Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(361,1014)]
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, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.i (of order \(6\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.385418 + 0.222521i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.361 |
Dual form | 1014.2.i.g.823.2 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 0.356896i | − | 0.159609i | −0.996811 | − | 0.0798043i | \(-0.974570\pi\) | ||
0.996811 | − | 0.0798043i | \(-0.0254296\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −3.50647 | − | 2.02446i | −1.32532 | − | 0.765173i | −0.340748 | − | 0.940155i | \(-0.610680\pi\) |
−0.984572 | + | 0.174981i | \(0.944013\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.178448 | + | 0.309081i | 0.0564302 | + | 0.0977400i | ||||
\(11\) | −0.789689 | + | 0.455927i | −0.238100 | + | 0.137467i | −0.614303 | − | 0.789070i | \(-0.710563\pi\) |
0.376203 | + | 0.926537i | \(0.377229\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.04892 | 1.08212 | ||||||||
\(15\) | −0.309081 | + | 0.178448i | −0.0798043 | + | 0.0460751i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.04892 | + | 1.81678i | −0.254400 | + | 0.440633i | −0.964732 | − | 0.263233i | \(-0.915211\pi\) |
0.710333 | + | 0.703866i | \(0.248545\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −4.31966 | − | 2.49396i | −0.990999 | − | 0.572153i | −0.0854262 | − | 0.996345i | \(-0.527225\pi\) |
−0.905573 | + | 0.424191i | \(0.860559\pi\) | |||||||
\(20\) | −0.309081 | − | 0.178448i | −0.0691126 | − | 0.0399022i | ||||
\(21\) | 4.04892i | 0.883546i | ||||||||
\(22\) | 0.455927 | − | 0.789689i | 0.0972040 | − | 0.168362i | ||||
\(23\) | 4.24698 | + | 7.35598i | 0.885556 | + | 1.53383i | 0.845075 | + | 0.534649i | \(0.179556\pi\) |
0.0404819 | + | 0.999180i | \(0.487111\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 4.87263 | 0.974525 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.50647 | + | 2.02446i | −0.662660 | + | 0.382587i | ||||
\(29\) | −4.25786 | − | 7.37484i | −0.790666 | − | 1.36947i | −0.925555 | − | 0.378612i | \(-0.876401\pi\) |
0.134890 | − | 0.990861i | \(-0.456932\pi\) | |||||||
\(30\) | 0.178448 | − | 0.309081i | 0.0325800 | − | 0.0564302i | ||||
\(31\) | 10.7899i | 1.93792i | 0.247227 | + | 0.968958i | \(0.420481\pi\) | ||||
−0.247227 | + | 0.968958i | \(0.579519\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0.789689 | + | 0.455927i | 0.137467 | + | 0.0793667i | ||||
\(34\) | − | 2.09783i | − | 0.359776i | ||||||
\(35\) | −0.722521 | + | 1.25144i | −0.122128 | + | 0.211532i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −0.533434 | + | 0.307979i | −0.0876961 | + | 0.0506314i | −0.543207 | − | 0.839599i | \(-0.682790\pi\) |
0.455511 | + | 0.890230i | \(0.349457\pi\) | |||||||
\(38\) | 4.98792 | 0.809147 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.356896 | 0.0564302 | ||||||||
\(41\) | 6.58515 | − | 3.80194i | 1.02843 | − | 0.593763i | 0.111894 | − | 0.993720i | \(-0.464308\pi\) |
0.916534 | + | 0.399957i | \(0.130975\pi\) | |||||||
\(42\) | −2.02446 | − | 3.50647i | −0.312381 | − | 0.541059i | ||||
\(43\) | −3.13706 | + | 5.43355i | −0.478398 | + | 0.828609i | −0.999693 | − | 0.0247671i | \(-0.992116\pi\) |
0.521296 | + | 0.853376i | \(0.325449\pi\) | |||||||
\(44\) | 0.911854i | 0.137467i | ||||||||
\(45\) | 0.309081 | + | 0.178448i | 0.0460751 | + | 0.0266014i | ||||
\(46\) | −7.35598 | − | 4.24698i | −1.08458 | − | 0.626183i | ||||
\(47\) | 1.78017i | 0.259664i | 0.991536 | + | 0.129832i | \(0.0414438\pi\) | ||||
−0.991536 | + | 0.129832i | \(0.958556\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 4.69687 | + | 8.13521i | 0.670981 | + | 1.16217i | ||||
\(50\) | −4.21982 | + | 2.43631i | −0.596772 | + | 0.344547i | ||||
\(51\) | 2.09783 | 0.293756 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4112 | 1.43009 | 0.715043 | − | 0.699080i | \(-0.246407\pi\) | ||||
0.715043 | + | 0.699080i | \(0.246407\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0.162718 | + | 0.281837i | 0.0219410 | + | 0.0380028i | ||||
\(56\) | 2.02446 | − | 3.50647i | 0.270530 | − | 0.468571i | ||||
\(57\) | 4.98792i | 0.660666i | ||||||||
\(58\) | 7.37484 | + | 4.25786i | 0.968364 | + | 0.559085i | ||||
\(59\) | 5.23852 | + | 3.02446i | 0.681997 | + | 0.393751i | 0.800607 | − | 0.599190i | \(-0.204511\pi\) |
−0.118610 | + | 0.992941i | \(0.537844\pi\) | |||||||
\(60\) | 0.356896i | 0.0460751i | ||||||||
\(61\) | 1.55496 | − | 2.69327i | 0.199092 | − | 0.344837i | −0.749142 | − | 0.662409i | \(-0.769534\pi\) |
0.948234 | + | 0.317572i | \(0.102867\pi\) | |||||||
\(62\) | −5.39493 | − | 9.34429i | −0.685157 | − | 1.18673i | ||||
\(63\) | 3.50647 | − | 2.02446i | 0.441773 | − | 0.255058i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.911854 | −0.112241 | ||||||||
\(67\) | −11.7604 | + | 6.78986i | −1.43676 | + | 0.829513i | −0.997623 | − | 0.0689079i | \(-0.978049\pi\) |
−0.439136 | + | 0.898421i | \(0.644715\pi\) | |||||||
\(68\) | 1.04892 | + | 1.81678i | 0.127200 | + | 0.220317i | ||||
\(69\) | 4.24698 | − | 7.35598i | 0.511276 | − | 0.885556i | ||||
\(70\) | − | 1.44504i | − | 0.172716i | ||||||
\(71\) | 9.94360 | + | 5.74094i | 1.18009 | + | 0.681324i | 0.956035 | − | 0.293253i | \(-0.0947378\pi\) |
0.224053 | + | 0.974577i | \(0.428071\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 0.533188i | 0.0624049i | 0.999513 | + | 0.0312025i | \(0.00993366\pi\) | ||||
−0.999513 | + | 0.0312025i | \(0.990066\pi\) | |||||||
\(74\) | 0.307979 | − | 0.533434i | 0.0358018 | − | 0.0620105i | ||||
\(75\) | −2.43631 | − | 4.21982i | −0.281321 | − | 0.487263i | ||||
\(76\) | −4.31966 | + | 2.49396i | −0.495499 | + | 0.286077i | ||||
\(77\) | 3.69202 | 0.420745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.7071 | −1.31715 | −0.658575 | − | 0.752515i | \(-0.728841\pi\) | ||||
−0.658575 | + | 0.752515i | \(0.728841\pi\) | |||||||
\(80\) | −0.309081 | + | 0.178448i | −0.0345563 | + | 0.0199511i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.80194 | + | 6.58515i | −0.419854 | + | 0.727208i | ||||
\(83\) | 6.49934i | 0.713395i | 0.934220 | + | 0.356697i | \(0.116097\pi\) | ||||
−0.934220 | + | 0.356697i | \(0.883903\pi\) | |||||||
\(84\) | 3.50647 | + | 2.02446i | 0.382587 | + | 0.220887i | ||||
\(85\) | 0.648401 | + | 0.374354i | 0.0703289 | + | 0.0406044i | ||||
\(86\) | − | 6.27413i | − | 0.676556i | ||||||
\(87\) | −4.25786 | + | 7.37484i | −0.456491 | + | 0.790666i | ||||
\(88\) | −0.455927 | − | 0.789689i | −0.0486020 | − | 0.0841811i | ||||
\(89\) | −5.62393 | + | 3.24698i | −0.596136 | + | 0.344179i | −0.767520 | − | 0.641025i | \(-0.778509\pi\) |
0.171384 | + | 0.985204i | \(0.445176\pi\) | |||||||
\(90\) | −0.356896 | −0.0376201 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.49396 | 0.885556 | ||||||||
\(93\) | 9.34429 | − | 5.39493i | 0.968958 | − | 0.559428i | ||||
\(94\) | −0.890084 | − | 1.54167i | −0.0918051 | − | 0.159011i | ||||
\(95\) | −0.890084 | + | 1.54167i | −0.0913207 | + | 0.158172i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −1.69808 | − | 0.980386i | −0.172414 | − | 0.0995431i | 0.411310 | − | 0.911496i | \(-0.365071\pi\) |
−0.583723 | + | 0.811953i | \(0.698405\pi\) | |||||||
\(98\) | −8.13521 | − | 4.69687i | −0.821780 | − | 0.474455i | ||||
\(99\) | − | 0.911854i | − | 0.0916448i | ||||||
\(100\) | 2.43631 | − | 4.21982i | 0.243631 | − | 0.421982i | ||||
\(101\) | 3.49127 | + | 6.04706i | 0.347394 | + | 0.601705i | 0.985786 | − | 0.168007i | \(-0.0537332\pi\) |
−0.638391 | + | 0.769712i | \(0.720400\pi\) | |||||||
\(102\) | −1.81678 | + | 1.04892i | −0.179888 | + | 0.103858i | ||||
\(103\) | −4.94869 | −0.487609 | −0.243804 | − | 0.969824i | \(-0.578396\pi\) | ||||
−0.243804 | + | 0.969824i | \(0.578396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.44504 | 0.141022 | ||||||||
\(106\) | −9.01636 | + | 5.20560i | −0.875746 | + | 0.505612i | ||||
\(107\) | 2.13437 | + | 3.69685i | 0.206338 | + | 0.357388i | 0.950558 | − | 0.310547i | \(-0.100512\pi\) |
−0.744220 | + | 0.667934i | \(0.767179\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 6.21983i | 0.595752i | 0.954605 | + | 0.297876i | \(0.0962782\pi\) | ||||
−0.954605 | + | 0.297876i | \(0.903722\pi\) | |||||||
\(110\) | −0.281837 | − | 0.162718i | −0.0268721 | − | 0.0155146i | ||||
\(111\) | 0.533434 | + | 0.307979i | 0.0506314 | + | 0.0292320i | ||||
\(112\) | 4.04892i | 0.382587i | ||||||||
\(113\) | −6.49396 | + | 11.2479i | −0.610900 | + | 1.05811i | 0.380189 | + | 0.924909i | \(0.375859\pi\) |
−0.991089 | + | 0.133201i | \(0.957474\pi\) | |||||||
\(114\) | −2.49396 | − | 4.31966i | −0.233581 | − | 0.404574i | ||||
\(115\) | 2.62532 | − | 1.51573i | 0.244812 | − | 0.141343i | ||||
\(116\) | −8.51573 | −0.790666 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.04892 | −0.556848 | ||||||||
\(119\) | 7.35598 | − | 4.24698i | 0.674322 | − | 0.389320i | ||||
\(120\) | −0.178448 | − | 0.309081i | −0.0162900 | − | 0.0282151i | ||||
\(121\) | −5.08426 | + | 8.80620i | −0.462206 | + | 0.800564i | ||||
\(122\) | 3.10992i | 0.281559i | ||||||||
\(123\) | −6.58515 | − | 3.80194i | −0.593763 | − | 0.342809i | ||||
\(124\) | 9.34429 | + | 5.39493i | 0.839142 | + | 0.484479i | ||||
\(125\) | − | 3.52350i | − | 0.315151i | ||||||
\(126\) | −2.02446 | + | 3.50647i | −0.180353 | + | 0.312381i | ||||
\(127\) | 4.61141 | + | 7.98719i | 0.409196 | + | 0.708749i | 0.994800 | − | 0.101849i | \(-0.0324758\pi\) |
−0.585604 | + | 0.810598i | \(0.699142\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 6.27413 | 0.552406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5526 | −1.27146 | −0.635732 | − | 0.771910i | \(-0.719302\pi\) | ||||
−0.635732 | + | 0.771910i | \(0.719302\pi\) | |||||||
\(132\) | 0.789689 | − | 0.455927i | 0.0687336 | − | 0.0396834i | ||||
\(133\) | 10.0978 | + | 17.4900i | 0.875593 | + | 1.51657i | ||||
\(134\) | 6.78986 | − | 11.7604i | 0.586554 | − | 1.01594i | ||||
\(135\) | − | 0.356896i | − | 0.0307167i | ||||||
\(136\) | −1.81678 | − | 1.04892i | −0.155787 | − | 0.0899439i | ||||
\(137\) | 13.3398 | + | 7.70171i | 1.13969 | + | 0.658002i | 0.946354 | − | 0.323131i | \(-0.104735\pi\) |
0.193338 | + | 0.981132i | \(0.438069\pi\) | |||||||
\(138\) | 8.49396i | 0.723054i | ||||||||
\(139\) | −1.35690 | + | 2.35021i | −0.115090 | + | 0.199342i | −0.917816 | − | 0.397006i | \(-0.870049\pi\) |
0.802725 | + | 0.596349i | \(0.203382\pi\) | |||||||
\(140\) | 0.722521 | + | 1.25144i | 0.0610642 | + | 0.105766i | ||||
\(141\) | 1.54167 | − | 0.890084i | 0.129832 | − | 0.0749586i | ||||
\(142\) | −11.4819 | −0.963538 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.63205 | + | 1.51961i | −0.218580 | + | 0.126197i | ||||
\(146\) | −0.266594 | − | 0.461754i | −0.0220635 | − | 0.0382151i | ||||
\(147\) | 4.69687 | − | 8.13521i | 0.387391 | − | 0.670981i | ||||
\(148\) | 0.615957i | 0.0506314i | ||||||||
\(149\) | −12.7614 | − | 7.36778i | −1.04545 | − | 0.603592i | −0.124079 | − | 0.992272i | \(-0.539598\pi\) |
−0.921373 | + | 0.388680i | \(0.872931\pi\) | |||||||
\(150\) | 4.21982 | + | 2.43631i | 0.344547 | + | 0.198924i | ||||
\(151\) | − | 15.8213i | − | 1.28752i | −0.765227 | − | 0.643760i | \(-0.777373\pi\) | ||
0.765227 | − | 0.643760i | \(-0.222627\pi\) | |||||||
\(152\) | 2.49396 | − | 4.31966i | 0.202287 | − | 0.350371i | ||||
\(153\) | −1.04892 | − | 1.81678i | −0.0847999 | − | 0.146878i | ||||
\(154\) | −3.19738 | + | 1.84601i | −0.257653 | + | 0.148756i | ||||
\(155\) | 3.85086 | 0.309308 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.27413 | −0.341112 | −0.170556 | − | 0.985348i | \(-0.554556\pi\) | ||||
−0.170556 | + | 0.985348i | \(0.554556\pi\) | |||||||
\(158\) | 10.1386 | − | 5.85354i | 0.806586 | − | 0.465683i | ||||
\(159\) | −5.20560 | − | 9.01636i | −0.412831 | − | 0.715043i | ||||
\(160\) | 0.178448 | − | 0.309081i | 0.0141075 | − | 0.0244350i | ||||
\(161\) | − | 34.3913i | − | 2.71042i | ||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | 0.275108 | + | 0.158834i | 0.0215481 | + | 0.0124408i | 0.510735 | − | 0.859738i | \(-0.329373\pi\) |
−0.489187 | + | 0.872179i | \(0.662707\pi\) | |||||||
\(164\) | − | 7.60388i | − | 0.593763i | ||||||
\(165\) | 0.162718 | − | 0.281837i | 0.0126676 | − | 0.0219410i | ||||
\(166\) | −3.24967 | − | 5.62859i | −0.252223 | − | 0.436863i | ||||
\(167\) | 10.7051 | − | 6.18060i | 0.828387 | − | 0.478269i | −0.0249130 | − | 0.999690i | \(-0.507931\pi\) |
0.853300 | + | 0.521420i | \(0.174598\pi\) | |||||||
\(168\) | −4.04892 | −0.312381 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.748709 | −0.0574233 | ||||||||
\(171\) | 4.31966 | − | 2.49396i | 0.330333 | − | 0.190718i | ||||
\(172\) | 3.13706 | + | 5.43355i | 0.239199 | + | 0.414305i | ||||
\(173\) | −8.53199 | + | 14.7778i | −0.648675 | + | 1.12354i | 0.334764 | + | 0.942302i | \(0.391343\pi\) |
−0.983440 | + | 0.181237i | \(0.941990\pi\) | |||||||
\(174\) | − | 8.51573i | − | 0.645576i | ||||||
\(175\) | −17.0857 | − | 9.86443i | −1.29156 | − | 0.745681i | ||||
\(176\) | 0.789689 | + | 0.455927i | 0.0595250 | + | 0.0343668i | ||||
\(177\) | − | 6.04892i | − | 0.454664i | ||||||
\(178\) | 3.24698 | − | 5.62393i | 0.243371 | − | 0.421532i | ||||
\(179\) | −12.4840 | − | 21.6230i | −0.933100 | − | 1.61618i | −0.777987 | − | 0.628281i | \(-0.783759\pi\) |
−0.155114 | − | 0.987897i | \(-0.549574\pi\) | |||||||
\(180\) | 0.309081 | − | 0.178448i | 0.0230375 | − | 0.0133007i | ||||
\(181\) | −5.26205 | −0.391125 | −0.195562 | − | 0.980691i | \(-0.562653\pi\) | ||||
−0.195562 | + | 0.980691i | \(0.562653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.10992 | −0.229892 | ||||||||
\(184\) | −7.35598 | + | 4.24698i | −0.542290 | + | 0.313091i | ||||
\(185\) | 0.109916 | + | 0.190381i | 0.00808120 | + | 0.0139971i | ||||
\(186\) | −5.39493 | + | 9.34429i | −0.395575 | + | 0.685157i | ||||
\(187\) | − | 1.91292i | − | 0.139886i | ||||||
\(188\) | 1.54167 | + | 0.890084i | 0.112438 | + | 0.0649160i | ||||
\(189\) | −3.50647 | − | 2.02446i | −0.255058 | − | 0.147258i | ||||
\(190\) | − | 1.78017i | − | 0.129147i | ||||||
\(191\) | −5.26875 | + | 9.12574i | −0.381233 | + | 0.660316i | −0.991239 | − | 0.132082i | \(-0.957834\pi\) |
0.610005 | + | 0.792397i | \(0.291167\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 2.96837 | − | 1.71379i | 0.213668 | − | 0.123361i | −0.389347 | − | 0.921091i | \(-0.627299\pi\) |
0.603015 | + | 0.797730i | \(0.293966\pi\) | |||||||
\(194\) | 1.96077 | 0.140775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.39373 | 0.670981 | ||||||||
\(197\) | −3.26906 | + | 1.88740i | −0.232911 | + | 0.134471i | −0.611914 | − | 0.790924i | \(-0.709600\pi\) |
0.379003 | + | 0.925395i | \(0.376267\pi\) | |||||||
\(198\) | 0.455927 | + | 0.789689i | 0.0324013 | + | 0.0561207i | ||||
\(199\) | 8.97703 | − | 15.5487i | 0.636365 | − | 1.10222i | −0.349859 | − | 0.936802i | \(-0.613771\pi\) |
0.986224 | − | 0.165414i | \(-0.0528961\pi\) | |||||||
\(200\) | 4.87263i | 0.344547i | ||||||||
\(201\) | 11.7604 | + | 6.78986i | 0.829513 | + | 0.478920i | ||||
\(202\) | −6.04706 | − | 3.49127i | −0.425470 | − | 0.245645i | ||||
\(203\) | 34.4795i | 2.41999i | ||||||||
\(204\) | 1.04892 | − | 1.81678i | 0.0734389 | − | 0.127200i | ||||
\(205\) | −1.35690 | − | 2.35021i | −0.0947697 | − | 0.164146i | ||||
\(206\) | 4.28569 | − | 2.47434i | 0.298598 | − | 0.172396i | ||||
\(207\) | −8.49396 | −0.590371 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.54825 | 0.314609 | ||||||||
\(210\) | −1.25144 | + | 0.722521i | −0.0863578 | + | 0.0498587i | ||||
\(211\) | 6.26875 | + | 10.8578i | 0.431559 | + | 0.747481i | 0.997008 | − | 0.0773018i | \(-0.0246305\pi\) |
−0.565449 | + | 0.824783i | \(0.691297\pi\) | |||||||
\(212\) | 5.20560 | − | 9.01636i | 0.357522 | − | 0.619246i | ||||
\(213\) | − | 11.4819i | − | 0.786725i | ||||||
\(214\) | −3.69685 | − | 2.13437i | −0.252711 | − | 0.145903i | ||||
\(215\) | 1.93921 | + | 1.11960i | 0.132253 | + | 0.0763564i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 21.8436 | − | 37.8343i | 1.48284 | − | 2.56836i | ||||
\(218\) | −3.10992 | − | 5.38653i | −0.210630 | − | 0.364822i | ||||
\(219\) | 0.461754 | − | 0.266594i | 0.0312025 | − | 0.0180147i | ||||
\(220\) | 0.325437 | 0.0219410 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.615957 | −0.0413403 | ||||||||
\(223\) | −4.70043 | + | 2.71379i | −0.314764 | + | 0.181729i | −0.649056 | − | 0.760740i | \(-0.724836\pi\) |
0.334292 | + | 0.942469i | \(0.391503\pi\) | |||||||
\(224\) | −2.02446 | − | 3.50647i | −0.135265 | − | 0.234286i | ||||
\(225\) | −2.43631 | + | 4.21982i | −0.162421 | + | 0.281321i | ||||
\(226\) | − | 12.9879i | − | 0.863943i | ||||||
\(227\) | 14.3559 | + | 8.28836i | 0.952832 | + | 0.550118i | 0.893960 | − | 0.448147i | \(-0.147916\pi\) |
0.0588728 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(228\) | 4.31966 | + | 2.49396i | 0.286077 | + | 0.165166i | ||||
\(229\) | − | 23.8780i | − | 1.57790i | −0.614456 | − | 0.788951i | \(-0.710624\pi\) | ||
0.614456 | − | 0.788951i | \(-0.289376\pi\) | |||||||
\(230\) | −1.51573 | + | 2.62532i | −0.0999442 | + | 0.173109i | ||||
\(231\) | −1.84601 | − | 3.19738i | −0.121459 | − | 0.210372i | ||||
\(232\) | 7.37484 | − | 4.25786i | 0.484182 | − | 0.279543i | ||||
\(233\) | −13.9952 | −0.916857 | −0.458428 | − | 0.888731i | \(-0.651587\pi\) | ||||
−0.458428 | + | 0.888731i | \(0.651587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.635334 | 0.0414446 | ||||||||
\(236\) | 5.23852 | − | 3.02446i | 0.340998 | − | 0.196875i | ||||
\(237\) | 5.85354 | + | 10.1386i | 0.380229 | + | 0.658575i | ||||
\(238\) | −4.24698 | + | 7.35598i | −0.275291 | + | 0.476818i | ||||
\(239\) | − | 13.2862i | − | 0.859413i | −0.902969 | − | 0.429707i | \(-0.858617\pi\) | ||
0.902969 | − | 0.429707i | \(-0.141383\pi\) | |||||||
\(240\) | 0.309081 | + | 0.178448i | 0.0199511 | + | 0.0115188i | ||||
\(241\) | −9.07499 | − | 5.23945i | −0.584571 | − | 0.337502i | 0.178377 | − | 0.983962i | \(-0.442915\pi\) |
−0.762948 | + | 0.646460i | \(0.776249\pi\) | |||||||
\(242\) | − | 10.1685i | − | 0.653657i | ||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −1.55496 | − | 2.69327i | −0.0995460 | − | 0.172419i | ||||
\(245\) | 2.90342 | − | 1.67629i | 0.185493 | − | 0.107094i | ||||
\(246\) | 7.60388 | 0.484805 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.7899 | −0.685157 | ||||||||
\(249\) | 5.62859 | − | 3.24967i | 0.356697 | − | 0.205939i | ||||
\(250\) | 1.76175 | + | 3.05144i | 0.111423 | + | 0.192990i | ||||
\(251\) | 1.74363 | − | 3.02005i | 0.110057 | − | 0.190624i | −0.805736 | − | 0.592275i | \(-0.798230\pi\) |
0.915793 | + | 0.401651i | \(0.131563\pi\) | |||||||
\(252\) | − | 4.04892i | − | 0.255058i | ||||||
\(253\) | −6.70758 | − | 3.87263i | −0.421702 | − | 0.243470i | ||||
\(254\) | −7.98719 | − | 4.61141i | −0.501161 | − | 0.289345i | ||||
\(255\) | − | 0.748709i | − | 0.0468859i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.26875 | + | 5.66164i | 0.203899 | + | 0.353163i | 0.949781 | − | 0.312914i | \(-0.101305\pi\) |
−0.745882 | + | 0.666078i | \(0.767972\pi\) | |||||||
\(258\) | −5.43355 | + | 3.13706i | −0.338278 | + | 0.195305i | ||||
\(259\) | 2.49396 | 0.154967 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.51573 | 0.527110 | ||||||||
\(262\) | 12.6029 | − | 7.27628i | 0.778609 | − | 0.449530i | ||||
\(263\) | −4.00969 | − | 6.94498i | −0.247248 | − | 0.428246i | 0.715513 | − | 0.698599i | \(-0.246193\pi\) |
−0.962761 | + | 0.270353i | \(0.912860\pi\) | |||||||
\(264\) | −0.455927 | + | 0.789689i | −0.0280604 | + | 0.0486020i | ||||
\(265\) | − | 3.71571i | − | 0.228254i | ||||||
\(266\) | −17.4900 | − | 10.0978i | −1.07238 | − | 0.619138i | ||||
\(267\) | 5.62393 | + | 3.24698i | 0.344179 | + | 0.198712i | ||||
\(268\) | 13.5797i | 0.829513i | ||||||||
\(269\) | 13.8366 | − | 23.9657i | 0.843633 | − | 1.46122i | −0.0431692 | − | 0.999068i | \(-0.513745\pi\) |
0.886803 | − | 0.462148i | \(-0.152921\pi\) | |||||||
\(270\) | 0.178448 | + | 0.309081i | 0.0108600 | + | 0.0188101i | ||||
\(271\) | 12.7556 | − | 7.36443i | 0.774845 | − | 0.447357i | −0.0597550 | − | 0.998213i | \(-0.519032\pi\) |
0.834600 | + | 0.550856i | \(0.185699\pi\) | |||||||
\(272\) | 2.09783 | 0.127200 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4034 | −0.930555 | ||||||||
\(275\) | −3.84786 | + | 2.22156i | −0.232035 | + | 0.133965i | ||||
\(276\) | −4.24698 | − | 7.35598i | −0.255638 | − | 0.442778i | ||||
\(277\) | 1.63102 | − | 2.82501i | 0.0979986 | − | 0.169739i | −0.812858 | − | 0.582463i | \(-0.802089\pi\) |
0.910856 | + | 0.412724i | \(0.135423\pi\) | |||||||
\(278\) | − | 2.71379i | − | 0.162762i | ||||||
\(279\) | −9.34429 | − | 5.39493i | −0.559428 | − | 0.322986i | ||||
\(280\) | −1.25144 | − | 0.722521i | −0.0747880 | − | 0.0431789i | ||||
\(281\) | 7.72587i | 0.460887i | 0.973086 | + | 0.230443i | \(0.0740177\pi\) | ||||
−0.973086 | + | 0.230443i | \(0.925982\pi\) | |||||||
\(282\) | −0.890084 | + | 1.54167i | −0.0530037 | + | 0.0918051i | ||||
\(283\) | −9.89008 | − | 17.1301i | −0.587904 | − | 1.01828i | −0.994506 | − | 0.104675i | \(-0.966620\pi\) |
0.406602 | − | 0.913605i | \(-0.366714\pi\) | |||||||
\(284\) | 9.94360 | − | 5.74094i | 0.590044 | − | 0.340662i | ||||
\(285\) | 1.78017 | 0.105448 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.7875 | −1.81733 | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | 6.29954 | + | 10.9111i | 0.370561 | + | 0.641831i | ||||
\(290\) | 1.51961 | − | 2.63205i | 0.0892348 | − | 0.154559i | ||||
\(291\) | 1.96077i | 0.114942i | ||||||||
\(292\) | 0.461754 | + | 0.266594i | 0.0270221 | + | 0.0156012i | ||||
\(293\) | 11.1820 | + | 6.45593i | 0.653259 | + | 0.377159i | 0.789704 | − | 0.613488i | \(-0.210234\pi\) |
−0.136445 | + | 0.990648i | \(0.543568\pi\) | |||||||
\(294\) | 9.39373i | 0.547854i | ||||||||
\(295\) | 1.07942 | − | 1.86960i | 0.0628461 | − | 0.108853i | ||||
\(296\) | −0.307979 | − | 0.533434i | −0.0179009 | − | 0.0310052i | ||||
\(297\) | −0.789689 | + | 0.455927i | −0.0458224 | + | 0.0264556i | ||||
\(298\) | 14.7356 | 0.853608 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.87263 | −0.281321 | ||||||||
\(301\) | 22.0000 | − | 12.7017i | 1.26806 | − | 0.732114i | ||||
\(302\) | 7.91066 | + | 13.7017i | 0.455207 | + | 0.788442i | ||||
\(303\) | 3.49127 | − | 6.04706i | 0.200568 | − | 0.347394i | ||||
\(304\) | 4.98792i | 0.286077i | ||||||||
\(305\) | −0.961216 | − | 0.554958i | −0.0550390 | − | 0.0317768i | ||||
\(306\) | 1.81678 | + | 1.04892i | 0.103858 | + | 0.0599626i | ||||
\(307\) | 19.9651i | 1.13947i | 0.821829 | + | 0.569734i | \(0.192954\pi\) | ||||
−0.821829 | + | 0.569734i | \(0.807046\pi\) | |||||||
\(308\) | 1.84601 | − | 3.19738i | 0.105186 | − | 0.182188i | ||||
\(309\) | 2.47434 | + | 4.28569i | 0.140761 | + | 0.243804i | ||||
\(310\) | −3.33494 | + | 1.92543i | −0.189412 | + | 0.109357i | ||||
\(311\) | −13.4819 | −0.764487 | −0.382244 | − | 0.924062i | \(-0.624848\pi\) | ||||
−0.382244 | + | 0.924062i | \(0.624848\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9245 | 0.730537 | 0.365269 | − | 0.930902i | \(-0.380977\pi\) | ||||
0.365269 | + | 0.930902i | \(0.380977\pi\) | |||||||
\(314\) | 3.70150 | − | 2.13706i | 0.208888 | − | 0.120601i | ||||
\(315\) | −0.722521 | − | 1.25144i | −0.0407094 | − | 0.0705108i | ||||
\(316\) | −5.85354 | + | 10.1386i | −0.329288 | + | 0.570343i | ||||
\(317\) | 11.8726i | 0.666833i | 0.942780 | + | 0.333417i | \(0.108202\pi\) | ||||
−0.942780 | + | 0.333417i | \(0.891798\pi\) | |||||||
\(318\) | 9.01636 | + | 5.20560i | 0.505612 | + | 0.291915i | ||||
\(319\) | 6.72478 | + | 3.88255i | 0.376515 | + | 0.217381i | ||||
\(320\) | 0.356896i | 0.0199511i | ||||||||
\(321\) | 2.13437 | − | 3.69685i | 0.119129 | − | 0.206338i | ||||
\(322\) | 17.1957 | + | 29.7838i | 0.958277 | + | 1.65978i | ||||
\(323\) | 9.06194 | − | 5.23191i | 0.504220 | − | 0.291111i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.317667 | −0.0175940 | ||||||||
\(327\) | 5.38653 | − | 3.10992i | 0.297876 | − | 0.171979i | ||||
\(328\) | 3.80194 | + | 6.58515i | 0.209927 | + | 0.363604i | ||||
\(329\) | 3.60388 | − | 6.24210i | 0.198688 | − | 0.344138i | ||||
\(330\) | 0.325437i | 0.0179147i | ||||||||
\(331\) | 8.86742 | + | 5.11960i | 0.487397 | + | 0.281399i | 0.723494 | − | 0.690331i | \(-0.242535\pi\) |
−0.236097 | + | 0.971730i | \(0.575868\pi\) | |||||||
\(332\) | 5.62859 | + | 3.24967i | 0.308909 | + | 0.178349i | ||||
\(333\) | − | 0.615957i | − | 0.0337542i | ||||||
\(334\) | −6.18060 | + | 10.7051i | −0.338188 | + | 0.585758i | ||||
\(335\) | 2.42327 | + | 4.19723i | 0.132397 | + | 0.229319i | ||||
\(336\) | 3.50647 | − | 2.02446i | 0.191293 | − | 0.110443i | ||||
\(337\) | −1.44935 | −0.0789513 | −0.0394757 | − | 0.999221i | \(-0.512569\pi\) | ||||
−0.0394757 | + | 0.999221i | \(0.512569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9879 | 0.705407 | ||||||||
\(340\) | 0.648401 | − | 0.374354i | 0.0351645 | − | 0.0203022i | ||||
\(341\) | −4.91939 | − | 8.52063i | −0.266400 | − | 0.461418i | ||||
\(342\) | −2.49396 | + | 4.31966i | −0.134858 | + | 0.233581i | ||||
\(343\) | − | 9.69202i | − | 0.523320i | ||||||
\(344\) | −5.43355 | − | 3.13706i | −0.292958 | − | 0.169139i | ||||
\(345\) | −2.62532 | − | 1.51573i | −0.141343 | − | 0.0816041i | ||||
\(346\) | − | 17.0640i | − | 0.917365i | ||||||
\(347\) | −3.42058 | + | 5.92462i | −0.183627 | + | 0.318050i | −0.943113 | − | 0.332473i | \(-0.892117\pi\) |
0.759486 | + | 0.650523i | \(0.225450\pi\) | |||||||
\(348\) | 4.25786 | + | 7.37484i | 0.228246 | + | 0.395333i | ||||
\(349\) | −29.7368 | + | 17.1685i | −1.59177 | + | 0.919010i | −0.598769 | + | 0.800922i | \(0.704343\pi\) |
−0.993003 | + | 0.118088i | \(0.962324\pi\) | |||||||
\(350\) | 19.7289 | 1.05455 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.911854 | −0.0486020 | ||||||||
\(353\) | −22.5595 | + | 13.0248i | −1.20072 | + | 0.693238i | −0.960716 | − | 0.277533i | \(-0.910483\pi\) |
−0.240007 | + | 0.970771i | \(0.577150\pi\) | |||||||
\(354\) | 3.02446 | + | 5.23852i | 0.160748 | + | 0.278424i | ||||
\(355\) | 2.04892 | − | 3.54883i | 0.108745 | − | 0.188352i | ||||
\(356\) | 6.49396i | 0.344179i | ||||||||
\(357\) | −7.35598 | − | 4.24698i | −0.389320 | − | 0.224774i | ||||
\(358\) | 21.6230 | + | 12.4840i | 1.14281 | + | 0.659802i | ||||
\(359\) | 8.49396i | 0.448294i | 0.974555 | + | 0.224147i | \(0.0719596\pi\) | ||||
−0.974555 | + | 0.224147i | \(0.928040\pi\) | |||||||
\(360\) | −0.178448 | + | 0.309081i | −0.00940503 | + | 0.0162900i | ||||
\(361\) | 2.93967 | + | 5.09165i | 0.154719 | + | 0.267982i | ||||
\(362\) | 4.55706 | − | 2.63102i | 0.239514 | − | 0.138283i | ||||
\(363\) | 10.1685 | 0.533709 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.190293 | 0.00996037 | ||||||||
\(366\) | 2.69327 | − | 1.55496i | 0.140779 | − | 0.0812790i | ||||
\(367\) | −13.7262 | − | 23.7744i | −0.716500 | − | 1.24101i | −0.962378 | − | 0.271714i | \(-0.912410\pi\) |
0.245878 | − | 0.969301i | \(-0.420924\pi\) | |||||||
\(368\) | 4.24698 | − | 7.35598i | 0.221389 | − | 0.383457i | ||||
\(369\) | 7.60388i | 0.395842i | ||||||||
\(370\) | −0.190381 | − | 0.109916i | −0.00989741 | − | 0.00571427i | ||||
\(371\) | −36.5065 | − | 21.0770i | −1.89532 | − | 1.09426i | ||||
\(372\) | − | 10.7899i | − | 0.559428i | ||||||
\(373\) | −13.3110 | + | 23.0553i | −0.689216 | + | 1.19376i | 0.282876 | + | 0.959156i | \(0.408711\pi\) |
−0.972092 | + | 0.234600i | \(0.924622\pi\) | |||||||
\(374\) | 0.956459 | + | 1.65664i | 0.0494573 | + | 0.0856626i | ||||
\(375\) | −3.05144 | + | 1.76175i | −0.157576 | + | 0.0909764i | ||||
\(376\) | −1.78017 | −0.0918051 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.04892 | 0.208254 | ||||||||
\(379\) | −10.0870 | + | 5.82371i | −0.518132 | + | 0.299144i | −0.736170 | − | 0.676797i | \(-0.763368\pi\) |
0.218038 | + | 0.975940i | \(0.430034\pi\) | |||||||
\(380\) | 0.890084 | + | 1.54167i | 0.0456603 | + | 0.0790860i | ||||
\(381\) | 4.61141 | − | 7.98719i | 0.236250 | − | 0.409196i | ||||
\(382\) | − | 10.5375i | − | 0.539145i | ||||||
\(383\) | 9.10896 | + | 5.25906i | 0.465446 | + | 0.268725i | 0.714331 | − | 0.699807i | \(-0.246731\pi\) |
−0.248885 | + | 0.968533i | \(0.580064\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | − | 1.31767i | − | 0.0671545i | ||||||
\(386\) | −1.71379 | + | 2.96837i | −0.0872297 | + | 0.151086i | ||||
\(387\) | −3.13706 | − | 5.43355i | −0.159466 | − | 0.276203i | ||||
\(388\) | −1.69808 | + | 0.980386i | −0.0862068 | + | 0.0497715i | ||||
\(389\) | 9.25965 | 0.469483 | 0.234742 | − | 0.972058i | \(-0.424576\pi\) | ||||
0.234742 | + | 0.972058i | \(0.424576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8189 | −0.901142 | ||||||||
\(392\) | −8.13521 | + | 4.69687i | −0.410890 | + | 0.237228i | ||||
\(393\) | 7.27628 | + | 12.6029i | 0.367040 | + | 0.635732i | ||||
\(394\) | 1.88740 | − | 3.26906i | 0.0950856 | − | 0.164693i | ||||
\(395\) | 4.17821i | 0.210229i | ||||||||
\(396\) | −0.789689 | − | 0.455927i | −0.0396834 | − | 0.0229112i | ||||
\(397\) | −12.5689 | − | 7.25667i | −0.630816 | − | 0.364202i | 0.150252 | − | 0.988648i | \(-0.451991\pi\) |
−0.781068 | + | 0.624446i | \(0.785325\pi\) | |||||||
\(398\) | 17.9541i | 0.899956i | ||||||||
\(399\) | 10.0978 | − | 17.4900i | 0.505524 | − | 0.875593i | ||||
\(400\) | −2.43631 | − | 4.21982i | −0.121816 | − | 0.210991i | ||||
\(401\) | −33.6379 | + | 19.4209i | −1.67980 | + | 0.969832i | −0.718013 | + | 0.696030i | \(0.754948\pi\) |
−0.961786 | + | 0.273803i | \(0.911718\pi\) | |||||||
\(402\) | −13.5797 | −0.677294 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.98254 | 0.347394 | ||||||||
\(405\) | −0.309081 | + | 0.178448i | −0.0153584 | + | 0.00886715i | ||||
\(406\) | −17.2397 | − | 29.8601i | −0.855594 | − | 1.48193i | ||||
\(407\) | 0.280831 | − | 0.486414i | 0.0139203 | − | 0.0241107i | ||||
\(408\) | 2.09783i | 0.103858i | ||||||||
\(409\) | 29.3774 | + | 16.9611i | 1.45262 | + | 0.838671i | 0.998630 | − | 0.0523356i | \(-0.0166665\pi\) |
0.453991 | + | 0.891006i | \(0.350000\pi\) | |||||||
\(410\) | 2.35021 | + | 1.35690i | 0.116069 | + | 0.0670123i | ||||
\(411\) | − | 15.4034i | − | 0.759795i | ||||||
\(412\) | −2.47434 | + | 4.28569i | −0.121902 | + | 0.211141i | ||||
\(413\) | −12.2458 | − | 21.2103i | −0.602576 | − | 1.04369i | ||||
\(414\) | 7.35598 | − | 4.24698i | 0.361527 | − | 0.208728i | ||||
\(415\) | 2.31959 | 0.113864 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.71379 | 0.132895 | ||||||||
\(418\) | −3.93890 | + | 2.27413i | −0.192658 | + | 0.111231i | ||||
\(419\) | −0.477697 | − | 0.827396i | −0.0233370 | − | 0.0404209i | 0.854121 | − | 0.520074i | \(-0.174096\pi\) |
−0.877458 | + | 0.479653i | \(0.840762\pi\) | |||||||
\(420\) | 0.722521 | − | 1.25144i | 0.0352554 | − | 0.0610642i | ||||
\(421\) | − | 5.68233i | − | 0.276940i | −0.990367 | − | 0.138470i | \(-0.955782\pi\) | ||
0.990367 | − | 0.138470i | \(-0.0442184\pi\) | |||||||
\(422\) | −10.8578 | − | 6.26875i | −0.528549 | − | 0.305158i | ||||
\(423\) | −1.54167 | − | 0.890084i | −0.0749586 | − | 0.0432774i | ||||
\(424\) | 10.4112i | 0.505612i | ||||||||
\(425\) | −5.11098 | + | 8.85248i | −0.247919 | + | 0.429408i | ||||
\(426\) | 5.74094 | + | 9.94360i | 0.278149 | + | 0.481769i | ||||
\(427\) | −10.9048 | + | 6.29590i | −0.527721 | + | 0.304680i | ||||
\(428\) | 4.26875 | 0.206338 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.23921 | −0.107984 | ||||||||
\(431\) | −12.8575 | + | 7.42327i | −0.619323 | + | 0.357566i | −0.776605 | − | 0.629987i | \(-0.783060\pi\) |
0.157282 | + | 0.987554i | \(0.449727\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −13.0749 | + | 22.6463i | −0.628338 | + | 1.08831i | 0.359547 | + | 0.933127i | \(0.382931\pi\) |
−0.987885 | + | 0.155187i | \(0.950402\pi\) | |||||||
\(434\) | 43.6872i | 2.09705i | ||||||||
\(435\) | 2.63205 | + | 1.51961i | 0.126197 | + | 0.0728599i | ||||
\(436\) | 5.38653 | + | 3.10992i | 0.257968 | + | 0.148938i | ||||
\(437\) | − | 42.3672i | − | 2.02670i | ||||||
\(438\) | −0.266594 | + | 0.461754i | −0.0127384 | + | 0.0220635i | ||||
\(439\) | −11.7751 | − | 20.3950i | −0.561994 | − | 0.973403i | −0.997322 | − | 0.0731307i | \(-0.976701\pi\) |
0.435328 | − | 0.900272i | \(-0.356632\pi\) | |||||||
\(440\) | −0.281837 | + | 0.162718i | −0.0134360 | + | 0.00775730i | ||||
\(441\) | −9.39373 | −0.447321 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.9433 | 1.04256 | 0.521279 | − | 0.853386i | \(-0.325455\pi\) | ||||
0.521279 | + | 0.853386i | \(0.325455\pi\) | |||||||
\(444\) | 0.533434 | − | 0.307979i | 0.0253157 | − | 0.0146160i | ||||
\(445\) | 1.15883 | + | 2.00716i | 0.0549340 | + | 0.0951484i | ||||
\(446\) | 2.71379 | − | 4.70043i | 0.128502 | − | 0.222572i | ||||
\(447\) | 14.7356i | 0.696968i | ||||||||
\(448\) | 3.50647 | + | 2.02446i | 0.165665 | + | 0.0956467i | ||||
\(449\) | 9.87565 | + | 5.70171i | 0.466061 | + | 0.269080i | 0.714589 | − | 0.699544i | \(-0.246614\pi\) |
−0.248528 | + | 0.968625i | \(0.579947\pi\) | |||||||
\(450\) | − | 4.87263i | − | 0.229698i | ||||||
\(451\) | −3.46681 | + | 6.00469i | −0.163246 | + | 0.282750i | ||||
\(452\) | 6.49396 | + | 11.2479i | 0.305450 | + | 0.529055i | ||||
\(453\) | −13.7017 | + | 7.91066i | −0.643760 | + | 0.371675i | ||||
\(454\) | −16.5767 | −0.777984 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.98792 | −0.233581 | ||||||||
\(457\) | 6.64171 | − | 3.83459i | 0.310686 | − | 0.179375i | −0.336547 | − | 0.941667i | \(-0.609259\pi\) |
0.647233 | + | 0.762292i | \(0.275926\pi\) | |||||||
\(458\) | 11.9390 | + | 20.6790i | 0.557873 | + | 0.966264i | ||||
\(459\) | −1.04892 | + | 1.81678i | −0.0489593 | + | 0.0847999i | ||||
\(460\) | − | 3.03146i | − | 0.141343i | ||||||
\(461\) | 24.6886 | + | 14.2540i | 1.14986 | + | 0.663874i | 0.948854 | − | 0.315715i | \(-0.102244\pi\) |
0.201010 | + | 0.979589i | \(0.435578\pi\) | |||||||
\(462\) | 3.19738 | + | 1.84601i | 0.148756 | + | 0.0858842i | ||||
\(463\) | 14.3284i | 0.665898i | 0.942945 | + | 0.332949i | \(0.108044\pi\) | ||||
−0.942945 | + | 0.332949i | \(0.891956\pi\) | |||||||
\(464\) | −4.25786 | + | 7.37484i | −0.197666 | + | 0.342368i | ||||
\(465\) | −1.92543 | − | 3.33494i | −0.0892896 | − | 0.154654i | ||||
\(466\) | 12.1202 | − | 6.99761i | 0.561458 | − | 0.324158i | ||||
\(467\) | −33.3207 | −1.54190 | −0.770948 | − | 0.636898i | \(-0.780217\pi\) | ||||
−0.770948 | + | 0.636898i | \(0.780217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.9831 | 2.53889 | ||||||||
\(470\) | −0.550216 | + | 0.317667i | −0.0253796 | + | 0.0146529i | ||||
\(471\) | 2.13706 | + | 3.70150i | 0.0984707 | + | 0.170556i | ||||
\(472\) | −3.02446 | + | 5.23852i | −0.139212 | + | 0.241122i | ||||
\(473\) | − | 5.72109i | − | 0.263056i | ||||||
\(474\) | −10.1386 | − | 5.85354i | −0.465683 | − | 0.268862i | ||||
\(475\) | −21.0481 | − | 12.1521i | −0.965753 | − | 0.557578i | ||||
\(476\) | − | 8.49396i | − | 0.389320i | ||||||
\(477\) | −5.20560 | + | 9.01636i | −0.238348 | + | 0.412831i | ||||
\(478\) | 6.64310 | + | 11.5062i | 0.303849 | + | 0.526281i | ||||
\(479\) | 19.1634 | − | 11.0640i | 0.875597 | − | 0.505526i | 0.00639300 | − | 0.999980i | \(-0.497965\pi\) |
0.869204 | + | 0.494453i | \(0.164632\pi\) | |||||||
\(480\) | −0.356896 | −0.0162900 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.4789 | 0.477301 | ||||||||
\(483\) | −29.7838 | + | 17.1957i | −1.35521 | + | 0.782430i | ||||
\(484\) | 5.08426 | + | 8.80620i | 0.231103 | + | 0.400282i | ||||
\(485\) | −0.349896 | + | 0.606037i | −0.0158879 | + | 0.0275187i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 0.109387 | + | 0.0631549i | 0.00495682 | + | 0.00286182i | 0.502476 | − | 0.864591i | \(-0.332422\pi\) |
−0.497520 | + | 0.867453i | \(0.665756\pi\) | |||||||
\(488\) | 2.69327 | + | 1.55496i | 0.121918 | + | 0.0703896i | ||||
\(489\) | − | 0.317667i | − | 0.0143654i | ||||||
\(490\) | −1.67629 | + | 2.90342i | −0.0757272 | + | 0.131163i | ||||
\(491\) | 6.97166 | + | 12.0753i | 0.314626 | + | 0.544949i | 0.979358 | − | 0.202133i | \(-0.0647874\pi\) |
−0.664732 | + | 0.747082i | \(0.731454\pi\) | |||||||
\(492\) | −6.58515 | + | 3.80194i | −0.296881 | + | 0.171405i | ||||
\(493\) | 17.8646 | 0.804581 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.325437 | −0.0146273 | ||||||||
\(496\) | 9.34429 | − | 5.39493i | 0.419571 | − | 0.242239i | ||||
\(497\) | −23.2446 | − | 40.2608i | −1.04266 | − | 1.80594i | ||||
\(498\) | −3.24967 | + | 5.62859i | −0.145621 | + | 0.252223i | ||||
\(499\) | 28.3913i | 1.27097i | 0.772113 | + | 0.635485i | \(0.219200\pi\) | ||||
−0.772113 | + | 0.635485i | \(0.780800\pi\) | |||||||
\(500\) | −3.05144 | − | 1.76175i | −0.136465 | − | 0.0787878i | ||||
\(501\) | −10.7051 | − | 6.18060i | −0.478269 | − | 0.276129i | ||||
\(502\) | 3.48725i | 0.155644i | ||||||||
\(503\) | −6.28382 | + | 10.8839i | −0.280181 | + | 0.485289i | −0.971429 | − | 0.237329i | \(-0.923728\pi\) |
0.691248 | + | 0.722618i | \(0.257061\pi\) | |||||||
\(504\) | 2.02446 | + | 3.50647i | 0.0901766 | + | 0.156190i | ||||
\(505\) | 2.15817 | − | 1.24602i | 0.0960373 | − | 0.0554472i | ||||
\(506\) | 7.74525 | 0.344318 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.22282 | 0.409196 | ||||||||
\(509\) | 3.79037 | − | 2.18837i | 0.168005 | − | 0.0969980i | −0.413640 | − | 0.910441i | \(-0.635743\pi\) |
0.581645 | + | 0.813443i | \(0.302409\pi\) | |||||||
\(510\) | 0.374354 | + | 0.648401i | 0.0165767 | + | 0.0287117i | ||||
\(511\) | 1.07942 | − | 1.86960i | 0.0477506 | − | 0.0827064i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −4.31966 | − | 2.49396i | −0.190718 | − | 0.110111i | ||||
\(514\) | −5.66164 | − | 3.26875i | −0.249724 | − | 0.144178i | ||||
\(515\) | 1.76617i | 0.0778266i | ||||||||
\(516\) | 3.13706 | − | 5.43355i | 0.138102 | − | 0.239199i | ||||
\(517\) | −0.811626 | − | 1.40578i | −0.0356953 | − | 0.0618261i | ||||
\(518\) | −2.15983 | + | 1.24698i | −0.0948976 | + | 0.0547891i | ||||
\(519\) | 17.0640 | 0.749026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.2707 | −1.01951 | −0.509753 | − | 0.860321i | \(-0.670263\pi\) | ||||
−0.509753 | + | 0.860321i | \(0.670263\pi\) | |||||||
\(522\) | −7.37484 | + | 4.25786i | −0.322788 | + | 0.186362i | ||||
\(523\) | −18.9976 | − | 32.9048i | −0.830707 | − | 1.43883i | −0.897478 | − | 0.441059i | \(-0.854603\pi\) |
0.0667707 | − | 0.997768i | \(-0.478730\pi\) | |||||||
\(524\) | −7.27628 | + | 12.6029i | −0.317866 | + | 0.550560i | ||||
\(525\) | 19.7289i | 0.861038i | ||||||||
\(526\) | 6.94498 | + | 4.00969i | 0.302816 | + | 0.174831i | ||||
\(527\) | −19.6028 | − | 11.3177i | −0.853910 | − | 0.493005i | ||||
\(528\) | − | 0.911854i | − | 0.0396834i | ||||||
\(529\) | −24.5737 | + | 42.5628i | −1.06842 | + | 1.85056i | ||||
\(530\) | 1.85786 | + | 3.21790i | 0.0807001 | + | 0.139777i | ||||
\(531\) | −5.23852 | + | 3.02446i | −0.227332 | + | 0.131250i | ||||
\(532\) | 20.1957 | 0.875593 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.49396 | −0.281021 | ||||||||
\(535\) | 1.31939 | − | 0.761750i | 0.0570422 | − | 0.0329333i | ||||
\(536\) | −6.78986 | − | 11.7604i | −0.293277 | − | 0.507971i | ||||
\(537\) | −12.4840 | + | 21.6230i | −0.538726 | + | 0.933100i | ||||
\(538\) | 27.6732i | 1.19308i | ||||||||
\(539\) | −7.41812 | − | 4.28286i | −0.319521 | − | 0.184476i | ||||
\(540\) | −0.309081 | − | 0.178448i | −0.0133007 | − | 0.00767918i | ||||
\(541\) | − | 3.16421i | − | 0.136040i | −0.997684 | − | 0.0680200i | \(-0.978332\pi\) | ||
0.997684 | − | 0.0680200i | \(-0.0216682\pi\) | |||||||
\(542\) | −7.36443 | + | 12.7556i | −0.316329 | + | 0.547898i | ||||
\(543\) | 2.63102 | + | 4.55706i | 0.112908 | + | 0.195562i | ||||
\(544\) | −1.81678 | + | 1.04892i | −0.0778937 | + | 0.0449720i | ||||
\(545\) | 2.21983 | 0.0950872 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.56033 | 0.323257 | 0.161628 | − | 0.986852i | \(-0.448325\pi\) | ||||
0.161628 | + | 0.986852i | \(0.448325\pi\) | |||||||
\(548\) | 13.3398 | − | 7.70171i | 0.569846 | − | 0.329001i | ||||
\(549\) | 1.55496 | + | 2.69327i | 0.0663640 | + | 0.114946i | ||||
\(550\) | 2.22156 | − | 3.84786i | 0.0947277 | − | 0.164073i | ||||
\(551\) | 42.4758i | 1.80953i | ||||||||
\(552\) | 7.35598 | + | 4.24698i | 0.313091 | + | 0.180763i | ||||
\(553\) | 41.0505 | + | 23.7005i | 1.74564 | + | 1.00785i | ||||
\(554\) | 3.26205i | 0.138591i | ||||||||
\(555\) | 0.109916 | − | 0.190381i | 0.00466569 | − | 0.00808120i | ||||
\(556\) | 1.35690 | + | 2.35021i | 0.0575452 | + | 0.0996712i | ||||
\(557\) | 0.359835 | − | 0.207751i | 0.0152467 | − | 0.00880269i | −0.492357 | − | 0.870393i | \(-0.663865\pi\) |
0.507604 | + | 0.861591i | \(0.330531\pi\) | |||||||
\(558\) | 10.7899 | 0.456771 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.44504 | 0.0610642 | ||||||||
\(561\) | −1.65664 | + | 0.956459i | −0.0699432 | + | 0.0403818i | ||||
\(562\) | −3.86294 | − | 6.69080i | −0.162948 | − | 0.282234i | ||||
\(563\) | −14.5233 | + | 25.1550i | −0.612083 | + | 1.06016i | 0.378806 | + | 0.925476i | \(0.376335\pi\) |
−0.990889 | + | 0.134682i | \(0.956999\pi\) | |||||||
\(564\) | − | 1.78017i | − | 0.0749586i | ||||||
\(565\) | 4.01432 | + | 2.31767i | 0.168884 | + | 0.0975050i | ||||
\(566\) | 17.1301 | + | 9.89008i | 0.720033 | + | 0.415711i | ||||
\(567\) | 4.04892i | 0.170039i | ||||||||
\(568\) | −5.74094 | + | 9.94360i | −0.240884 | + | 0.417224i | ||||
\(569\) | 19.8431 | + | 34.3692i | 0.831865 | + | 1.44083i | 0.896557 | + | 0.442928i | \(0.146060\pi\) |
−0.0646918 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(570\) | −1.54167 | + | 0.890084i | −0.0645735 | + | 0.0372815i | ||||
\(571\) | 7.09651 | 0.296980 | 0.148490 | − | 0.988914i | \(-0.452559\pi\) | ||||
0.148490 | + | 0.988914i | \(0.452559\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5375 | 0.440210 | ||||||||
\(574\) | 26.6627 | − | 15.3937i | 1.11288 | − | 0.642522i | ||||
\(575\) | 20.6939 | + | 35.8430i | 0.862997 | + | 1.49475i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 8.78687i | − | 0.365802i | −0.983131 | − | 0.182901i | \(-0.941451\pi\) | ||
0.983131 | − | 0.182901i | \(-0.0585488\pi\) | |||||||
\(578\) | −10.9111 | − | 6.29954i | −0.453843 | − | 0.262027i | ||||
\(579\) | −2.96837 | − | 1.71379i | −0.123361 | − | 0.0712228i | ||||
\(580\) | 3.03923i | 0.126197i | ||||||||
\(581\) | 13.1576 | − | 22.7897i | 0.545871 | − | 0.945476i | ||||
\(582\) | −0.980386 | − | 1.69808i | −0.0406383 | − | 0.0703876i | ||||
\(583\) | −8.22160 | + | 4.74674i | −0.340504 | + | 0.196590i | ||||
\(584\) | −0.533188 | −0.0220635 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.9119 | −0.533384 | ||||||||
\(587\) | −31.7889 | + | 18.3533i | −1.31207 | + | 0.757522i | −0.982438 | − | 0.186589i | \(-0.940257\pi\) |
−0.329629 | + | 0.944111i | \(0.606923\pi\) | |||||||
\(588\) | −4.69687 | − | 8.13521i | −0.193695 | − | 0.335490i | ||||
\(589\) | 26.9095 | − | 46.6086i | 1.10879 | − | 1.92047i | ||||
\(590\) | 2.15883i | 0.0888778i | ||||||||
\(591\) | 3.26906 | + | 1.88740i | 0.134471 | + | 0.0776371i | ||||
\(592\) | 0.533434 | + | 0.307979i | 0.0219240 | + | 0.0126578i | ||||
\(593\) | 10.8310i | 0.444776i | 0.974958 | + | 0.222388i | \(0.0713852\pi\) | ||||
−0.974958 | + | 0.222388i | \(0.928615\pi\) | |||||||
\(594\) | 0.455927 | − | 0.789689i | 0.0187069 | − | 0.0324013i | ||||
\(595\) | −1.51573 | − | 2.62532i | −0.0621389 | − | 0.107628i | ||||
\(596\) | −12.7614 | + | 7.36778i | −0.522726 | + | 0.301796i | ||||
\(597\) | −17.9541 | −0.734811 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.5254 | 0.961223 | 0.480611 | − | 0.876934i | \(-0.340415\pi\) | ||||
0.480611 | + | 0.876934i | \(0.340415\pi\) | |||||||
\(600\) | 4.21982 | − | 2.43631i | 0.172273 | − | 0.0994620i | ||||
\(601\) | −13.9107 | − | 24.0940i | −0.567428 | − | 0.982813i | −0.996819 | − | 0.0796950i | \(-0.974605\pi\) |
0.429392 | − | 0.903118i | \(-0.358728\pi\) | |||||||
\(602\) | −12.7017 | + | 22.0000i | −0.517683 | + | 0.896653i | ||||
\(603\) | − | 13.5797i | − | 0.553009i | ||||||
\(604\) | −13.7017 | − | 7.91066i | −0.557513 | − | 0.321880i | ||||
\(605\) | 3.14290 | + | 1.81455i | 0.127777 | + | 0.0737720i | ||||
\(606\) | 6.98254i | 0.283646i | ||||||||
\(607\) | −0.0486218 | + | 0.0842155i | −0.00197350 | + | 0.00341820i | −0.867010 | − | 0.498290i | \(-0.833962\pi\) |
0.865037 | + | 0.501708i | \(0.167295\pi\) | |||||||
\(608\) | −2.49396 | − | 4.31966i | −0.101143 | − | 0.175186i | ||||
\(609\) | 29.8601 | − | 17.2397i | 1.20999 | − | 0.698590i | ||||
\(610\) | 1.10992 | 0.0449392 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.09783 | −0.0847999 | ||||||||
\(613\) | 6.98454 | − | 4.03252i | 0.282103 | − | 0.162872i | −0.352272 | − | 0.935898i | \(-0.614591\pi\) |
0.634375 | + | 0.773025i | \(0.281258\pi\) | |||||||
\(614\) | −9.98254 | − | 17.2903i | −0.402863 | − | 0.697778i | ||||
\(615\) | −1.35690 | + | 2.35021i | −0.0547153 | + | 0.0947697i | ||||
\(616\) | 3.69202i | 0.148756i | ||||||||
\(617\) | 16.6437 | + | 9.60925i | 0.670051 | + | 0.386854i | 0.796096 | − | 0.605171i | \(-0.206895\pi\) |
−0.126045 | + | 0.992025i | \(0.540228\pi\) | |||||||
\(618\) | −4.28569 | − | 2.47434i | −0.172396 | − | 0.0995327i | ||||
\(619\) | − | 12.3827i | − | 0.497703i | −0.968542 | − | 0.248852i | \(-0.919947\pi\) | ||
0.968542 | − | 0.248852i | \(-0.0800532\pi\) | |||||||
\(620\) | 1.92543 | − | 3.33494i | 0.0773270 | − | 0.133934i | ||||
\(621\) | 4.24698 | + | 7.35598i | 0.170425 | + | 0.295185i | ||||
\(622\) | 11.6756 | − | 6.74094i | 0.468151 | − | 0.270287i | ||||
\(623\) | 26.2935 | 1.05343 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1056 | 0.924224 | ||||||||
\(626\) | −11.1930 | + | 6.46226i | −0.447361 | + | 0.258284i | ||||
\(627\) | −2.27413 | − | 3.93890i | −0.0908199 | − | 0.157305i | ||||
\(628\) | −2.13706 | + | 3.70150i | −0.0852781 | + | 0.147706i | ||||
\(629\) | − | 1.29218i | − | 0.0515224i | ||||||
\(630\) | 1.25144 | + | 0.722521i | 0.0498587 | + | 0.0287859i | ||||
\(631\) | −4.10785 | − | 2.37167i | −0.163531 | − | 0.0944145i | 0.416001 | − | 0.909364i | \(-0.363431\pi\) |
−0.579532 | + | 0.814950i | \(0.696765\pi\) | |||||||
\(632\) | − | 11.7071i | − | 0.465683i | ||||||
\(633\) | 6.26875 | − | 10.8578i | 0.249160 | − | 0.431559i | ||||
\(634\) | −5.93631 | − | 10.2820i | −0.235761 | − | 0.408350i | ||||
\(635\) | 2.85060 | − | 1.64579i | 0.113122 | − | 0.0653113i | ||||
\(636\) | −10.4112 | −0.412831 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.76510 | −0.307423 | ||||||||
\(639\) | −9.94360 | + | 5.74094i | −0.393363 | + | 0.227108i | ||||
\(640\) | −0.178448 | − | 0.309081i | −0.00705377 | − | 0.0122175i | ||||
\(641\) | −8.22282 | + | 14.2423i | −0.324782 | + | 0.562538i | −0.981468 | − | 0.191625i | \(-0.938624\pi\) |
0.656686 | + | 0.754164i | \(0.271958\pi\) | |||||||
\(642\) | 4.26875i | 0.168474i | ||||||||
\(643\) | −1.51143 | − | 0.872625i | −0.0596050 | − | 0.0344130i | 0.469901 | − | 0.882719i | \(-0.344289\pi\) |
−0.529506 | + | 0.848306i | \(0.677623\pi\) | |||||||
\(644\) | −29.7838 | − | 17.1957i | −1.17365 | − | 0.677604i | ||||
\(645\) | − | 2.23921i | − | 0.0881688i | ||||||
\(646\) | −5.23191 | + | 9.06194i | −0.205847 | + | 0.356537i | ||||
\(647\) | 14.3817 | + | 24.9097i | 0.565401 | + | 0.979303i | 0.997012 | + | 0.0772436i | \(0.0246119\pi\) |
−0.431611 | + | 0.902060i | \(0.642055\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −5.51573 | −0.216511 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −43.6872 | −1.71224 | ||||||||
\(652\) | 0.275108 | − | 0.158834i | 0.0107741 | − | 0.00622040i | ||||
\(653\) | 8.08306 | + | 14.0003i | 0.316315 | + | 0.547873i | 0.979716 | − | 0.200391i | \(-0.0642211\pi\) |
−0.663401 | + | 0.748264i | \(0.730888\pi\) | |||||||
\(654\) | −3.10992 | + | 5.38653i | −0.121607 | + | 0.210630i | ||||
\(655\) | 5.19375i | 0.202937i | ||||||||
\(656\) | −6.58515 | − | 3.80194i | −0.257107 | − | 0.148441i | ||||
\(657\) | −0.461754 | − | 0.266594i | −0.0180147 | − | 0.0104008i | ||||
\(658\) | 7.20775i | 0.280987i | ||||||||
\(659\) | 8.17792 | − | 14.1646i | 0.318566 | − | 0.551773i | −0.661623 | − | 0.749837i | \(-0.730132\pi\) |
0.980189 | + | 0.198064i | \(0.0634653\pi\) | |||||||
\(660\) | −0.162718 | − | 0.281837i | −0.00633381 | − | 0.0109705i | ||||
\(661\) | 28.6792 | − | 16.5579i | 1.11549 | − | 0.644029i | 0.175245 | − | 0.984525i | \(-0.443928\pi\) |
0.940246 | + | 0.340495i | \(0.110595\pi\) | |||||||
\(662\) | −10.2392 | −0.397958 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.49934 | −0.252223 | ||||||||
\(665\) | 6.24210 | − | 3.60388i | 0.242058 | − | 0.139752i | ||||
\(666\) | 0.307979 | + | 0.533434i | 0.0119339 | + | 0.0206702i | ||||
\(667\) | 36.1661 | − | 62.6416i | 1.40036 | − | 2.42549i | ||||
\(668\) | − | 12.3612i | − | 0.478269i | ||||||
\(669\) | 4.70043 | + | 2.71379i | 0.181729 | + | 0.104921i | ||||
\(670\) | −4.19723 | − | 2.42327i | −0.162153 | − | 0.0936191i | ||||
\(671\) | 2.83579i | 0.109474i | ||||||||
\(672\) | −2.02446 | + | 3.50647i | −0.0780952 | + | 0.135265i | ||||
\(673\) | −17.5770 | − | 30.4443i | −0.677544 | − | 1.17354i | −0.975718 | − | 0.219030i | \(-0.929711\pi\) |
0.298174 | − | 0.954512i | \(-0.403623\pi\) | |||||||
\(674\) | 1.25518 | − | 0.724677i | 0.0483476 | − | 0.0279135i | ||||
\(675\) | 4.87263 | 0.187547 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.7855 | 0.914153 | 0.457076 | − | 0.889427i | \(-0.348897\pi\) | ||||
0.457076 | + | 0.889427i | \(0.348897\pi\) | |||||||
\(678\) | −11.2479 | + | 6.49396i | −0.431972 | + | 0.249399i | ||||
\(679\) | 3.96950 | + | 6.87538i | 0.152335 | + | 0.263853i | ||||
\(680\) | −0.374354 | + | 0.648401i | −0.0143558 | + | 0.0248650i | ||||
\(681\) | − | 16.5767i | − | 0.635222i | ||||||
\(682\) | 8.52063 | + | 4.91939i | 0.326272 | + | 0.188373i | ||||
\(683\) | 2.59135 | + | 1.49612i | 0.0991552 | + | 0.0572473i | 0.548758 | − | 0.835982i | \(-0.315101\pi\) |
−0.449602 | + | 0.893229i | \(0.648434\pi\) | |||||||
\(684\) | − | 4.98792i | − | 0.190718i | ||||||
\(685\) | 2.74871 | − | 4.76090i | 0.105023 | − | 0.181905i | ||||
\(686\) | 4.84601 | + | 8.39354i | 0.185022 | + | 0.320467i | ||||
\(687\) | −20.6790 | + | 11.9390i | −0.788951 | + | 0.455501i | ||||
\(688\) | 6.27413 | 0.239199 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.03146 | 0.115406 | ||||||||
\(691\) | 10.0660 | − | 5.81163i | 0.382930 | − | 0.221085i | −0.296162 | − | 0.955138i | \(-0.595707\pi\) |
0.679092 | + | 0.734053i | \(0.262374\pi\) | |||||||
\(692\) | 8.53199 | + | 14.7778i | 0.324338 | + | 0.561769i | ||||
\(693\) | −1.84601 | + | 3.19738i | −0.0701241 | + | 0.121459i | ||||
\(694\) | − | 6.84117i | − | 0.259687i | ||||||
\(695\) | 0.838781 | + | 0.484271i | 0.0318168 | + | 0.0183694i | ||||
\(696\) | −7.37484 | − | 4.25786i | −0.279543 | − | 0.161394i | ||||
\(697\) | 15.9517i | 0.604213i | ||||||||
\(698\) | 17.1685 | − | 29.7368i | 0.649838 | − | 1.12555i | ||||
\(699\) | 6.99761 | + | 12.1202i | 0.264674 | + | 0.458428i | ||||
\(700\) | −17.0857 | + | 9.86443i | −0.645778 | + | 0.372840i | ||||
\(701\) | 33.8431 | 1.27824 | 0.639118 | − | 0.769109i | \(-0.279300\pi\) | ||||
0.639118 | + | 0.769109i | \(0.279300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.07234 | 0.115876 | ||||||||
\(704\) | 0.789689 | − | 0.455927i | 0.0297625 | − | 0.0171834i | ||||
\(705\) | −0.317667 | − | 0.550216i | −0.0119640 | − | 0.0207223i | ||||
\(706\) | 13.0248 | − | 22.5595i | 0.490193 | − | 0.849039i | ||||
\(707\) | − | 28.2717i | − | 1.06327i | ||||||
\(708\) | −5.23852 | − | 3.02446i | −0.196875 | − | 0.113666i | ||||
\(709\) | −22.6820 | − | 13.0954i | −0.851839 | − | 0.491810i | 0.00943173 | − | 0.999956i | \(-0.496998\pi\) |
−0.861271 | + | 0.508146i | \(0.830331\pi\) | |||||||
\(710\) | 4.09783i | 0.153789i | ||||||||
\(711\) | 5.85354 | − | 10.1386i | 0.219525 | − | 0.380229i | ||||
\(712\) | −3.24698 | − | 5.62393i | −0.121686 | − | 0.210766i | ||||
\(713\) | −79.3700 | + | 45.8243i | −2.97243 | + | 1.71613i | ||||
\(714\) | 8.49396 | 0.317878 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.9681 | −0.933100 | ||||||||
\(717\) | −11.5062 | + | 6.64310i | −0.429707 | + | 0.248091i | ||||
\(718\) | −4.24698 | − | 7.35598i | −0.158496 | − | 0.274523i | ||||
\(719\) | −10.8672 | + | 18.8226i | −0.405280 | + | 0.701966i | −0.994354 | − | 0.106114i | \(-0.966159\pi\) |
0.589074 | + | 0.808079i | \(0.299493\pi\) | |||||||
\(720\) | − | 0.356896i | − | 0.0133007i | ||||||
\(721\) | 17.3524 | + | 10.0184i | 0.646237 | + | 0.373105i | ||||
\(722\) | −5.09165 | − | 2.93967i | −0.189492 | − | 0.109403i | ||||
\(723\) | 10.4789i | 0.389714i | ||||||||
\(724\) | −2.63102 | + | 4.55706i | −0.0977812 | + | 0.169362i | ||||
\(725\) | −20.7470 | − | 35.9348i | −0.770523 | − | 1.33459i | ||||
\(726\) | −8.80620 | + | 5.08426i | −0.326829 | + | 0.188695i | ||||
\(727\) | 2.01400 | 0.0746951 | 0.0373476 | − | 0.999302i | \(-0.488109\pi\) | ||||
0.0373476 | + | 0.999302i | \(0.488109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.164798 | + | 0.0951463i | −0.00609945 | + | 0.00352152i | ||||
\(731\) | −6.58104 | − | 11.3987i | −0.243409 | − | 0.421596i | ||||
\(732\) | −1.55496 | + | 2.69327i | −0.0574729 | + | 0.0995460i | ||||
\(733\) | 13.5013i | 0.498680i | 0.968416 | + | 0.249340i | \(0.0802137\pi\) | ||||
−0.968416 | + | 0.249340i | \(0.919786\pi\) | |||||||
\(734\) | 23.7744 | + | 13.7262i | 0.877530 | + | 0.506642i | ||||
\(735\) | −2.90342 | − | 1.67629i | −0.107094 | − | 0.0618310i | ||||
\(736\) | 8.49396i | 0.313091i | ||||||||
\(737\) | 6.19136 | − | 10.7237i | 0.228062 | − | 0.395014i | ||||
\(738\) | −3.80194 | − | 6.58515i | −0.139951 | − | 0.242403i | ||||
\(739\) | 14.3689 | − | 8.29590i | 0.528569 | − | 0.305170i | −0.211864 | − | 0.977299i | \(-0.567954\pi\) |
0.740434 | + | 0.672130i | \(0.234620\pi\) | |||||||
\(740\) | 0.219833 | 0.00808120 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 42.1540 | 1.54752 | ||||||||
\(743\) | −17.1888 | + | 9.92394i | −0.630594 | + | 0.364074i | −0.780982 | − | 0.624553i | \(-0.785281\pi\) |
0.150388 | + | 0.988627i | \(0.451948\pi\) | |||||||
\(744\) | 5.39493 | + | 9.34429i | 0.197788 | + | 0.342578i | ||||
\(745\) | −2.62953 | + | 4.55448i | −0.0963385 | + | 0.166863i | ||||
\(746\) | − | 26.6219i | − | 0.974698i | ||||||
\(747\) | −5.62859 | − | 3.24967i | −0.205939 | − | 0.118899i | ||||
\(748\) | −1.65664 | − | 0.956459i | −0.0605726 | − | 0.0349716i | ||||
\(749\) | − | 17.2838i | − | 0.631537i | ||||||
\(750\) | 1.76175 | − | 3.05144i | 0.0643300 | − | 0.111423i | ||||
\(751\) | 13.9673 | + | 24.1922i | 0.509676 | + | 0.882784i | 0.999937 | + | 0.0112087i | \(0.00356793\pi\) |
−0.490262 | + | 0.871575i | \(0.663099\pi\) | |||||||
\(752\) | 1.54167 | − | 0.890084i | 0.0562189 | − | 0.0324580i | ||||
\(753\) | −3.48725 | −0.127083 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.64656 | −0.205499 | ||||||||
\(756\) | −3.50647 | + | 2.02446i | −0.127529 | + | 0.0736288i | ||||
\(757\) | 0.274127 | + | 0.474801i | 0.00996330 | + | 0.0172569i | 0.870964 | − | 0.491347i | \(-0.163495\pi\) |
−0.861001 | + | 0.508604i | \(0.830162\pi\) | |||||||
\(758\) | 5.82371 | − | 10.0870i | 0.211527 | − | 0.366375i | ||||
\(759\) | 7.74525i | 0.281135i | ||||||||
\(760\) | −1.54167 | − | 0.890084i | −0.0559223 | − | 0.0322867i | ||||
\(761\) | 1.71112 | + | 0.987918i | 0.0620282 | + | 0.0358120i | 0.530693 | − | 0.847564i | \(-0.321932\pi\) |
−0.468665 | + | 0.883376i | \(0.655265\pi\) | |||||||
\(762\) | 9.22282i | 0.334107i | ||||||||
\(763\) | 12.5918 | − | 21.8096i | 0.455854 | − | 0.789562i | ||||
\(764\) | 5.26875 | + | 9.12574i | 0.190617 | + | 0.330158i | ||||
\(765\) | −0.648401 | + | 0.374354i | −0.0234430 | + | 0.0135348i | ||||
\(766\) | −10.5181 | −0.380035 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 24.7780 | − | 14.3056i | 0.893518 | − | 0.515873i | 0.0184261 | − | 0.999830i | \(-0.494134\pi\) |
0.875091 | + | 0.483958i | \(0.160801\pi\) | |||||||
\(770\) | 0.658834 | + | 1.14113i | 0.0237427 | + | 0.0411236i | ||||
\(771\) | 3.26875 | − | 5.66164i | 0.117721 | − | 0.203899i | ||||
\(772\) | − | 3.42758i | − | 0.123361i | ||||||
\(773\) | −45.4732 | − | 26.2540i | −1.63556 | − | 0.944290i | −0.982336 | − | 0.187123i | \(-0.940084\pi\) |
−0.653222 | − | 0.757167i | \(-0.726583\pi\) | |||||||
\(774\) | 5.43355 | + | 3.13706i | 0.195305 | + | 0.112759i | ||||
\(775\) | 52.5749i | 1.88855i | ||||||||
\(776\) | 0.980386 | − | 1.69808i | 0.0351938 | − | 0.0609574i | ||||
\(777\) | −1.24698 | − | 2.15983i | −0.0447351 | − | 0.0774835i | ||||
\(778\) | −8.01909 | + | 4.62983i | −0.287498 | + | 0.165987i | ||||
\(779\) | −37.9275 | −1.35889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.4698 | −0.374639 | ||||||||
\(782\) | 15.4316 | − | 8.90946i | 0.551834 | − | 0.318602i | ||||
\(783\) | −4.25786 | − | 7.37484i | −0.152164 | − | 0.263555i | ||||
\(784\) | 4.69687 | − | 8.13521i | 0.167745 | − | 0.290543i | ||||
\(785\) | 1.52542i | 0.0544445i | ||||||||
\(786\) | −12.6029 | − | 7.27628i | −0.449530 | − | 0.259536i | ||||
\(787\) | 20.4751 | + | 11.8213i | 0.729859 | + | 0.421384i | 0.818371 | − | 0.574691i | \(-0.194878\pi\) |
−0.0885115 | + | 0.996075i | \(0.528211\pi\) | |||||||
\(788\) | 3.77479i | 0.134471i | ||||||||
\(789\) | −4.00969 | + | 6.94498i | −0.142749 | + | 0.247248i | ||||
\(790\) | −2.08911 | − | 3.61844i | −0.0743270 | − | 0.128738i | ||||
\(791\) | 45.5417 | − | 26.2935i | 1.61928 | − | 0.934889i | ||||
\(792\) | 0.911854 | 0.0324013 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 14.5133 | 0.515059 | ||||||||
\(795\) | −3.21790 | + | 1.85786i | −0.114127 | + | 0.0658913i | ||||
\(796\) | −8.97703 | − | 15.5487i | −0.318183 | − | 0.551108i | ||||
\(797\) | 20.8279 | − | 36.0750i | 0.737762 | − | 1.27784i | −0.215739 | − | 0.976451i | \(-0.569216\pi\) |
0.953501 | − | 0.301390i | \(-0.0974505\pi\) | |||||||
\(798\) | 20.1957i | 0.714919i | ||||||||
\(799\) | −3.23417 | − | 1.86725i | −0.114417 | − | 0.0660585i | ||||
\(800\) | 4.21982 | + | 2.43631i | 0.149193 | + | 0.0861367i | ||||
\(801\) | − | 6.49396i | − | 0.229453i | ||||||
\(802\) | 19.4209 | − | 33.6379i | 0.685775 | − | 1.18780i | ||||
\(803\) | −0.243095 | − | 0.421052i | −0.00857863 | − | 0.0148586i | ||||
\(804\) | 11.7604 | − | 6.78986i | 0.414756 | − | 0.239460i | ||||
\(805\) | −12.2741 | −0.432606 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.6732 | −0.974144 | ||||||||
\(808\) | −6.04706 | + | 3.49127i | −0.212735 | + | 0.122822i | ||||
\(809\) | 22.1196 | + | 38.3123i | 0.777684 | + | 1.34699i | 0.933274 | + | 0.359166i | \(0.116939\pi\) |
−0.155590 | + | 0.987822i | \(0.549728\pi\) | |||||||
\(810\) | 0.178448 | − | 0.309081i | 0.00627002 | − | 0.0108600i | ||||
\(811\) | − | 52.3913i | − | 1.83971i | −0.392260 | − | 0.919854i | \(-0.628307\pi\) | ||
0.392260 | − | 0.919854i | \(-0.371693\pi\) | |||||||
\(812\) | 29.8601 | + | 17.2397i | 1.04788 | + | 0.604996i | ||||
\(813\) | −12.7556 | − | 7.36443i | −0.447357 | − | 0.258282i | ||||
\(814\) | 0.561663i | 0.0196863i | ||||||||
\(815\) | 0.0566871 | − | 0.0981849i | 0.00198566 | − | 0.00343927i | ||||
\(816\) | −1.04892 | − | 1.81678i | −0.0367195 | − | 0.0636000i | ||||
\(817\) | 27.1021 | − | 15.6474i | 0.948183 | − | 0.547434i | ||||
\(818\) | −33.9221 | −1.18606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.71379 | −0.0947697 | ||||||||
\(821\) | 22.1941 | − | 12.8138i | 0.774580 | − | 0.447204i | −0.0599259 | − | 0.998203i | \(-0.519086\pi\) |
0.834506 | + | 0.550999i | \(0.185753\pi\) | |||||||
\(822\) | 7.70171 | + | 13.3398i | 0.268628 | + | 0.465277i | ||||
\(823\) | −20.1277 | + | 34.8621i | −0.701606 | + | 1.21522i | 0.266296 | + | 0.963891i | \(0.414200\pi\) |
−0.967902 | + | 0.251327i | \(0.919133\pi\) | |||||||
\(824\) | − | 4.94869i | − | 0.172396i | ||||||
\(825\) | 3.84786 | + | 2.22156i | 0.133965 | + | 0.0773448i | ||||
\(826\) | 21.2103 | + | 12.2458i | 0.738001 | + | 0.426085i | ||||
\(827\) | − | 18.0519i | − | 0.627726i | −0.949468 | − | 0.313863i | \(-0.898377\pi\) | ||
0.949468 | − | 0.313863i | \(-0.101623\pi\) | |||||||
\(828\) | −4.24698 | + | 7.35598i | −0.147593 | + | 0.255638i | ||||
\(829\) | 11.3327 | + | 19.6289i | 0.393602 | + | 0.681739i | 0.992922 | − | 0.118771i | \(-0.0378955\pi\) |
−0.599320 | + | 0.800510i | \(0.704562\pi\) | |||||||
\(830\) | −2.00882 | + | 1.15979i | −0.0697272 | + | 0.0402570i | ||||
\(831\) | −3.26205 | −0.113159 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.7065 | −0.682790 | ||||||||
\(834\) | −2.35021 | + | 1.35690i | −0.0813812 | + | 0.0469855i | ||||
\(835\) | −2.20583 | − | 3.82061i | −0.0763360 | − | 0.132218i | ||||
\(836\) | 2.27413 | − | 3.93890i | 0.0786523 | − | 0.136230i | ||||
\(837\) | 10.7899i | 0.372952i | ||||||||
\(838\) | 0.827396 | + | 0.477697i | 0.0285819 | + | 0.0165018i | ||||
\(839\) | −19.1238 | − | 11.0411i | −0.660228 | − | 0.381183i | 0.132136 | − | 0.991232i | \(-0.457816\pi\) |
−0.792364 | + | 0.610049i | \(0.791150\pi\) | |||||||
\(840\) | 1.44504i | 0.0498587i | ||||||||
\(841\) | −21.7588 | + | 37.6874i | −0.750304 | + | 1.29957i | ||||
\(842\) | 2.84117 | + | 4.92104i | 0.0979131 | + | 0.169590i | ||||
\(843\) | 6.69080 | − | 3.86294i | 0.230443 | − | 0.133047i | ||||
\(844\) | 12.5375 | 0.431559 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.78017 | 0.0612034 | ||||||||
\(847\) | 35.6556 | − | 20.5858i | 1.22514 | − | 0.707335i | ||||
\(848\) | −5.20560 | − | 9.01636i | −0.178761 | − | 0.309623i | ||||
\(849\) | −9.89008 | + | 17.1301i | −0.339427 | + | 0.587904i | ||||
\(850\) | − | 10.2220i | − | 0.350610i | ||||||
\(851\) | −4.53097 | − | 2.61596i | −0.155320 | − | 0.0896739i | ||||
\(852\) | −9.94360 | − | 5.74094i | −0.340662 | − | 0.196681i | ||||
\(853\) | 28.9831i | 0.992364i | 0.868219 | + | 0.496182i | \(0.165265\pi\) | ||||
−0.868219 | + | 0.496182i | \(0.834735\pi\) | |||||||
\(854\) | 6.29590 | − | 10.9048i | 0.215441 | − | 0.373155i | ||||
\(855\) | −0.890084 | − | 1.54167i | −0.0304402 | − | 0.0527240i | ||||
\(856\) | −3.69685 | + | 2.13437i | −0.126356 | + | 0.0729514i | ||||
\(857\) | 42.9047 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.0616 | −1.60572 | −0.802860 | − | 0.596167i | \(-0.796690\pi\) | ||||
−0.802860 | + | 0.596167i | \(0.796690\pi\) | |||||||
\(860\) | 1.93921 | − | 1.11960i | 0.0661266 | − | 0.0381782i | ||||
\(861\) | 15.3937 | + | 26.6627i | 0.524617 | + | 0.908663i | ||||
\(862\) | 7.42327 | − | 12.8575i | 0.252838 | − | 0.437928i | ||||
\(863\) | − | 42.6064i | − | 1.45034i | −0.688571 | − | 0.725169i | \(-0.741762\pi\) | ||
0.688571 | − | 0.725169i | \(-0.258238\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 5.27415 | + | 3.04503i | 0.179327 | + | 0.103534i | ||||
\(866\) | − | 26.1497i | − | 0.888604i | ||||||
\(867\) | 6.29954 | − | 10.9111i | 0.213944 | − | 0.370561i | ||||
\(868\) | −21.8436 | − | 37.8343i | −0.741421 | − | 1.28418i | ||||
\(869\) | 9.24495 | − | 5.33758i | 0.313614 | − | 0.181065i | ||||
\(870\) | −3.03923 | −0.103040 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.21983 | −0.210630 | ||||||||
\(873\) | 1.69808 | − | 0.980386i | 0.0574712 | − | 0.0331810i | ||||
\(874\) | 21.1836 | + | 36.6911i | 0.716546 | + | 1.24109i | ||||
\(875\) | −7.13318 | + | 12.3550i | −0.241145 | + | 0.417676i | ||||
\(876\) | − | 0.533188i | − | 0.0180147i | ||||||
\(877\) | −23.7362 | − | 13.7041i | −0.801515 | − | 0.462755i | 0.0424859 | − | 0.999097i | \(-0.486472\pi\) |
−0.844000 | + | 0.536342i | \(0.819806\pi\) | |||||||
\(878\) | 20.3950 | + | 11.7751i | 0.688300 | + | 0.397390i | ||||
\(879\) | − | 12.9119i | − | 0.435506i | ||||||
\(880\) | 0.162718 | − | 0.281837i | 0.00548524 | − | 0.00950071i | ||||
\(881\) | 12.1588 | + | 21.0597i | 0.409642 | + | 0.709520i | 0.994849 | − | 0.101363i | \(-0.0323205\pi\) |
−0.585208 | + | 0.810883i | \(0.698987\pi\) | |||||||
\(882\) | 8.13521 | − | 4.69687i | 0.273927 | − | 0.158152i | ||||
\(883\) | 32.2306 | 1.08465 | 0.542323 | − | 0.840170i | \(-0.317545\pi\) | ||||
0.542323 | + | 0.840170i | \(0.317545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.15883 | −0.0725684 | ||||||||
\(886\) | −19.0035 | + | 10.9717i | −0.638434 | + | 0.368600i | ||||
\(887\) | 17.5821 | + | 30.4531i | 0.590349 | + | 1.02252i | 0.994185 | + | 0.107684i | \(0.0343433\pi\) |
−0.403836 | + | 0.914831i | \(0.632323\pi\) | |||||||
\(888\) | −0.307979 | + | 0.533434i | −0.0103351 | + | 0.0179009i | ||||
\(889\) | − | 37.3424i | − | 1.25242i | ||||||
\(890\) | −2.00716 | − | 1.15883i | −0.0672801 | − | 0.0388442i | ||||
\(891\) | 0.789689 | + | 0.455927i | 0.0264556 | + | 0.0152741i | ||||
\(892\) | 5.42758i | 0.181729i | ||||||||
\(893\) | 4.43967 | − | 7.68973i | 0.148568 | − | 0.257327i | ||||
\(894\) | −7.36778 | − | 12.7614i | −0.246415 | − | 0.426804i | ||||
\(895\) | −7.71715 | + | 4.45550i | −0.257956 | + | 0.148931i | ||||
\(896\) | −4.04892 | −0.135265 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.4034 | −0.380537 | ||||||||
\(899\) | 79.5734 | − | 45.9417i | 2.65392 | − | 1.53224i | ||||
\(900\) | 2.43631 | + | 4.21982i | 0.0812104 | + | 0.140661i | ||||
\(901\) | −10.9205 | + | 18.9148i | −0.363814 | + | 0.630144i | ||||
\(902\) | − | 6.93362i | − | 0.230864i | ||||||
\(903\) | −22.0000 | − | 12.7017i | −0.732114 | − | 0.422686i | ||||
\(904\) | −11.2479 | − | 6.49396i | −0.374099 | − | 0.215986i | ||||
\(905\) | 1.87800i | 0.0624269i | ||||||||
\(906\) | 7.91066 | − | 13.7017i | 0.262814 | − | 0.455207i | ||||
\(907\) | −6.56033 | − | 11.3628i | −0.217832 | − | 0.377297i | 0.736313 | − | 0.676641i | \(-0.236565\pi\) |
−0.954145 | + | 0.299345i | \(0.903232\pi\) | |||||||
\(908\) | 14.3559 | − | 8.28836i | 0.476416 | − | 0.275059i | ||||
\(909\) | −6.98254 | −0.231596 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.7453 | 1.51561 | 0.757804 | − | 0.652482i | \(-0.226272\pi\) | ||||
0.757804 | + | 0.652482i | \(0.226272\pi\) | |||||||
\(912\) | 4.31966 | − | 2.49396i | 0.143038 | − | 0.0825832i | ||||
\(913\) | −2.96322 | − | 5.13245i | −0.0980684 | − | 0.169859i | ||||
\(914\) | −3.83459 | + | 6.64171i | −0.126837 | + | 0.219688i | ||||
\(915\) | 1.10992i | 0.0366927i | ||||||||
\(916\) | −20.6790 | − | 11.9390i | −0.683252 | − | 0.394476i | ||||
\(917\) | 51.0281 | + | 29.4611i | 1.68510 | + | 0.972890i | ||||
\(918\) | − | 2.09783i | − | 0.0692389i | ||||||
\(919\) | −8.99247 | + | 15.5754i | −0.296634 | + | 0.513785i | −0.975364 | − | 0.220603i | \(-0.929198\pi\) |
0.678730 | + | 0.734388i | \(0.262531\pi\) | |||||||
\(920\) | 1.51573 | + | 2.62532i | 0.0499721 | + | 0.0865543i | ||||
\(921\) | 17.2903 | − | 9.98254i | 0.569734 | − | 0.328936i | ||||
\(922\) | −28.5080 | −0.938860 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.69202 | −0.121459 | ||||||||
\(925\) | −2.59923 | + | 1.50066i | −0.0854620 | + | 0.0493415i | ||||
\(926\) | −7.16421 | − | 12.4088i | −0.235431 | − | 0.407778i | ||||
\(927\) | 2.47434 | − | 4.28569i | 0.0812681 | − | 0.140761i | ||||
\(928\) | − | 8.51573i | − | 0.279543i | ||||||
\(929\) | −27.4429 | − | 15.8442i | −0.900371 | − | 0.519830i | −0.0230508 | − | 0.999734i | \(-0.507338\pi\) |
−0.877321 | + | 0.479905i | \(0.840671\pi\) | |||||||
\(930\) | 3.33494 | + | 1.92543i | 0.109357 | + | 0.0631373i | ||||
\(931\) | − | 46.8552i | − | 1.53562i | ||||||
\(932\) | −6.99761 | + | 12.1202i | −0.229214 | + | 0.397011i | ||||
\(933\) | 6.74094 | + | 11.6756i | 0.220688 | + | 0.382244i | ||||
\(934\) | 28.8565 | − | 16.6603i | 0.944215 | − | 0.545143i | ||||
\(935\) | −0.682713 | −0.0223271 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.0484 | −1.73302 | −0.866509 | − | 0.499162i | \(-0.833641\pi\) | ||||
−0.866509 | + | 0.499162i | \(0.833641\pi\) | |||||||
\(938\) | −47.6168 | + | 27.4916i | −1.55474 | + | 0.897631i | ||||
\(939\) | −6.46226 | − | 11.1930i | −0.210888 | − | 0.365269i | ||||
\(940\) | 0.317667 | − | 0.550216i | 0.0103612 | − | 0.0179461i | ||||
\(941\) | 21.9433i | 0.715332i | 0.933850 | + | 0.357666i | \(0.116427\pi\) | ||||
−0.933850 | + | 0.357666i | \(0.883573\pi\) | |||||||
\(942\) | −3.70150 | − | 2.13706i | −0.120601 | − | 0.0696293i | ||||
\(943\) | 55.9340 | + | 32.2935i | 1.82146 | + | 1.05162i | ||||
\(944\) | − | 6.04892i | − | 0.196875i | ||||||
\(945\) | −0.722521 | + | 1.25144i | −0.0235036 | + | 0.0407094i | ||||
\(946\) | 2.86054 | + | 4.95461i | 0.0930043 | + | 0.161088i | ||||
\(947\) | −10.5864 | + | 6.11207i | −0.344012 | + | 0.198616i | −0.662045 | − | 0.749464i | \(-0.730311\pi\) |
0.318033 | + | 0.948080i | \(0.396978\pi\) | |||||||
\(948\) | 11.7071 | 0.380229 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 24.3043 | 0.788534 | ||||||||
\(951\) | 10.2820 | − | 5.93631i | 0.333417 | − | 0.192498i | ||||
\(952\) | 4.24698 | + | 7.35598i | 0.137645 | + | 0.238409i | ||||
\(953\) | −1.92931 | + | 3.34167i | −0.0624966 | + | 0.108247i | −0.895581 | − | 0.444899i | \(-0.853240\pi\) |
0.833084 | + | 0.553146i | \(0.186573\pi\) | |||||||
\(954\) | − | 10.4112i | − | 0.337075i | ||||||
\(955\) | 3.25694 | + | 1.88040i | 0.105392 | + | 0.0608482i | ||||
\(956\) | −11.5062 | − | 6.64310i | −0.372137 | − | 0.214853i | ||||
\(957\) | − | 7.76510i | − | 0.251010i | ||||||
\(958\) | −11.0640 | + | 19.1634i | −0.357461 | + | 0.619141i | ||||
\(959\) | −31.1836 | − | 54.0116i | −1.00697 | − | 1.74412i | ||||
\(960\) | 0.309081 | − | 0.178448i | 0.00997554 | − | 0.00575938i | ||||
\(961\) | −85.4210 | −2.75552 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.26875 | −0.137559 | ||||||||
\(964\) | −9.07499 | + | 5.23945i | −0.292286 | + | 0.168751i | ||||
\(965\) | −0.611645 | − | 1.05940i | −0.0196896 | − | 0.0341033i | ||||
\(966\) | 17.1957 | − | 29.7838i | 0.553262 | − | 0.958277i | ||||
\(967\) | − | 0.613564i | − | 0.0197309i | −0.999951 | − | 0.00986545i | \(-0.996860\pi\) | ||
0.999951 | − | 0.00986545i | \(-0.00314032\pi\) | |||||||
\(968\) | −8.80620 | − | 5.08426i | −0.283042 | − | 0.163414i | ||||
\(969\) | −9.06194 | − | 5.23191i | −0.291111 | − | 0.168073i | ||||
\(970\) | − | 0.699791i | − | 0.0224689i | ||||||
\(971\) | 6.48845 | − | 11.2383i | 0.208224 | − | 0.360655i | −0.742931 | − | 0.669368i | \(-0.766565\pi\) |
0.951155 | + | 0.308713i | \(0.0998983\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 9.51582 | − | 5.49396i | 0.305063 | − | 0.176128i | ||||
\(974\) | −0.126310 | −0.00404722 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.10992 | −0.0995460 | ||||||||
\(977\) | −32.0963 | + | 18.5308i | −1.02685 | + | 0.592853i | −0.916081 | − | 0.400993i | \(-0.868665\pi\) |
−0.110770 | + | 0.993846i | \(0.535332\pi\) | |||||||
\(978\) | 0.158834 | + | 0.275108i | 0.00507894 | + | 0.00879698i | ||||
\(979\) | 2.96077 | − | 5.12821i | 0.0946267 | − | 0.163898i | ||||
\(980\) | − | 3.35258i | − | 0.107094i | ||||||
\(981\) | −5.38653 | − | 3.10992i | −0.171979 | − | 0.0992920i | ||||
\(982\) | −12.0753 | − | 6.97166i | −0.385337 | − | 0.222474i | ||||
\(983\) | 14.1193i | 0.450337i | 0.974320 | + | 0.225169i | \(0.0722933\pi\) | ||||
−0.974320 | + | 0.225169i | \(0.927707\pi\) | |||||||
\(984\) | 3.80194 | − | 6.58515i | 0.121201 | − | 0.209927i | ||||
\(985\) | 0.673604 | + | 1.16672i | 0.0214628 | + | 0.0371747i | ||||
\(986\) | −15.4712 | + | 8.93230i | −0.492703 | + | 0.284462i | ||||
\(987\) | −7.20775 | −0.229425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.2922 | −1.69459 | ||||||||
\(990\) | 0.281837 | − | 0.162718i | 0.00895736 | − | 0.00517153i | ||||
\(991\) | −14.2696 | − | 24.7156i | −0.453288 | − | 0.785118i | 0.545300 | − | 0.838241i | \(-0.316416\pi\) |
−0.998588 | + | 0.0531230i | \(0.983082\pi\) | |||||||
\(992\) | −5.39493 | + | 9.34429i | −0.171289 | + | 0.296681i | ||||
\(993\) | − | 10.2392i | − | 0.324932i | ||||||
\(994\) | 40.2608 | + | 23.2446i | 1.27700 | + | 0.737274i | ||||
\(995\) | −5.54926 | − | 3.20387i | −0.175923 | − | 0.101569i | ||||
\(996\) | − | 6.49934i | − | 0.205939i | ||||||
\(997\) | 9.44265 | − | 16.3551i | 0.299052 | − | 0.517973i | −0.676868 | − | 0.736105i | \(-0.736663\pi\) |
0.975919 | + | 0.218132i | \(0.0699964\pi\) | |||||||
\(998\) | −14.1957 | − | 24.5876i | −0.449356 | − | 0.778308i | ||||
\(999\) | −0.533434 | + | 0.307979i | −0.0168771 | + | 0.00974401i |
(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.i.g.361.2 | 12 | ||
13.2 | odd | 12 | 1014.2.a.m.1.2 | ✓ | 3 | ||
13.3 | even | 3 | 1014.2.b.g.337.2 | 6 | |||
13.4 | even | 6 | inner | 1014.2.i.g.823.2 | 12 | ||
13.5 | odd | 4 | 1014.2.e.m.991.2 | 6 | |||
13.6 | odd | 12 | 1014.2.e.m.529.2 | 6 | |||
13.7 | odd | 12 | 1014.2.e.k.529.2 | 6 | |||
13.8 | odd | 4 | 1014.2.e.k.991.2 | 6 | |||
13.9 | even | 3 | inner | 1014.2.i.g.823.5 | 12 | ||
13.10 | even | 6 | 1014.2.b.g.337.5 | 6 | |||
13.11 | odd | 12 | 1014.2.a.o.1.2 | yes | 3 | ||
13.12 | even | 2 | inner | 1014.2.i.g.361.5 | 12 | ||
39.2 | even | 12 | 3042.2.a.be.1.2 | 3 | |||
39.11 | even | 12 | 3042.2.a.bd.1.2 | 3 | |||
39.23 | odd | 6 | 3042.2.b.r.1351.2 | 6 | |||
39.29 | odd | 6 | 3042.2.b.r.1351.5 | 6 | |||
52.11 | even | 12 | 8112.2.a.bz.1.2 | 3 | |||
52.15 | even | 12 | 8112.2.a.ce.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.2 | ✓ | 3 | 13.2 | odd | 12 | ||
1014.2.a.o.1.2 | yes | 3 | 13.11 | odd | 12 | ||
1014.2.b.g.337.2 | 6 | 13.3 | even | 3 | |||
1014.2.b.g.337.5 | 6 | 13.10 | even | 6 | |||
1014.2.e.k.529.2 | 6 | 13.7 | odd | 12 | |||
1014.2.e.k.991.2 | 6 | 13.8 | odd | 4 | |||
1014.2.e.m.529.2 | 6 | 13.6 | odd | 12 | |||
1014.2.e.m.991.2 | 6 | 13.5 | odd | 4 | |||
1014.2.i.g.361.2 | 12 | 1.1 | even | 1 | trivial | ||
1014.2.i.g.361.5 | 12 | 13.12 | even | 2 | inner | ||
1014.2.i.g.823.2 | 12 | 13.4 | even | 6 | inner | ||
1014.2.i.g.823.5 | 12 | 13.9 | even | 3 | inner | ||
3042.2.a.bd.1.2 | 3 | 39.11 | even | 12 | |||
3042.2.a.be.1.2 | 3 | 39.2 | even | 12 | |||
3042.2.b.r.1351.2 | 6 | 39.23 | odd | 6 | |||
3042.2.b.r.1351.5 | 6 | 39.29 | odd | 6 | |||
8112.2.a.bz.1.2 | 3 | 52.11 | even | 12 | |||
8112.2.a.ce.1.2 | 3 | 52.15 | even | 12 |