Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,2,Mod(100,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, 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("143.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14186074890\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1714608.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.2 | ||
Root | \(0.500000 - 1.75780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 143.100 |
Dual form | 143.2.e.a.133.2 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) |
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | 0.169938 | − | 0.294342i | 0.0981140 | − | 0.169938i | −0.812790 | − | 0.582557i | \(-0.802052\pi\) |
0.910904 | + | 0.412618i | \(0.135386\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −2.88448 | −1.28998 | −0.644990 | − | 0.764191i | \(-0.723139\pi\) | ||||
−0.644990 | + | 0.764191i | \(0.723139\pi\) | |||||||
\(6\) | 0.169938 | + | 0.294342i | 0.0693771 | + | 0.120165i | ||||
\(7\) | 1.77230 | + | 3.06972i | 0.669868 | + | 1.16024i | 0.977941 | + | 0.208882i | \(0.0669825\pi\) |
−0.308073 | + | 0.951363i | \(0.599684\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 1.44224 | + | 2.49804i | 0.480747 | + | 0.832679i | ||||
\(10\) | 1.44224 | − | 2.49804i | 0.456077 | − | 0.789948i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0.339877 | 0.0981140 | ||||||||
\(13\) | 1.66994 | − | 3.19551i | 0.463158 | − | 0.886276i | ||||
\(14\) | −3.54461 | −0.947336 | ||||||||
\(15\) | −0.490185 | + | 0.849025i | −0.126565 | + | 0.219217i | ||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 2.61218 | + | 4.52443i | 0.633547 | + | 1.09734i | 0.986821 | + | 0.161815i | \(0.0517349\pi\) |
−0.353274 | + | 0.935520i | \(0.614932\pi\) | |||||||
\(18\) | −2.88448 | −0.679879 | ||||||||
\(19\) | −3.11218 | − | 5.39045i | −0.713983 | − | 1.23666i | −0.963350 | − | 0.268246i | \(-0.913556\pi\) |
0.249367 | − | 0.968409i | \(-0.419777\pi\) | |||||||
\(20\) | −1.44224 | − | 2.49804i | −0.322495 | − | 0.558578i | ||||
\(21\) | 1.20473 | 0.262894 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | −0.339877 | + | 0.588684i | −0.0708692 | + | 0.122749i | −0.899282 | − | 0.437368i | \(-0.855911\pi\) |
0.828413 | + | 0.560117i | \(0.189244\pi\) | |||||||
\(24\) | −0.509815 | + | 0.883026i | −0.104066 | + | 0.180247i | ||||
\(25\) | 3.32025 | 0.664049 | ||||||||
\(26\) | 1.93243 | + | 3.04397i | 0.378980 | + | 0.596971i | ||||
\(27\) | 2.00000 | 0.384900 | ||||||||
\(28\) | −1.77230 | + | 3.06972i | −0.334934 | + | 0.580122i | ||||
\(29\) | 4.21455 | − | 7.29981i | 0.782621 | − | 1.35554i | −0.147788 | − | 0.989019i | \(-0.547215\pi\) |
0.930410 | − | 0.366521i | \(-0.119451\pi\) | |||||||
\(30\) | −0.490185 | − | 0.849025i | −0.0894951 | − | 0.155010i | ||||
\(31\) | 8.40946 | 1.51038 | 0.755192 | − | 0.655504i | \(-0.227544\pi\) | ||||
0.755192 | + | 0.655504i | \(0.227544\pi\) | |||||||
\(32\) | −2.50000 | − | 4.33013i | −0.441942 | − | 0.765466i | ||||
\(33\) | 0.169938 | + | 0.294342i | 0.0295825 | + | 0.0512384i | ||||
\(34\) | −5.22436 | −0.895970 | ||||||||
\(35\) | −5.11218 | − | 8.85456i | −0.864116 | − | 1.49669i | ||||
\(36\) | −1.44224 | + | 2.49804i | −0.240374 | + | 0.416339i | ||||
\(37\) | −1.76249 | + | 3.05272i | −0.289751 | + | 0.501864i | −0.973750 | − | 0.227619i | \(-0.926906\pi\) |
0.683999 | + | 0.729483i | \(0.260239\pi\) | |||||||
\(38\) | 6.22436 | 1.00972 | ||||||||
\(39\) | −0.656787 | − | 1.03457i | −0.105170 | − | 0.165664i | ||||
\(40\) | 8.65345 | 1.36823 | ||||||||
\(41\) | 2.87467 | − | 4.97907i | 0.448948 | − | 0.777600i | −0.549370 | − | 0.835579i | \(-0.685132\pi\) |
0.998318 | + | 0.0579788i | \(0.0184656\pi\) | |||||||
\(42\) | −0.602365 | + | 1.04333i | −0.0929469 | + | 0.160989i | ||||
\(43\) | 0.660123 | + | 1.14337i | 0.100668 | + | 0.174362i | 0.911960 | − | 0.410279i | \(-0.134569\pi\) |
−0.811292 | + | 0.584641i | \(0.801235\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −4.16012 | − | 7.20554i | −0.620155 | − | 1.07414i | ||||
\(46\) | −0.339877 | − | 0.588684i | −0.0501121 | − | 0.0867967i | ||||
\(47\) | 6.10884 | 0.891067 | 0.445533 | − | 0.895265i | \(-0.353014\pi\) | ||||
0.445533 | + | 0.895265i | \(0.353014\pi\) | |||||||
\(48\) | −0.169938 | − | 0.294342i | −0.0245285 | − | 0.0424846i | ||||
\(49\) | −2.78212 | + | 4.81877i | −0.397446 | + | 0.688396i | ||||
\(50\) | −1.66012 | + | 2.87542i | −0.234777 | + | 0.406645i | ||||
\(51\) | 1.77564 | 0.248639 | ||||||||
\(52\) | 3.60236 | − | 0.151548i | 0.499558 | − | 0.0210159i | ||||
\(53\) | −6.08921 | −0.836418 | −0.418209 | − | 0.908351i | \(-0.637342\pi\) | ||||
−0.418209 | + | 0.908351i | \(0.637342\pi\) | |||||||
\(54\) | −1.00000 | + | 1.73205i | −0.136083 | + | 0.235702i | ||||
\(55\) | 1.44224 | − | 2.49804i | 0.194472 | − | 0.336835i | ||||
\(56\) | −5.31691 | − | 9.20916i | −0.710502 | − | 1.23063i | ||||
\(57\) | −2.11552 | −0.280207 | ||||||||
\(58\) | 4.21455 | + | 7.29981i | 0.553397 | + | 0.958512i | ||||
\(59\) | 7.05442 | + | 12.2186i | 0.918408 | + | 1.59073i | 0.801834 | + | 0.597546i | \(0.203858\pi\) |
0.116573 | + | 0.993182i | \(0.462809\pi\) | |||||||
\(60\) | −0.980369 | −0.126565 | ||||||||
\(61\) | −2.00982 | − | 3.48110i | −0.257330 | − | 0.445709i | 0.708195 | − | 0.706016i | \(-0.249510\pi\) |
−0.965526 | + | 0.260307i | \(0.916176\pi\) | |||||||
\(62\) | −4.20473 | + | 7.28281i | −0.534001 | + | 0.924917i | ||||
\(63\) | −5.11218 | + | 8.85456i | −0.644074 | + | 1.11557i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −4.81691 | + | 9.21741i | −0.597464 | + | 1.14328i | ||||
\(66\) | −0.339877 | −0.0418360 | ||||||||
\(67\) | −6.05442 | + | 10.4866i | −0.739665 | + | 1.28114i | 0.212981 | + | 0.977056i | \(0.431683\pi\) |
−0.952646 | + | 0.304082i | \(0.901650\pi\) | |||||||
\(68\) | −2.61218 | + | 4.52443i | −0.316773 | + | 0.548668i | ||||
\(69\) | 0.115516 | + | 0.200080i | 0.0139065 | + | 0.0240868i | ||||
\(70\) | 10.2244 | 1.22204 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | −4.32673 | − | 7.49411i | −0.509909 | − | 0.883189i | ||||
\(73\) | −16.0825 | −1.88232 | −0.941160 | − | 0.337963i | \(-0.890262\pi\) | ||||
−0.941160 | + | 0.337963i | \(0.890262\pi\) | |||||||
\(74\) | −1.76249 | − | 3.05272i | −0.204885 | − | 0.354871i | ||||
\(75\) | 0.564237 | − | 0.977288i | 0.0651525 | − | 0.112847i | ||||
\(76\) | 3.11218 | − | 5.39045i | 0.356992 | − | 0.618328i | ||||
\(77\) | −3.54461 | −0.403945 | ||||||||
\(78\) | 1.22436 | − | 0.0515075i | 0.138632 | − | 0.00583208i | ||||
\(79\) | 0.904114 | 0.101721 | 0.0508604 | − | 0.998706i | \(-0.483804\pi\) | ||||
0.0508604 | + | 0.998706i | \(0.483804\pi\) | |||||||
\(80\) | −1.44224 | + | 2.49804i | −0.161248 | + | 0.279289i | ||||
\(81\) | −3.98685 | + | 6.90542i | −0.442983 | + | 0.767269i | ||||
\(82\) | 2.87467 | + | 4.97907i | 0.317454 | + | 0.549846i | ||||
\(83\) | 4.90411 | 0.538296 | 0.269148 | − | 0.963099i | \(-0.413258\pi\) | ||||
0.269148 | + | 0.963099i | \(0.413258\pi\) | |||||||
\(84\) | 0.602365 | + | 1.04333i | 0.0657234 | + | 0.113836i | ||||
\(85\) | −7.53479 | − | 13.0506i | −0.817263 | − | 1.41554i | ||||
\(86\) | −1.32025 | −0.142366 | ||||||||
\(87\) | −1.43243 | − | 2.48104i | −0.153572 | − | 0.265995i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | 2.82673 | − | 4.89603i | 0.299632 | − | 0.518978i | −0.676420 | − | 0.736517i | \(-0.736469\pi\) |
0.976052 | + | 0.217538i | \(0.0698027\pi\) | |||||||
\(90\) | 8.32025 | 0.877031 | ||||||||
\(91\) | 12.7690 | − | 0.537177i | 1.33855 | − | 0.0563114i | ||||
\(92\) | −0.679754 | −0.0708692 | ||||||||
\(93\) | 1.42909 | − | 2.47526i | 0.148190 | − | 0.256672i | ||||
\(94\) | −3.05442 | + | 5.29041i | −0.315040 | + | 0.545665i | ||||
\(95\) | 8.97703 | + | 15.5487i | 0.921024 | + | 1.59526i | ||||
\(96\) | −1.69938 | −0.173443 | ||||||||
\(97\) | −1.39764 | − | 2.42077i | −0.141908 | − | 0.245792i | 0.786307 | − | 0.617836i | \(-0.211990\pi\) |
−0.928215 | + | 0.372044i | \(0.878657\pi\) | |||||||
\(98\) | −2.78212 | − | 4.81877i | −0.281036 | − | 0.486769i | ||||
\(99\) | −2.88448 | −0.289902 | ||||||||
\(100\) | 1.66012 | + | 2.87542i | 0.166012 | + | 0.287542i | ||||
\(101\) | 4.93243 | − | 8.54321i | 0.490795 | − | 0.850081i | −0.509149 | − | 0.860678i | \(-0.670040\pi\) |
0.999944 | + | 0.0105969i | \(0.00337315\pi\) | |||||||
\(102\) | −0.887820 | + | 1.53775i | −0.0879073 | + | 0.152260i | ||||
\(103\) | 5.35951 | 0.528088 | 0.264044 | − | 0.964511i | \(-0.414944\pi\) | ||||
0.264044 | + | 0.964511i | \(0.414944\pi\) | |||||||
\(104\) | −5.00982 | + | 9.58654i | −0.491253 | + | 0.940038i | ||||
\(105\) | −3.47502 | −0.339128 | ||||||||
\(106\) | 3.04461 | − | 5.27341i | 0.295718 | − | 0.512199i | ||||
\(107\) | −1.65679 | + | 2.86964i | −0.160168 | + | 0.277419i | −0.934929 | − | 0.354836i | \(-0.884537\pi\) |
0.774761 | + | 0.632254i | \(0.217870\pi\) | |||||||
\(108\) | 1.00000 | + | 1.73205i | 0.0962250 | + | 0.166667i | ||||
\(109\) | 2.15478 | 0.206390 | 0.103195 | − | 0.994661i | \(-0.467093\pi\) | ||||
0.103195 | + | 0.994661i | \(0.467093\pi\) | |||||||
\(110\) | 1.44224 | + | 2.49804i | 0.137512 | + | 0.238178i | ||||
\(111\) | 0.599029 | + | 1.03755i | 0.0568573 | + | 0.0984798i | ||||
\(112\) | 3.54461 | 0.334934 | ||||||||
\(113\) | −1.89764 | − | 3.28680i | −0.178514 | − | 0.309196i | 0.762857 | − | 0.646567i | \(-0.223796\pi\) |
−0.941372 | + | 0.337371i | \(0.890462\pi\) | |||||||
\(114\) | 1.05776 | − | 1.83209i | 0.0990681 | − | 0.171591i | ||||
\(115\) | 0.980369 | − | 1.69805i | 0.0914199 | − | 0.158344i | ||||
\(116\) | 8.42909 | 0.782621 | ||||||||
\(117\) | 10.3910 | − | 0.437136i | 0.960645 | − | 0.0404133i | ||||
\(118\) | −14.1088 | −1.29882 | ||||||||
\(119\) | −9.25915 | + | 16.0373i | −0.848785 | + | 1.47014i | ||||
\(120\) | 1.47055 | − | 2.54707i | 0.134243 | − | 0.232515i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 4.01963 | 0.363920 | ||||||||
\(123\) | −0.977033 | − | 1.69227i | −0.0880961 | − | 0.152587i | ||||
\(124\) | 4.20473 | + | 7.28281i | 0.377596 | + | 0.654015i | ||||
\(125\) | 4.84522 | 0.433370 | ||||||||
\(126\) | −5.11218 | − | 8.85456i | −0.455429 | − | 0.788827i | ||||
\(127\) | 8.08921 | − | 14.0109i | 0.717802 | − | 1.24327i | −0.244067 | − | 0.969758i | \(-0.578482\pi\) |
0.961869 | − | 0.273511i | \(-0.0881849\pi\) | |||||||
\(128\) | 1.50000 | − | 2.59808i | 0.132583 | − | 0.229640i | ||||
\(129\) | 0.448721 | 0.0395077 | ||||||||
\(130\) | −5.57405 | − | 8.78027i | −0.488877 | − | 0.770081i | ||||
\(131\) | −3.31357 | −0.289508 | −0.144754 | − | 0.989468i | \(-0.546239\pi\) | ||||
−0.144754 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(132\) | −0.169938 | + | 0.294342i | −0.0147912 | + | 0.0256192i | ||||
\(133\) | 11.0315 | − | 19.1070i | 0.956549 | − | 1.65679i | ||||
\(134\) | −6.05442 | − | 10.4866i | −0.523022 | − | 0.905901i | ||||
\(135\) | −5.76897 | −0.496514 | ||||||||
\(136\) | −7.83654 | − | 13.5733i | −0.671978 | − | 1.16390i | ||||
\(137\) | −6.87133 | − | 11.9015i | −0.587058 | − | 1.01681i | −0.994615 | − | 0.103634i | \(-0.966953\pi\) |
0.407558 | − | 0.913179i | \(-0.366380\pi\) | |||||||
\(138\) | −0.231033 | −0.0196668 | ||||||||
\(139\) | −1.20473 | − | 2.08665i | −0.102184 | − | 0.176988i | 0.810400 | − | 0.585877i | \(-0.199250\pi\) |
−0.912584 | + | 0.408889i | \(0.865916\pi\) | |||||||
\(140\) | 5.11218 | − | 8.85456i | 0.432058 | − | 0.748347i | ||||
\(141\) | 1.03813 | − | 1.79809i | 0.0874261 | − | 0.151426i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 1.93243 | + | 3.04397i | 0.161598 | + | 0.254549i | ||||
\(144\) | 2.88448 | 0.240374 | ||||||||
\(145\) | −12.1568 | + | 21.0562i | −1.00957 | + | 1.74862i | ||||
\(146\) | 8.04127 | − | 13.9279i | 0.665500 | − | 1.15268i | ||||
\(147\) | 0.945578 | + | 1.63779i | 0.0779899 | + | 0.135083i | ||||
\(148\) | −3.52498 | −0.289751 | ||||||||
\(149\) | 1.27230 | + | 2.20369i | 0.104231 | + | 0.180534i | 0.913424 | − | 0.407010i | \(-0.133428\pi\) |
−0.809193 | + | 0.587543i | \(0.800095\pi\) | |||||||
\(150\) | 0.564237 | + | 0.977288i | 0.0460698 | + | 0.0797952i | ||||
\(151\) | 8.44872 | 0.687547 | 0.343774 | − | 0.939053i | \(-0.388295\pi\) | ||||
0.343774 | + | 0.939053i | \(0.388295\pi\) | |||||||
\(152\) | 9.33654 | + | 16.1714i | 0.757293 | + | 1.31167i | ||||
\(153\) | −7.53479 | + | 13.0506i | −0.609152 | + | 1.05508i | ||||
\(154\) | 1.77230 | − | 3.06972i | 0.142816 | − | 0.247365i | ||||
\(155\) | −24.2569 | −1.94837 | ||||||||
\(156\) | 0.567573 | − | 1.08608i | 0.0454422 | − | 0.0869561i | ||||
\(157\) | −16.3595 | −1.30563 | −0.652815 | − | 0.757517i | \(-0.726412\pi\) | ||||
−0.652815 | + | 0.757517i | \(0.726412\pi\) | |||||||
\(158\) | −0.452057 | + | 0.782986i | −0.0359637 | + | 0.0622910i | ||||
\(159\) | −1.03479 | + | 1.79231i | −0.0820643 | + | 0.142140i | ||||
\(160\) | 7.21121 | + | 12.4902i | 0.570096 | + | 0.987435i | ||||
\(161\) | −2.40946 | −0.189892 | ||||||||
\(162\) | −3.98685 | − | 6.90542i | −0.313236 | − | 0.542541i | ||||
\(163\) | 5.39430 | + | 9.34320i | 0.422514 | + | 0.731816i | 0.996185 | − | 0.0872702i | \(-0.0278144\pi\) |
−0.573671 | + | 0.819086i | \(0.694481\pi\) | |||||||
\(164\) | 5.74934 | 0.448948 | ||||||||
\(165\) | −0.490185 | − | 0.849025i | −0.0381608 | − | 0.0660965i | ||||
\(166\) | −2.45206 | + | 4.24709i | −0.190317 | + | 0.329638i | ||||
\(167\) | −3.52498 | + | 6.10544i | −0.272771 | + | 0.472453i | −0.969570 | − | 0.244813i | \(-0.921273\pi\) |
0.696799 | + | 0.717266i | \(0.254607\pi\) | |||||||
\(168\) | −3.61419 | −0.278841 | ||||||||
\(169\) | −7.42261 | − | 10.6726i | −0.570970 | − | 0.820971i | ||||
\(170\) | 15.0696 | 1.15578 | ||||||||
\(171\) | 8.97703 | − | 15.5487i | 0.686491 | − | 1.18904i | ||||
\(172\) | −0.660123 | + | 1.14337i | −0.0503339 | + | 0.0871809i | ||||
\(173\) | 0.922611 | + | 1.59801i | 0.0701448 | + | 0.121494i | 0.898965 | − | 0.438021i | \(-0.144321\pi\) |
−0.828820 | + | 0.559516i | \(0.810987\pi\) | |||||||
\(174\) | 2.86485 | 0.217184 | ||||||||
\(175\) | 5.88448 | + | 10.1922i | 0.444825 | + | 0.770460i | ||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | 4.79527 | 0.360435 | ||||||||
\(178\) | 2.82673 | + | 4.89603i | 0.211872 | + | 0.366973i | ||||
\(179\) | −2.71455 | + | 4.70173i | −0.202895 | + | 0.351424i | −0.949460 | − | 0.313888i | \(-0.898368\pi\) |
0.746565 | + | 0.665312i | \(0.231702\pi\) | |||||||
\(180\) | 4.16012 | − | 7.20554i | 0.310077 | − | 0.537070i | ||||
\(181\) | −4.47502 | −0.332626 | −0.166313 | − | 0.986073i | \(-0.553186\pi\) | ||||
−0.166313 | + | 0.986073i | \(0.553186\pi\) | |||||||
\(182\) | −5.91928 | + | 11.3268i | −0.438766 | + | 0.839601i | ||||
\(183\) | −1.36618 | −0.100991 | ||||||||
\(184\) | 1.01963 | − | 1.76605i | 0.0751682 | − | 0.130195i | ||||
\(185\) | 5.08387 | − | 8.80552i | 0.373773 | − | 0.647395i | ||||
\(186\) | 1.42909 | + | 2.47526i | 0.104786 | + | 0.181495i | ||||
\(187\) | −5.22436 | −0.382043 | ||||||||
\(188\) | 3.05442 | + | 5.29041i | 0.222767 | + | 0.385843i | ||||
\(189\) | 3.54461 | + | 6.13944i | 0.257832 | + | 0.446578i | ||||
\(190\) | −17.9541 | −1.30252 | ||||||||
\(191\) | −4.94558 | − | 8.56599i | −0.357849 | − | 0.619813i | 0.629752 | − | 0.776796i | \(-0.283157\pi\) |
−0.987601 | + | 0.156983i | \(0.949823\pi\) | |||||||
\(192\) | 1.18957 | − | 2.06039i | 0.0858498 | − | 0.148696i | ||||
\(193\) | −2.55442 | + | 4.42439i | −0.183871 | + | 0.318474i | −0.943196 | − | 0.332238i | \(-0.892196\pi\) |
0.759324 | + | 0.650712i | \(0.225530\pi\) | |||||||
\(194\) | 2.79527 | 0.200689 | ||||||||
\(195\) | 1.89449 | + | 2.98421i | 0.135667 | + | 0.213704i | ||||
\(196\) | −5.56424 | −0.397446 | ||||||||
\(197\) | −1.11552 | + | 1.93213i | −0.0794772 | + | 0.137659i | −0.903025 | − | 0.429589i | \(-0.858658\pi\) |
0.823547 | + | 0.567248i | \(0.191992\pi\) | |||||||
\(198\) | 1.44224 | − | 2.49804i | 0.102496 | − | 0.177528i | ||||
\(199\) | −8.93891 | − | 15.4826i | −0.633662 | − | 1.09754i | −0.986797 | − | 0.161963i | \(-0.948218\pi\) |
0.353135 | − | 0.935573i | \(-0.385116\pi\) | |||||||
\(200\) | −9.96074 | −0.704331 | ||||||||
\(201\) | 2.05776 | + | 3.56414i | 0.145143 | + | 0.251395i | ||||
\(202\) | 4.93243 | + | 8.54321i | 0.347044 | + | 0.601098i | ||||
\(203\) | 29.8778 | 2.09701 | ||||||||
\(204\) | 0.887820 | + | 1.53775i | 0.0621598 | + | 0.107664i | ||||
\(205\) | −8.29193 | + | 14.3621i | −0.579134 | + | 1.00309i | ||||
\(206\) | −2.67975 | + | 4.64147i | −0.186707 | + | 0.323387i | ||||
\(207\) | −1.96074 | −0.136281 | ||||||||
\(208\) | −1.93243 | − | 3.04397i | −0.133990 | − | 0.211061i | ||||
\(209\) | 6.22436 | 0.430548 | ||||||||
\(210\) | 1.73751 | − | 3.00946i | 0.119900 | − | 0.207672i | ||||
\(211\) | −5.45206 | + | 9.44324i | −0.375335 | + | 0.650099i | −0.990377 | − | 0.138395i | \(-0.955806\pi\) |
0.615042 | + | 0.788494i | \(0.289139\pi\) | |||||||
\(212\) | −3.04461 | − | 5.27341i | −0.209104 | − | 0.362180i | ||||
\(213\) | −2.03926 | −0.139728 | ||||||||
\(214\) | −1.65679 | − | 2.86964i | −0.113256 | − | 0.196165i | ||||
\(215\) | −1.90411 | − | 3.29802i | −0.129860 | − | 0.224923i | ||||
\(216\) | −6.00000 | −0.408248 | ||||||||
\(217\) | 14.9041 | + | 25.8147i | 1.01176 | + | 1.75241i | ||||
\(218\) | −1.07739 | + | 1.86609i | −0.0729700 | + | 0.126388i | ||||
\(219\) | −2.73304 | + | 4.73377i | −0.184682 | + | 0.319878i | ||||
\(220\) | 2.88448 | 0.194472 | ||||||||
\(221\) | 18.8201 | − | 0.791739i | 1.26597 | − | 0.0532581i | ||||
\(222\) | −1.19806 | −0.0804084 | ||||||||
\(223\) | 9.71455 | − | 16.8261i | 0.650534 | − | 1.12676i | −0.332459 | − | 0.943118i | \(-0.607878\pi\) |
0.982993 | − | 0.183640i | \(-0.0587882\pi\) | |||||||
\(224\) | 8.86152 | − | 15.3486i | 0.592085 | − | 1.02552i | ||||
\(225\) | 4.78860 | + | 8.29410i | 0.319240 | + | 0.552940i | ||||
\(226\) | 3.79527 | 0.252458 | ||||||||
\(227\) | 3.66012 | + | 6.33952i | 0.242931 | + | 0.420769i | 0.961548 | − | 0.274637i | \(-0.0885578\pi\) |
−0.718617 | + | 0.695406i | \(0.755225\pi\) | |||||||
\(228\) | −1.05776 | − | 1.83209i | −0.0700517 | − | 0.121333i | ||||
\(229\) | 14.5642 | 0.962432 | 0.481216 | − | 0.876602i | \(-0.340195\pi\) | ||||
0.481216 | + | 0.876602i | \(0.340195\pi\) | |||||||
\(230\) | 0.980369 | + | 1.69805i | 0.0646436 | + | 0.111966i | ||||
\(231\) | −0.602365 | + | 1.04333i | −0.0396327 | + | 0.0686459i | ||||
\(232\) | −12.6436 | + | 21.8994i | −0.830095 | + | 1.43777i | ||||
\(233\) | 6.44872 | 0.422470 | 0.211235 | − | 0.977435i | \(-0.432252\pi\) | ||||
0.211235 | + | 0.977435i | \(0.432252\pi\) | |||||||
\(234\) | −4.81691 | + | 9.21741i | −0.314891 | + | 0.602561i | ||||
\(235\) | −17.6209 | −1.14946 | ||||||||
\(236\) | −7.05442 | + | 12.2186i | −0.459204 | + | 0.795364i | ||||
\(237\) | 0.153644 | − | 0.266119i | 0.00998024 | − | 0.0172863i | ||||
\(238\) | −9.25915 | − | 16.0373i | −0.600182 | − | 1.03955i | ||||
\(239\) | −0.270294 | −0.0174839 | −0.00874193 | − | 0.999962i | \(-0.502783\pi\) | ||||
−0.00874193 | + | 0.999962i | \(0.502783\pi\) | |||||||
\(240\) | 0.490185 | + | 0.849025i | 0.0316413 | + | 0.0548043i | ||||
\(241\) | −15.2656 | − | 26.4408i | −0.983346 | − | 1.70320i | −0.649068 | − | 0.760730i | \(-0.724841\pi\) |
−0.334277 | − | 0.942475i | \(-0.608492\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 4.35504 | + | 7.54315i | 0.279376 | + | 0.483893i | ||||
\(244\) | 2.00982 | − | 3.48110i | 0.128665 | − | 0.222855i | ||||
\(245\) | 8.02498 | − | 13.8997i | 0.512697 | − | 0.888017i | ||||
\(246\) | 1.95407 | 0.124587 | ||||||||
\(247\) | −22.4224 | + | 0.943287i | −1.42670 | + | 0.0600199i | ||||
\(248\) | −25.2284 | −1.60200 | ||||||||
\(249\) | 0.833398 | − | 1.44349i | 0.0528144 | − | 0.0914773i | ||||
\(250\) | −2.42261 | + | 4.19609i | −0.153219 | + | 0.265384i | ||||
\(251\) | −5.23952 | − | 9.07512i | −0.330716 | − | 0.572816i | 0.651937 | − | 0.758273i | \(-0.273957\pi\) |
−0.982652 | + | 0.185457i | \(0.940623\pi\) | |||||||
\(252\) | −10.2244 | −0.644074 | ||||||||
\(253\) | −0.339877 | − | 0.588684i | −0.0213679 | − | 0.0370102i | ||||
\(254\) | 8.08921 | + | 14.0109i | 0.507562 | + | 0.879124i | ||||
\(255\) | −5.12180 | −0.320740 | ||||||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | −2.87800 | + | 4.98485i | −0.179525 | + | 0.310946i | −0.941718 | − | 0.336404i | \(-0.890789\pi\) |
0.762193 | + | 0.647350i | \(0.224123\pi\) | |||||||
\(258\) | −0.224361 | + | 0.388604i | −0.0139681 | + | 0.0241934i | ||||
\(259\) | −12.4947 | −0.776380 | ||||||||
\(260\) | −10.3910 | + | 0.437136i | −0.644420 | + | 0.0271101i | ||||
\(261\) | 24.3136 | 1.50497 | ||||||||
\(262\) | 1.65679 | − | 2.86964i | 0.102357 | − | 0.177287i | ||||
\(263\) | −4.22436 | + | 7.31681i | −0.260485 | + | 0.451174i | −0.966371 | − | 0.257152i | \(-0.917216\pi\) |
0.705886 | + | 0.708326i | \(0.250549\pi\) | |||||||
\(264\) | −0.509815 | − | 0.883026i | −0.0313770 | − | 0.0543465i | ||||
\(265\) | 17.5642 | 1.07896 | ||||||||
\(266\) | 11.0315 | + | 19.1070i | 0.676382 | + | 1.17153i | ||||
\(267\) | −0.960739 | − | 1.66405i | −0.0587963 | − | 0.101838i | ||||
\(268\) | −12.1088 | −0.739665 | ||||||||
\(269\) | −12.5446 | − | 21.7279i | −0.764858 | − | 1.32477i | −0.940322 | − | 0.340287i | \(-0.889476\pi\) |
0.175463 | − | 0.984486i | \(-0.443858\pi\) | |||||||
\(270\) | 2.88448 | − | 4.99607i | 0.175544 | − | 0.304051i | ||||
\(271\) | 5.22436 | − | 9.04886i | 0.317357 | − | 0.549679i | −0.662578 | − | 0.748993i | \(-0.730538\pi\) |
0.979936 | + | 0.199314i | \(0.0638712\pi\) | |||||||
\(272\) | 5.22436 | 0.316773 | ||||||||
\(273\) | 2.01182 | − | 3.84973i | 0.121761 | − | 0.232996i | ||||
\(274\) | 13.7427 | 0.830225 | ||||||||
\(275\) | −1.66012 | + | 2.87542i | −0.100109 | + | 0.173394i | ||||
\(276\) | −0.115516 | + | 0.200080i | −0.00695326 | + | 0.0120434i | ||||
\(277\) | −4.31043 | − | 7.46589i | −0.258989 | − | 0.448582i | 0.706983 | − | 0.707231i | \(-0.250056\pi\) |
−0.965971 | + | 0.258649i | \(0.916723\pi\) | |||||||
\(278\) | 2.40946 | 0.144510 | ||||||||
\(279\) | 12.1285 | + | 21.0071i | 0.726113 | + | 1.25766i | ||||
\(280\) | 15.3365 | + | 26.5637i | 0.916534 | + | 1.58748i | ||||
\(281\) | −1.98037 | −0.118139 | −0.0590695 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590695 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(282\) | 1.03813 | + | 1.79809i | 0.0618196 | + | 0.107075i | ||||
\(283\) | −1.09255 | + | 1.89235i | −0.0649453 | + | 0.112489i | −0.896670 | − | 0.442700i | \(-0.854021\pi\) |
0.831724 | + | 0.555189i | \(0.187354\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 6.10217 | 0.361461 | ||||||||
\(286\) | −3.60236 | + | 0.151548i | −0.213012 | + | 0.00896120i | ||||
\(287\) | 20.3791 | 1.20294 | ||||||||
\(288\) | 7.21121 | − | 12.4902i | 0.424925 | − | 0.735991i | ||||
\(289\) | −5.14697 | + | 8.91482i | −0.302763 | + | 0.524401i | ||||
\(290\) | −12.1568 | − | 21.0562i | −0.713871 | − | 1.23646i | ||||
\(291\) | −0.950048 | −0.0556928 | ||||||||
\(292\) | −8.04127 | − | 13.9279i | −0.470580 | − | 0.815068i | ||||
\(293\) | −3.06757 | − | 5.31319i | −0.179210 | − | 0.310400i | 0.762400 | − | 0.647105i | \(-0.224021\pi\) |
−0.941610 | + | 0.336705i | \(0.890687\pi\) | |||||||
\(294\) | −1.89116 | −0.110294 | ||||||||
\(295\) | −20.3484 | − | 35.2444i | −1.18473 | − | 2.05201i | ||||
\(296\) | 5.28746 | − | 9.15816i | 0.307328 | − | 0.532307i | ||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | −2.54461 | −0.147405 | ||||||||
\(299\) | 1.31357 | + | 2.06915i | 0.0759660 | + | 0.119662i | ||||
\(300\) | 1.12847 | 0.0651525 | ||||||||
\(301\) | −2.33988 | + | 4.05279i | −0.134868 | + | 0.233599i | ||||
\(302\) | −4.22436 | + | 7.31681i | −0.243085 | + | 0.421035i | ||||
\(303\) | −1.67642 | − | 2.90364i | −0.0963077 | − | 0.166810i | ||||
\(304\) | −6.22436 | −0.356992 | ||||||||
\(305\) | 5.79728 | + | 10.0412i | 0.331951 | + | 0.574956i | ||||
\(306\) | −7.53479 | − | 13.0506i | −0.430735 | − | 0.746056i | ||||
\(307\) | 6.18510 | 0.353002 | 0.176501 | − | 0.984300i | \(-0.443522\pi\) | ||||
0.176501 | + | 0.984300i | \(0.443522\pi\) | |||||||
\(308\) | −1.77230 | − | 3.06972i | −0.100986 | − | 0.174914i | ||||
\(309\) | 0.910786 | − | 1.57753i | 0.0518128 | − | 0.0897424i | ||||
\(310\) | 12.1285 | − | 21.0071i | 0.688851 | − | 1.19313i | ||||
\(311\) | −1.28992 | −0.0731449 | −0.0365725 | − | 0.999331i | \(-0.511644\pi\) | ||||
−0.0365725 | + | 0.999331i | \(0.511644\pi\) | |||||||
\(312\) | 1.97036 | + | 3.10372i | 0.111550 | + | 0.175714i | ||||
\(313\) | −0.293944 | −0.0166147 | −0.00830734 | − | 0.999965i | \(-0.502644\pi\) | ||||
−0.00830734 | + | 0.999965i | \(0.502644\pi\) | |||||||
\(314\) | 8.17975 | − | 14.1677i | 0.461610 | − | 0.799532i | ||||
\(315\) | 14.7460 | − | 25.5408i | 0.830843 | − | 1.43906i | ||||
\(316\) | 0.452057 | + | 0.782986i | 0.0254302 | + | 0.0440464i | ||||
\(317\) | −22.0522 | −1.23858 | −0.619288 | − | 0.785164i | \(-0.712579\pi\) | ||||
−0.619288 | + | 0.785164i | \(0.712579\pi\) | |||||||
\(318\) | −1.03479 | − | 1.79231i | −0.0580282 | − | 0.100508i | ||||
\(319\) | 4.21455 | + | 7.29981i | 0.235969 | + | 0.408711i | ||||
\(320\) | −20.1914 | −1.12873 | ||||||||
\(321\) | 0.563104 | + | 0.975324i | 0.0314294 | + | 0.0544373i | ||||
\(322\) | 1.20473 | − | 2.08665i | 0.0671370 | − | 0.116285i | ||||
\(323\) | 16.2592 | − | 28.1617i | 0.904683 | − | 1.56696i | ||||
\(324\) | −7.97370 | −0.442983 | ||||||||
\(325\) | 5.54461 | − | 10.6099i | 0.307559 | − | 0.588531i | ||||
\(326\) | −10.7886 | −0.597525 | ||||||||
\(327\) | 0.366180 | − | 0.634242i | 0.0202498 | − | 0.0350736i | ||||
\(328\) | −8.62401 | + | 14.9372i | −0.476181 | + | 0.824770i | ||||
\(329\) | 10.8267 | + | 18.7524i | 0.596897 | + | 1.03386i | ||||
\(330\) | 0.980369 | 0.0539676 | ||||||||
\(331\) | 7.22436 | + | 12.5130i | 0.397087 | + | 0.687774i | 0.993365 | − | 0.115003i | \(-0.0366879\pi\) |
−0.596278 | + | 0.802778i | \(0.703355\pi\) | |||||||
\(332\) | 2.45206 | + | 4.24709i | 0.134574 | + | 0.233089i | ||||
\(333\) | −10.1677 | −0.557189 | ||||||||
\(334\) | −3.52498 | − | 6.10544i | −0.192878 | − | 0.334075i | ||||
\(335\) | 17.4639 | − | 30.2483i | 0.954154 | − | 1.65264i | ||||
\(336\) | 0.602365 | − | 1.04333i | 0.0328617 | − | 0.0569181i | ||||
\(337\) | −18.5053 | −1.00805 | −0.504025 | − | 0.863689i | \(-0.668148\pi\) | ||||
−0.504025 | + | 0.863689i | \(0.668148\pi\) | |||||||
\(338\) | 12.9541 | − | 1.09186i | 0.704608 | − | 0.0593893i | ||||
\(339\) | −1.28992 | −0.0700591 | ||||||||
\(340\) | 7.53479 | − | 13.0506i | 0.408631 | − | 0.707770i | ||||
\(341\) | −4.20473 | + | 7.28281i | −0.227699 | + | 0.394386i | ||||
\(342\) | 8.97703 | + | 15.5487i | 0.485422 | + | 0.840776i | ||||
\(343\) | 5.08921 | 0.274792 | ||||||||
\(344\) | −1.98037 | − | 3.43010i | −0.106774 | − | 0.184939i | ||||
\(345\) | −0.333205 | − | 0.577128i | −0.0179391 | − | 0.0310715i | ||||
\(346\) | −1.84522 | −0.0991998 | ||||||||
\(347\) | 7.77230 | + | 13.4620i | 0.417239 | + | 0.722679i | 0.995661 | − | 0.0930587i | \(-0.0296644\pi\) |
−0.578422 | + | 0.815738i | \(0.696331\pi\) | |||||||
\(348\) | 1.43243 | − | 2.48104i | 0.0767861 | − | 0.132997i | ||||
\(349\) | −15.0000 | + | 25.9808i | −0.802932 | + | 1.39072i | 0.114747 | + | 0.993395i | \(0.463394\pi\) |
−0.917679 | + | 0.397324i | \(0.869939\pi\) | |||||||
\(350\) | −11.7690 | −0.629078 | ||||||||
\(351\) | 3.33988 | − | 6.39103i | 0.178269 | − | 0.341128i | ||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | 2.16012 | − | 3.74144i | 0.114972 | − | 0.199137i | −0.802797 | − | 0.596253i | \(-0.796656\pi\) |
0.917768 | + | 0.397116i | \(0.129989\pi\) | |||||||
\(354\) | −2.39764 | + | 4.15283i | −0.127433 | + | 0.220720i | ||||
\(355\) | 8.65345 | + | 14.9882i | 0.459277 | + | 0.795492i | ||||
\(356\) | 5.65345 | 0.299632 | ||||||||
\(357\) | 3.14697 | + | 5.45072i | 0.166555 | + | 0.288482i | ||||
\(358\) | −2.71455 | − | 4.70173i | −0.143468 | − | 0.248494i | ||||
\(359\) | −0.231033 | −0.0121934 | −0.00609672 | − | 0.999981i | \(-0.501941\pi\) | ||||
−0.00609672 | + | 0.999981i | \(0.501941\pi\) | |||||||
\(360\) | 12.4804 | + | 21.6166i | 0.657773 | + | 1.13930i | ||||
\(361\) | −9.87133 | + | 17.0976i | −0.519544 | + | 0.899876i | ||||
\(362\) | 2.23751 | − | 3.87548i | 0.117601 | − | 0.203691i | ||||
\(363\) | −0.339877 | −0.0178389 | ||||||||
\(364\) | 6.84969 | + | 10.7897i | 0.359021 | + | 0.565532i | ||||
\(365\) | 46.3898 | 2.42815 | ||||||||
\(366\) | 0.683090 | − | 1.18315i | 0.0357057 | − | 0.0618440i | ||||
\(367\) | −9.90411 | + | 17.1544i | −0.516991 | + | 0.895454i | 0.482815 | + | 0.875723i | \(0.339614\pi\) |
−0.999805 | + | 0.0197314i | \(0.993719\pi\) | |||||||
\(368\) | 0.339877 | + | 0.588684i | 0.0177173 | + | 0.0306873i | ||||
\(369\) | 16.5839 | 0.863322 | ||||||||
\(370\) | 5.08387 | + | 8.80552i | 0.264298 | + | 0.457777i | ||||
\(371\) | −10.7919 | − | 18.6922i | −0.560289 | − | 0.970450i | ||||
\(372\) | 2.85818 | 0.148190 | ||||||||
\(373\) | 7.45740 | + | 12.9166i | 0.386130 | + | 0.668796i | 0.991925 | − | 0.126824i | \(-0.0404784\pi\) |
−0.605796 | + | 0.795620i | \(0.707145\pi\) | |||||||
\(374\) | 2.61218 | − | 4.52443i | 0.135073 | − | 0.233953i | ||||
\(375\) | 0.823390 | − | 1.42615i | 0.0425197 | − | 0.0736462i | ||||
\(376\) | −18.3265 | −0.945119 | ||||||||
\(377\) | −16.2886 | − | 25.6579i | −0.838905 | − | 1.32145i | ||||
\(378\) | −7.08921 | −0.364630 | ||||||||
\(379\) | −3.32025 | + | 5.75084i | −0.170550 | + | 0.295401i | −0.938612 | − | 0.344974i | \(-0.887888\pi\) |
0.768063 | + | 0.640375i | \(0.221221\pi\) | |||||||
\(380\) | −8.97703 | + | 15.5487i | −0.460512 | + | 0.797630i | ||||
\(381\) | −2.74934 | − | 4.76199i | −0.140853 | − | 0.243964i | ||||
\(382\) | 9.89116 | 0.506076 | ||||||||
\(383\) | 2.57091 | + | 4.45295i | 0.131367 | + | 0.227535i | 0.924204 | − | 0.381899i | \(-0.124730\pi\) |
−0.792837 | + | 0.609434i | \(0.791397\pi\) | |||||||
\(384\) | −0.509815 | − | 0.883026i | −0.0260164 | − | 0.0450617i | ||||
\(385\) | 10.2244 | 0.521082 | ||||||||
\(386\) | −2.55442 | − | 4.42439i | −0.130017 | − | 0.225195i | ||||
\(387\) | −1.90411 | + | 3.29802i | −0.0967916 | + | 0.167648i | ||||
\(388\) | 1.39764 | − | 2.42077i | 0.0709542 | − | 0.122896i | ||||
\(389\) | −33.2806 | −1.68739 | −0.843697 | − | 0.536820i | \(-0.819625\pi\) | ||||
−0.843697 | + | 0.536820i | \(0.819625\pi\) | |||||||
\(390\) | −3.53165 | + | 0.148573i | −0.178832 | + | 0.00752327i | ||||
\(391\) | −3.55128 | −0.179596 | ||||||||
\(392\) | 8.34636 | − | 14.4563i | 0.421555 | − | 0.730154i | ||||
\(393\) | −0.563104 | + | 0.975324i | −0.0284048 | + | 0.0491986i | ||||
\(394\) | −1.11552 | − | 1.93213i | −0.0561989 | − | 0.0973393i | ||||
\(395\) | −2.60790 | −0.131218 | ||||||||
\(396\) | −1.44224 | − | 2.49804i | −0.0724754 | − | 0.125531i | ||||
\(397\) | −4.30175 | − | 7.45085i | −0.215899 | − | 0.373947i | 0.737652 | − | 0.675182i | \(-0.235935\pi\) |
−0.953550 | + | 0.301234i | \(0.902601\pi\) | |||||||
\(398\) | 17.8778 | 0.896134 | ||||||||
\(399\) | −3.74934 | − | 6.49404i | −0.187702 | − | 0.325109i | ||||
\(400\) | 1.66012 | − | 2.87542i | 0.0830062 | − | 0.143771i | ||||
\(401\) | 2.83988 | − | 4.91881i | 0.141817 | − | 0.245634i | −0.786364 | − | 0.617763i | \(-0.788039\pi\) |
0.928181 | + | 0.372130i | \(0.121372\pi\) | |||||||
\(402\) | −4.11552 | −0.205263 | ||||||||
\(403\) | 14.0433 | − | 26.8725i | 0.699546 | − | 1.33862i | ||||
\(404\) | 9.86485 | 0.490795 | ||||||||
\(405\) | 11.5000 | − | 19.9186i | 0.571440 | − | 0.989762i | ||||
\(406\) | −14.9389 | + | 25.8749i | −0.741405 | + | 1.28415i | ||||
\(407\) | −1.76249 | − | 3.05272i | −0.0873633 | − | 0.151318i | ||||
\(408\) | −5.32692 | −0.263722 | ||||||||
\(409\) | −11.4967 | − | 19.9128i | −0.568473 | − | 0.984625i | −0.996717 | − | 0.0809616i | \(-0.974201\pi\) |
0.428244 | − | 0.903663i | \(-0.359132\pi\) | |||||||
\(410\) | −8.29193 | − | 14.3621i | −0.409509 | − | 0.709291i | ||||
\(411\) | −4.67081 | −0.230394 | ||||||||
\(412\) | 2.67975 | + | 4.64147i | 0.132022 | + | 0.228669i | ||||
\(413\) | −25.0052 | + | 43.3102i | −1.23042 | + | 2.13116i | ||||
\(414\) | 0.980369 | − | 1.69805i | 0.0481825 | − | 0.0834546i | ||||
\(415\) | −14.1458 | −0.694392 | ||||||||
\(416\) | −18.0118 | + | 0.757738i | −0.883102 | + | 0.0371512i | ||||
\(417\) | −0.818920 | −0.0401027 | ||||||||
\(418\) | −3.11218 | + | 5.39045i | −0.152222 | + | 0.263656i | ||||
\(419\) | −15.4291 | + | 26.7240i | −0.753760 | + | 1.30555i | 0.192228 | + | 0.981350i | \(0.438429\pi\) |
−0.945988 | + | 0.324201i | \(0.894905\pi\) | |||||||
\(420\) | −1.73751 | − | 3.00946i | −0.0847819 | − | 0.146847i | ||||
\(421\) | 23.6035 | 1.15036 | 0.575182 | − | 0.818025i | \(-0.304931\pi\) | ||||
0.575182 | + | 0.818025i | \(0.304931\pi\) | |||||||
\(422\) | −5.45206 | − | 9.44324i | −0.265402 | − | 0.459690i | ||||
\(423\) | 8.81043 | + | 15.2601i | 0.428378 | + | 0.741972i | ||||
\(424\) | 18.2676 | 0.887155 | ||||||||
\(425\) | 8.67308 | + | 15.0222i | 0.420706 | + | 0.728685i | ||||
\(426\) | 1.01963 | − | 1.76605i | 0.0494013 | − | 0.0855655i | ||||
\(427\) | 7.12401 | − | 12.3391i | 0.344755 | − | 0.597133i | ||||
\(428\) | −3.31357 | −0.160168 | ||||||||
\(429\) | 1.22436 | − | 0.0515075i | 0.0591127 | − | 0.00248681i | ||||
\(430\) | 3.80823 | 0.183649 | ||||||||
\(431\) | −14.3169 | + | 24.7976i | −0.689621 | + | 1.19446i | 0.282339 | + | 0.959315i | \(0.408890\pi\) |
−0.971960 | + | 0.235144i | \(0.924444\pi\) | |||||||
\(432\) | 1.00000 | − | 1.73205i | 0.0481125 | − | 0.0833333i | ||||
\(433\) | 14.3267 | + | 24.8146i | 0.688498 | + | 1.19251i | 0.972324 | + | 0.233638i | \(0.0750632\pi\) |
−0.283825 | + | 0.958876i | \(0.591604\pi\) | |||||||
\(434\) | −29.8082 | −1.43084 | ||||||||
\(435\) | 4.13181 | + | 7.15651i | 0.198105 | + | 0.343128i | ||||
\(436\) | 1.07739 | + | 1.86609i | 0.0515976 | + | 0.0893696i | ||||
\(437\) | 4.23103 | 0.202398 | ||||||||
\(438\) | −2.73304 | − | 4.73377i | −0.130590 | − | 0.226188i | ||||
\(439\) | 4.54794 | − | 7.87727i | 0.217061 | − | 0.375961i | −0.736847 | − | 0.676060i | \(-0.763686\pi\) |
0.953908 | + | 0.300098i | \(0.0970195\pi\) | |||||||
\(440\) | −4.32673 | + | 7.49411i | −0.206269 | + | 0.357268i | ||||
\(441\) | −16.0500 | −0.764283 | ||||||||
\(442\) | −8.72436 | + | 16.6945i | −0.414976 | + | 0.794077i | ||||
\(443\) | 0.518304 | 0.0246254 | 0.0123127 | − | 0.999924i | \(-0.496081\pi\) | ||||
0.0123127 | + | 0.999924i | \(0.496081\pi\) | |||||||
\(444\) | −0.599029 | + | 1.03755i | −0.0284287 | + | 0.0492399i | ||||
\(445\) | −8.15364 | + | 14.1225i | −0.386520 | + | 0.669472i | ||||
\(446\) | 9.71455 | + | 16.8261i | 0.459997 | + | 0.796738i | ||||
\(447\) | 0.864853 | 0.0409061 | ||||||||
\(448\) | 12.4061 | + | 21.4880i | 0.586134 | + | 1.01521i | ||||
\(449\) | 16.5261 | + | 28.6241i | 0.779915 | + | 1.35085i | 0.931990 | + | 0.362484i | \(0.118071\pi\) |
−0.152075 | + | 0.988369i | \(0.548595\pi\) | |||||||
\(450\) | −9.57720 | −0.451473 | ||||||||
\(451\) | 2.87467 | + | 4.97907i | 0.135363 | + | 0.234455i | ||||
\(452\) | 1.89764 | − | 3.28680i | 0.0892572 | − | 0.154598i | ||||
\(453\) | 1.43576 | − | 2.48681i | 0.0674580 | − | 0.116841i | ||||
\(454\) | −7.32025 | −0.343556 | ||||||||
\(455\) | −36.8319 | + | 1.54948i | −1.72671 | + | 0.0726406i | ||||
\(456\) | 6.34655 | 0.297204 | ||||||||
\(457\) | 13.6633 | − | 23.6655i | 0.639141 | − | 1.10702i | −0.346481 | − | 0.938057i | \(-0.612624\pi\) |
0.985622 | − | 0.168967i | \(-0.0540432\pi\) | |||||||
\(458\) | −7.28212 | + | 12.6130i | −0.340271 | + | 0.589367i | ||||
\(459\) | 5.22436 | + | 9.04886i | 0.243852 | + | 0.422365i | ||||
\(460\) | 1.96074 | 0.0914199 | ||||||||
\(461\) | −6.64364 | − | 11.5071i | −0.309425 | − | 0.535940i | 0.668812 | − | 0.743432i | \(-0.266803\pi\) |
−0.978237 | + | 0.207492i | \(0.933470\pi\) | |||||||
\(462\) | −0.602365 | − | 1.04333i | −0.0280246 | − | 0.0485400i | ||||
\(463\) | 18.2480 | 0.848057 | 0.424028 | − | 0.905649i | \(-0.360616\pi\) | ||||
0.424028 | + | 0.905649i | \(0.360616\pi\) | |||||||
\(464\) | −4.21455 | − | 7.29981i | −0.195655 | − | 0.338885i | ||||
\(465\) | −4.12219 | + | 7.13984i | −0.191162 | + | 0.331102i | ||||
\(466\) | −3.22436 | + | 5.58476i | −0.149366 | + | 0.258709i | ||||
\(467\) | 28.2873 | 1.30898 | 0.654489 | − | 0.756071i | \(-0.272884\pi\) | ||||
0.654489 | + | 0.756071i | \(0.272884\pi\) | |||||||
\(468\) | 5.57405 | + | 8.78027i | 0.257661 | + | 0.405868i | ||||
\(469\) | −42.9211 | −1.98191 | ||||||||
\(470\) | 8.81043 | − | 15.2601i | 0.406395 | − | 0.703897i | ||||
\(471\) | −2.78011 | + | 4.81529i | −0.128101 | + | 0.221877i | ||||
\(472\) | −21.1633 | − | 36.6559i | −0.974118 | − | 1.68722i | ||||
\(473\) | −1.32025 | −0.0607050 | ||||||||
\(474\) | 0.153644 | + | 0.266119i | 0.00705709 | + | 0.0122232i | ||||
\(475\) | −10.3332 | − | 17.8976i | −0.474120 | − | 0.821200i | ||||
\(476\) | −18.5183 | −0.848785 | ||||||||
\(477\) | −8.78212 | − | 15.2111i | −0.402106 | − | 0.696467i | ||||
\(478\) | 0.135147 | − | 0.234081i | 0.00618148 | − | 0.0107066i | ||||
\(479\) | −7.77230 | + | 13.4620i | −0.355126 | + | 0.615096i | −0.987139 | − | 0.159861i | \(-0.948895\pi\) |
0.632014 | + | 0.774957i | \(0.282229\pi\) | |||||||
\(480\) | 4.90185 | 0.223738 | ||||||||
\(481\) | 6.81176 | + | 10.7299i | 0.310589 | + | 0.489242i | ||||
\(482\) | 30.5313 | 1.39066 | ||||||||
\(483\) | −0.409460 | + | 0.709205i | −0.0186311 | + | 0.0322700i | ||||
\(484\) | 0.500000 | − | 0.866025i | 0.0227273 | − | 0.0393648i | ||||
\(485\) | 4.03146 | + | 6.98269i | 0.183059 | + | 0.317067i | ||||
\(486\) | −8.71008 | −0.395097 | ||||||||
\(487\) | −16.1633 | − | 27.9956i | −0.732428 | − | 1.26860i | −0.955843 | − | 0.293878i | \(-0.905054\pi\) |
0.223415 | − | 0.974723i | \(-0.428279\pi\) | |||||||
\(488\) | 6.02945 | + | 10.4433i | 0.272940 | + | 0.472746i | ||||
\(489\) | 3.66680 | 0.165818 | ||||||||
\(490\) | 8.02498 | + | 13.8997i | 0.362531 | + | 0.627923i | ||||
\(491\) | −5.77230 | + | 9.99792i | −0.260500 | + | 0.451200i | −0.966375 | − | 0.257137i | \(-0.917221\pi\) |
0.705875 | + | 0.708337i | \(0.250554\pi\) | |||||||
\(492\) | 0.977033 | − | 1.69227i | 0.0440481 | − | 0.0762935i | ||||
\(493\) | 44.0366 | 1.98331 | ||||||||
\(494\) | 10.3943 | − | 19.8900i | 0.467662 | − | 0.894895i | ||||
\(495\) | 8.32025 | 0.373967 | ||||||||
\(496\) | 4.20473 | − | 7.28281i | 0.188798 | − | 0.327008i | ||||
\(497\) | 10.6338 | − | 18.4183i | 0.476992 | − | 0.826174i | ||||
\(498\) | 0.833398 | + | 1.44349i | 0.0373454 | + | 0.0646842i | ||||
\(499\) | −27.7859 | −1.24387 | −0.621935 | − | 0.783069i | \(-0.713653\pi\) | ||||
−0.621935 | + | 0.783069i | \(0.713653\pi\) | |||||||
\(500\) | 2.42261 | + | 4.19609i | 0.108342 | + | 0.187655i | ||||
\(501\) | 1.19806 | + | 2.07510i | 0.0535253 | + | 0.0927085i | ||||
\(502\) | 10.4790 | 0.467703 | ||||||||
\(503\) | 2.70272 | + | 4.68125i | 0.120508 | + | 0.208727i | 0.919968 | − | 0.391993i | \(-0.128214\pi\) |
−0.799460 | + | 0.600719i | \(0.794881\pi\) | |||||||
\(504\) | 15.3365 | − | 26.5637i | 0.683144 | − | 1.18324i | ||||
\(505\) | −14.2275 | + | 24.6428i | −0.633116 | + | 1.09659i | ||||
\(506\) | 0.679754 | 0.0302187 | ||||||||
\(507\) | −4.40279 | + | 0.371098i | −0.195535 | + | 0.0164810i | ||||
\(508\) | 16.1784 | 0.717802 | ||||||||
\(509\) | 12.7047 | − | 22.0052i | 0.563127 | − | 0.975365i | −0.434094 | − | 0.900868i | \(-0.642931\pi\) |
0.997221 | − | 0.0744974i | \(-0.0237353\pi\) | |||||||
\(510\) | 2.56090 | − | 4.43561i | 0.113399 | − | 0.196412i | ||||
\(511\) | −28.5031 | − | 49.3689i | −1.26090 | − | 2.18395i | ||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | −6.22436 | − | 10.7809i | −0.274812 | − | 0.475989i | ||||
\(514\) | −2.87800 | − | 4.98485i | −0.126943 | − | 0.219872i | ||||
\(515\) | −15.4594 | −0.681223 | ||||||||
\(516\) | 0.224361 | + | 0.388604i | 0.00987692 | + | 0.0171073i | ||||
\(517\) | −3.05442 | + | 5.29041i | −0.134333 | + | 0.232672i | ||||
\(518\) | 6.24733 | − | 10.8207i | 0.274492 | − | 0.475434i | ||||
\(519\) | 0.627148 | 0.0275288 | ||||||||
\(520\) | 14.4507 | − | 27.6522i | 0.633706 | − | 1.21263i | ||||
\(521\) | 33.1784 | 1.45357 | 0.726787 | − | 0.686863i | \(-0.241013\pi\) | ||||
0.726787 | + | 0.686863i | \(0.241013\pi\) | |||||||
\(522\) | −12.1568 | + | 21.0562i | −0.532088 | + | 0.921604i | ||||
\(523\) | 9.38649 | − | 16.2579i | 0.410443 | − | 0.710908i | −0.584495 | − | 0.811397i | \(-0.698708\pi\) |
0.994938 | + | 0.100489i | \(0.0320409\pi\) | |||||||
\(524\) | −1.65679 | − | 2.86964i | −0.0723771 | − | 0.125361i | ||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | −4.22436 | − | 7.31681i | −0.184191 | − | 0.319028i | ||||
\(527\) | 21.9670 | + | 38.0480i | 0.956899 | + | 1.65740i | ||||
\(528\) | 0.339877 | 0.0147912 | ||||||||
\(529\) | 11.2690 | + | 19.5184i | 0.489955 | + | 0.848627i | ||||
\(530\) | −8.78212 | + | 15.2111i | −0.381471 | + | 0.660727i | ||||
\(531\) | −20.3484 | + | 35.2444i | −0.883044 | + | 1.52948i | ||||
\(532\) | 22.0629 | 0.956549 | ||||||||
\(533\) | −11.1102 | − | 17.5008i | −0.481235 | − | 0.758043i | ||||
\(534\) | 1.92148 | 0.0831505 | ||||||||
\(535\) | 4.77898 | − | 8.27743i | 0.206613 | − | 0.357864i | ||||
\(536\) | 18.1633 | − | 31.4597i | 0.784534 | − | 1.35885i | ||||
\(537\) | 0.922611 | + | 1.59801i | 0.0398136 | + | 0.0689592i | ||||
\(538\) | 25.0892 | 1.08167 | ||||||||
\(539\) | −2.78212 | − | 4.81877i | −0.119834 | − | 0.207559i | ||||
\(540\) | −2.88448 | − | 4.99607i | −0.124128 | − | 0.214997i | ||||
\(541\) | 42.8016 | 1.84018 | 0.920091 | − | 0.391704i | \(-0.128114\pi\) | ||||
0.920091 | + | 0.391704i | \(0.128114\pi\) | |||||||
\(542\) | 5.22436 | + | 9.04886i | 0.224406 | + | 0.388682i | ||||
\(543\) | −0.760479 | + | 1.31719i | −0.0326353 | + | 0.0565259i | ||||
\(544\) | 13.0609 | − | 22.6221i | 0.559982 | − | 0.969916i | ||||
\(545\) | −6.21542 | −0.266239 | ||||||||
\(546\) | 2.32805 | + | 3.66716i | 0.0996314 | + | 0.156940i | ||||
\(547\) | −33.7556 | −1.44329 | −0.721643 | − | 0.692265i | \(-0.756613\pi\) | ||||
−0.721643 | + | 0.692265i | \(0.756613\pi\) | |||||||
\(548\) | 6.87133 | − | 11.9015i | 0.293529 | − | 0.508407i | ||||
\(549\) | 5.79728 | − | 10.0412i | 0.247422 | − | 0.428547i | ||||
\(550\) | −1.66012 | − | 2.87542i | −0.0707879 | − | 0.122608i | ||||
\(551\) | −52.4657 | −2.23511 | ||||||||
\(552\) | −0.346549 | − | 0.600240i | −0.0147501 | − | 0.0255479i | ||||
\(553\) | 1.60236 | + | 2.77538i | 0.0681395 | + | 0.118021i | ||||
\(554\) | 8.62086 | 0.366265 | ||||||||
\(555\) | −1.72789 | − | 2.99279i | −0.0733448 | − | 0.127037i | ||||
\(556\) | 1.20473 | − | 2.08665i | 0.0510919 | − | 0.0884938i | ||||
\(557\) | 0.894299 | − | 1.54897i | 0.0378927 | − | 0.0656320i | −0.846457 | − | 0.532457i | \(-0.821269\pi\) |
0.884350 | + | 0.466825i | \(0.154602\pi\) | |||||||
\(558\) | −24.2569 | −1.02688 | ||||||||
\(559\) | 4.75601 | − | 0.200080i | 0.201158 | − | 0.00846249i | ||||
\(560\) | −10.2244 | −0.432058 | ||||||||
\(561\) | −0.887820 | + | 1.53775i | −0.0374838 | + | 0.0649238i | ||||
\(562\) | 0.990185 | − | 1.71505i | 0.0417684 | − | 0.0723450i | ||||
\(563\) | 3.84189 | + | 6.65434i | 0.161916 | + | 0.280447i | 0.935556 | − | 0.353179i | \(-0.114899\pi\) |
−0.773640 | + | 0.633626i | \(0.781566\pi\) | |||||||
\(564\) | 2.07625 | 0.0874261 | ||||||||
\(565\) | 5.47370 | + | 9.48072i | 0.230280 | + | 0.398857i | ||||
\(566\) | −1.09255 | − | 1.89235i | −0.0459233 | − | 0.0795415i | ||||
\(567\) | −28.2636 | −1.18696 | ||||||||
\(568\) | 9.00000 | + | 15.5885i | 0.377632 | + | 0.654077i | ||||
\(569\) | 13.0629 | − | 22.6256i | 0.547626 | − | 0.948516i | −0.450811 | − | 0.892619i | \(-0.648865\pi\) |
0.998437 | − | 0.0558961i | \(-0.0178016\pi\) | |||||||
\(570\) | −3.05109 | + | 5.28464i | −0.127796 | + | 0.221349i | ||||
\(571\) | −11.6624 | −0.488056 | −0.244028 | − | 0.969768i | \(-0.578469\pi\) | ||||
−0.244028 | + | 0.969768i | \(0.578469\pi\) | |||||||
\(572\) | −1.66994 | + | 3.19551i | −0.0698236 | + | 0.133611i | ||||
\(573\) | −3.36178 | −0.140440 | ||||||||
\(574\) | −10.1896 | + | 17.6489i | −0.425304 | + | 0.736649i | ||||
\(575\) | −1.12847 | + | 1.95458i | −0.0470607 | + | 0.0815115i | ||||
\(576\) | 10.0957 | + | 17.4863i | 0.420654 | + | 0.728594i | ||||
\(577\) | 28.6008 | 1.19067 | 0.595334 | − | 0.803478i | \(-0.297020\pi\) | ||||
0.595334 | + | 0.803478i | \(0.297020\pi\) | |||||||
\(578\) | −5.14697 | − | 8.91482i | −0.214086 | − | 0.370807i | ||||
\(579\) | 0.868189 | + | 1.50375i | 0.0360807 | + | 0.0624936i | ||||
\(580\) | −24.3136 | −1.00957 | ||||||||
\(581\) | 8.69158 | + | 15.0543i | 0.360587 | + | 0.624556i | ||||
\(582\) | 0.475024 | − | 0.822765i | 0.0196904 | − | 0.0341047i | ||||
\(583\) | 3.04461 | − | 5.27341i | 0.126095 | − | 0.218402i | ||||
\(584\) | 48.2476 | 1.99650 | ||||||||
\(585\) | −29.9726 | + | 1.26091i | −1.23921 | + | 0.0521323i | ||||
\(586\) | 6.13515 | 0.253441 | ||||||||
\(587\) | 17.5727 | − | 30.4369i | 0.725304 | − | 1.25626i | −0.233545 | − | 0.972346i | \(-0.575033\pi\) |
0.958849 | − | 0.283917i | \(-0.0916341\pi\) | |||||||
\(588\) | −0.945578 | + | 1.63779i | −0.0389950 | + | 0.0675413i | ||||
\(589\) | −26.1718 | − | 45.3308i | −1.07839 | − | 1.86782i | ||||
\(590\) | 40.6967 | 1.67546 | ||||||||
\(591\) | 0.379138 | + | 0.656687i | 0.0155957 | + | 0.0270125i | ||||
\(592\) | 1.76249 | + | 3.05272i | 0.0724378 | + | 0.125466i | ||||
\(593\) | −25.2087 | −1.03520 | −0.517600 | − | 0.855623i | \(-0.673174\pi\) | ||||
−0.517600 | + | 0.855623i | \(0.673174\pi\) | |||||||
\(594\) | −1.00000 | − | 1.73205i | −0.0410305 | − | 0.0710669i | ||||
\(595\) | 26.7079 | − | 46.2594i | 1.09492 | − | 1.89645i | ||||
\(596\) | −1.27230 | + | 2.20369i | −0.0521156 | + | 0.0902668i | ||||
\(597\) | −6.07625 | −0.248685 | ||||||||
\(598\) | −2.44872 | + | 0.103015i | −0.100136 | + | 0.00421260i | ||||
\(599\) | 26.8582 | 1.09740 | 0.548698 | − | 0.836021i | \(-0.315124\pi\) | ||||
0.548698 | + | 0.836021i | \(0.315124\pi\) | |||||||
\(600\) | −1.69271 | + | 2.93186i | −0.0691047 | + | 0.119693i | ||||
\(601\) | −16.2841 | + | 28.2049i | −0.664243 | + | 1.15050i | 0.315246 | + | 0.949010i | \(0.397913\pi\) |
−0.979490 | + | 0.201494i | \(0.935420\pi\) | |||||||
\(602\) | −2.33988 | − | 4.05279i | −0.0953663 | − | 0.165179i | ||||
\(603\) | −34.9278 | −1.42237 | ||||||||
\(604\) | 4.22436 | + | 7.31681i | 0.171887 | + | 0.297717i | ||||
\(605\) | 1.44224 | + | 2.49804i | 0.0586355 | + | 0.101560i | ||||
\(606\) | 3.35284 | 0.136200 | ||||||||
\(607\) | −20.3865 | − | 35.3104i | −0.827462 | − | 1.43321i | −0.900023 | − | 0.435843i | \(-0.856450\pi\) |
0.0725607 | − | 0.997364i | \(-0.476883\pi\) | |||||||
\(608\) | −15.5609 | + | 26.9523i | −0.631078 | + | 1.09306i | ||||
\(609\) | 5.07739 | − | 8.79430i | 0.205746 | − | 0.356363i | ||||
\(610\) | −11.5946 | −0.469450 | ||||||||
\(611\) | 10.2014 | − | 19.5209i | 0.412704 | − | 0.789731i | ||||
\(612\) | −15.0696 | −0.609152 | ||||||||
\(613\) | 11.6818 | − | 20.2334i | 0.471822 | − | 0.817220i | −0.527658 | − | 0.849457i | \(-0.676930\pi\) |
0.999480 | + | 0.0322371i | \(0.0102632\pi\) | |||||||
\(614\) | −3.09255 | + | 5.35645i | −0.124805 | + | 0.216169i | ||||
\(615\) | 2.81824 | + | 4.88133i | 0.113642 | + | 0.196834i | ||||
\(616\) | 10.6338 | 0.428449 | ||||||||
\(617\) | 9.70473 | + | 16.8091i | 0.390698 | + | 0.676708i | 0.992542 | − | 0.121905i | \(-0.0389004\pi\) |
−0.601844 | + | 0.798614i | \(0.705567\pi\) | |||||||
\(618\) | 0.910786 | + | 1.57753i | 0.0366372 | + | 0.0634575i | ||||
\(619\) | −0.941108 | −0.0378263 | −0.0189132 | − | 0.999821i | \(-0.506021\pi\) | ||||
−0.0189132 | + | 0.999821i | \(0.506021\pi\) | |||||||
\(620\) | −12.1285 | − | 21.0071i | −0.487091 | − | 0.843667i | ||||
\(621\) | −0.679754 | + | 1.17737i | −0.0272776 | + | 0.0472462i | ||||
\(622\) | 0.644962 | − | 1.11711i | 0.0258606 | − | 0.0447919i | ||||
\(623\) | 20.0393 | 0.802856 | ||||||||
\(624\) | −1.22436 | + | 0.0515075i | −0.0490137 | + | 0.00206195i | ||||
\(625\) | −30.5772 | −1.22309 | ||||||||
\(626\) | 0.146972 | − | 0.254563i | 0.00587417 | − | 0.0101744i | ||||
\(627\) | 1.05776 | − | 1.83209i | 0.0422428 | − | 0.0731667i | ||||
\(628\) | −8.17975 | − | 14.1677i | −0.326408 | − | 0.565355i | ||||
\(629\) | −18.4157 | −0.734284 | ||||||||
\(630\) | 14.7460 | + | 25.5408i | 0.587495 | + | 1.01757i | ||||
\(631\) | 10.7342 | + | 18.5921i | 0.427321 | + | 0.740141i | 0.996634 | − | 0.0819794i | \(-0.0261242\pi\) |
−0.569313 | + | 0.822121i | \(0.692791\pi\) | |||||||
\(632\) | −2.71234 | −0.107891 | ||||||||
\(633\) | 1.85303 | + | 3.20954i | 0.0736513 | + | 0.127568i | ||||
\(634\) | 11.0261 | − | 19.0978i | 0.437903 | − | 0.758470i | ||||
\(635\) | −23.3332 | + | 40.4143i | −0.925950 | + | 1.60379i | ||||
\(636\) | −2.06958 | −0.0820643 | ||||||||
\(637\) | 10.7525 | + | 16.9373i | 0.426029 | + | 0.671082i | ||||
\(638\) | −8.42909 | −0.333711 | ||||||||
\(639\) | 8.65345 | − | 14.9882i | 0.342325 | − | 0.592925i | ||||
\(640\) | −4.32673 | + | 7.49411i | −0.171029 | + | 0.296231i | ||||
\(641\) | 12.2690 | + | 21.2505i | 0.484595 | + | 0.839343i | 0.999843 | − | 0.0176977i | \(-0.00563363\pi\) |
−0.515248 | + | 0.857041i | \(0.672300\pi\) | |||||||
\(642\) | −1.12621 | −0.0444479 | ||||||||
\(643\) | 8.37467 | + | 14.5054i | 0.330265 | + | 0.572035i | 0.982564 | − | 0.185927i | \(-0.0595287\pi\) |
−0.652299 | + | 0.757962i | \(0.726195\pi\) | |||||||
\(644\) | −1.20473 | − | 2.08665i | −0.0474730 | − | 0.0822257i | ||||
\(645\) | −1.29433 | −0.0509642 | ||||||||
\(646\) | 16.2592 | + | 28.1617i | 0.639708 | + | 1.10801i | ||||
\(647\) | −17.7993 | + | 30.8293i | −0.699762 | + | 1.21202i | 0.268786 | + | 0.963200i | \(0.413377\pi\) |
−0.968549 | + | 0.248824i | \(0.919956\pi\) | |||||||
\(648\) | 11.9605 | − | 20.7163i | 0.469855 | − | 0.813812i | ||||
\(649\) | −14.1088 | −0.553821 | ||||||||
\(650\) | 6.41613 | + | 10.1067i | 0.251661 | + | 0.396418i | ||||
\(651\) | 10.1311 | 0.397070 | ||||||||
\(652\) | −5.39430 | + | 9.34320i | −0.211257 | + | 0.365908i | ||||
\(653\) | 3.51315 | − | 6.08496i | 0.137480 | − | 0.238123i | −0.789062 | − | 0.614314i | \(-0.789433\pi\) |
0.926542 | + | 0.376191i | \(0.122766\pi\) | |||||||
\(654\) | 0.366180 | + | 0.634242i | 0.0143188 | + | 0.0248008i | ||||
\(655\) | 9.55795 | 0.373460 | ||||||||
\(656\) | −2.87467 | − | 4.97907i | −0.112237 | − | 0.194400i | ||||
\(657\) | −23.1949 | − | 40.1748i | −0.904920 | − | 1.56737i | ||||
\(658\) | −21.6535 | −0.844139 | ||||||||
\(659\) | −21.4454 | − | 37.1445i | −0.835394 | − | 1.44694i | −0.893710 | − | 0.448646i | \(-0.851906\pi\) |
0.0583160 | − | 0.998298i | \(-0.481427\pi\) | |||||||
\(660\) | 0.490185 | − | 0.849025i | 0.0190804 | − | 0.0330482i | ||||
\(661\) | −18.3267 | + | 31.7428i | −0.712827 | + | 1.23465i | 0.250965 | + | 0.967996i | \(0.419252\pi\) |
−0.963792 | + | 0.266656i | \(0.914081\pi\) | |||||||
\(662\) | −14.4487 | −0.561565 | ||||||||
\(663\) | 2.96521 | − | 5.67408i | 0.115159 | − | 0.220363i | ||||
\(664\) | −14.7123 | −0.570950 | ||||||||
\(665\) | −31.8201 | + | 55.1139i | −1.23393 | + | 2.13723i | ||||
\(666\) | 5.08387 | − | 8.80552i | 0.196996 | − | 0.341207i | ||||
\(667\) | 2.86485 | + | 4.96207i | 0.110928 | + | 0.192132i | ||||
\(668\) | −7.04995 | −0.272771 | ||||||||
\(669\) | −3.30175 | − | 5.71880i | −0.127653 | − | 0.221101i | ||||
\(670\) | 17.4639 | + | 30.2483i | 0.674689 | + | 1.16859i | ||||
\(671\) | 4.01963 | 0.155176 | ||||||||
\(672\) | −3.01182 | − | 5.21663i | −0.116184 | − | 0.201236i | ||||
\(673\) | 1.36932 | − | 2.37174i | 0.0527835 | − | 0.0914237i | −0.838426 | − | 0.545015i | \(-0.816524\pi\) |
0.891210 | + | 0.453591i | \(0.149857\pi\) | |||||||
\(674\) | 9.25267 | − | 16.0261i | 0.356400 | − | 0.617302i | ||||
\(675\) | 6.64049 | 0.255593 | ||||||||
\(676\) | 5.53146 | − | 11.7645i | 0.212748 | − | 0.452480i | ||||
\(677\) | 17.3069 | 0.665158 | 0.332579 | − | 0.943075i | \(-0.392081\pi\) | ||||
0.332579 | + | 0.943075i | \(0.392081\pi\) | |||||||
\(678\) | 0.644962 | − | 1.11711i | 0.0247696 | − | 0.0429023i | ||||
\(679\) | 4.95407 | − | 8.58070i | 0.190120 | − | 0.329297i | ||||
\(680\) | 22.6044 | + | 39.1519i | 0.866838 | + | 1.50141i | ||||
\(681\) | 2.48798 | 0.0953397 | ||||||||
\(682\) | −4.20473 | − | 7.28281i | −0.161007 | − | 0.278873i | ||||
\(683\) | −23.3635 | − | 40.4668i | −0.893980 | − | 1.54842i | −0.835061 | − | 0.550157i | \(-0.814568\pi\) |
−0.0589192 | − | 0.998263i | \(-0.518765\pi\) | |||||||
\(684\) | 17.9541 | 0.686491 | ||||||||
\(685\) | 19.8202 | + | 34.3297i | 0.757293 | + | 1.31167i | ||||
\(686\) | −2.54461 | + | 4.40739i | −0.0971535 | + | 0.168275i | ||||
\(687\) | 2.47502 | − | 4.28687i | 0.0944280 | − | 0.163554i | ||||
\(688\) | 1.32025 | 0.0503339 | ||||||||
\(689\) | −10.1686 | + | 19.4582i | −0.387393 | + | 0.741297i | ||||
\(690\) | 0.666410 | 0.0253698 | ||||||||
\(691\) | 5.97370 | − | 10.3467i | 0.227250 | − | 0.393609i | −0.729742 | − | 0.683723i | \(-0.760360\pi\) |
0.956992 | + | 0.290114i | \(0.0936932\pi\) | |||||||
\(692\) | −0.922611 | + | 1.59801i | −0.0350724 | + | 0.0607472i | ||||
\(693\) | −5.11218 | − | 8.85456i | −0.194196 | − | 0.336357i | ||||
\(694\) | −15.5446 | −0.590065 | ||||||||
\(695\) | 3.47502 | + | 6.01892i | 0.131815 | + | 0.228311i | ||||
\(696\) | 4.29728 | + | 7.44311i | 0.162888 | + | 0.282130i | ||||
\(697\) | 30.0366 | 1.13772 | ||||||||
\(698\) | −15.0000 | − | 25.9808i | −0.567758 | − | 0.983386i | ||||
\(699\) | 1.09589 | − | 1.89813i | 0.0414502 | − | 0.0717939i | ||||
\(700\) | −5.88448 | + | 10.1922i | −0.222413 | + | 0.385230i | ||||
\(701\) | −19.2833 | −0.728318 | −0.364159 | − | 0.931337i | \(-0.618644\pi\) | ||||
−0.364159 | + | 0.931337i | \(0.618644\pi\) | |||||||
\(702\) | 3.86485 | + | 6.08793i | 0.145869 | + | 0.229774i | ||||
\(703\) | 21.9407 | 0.827510 | ||||||||
\(704\) | −3.50000 | + | 6.06218i | −0.131911 | + | 0.228477i | ||||
\(705\) | −2.99446 | + | 5.18656i | −0.112778 | + | 0.195337i | ||||
\(706\) | 2.16012 | + | 3.74144i | 0.0812973 | + | 0.140811i | ||||
\(707\) | 34.9670 | 1.31507 | ||||||||
\(708\) | 2.39764 | + | 4.15283i | 0.0901086 | + | 0.156073i | ||||
\(709\) | 20.8528 | + | 36.1182i | 0.783145 | + | 1.35645i | 0.930101 | + | 0.367303i | \(0.119719\pi\) |
−0.146957 | + | 0.989143i | \(0.546948\pi\) | |||||||
\(710\) | −17.3069 | −0.649516 | ||||||||
\(711\) | 1.30395 | + | 2.25851i | 0.0489020 | + | 0.0847008i | ||||
\(712\) | −8.48018 | + | 14.6881i | −0.317808 | + | 0.550460i | ||||
\(713\) | −2.85818 | + | 4.95051i | −0.107040 | + | 0.185398i | ||||
\(714\) | −6.29394 | −0.235545 | ||||||||
\(715\) | −5.57405 | − | 8.78027i | −0.208458 | − | 0.328363i | ||||
\(716\) | −5.42909 | −0.202895 | ||||||||
\(717\) | −0.0459333 | + | 0.0795589i | −0.00171541 | + | 0.00297118i | ||||
\(718\) | 0.115516 | − | 0.200080i | 0.00431103 | − | 0.00746692i | ||||
\(719\) | 12.3136 | + | 21.3277i | 0.459219 | + | 0.795390i | 0.998920 | − | 0.0464664i | \(-0.0147960\pi\) |
−0.539701 | + | 0.841857i | \(0.681463\pi\) | |||||||
\(720\) | −8.32025 | −0.310077 | ||||||||
\(721\) | 9.49867 | + | 16.4522i | 0.353749 | + | 0.612711i | ||||
\(722\) | −9.87133 | − | 17.0976i | −0.367373 | − | 0.636309i | ||||
\(723\) | −10.3769 | −0.385920 | ||||||||
\(724\) | −2.23751 | − | 3.87548i | −0.0831565 | − | 0.144031i | ||||
\(725\) | 13.9933 | − | 24.2372i | 0.519699 | − | 0.900145i | ||||
\(726\) | 0.169938 | − | 0.294342i | 0.00630701 | − | 0.0109241i | ||||
\(727\) | 5.82157 | 0.215910 | 0.107955 | − | 0.994156i | \(-0.465570\pi\) | ||||
0.107955 | + | 0.994156i | \(0.465570\pi\) | |||||||
\(728\) | −38.3069 | + | 1.61153i | −1.41975 | + | 0.0597273i | ||||
\(729\) | −20.9607 | −0.776324 | ||||||||
\(730\) | −23.1949 | + | 40.1748i | −0.858482 | + | 1.48693i | ||||
\(731\) | −3.44872 | + | 5.97336i | −0.127556 | + | 0.220933i | ||||
\(732\) | −0.683090 | − | 1.18315i | −0.0252477 | − | 0.0437303i | ||||
\(733\) | 32.1588 | 1.18781 | 0.593906 | − | 0.804534i | \(-0.297585\pi\) | ||||
0.593906 | + | 0.804534i | \(0.297585\pi\) | |||||||
\(734\) | −9.90411 | − | 17.1544i | −0.365568 | − | 0.633182i | ||||
\(735\) | −2.72750 | − | 4.72418i | −0.100605 | − | 0.174254i | ||||
\(736\) | 3.39877 | 0.125280 | ||||||||
\(737\) | −6.05442 | − | 10.4866i | −0.223018 | − | 0.386278i | ||||
\(738\) | −8.29193 | + | 14.3621i | −0.305230 | + | 0.528674i | ||||
\(739\) | 0.185099 | − | 0.320601i | 0.00680899 | − | 0.0117935i | −0.862601 | − | 0.505885i | \(-0.831166\pi\) |
0.869410 | + | 0.494092i | \(0.164499\pi\) | |||||||
\(740\) | 10.1677 | 0.373773 | ||||||||
\(741\) | −3.53278 | + | 6.76016i | −0.129780 | + | 0.248341i | ||||
\(742\) | 21.5839 | 0.792369 | ||||||||
\(743\) | −16.0466 | + | 27.7936i | −0.588693 | + | 1.01965i | 0.405711 | + | 0.914002i | \(0.367024\pi\) |
−0.994404 | + | 0.105645i | \(0.966309\pi\) | |||||||
\(744\) | −4.28727 | + | 7.42577i | −0.157179 | + | 0.272242i | ||||
\(745\) | −3.66994 | − | 6.35652i | −0.134456 | − | 0.232885i | ||||
\(746\) | −14.9148 | −0.546070 | ||||||||
\(747\) | 7.07292 | + | 12.2507i | 0.258785 | + | 0.448228i | ||||
\(748\) | −2.61218 | − | 4.52443i | −0.0955108 | − | 0.165430i | ||||
\(749\) | −11.7453 | −0.429165 | ||||||||
\(750\) | 0.823390 | + | 1.42615i | 0.0300659 | + | 0.0520757i | ||||
\(751\) | −5.38983 | + | 9.33546i | −0.196678 | + | 0.340656i | −0.947449 | − | 0.319906i | \(-0.896349\pi\) |
0.750772 | + | 0.660562i | \(0.229682\pi\) | |||||||
\(752\) | 3.05442 | − | 5.29041i | 0.111383 | − | 0.192922i | ||||
\(753\) | −3.56158 | −0.129791 | ||||||||
\(754\) | 30.3647 | − | 1.27741i | 1.10582 | − | 0.0465205i | ||||
\(755\) | −24.3702 | −0.886922 | ||||||||
\(756\) | −3.54461 | + | 6.13944i | −0.128916 | + | 0.223289i | ||||
\(757\) | 25.8397 | − | 44.7556i | 0.939159 | − | 1.62667i | 0.172116 | − | 0.985077i | \(-0.444940\pi\) |
0.767044 | − | 0.641595i | \(-0.221727\pi\) | |||||||
\(758\) | −3.32025 | − | 5.75084i | −0.120597 | − | 0.208880i | ||||
\(759\) | −0.231033 | −0.00838595 | ||||||||
\(760\) | −26.9311 | − | 46.6460i | −0.976894 | − | 1.69203i | ||||
\(761\) | 19.1392 | + | 33.1500i | 0.693794 | + | 1.20169i | 0.970585 | + | 0.240757i | \(0.0773956\pi\) |
−0.276791 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(762\) | 5.49867 | 0.199196 | ||||||||
\(763\) | 3.81892 | + | 6.61456i | 0.138254 | + | 0.239463i | ||||
\(764\) | 4.94558 | − | 8.56599i | 0.178925 | − | 0.309907i | ||||
\(765\) | 21.7340 | − | 37.6444i | 0.785794 | − | 1.36103i | ||||
\(766\) | −5.14182 | −0.185781 | ||||||||
\(767\) | 50.8252 | − | 2.13816i | 1.83519 | − | 0.0772045i | ||||
\(768\) | 5.77791 | 0.208492 | ||||||||
\(769\) | −23.2873 | + | 40.3347i | −0.839760 | + | 1.45451i | 0.0503343 | + | 0.998732i | \(0.483971\pi\) |
−0.890095 | + | 0.455775i | \(0.849362\pi\) | |||||||
\(770\) | −5.11218 | + | 8.85456i | −0.184230 | + | 0.319096i | ||||
\(771\) | 0.978167 | + | 1.69424i | 0.0352278 | + | 0.0610164i | ||||
\(772\) | −5.10884 | −0.183871 | ||||||||
\(773\) | −11.3910 | − | 19.7297i | −0.409704 | − | 0.709629i | 0.585152 | − | 0.810924i | \(-0.301035\pi\) |
−0.994856 | + | 0.101295i | \(0.967702\pi\) | |||||||
\(774\) | −1.90411 | − | 3.29802i | −0.0684420 | − | 0.118545i | ||||
\(775\) | 27.9215 | 1.00297 | ||||||||
\(776\) | 4.19291 | + | 7.26232i | 0.150517 | + | 0.260702i | ||||
\(777\) | −2.12332 | + | 3.67770i | −0.0761738 | + | 0.131937i | ||||
\(778\) | 16.6403 | − | 28.8218i | 0.596584 | − | 1.03331i | ||||
\(779\) | −35.7859 | −1.28216 | ||||||||
\(780\) | −1.63716 | + | 3.13278i | −0.0586196 | + | 0.112172i | ||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 1.77564 | − | 3.07550i | 0.0634967 | − | 0.109980i | ||||
\(783\) | 8.42909 | − | 14.5996i | 0.301231 | − | 0.521748i | ||||
\(784\) | 2.78212 | + | 4.81877i | 0.0993614 | + | 0.172099i | ||||
\(785\) | 47.1887 | 1.68424 | ||||||||
\(786\) | −0.563104 | − | 0.975324i | −0.0200852 | − | 0.0347887i | ||||
\(787\) | −2.23437 | − | 3.87004i | −0.0796466 | − | 0.137952i | 0.823451 | − | 0.567388i | \(-0.192046\pi\) |
−0.903097 | + | 0.429436i | \(0.858713\pi\) | |||||||
\(788\) | −2.23103 | −0.0794772 | ||||||||
\(789\) | 1.43576 | + | 2.48681i | 0.0511145 | + | 0.0885329i | ||||
\(790\) | 1.30395 | − | 2.25851i | 0.0463925 | − | 0.0803542i | ||||
\(791\) | 6.72637 | − | 11.6504i | 0.239162 | − | 0.414241i | ||||
\(792\) | 8.65345 | 0.307487 | ||||||||
\(793\) | −14.4802 | + | 0.609165i | −0.514206 | + | 0.0216321i | ||||
\(794\) | 8.60350 | 0.305327 | ||||||||
\(795\) | 2.98484 | − | 5.16989i | 0.105861 | − | 0.183357i | ||||
\(796\) | 8.93891 | − | 15.4826i | 0.316831 | − | 0.548768i | ||||
\(797\) | −15.6153 | − | 27.0465i | −0.553123 | − | 0.958037i | −0.998047 | − | 0.0624689i | \(-0.980103\pi\) |
0.444924 | − | 0.895568i | \(-0.353231\pi\) | |||||||
\(798\) | 7.49867 | 0.265450 | ||||||||
\(799\) | 15.9574 | + | 27.6390i | 0.564532 | + | 0.977799i | ||||
\(800\) | −8.30062 | − | 14.3771i | −0.293471 | − | 0.508307i | ||||
\(801\) | 16.3073 | 0.576190 | ||||||||
\(802\) | 2.83988 | + | 4.91881i | 0.100280 | + | 0.173689i | ||||
\(803\) | 8.04127 | − | 13.9279i | 0.283770 | − | 0.491505i | ||||
\(804\) | −2.05776 | + | 3.56414i | −0.0725715 | + | 0.125698i | ||||
\(805\) | 6.95005 | 0.244957 | ||||||||
\(806\) | 16.2507 | + | 25.5981i | 0.572405 | + | 0.901655i | ||||
\(807\) | −8.52724 | −0.300173 | ||||||||
\(808\) | −14.7973 | + | 25.6296i | −0.520566 | + | 0.901648i | ||||
\(809\) | 5.70807 | − | 9.88666i | 0.200685 | − | 0.347596i | −0.748064 | − | 0.663626i | \(-0.769017\pi\) |
0.948749 | + | 0.316030i | \(0.102350\pi\) | |||||||
\(810\) | 11.5000 | + | 19.9186i | 0.404069 | + | 0.699868i | ||||
\(811\) | 2.13917 | 0.0751163 | 0.0375581 | − | 0.999294i | \(-0.488042\pi\) | ||||
0.0375581 | + | 0.999294i | \(0.488042\pi\) | |||||||
\(812\) | 14.9389 | + | 25.8749i | 0.524253 | + | 0.908033i | ||||
\(813\) | −1.77564 | − | 3.07550i | −0.0622744 | − | 0.107862i | ||||
\(814\) | 3.52498 | 0.123550 | ||||||||
\(815\) | −15.5598 | − | 26.9503i | −0.545035 | − | 0.944028i | ||||
\(816\) | 0.887820 | − | 1.53775i | 0.0310799 | − | 0.0538320i | ||||
\(817\) | 4.10884 | − | 7.11673i | 0.143750 | − | 0.248983i | ||||
\(818\) | 22.9933 | 0.803943 | ||||||||
\(819\) | 19.7578 | + | 31.1226i | 0.690394 | + | 1.08751i | ||||
\(820\) | −16.5839 | −0.579134 | ||||||||
\(821\) | −12.9933 | + | 22.5051i | −0.453470 | + | 0.785434i | −0.998599 | − | 0.0529189i | \(-0.983148\pi\) |
0.545129 | + | 0.838352i | \(0.316481\pi\) | |||||||
\(822\) | 2.33541 | − | 4.04504i | 0.0814567 | − | 0.141087i | ||||
\(823\) | 12.5379 | + | 21.7163i | 0.437045 | + | 0.756984i | 0.997460 | − | 0.0712278i | \(-0.0226917\pi\) |
−0.560415 | + | 0.828212i | \(0.689358\pi\) | |||||||
\(824\) | −16.0785 | −0.560122 | ||||||||
\(825\) | 0.564237 | + | 0.977288i | 0.0196442 | + | 0.0340248i | ||||
\(826\) | −25.0052 | − | 43.3102i | −0.870041 | − | 1.50695i | ||||
\(827\) | −43.0692 | −1.49766 | −0.748831 | − | 0.662761i | \(-0.769385\pi\) | ||||
−0.748831 | + | 0.662761i | \(0.769385\pi\) | |||||||
\(828\) | −0.980369 | − | 1.69805i | −0.0340702 | − | 0.0590113i | ||||
\(829\) | 1.21788 | − | 2.10943i | 0.0422988 | − | 0.0732636i | −0.844101 | − | 0.536184i | \(-0.819865\pi\) |
0.886400 | + | 0.462921i | \(0.153199\pi\) | |||||||
\(830\) | 7.07292 | − | 12.2507i | 0.245505 | − | 0.425226i | ||||
\(831\) | −2.93003 | −0.101642 | ||||||||
\(832\) | 11.6896 | − | 22.3686i | 0.405263 | − | 0.775491i | ||||
\(833\) | −29.0696 | −1.00720 | ||||||||
\(834\) | 0.409460 | − | 0.709205i | 0.0141784 | − | 0.0245578i | ||||
\(835\) | 10.1677 | − | 17.6110i | 0.351869 | − | 0.609455i | ||||
\(836\) | 3.11218 | + | 5.39045i | 0.107637 | + | 0.186433i | ||||
\(837\) | 16.8189 | 0.581347 | ||||||||
\(838\) | −15.4291 | − | 26.7240i | −0.532989 | − | 0.923164i | ||||
\(839\) | −23.1173 | − | 40.0404i | −0.798099 | − | 1.38235i | −0.920853 | − | 0.389911i | \(-0.872506\pi\) |
0.122754 | − | 0.992437i | \(-0.460827\pi\) | |||||||
\(840\) | 10.4251 | 0.359699 | ||||||||
\(841\) | −21.0248 | − | 36.4160i | −0.724993 | − | 1.25572i | ||||
\(842\) | −11.8017 | + | 20.4412i | −0.406715 | + | 0.704451i | ||||
\(843\) | −0.336541 | + | 0.582906i | −0.0115911 | + | 0.0200763i | ||||
\(844\) | −10.9041 | −0.375335 | ||||||||
\(845\) | 21.4104 | + | 30.7850i | 0.736540 | + | 1.05904i | ||||
\(846\) | −17.6209 | −0.605818 | ||||||||
\(847\) | 1.77230 | − | 3.06972i | 0.0608971 | − | 0.105477i | ||||
\(848\) | −3.04461 | + | 5.27341i | −0.104552 | + | 0.181090i | ||||
\(849\) | 0.371332 | + | 0.643167i | 0.0127441 | + | 0.0220734i | ||||
\(850\) | −17.3462 | −0.594969 | ||||||||
\(851\) | −1.19806 | − | 2.07510i | −0.0410689 | − | 0.0711334i | ||||
\(852\) | −1.01963 | − | 1.76605i | −0.0349320 | − | 0.0605039i | ||||
\(853\) | −19.0562 | −0.652473 | −0.326237 | − | 0.945288i | \(-0.605781\pi\) | ||||
−0.326237 | + | 0.945288i | \(0.605781\pi\) | |||||||
\(854\) | 7.12401 | + | 12.3391i | 0.243778 | + | 0.422237i | ||||
\(855\) | −25.8941 | + | 44.8499i | −0.885560 | + | 1.53383i | ||||
\(856\) | 4.97036 | − | 8.60892i | 0.169883 | − | 0.294247i | ||||
\(857\) | −7.86712 | −0.268736 | −0.134368 | − | 0.990932i | \(-0.542900\pi\) | ||||
−0.134368 | + | 0.990932i | \(0.542900\pi\) | |||||||
\(858\) | −0.567573 | + | 1.08608i | −0.0193766 | + | 0.0370782i | ||||
\(859\) | −0.993713 | −0.0339051 | −0.0169525 | − | 0.999856i | \(-0.505396\pi\) | ||||
−0.0169525 | + | 0.999856i | \(0.505396\pi\) | |||||||
\(860\) | 1.90411 | − | 3.29802i | 0.0649298 | − | 0.112462i | ||||
\(861\) | 3.46320 | − | 5.99844i | 0.118026 | − | 0.204426i | ||||
\(862\) | −14.3169 | − | 24.7976i | −0.487636 | − | 0.844610i | ||||
\(863\) | −29.3069 | −0.997619 | −0.498809 | − | 0.866712i | \(-0.666229\pi\) | ||||
−0.498809 | + | 0.866712i | \(0.666229\pi\) | |||||||
\(864\) | −5.00000 | − | 8.66025i | −0.170103 | − | 0.294628i | ||||
\(865\) | −2.66126 | − | 4.60943i | −0.0904855 | − | 0.156725i | ||||
\(866\) | −28.6535 | −0.973684 | ||||||||
\(867\) | 1.74934 | + | 3.02994i | 0.0594106 | + | 0.102902i | ||||
\(868\) | −14.9041 | + | 25.8147i | −0.505879 | + | 0.876207i | ||||
\(869\) | −0.452057 | + | 0.782986i | −0.0153350 | + | 0.0265610i | ||||
\(870\) | −8.26362 | −0.280163 | ||||||||
\(871\) | 23.3995 | + | 36.8589i | 0.792860 | + | 1.24892i | ||||
\(872\) | −6.46433 | −0.218910 | ||||||||
\(873\) | 4.03146 | − | 6.98269i | 0.136444 | − | 0.236328i | ||||
\(874\) | −2.11552 | + | 3.66418i | −0.0715584 | + | 0.123943i | ||||
\(875\) | 8.58720 | + | 14.8735i | 0.290300 | + | 0.502815i | ||||
\(876\) | −5.46608 | −0.184682 | ||||||||
\(877\) | −25.2067 | − | 43.6594i | −0.851171 | − | 1.47427i | −0.880152 | − | 0.474692i | \(-0.842560\pi\) |
0.0289811 | − | 0.999580i | \(-0.490774\pi\) | |||||||
\(878\) | 4.54794 | + | 7.87727i | 0.153486 | + | 0.265845i | ||||
\(879\) | −2.08519 | −0.0703319 | ||||||||
\(880\) | −1.44224 | − | 2.49804i | −0.0486180 | − | 0.0842088i | ||||
\(881\) | 8.79394 | − | 15.2316i | 0.296275 | − | 0.513164i | −0.679005 | − | 0.734133i | \(-0.737589\pi\) |
0.975281 | + | 0.220969i | \(0.0709220\pi\) | |||||||
\(882\) | 8.02498 | − | 13.8997i | 0.270215 | − | 0.468026i | ||||
\(883\) | 42.3702 | 1.42587 | 0.712935 | − | 0.701230i | \(-0.247365\pi\) | ||||
0.712935 | + | 0.701230i | \(0.247365\pi\) | |||||||
\(884\) | 10.0957 | + | 15.9028i | 0.339555 | + | 0.534868i | ||||
\(885\) | −13.8319 | −0.464954 | ||||||||
\(886\) | −0.259152 | + | 0.448865i | −0.00870638 | + | 0.0150799i | ||||
\(887\) | −1.17843 | + | 2.04110i | −0.0395677 | + | 0.0685333i | −0.885131 | − | 0.465342i | \(-0.845931\pi\) |
0.845563 | + | 0.533875i | \(0.179265\pi\) | |||||||
\(888\) | −1.79709 | − | 3.11265i | −0.0603063 | − | 0.104454i | ||||
\(889\) | 57.3462 | 1.92333 | ||||||||
\(890\) | −8.15364 | − | 14.1225i | −0.273311 | − | 0.473388i | ||||
\(891\) | −3.98685 | − | 6.90542i | −0.133564 | − | 0.231340i | ||||
\(892\) | 19.4291 | 0.650534 | ||||||||
\(893\) | −19.0118 | − | 32.9294i | −0.636206 | − | 1.10194i | ||||
\(894\) | −0.432427 | + | 0.748985i | −0.0144625 | + | 0.0250498i | ||||
\(895\) | 7.83006 | − | 13.5621i | 0.261730 | − | 0.453330i | ||||
\(896\) | 10.6338 | 0.355251 | ||||||||
\(897\) | 0.832264 | − | 0.0350124i | 0.0277885 | − | 0.00116903i | ||||
\(898\) | −33.0522 | −1.10297 | ||||||||
\(899\) | 35.4420 | − | 61.3874i | 1.18206 | − | 2.04739i | ||||
\(900\) | −4.78860 | + | 8.29410i | −0.159620 | + | 0.276470i | ||||
\(901\) | −15.9061 | − | 27.5502i | −0.529910 | − | 0.917831i | ||||
\(902\) | −5.74934 | −0.191432 | ||||||||
\(903\) | 0.795270 | + | 1.37745i | 0.0264649 | + | 0.0458386i | ||||
\(904\) | 5.69291 | + | 9.86040i | 0.189343 | + | 0.327952i | ||||
\(905\) | 12.9081 | 0.429081 | ||||||||
\(906\) | 1.43576 | + | 2.48681i | 0.0477000 | + | 0.0826188i | ||||
\(907\) | 8.76048 | − | 15.1736i | 0.290887 | − | 0.503831i | −0.683133 | − | 0.730294i | \(-0.739383\pi\) |
0.974020 | + | 0.226463i | \(0.0727163\pi\) | |||||||
\(908\) | −3.66012 | + | 6.33952i | −0.121465 | + | 0.210384i | ||||
\(909\) | 28.4550 | 0.943793 | ||||||||
\(910\) | 17.0741 | − | 32.6721i | 0.565999 | − | 1.08307i | ||||
\(911\) | 10.2873 | 0.340833 | 0.170416 | − | 0.985372i | \(-0.445489\pi\) | ||||
0.170416 | + | 0.985372i | \(0.445489\pi\) | |||||||
\(912\) | −1.05776 | + | 1.83209i | −0.0350259 | + | 0.0606666i | ||||
\(913\) | −2.45206 | + | 4.24709i | −0.0811512 | + | 0.140558i | ||||
\(914\) | 13.6633 | + | 23.6655i | 0.451941 | + | 0.782784i | ||||
\(915\) | 3.94072 | 0.130276 | ||||||||
\(916\) | 7.28212 | + | 12.6130i | 0.240608 | + | 0.416745i | ||||
\(917\) | −5.87266 | − | 10.1717i | −0.193932 | − | 0.335901i | ||||
\(918\) | −10.4487 | −0.344859 | ||||||||
\(919\) | 15.5772 | + | 26.9805i | 0.513844 | + | 0.890004i | 0.999871 | + | 0.0160605i | \(0.00511243\pi\) |
−0.486027 | + | 0.873944i | \(0.661554\pi\) | |||||||
\(920\) | −2.94111 | + | 5.09415i | −0.0969655 | + | 0.167949i | ||||
\(921\) | 1.05109 | − | 1.82053i | 0.0346345 | − | 0.0599887i | ||||
\(922\) | 13.2873 | 0.437593 | ||||||||
\(923\) | −21.6142 | + | 0.909285i | −0.711440 | + | 0.0299295i | ||||
\(924\) | −1.20473 | −0.0396327 | ||||||||
\(925\) | −5.85189 | + | 10.1358i | −0.192409 | + | 0.333262i | ||||
\(926\) | −9.12401 | + | 15.8032i | −0.299833 | + | 0.519327i | ||||
\(927\) | 7.72971 | + | 13.3882i | 0.253877 | + | 0.439728i | ||||
\(928\) | −42.1455 | −1.38349 | ||||||||
\(929\) | −19.2297 | − | 33.3068i | −0.630906 | − | 1.09276i | −0.987367 | − | 0.158451i | \(-0.949350\pi\) |
0.356461 | − | 0.934310i | \(-0.383983\pi\) | |||||||
\(930\) | −4.12219 | − | 7.13984i | −0.135172 | − | 0.234125i | ||||
\(931\) | 34.6338 | 1.13508 | ||||||||
\(932\) | 3.22436 | + | 5.58476i | 0.105617 | + | 0.182935i | ||||
\(933\) | −0.219208 | + | 0.379679i | −0.00717654 | + | 0.0124301i | ||||
\(934\) | −14.1436 | + | 24.4975i | −0.462794 | + | 0.801583i | ||||
\(935\) | 15.0696 | 0.492828 | ||||||||
\(936\) | −31.1729 | + | 1.31141i | −1.01892 | + | 0.0428648i | ||||
\(937\) | 21.6182 | 0.706236 | 0.353118 | − | 0.935579i | \(-0.385121\pi\) | ||||
0.353118 | + | 0.935579i | \(0.385121\pi\) | |||||||
\(938\) | 21.4605 | − | 37.1708i | 0.700712 | − | 1.21367i | ||||
\(939\) | −0.0499523 | + | 0.0865199i | −0.00163013 | + | 0.00282347i | ||||
\(940\) | −8.81043 | − | 15.2601i | −0.287365 | − | 0.497730i | ||||
\(941\) | −6.44872 | −0.210222 | −0.105111 | − | 0.994460i | \(-0.533520\pi\) | ||||
−0.105111 | + | 0.994460i | \(0.533520\pi\) | |||||||
\(942\) | −2.78011 | − | 4.81529i | −0.0905809 | − | 0.156891i | ||||
\(943\) | 1.95407 | + | 3.38454i | 0.0636332 | + | 0.110216i | ||||
\(944\) | 14.1088 | 0.459204 | ||||||||
\(945\) | −10.2244 | − | 17.7091i | −0.332598 | − | 0.576077i | ||||
\(946\) | 0.660123 | − | 1.14337i | 0.0214625 | − | 0.0371741i | ||||
\(947\) | −7.76897 | + | 13.4562i | −0.252458 | + | 0.437269i | −0.964202 | − | 0.265169i | \(-0.914572\pi\) |
0.711744 | + | 0.702439i | \(0.247905\pi\) | |||||||
\(948\) | 0.307288 | 0.00998024 | ||||||||
\(949\) | −26.8569 | + | 51.3920i | −0.871810 | + | 1.66825i | ||||
\(950\) | 20.6664 | 0.670507 | ||||||||
\(951\) | −3.74752 | + | 6.49089i | −0.121522 | + | 0.210482i | ||||
\(952\) | 27.7775 | − | 48.1120i | 0.900273 | − | 1.55932i | ||||
\(953\) | 7.94338 | + | 13.7583i | 0.257311 | + | 0.445676i | 0.965521 | − | 0.260326i | \(-0.0838301\pi\) |
−0.708210 | + | 0.706002i | \(0.750497\pi\) | |||||||
\(954\) | 17.5642 | 0.568663 | ||||||||
\(955\) | 14.2654 | + | 24.7085i | 0.461619 | + | 0.799547i | ||||
\(956\) | −0.135147 | − | 0.234081i | −0.00437096 | − | 0.00757073i | ||||
\(957\) | 2.86485 | 0.0926075 | ||||||||
\(958\) | −7.77230 | − | 13.4620i | −0.251112 | − | 0.434938i | ||||
\(959\) | 24.3562 | − | 42.1861i | 0.786502 | − | 1.36226i | ||||
\(960\) | −3.43129 | + | 5.94317i | −0.110744 | + | 0.191815i | ||||
\(961\) | 39.7190 | 1.28126 | ||||||||
\(962\) | −12.6983 | + | 0.534202i | −0.409408 | + | 0.0172233i | ||||
\(963\) | −9.55795 | −0.308001 | ||||||||
\(964\) | 15.2656 | − | 26.4408i | 0.491673 | − | 0.851602i | ||||
\(965\) | 7.36819 | − | 12.7621i | 0.237190 | − | 0.410826i | ||||
\(966\) | −0.409460 | − | 0.709205i | −0.0131742 | − | 0.0228183i | ||||
\(967\) | 1.28766 | 0.0414083 | 0.0207041 | − | 0.999786i | \(-0.493409\pi\) | ||||
0.0207041 | + | 0.999786i | \(0.493409\pi\) | |||||||
\(968\) | 1.50000 | + | 2.59808i | 0.0482118 | + | 0.0835053i | ||||
\(969\) | −5.52611 | − | 9.57150i | −0.177524 | − | 0.307481i | ||||
\(970\) | −8.06291 | −0.258884 | ||||||||
\(971\) | 9.55977 | + | 16.5580i | 0.306788 | + | 0.531372i | 0.977658 | − | 0.210203i | \(-0.0674126\pi\) |
−0.670870 | + | 0.741575i | \(0.734079\pi\) | |||||||
\(972\) | −4.35504 | + | 7.54315i | −0.139688 | + | 0.241947i | ||||
\(973\) | 4.27029 | − | 7.39637i | 0.136899 | − | 0.237117i | ||||
\(974\) | 32.3265 | 1.03581 | ||||||||
\(975\) | −2.18069 | − | 3.43504i | −0.0698381 | − | 0.110009i | ||||
\(976\) | −4.01963 | −0.128665 | ||||||||
\(977\) | −13.5052 | + | 23.3916i | −0.432068 | + | 0.748364i | −0.997051 | − | 0.0767385i | \(-0.975549\pi\) |
0.564983 | + | 0.825102i | \(0.308883\pi\) | |||||||
\(978\) | −1.83340 | + | 3.17554i | −0.0586256 | + | 0.101542i | ||||
\(979\) | 2.82673 | + | 4.89603i | 0.0903425 | + | 0.156478i | ||||
\(980\) | 16.0500 | 0.512697 | ||||||||
\(981\) | 3.10771 | + | 5.38271i | 0.0992216 | + | 0.171857i | ||||
\(982\) | −5.77230 | − | 9.99792i | −0.184202 | − | 0.319047i | ||||
\(983\) | −9.35951 | −0.298522 | −0.149261 | − | 0.988798i | \(-0.547689\pi\) | ||||
−0.149261 | + | 0.988798i | \(0.547689\pi\) | |||||||
\(984\) | 2.93110 | + | 5.07681i | 0.0934401 | + | 0.161843i | ||||
\(985\) | 3.21769 | − | 5.57320i | 0.102524 | − | 0.177577i | ||||
\(986\) | −22.0183 | + | 38.1368i | −0.701206 | + | 1.21452i | ||||
\(987\) | 7.35951 | 0.234256 | ||||||||
\(988\) | −12.0281 | − | 18.9467i | −0.382665 | − | 0.602776i | ||||
\(989\) | −0.897442 | −0.0285370 | ||||||||
\(990\) | −4.16012 | + | 7.20554i | −0.132217 | + | 0.229007i | ||||
\(991\) | −7.44425 | + | 12.8938i | −0.236474 | + | 0.409586i | −0.959700 | − | 0.281026i | \(-0.909325\pi\) |
0.723226 | + | 0.690612i | \(0.242659\pi\) | |||||||
\(992\) | −21.0236 | − | 36.4140i | −0.667502 | − | 1.15615i | ||||
\(993\) | 4.91079 | 0.155839 | ||||||||
\(994\) | 10.6338 | + | 18.4183i | 0.337284 | + | 0.584194i | ||||
\(995\) | 25.7841 | + | 44.6594i | 0.817412 | + | 1.41580i | ||||
\(996\) | 1.66680 | 0.0528144 | ||||||||
\(997\) | 10.1068 | + | 17.5056i | 0.320087 | + | 0.554406i | 0.980506 | − | 0.196491i | \(-0.0629546\pi\) |
−0.660419 | + | 0.750897i | \(0.729621\pi\) | |||||||
\(998\) | 13.8930 | − | 24.0633i | 0.439774 | − | 0.761712i | ||||
\(999\) | −3.52498 | + | 6.10544i | −0.111525 | + | 0.193168i |
(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 | 143.2.e.a.100.2 | ✓ | 6 | |
13.3 | even | 3 | inner | 143.2.e.a.133.2 | yes | 6 | |
13.4 | even | 6 | 1859.2.a.e.1.2 | 3 | |||
13.9 | even | 3 | 1859.2.a.h.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.a.100.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
143.2.e.a.133.2 | yes | 6 | 13.3 | even | 3 | inner | |
1859.2.a.e.1.2 | 3 | 13.4 | even | 6 | |||
1859.2.a.h.1.2 | 3 | 13.9 | even | 3 |