Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(529,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(8.09683076496\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.2 | ||
Root | \(0.222521 + 0.385418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.529 |
Dual form | 1014.2.e.m.991.2 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.356896 | −0.159609 | −0.0798043 | − | 0.996811i | \(-0.525430\pi\) | ||||
−0.0798043 | + | 0.996811i | \(0.525430\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 2.02446 | + | 3.50647i | 0.765173 | + | 1.32532i | 0.940155 | + | 0.340748i | \(0.110680\pi\) |
−0.174981 | + | 0.984572i | \(0.555987\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.178448 | + | 0.309081i | −0.0564302 | + | 0.0977400i | ||||
\(11\) | −0.455927 | + | 0.789689i | −0.137467 | + | 0.238100i | −0.926537 | − | 0.376203i | \(-0.877229\pi\) |
0.789070 | + | 0.614303i | \(0.210563\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.04892 | 1.08212 | ||||||||
\(15\) | 0.178448 | − | 0.309081i | 0.0460751 | − | 0.0798043i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.04892 | + | 1.81678i | 0.254400 | + | 0.440633i | 0.964732 | − | 0.263233i | \(-0.0847888\pi\) |
−0.710333 | + | 0.703866i | \(0.751455\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.49396 | − | 4.31966i | −0.572153 | − | 0.990999i | −0.996345 | − | 0.0854262i | \(-0.972775\pi\) |
0.424191 | − | 0.905573i | \(-0.360559\pi\) | |||||||
\(20\) | 0.178448 | + | 0.309081i | 0.0399022 | + | 0.0691126i | ||||
\(21\) | −4.04892 | −0.883546 | ||||||||
\(22\) | 0.455927 | + | 0.789689i | 0.0972040 | + | 0.168362i | ||||
\(23\) | −4.24698 | + | 7.35598i | −0.885556 | + | 1.53383i | −0.0404819 | + | 0.999180i | \(0.512889\pi\) |
−0.845075 | + | 0.534649i | \(0.820444\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −4.87263 | −0.974525 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.02446 | − | 3.50647i | 0.382587 | − | 0.662660i | ||||
\(29\) | −4.25786 | + | 7.37484i | −0.790666 | + | 1.36947i | 0.134890 | + | 0.990861i | \(0.456932\pi\) |
−0.925555 | + | 0.378612i | \(0.876401\pi\) | |||||||
\(30\) | −0.178448 | − | 0.309081i | −0.0325800 | − | 0.0564302i | ||||
\(31\) | 10.7899 | 1.93792 | 0.968958 | − | 0.247227i | \(-0.0795192\pi\) | ||||
0.968958 | + | 0.247227i | \(0.0795192\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.455927 | − | 0.789689i | −0.0793667 | − | 0.137467i | ||||
\(34\) | 2.09783 | 0.359776 | ||||||||
\(35\) | −0.722521 | − | 1.25144i | −0.122128 | − | 0.211532i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −0.307979 | + | 0.533434i | −0.0506314 | + | 0.0876961i | −0.890230 | − | 0.455511i | \(-0.849457\pi\) |
0.839599 | + | 0.543207i | \(0.182790\pi\) | |||||||
\(38\) | −4.98792 | −0.809147 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.356896 | 0.0564302 | ||||||||
\(41\) | −3.80194 | + | 6.58515i | −0.593763 | + | 1.02843i | 0.399957 | + | 0.916534i | \(0.369025\pi\) |
−0.993720 | + | 0.111894i | \(0.964308\pi\) | |||||||
\(42\) | −2.02446 | + | 3.50647i | −0.312381 | + | 0.541059i | ||||
\(43\) | 3.13706 | + | 5.43355i | 0.478398 | + | 0.828609i | 0.999693 | − | 0.0247671i | \(-0.00788442\pi\) |
−0.521296 | + | 0.853376i | \(0.674551\pi\) | |||||||
\(44\) | 0.911854 | 0.137467 | ||||||||
\(45\) | 0.178448 | + | 0.309081i | 0.0266014 | + | 0.0460751i | ||||
\(46\) | 4.24698 | + | 7.35598i | 0.626183 | + | 1.08458i | ||||
\(47\) | −1.78017 | −0.259664 | −0.129832 | − | 0.991536i | \(-0.541444\pi\) | ||||
−0.129832 | + | 0.991536i | \(0.541444\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −4.69687 | + | 8.13521i | −0.670981 | + | 1.16217i | ||||
\(50\) | −2.43631 | + | 4.21982i | −0.344547 | + | 0.596772i | ||||
\(51\) | −2.09783 | −0.293756 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4112 | 1.43009 | 0.715043 | − | 0.699080i | \(-0.246407\pi\) | ||||
0.715043 | + | 0.699080i | \(0.246407\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0.162718 | − | 0.281837i | 0.0219410 | − | 0.0380028i | ||||
\(56\) | −2.02446 | − | 3.50647i | −0.270530 | − | 0.468571i | ||||
\(57\) | 4.98792 | 0.660666 | ||||||||
\(58\) | 4.25786 | + | 7.37484i | 0.559085 | + | 0.968364i | ||||
\(59\) | −3.02446 | − | 5.23852i | −0.393751 | − | 0.681997i | 0.599190 | − | 0.800607i | \(-0.295489\pi\) |
−0.992941 | + | 0.118610i | \(0.962156\pi\) | |||||||
\(60\) | −0.356896 | −0.0460751 | ||||||||
\(61\) | 1.55496 | + | 2.69327i | 0.199092 | + | 0.344837i | 0.948234 | − | 0.317572i | \(-0.102867\pi\) |
−0.749142 | + | 0.662409i | \(0.769534\pi\) | |||||||
\(62\) | 5.39493 | − | 9.34429i | 0.685157 | − | 1.18673i | ||||
\(63\) | 2.02446 | − | 3.50647i | 0.255058 | − | 0.441773i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.911854 | −0.112241 | ||||||||
\(67\) | 6.78986 | − | 11.7604i | 0.829513 | − | 1.43676i | −0.0689079 | − | 0.997623i | \(-0.521951\pi\) |
0.898421 | − | 0.439136i | \(-0.144715\pi\) | |||||||
\(68\) | 1.04892 | − | 1.81678i | 0.127200 | − | 0.220317i | ||||
\(69\) | −4.24698 | − | 7.35598i | −0.511276 | − | 0.885556i | ||||
\(70\) | −1.44504 | −0.172716 | ||||||||
\(71\) | 5.74094 | + | 9.94360i | 0.681324 | + | 1.18009i | 0.974577 | + | 0.224053i | \(0.0719289\pi\) |
−0.293253 | + | 0.956035i | \(0.594738\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −0.533188 | −0.0624049 | −0.0312025 | − | 0.999513i | \(-0.509934\pi\) | ||||
−0.0312025 | + | 0.999513i | \(0.509934\pi\) | |||||||
\(74\) | 0.307979 | + | 0.533434i | 0.0358018 | + | 0.0620105i | ||||
\(75\) | 2.43631 | − | 4.21982i | 0.281321 | − | 0.487263i | ||||
\(76\) | −2.49396 | + | 4.31966i | −0.286077 | + | 0.495499i | ||||
\(77\) | −3.69202 | −0.420745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.7071 | −1.31715 | −0.658575 | − | 0.752515i | \(-0.728841\pi\) | ||||
−0.658575 | + | 0.752515i | \(0.728841\pi\) | |||||||
\(80\) | 0.178448 | − | 0.309081i | 0.0199511 | − | 0.0345563i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.80194 | + | 6.58515i | 0.419854 | + | 0.727208i | ||||
\(83\) | 6.49934 | 0.713395 | 0.356697 | − | 0.934220i | \(-0.383903\pi\) | ||||
0.356697 | + | 0.934220i | \(0.383903\pi\) | |||||||
\(84\) | 2.02446 | + | 3.50647i | 0.220887 | + | 0.382587i | ||||
\(85\) | −0.374354 | − | 0.648401i | −0.0406044 | − | 0.0703289i | ||||
\(86\) | 6.27413 | 0.676556 | ||||||||
\(87\) | −4.25786 | − | 7.37484i | −0.456491 | − | 0.790666i | ||||
\(88\) | 0.455927 | − | 0.789689i | 0.0486020 | − | 0.0841811i | ||||
\(89\) | −3.24698 | + | 5.62393i | −0.344179 | + | 0.596136i | −0.985204 | − | 0.171384i | \(-0.945176\pi\) |
0.641025 | + | 0.767520i | \(0.278509\pi\) | |||||||
\(90\) | 0.356896 | 0.0376201 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.49396 | 0.885556 | ||||||||
\(93\) | −5.39493 | + | 9.34429i | −0.559428 | + | 0.968958i | ||||
\(94\) | −0.890084 | + | 1.54167i | −0.0918051 | + | 0.159011i | ||||
\(95\) | 0.890084 | + | 1.54167i | 0.0913207 | + | 0.158172i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −0.980386 | − | 1.69808i | −0.0995431 | − | 0.172414i | 0.811953 | − | 0.583723i | \(-0.198405\pi\) |
−0.911496 | + | 0.411310i | \(0.865071\pi\) | |||||||
\(98\) | 4.69687 | + | 8.13521i | 0.474455 | + | 0.821780i | ||||
\(99\) | 0.911854 | 0.0916448 | ||||||||
\(100\) | 2.43631 | + | 4.21982i | 0.243631 | + | 0.421982i | ||||
\(101\) | −3.49127 | + | 6.04706i | −0.347394 | + | 0.601705i | −0.985786 | − | 0.168007i | \(-0.946267\pi\) |
0.638391 | + | 0.769712i | \(0.279600\pi\) | |||||||
\(102\) | −1.04892 | + | 1.81678i | −0.103858 | + | 0.179888i | ||||
\(103\) | 4.94869 | 0.487609 | 0.243804 | − | 0.969824i | \(-0.421604\pi\) | ||||
0.243804 | + | 0.969824i | \(0.421604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.44504 | 0.141022 | ||||||||
\(106\) | 5.20560 | − | 9.01636i | 0.505612 | − | 0.875746i | ||||
\(107\) | 2.13437 | − | 3.69685i | 0.206338 | − | 0.357388i | −0.744220 | − | 0.667934i | \(-0.767179\pi\) |
0.950558 | + | 0.310547i | \(0.100512\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 6.21983 | 0.595752 | 0.297876 | − | 0.954605i | \(-0.403722\pi\) | ||||
0.297876 | + | 0.954605i | \(0.403722\pi\) | |||||||
\(110\) | −0.162718 | − | 0.281837i | −0.0155146 | − | 0.0268721i | ||||
\(111\) | −0.307979 | − | 0.533434i | −0.0292320 | − | 0.0506314i | ||||
\(112\) | −4.04892 | −0.382587 | ||||||||
\(113\) | −6.49396 | − | 11.2479i | −0.610900 | − | 1.05811i | −0.991089 | − | 0.133201i | \(-0.957474\pi\) |
0.380189 | − | 0.924909i | \(-0.375859\pi\) | |||||||
\(114\) | 2.49396 | − | 4.31966i | 0.233581 | − | 0.404574i | ||||
\(115\) | 1.51573 | − | 2.62532i | 0.141343 | − | 0.244812i | ||||
\(116\) | 8.51573 | 0.790666 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.04892 | −0.556848 | ||||||||
\(119\) | −4.24698 | + | 7.35598i | −0.389320 | + | 0.674322i | ||||
\(120\) | −0.178448 | + | 0.309081i | −0.0162900 | + | 0.0282151i | ||||
\(121\) | 5.08426 | + | 8.80620i | 0.462206 | + | 0.800564i | ||||
\(122\) | 3.10992 | 0.281559 | ||||||||
\(123\) | −3.80194 | − | 6.58515i | −0.342809 | − | 0.593763i | ||||
\(124\) | −5.39493 | − | 9.34429i | −0.484479 | − | 0.839142i | ||||
\(125\) | 3.52350 | 0.315151 | ||||||||
\(126\) | −2.02446 | − | 3.50647i | −0.180353 | − | 0.312381i | ||||
\(127\) | −4.61141 | + | 7.98719i | −0.409196 | + | 0.708749i | −0.994800 | − | 0.101849i | \(-0.967524\pi\) |
0.585604 | + | 0.810598i | \(0.300858\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −6.27413 | −0.552406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5526 | −1.27146 | −0.635732 | − | 0.771910i | \(-0.719302\pi\) | ||||
−0.635732 | + | 0.771910i | \(0.719302\pi\) | |||||||
\(132\) | −0.455927 | + | 0.789689i | −0.0396834 | + | 0.0687336i | ||||
\(133\) | 10.0978 | − | 17.4900i | 0.875593 | − | 1.51657i | ||||
\(134\) | −6.78986 | − | 11.7604i | −0.586554 | − | 1.01594i | ||||
\(135\) | −0.356896 | −0.0307167 | ||||||||
\(136\) | −1.04892 | − | 1.81678i | −0.0899439 | − | 0.155787i | ||||
\(137\) | −7.70171 | − | 13.3398i | −0.658002 | − | 1.13969i | −0.981132 | − | 0.193338i | \(-0.938069\pi\) |
0.323131 | − | 0.946354i | \(-0.395265\pi\) | |||||||
\(138\) | −8.49396 | −0.723054 | ||||||||
\(139\) | −1.35690 | − | 2.35021i | −0.115090 | − | 0.199342i | 0.802725 | − | 0.596349i | \(-0.203382\pi\) |
−0.917816 | + | 0.397006i | \(0.870049\pi\) | |||||||
\(140\) | −0.722521 | + | 1.25144i | −0.0610642 | + | 0.105766i | ||||
\(141\) | 0.890084 | − | 1.54167i | 0.0749586 | − | 0.129832i | ||||
\(142\) | 11.4819 | 0.963538 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.51961 | − | 2.63205i | 0.126197 | − | 0.218580i | ||||
\(146\) | −0.266594 | + | 0.461754i | −0.0220635 | + | 0.0382151i | ||||
\(147\) | −4.69687 | − | 8.13521i | −0.387391 | − | 0.670981i | ||||
\(148\) | 0.615957 | 0.0506314 | ||||||||
\(149\) | −7.36778 | − | 12.7614i | −0.603592 | − | 1.04545i | −0.992272 | − | 0.124079i | \(-0.960402\pi\) |
0.388680 | − | 0.921373i | \(-0.372931\pi\) | |||||||
\(150\) | −2.43631 | − | 4.21982i | −0.198924 | − | 0.344547i | ||||
\(151\) | 15.8213 | 1.28752 | 0.643760 | − | 0.765227i | \(-0.277373\pi\) | ||||
0.643760 | + | 0.765227i | \(0.277373\pi\) | |||||||
\(152\) | 2.49396 | + | 4.31966i | 0.202287 | + | 0.350371i | ||||
\(153\) | 1.04892 | − | 1.81678i | 0.0847999 | − | 0.146878i | ||||
\(154\) | −1.84601 | + | 3.19738i | −0.148756 | + | 0.257653i | ||||
\(155\) | −3.85086 | −0.309308 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.27413 | −0.341112 | −0.170556 | − | 0.985348i | \(-0.554556\pi\) | ||||
−0.170556 | + | 0.985348i | \(0.554556\pi\) | |||||||
\(158\) | −5.85354 | + | 10.1386i | −0.465683 | + | 0.806586i | ||||
\(159\) | −5.20560 | + | 9.01636i | −0.412831 | + | 0.715043i | ||||
\(160\) | −0.178448 | − | 0.309081i | −0.0141075 | − | 0.0244350i | ||||
\(161\) | −34.3913 | −2.71042 | ||||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −0.158834 | − | 0.275108i | −0.0124408 | − | 0.0215481i | 0.859738 | − | 0.510735i | \(-0.170627\pi\) |
−0.872179 | + | 0.489187i | \(0.837293\pi\) | |||||||
\(164\) | 7.60388 | 0.593763 | ||||||||
\(165\) | 0.162718 | + | 0.281837i | 0.0126676 | + | 0.0219410i | ||||
\(166\) | 3.24967 | − | 5.62859i | 0.252223 | − | 0.436863i | ||||
\(167\) | 6.18060 | − | 10.7051i | 0.478269 | − | 0.828387i | −0.521420 | − | 0.853300i | \(-0.674598\pi\) |
0.999690 | + | 0.0249130i | \(0.00793089\pi\) | |||||||
\(168\) | 4.04892 | 0.312381 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.748709 | −0.0574233 | ||||||||
\(171\) | −2.49396 | + | 4.31966i | −0.190718 | + | 0.330333i | ||||
\(172\) | 3.13706 | − | 5.43355i | 0.239199 | − | 0.414305i | ||||
\(173\) | 8.53199 | + | 14.7778i | 0.648675 | + | 1.12354i | 0.983440 | + | 0.181237i | \(0.0580100\pi\) |
−0.334764 | + | 0.942302i | \(0.608657\pi\) | |||||||
\(174\) | −8.51573 | −0.645576 | ||||||||
\(175\) | −9.86443 | − | 17.0857i | −0.745681 | − | 1.29156i | ||||
\(176\) | −0.455927 | − | 0.789689i | −0.0343668 | − | 0.0595250i | ||||
\(177\) | 6.04892 | 0.454664 | ||||||||
\(178\) | 3.24698 | + | 5.62393i | 0.243371 | + | 0.421532i | ||||
\(179\) | 12.4840 | − | 21.6230i | 0.933100 | − | 1.61618i | 0.155114 | − | 0.987897i | \(-0.450426\pi\) |
0.777987 | − | 0.628281i | \(-0.216241\pi\) | |||||||
\(180\) | 0.178448 | − | 0.309081i | 0.0133007 | − | 0.0230375i | ||||
\(181\) | 5.26205 | 0.391125 | 0.195562 | − | 0.980691i | \(-0.437347\pi\) | ||||
0.195562 | + | 0.980691i | \(0.437347\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.10992 | −0.229892 | ||||||||
\(184\) | 4.24698 | − | 7.35598i | 0.313091 | − | 0.542290i | ||||
\(185\) | 0.109916 | − | 0.190381i | 0.00808120 | − | 0.0139971i | ||||
\(186\) | 5.39493 | + | 9.34429i | 0.395575 | + | 0.685157i | ||||
\(187\) | −1.91292 | −0.139886 | ||||||||
\(188\) | 0.890084 | + | 1.54167i | 0.0649160 | + | 0.112438i | ||||
\(189\) | 2.02446 | + | 3.50647i | 0.147258 | + | 0.255058i | ||||
\(190\) | 1.78017 | 0.129147 | ||||||||
\(191\) | −5.26875 | − | 9.12574i | −0.381233 | − | 0.660316i | 0.610005 | − | 0.792397i | \(-0.291167\pi\) |
−0.991239 | + | 0.132082i | \(0.957834\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 1.71379 | − | 2.96837i | 0.123361 | − | 0.213668i | −0.797730 | − | 0.603015i | \(-0.793966\pi\) |
0.921091 | + | 0.389347i | \(0.127299\pi\) | |||||||
\(194\) | −1.96077 | −0.140775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.39373 | 0.670981 | ||||||||
\(197\) | 1.88740 | − | 3.26906i | 0.134471 | − | 0.232911i | −0.790924 | − | 0.611914i | \(-0.790400\pi\) |
0.925395 | + | 0.379003i | \(0.123733\pi\) | |||||||
\(198\) | 0.455927 | − | 0.789689i | 0.0324013 | − | 0.0561207i | ||||
\(199\) | −8.97703 | − | 15.5487i | −0.636365 | − | 1.10222i | −0.986224 | − | 0.165414i | \(-0.947104\pi\) |
0.349859 | − | 0.936802i | \(-0.386229\pi\) | |||||||
\(200\) | 4.87263 | 0.344547 | ||||||||
\(201\) | 6.78986 | + | 11.7604i | 0.478920 | + | 0.829513i | ||||
\(202\) | 3.49127 | + | 6.04706i | 0.245645 | + | 0.425470i | ||||
\(203\) | −34.4795 | −2.41999 | ||||||||
\(204\) | 1.04892 | + | 1.81678i | 0.0734389 | + | 0.127200i | ||||
\(205\) | 1.35690 | − | 2.35021i | 0.0947697 | − | 0.164146i | ||||
\(206\) | 2.47434 | − | 4.28569i | 0.172396 | − | 0.298598i | ||||
\(207\) | 8.49396 | 0.590371 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.54825 | 0.314609 | ||||||||
\(210\) | 0.722521 | − | 1.25144i | 0.0498587 | − | 0.0863578i | ||||
\(211\) | 6.26875 | − | 10.8578i | 0.431559 | − | 0.747481i | −0.565449 | − | 0.824783i | \(-0.691297\pi\) |
0.997008 | + | 0.0773018i | \(0.0246305\pi\) | |||||||
\(212\) | −5.20560 | − | 9.01636i | −0.357522 | − | 0.619246i | ||||
\(213\) | −11.4819 | −0.786725 | ||||||||
\(214\) | −2.13437 | − | 3.69685i | −0.145903 | − | 0.252711i | ||||
\(215\) | −1.11960 | − | 1.93921i | −0.0763564 | − | 0.132253i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 21.8436 | + | 37.8343i | 1.48284 | + | 2.56836i | ||||
\(218\) | 3.10992 | − | 5.38653i | 0.210630 | − | 0.364822i | ||||
\(219\) | 0.266594 | − | 0.461754i | 0.0180147 | − | 0.0312025i | ||||
\(220\) | −0.325437 | −0.0219410 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.615957 | −0.0413403 | ||||||||
\(223\) | 2.71379 | − | 4.70043i | 0.181729 | − | 0.314764i | −0.760740 | − | 0.649056i | \(-0.775164\pi\) |
0.942469 | + | 0.334292i | \(0.108497\pi\) | |||||||
\(224\) | −2.02446 | + | 3.50647i | −0.135265 | + | 0.234286i | ||||
\(225\) | 2.43631 | + | 4.21982i | 0.162421 | + | 0.281321i | ||||
\(226\) | −12.9879 | −0.863943 | ||||||||
\(227\) | 8.28836 | + | 14.3559i | 0.550118 | + | 0.952832i | 0.998265 | + | 0.0588728i | \(0.0187506\pi\) |
−0.448147 | + | 0.893960i | \(0.647916\pi\) | |||||||
\(228\) | −2.49396 | − | 4.31966i | −0.165166 | − | 0.286077i | ||||
\(229\) | 23.8780 | 1.57790 | 0.788951 | − | 0.614456i | \(-0.210624\pi\) | ||||
0.788951 | + | 0.614456i | \(0.210624\pi\) | |||||||
\(230\) | −1.51573 | − | 2.62532i | −0.0999442 | − | 0.173109i | ||||
\(231\) | 1.84601 | − | 3.19738i | 0.121459 | − | 0.210372i | ||||
\(232\) | 4.25786 | − | 7.37484i | 0.279543 | − | 0.484182i | ||||
\(233\) | 13.9952 | 0.916857 | 0.458428 | − | 0.888731i | \(-0.348413\pi\) | ||||
0.458428 | + | 0.888731i | \(0.348413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.635334 | 0.0414446 | ||||||||
\(236\) | −3.02446 | + | 5.23852i | −0.196875 | + | 0.340998i | ||||
\(237\) | 5.85354 | − | 10.1386i | 0.380229 | − | 0.658575i | ||||
\(238\) | 4.24698 | + | 7.35598i | 0.275291 | + | 0.476818i | ||||
\(239\) | −13.2862 | −0.859413 | −0.429707 | − | 0.902969i | \(-0.641383\pi\) | ||||
−0.429707 | + | 0.902969i | \(0.641383\pi\) | |||||||
\(240\) | 0.178448 | + | 0.309081i | 0.0115188 | + | 0.0199511i | ||||
\(241\) | 5.23945 | + | 9.07499i | 0.337502 | + | 0.584571i | 0.983962 | − | 0.178377i | \(-0.0570845\pi\) |
−0.646460 | + | 0.762948i | \(0.723751\pi\) | |||||||
\(242\) | 10.1685 | 0.653657 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 1.55496 | − | 2.69327i | 0.0995460 | − | 0.172419i | ||||
\(245\) | 1.67629 | − | 2.90342i | 0.107094 | − | 0.185493i | ||||
\(246\) | −7.60388 | −0.484805 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.7899 | −0.685157 | ||||||||
\(249\) | −3.24967 | + | 5.62859i | −0.205939 | + | 0.356697i | ||||
\(250\) | 1.76175 | − | 3.05144i | 0.111423 | − | 0.192990i | ||||
\(251\) | −1.74363 | − | 3.02005i | −0.110057 | − | 0.190624i | 0.805736 | − | 0.592275i | \(-0.201770\pi\) |
−0.915793 | + | 0.401651i | \(0.868437\pi\) | |||||||
\(252\) | −4.04892 | −0.255058 | ||||||||
\(253\) | −3.87263 | − | 6.70758i | −0.243470 | − | 0.421702i | ||||
\(254\) | 4.61141 | + | 7.98719i | 0.289345 | + | 0.501161i | ||||
\(255\) | 0.748709 | 0.0468859 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.26875 | + | 5.66164i | −0.203899 | + | 0.353163i | −0.949781 | − | 0.312914i | \(-0.898695\pi\) |
0.745882 | + | 0.666078i | \(0.232028\pi\) | |||||||
\(258\) | −3.13706 | + | 5.43355i | −0.195305 | + | 0.338278i | ||||
\(259\) | −2.49396 | −0.154967 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.51573 | 0.527110 | ||||||||
\(262\) | −7.27628 | + | 12.6029i | −0.449530 | + | 0.778609i | ||||
\(263\) | −4.00969 | + | 6.94498i | −0.247248 | + | 0.428246i | −0.962761 | − | 0.270353i | \(-0.912860\pi\) |
0.715513 | + | 0.698599i | \(0.246193\pi\) | |||||||
\(264\) | 0.455927 | + | 0.789689i | 0.0280604 | + | 0.0486020i | ||||
\(265\) | −3.71571 | −0.228254 | ||||||||
\(266\) | −10.0978 | − | 17.4900i | −0.619138 | − | 1.07238i | ||||
\(267\) | −3.24698 | − | 5.62393i | −0.198712 | − | 0.344179i | ||||
\(268\) | −13.5797 | −0.829513 | ||||||||
\(269\) | 13.8366 | + | 23.9657i | 0.843633 | + | 1.46122i | 0.886803 | + | 0.462148i | \(0.152921\pi\) |
−0.0431692 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(270\) | −0.178448 | + | 0.309081i | −0.0108600 | + | 0.0188101i | ||||
\(271\) | 7.36443 | − | 12.7556i | 0.447357 | − | 0.774845i | −0.550856 | − | 0.834600i | \(-0.685699\pi\) |
0.998213 | + | 0.0597550i | \(0.0190319\pi\) | |||||||
\(272\) | −2.09783 | −0.127200 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4034 | −0.930555 | ||||||||
\(275\) | 2.22156 | − | 3.84786i | 0.133965 | − | 0.232035i | ||||
\(276\) | −4.24698 | + | 7.35598i | −0.255638 | + | 0.442778i | ||||
\(277\) | −1.63102 | − | 2.82501i | −0.0979986 | − | 0.169739i | 0.812858 | − | 0.582463i | \(-0.197911\pi\) |
−0.910856 | + | 0.412724i | \(0.864577\pi\) | |||||||
\(278\) | −2.71379 | −0.162762 | ||||||||
\(279\) | −5.39493 | − | 9.34429i | −0.322986 | − | 0.559428i | ||||
\(280\) | 0.722521 | + | 1.25144i | 0.0431789 | + | 0.0747880i | ||||
\(281\) | −7.72587 | −0.460887 | −0.230443 | − | 0.973086i | \(-0.574018\pi\) | ||||
−0.230443 | + | 0.973086i | \(0.574018\pi\) | |||||||
\(282\) | −0.890084 | − | 1.54167i | −0.0530037 | − | 0.0918051i | ||||
\(283\) | 9.89008 | − | 17.1301i | 0.587904 | − | 1.01828i | −0.406602 | − | 0.913605i | \(-0.633286\pi\) |
0.994506 | − | 0.104675i | \(-0.0333802\pi\) | |||||||
\(284\) | 5.74094 | − | 9.94360i | 0.340662 | − | 0.590044i | ||||
\(285\) | −1.78017 | −0.105448 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.7875 | −1.81733 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 6.29954 | − | 10.9111i | 0.370561 | − | 0.641831i | ||||
\(290\) | −1.51961 | − | 2.63205i | −0.0892348 | − | 0.154559i | ||||
\(291\) | 1.96077 | 0.114942 | ||||||||
\(292\) | 0.266594 | + | 0.461754i | 0.0156012 | + | 0.0270221i | ||||
\(293\) | −6.45593 | − | 11.1820i | −0.377159 | − | 0.653259i | 0.613488 | − | 0.789704i | \(-0.289766\pi\) |
−0.990648 | + | 0.136445i | \(0.956432\pi\) | |||||||
\(294\) | −9.39373 | −0.547854 | ||||||||
\(295\) | 1.07942 | + | 1.86960i | 0.0628461 | + | 0.108853i | ||||
\(296\) | 0.307979 | − | 0.533434i | 0.0179009 | − | 0.0310052i | ||||
\(297\) | −0.455927 | + | 0.789689i | −0.0264556 | + | 0.0458224i | ||||
\(298\) | −14.7356 | −0.853608 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.87263 | −0.281321 | ||||||||
\(301\) | −12.7017 | + | 22.0000i | −0.732114 | + | 1.26806i | ||||
\(302\) | 7.91066 | − | 13.7017i | 0.455207 | − | 0.788442i | ||||
\(303\) | −3.49127 | − | 6.04706i | −0.200568 | − | 0.347394i | ||||
\(304\) | 4.98792 | 0.286077 | ||||||||
\(305\) | −0.554958 | − | 0.961216i | −0.0317768 | − | 0.0550390i | ||||
\(306\) | −1.04892 | − | 1.81678i | −0.0599626 | − | 0.103858i | ||||
\(307\) | −19.9651 | −1.13947 | −0.569734 | − | 0.821829i | \(-0.692954\pi\) | ||||
−0.569734 | + | 0.821829i | \(0.692954\pi\) | |||||||
\(308\) | 1.84601 | + | 3.19738i | 0.105186 | + | 0.182188i | ||||
\(309\) | −2.47434 | + | 4.28569i | −0.140761 | + | 0.243804i | ||||
\(310\) | −1.92543 | + | 3.33494i | −0.109357 | + | 0.189412i | ||||
\(311\) | 13.4819 | 0.764487 | 0.382244 | − | 0.924062i | \(-0.375152\pi\) | ||||
0.382244 | + | 0.924062i | \(0.375152\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9245 | 0.730537 | 0.365269 | − | 0.930902i | \(-0.380977\pi\) | ||||
0.365269 | + | 0.930902i | \(0.380977\pi\) | |||||||
\(314\) | −2.13706 | + | 3.70150i | −0.120601 | + | 0.208888i | ||||
\(315\) | −0.722521 | + | 1.25144i | −0.0407094 | + | 0.0705108i | ||||
\(316\) | 5.85354 | + | 10.1386i | 0.329288 | + | 0.570343i | ||||
\(317\) | 11.8726 | 0.666833 | 0.333417 | − | 0.942780i | \(-0.391798\pi\) | ||||
0.333417 | + | 0.942780i | \(0.391798\pi\) | |||||||
\(318\) | 5.20560 | + | 9.01636i | 0.291915 | + | 0.505612i | ||||
\(319\) | −3.88255 | − | 6.72478i | −0.217381 | − | 0.376515i | ||||
\(320\) | −0.356896 | −0.0199511 | ||||||||
\(321\) | 2.13437 | + | 3.69685i | 0.119129 | + | 0.206338i | ||||
\(322\) | −17.1957 | + | 29.7838i | −0.958277 | + | 1.65978i | ||||
\(323\) | 5.23191 | − | 9.06194i | 0.291111 | − | 0.504220i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.317667 | −0.0175940 | ||||||||
\(327\) | −3.10992 | + | 5.38653i | −0.171979 | + | 0.297876i | ||||
\(328\) | 3.80194 | − | 6.58515i | 0.209927 | − | 0.363604i | ||||
\(329\) | −3.60388 | − | 6.24210i | −0.198688 | − | 0.344138i | ||||
\(330\) | 0.325437 | 0.0179147 | ||||||||
\(331\) | 5.11960 | + | 8.86742i | 0.281399 | + | 0.487397i | 0.971730 | − | 0.236097i | \(-0.0758682\pi\) |
−0.690331 | + | 0.723494i | \(0.742535\pi\) | |||||||
\(332\) | −3.24967 | − | 5.62859i | −0.178349 | − | 0.308909i | ||||
\(333\) | 0.615957 | 0.0337542 | ||||||||
\(334\) | −6.18060 | − | 10.7051i | −0.338188 | − | 0.585758i | ||||
\(335\) | −2.42327 | + | 4.19723i | −0.132397 | + | 0.229319i | ||||
\(336\) | 2.02446 | − | 3.50647i | 0.110443 | − | 0.191293i | ||||
\(337\) | 1.44935 | 0.0789513 | 0.0394757 | − | 0.999221i | \(-0.487431\pi\) | ||||
0.0394757 | + | 0.999221i | \(0.487431\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9879 | 0.705407 | ||||||||
\(340\) | −0.374354 | + | 0.648401i | −0.0203022 | + | 0.0351645i | ||||
\(341\) | −4.91939 | + | 8.52063i | −0.266400 | + | 0.461418i | ||||
\(342\) | 2.49396 | + | 4.31966i | 0.134858 | + | 0.233581i | ||||
\(343\) | −9.69202 | −0.523320 | ||||||||
\(344\) | −3.13706 | − | 5.43355i | −0.169139 | − | 0.292958i | ||||
\(345\) | 1.51573 | + | 2.62532i | 0.0816041 | + | 0.141343i | ||||
\(346\) | 17.0640 | 0.917365 | ||||||||
\(347\) | −3.42058 | − | 5.92462i | −0.183627 | − | 0.318050i | 0.759486 | − | 0.650523i | \(-0.225450\pi\) |
−0.943113 | + | 0.332473i | \(0.892117\pi\) | |||||||
\(348\) | −4.25786 | + | 7.37484i | −0.228246 | + | 0.395333i | ||||
\(349\) | −17.1685 | + | 29.7368i | −0.919010 | + | 1.59177i | −0.118088 | + | 0.993003i | \(0.537676\pi\) |
−0.800922 | + | 0.598769i | \(0.795657\pi\) | |||||||
\(350\) | −19.7289 | −1.05455 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.911854 | −0.0486020 | ||||||||
\(353\) | 13.0248 | − | 22.5595i | 0.693238 | − | 1.20072i | −0.277533 | − | 0.960716i | \(-0.589517\pi\) |
0.970771 | − | 0.240007i | \(-0.0771497\pi\) | |||||||
\(354\) | 3.02446 | − | 5.23852i | 0.160748 | − | 0.278424i | ||||
\(355\) | −2.04892 | − | 3.54883i | −0.108745 | − | 0.188352i | ||||
\(356\) | 6.49396 | 0.344179 | ||||||||
\(357\) | −4.24698 | − | 7.35598i | −0.224774 | − | 0.389320i | ||||
\(358\) | −12.4840 | − | 21.6230i | −0.659802 | − | 1.14281i | ||||
\(359\) | −8.49396 | −0.448294 | −0.224147 | − | 0.974555i | \(-0.571960\pi\) | ||||
−0.224147 | + | 0.974555i | \(0.571960\pi\) | |||||||
\(360\) | −0.178448 | − | 0.309081i | −0.00940503 | − | 0.0162900i | ||||
\(361\) | −2.93967 | + | 5.09165i | −0.154719 | + | 0.267982i | ||||
\(362\) | 2.63102 | − | 4.55706i | 0.138283 | − | 0.239514i | ||||
\(363\) | −10.1685 | −0.533709 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.190293 | 0.00996037 | ||||||||
\(366\) | −1.55496 | + | 2.69327i | −0.0812790 | + | 0.140779i | ||||
\(367\) | −13.7262 | + | 23.7744i | −0.716500 | + | 1.24101i | 0.245878 | + | 0.969301i | \(0.420924\pi\) |
−0.962378 | + | 0.271714i | \(0.912410\pi\) | |||||||
\(368\) | −4.24698 | − | 7.35598i | −0.221389 | − | 0.383457i | ||||
\(369\) | 7.60388 | 0.395842 | ||||||||
\(370\) | −0.109916 | − | 0.190381i | −0.00571427 | − | 0.00989741i | ||||
\(371\) | 21.0770 | + | 36.5065i | 1.09426 | + | 1.89532i | ||||
\(372\) | 10.7899 | 0.559428 | ||||||||
\(373\) | −13.3110 | − | 23.0553i | −0.689216 | − | 1.19376i | −0.972092 | − | 0.234600i | \(-0.924622\pi\) |
0.282876 | − | 0.959156i | \(-0.408711\pi\) | |||||||
\(374\) | −0.956459 | + | 1.65664i | −0.0494573 | + | 0.0856626i | ||||
\(375\) | −1.76175 | + | 3.05144i | −0.0909764 | + | 0.157576i | ||||
\(376\) | 1.78017 | 0.0918051 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.04892 | 0.208254 | ||||||||
\(379\) | 5.82371 | − | 10.0870i | 0.299144 | − | 0.518132i | −0.676797 | − | 0.736170i | \(-0.736632\pi\) |
0.975940 | + | 0.218038i | \(0.0699656\pi\) | |||||||
\(380\) | 0.890084 | − | 1.54167i | 0.0456603 | − | 0.0790860i | ||||
\(381\) | −4.61141 | − | 7.98719i | −0.236250 | − | 0.409196i | ||||
\(382\) | −10.5375 | −0.539145 | ||||||||
\(383\) | 5.25906 | + | 9.10896i | 0.268725 | + | 0.465446i | 0.968533 | − | 0.248885i | \(-0.0800642\pi\) |
−0.699807 | + | 0.714331i | \(0.746731\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 1.31767 | 0.0671545 | ||||||||
\(386\) | −1.71379 | − | 2.96837i | −0.0872297 | − | 0.151086i | ||||
\(387\) | 3.13706 | − | 5.43355i | 0.159466 | − | 0.276203i | ||||
\(388\) | −0.980386 | + | 1.69808i | −0.0497715 | + | 0.0862068i | ||||
\(389\) | −9.25965 | −0.469483 | −0.234742 | − | 0.972058i | \(-0.575424\pi\) | ||||
−0.234742 | + | 0.972058i | \(0.575424\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8189 | −0.901142 | ||||||||
\(392\) | 4.69687 | − | 8.13521i | 0.237228 | − | 0.410890i | ||||
\(393\) | 7.27628 | − | 12.6029i | 0.367040 | − | 0.635732i | ||||
\(394\) | −1.88740 | − | 3.26906i | −0.0950856 | − | 0.164693i | ||||
\(395\) | 4.17821 | 0.210229 | ||||||||
\(396\) | −0.455927 | − | 0.789689i | −0.0229112 | − | 0.0396834i | ||||
\(397\) | 7.25667 | + | 12.5689i | 0.364202 | + | 0.630816i | 0.988648 | − | 0.150252i | \(-0.0480085\pi\) |
−0.624446 | + | 0.781068i | \(0.714675\pi\) | |||||||
\(398\) | −17.9541 | −0.899956 | ||||||||
\(399\) | 10.0978 | + | 17.4900i | 0.505524 | + | 0.875593i | ||||
\(400\) | 2.43631 | − | 4.21982i | 0.121816 | − | 0.210991i | ||||
\(401\) | −19.4209 | + | 33.6379i | −0.969832 | + | 1.67980i | −0.273803 | + | 0.961786i | \(0.588282\pi\) |
−0.696030 | + | 0.718013i | \(0.745052\pi\) | |||||||
\(402\) | 13.5797 | 0.677294 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.98254 | 0.347394 | ||||||||
\(405\) | 0.178448 | − | 0.309081i | 0.00886715 | − | 0.0153584i | ||||
\(406\) | −17.2397 | + | 29.8601i | −0.855594 | + | 1.48193i | ||||
\(407\) | −0.280831 | − | 0.486414i | −0.0139203 | − | 0.0241107i | ||||
\(408\) | 2.09783 | 0.103858 | ||||||||
\(409\) | 16.9611 | + | 29.3774i | 0.838671 | + | 1.45262i | 0.891006 | + | 0.453991i | \(0.150000\pi\) |
−0.0523356 | + | 0.998630i | \(0.516667\pi\) | |||||||
\(410\) | −1.35690 | − | 2.35021i | −0.0670123 | − | 0.116069i | ||||
\(411\) | 15.4034 | 0.759795 | ||||||||
\(412\) | −2.47434 | − | 4.28569i | −0.121902 | − | 0.211141i | ||||
\(413\) | 12.2458 | − | 21.2103i | 0.602576 | − | 1.04369i | ||||
\(414\) | 4.24698 | − | 7.35598i | 0.208728 | − | 0.361527i | ||||
\(415\) | −2.31959 | −0.113864 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.71379 | 0.132895 | ||||||||
\(418\) | 2.27413 | − | 3.93890i | 0.111231 | − | 0.192658i | ||||
\(419\) | −0.477697 | + | 0.827396i | −0.0233370 | + | 0.0404209i | −0.877458 | − | 0.479653i | \(-0.840762\pi\) |
0.854121 | + | 0.520074i | \(0.174096\pi\) | |||||||
\(420\) | −0.722521 | − | 1.25144i | −0.0352554 | − | 0.0610642i | ||||
\(421\) | −5.68233 | −0.276940 | −0.138470 | − | 0.990367i | \(-0.544218\pi\) | ||||
−0.138470 | + | 0.990367i | \(0.544218\pi\) | |||||||
\(422\) | −6.26875 | − | 10.8578i | −0.305158 | − | 0.528549i | ||||
\(423\) | 0.890084 | + | 1.54167i | 0.0432774 | + | 0.0749586i | ||||
\(424\) | −10.4112 | −0.505612 | ||||||||
\(425\) | −5.11098 | − | 8.85248i | −0.247919 | − | 0.429408i | ||||
\(426\) | −5.74094 | + | 9.94360i | −0.278149 | + | 0.481769i | ||||
\(427\) | −6.29590 | + | 10.9048i | −0.304680 | + | 0.527721i | ||||
\(428\) | −4.26875 | −0.206338 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.23921 | −0.107984 | ||||||||
\(431\) | 7.42327 | − | 12.8575i | 0.357566 | − | 0.619323i | −0.629987 | − | 0.776605i | \(-0.716940\pi\) |
0.987554 | + | 0.157282i | \(0.0502732\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 13.0749 | + | 22.6463i | 0.628338 | + | 1.08831i | 0.987885 | + | 0.155187i | \(0.0495979\pi\) |
−0.359547 | + | 0.933127i | \(0.617069\pi\) | |||||||
\(434\) | 43.6872 | 2.09705 | ||||||||
\(435\) | 1.51961 | + | 2.63205i | 0.0728599 | + | 0.126197i | ||||
\(436\) | −3.10992 | − | 5.38653i | −0.148938 | − | 0.257968i | ||||
\(437\) | 42.3672 | 2.02670 | ||||||||
\(438\) | −0.266594 | − | 0.461754i | −0.0127384 | − | 0.0220635i | ||||
\(439\) | 11.7751 | − | 20.3950i | 0.561994 | − | 0.973403i | −0.435328 | − | 0.900272i | \(-0.643368\pi\) |
0.997322 | − | 0.0731307i | \(-0.0232990\pi\) | |||||||
\(440\) | −0.162718 | + | 0.281837i | −0.00775730 | + | 0.0134360i | ||||
\(441\) | 9.39373 | 0.447321 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.9433 | 1.04256 | 0.521279 | − | 0.853386i | \(-0.325455\pi\) | ||||
0.521279 | + | 0.853386i | \(0.325455\pi\) | |||||||
\(444\) | −0.307979 | + | 0.533434i | −0.0146160 | + | 0.0253157i | ||||
\(445\) | 1.15883 | − | 2.00716i | 0.0549340 | − | 0.0951484i | ||||
\(446\) | −2.71379 | − | 4.70043i | −0.128502 | − | 0.222572i | ||||
\(447\) | 14.7356 | 0.696968 | ||||||||
\(448\) | 2.02446 | + | 3.50647i | 0.0956467 | + | 0.165665i | ||||
\(449\) | −5.70171 | − | 9.87565i | −0.269080 | − | 0.466061i | 0.699544 | − | 0.714589i | \(-0.253386\pi\) |
−0.968625 | + | 0.248528i | \(0.920053\pi\) | |||||||
\(450\) | 4.87263 | 0.229698 | ||||||||
\(451\) | −3.46681 | − | 6.00469i | −0.163246 | − | 0.282750i | ||||
\(452\) | −6.49396 | + | 11.2479i | −0.305450 | + | 0.529055i | ||||
\(453\) | −7.91066 | + | 13.7017i | −0.371675 | + | 0.643760i | ||||
\(454\) | 16.5767 | 0.777984 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.98792 | −0.233581 | ||||||||
\(457\) | −3.83459 | + | 6.64171i | −0.179375 | + | 0.310686i | −0.941667 | − | 0.336547i | \(-0.890741\pi\) |
0.762292 | + | 0.647233i | \(0.224074\pi\) | |||||||
\(458\) | 11.9390 | − | 20.6790i | 0.557873 | − | 0.966264i | ||||
\(459\) | 1.04892 | + | 1.81678i | 0.0489593 | + | 0.0847999i | ||||
\(460\) | −3.03146 | −0.141343 | ||||||||
\(461\) | 14.2540 | + | 24.6886i | 0.663874 | + | 1.14986i | 0.979589 | + | 0.201010i | \(0.0644222\pi\) |
−0.315715 | + | 0.948854i | \(0.602244\pi\) | |||||||
\(462\) | −1.84601 | − | 3.19738i | −0.0858842 | − | 0.148756i | ||||
\(463\) | −14.3284 | −0.665898 | −0.332949 | − | 0.942945i | \(-0.608044\pi\) | ||||
−0.332949 | + | 0.942945i | \(0.608044\pi\) | |||||||
\(464\) | −4.25786 | − | 7.37484i | −0.197666 | − | 0.342368i | ||||
\(465\) | 1.92543 | − | 3.33494i | 0.0892896 | − | 0.154654i | ||||
\(466\) | 6.99761 | − | 12.1202i | 0.324158 | − | 0.561458i | ||||
\(467\) | 33.3207 | 1.54190 | 0.770948 | − | 0.636898i | \(-0.219783\pi\) | ||||
0.770948 | + | 0.636898i | \(0.219783\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.9831 | 2.53889 | ||||||||
\(470\) | 0.317667 | − | 0.550216i | 0.0146529 | − | 0.0253796i | ||||
\(471\) | 2.13706 | − | 3.70150i | 0.0984707 | − | 0.170556i | ||||
\(472\) | 3.02446 | + | 5.23852i | 0.139212 | + | 0.241122i | ||||
\(473\) | −5.72109 | −0.263056 | ||||||||
\(474\) | −5.85354 | − | 10.1386i | −0.268862 | − | 0.465683i | ||||
\(475\) | 12.1521 | + | 21.0481i | 0.557578 | + | 0.965753i | ||||
\(476\) | 8.49396 | 0.389320 | ||||||||
\(477\) | −5.20560 | − | 9.01636i | −0.238348 | − | 0.412831i | ||||
\(478\) | −6.64310 | + | 11.5062i | −0.303849 | + | 0.526281i | ||||
\(479\) | 11.0640 | − | 19.1634i | 0.505526 | − | 0.875597i | −0.494453 | − | 0.869204i | \(-0.664632\pi\) |
0.999980 | − | 0.00639300i | \(-0.00203497\pi\) | |||||||
\(480\) | 0.356896 | 0.0162900 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.4789 | 0.477301 | ||||||||
\(483\) | 17.1957 | − | 29.7838i | 0.782430 | − | 1.35521i | ||||
\(484\) | 5.08426 | − | 8.80620i | 0.231103 | − | 0.400282i | ||||
\(485\) | 0.349896 | + | 0.606037i | 0.0158879 | + | 0.0275187i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 0.0631549 | + | 0.109387i | 0.00286182 | + | 0.00495682i | 0.867453 | − | 0.497520i | \(-0.165756\pi\) |
−0.864591 | + | 0.502476i | \(0.832422\pi\) | |||||||
\(488\) | −1.55496 | − | 2.69327i | −0.0703896 | − | 0.121918i | ||||
\(489\) | 0.317667 | 0.0143654 | ||||||||
\(490\) | −1.67629 | − | 2.90342i | −0.0757272 | − | 0.131163i | ||||
\(491\) | −6.97166 | + | 12.0753i | −0.314626 | + | 0.544949i | −0.979358 | − | 0.202133i | \(-0.935213\pi\) |
0.664732 | + | 0.747082i | \(0.268546\pi\) | |||||||
\(492\) | −3.80194 | + | 6.58515i | −0.171405 | + | 0.296881i | ||||
\(493\) | −17.8646 | −0.804581 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.325437 | −0.0146273 | ||||||||
\(496\) | −5.39493 | + | 9.34429i | −0.242239 | + | 0.419571i | ||||
\(497\) | −23.2446 | + | 40.2608i | −1.04266 | + | 1.80594i | ||||
\(498\) | 3.24967 | + | 5.62859i | 0.145621 | + | 0.252223i | ||||
\(499\) | 28.3913 | 1.27097 | 0.635485 | − | 0.772113i | \(-0.280800\pi\) | ||||
0.635485 | + | 0.772113i | \(0.280800\pi\) | |||||||
\(500\) | −1.76175 | − | 3.05144i | −0.0787878 | − | 0.136465i | ||||
\(501\) | 6.18060 | + | 10.7051i | 0.276129 | + | 0.478269i | ||||
\(502\) | −3.48725 | −0.155644 | ||||||||
\(503\) | −6.28382 | − | 10.8839i | −0.280181 | − | 0.485289i | 0.691248 | − | 0.722618i | \(-0.257061\pi\) |
−0.971429 | + | 0.237329i | \(0.923728\pi\) | |||||||
\(504\) | −2.02446 | + | 3.50647i | −0.0901766 | + | 0.156190i | ||||
\(505\) | 1.24602 | − | 2.15817i | 0.0554472 | − | 0.0960373i | ||||
\(506\) | −7.74525 | −0.344318 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.22282 | 0.409196 | ||||||||
\(509\) | −2.18837 | + | 3.79037i | −0.0969980 | + | 0.168005i | −0.910441 | − | 0.413640i | \(-0.864257\pi\) |
0.813443 | + | 0.581645i | \(0.197591\pi\) | |||||||
\(510\) | 0.374354 | − | 0.648401i | 0.0165767 | − | 0.0287117i | ||||
\(511\) | −1.07942 | − | 1.86960i | −0.0477506 | − | 0.0827064i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.49396 | − | 4.31966i | −0.110111 | − | 0.190718i | ||||
\(514\) | 3.26875 | + | 5.66164i | 0.144178 | + | 0.249724i | ||||
\(515\) | −1.76617 | −0.0778266 | ||||||||
\(516\) | 3.13706 | + | 5.43355i | 0.138102 | + | 0.239199i | ||||
\(517\) | 0.811626 | − | 1.40578i | 0.0356953 | − | 0.0618261i | ||||
\(518\) | −1.24698 | + | 2.15983i | −0.0547891 | + | 0.0948976i | ||||
\(519\) | −17.0640 | −0.749026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.2707 | −1.01951 | −0.509753 | − | 0.860321i | \(-0.670263\pi\) | ||||
−0.509753 | + | 0.860321i | \(0.670263\pi\) | |||||||
\(522\) | 4.25786 | − | 7.37484i | 0.186362 | − | 0.322788i | ||||
\(523\) | −18.9976 | + | 32.9048i | −0.830707 | + | 1.43883i | 0.0667707 | + | 0.997768i | \(0.478730\pi\) |
−0.897478 | + | 0.441059i | \(0.854603\pi\) | |||||||
\(524\) | 7.27628 | + | 12.6029i | 0.317866 | + | 0.550560i | ||||
\(525\) | 19.7289 | 0.861038 | ||||||||
\(526\) | 4.00969 | + | 6.94498i | 0.174831 | + | 0.302816i | ||||
\(527\) | 11.3177 | + | 19.6028i | 0.493005 | + | 0.853910i | ||||
\(528\) | 0.911854 | 0.0396834 | ||||||||
\(529\) | −24.5737 | − | 42.5628i | −1.06842 | − | 1.85056i | ||||
\(530\) | −1.85786 | + | 3.21790i | −0.0807001 | + | 0.139777i | ||||
\(531\) | −3.02446 | + | 5.23852i | −0.131250 | + | 0.227332i | ||||
\(532\) | −20.1957 | −0.875593 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.49396 | −0.281021 | ||||||||
\(535\) | −0.761750 | + | 1.31939i | −0.0329333 | + | 0.0570422i | ||||
\(536\) | −6.78986 | + | 11.7604i | −0.293277 | + | 0.507971i | ||||
\(537\) | 12.4840 | + | 21.6230i | 0.538726 | + | 0.933100i | ||||
\(538\) | 27.6732 | 1.19308 | ||||||||
\(539\) | −4.28286 | − | 7.41812i | −0.184476 | − | 0.319521i | ||||
\(540\) | 0.178448 | + | 0.309081i | 0.00767918 | + | 0.0133007i | ||||
\(541\) | 3.16421 | 0.136040 | 0.0680200 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680200 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(542\) | −7.36443 | − | 12.7556i | −0.316329 | − | 0.547898i | ||||
\(543\) | −2.63102 | + | 4.55706i | −0.112908 | + | 0.195562i | ||||
\(544\) | −1.04892 | + | 1.81678i | −0.0449720 | + | 0.0778937i | ||||
\(545\) | −2.21983 | −0.0950872 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.56033 | 0.323257 | 0.161628 | − | 0.986852i | \(-0.448325\pi\) | ||||
0.161628 | + | 0.986852i | \(0.448325\pi\) | |||||||
\(548\) | −7.70171 | + | 13.3398i | −0.329001 | + | 0.569846i | ||||
\(549\) | 1.55496 | − | 2.69327i | 0.0663640 | − | 0.114946i | ||||
\(550\) | −2.22156 | − | 3.84786i | −0.0947277 | − | 0.164073i | ||||
\(551\) | 42.4758 | 1.80953 | ||||||||
\(552\) | 4.24698 | + | 7.35598i | 0.180763 | + | 0.313091i | ||||
\(553\) | −23.7005 | − | 41.0505i | −1.00785 | − | 1.74564i | ||||
\(554\) | −3.26205 | −0.138591 | ||||||||
\(555\) | 0.109916 | + | 0.190381i | 0.00466569 | + | 0.00808120i | ||||
\(556\) | −1.35690 | + | 2.35021i | −0.0575452 | + | 0.0996712i | ||||
\(557\) | 0.207751 | − | 0.359835i | 0.00880269 | − | 0.0152467i | −0.861591 | − | 0.507604i | \(-0.830531\pi\) |
0.870393 | + | 0.492357i | \(0.163865\pi\) | |||||||
\(558\) | −10.7899 | −0.456771 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.44504 | 0.0610642 | ||||||||
\(561\) | 0.956459 | − | 1.65664i | 0.0403818 | − | 0.0699432i | ||||
\(562\) | −3.86294 | + | 6.69080i | −0.162948 | + | 0.282234i | ||||
\(563\) | 14.5233 | + | 25.1550i | 0.612083 | + | 1.06016i | 0.990889 | + | 0.134682i | \(0.0430013\pi\) |
−0.378806 | + | 0.925476i | \(0.623665\pi\) | |||||||
\(564\) | −1.78017 | −0.0749586 | ||||||||
\(565\) | 2.31767 | + | 4.01432i | 0.0975050 | + | 0.168884i | ||||
\(566\) | −9.89008 | − | 17.1301i | −0.415711 | − | 0.720033i | ||||
\(567\) | −4.04892 | −0.170039 | ||||||||
\(568\) | −5.74094 | − | 9.94360i | −0.240884 | − | 0.417224i | ||||
\(569\) | −19.8431 | + | 34.3692i | −0.831865 | + | 1.44083i | 0.0646918 | + | 0.997905i | \(0.479394\pi\) |
−0.896557 | + | 0.442928i | \(0.853940\pi\) | |||||||
\(570\) | −0.890084 | + | 1.54167i | −0.0372815 | + | 0.0645735i | ||||
\(571\) | −7.09651 | −0.296980 | −0.148490 | − | 0.988914i | \(-0.547441\pi\) | ||||
−0.148490 | + | 0.988914i | \(0.547441\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5375 | 0.440210 | ||||||||
\(574\) | −15.3937 | + | 26.6627i | −0.642522 | + | 1.11288i | ||||
\(575\) | 20.6939 | − | 35.8430i | 0.862997 | − | 1.49475i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −8.78687 | −0.365802 | −0.182901 | − | 0.983131i | \(-0.558549\pi\) | ||||
−0.182901 | + | 0.983131i | \(0.558549\pi\) | |||||||
\(578\) | −6.29954 | − | 10.9111i | −0.262027 | − | 0.453843i | ||||
\(579\) | 1.71379 | + | 2.96837i | 0.0712228 | + | 0.123361i | ||||
\(580\) | −3.03923 | −0.126197 | ||||||||
\(581\) | 13.1576 | + | 22.7897i | 0.545871 | + | 0.945476i | ||||
\(582\) | 0.980386 | − | 1.69808i | 0.0406383 | − | 0.0703876i | ||||
\(583\) | −4.74674 | + | 8.22160i | −0.196590 | + | 0.340504i | ||||
\(584\) | 0.533188 | 0.0220635 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.9119 | −0.533384 | ||||||||
\(587\) | 18.3533 | − | 31.7889i | 0.757522 | − | 1.31207i | −0.186589 | − | 0.982438i | \(-0.559743\pi\) |
0.944111 | − | 0.329629i | \(-0.106923\pi\) | |||||||
\(588\) | −4.69687 | + | 8.13521i | −0.193695 | + | 0.335490i | ||||
\(589\) | −26.9095 | − | 46.6086i | −1.10879 | − | 1.92047i | ||||
\(590\) | 2.15883 | 0.0888778 | ||||||||
\(591\) | 1.88740 | + | 3.26906i | 0.0776371 | + | 0.134471i | ||||
\(592\) | −0.307979 | − | 0.533434i | −0.0126578 | − | 0.0219240i | ||||
\(593\) | −10.8310 | −0.444776 | −0.222388 | − | 0.974958i | \(-0.571385\pi\) | ||||
−0.222388 | + | 0.974958i | \(0.571385\pi\) | |||||||
\(594\) | 0.455927 | + | 0.789689i | 0.0187069 | + | 0.0324013i | ||||
\(595\) | 1.51573 | − | 2.62532i | 0.0621389 | − | 0.107628i | ||||
\(596\) | −7.36778 | + | 12.7614i | −0.301796 | + | 0.522726i | ||||
\(597\) | 17.9541 | 0.734811 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.5254 | 0.961223 | 0.480611 | − | 0.876934i | \(-0.340415\pi\) | ||||
0.480611 | + | 0.876934i | \(0.340415\pi\) | |||||||
\(600\) | −2.43631 | + | 4.21982i | −0.0994620 | + | 0.172273i | ||||
\(601\) | −13.9107 | + | 24.0940i | −0.567428 | + | 0.982813i | 0.429392 | + | 0.903118i | \(0.358728\pi\) |
−0.996819 | + | 0.0796950i | \(0.974605\pi\) | |||||||
\(602\) | 12.7017 | + | 22.0000i | 0.517683 | + | 0.896653i | ||||
\(603\) | −13.5797 | −0.553009 | ||||||||
\(604\) | −7.91066 | − | 13.7017i | −0.321880 | − | 0.557513i | ||||
\(605\) | −1.81455 | − | 3.14290i | −0.0737720 | − | 0.127777i | ||||
\(606\) | −6.98254 | −0.283646 | ||||||||
\(607\) | −0.0486218 | − | 0.0842155i | −0.00197350 | − | 0.00341820i | 0.865037 | − | 0.501708i | \(-0.167295\pi\) |
−0.867010 | + | 0.498290i | \(0.833962\pi\) | |||||||
\(608\) | 2.49396 | − | 4.31966i | 0.101143 | − | 0.175186i | ||||
\(609\) | 17.2397 | − | 29.8601i | 0.698590 | − | 1.20999i | ||||
\(610\) | −1.10992 | −0.0449392 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.09783 | −0.0847999 | ||||||||
\(613\) | −4.03252 | + | 6.98454i | −0.162872 | + | 0.282103i | −0.935898 | − | 0.352272i | \(-0.885409\pi\) |
0.773025 | + | 0.634375i | \(0.218742\pi\) | |||||||
\(614\) | −9.98254 | + | 17.2903i | −0.402863 | + | 0.697778i | ||||
\(615\) | 1.35690 | + | 2.35021i | 0.0547153 | + | 0.0947697i | ||||
\(616\) | 3.69202 | 0.148756 | ||||||||
\(617\) | 9.60925 | + | 16.6437i | 0.386854 | + | 0.670051i | 0.992025 | − | 0.126045i | \(-0.0402284\pi\) |
−0.605171 | + | 0.796096i | \(0.706895\pi\) | |||||||
\(618\) | 2.47434 | + | 4.28569i | 0.0995327 | + | 0.172396i | ||||
\(619\) | 12.3827 | 0.497703 | 0.248852 | − | 0.968542i | \(-0.419947\pi\) | ||||
0.248852 | + | 0.968542i | \(0.419947\pi\) | |||||||
\(620\) | 1.92543 | + | 3.33494i | 0.0773270 | + | 0.133934i | ||||
\(621\) | −4.24698 | + | 7.35598i | −0.170425 | + | 0.295185i | ||||
\(622\) | 6.74094 | − | 11.6756i | 0.270287 | − | 0.468151i | ||||
\(623\) | −26.2935 | −1.05343 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1056 | 0.924224 | ||||||||
\(626\) | 6.46226 | − | 11.1930i | 0.258284 | − | 0.447361i | ||||
\(627\) | −2.27413 | + | 3.93890i | −0.0908199 | + | 0.157305i | ||||
\(628\) | 2.13706 | + | 3.70150i | 0.0852781 | + | 0.147706i | ||||
\(629\) | −1.29218 | −0.0515224 | ||||||||
\(630\) | 0.722521 | + | 1.25144i | 0.0287859 | + | 0.0498587i | ||||
\(631\) | 2.37167 | + | 4.10785i | 0.0944145 | + | 0.163531i | 0.909364 | − | 0.416001i | \(-0.136569\pi\) |
−0.814950 | + | 0.579532i | \(0.803235\pi\) | |||||||
\(632\) | 11.7071 | 0.465683 | ||||||||
\(633\) | 6.26875 | + | 10.8578i | 0.249160 | + | 0.431559i | ||||
\(634\) | 5.93631 | − | 10.2820i | 0.235761 | − | 0.408350i | ||||
\(635\) | 1.64579 | − | 2.85060i | 0.0653113 | − | 0.113122i | ||||
\(636\) | 10.4112 | 0.412831 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.76510 | −0.307423 | ||||||||
\(639\) | 5.74094 | − | 9.94360i | 0.227108 | − | 0.393363i | ||||
\(640\) | −0.178448 | + | 0.309081i | −0.00705377 | + | 0.0122175i | ||||
\(641\) | 8.22282 | + | 14.2423i | 0.324782 | + | 0.562538i | 0.981468 | − | 0.191625i | \(-0.0613758\pi\) |
−0.656686 | + | 0.754164i | \(0.728042\pi\) | |||||||
\(642\) | 4.26875 | 0.168474 | ||||||||
\(643\) | −0.872625 | − | 1.51143i | −0.0344130 | − | 0.0596050i | 0.848306 | − | 0.529506i | \(-0.177623\pi\) |
−0.882719 | + | 0.469901i | \(0.844289\pi\) | |||||||
\(644\) | 17.1957 | + | 29.7838i | 0.677604 | + | 1.17365i | ||||
\(645\) | 2.23921 | 0.0881688 | ||||||||
\(646\) | −5.23191 | − | 9.06194i | −0.205847 | − | 0.356537i | ||||
\(647\) | −14.3817 | + | 24.9097i | −0.565401 | + | 0.979303i | 0.431611 | + | 0.902060i | \(0.357945\pi\) |
−0.997012 | + | 0.0772436i | \(0.975388\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 5.51573 | 0.216511 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −43.6872 | −1.71224 | ||||||||
\(652\) | −0.158834 | + | 0.275108i | −0.00622040 | + | 0.0107741i | ||||
\(653\) | 8.08306 | − | 14.0003i | 0.316315 | − | 0.547873i | −0.663401 | − | 0.748264i | \(-0.730888\pi\) |
0.979716 | + | 0.200391i | \(0.0642211\pi\) | |||||||
\(654\) | 3.10992 | + | 5.38653i | 0.121607 | + | 0.210630i | ||||
\(655\) | 5.19375 | 0.202937 | ||||||||
\(656\) | −3.80194 | − | 6.58515i | −0.148441 | − | 0.257107i | ||||
\(657\) | 0.266594 | + | 0.461754i | 0.0104008 | + | 0.0180147i | ||||
\(658\) | −7.20775 | −0.280987 | ||||||||
\(659\) | 8.17792 | + | 14.1646i | 0.318566 | + | 0.551773i | 0.980189 | − | 0.198064i | \(-0.0634653\pi\) |
−0.661623 | + | 0.749837i | \(0.730132\pi\) | |||||||
\(660\) | 0.162718 | − | 0.281837i | 0.00633381 | − | 0.0109705i | ||||
\(661\) | 16.5579 | − | 28.6792i | 0.644029 | − | 1.11549i | −0.340495 | − | 0.940246i | \(-0.610595\pi\) |
0.984525 | − | 0.175245i | \(-0.0560719\pi\) | |||||||
\(662\) | 10.2392 | 0.397958 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.49934 | −0.252223 | ||||||||
\(665\) | −3.60388 | + | 6.24210i | −0.139752 | + | 0.242058i | ||||
\(666\) | 0.307979 | − | 0.533434i | 0.0119339 | − | 0.0206702i | ||||
\(667\) | −36.1661 | − | 62.6416i | −1.40036 | − | 2.42549i | ||||
\(668\) | −12.3612 | −0.478269 | ||||||||
\(669\) | 2.71379 | + | 4.70043i | 0.104921 | + | 0.181729i | ||||
\(670\) | 2.42327 | + | 4.19723i | 0.0936191 | + | 0.162153i | ||||
\(671\) | −2.83579 | −0.109474 | ||||||||
\(672\) | −2.02446 | − | 3.50647i | −0.0780952 | − | 0.135265i | ||||
\(673\) | 17.5770 | − | 30.4443i | 0.677544 | − | 1.17354i | −0.298174 | − | 0.954512i | \(-0.596377\pi\) |
0.975718 | − | 0.219030i | \(-0.0702892\pi\) | |||||||
\(674\) | 0.724677 | − | 1.25518i | 0.0279135 | − | 0.0483476i | ||||
\(675\) | −4.87263 | −0.187547 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.7855 | 0.914153 | 0.457076 | − | 0.889427i | \(-0.348897\pi\) | ||||
0.457076 | + | 0.889427i | \(0.348897\pi\) | |||||||
\(678\) | 6.49396 | − | 11.2479i | 0.249399 | − | 0.431972i | ||||
\(679\) | 3.96950 | − | 6.87538i | 0.152335 | − | 0.263853i | ||||
\(680\) | 0.374354 | + | 0.648401i | 0.0143558 | + | 0.0248650i | ||||
\(681\) | −16.5767 | −0.635222 | ||||||||
\(682\) | 4.91939 | + | 8.52063i | 0.188373 | + | 0.326272i | ||||
\(683\) | −1.49612 | − | 2.59135i | −0.0572473 | − | 0.0991552i | 0.835982 | − | 0.548758i | \(-0.184899\pi\) |
−0.893229 | + | 0.449602i | \(0.851566\pi\) | |||||||
\(684\) | 4.98792 | 0.190718 | ||||||||
\(685\) | 2.74871 | + | 4.76090i | 0.105023 | + | 0.181905i | ||||
\(686\) | −4.84601 | + | 8.39354i | −0.185022 | + | 0.320467i | ||||
\(687\) | −11.9390 | + | 20.6790i | −0.455501 | + | 0.788951i | ||||
\(688\) | −6.27413 | −0.239199 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.03146 | 0.115406 | ||||||||
\(691\) | −5.81163 | + | 10.0660i | −0.221085 | + | 0.382930i | −0.955138 | − | 0.296162i | \(-0.904293\pi\) |
0.734053 | + | 0.679092i | \(0.237626\pi\) | |||||||
\(692\) | 8.53199 | − | 14.7778i | 0.324338 | − | 0.561769i | ||||
\(693\) | 1.84601 | + | 3.19738i | 0.0701241 | + | 0.121459i | ||||
\(694\) | −6.84117 | −0.259687 | ||||||||
\(695\) | 0.484271 | + | 0.838781i | 0.0183694 | + | 0.0318168i | ||||
\(696\) | 4.25786 | + | 7.37484i | 0.161394 | + | 0.279543i | ||||
\(697\) | −15.9517 | −0.604213 | ||||||||
\(698\) | 17.1685 | + | 29.7368i | 0.649838 | + | 1.12555i | ||||
\(699\) | −6.99761 | + | 12.1202i | −0.264674 | + | 0.458428i | ||||
\(700\) | −9.86443 | + | 17.0857i | −0.372840 | + | 0.645778i | ||||
\(701\) | −33.8431 | −1.27824 | −0.639118 | − | 0.769109i | \(-0.720700\pi\) | ||||
−0.639118 | + | 0.769109i | \(0.720700\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.07234 | 0.115876 | ||||||||
\(704\) | −0.455927 | + | 0.789689i | −0.0171834 | + | 0.0297625i | ||||
\(705\) | −0.317667 | + | 0.550216i | −0.0119640 | + | 0.0207223i | ||||
\(706\) | −13.0248 | − | 22.5595i | −0.490193 | − | 0.849039i | ||||
\(707\) | −28.2717 | −1.06327 | ||||||||
\(708\) | −3.02446 | − | 5.23852i | −0.113666 | − | 0.196875i | ||||
\(709\) | 13.0954 | + | 22.6820i | 0.491810 | + | 0.851839i | 0.999956 | − | 0.00943173i | \(-0.00300226\pi\) |
−0.508146 | + | 0.861271i | \(0.669669\pi\) | |||||||
\(710\) | −4.09783 | −0.153789 | ||||||||
\(711\) | 5.85354 | + | 10.1386i | 0.219525 | + | 0.380229i | ||||
\(712\) | 3.24698 | − | 5.62393i | 0.121686 | − | 0.210766i | ||||
\(713\) | −45.8243 | + | 79.3700i | −1.71613 | + | 2.97243i | ||||
\(714\) | −8.49396 | −0.317878 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.9681 | −0.933100 | ||||||||
\(717\) | 6.64310 | − | 11.5062i | 0.248091 | − | 0.429707i | ||||
\(718\) | −4.24698 | + | 7.35598i | −0.158496 | + | 0.274523i | ||||
\(719\) | 10.8672 | + | 18.8226i | 0.405280 | + | 0.701966i | 0.994354 | − | 0.106114i | \(-0.0338407\pi\) |
−0.589074 | + | 0.808079i | \(0.700507\pi\) | |||||||
\(720\) | −0.356896 | −0.0133007 | ||||||||
\(721\) | 10.0184 | + | 17.3524i | 0.373105 | + | 0.646237i | ||||
\(722\) | 2.93967 | + | 5.09165i | 0.109403 | + | 0.189492i | ||||
\(723\) | −10.4789 | −0.389714 | ||||||||
\(724\) | −2.63102 | − | 4.55706i | −0.0977812 | − | 0.169362i | ||||
\(725\) | 20.7470 | − | 35.9348i | 0.770523 | − | 1.33459i | ||||
\(726\) | −5.08426 | + | 8.80620i | −0.188695 | + | 0.326829i | ||||
\(727\) | −2.01400 | −0.0746951 | −0.0373476 | − | 0.999302i | \(-0.511891\pi\) | ||||
−0.0373476 | + | 0.999302i | \(0.511891\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.0951463 | − | 0.164798i | 0.00352152 | − | 0.00609945i | ||||
\(731\) | −6.58104 | + | 11.3987i | −0.243409 | + | 0.421596i | ||||
\(732\) | 1.55496 | + | 2.69327i | 0.0574729 | + | 0.0995460i | ||||
\(733\) | 13.5013 | 0.498680 | 0.249340 | − | 0.968416i | \(-0.419786\pi\) | ||||
0.249340 | + | 0.968416i | \(0.419786\pi\) | |||||||
\(734\) | 13.7262 | + | 23.7744i | 0.506642 | + | 0.877530i | ||||
\(735\) | 1.67629 | + | 2.90342i | 0.0618310 | + | 0.107094i | ||||
\(736\) | −8.49396 | −0.313091 | ||||||||
\(737\) | 6.19136 | + | 10.7237i | 0.228062 | + | 0.395014i | ||||
\(738\) | 3.80194 | − | 6.58515i | 0.139951 | − | 0.242403i | ||||
\(739\) | 8.29590 | − | 14.3689i | 0.305170 | − | 0.528569i | −0.672130 | − | 0.740434i | \(-0.734620\pi\) |
0.977299 | + | 0.211864i | \(0.0679535\pi\) | |||||||
\(740\) | −0.219833 | −0.00808120 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 42.1540 | 1.54752 | ||||||||
\(743\) | 9.92394 | − | 17.1888i | 0.364074 | − | 0.630594i | −0.624553 | − | 0.780982i | \(-0.714719\pi\) |
0.988627 | + | 0.150388i | \(0.0480522\pi\) | |||||||
\(744\) | 5.39493 | − | 9.34429i | 0.197788 | − | 0.342578i | ||||
\(745\) | 2.62953 | + | 4.55448i | 0.0963385 | + | 0.166863i | ||||
\(746\) | −26.6219 | −0.974698 | ||||||||
\(747\) | −3.24967 | − | 5.62859i | −0.118899 | − | 0.205939i | ||||
\(748\) | 0.956459 | + | 1.65664i | 0.0349716 | + | 0.0605726i | ||||
\(749\) | 17.2838 | 0.631537 | ||||||||
\(750\) | 1.76175 | + | 3.05144i | 0.0643300 | + | 0.111423i | ||||
\(751\) | −13.9673 | + | 24.1922i | −0.509676 | + | 0.882784i | 0.490262 | + | 0.871575i | \(0.336901\pi\) |
−0.999937 | + | 0.0112087i | \(0.996432\pi\) | |||||||
\(752\) | 0.890084 | − | 1.54167i | 0.0324580 | − | 0.0562189i | ||||
\(753\) | 3.48725 | 0.127083 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.64656 | −0.205499 | ||||||||
\(756\) | 2.02446 | − | 3.50647i | 0.0736288 | − | 0.127529i | ||||
\(757\) | 0.274127 | − | 0.474801i | 0.00996330 | − | 0.0172569i | −0.861001 | − | 0.508604i | \(-0.830162\pi\) |
0.870964 | + | 0.491347i | \(0.163495\pi\) | |||||||
\(758\) | −5.82371 | − | 10.0870i | −0.211527 | − | 0.366375i | ||||
\(759\) | 7.74525 | 0.281135 | ||||||||
\(760\) | −0.890084 | − | 1.54167i | −0.0322867 | − | 0.0559223i | ||||
\(761\) | −0.987918 | − | 1.71112i | −0.0358120 | − | 0.0620282i | 0.847564 | − | 0.530693i | \(-0.178068\pi\) |
−0.883376 | + | 0.468665i | \(0.844735\pi\) | |||||||
\(762\) | −9.22282 | −0.334107 | ||||||||
\(763\) | 12.5918 | + | 21.8096i | 0.455854 | + | 0.789562i | ||||
\(764\) | −5.26875 | + | 9.12574i | −0.190617 | + | 0.330158i | ||||
\(765\) | −0.374354 | + | 0.648401i | −0.0135348 | + | 0.0234430i | ||||
\(766\) | 10.5181 | 0.380035 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −14.3056 | + | 24.7780i | −0.515873 | + | 0.893518i | 0.483958 | + | 0.875091i | \(0.339199\pi\) |
−0.999830 | + | 0.0184261i | \(0.994134\pi\) | |||||||
\(770\) | 0.658834 | − | 1.14113i | 0.0237427 | − | 0.0411236i | ||||
\(771\) | −3.26875 | − | 5.66164i | −0.117721 | − | 0.203899i | ||||
\(772\) | −3.42758 | −0.123361 | ||||||||
\(773\) | −26.2540 | − | 45.4732i | −0.944290 | − | 1.63556i | −0.757167 | − | 0.653222i | \(-0.773417\pi\) |
−0.187123 | − | 0.982336i | \(-0.559916\pi\) | |||||||
\(774\) | −3.13706 | − | 5.43355i | −0.112759 | − | 0.195305i | ||||
\(775\) | −52.5749 | −1.88855 | ||||||||
\(776\) | 0.980386 | + | 1.69808i | 0.0351938 | + | 0.0609574i | ||||
\(777\) | 1.24698 | − | 2.15983i | 0.0447351 | − | 0.0774835i | ||||
\(778\) | −4.62983 | + | 8.01909i | −0.165987 | + | 0.287498i | ||||
\(779\) | 37.9275 | 1.35889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.4698 | −0.374639 | ||||||||
\(782\) | −8.90946 | + | 15.4316i | −0.318602 | + | 0.551834i | ||||
\(783\) | −4.25786 | + | 7.37484i | −0.152164 | + | 0.263555i | ||||
\(784\) | −4.69687 | − | 8.13521i | −0.167745 | − | 0.290543i | ||||
\(785\) | 1.52542 | 0.0544445 | ||||||||
\(786\) | −7.27628 | − | 12.6029i | −0.259536 | − | 0.449530i | ||||
\(787\) | −11.8213 | − | 20.4751i | −0.421384 | − | 0.729859i | 0.574691 | − | 0.818371i | \(-0.305122\pi\) |
−0.996075 | + | 0.0885115i | \(0.971789\pi\) | |||||||
\(788\) | −3.77479 | −0.134471 | ||||||||
\(789\) | −4.00969 | − | 6.94498i | −0.142749 | − | 0.247248i | ||||
\(790\) | 2.08911 | − | 3.61844i | 0.0743270 | − | 0.128738i | ||||
\(791\) | 26.2935 | − | 45.5417i | 0.934889 | − | 1.61928i | ||||
\(792\) | −0.911854 | −0.0324013 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 14.5133 | 0.515059 | ||||||||
\(795\) | 1.85786 | − | 3.21790i | 0.0658913 | − | 0.114127i | ||||
\(796\) | −8.97703 | + | 15.5487i | −0.318183 | + | 0.551108i | ||||
\(797\) | −20.8279 | − | 36.0750i | −0.737762 | − | 1.27784i | −0.953501 | − | 0.301390i | \(-0.902549\pi\) |
0.215739 | − | 0.976451i | \(-0.430784\pi\) | |||||||
\(798\) | 20.1957 | 0.714919 | ||||||||
\(799\) | −1.86725 | − | 3.23417i | −0.0660585 | − | 0.114417i | ||||
\(800\) | −2.43631 | − | 4.21982i | −0.0861367 | − | 0.149193i | ||||
\(801\) | 6.49396 | 0.229453 | ||||||||
\(802\) | 19.4209 | + | 33.6379i | 0.685775 | + | 1.18780i | ||||
\(803\) | 0.243095 | − | 0.421052i | 0.00857863 | − | 0.0148586i | ||||
\(804\) | 6.78986 | − | 11.7604i | 0.239460 | − | 0.414756i | ||||
\(805\) | 12.2741 | 0.432606 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.6732 | −0.974144 | ||||||||
\(808\) | 3.49127 | − | 6.04706i | 0.122822 | − | 0.212735i | ||||
\(809\) | 22.1196 | − | 38.3123i | 0.777684 | − | 1.34699i | −0.155590 | − | 0.987822i | \(-0.549728\pi\) |
0.933274 | − | 0.359166i | \(-0.116939\pi\) | |||||||
\(810\) | −0.178448 | − | 0.309081i | −0.00627002 | − | 0.0108600i | ||||
\(811\) | −52.3913 | −1.83971 | −0.919854 | − | 0.392260i | \(-0.871693\pi\) | ||||
−0.919854 | + | 0.392260i | \(0.871693\pi\) | |||||||
\(812\) | 17.2397 | + | 29.8601i | 0.604996 | + | 1.04788i | ||||
\(813\) | 7.36443 | + | 12.7556i | 0.258282 | + | 0.447357i | ||||
\(814\) | −0.561663 | −0.0196863 | ||||||||
\(815\) | 0.0566871 | + | 0.0981849i | 0.00198566 | + | 0.00343927i | ||||
\(816\) | 1.04892 | − | 1.81678i | 0.0367195 | − | 0.0636000i | ||||
\(817\) | 15.6474 | − | 27.1021i | 0.547434 | − | 0.948183i | ||||
\(818\) | 33.9221 | 1.18606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.71379 | −0.0947697 | ||||||||
\(821\) | −12.8138 | + | 22.1941i | −0.447204 | + | 0.774580i | −0.998203 | − | 0.0599259i | \(-0.980914\pi\) |
0.550999 | + | 0.834506i | \(0.314247\pi\) | |||||||
\(822\) | 7.70171 | − | 13.3398i | 0.268628 | − | 0.465277i | ||||
\(823\) | 20.1277 | + | 34.8621i | 0.701606 | + | 1.21522i | 0.967902 | + | 0.251327i | \(0.0808669\pi\) |
−0.266296 | + | 0.963891i | \(0.585800\pi\) | |||||||
\(824\) | −4.94869 | −0.172396 | ||||||||
\(825\) | 2.22156 | + | 3.84786i | 0.0773448 | + | 0.133965i | ||||
\(826\) | −12.2458 | − | 21.2103i | −0.426085 | − | 0.738001i | ||||
\(827\) | 18.0519 | 0.627726 | 0.313863 | − | 0.949468i | \(-0.398377\pi\) | ||||
0.313863 | + | 0.949468i | \(0.398377\pi\) | |||||||
\(828\) | −4.24698 | − | 7.35598i | −0.147593 | − | 0.255638i | ||||
\(829\) | −11.3327 | + | 19.6289i | −0.393602 | + | 0.681739i | −0.992922 | − | 0.118771i | \(-0.962105\pi\) |
0.599320 | + | 0.800510i | \(0.295438\pi\) | |||||||
\(830\) | −1.15979 | + | 2.00882i | −0.0402570 | + | 0.0697272i | ||||
\(831\) | 3.26205 | 0.113159 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.7065 | −0.682790 | ||||||||
\(834\) | 1.35690 | − | 2.35021i | 0.0469855 | − | 0.0813812i | ||||
\(835\) | −2.20583 | + | 3.82061i | −0.0763360 | + | 0.132218i | ||||
\(836\) | −2.27413 | − | 3.93890i | −0.0786523 | − | 0.136230i | ||||
\(837\) | 10.7899 | 0.372952 | ||||||||
\(838\) | 0.477697 | + | 0.827396i | 0.0165018 | + | 0.0285819i | ||||
\(839\) | 11.0411 | + | 19.1238i | 0.381183 | + | 0.660228i | 0.991232 | − | 0.132136i | \(-0.0421835\pi\) |
−0.610049 | + | 0.792364i | \(0.708850\pi\) | |||||||
\(840\) | −1.44504 | −0.0498587 | ||||||||
\(841\) | −21.7588 | − | 37.6874i | −0.750304 | − | 1.29957i | ||||
\(842\) | −2.84117 | + | 4.92104i | −0.0979131 | + | 0.169590i | ||||
\(843\) | 3.86294 | − | 6.69080i | 0.133047 | − | 0.230443i | ||||
\(844\) | −12.5375 | −0.431559 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.78017 | 0.0612034 | ||||||||
\(847\) | −20.5858 | + | 35.6556i | −0.707335 | + | 1.22514i | ||||
\(848\) | −5.20560 | + | 9.01636i | −0.178761 | + | 0.309623i | ||||
\(849\) | 9.89008 | + | 17.1301i | 0.339427 | + | 0.587904i | ||||
\(850\) | −10.2220 | −0.350610 | ||||||||
\(851\) | −2.61596 | − | 4.53097i | −0.0896739 | − | 0.155320i | ||||
\(852\) | 5.74094 | + | 9.94360i | 0.196681 | + | 0.340662i | ||||
\(853\) | −28.9831 | −0.992364 | −0.496182 | − | 0.868219i | \(-0.665265\pi\) | ||||
−0.496182 | + | 0.868219i | \(0.665265\pi\) | |||||||
\(854\) | 6.29590 | + | 10.9048i | 0.215441 | + | 0.373155i | ||||
\(855\) | 0.890084 | − | 1.54167i | 0.0304402 | − | 0.0527240i | ||||
\(856\) | −2.13437 | + | 3.69685i | −0.0729514 | + | 0.126356i | ||||
\(857\) | −42.9047 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.0616 | −1.60572 | −0.802860 | − | 0.596167i | \(-0.796690\pi\) | ||||
−0.802860 | + | 0.596167i | \(0.796690\pi\) | |||||||
\(860\) | −1.11960 | + | 1.93921i | −0.0381782 | + | 0.0661266i | ||||
\(861\) | 15.3937 | − | 26.6627i | 0.524617 | − | 0.908663i | ||||
\(862\) | −7.42327 | − | 12.8575i | −0.252838 | − | 0.437928i | ||||
\(863\) | −42.6064 | −1.45034 | −0.725169 | − | 0.688571i | \(-0.758238\pi\) | ||||
−0.725169 | + | 0.688571i | \(0.758238\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −3.04503 | − | 5.27415i | −0.103534 | − | 0.179327i | ||||
\(866\) | 26.1497 | 0.888604 | ||||||||
\(867\) | 6.29954 | + | 10.9111i | 0.213944 | + | 0.370561i | ||||
\(868\) | 21.8436 | − | 37.8343i | 0.741421 | − | 1.28418i | ||||
\(869\) | 5.33758 | − | 9.24495i | 0.181065 | − | 0.313614i | ||||
\(870\) | 3.03923 | 0.103040 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.21983 | −0.210630 | ||||||||
\(873\) | −0.980386 | + | 1.69808i | −0.0331810 | + | 0.0574712i | ||||
\(874\) | 21.1836 | − | 36.6911i | 0.716546 | − | 1.24109i | ||||
\(875\) | 7.13318 | + | 12.3550i | 0.241145 | + | 0.417676i | ||||
\(876\) | −0.533188 | −0.0180147 | ||||||||
\(877\) | −13.7041 | − | 23.7362i | −0.462755 | − | 0.801515i | 0.536342 | − | 0.844000i | \(-0.319806\pi\) |
−0.999097 | + | 0.0424859i | \(0.986472\pi\) | |||||||
\(878\) | −11.7751 | − | 20.3950i | −0.397390 | − | 0.688300i | ||||
\(879\) | 12.9119 | 0.435506 | ||||||||
\(880\) | 0.162718 | + | 0.281837i | 0.00548524 | + | 0.00950071i | ||||
\(881\) | −12.1588 | + | 21.0597i | −0.409642 | + | 0.709520i | −0.994849 | − | 0.101363i | \(-0.967680\pi\) |
0.585208 | + | 0.810883i | \(0.301013\pi\) | |||||||
\(882\) | 4.69687 | − | 8.13521i | 0.158152 | − | 0.273927i | ||||
\(883\) | −32.2306 | −1.08465 | −0.542323 | − | 0.840170i | \(-0.682455\pi\) | ||||
−0.542323 | + | 0.840170i | \(0.682455\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.15883 | −0.0725684 | ||||||||
\(886\) | 10.9717 | − | 19.0035i | 0.368600 | − | 0.638434i | ||||
\(887\) | 17.5821 | − | 30.4531i | 0.590349 | − | 1.02252i | −0.403836 | − | 0.914831i | \(-0.632323\pi\) |
0.994185 | − | 0.107684i | \(-0.0343433\pi\) | |||||||
\(888\) | 0.307979 | + | 0.533434i | 0.0103351 | + | 0.0179009i | ||||
\(889\) | −37.3424 | −1.25242 | ||||||||
\(890\) | −1.15883 | − | 2.00716i | −0.0388442 | − | 0.0672801i | ||||
\(891\) | −0.455927 | − | 0.789689i | −0.0152741 | − | 0.0264556i | ||||
\(892\) | −5.42758 | −0.181729 | ||||||||
\(893\) | 4.43967 | + | 7.68973i | 0.148568 | + | 0.257327i | ||||
\(894\) | 7.36778 | − | 12.7614i | 0.246415 | − | 0.426804i | ||||
\(895\) | −4.45550 | + | 7.71715i | −0.148931 | + | 0.257956i | ||||
\(896\) | 4.04892 | 0.135265 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.4034 | −0.380537 | ||||||||
\(899\) | −45.9417 | + | 79.5734i | −1.53224 | + | 2.65392i | ||||
\(900\) | 2.43631 | − | 4.21982i | 0.0812104 | − | 0.140661i | ||||
\(901\) | 10.9205 | + | 18.9148i | 0.363814 | + | 0.630144i | ||||
\(902\) | −6.93362 | −0.230864 | ||||||||
\(903\) | −12.7017 | − | 22.0000i | −0.422686 | − | 0.732114i | ||||
\(904\) | 6.49396 | + | 11.2479i | 0.215986 | + | 0.374099i | ||||
\(905\) | −1.87800 | −0.0624269 | ||||||||
\(906\) | 7.91066 | + | 13.7017i | 0.262814 | + | 0.455207i | ||||
\(907\) | 6.56033 | − | 11.3628i | 0.217832 | − | 0.377297i | −0.736313 | − | 0.676641i | \(-0.763435\pi\) |
0.954145 | + | 0.299345i | \(0.0967681\pi\) | |||||||
\(908\) | 8.28836 | − | 14.3559i | 0.275059 | − | 0.476416i | ||||
\(909\) | 6.98254 | 0.231596 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.7453 | 1.51561 | 0.757804 | − | 0.652482i | \(-0.226272\pi\) | ||||
0.757804 | + | 0.652482i | \(0.226272\pi\) | |||||||
\(912\) | −2.49396 | + | 4.31966i | −0.0825832 | + | 0.143038i | ||||
\(913\) | −2.96322 | + | 5.13245i | −0.0980684 | + | 0.169859i | ||||
\(914\) | 3.83459 | + | 6.64171i | 0.126837 | + | 0.219688i | ||||
\(915\) | 1.10992 | 0.0366927 | ||||||||
\(916\) | −11.9390 | − | 20.6790i | −0.394476 | − | 0.683252i | ||||
\(917\) | −29.4611 | − | 51.0281i | −0.972890 | − | 1.68510i | ||||
\(918\) | 2.09783 | 0.0692389 | ||||||||
\(919\) | −8.99247 | − | 15.5754i | −0.296634 | − | 0.513785i | 0.678730 | − | 0.734388i | \(-0.262531\pi\) |
−0.975364 | + | 0.220603i | \(0.929198\pi\) | |||||||
\(920\) | −1.51573 | + | 2.62532i | −0.0499721 | + | 0.0865543i | ||||
\(921\) | 9.98254 | − | 17.2903i | 0.328936 | − | 0.569734i | ||||
\(922\) | 28.5080 | 0.938860 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.69202 | −0.121459 | ||||||||
\(925\) | 1.50066 | − | 2.59923i | 0.0493415 | − | 0.0854620i | ||||
\(926\) | −7.16421 | + | 12.4088i | −0.235431 | + | 0.407778i | ||||
\(927\) | −2.47434 | − | 4.28569i | −0.0812681 | − | 0.140761i | ||||
\(928\) | −8.51573 | −0.279543 | ||||||||
\(929\) | −15.8442 | − | 27.4429i | −0.519830 | − | 0.900371i | −0.999734 | − | 0.0230508i | \(-0.992662\pi\) |
0.479905 | − | 0.877321i | \(-0.340671\pi\) | |||||||
\(930\) | −1.92543 | − | 3.33494i | −0.0631373 | − | 0.109357i | ||||
\(931\) | 46.8552 | 1.53562 | ||||||||
\(932\) | −6.99761 | − | 12.1202i | −0.229214 | − | 0.397011i | ||||
\(933\) | −6.74094 | + | 11.6756i | −0.220688 | + | 0.382244i | ||||
\(934\) | 16.6603 | − | 28.8565i | 0.545143 | − | 0.944215i | ||||
\(935\) | 0.682713 | 0.0223271 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.0484 | −1.73302 | −0.866509 | − | 0.499162i | \(-0.833641\pi\) | ||||
−0.866509 | + | 0.499162i | \(0.833641\pi\) | |||||||
\(938\) | 27.4916 | − | 47.6168i | 0.897631 | − | 1.55474i | ||||
\(939\) | −6.46226 | + | 11.1930i | −0.210888 | + | 0.365269i | ||||
\(940\) | −0.317667 | − | 0.550216i | −0.0103612 | − | 0.0179461i | ||||
\(941\) | 21.9433 | 0.715332 | 0.357666 | − | 0.933850i | \(-0.383573\pi\) | ||||
0.357666 | + | 0.933850i | \(0.383573\pi\) | |||||||
\(942\) | −2.13706 | − | 3.70150i | −0.0696293 | − | 0.120601i | ||||
\(943\) | −32.2935 | − | 55.9340i | −1.05162 | − | 1.82146i | ||||
\(944\) | 6.04892 | 0.196875 | ||||||||
\(945\) | −0.722521 | − | 1.25144i | −0.0235036 | − | 0.0407094i | ||||
\(946\) | −2.86054 | + | 4.95461i | −0.0930043 | + | 0.161088i | ||||
\(947\) | −6.11207 | + | 10.5864i | −0.198616 | + | 0.344012i | −0.948080 | − | 0.318033i | \(-0.896978\pi\) |
0.749464 | + | 0.662045i | \(0.230311\pi\) | |||||||
\(948\) | −11.7071 | −0.380229 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 24.3043 | 0.788534 | ||||||||
\(951\) | −5.93631 | + | 10.2820i | −0.192498 | + | 0.333417i | ||||
\(952\) | 4.24698 | − | 7.35598i | 0.137645 | − | 0.238409i | ||||
\(953\) | 1.92931 | + | 3.34167i | 0.0624966 | + | 0.108247i | 0.895581 | − | 0.444899i | \(-0.146760\pi\) |
−0.833084 | + | 0.553146i | \(0.813427\pi\) | |||||||
\(954\) | −10.4112 | −0.337075 | ||||||||
\(955\) | 1.88040 | + | 3.25694i | 0.0608482 | + | 0.105392i | ||||
\(956\) | 6.64310 | + | 11.5062i | 0.214853 | + | 0.372137i | ||||
\(957\) | 7.76510 | 0.251010 | ||||||||
\(958\) | −11.0640 | − | 19.1634i | −0.357461 | − | 0.619141i | ||||
\(959\) | 31.1836 | − | 54.0116i | 1.00697 | − | 1.74412i | ||||
\(960\) | 0.178448 | − | 0.309081i | 0.00575938 | − | 0.00997554i | ||||
\(961\) | 85.4210 | 2.75552 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.26875 | −0.137559 | ||||||||
\(964\) | 5.23945 | − | 9.07499i | 0.168751 | − | 0.292286i | ||||
\(965\) | −0.611645 | + | 1.05940i | −0.0196896 | + | 0.0341033i | ||||
\(966\) | −17.1957 | − | 29.7838i | −0.553262 | − | 0.958277i | ||||
\(967\) | −0.613564 | −0.0197309 | −0.00986545 | − | 0.999951i | \(-0.503140\pi\) | ||||
−0.00986545 | + | 0.999951i | \(0.503140\pi\) | |||||||
\(968\) | −5.08426 | − | 8.80620i | −0.163414 | − | 0.283042i | ||||
\(969\) | 5.23191 | + | 9.06194i | 0.168073 | + | 0.291111i | ||||
\(970\) | 0.699791 | 0.0224689 | ||||||||
\(971\) | 6.48845 | + | 11.2383i | 0.208224 | + | 0.360655i | 0.951155 | − | 0.308713i | \(-0.0998983\pi\) |
−0.742931 | + | 0.669368i | \(0.766565\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 5.49396 | − | 9.51582i | 0.176128 | − | 0.305063i | ||||
\(974\) | 0.126310 | 0.00404722 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.10992 | −0.0995460 | ||||||||
\(977\) | 18.5308 | − | 32.0963i | 0.592853 | − | 1.02685i | −0.400993 | − | 0.916081i | \(-0.631335\pi\) |
0.993846 | − | 0.110770i | \(-0.0353317\pi\) | |||||||
\(978\) | 0.158834 | − | 0.275108i | 0.00507894 | − | 0.00879698i | ||||
\(979\) | −2.96077 | − | 5.12821i | −0.0946267 | − | 0.163898i | ||||
\(980\) | −3.35258 | −0.107094 | ||||||||
\(981\) | −3.10992 | − | 5.38653i | −0.0992920 | − | 0.171979i | ||||
\(982\) | 6.97166 | + | 12.0753i | 0.222474 | + | 0.385337i | ||||
\(983\) | −14.1193 | −0.450337 | −0.225169 | − | 0.974320i | \(-0.572293\pi\) | ||||
−0.225169 | + | 0.974320i | \(0.572293\pi\) | |||||||
\(984\) | 3.80194 | + | 6.58515i | 0.121201 | + | 0.209927i | ||||
\(985\) | −0.673604 | + | 1.16672i | −0.0214628 | + | 0.0371747i | ||||
\(986\) | −8.93230 | + | 15.4712i | −0.284462 | + | 0.492703i | ||||
\(987\) | 7.20775 | 0.229425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.2922 | −1.69459 | ||||||||
\(990\) | −0.162718 | + | 0.281837i | −0.00517153 | + | 0.00895736i | ||||
\(991\) | −14.2696 | + | 24.7156i | −0.453288 | + | 0.785118i | −0.998588 | − | 0.0531230i | \(-0.983082\pi\) |
0.545300 | + | 0.838241i | \(0.316416\pi\) | |||||||
\(992\) | 5.39493 | + | 9.34429i | 0.171289 | + | 0.296681i | ||||
\(993\) | −10.2392 | −0.324932 | ||||||||
\(994\) | 23.2446 | + | 40.2608i | 0.737274 | + | 1.27700i | ||||
\(995\) | 3.20387 | + | 5.54926i | 0.101569 | + | 0.175923i | ||||
\(996\) | 6.49934 | 0.205939 | ||||||||
\(997\) | 9.44265 | + | 16.3551i | 0.299052 | + | 0.517973i | 0.975919 | − | 0.218132i | \(-0.0699964\pi\) |
−0.676868 | + | 0.736105i | \(0.736663\pi\) | |||||||
\(998\) | 14.1957 | − | 24.5876i | 0.449356 | − | 0.778308i | ||||
\(999\) | −0.307979 | + | 0.533434i | −0.00974401 | + | 0.0168771i |
(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 | 1014.2.e.m.529.2 | 6 | ||
13.2 | odd | 12 | 1014.2.i.g.361.5 | 12 | |||
13.3 | even | 3 | inner | 1014.2.e.m.991.2 | 6 | ||
13.4 | even | 6 | 1014.2.a.o.1.2 | yes | 3 | ||
13.5 | odd | 4 | 1014.2.i.g.823.2 | 12 | |||
13.6 | odd | 12 | 1014.2.b.g.337.5 | 6 | |||
13.7 | odd | 12 | 1014.2.b.g.337.2 | 6 | |||
13.8 | odd | 4 | 1014.2.i.g.823.5 | 12 | |||
13.9 | even | 3 | 1014.2.a.m.1.2 | ✓ | 3 | ||
13.10 | even | 6 | 1014.2.e.k.991.2 | 6 | |||
13.11 | odd | 12 | 1014.2.i.g.361.2 | 12 | |||
13.12 | even | 2 | 1014.2.e.k.529.2 | 6 | |||
39.17 | odd | 6 | 3042.2.a.bd.1.2 | 3 | |||
39.20 | even | 12 | 3042.2.b.r.1351.5 | 6 | |||
39.32 | even | 12 | 3042.2.b.r.1351.2 | 6 | |||
39.35 | odd | 6 | 3042.2.a.be.1.2 | 3 | |||
52.35 | odd | 6 | 8112.2.a.ce.1.2 | 3 | |||
52.43 | odd | 6 | 8112.2.a.bz.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.2 | ✓ | 3 | 13.9 | even | 3 | ||
1014.2.a.o.1.2 | yes | 3 | 13.4 | even | 6 | ||
1014.2.b.g.337.2 | 6 | 13.7 | odd | 12 | |||
1014.2.b.g.337.5 | 6 | 13.6 | odd | 12 | |||
1014.2.e.k.529.2 | 6 | 13.12 | even | 2 | |||
1014.2.e.k.991.2 | 6 | 13.10 | even | 6 | |||
1014.2.e.m.529.2 | 6 | 1.1 | even | 1 | trivial | ||
1014.2.e.m.991.2 | 6 | 13.3 | even | 3 | inner | ||
1014.2.i.g.361.2 | 12 | 13.11 | odd | 12 | |||
1014.2.i.g.361.5 | 12 | 13.2 | odd | 12 | |||
1014.2.i.g.823.2 | 12 | 13.5 | odd | 4 | |||
1014.2.i.g.823.5 | 12 | 13.8 | odd | 4 | |||
3042.2.a.bd.1.2 | 3 | 39.17 | odd | 6 | |||
3042.2.a.be.1.2 | 3 | 39.35 | odd | 6 | |||
3042.2.b.r.1351.2 | 6 | 39.32 | even | 12 | |||
3042.2.b.r.1351.5 | 6 | 39.20 | even | 12 | |||
8112.2.a.bz.1.2 | 3 | 52.43 | odd | 6 | |||
8112.2.a.ce.1.2 | 3 | 52.35 | odd | 6 |