.449036 | + | 0.777754i | ||||
\(722\) | −2.70583 | + | 4.68664i | −0.100701 | + | 0.174419i | ||||
\(723\) | 8.63102 | 0.320991 | ||||||||
\(724\) | −12.1506 | + | 21.0455i | −0.451575 | + | 0.782151i | ||||
\(725\) | −14.6664 | − | 25.4029i | −0.544695 | − | 0.943440i | ||||
\(726\) | −4.66272 | − | 8.07607i | −0.173050 | − | 0.299731i | ||||
\(727\) | −16.5472 | −0.613701 | −0.306851 | − | 0.951758i | \(-0.599275\pi\) | ||||
−0.306851 | + | 0.951758i | \(0.599275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.404321 | + | 0.700305i | 0.0149646 | + | 0.0259194i | ||||
\(731\) | 3.25786 | + | 5.64279i | 0.120496 | + | 0.208706i | ||||
\(732\) | −7.67241 | + | 13.2890i | −0.283580 | + | 0.491176i | ||||
\(733\) | 18.8750 | 0.697165 | 0.348582 | − | 0.937278i | \(-0.386663\pi\) | ||||
0.348582 | + | 0.937278i | \(0.386663\pi\) | |||||||
\(734\) | 0.262414 | − | 0.454514i | 0.00968586 | − | 0.0167764i | ||||
\(735\) | −0.484935 | + | 0.839931i | −0.0178871 | + | 0.0309813i | ||||
\(736\) | 38.8267 | 1.43117 | ||||||||
\(737\) | −16.8475 | + | 29.1807i | −0.620586 | + | 1.07489i | ||||
\(738\) | −0.0990311 | − | 0.171527i | −0.00364539 | − | 0.00631399i | ||||
\(739\) | −23.6619 | − | 40.9837i | −0.870419 | − | 1.50761i | −0.861564 | − | 0.507649i | \(-0.830515\pi\) |
−0.00885483 | − | 0.999961i | \(-0.502819\pi\) | |||||||
\(740\) | 1.42327 | 0.0523205 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.827757 | −0.0303879 | ||||||||
\(743\) | 4.44385 | + | 7.69697i | 0.163029 | + | 0.282374i | 0.935954 | − | 0.352124i | \(-0.114540\pi\) |
−0.772925 | + | 0.634498i | \(0.781207\pi\) | |||||||
\(744\) | 4.45742 | + | 7.72048i | 0.163417 | + | 0.283046i | ||||
\(745\) | −1.90030 | + | 3.29142i | −0.0696218 | + | 0.120588i | ||||
\(746\) | −13.3924 | −0.490331 | ||||||||
\(747\) | 5.09299 | − | 8.82132i | 0.186343 | − | 0.322755i | ||||
\(748\) | −19.3632 | + | 33.5381i | −0.707990 | + | 1.22627i | ||||
\(749\) | −22.4685 | −0.820980 | ||||||||
\(750\) | −0.546229 | + | 0.946096i | −0.0199455 | + | 0.0345466i | ||||
\(751\) | −0.355404 | − | 0.615578i | −0.0129689 | − | 0.0224627i | 0.859468 | − | 0.511189i | \(-0.170795\pi\) |
−0.872437 | + | 0.488727i | \(0.837462\pi\) | |||||||
\(752\) | 9.60106 | + | 16.6295i | 0.350114 | + | 0.606416i | ||||
\(753\) | −3.80194 | −0.138550 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.907542 | 0.0330288 | ||||||||
\(756\) | 1.57942 | + | 2.73563i | 0.0574428 | + | 0.0994939i | ||||
\(757\) | −4.89277 | − | 8.47453i | −0.177831 | − | 0.308012i | 0.763306 | − | 0.646037i | \(-0.223575\pi\) |
−0.941137 | + | 0.338025i | \(0.890241\pi\) | |||||||
\(758\) | 4.26420 | − | 7.38581i | 0.154883 | − | 0.268265i | ||||
\(759\) | 47.1715 | 1.71222 | ||||||||
\(760\) | −1.16637 | + | 2.02021i | −0.0423086 | + | 0.0732806i | ||||
\(761\) | 9.44049 | − | 16.3514i | 0.342218 | − | 0.592738i | −0.642627 | − | 0.766180i | \(-0.722155\pi\) |
0.984844 | + | 0.173441i | \(0.0554887\pi\) | |||||||
\(762\) | 4.80625 | 0.174112 | ||||||||
\(763\) | −10.6468 | + | 18.4407i | −0.385438 | + | 0.667599i | ||||
\(764\) | −1.17241 | − | 2.03067i | −0.0424162 | − | 0.0734670i | ||||
\(765\) | −0.469501 | − | 0.813199i | −0.0169748 | − | 0.0294013i | ||||
\(766\) | −6.84846 | −0.247445 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.40150 | 0.0866567 | ||||||||
\(769\) | 6.21744 | + | 10.7689i | 0.224207 | + | 0.388337i | 0.956081 | − | 0.293102i | \(-0.0946876\pi\) |
−0.731875 | + | 0.681439i | \(0.761354\pi\) | |||||||
\(770\) | 0.544605 | + | 0.943284i | 0.0196262 | + | 0.0339936i | ||||
\(771\) | 10.2981 | − | 17.8368i | 0.370875 | − | 0.642375i | ||||
\(772\) | 16.5700 | 0.596368 | ||||||||
\(773\) | −22.8373 | + | 39.5553i | −0.821400 | + | 1.42271i | 0.0832399 | + | 0.996530i | \(0.473473\pi\) |
−0.904640 | + | 0.426177i | \(0.859860\pi\) | |||||||
\(774\) | −0.381355 | + | 0.660525i | −0.0137075 | + | 0.0237421i | ||||
\(775\) | −26.0224 | −0.934751 | ||||||||
\(776\) | −11.5816 | + | 20.0599i | −0.415754 | + | 0.720107i | ||||
\(777\) | −2.80313 | − | 4.85517i | −0.100562 | − | 0.174178i | ||||
\(778\) | 5.34750 | + | 9.26215i | 0.191717 | + | 0.332064i | ||||
\(779\) | 2.48427 | 0.0890082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.3293 | −1.15683 | ||||||||
\(782\) | 7.05980 | + | 12.2279i | 0.252458 | + | 0.437270i | ||||
\(783\) | 2.96950 | + | 5.14333i | 0.106121 | + | 0.183807i | ||||
\(784\) | 5.59754 | − | 9.69522i | 0.199912 | − | 0.346258i | ||||
\(785\) | 1.20477 | 0.0430000 | ||||||||
\(786\) | −0.201947 | + | 0.349783i | −0.00720322 | + | 0.0124763i | ||||
\(787\) | 2.25936 | − | 3.91332i | 0.0805374 | − | 0.139495i | −0.822944 | − | 0.568123i | \(-0.807670\pi\) |
0.903481 | + | 0.428628i | \(0.141003\pi\) | |||||||
\(788\) | −7.41013 | −0.263975 | ||||||||
\(789\) | −0.166366 | + | 0.288155i | −0.00592280 | + | 0.0102586i | ||||
\(790\) | 0.244824 | + | 0.424047i | 0.00871044 | + | 0.0150869i | ||||
\(791\) | 1.43548 | + | 2.48633i | 0.0510400 | + | 0.0884038i | ||||
\(792\) | −9.56465 | −0.339865 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.1739 | 0.467524 | ||||||||
\(795\) | −0.131023 | − | 0.226938i | −0.00464689 | − | 0.00804865i | ||||
\(796\) | −22.3192 | − | 38.6579i | −0.791082 | − | 1.37019i | ||||
\(797\) | 14.3696 | − | 24.8888i | 0.508996 | − | 0.881607i | −0.490949 | − | 0.871188i | \(-0.663350\pi\) |
0.999946 | − | 0.0104193i | \(-0.00331662\pi\) | |||||||
\(798\) | 4.35498 | 0.154165 | ||||||||
\(799\) | −12.8041 | + | 22.1773i | −0.452976 | + | 0.784578i | ||||
\(800\) | 11.4901 | − | 19.9014i | 0.406235 | − | 0.703620i | ||||
\(801\) | 0.137063 | 0.00484289 | ||||||||
\(802\) | 4.69591 | − | 8.13355i | 0.165818 | − | 0.287206i | ||||
\(803\) | −20.7935 | − | 36.0154i | −0.733787 | − | 1.27096i | ||||
\(804\) | 5.37047 | + | 9.30193i | 0.189402 | + | 0.328054i | ||||
\(805\) | −3.61297 | −0.127341 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.3032 | 0.961118 | ||||||||
\(808\) | −4.57792 | − | 7.92920i | −0.161051 | − | 0.278948i | ||||
\(809\) | −2.71446 | − | 4.70158i | −0.0954352 | − | 0.165299i | 0.814355 | − | 0.580367i | \(-0.197091\pi\) |
−0.909790 | + | 0.415069i | \(0.863758\pi\) | |||||||
\(810\) | 0.0549581 | − | 0.0951903i | 0.00193103 | − | 0.00334465i | ||||
\(811\) | 0.629104 | 0.0220908 | 0.0110454 | − | 0.999939i | \(-0.496484\pi\) | ||||
0.0110454 | + | 0.999939i | \(0.496484\pi\) | |||||||
\(812\) | −9.38016 | + | 16.2469i | −0.329179 | + | 0.570155i | ||||
\(813\) | −13.9928 | + | 24.2362i | −0.490748 | + | 0.850000i | ||||
\(814\) | 8.04546 | 0.281993 | ||||||||
\(815\) | 1.06584 | − | 1.84609i | 0.0373349 | − | 0.0646659i | ||||
\(816\) | 5.41939 | + | 9.38665i | 0.189716 | + | 0.328599i | ||||
\(817\) | −4.78328 | − | 8.28489i | −0.167346 | − | 0.289852i | ||||
\(818\) | −16.0315 | −0.560527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.198062 | 0.00691663 | ||||||||
\(821\) | −18.1320 | − | 31.4055i | −0.632811 | − | 1.09606i | −0.986975 | − | 0.160877i | \(-0.948568\pi\) |
0.354164 | − | 0.935183i | \(-0.384765\pi\) | |||||||
\(822\) | 2.12469 | + | 3.68006i | 0.0741069 | + | 0.128357i | ||||
\(823\) | −20.8698 | + | 36.1476i | −0.727476 | + | 1.26002i | 0.230471 | + | 0.973079i | \(0.425973\pi\) |
−0.957947 | + | 0.286946i | \(0.907360\pi\) | |||||||
\(824\) | −23.2755 | −0.810839 | ||||||||
\(825\) | 13.9596 | − | 24.1787i | 0.486010 | − | 0.841794i | ||||
\(826\) | 5.34481 | − | 9.25749i | 0.185970 | − | 0.322109i | ||||
\(827\) | 38.1997 | 1.32833 | 0.664167 | − | 0.747584i | \(-0.268786\pi\) | ||||
0.664167 | + | 0.747584i | \(0.268786\pi\) | |||||||
\(828\) | 7.51842 | − | 13.0223i | 0.261283 | − | 0.452556i | ||||
\(829\) | −7.98941 | − | 13.8381i | −0.277484 | − | 0.480616i | 0.693275 | − | 0.720673i | \(-0.256167\pi\) |
−0.970759 | + | 0.240057i | \(0.922834\pi\) | |||||||
\(830\) | −0.559802 | − | 0.969606i | −0.0194310 | − | 0.0336555i | ||||
\(831\) | −2.10321 | −0.0729596 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.9299 | 0.517290 | ||||||||
\(834\) | 0.910658 | + | 1.57731i | 0.0315335 | + | 0.0546176i | ||||
\(835\) | 1.16942 | + | 2.02550i | 0.0404696 | + | 0.0700953i | ||||
\(836\) | 28.4296 | − | 49.2415i | 0.983259 | − | 1.70305i | ||||
\(837\) | 5.26875 | 0.182115 | ||||||||
\(838\) | −1.32813 | + | 2.30038i | −0.0458793 | + | 0.0794653i | ||||
\(839\) | 2.31940 | − | 4.01731i | 0.0800744 | − | 0.138693i | −0.823207 | − | 0.567741i | \(-0.807818\pi\) |
0.903282 | + | 0.429048i | \(0.141151\pi\) | |||||||
\(840\) | 0.732578 | 0.0252763 | ||||||||
\(841\) | −3.13587 | + | 5.43148i | −0.108133 | + | 0.187292i | ||||
\(842\) | 0.466280 | + | 0.807620i | 0.0160691 | + | 0.0278324i | ||||
\(843\) | −13.6174 | − | 23.5861i | −0.469010 | − | 0.812349i | ||||
\(844\) | 10.7017 | 0.368368 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.99761 | −0.103060 | ||||||||
\(847\) | −18.3665 | − | 31.8116i | −0.631079 | − | 1.09306i | ||||
\(848\) | 1.51238 | + | 2.61951i | 0.0519352 | + | 0.0899545i | ||||
\(849\) | −2.64191 | + | 4.57592i | −0.0906700 | + | 0.157045i | ||||
\(850\) | 8.35690 | 0.286639 | ||||||||
\(851\) | −13.3436 | + | 23.1118i | −0.457413 | + | 0.792263i | ||||
\(852\) | −5.15279 | + | 8.92490i | −0.176532 | + | 0.305762i | ||||
\(853\) | 18.3884 | 0.629605 | 0.314803 | − | 0.949157i | \(-0.398062\pi\) | ||||
0.314803 | + | 0.949157i | \(0.398062\pi\) | |||||||
\(854\) | 3.32185 | − | 5.75361i | 0.113671 | − | 0.196884i | ||||
\(855\) | 0.689333 | + | 1.19396i | 0.0235747 | + | 0.0408326i | ||||
\(856\) | −10.8433 | − | 18.7812i | −0.370617 | − | 0.641928i | ||||
\(857\) | 28.1849 | 0.962778 | 0.481389 | − | 0.876507i | \(-0.340132\pi\) | ||||
0.481389 | + | 0.876507i | \(0.340132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.3957 | 1.13944 | 0.569722 | − | 0.821837i | \(-0.307051\pi\) | ||||
0.569722 | + | 0.821837i | \(0.307051\pi\) | |||||||
\(860\) | −0.381355 | − | 0.660525i | −0.0130041 | − | 0.0225237i | ||||
\(861\) | −0.390084 | − | 0.675645i | −0.0132940 | − | 0.0230259i | ||||
\(862\) | 0.642145 | − | 1.11223i | 0.0218715 | − | 0.0378826i | ||||
\(863\) | −43.0640 | −1.46592 | −0.732958 | − | 0.680274i | \(-0.761861\pi\) | ||||
−0.732958 | + | 0.680274i | \(0.761861\pi\) | |||||||
\(864\) | −2.32640 | + | 4.02944i | −0.0791456 | + | 0.137084i | ||||
\(865\) | 0.589638 | − | 1.02128i | 0.0200483 | − | 0.0347247i | ||||
\(866\) | −5.62910 | −0.191285 | ||||||||
\(867\) | 1.27263 | − | 2.20427i | 0.0432209 | − | 0.0748609i | ||||
\(868\) | 8.32155 | + | 14.4134i | 0.282452 | + | 0.489221i | ||||
\(869\) | −12.5908 | − | 21.8080i | −0.427115 | − | 0.739785i | ||||
\(870\) | 0.652793 | 0.0221317 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.5526 | −0.695998 | ||||||||
\(873\) | 6.84481 | + | 11.8556i | 0.231662 | + | 0.401250i | ||||
\(874\) | −10.3654 | − | 17.9534i | −0.350614 | − | 0.607282i | ||||
\(875\) | −2.15160 | + | 3.72667i | −0.0727372 | + | 0.125985i | ||||
\(876\) | −13.2567 | −0.447901 | ||||||||
\(877\) | 15.0851 | − | 26.1281i | 0.509387 | − | 0.882285i | −0.490554 | − | 0.871411i | \(-0.663205\pi\) |
0.999941 | − | 0.0108736i | \(-0.00346125\pi\) | |||||||
\(878\) | 2.43147 | − | 4.21143i | 0.0820581 | − | 0.142129i | ||||
\(879\) | 32.6625 | 1.10168 | ||||||||
\(880\) | 1.99007 | − | 3.44691i | 0.0670854 | − | 0.116195i | ||||
\(881\) | 1.78136 | + | 3.08541i | 0.0600157 | + | 0.103950i | 0.894472 | − | 0.447124i | \(-0.147552\pi\) |
−0.834456 | + | 0.551074i | \(0.814218\pi\) | |||||||
\(882\) | 0.873822 | + | 1.51350i | 0.0294231 | + | 0.0509623i | ||||
\(883\) | −10.2088 | −0.343554 | −0.171777 | − | 0.985136i | \(-0.554951\pi\) | ||||
−0.171777 | + | 0.985136i | \(0.554951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.38404 | 0.113753 | ||||||||
\(886\) | 4.28136 | + | 7.41554i | 0.143835 | + | 0.249130i | ||||
\(887\) | 4.66823 | + | 8.08561i | 0.156744 | + | 0.271488i | 0.933693 | − | 0.358076i | \(-0.116567\pi\) |
−0.776949 | + | 0.629564i | \(0.783234\pi\) | |||||||
\(888\) | 2.70560 | − | 4.68623i | 0.0907938 | − | 0.157260i | ||||
\(889\) | 18.9318 | 0.634953 | ||||||||
\(890\) | 0.00753275 | − | 0.0130471i | 0.000252498 | − | 0.000437340i | ||||
\(891\) | −2.82640 | + | 4.89546i | −0.0946878 | + | 0.164004i | ||||
\(892\) | −25.5894 | −0.856797 | ||||||||
\(893\) | 18.7993 | − | 32.5614i | 0.629095 | − | 1.08962i | ||||
\(894\) | 3.42423 | + | 5.93094i | 0.114523 | + | 0.198360i | ||||
\(895\) | 0.424231 | + | 0.734790i | 0.0141805 | + | 0.0245613i | ||||
\(896\) | −19.1457 | −0.639613 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8261 | −0.428013 | ||||||||
\(899\) | 15.6456 | + | 27.0989i | 0.521808 | + | 0.903799i | ||||
\(900\) | −4.44989 | − | 7.70743i | −0.148330 | − | 0.256914i | ||||
\(901\) | −2.01693 | + | 3.49342i | −0.0671935 | + | 0.116383i | ||||
\(902\) | 1.11960 | 0.0372788 | ||||||||
\(903\) | −1.50216 | + | 2.60181i | −0.0499886 | + | 0.0865828i | ||||
\(904\) | −1.38553 | + | 2.39982i | −0.0460822 | + | 0.0798167i | ||||
\(905\) | 3.33081 | 0.110720 | ||||||||
\(906\) | 0.817667 | − | 1.41624i | 0.0271652 | − | 0.0470515i | ||||
\(907\) | 20.5402 | + | 35.5766i | 0.682026 | + | 1.18130i | 0.974362 | + | 0.224988i | \(0.0722341\pi\) |
−0.292336 | + | 0.956316i | \(0.594433\pi\) | |||||||
\(908\) | 14.4221 | + | 24.9798i | 0.478613 | + | 0.828983i | ||||
\(909\) | −5.41119 | −0.179478 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9705 | −0.628519 | −0.314260 | − | 0.949337i | \(-0.601756\pi\) | ||||
−0.314260 | + | 0.949337i | \(0.601756\pi\) | |||||||
\(912\) | −7.95689 | − | 13.7817i | −0.263479 | − | 0.456359i | ||||
\(913\) | 28.7896 | + | 49.8651i | 0.952797 | + | 1.65029i | ||||
\(914\) | 4.02111 | − | 6.96476i | 0.133006 | − | 0.230374i | ||||
\(915\) | 2.10321 | 0.0695300 | ||||||||
\(916\) | 1.65883 | − | 2.87318i | 0.0548094 | − | 0.0949327i | ||||
\(917\) | −0.795470 | + | 1.37779i | −0.0262687 | + | 0.0454988i | ||||
\(918\) | −1.69202 | −0.0558450 | ||||||||
\(919\) | −14.5010 | + | 25.1164i | −0.478343 | + | 0.828514i | −0.999692 | − | 0.0248299i | \(-0.992096\pi\) |
0.521349 | + | 0.853343i | \(0.325429\pi\) | |||||||
\(920\) | −1.74363 | − | 3.02005i | −0.0574857 | − | 0.0995681i | ||||
\(921\) | 10.3807 | + | 17.9799i | 0.342055 | + | 0.592457i | ||||
\(922\) | −3.36791 | −0.110916 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −17.8562 | −0.587427 | ||||||||
\(925\) | 7.89762 | + | 13.6791i | 0.259672 | + | 0.449765i | ||||
\(926\) | −7.86725 | − | 13.6265i | −0.258534 | − | 0.447794i | ||||
\(927\) | −6.87800 | + | 11.9130i | −0.225903 | + | 0.391276i | ||||
\(928\) | −27.6329 | −0.907096 | ||||||||
\(929\) | 25.3605 | − | 43.9258i | 0.832052 | − | 1.44116i | −0.0643554 | − | 0.997927i | \(-0.520499\pi\) |
0.896408 | − | 0.443230i | \(-0.146168\pi\) | |||||||
\(930\) | 0.289561 | − | 0.501534i | 0.00949507 | − | 0.0164459i | ||||
\(931\) | −21.9205 | −0.718415 | ||||||||
\(932\) | −21.1054 | + | 36.5556i | −0.691329 | + | 1.19742i | ||||
\(933\) | 5.65064 | + | 9.78719i | 0.184994 | + | 0.320418i | ||||
\(934\) | −2.89277 | − | 5.01043i | −0.0946544 | − | 0.163946i | ||||
\(935\) | 5.30798 | 0.173589 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.3051 | 1.67606 | 0.838032 | − | 0.545620i | \(-0.183706\pi\) | ||||
0.838032 | + | 0.545620i | \(0.183706\pi\) | |||||||
\(938\) | −2.32520 | − | 4.02736i | −0.0759205 | − | 0.131498i | ||||
\(939\) | 2.13587 | + | 3.69943i | 0.0697014 | + | 0.120726i | ||||
\(940\) | 1.49880 | − | 2.59600i | 0.0488856 | − | 0.0846723i | ||||
\(941\) | −34.7036 | −1.13131 | −0.565653 | − | 0.824643i | \(-0.691376\pi\) | ||||
−0.565653 | + | 0.824643i | \(0.691376\pi\) | |||||||
\(942\) | 1.08546 | − | 1.88007i | 0.0353661 | − | 0.0612559i | ||||
\(943\) | −1.85690 | + | 3.21624i | −0.0604688 | + | 0.104735i | ||||
\(944\) | −39.0616 | −1.27135 | ||||||||
\(945\) | 0.216480 | − | 0.374955i | 0.00704210 | − | 0.0121973i | ||||
\(946\) | −2.15572 | − | 3.73381i | −0.0700884 | − | 0.121397i | ||||
\(947\) | 6.50634 | + | 11.2693i | 0.211428 | + | 0.366203i | 0.952162 | − | 0.305595i | \(-0.0988554\pi\) |
−0.740734 | + | 0.671798i | \(0.765522\pi\) | |||||||
\(948\) | −8.02715 | −0.260710 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12.2698 | −0.398085 | ||||||||
\(951\) | −7.73878 | − | 13.4040i | −0.250947 | − | 0.434653i | ||||
\(952\) | −5.63856 | − | 9.76626i | −0.182747 | − | 0.316526i | ||||
\(953\) | −13.0075 | + | 22.5297i | −0.421355 | + | 0.729809i | −0.996072 | − | 0.0885434i | \(-0.971779\pi\) |
0.574717 | + | 0.818352i | \(0.305112\pi\) | |||||||
\(954\) | −0.472189 | −0.0152877 | ||||||||
\(955\) | −0.160694 | + | 0.278330i | −0.00519994 | + | 0.00900656i | ||||
\(956\) | 13.1555 | − | 22.7860i | 0.425479 | − | 0.736951i | ||||
\(957\) | −33.5719 | −1.08523 | ||||||||
\(958\) | 5.68018 | − | 9.83835i | 0.183518 | − | 0.317863i | ||||
\(959\) | 8.36914 | + | 14.4958i | 0.270254 | + | 0.468093i | ||||
\(960\) | −0.448394 | − | 0.776642i | −0.0144719 | − | 0.0250660i | ||||
\(961\) | −3.24027 | −0.104525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.8170 | −0.413022 | ||||||||
\(964\) | 7.77628 | + | 13.4689i | 0.250457 | + | 0.433805i | ||||
\(965\) | −1.13557 | − | 1.96687i | −0.0365553 | − | 0.0633157i | ||||
\(966\) | −3.25518 | + | 5.63813i | −0.104734 | + | 0.181404i | ||||
\(967\) | 36.6644 | 1.17905 | 0.589524 | − | 0.807751i | \(-0.299315\pi\) | ||||
0.589524 | + | 0.807751i | \(0.299315\pi\) | |||||||
\(968\) | 17.7274 | − | 30.7047i | 0.569779 | − | 0.986886i | ||||
\(969\) | 10.6114 | − | 18.3795i | 0.340888 | − | 0.590435i | ||||
\(970\) | 1.50471 | 0.0483134 | ||||||||
\(971\) | 18.9233 | − | 32.7761i | 0.607277 | − | 1.05183i | −0.384411 | − | 0.923162i | \(-0.625595\pi\) |
0.991687 | − | 0.128672i | \(-0.0410714\pi\) | |||||||
\(972\) | 0.900969 | + | 1.56052i | 0.0288986 | + | 0.0500538i | ||||
\(973\) | 3.58708 | + | 6.21301i | 0.114997 | + | 0.199180i | ||||
\(974\) | 7.12392 | 0.228265 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.2771 | −0.777091 | ||||||||
\(977\) | −14.4499 | − | 25.0279i | −0.462293 | − | 0.800715i | 0.536782 | − | 0.843721i | \(-0.319640\pi\) |
−0.999075 | + | 0.0430063i | \(0.986306\pi\) | |||||||
\(978\) | −1.92058 | − | 3.32655i | −0.0614135 | − | 0.106371i | ||||
\(979\) | −0.387395 | + | 0.670988i | −0.0123812 | + | 0.0214449i | ||||
\(980\) | −1.74764 | −0.0558264 | ||||||||
\(981\) | −6.07338 | + | 10.5194i | −0.193908 | + | 0.335858i | ||||
\(982\) | −4.61476 | + | 7.99300i | −0.147263 | + | 0.255067i | ||||
\(983\) | −19.3991 | −0.618735 | −0.309368 | − | 0.950942i | \(-0.600117\pi\) | ||||
−0.309368 | + | 0.950942i | \(0.600117\pi\) | |||||||
\(984\) | 0.376510 | − | 0.652135i | 0.0120027 | − | 0.0207893i | ||||
\(985\) | 0.507828 | + | 0.879584i | 0.0161808 | + | 0.0280259i | ||||
\(986\) | −5.02446 | − | 8.70262i | −0.160011 | − | 0.277148i | ||||
\(987\) | −11.8076 | −0.375839 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3013 | 0.454754 | ||||||||
\(990\) | 0.310667 | + | 0.538091i | 0.00987364 | + | 0.0171017i | ||||
\(991\) | 2.59150 | + | 4.48861i | 0.0823217 | + | 0.142585i | 0.904247 | − | 0.427010i | \(-0.140433\pi\) |
−0.821925 | + | 0.569596i | \(0.807100\pi\) | |||||||
\(992\) | −12.2572 | + | 21.2301i | −0.389167 | + | 0.674056i | ||||
\(993\) | 6.06829 | 0.192572 | ||||||||
\(994\) | 2.23095 | − | 3.86413i | 0.0707616 | − | 0.122563i | ||||
\(995\) | −3.05914 | + | 5.29858i | −0.0969812 | + | 0.167976i | ||||
\(996\) | 18.3545 | 0.581585 | ||||||||
\(997\) | 24.6821 | − | 42.7506i | 0.781690 | − | 1.35393i | −0.149267 | − | 0.988797i | \(-0.547691\pi\) |
0.930957 | − | 0.365130i | \(-0.118975\pi\) | |||||||
\(998\) | 1.79523 | + | 3.10943i | 0.0568271 | + | 0.0984274i | ||||
\(999\) | −1.59903 | − | 2.76960i | −0.0505911 | − | 0.0876264i |
(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 | 507.2.e.j.484.2 | 6 | ||
13.2 | odd | 12 | 507.2.b.g.337.3 | 6 | |||
13.3 | even | 3 | 507.2.a.k.1.2 | yes | 3 | ||
13.4 | even | 6 | 507.2.e.k.22.2 | 6 | |||
13.5 | odd | 4 | 507.2.j.h.361.3 | 12 | |||
13.6 | odd | 12 | 507.2.j.h.316.4 | 12 | |||
13.7 | odd | 12 | 507.2.j.h.316.3 | 12 | |||
13.8 | odd | 4 | 507.2.j.h.361.4 | 12 | |||
13.9 | even | 3 | inner | 507.2.e.j.22.2 | 6 | ||
13.10 | even | 6 | 507.2.a.j.1.2 | ✓ | 3 | ||
13.11 | odd | 12 | 507.2.b.g.337.4 | 6 | |||
13.12 | even | 2 | 507.2.e.k.484.2 | 6 | |||
39.2 | even | 12 | 1521.2.b.m.1351.4 | 6 | |||
39.11 | even | 12 | 1521.2.b.m.1351.3 | 6 | |||
39.23 | odd | 6 | 1521.2.a.q.1.2 | 3 | |||
39.29 | odd | 6 | 1521.2.a.p.1.2 | 3 | |||
52.3 | odd | 6 | 8112.2.a.cf.1.1 | 3 | |||
52.23 | odd | 6 | 8112.2.a.by.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.j.1.2 | ✓ | 3 | 13.10 | even | 6 | ||
507.2.a.k.1.2 | yes | 3 | 13.3 | even | 3 | ||
507.2.b.g.337.3 | 6 | 13.2 | odd | 12 | |||
507.2.b.g.337.4 | 6 | 13.11 | odd | 12 | |||
507.2.e.j.22.2 | 6 | 13.9 | even | 3 | inner | ||
507.2.e.j.484.2 | 6 | 1.1 | even | 1 | trivial | ||
507.2.e.k.22.2 | 6 | 13.4 | even | 6 | |||
507.2.e.k.484.2 | 6 | 13.12 | even | 2 | |||
507.2.j.h.316.3 | 12 | 13.7 | odd | 12 | |||
507.2.j.h.316.4 | 12 | 13.6 | odd | 12 | |||
507.2.j.h.361.3 | 12 | 13.5 | odd | 4 | |||
507.2.j.h.361.4 | 12 | 13.8 | odd | 4 | |||
1521.2.a.p.1.2 | 3 | 39.29 | odd | 6 | |||
1521.2.a.q.1.2 | 3 | 39.23 | odd | 6 | |||
1521.2.b.m.1351.3 | 6 | 39.11 | even | 12 | |||
1521.2.b.m.1351.4 | 6 | 39.2 | even | 12 | |||
8112.2.a.by.1.3 | 3 | 52.23 | odd | 6 | |||
8112.2.a.cf.1.1 | 3 | 52.3 | odd | 6 |